Master_Thesis_P.H.Dorst.pdf

Modelling the phreatic surface in
regional flood defences
P.H. Dorst

Cover: The Duifkade near Schipluiden, a regional flood defence and one of the research cases in this
thesis. Picture taken on 17-12-2018.

i
Modelling the phreatic surface in
regional flood defences
By
P.H. Dorst
in partial fulfilment of the requirements for the degree of
Master of Science
in Civil Engineering
at the Delft University of Technology,
to be defended publicly on Wednesday April 3rd, 2019 at 14:00.
Thesis committee: Prof. dr. ir. M. Kok TU Delft
Ir. S.J.H. Rikkert TU Delft
Dr. A. Askarinejad TU Delft
Ir. M. Monden Iv-Infra
Ir. G. Willemsen Hoogheemraadschap van Delfland
An electronic version of this thesis is available at http://repository.tudelft.nl/

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Preface
This thesis report is the product of my graduation research completing my master Hydraulic
Engineering at the Delft University of Technology. The research has been conducted in
cooperation with Iv-Infra in Sliedrecht. This report presents the research method, results, and
conclusions of the research.
I would like to thank Iv-Infra for providing the opportunity and resources to write this master
thesis. In particular I would like to express my gratitude to my supervisor Martijn Monden for his
guidance and positive feedback during the entire process of writing this thesis. I would also like
to extend my appreciation to all the other colleagues at Iv-Infra for their help and making it a
pleasant period.
Furthermore, I would like to express my gratitude to the other members of my thesis committee,
Prof. Dr. Ir. Matthijs Kok, Ir. Stephan Rikkert, Dr. Amin Askarinejad, and Ir. Geert Willemsen, for
all their advice and constructive feedback. Special thanks go out to Stephan for proposing this
thesis subject, and to Geert for supplying all the information I needed from the water board of
Delfland. Many thanks also to the water board for making this information available.
Finally, I would like to thank my friends and family for their help and support throughout my
entire study period at TU Delft.
Pieter Hendrik Dorst
Klaaswaal, March 2019

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Summary
Apart from the primary flood defences that protect the land from the sea, the big rivers, and the
lakes, many smaller flood defences can be found in the Netherlands. These regional flood defences
protect the land against smaller bodies of water inside the primary flood defences. The
groundwater table inside these regional flood defences has an important influence on the stability
and therefore the safety of these flood defences. This groundwater table, called the phreatic
surface, is dependent on many factors which complicates the determination of its position in the
flood defence. For stability calculations usually a schematisation of the phreatic surface is used,
based on the geometry of the flood defence and the water levels. No precipitation or soil
characteristics are explicitly included in these schematisations, which means they are potentially
inaccurate and therefore might result in a higher or lower calculated stability than in reality is the
case.
A possible method to determine the location and the fluctuations of the phreatic surface based on
external factors, could be to model the phreatic surface using a numerical model. Research has
been conducted with the use of such models, but in most cases the models cannot be verified due
to lack of measurements of the phreatic surface. It is therefore unclear to which extent a
numerical model is able to simulate the phreatic surface. Based on this problem the main research
question for this thesis was composed: Can a numerical model contribute to a more accurate
estimation of the phreatic surface in a regional flood defence during extreme conditions?
To answer the research question, a case study was performed on three regional flood defences
for which the phreatic surface has been monitored for a certain period. For these flood defences
a groundwater flow model was set up in which the phreatic surface was simulated. To analyse the
accuracy of the simulation, the results of these models were compared to the measurements. Two
of the research cases are located in the area of the water board of Delfland, and had a
measurement set of 4 years available. The third research case is part of a research project in the
area of the water board of Rijnland, which was ongoing during the writing of this thesis. The
measurement set therefore had a length of only several months, but despite this the research case
was included because the conductivity of the soil was measured, and because four measurement
points were used in the cross-section. For the other locations no conductivities were measured,
and only three monitoring wells were used.
To construct the three models a numerical model had to be chosen. Eventually the choice was
made to use the numerical model MODFLOW in combination with a Python package called FloPy,
which is able to facilitate the input and output of the model. The models were calibrated by
variation of the soil parameters, most notably the hydraulic conductivity. The parameters can be
variated for each soil layer, which means many combinations of parameters had to be tested to
find an optimum calibration.
For all models it was possible to simulate head fluctuations similar to those in the measurements.
How accurately the fluctuations were modelled was different between the research cases and
between different points in the cross-section. On average the difference between the model and
the measurements was about 10 cm. This difference was smaller for high phreatic surfaces and
larger for low phreatic surfaces. For one of the models the effect of this error on the macro-
stability was assessed, and this effect was sufficiently small. Considering the necessary
simplifications needed to construct the models, it is therefore concluded that it is possible to
simulate the head measurements with sufficient accuracy.
However, this sufficiently good fit of the models was only reached after extensive calibration of
the models to the measurement sets. Comparison between calibrated and uncalibrated models
has shown that calibration is necessary to obtain an accurate model. This means measurements
are a necessary part of the construction and calibration of a numerical model. The calibration

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itself can be a long-drawn process, due to the large amount of parameter variations. The large
amount of required data and the difficult calibration process make it questionable whether it is
always worthwhile to construct a numerical model to determine the position of the phreatic
surface.
Apart from simulating the measurements sets in the numerical model, some extra simulations
were carried out. Extreme precipitation events of various duration, intensities and time patterns
were imposed on the models. This analysis confirmed conclusions from earlier research that
precipitation with a long duration has a larger effect on the phreatic surface than short, intense
events. The analysis also confirmed that the phreatic surface eventually reaches an equilibrium
position, where it rises no further. The three research cases responded similarly, with differences
in response time dependent on the soil characteristics. The precipitation patterns containing a
single peak resulted in the most critical phreatic surface. For this pattern first the equilibrium
situation is reached, and the peak then induces a small extra head rise.
Furthermore, for one of the research cases a simulation using 31 years of meteorological data was
performed. From this simulation it was found that the schematisation of the phreatic surface
according to the guidelines of the water board maintaining the flood defence is exceeded
regularly. These exceedances only occurred near the toe and the inside drainage ditch. In the main
simulation of the same model a slight exceedance in the outer crest was found as well. In the inner
crest the schematisation remained well above the modelled phreatic surface. This indicates that
potential improvements to the schematisation can be made in these areas.
From the long-term simulation it was also found that the probability of a certain height of the
phreatic surface can be described with a lognormal distribution. The fluctuations and therefore
the standard deviation of the distribution vary over the cross-section. These fluctuations are
largest at the inner crest.
Several stability calculations were performed to determine the effect of a change in the phreatic
surface on the stability. A change had the largest effect at the inner crest and at the toe. Stability
calculations using the highest phreatic surface from the simulations lead to slightly higher
stability than when using the current schematisation.

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Table of contents
1 Introduction............................................................................................................................................. 1
1.1 Regional flood defences..............................................................................................................................1
1.2 Background......................................................................................................................................................1
1.3 Objective ...........................................................................................................................................................4
1.4 Research questions.......................................................................................................................................4
1.5 Research method...........................................................................................................................................4
2 Literature.................................................................................................................................................. 7
2.1 Schematisation of the phreatic surface................................................................................................7
2.2 Factors of influence on the phreatic surface................................................................................... 10
2.3 Modelling the phreatic surface using numerical models........................................................... 16
3 Numerical model..................................................................................................................................17
3.1 Theory on groundwater flow................................................................................................................ 17
3.2 Possibly suitable models......................................................................................................................... 20
3.3 Model choice................................................................................................................................................. 22
4 Research cases......................................................................................................................................25
4.1 Vlaardingsekade (Delfland location 24)........................................................................................... 25
4.2 Duifkade (Delfland location 25)........................................................................................................... 26
4.3 Hogedijk (Rijnland)................................................................................................................................... 27
4.4 Measurement data..................................................................................................................................... 28
4.5 Influence of precipitation on the phreatic surface....................................................................... 31
4.6 Histograms.................................................................................................................................................... 35
5 Model set-up ..........................................................................................................................................37
5.1 Input data ...................................................................................................................................................... 37
5.2 Model grid and soil composition.......................................................................................................... 42
5.3 Boundary conditions................................................................................................................................. 44
5.4 Calibration..................................................................................................................................................... 51
6 Results .....................................................................................................................................................57
6.1 Main simulation.......................................................................................................................................... 57
6.2 Extreme simulated phreatic surfaces ................................................................................................ 65
6.3 Fictitious precipitation event................................................................................................................ 71
6.4 Long term precipitation........................................................................................................................... 78
6.5 Uncalibrated model................................................................................................................................... 81
6.6 Relation to macro-stability..................................................................................................................... 83

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7 Conclusions............................................................................................................................................87
7.1 Conclusions................................................................................................................................................... 87
7.2 Discussion ..................................................................................................................................................... 92
7.3 Recommendations..................................................................................................................................... 93
References.......................................................................................................................................................95
Appendices......................................................................................................................................................97
A Glossary...................................................................................................................................................98
B List of symbols ......................................................................................................................................99
C Meteorological data ......................................................................................................................... 101
D Measurement data............................................................................................................................ 107
E Cross-sections and soil data..........................................................................................................115
F Calibration of the models...............................................................................................................128
G Model results......................................................................................................................................151
H Extreme events..................................................................................................................................159

1.1. Regional flood defences
1
1 Introduction
1.1 Regional flood defences
A large part of the Netherlands is formed by the delta of the rivers Rhine and Meuse. Due the low
elevation of the land in this region, it has since long been subject to flooding. From about the
twelfth century onwards, the inhabitants of these lands started building dikes to protect the
region against this threat. These dikes form the system of primary flood defences which protects
the Netherlands from outside water like the sea and rivers.
Apart from this system of primary flood defences a system of regional flood defences was
constructed. These regional flood defences are located inside of the primary flood defences and
protect the land from smaller bodies of water like canals and small rivers. The loads and protected
area of these regional flood defences are usually much smaller than those of primary flood
defences. For this reason regional flood defences usually have smaller dimensions than their
primary counterparts.
Several types of regional flood defences can be distinguished, for example compartment dikes
and flood defences along regional rivers. A large part consists of the so called ‘boezemkaden’.
These are regional flood defences that protect low-lying areas from the water in regional canals.
The low-lying areas, called polders, are constantly filled with water from precipitation and
seepage, and are therefore vulnerable to flooding. To prevent this flooding, the excess water has
to be pumped out. The water is pumped into a system of regional storage canals called the
‘boezem’, which stores the water and transports it towards the outside water. In this boezem a
constant water level is maintained, which is higher than the water level in the polders. The
boezemkaden are the barriers between the boezem and the polder. This specific type of regional
flood defences is the subject of this study. For practical reasons it is referred to as regional flood
defences in this thesis, even though it is actually just a single type of regional flood defences.
1.2 Background
By Dutch law, flood defences have to be assessed on safety in regular periods. There are several
failure mechanisms that have to be assessed in order to classify a regional flood defence as safe
(STOWA, 2015):
• Overflow;
• Wave overtopping;
• Piping and heave;
• Macro-stability of the inner slope;
• Macro-stability of the outer slope;
• Micro-stability;
• Cover of the slopes;
• Stability of the foreshore.
One of the most important failure mechanisms for regional flood defences is macro-instability of
the inner slope. The macro-stability of a soil structure can be defined as the ability to withstand
loads without loss of function due to large deformations (TAW, 2001). Usually the macro-stability
is assessed using a slip plane analysis, which assumes a slide occurs along a certain slip plane.
This is illustrated in figure 1.1. The slip plane is subdivided into vertical slices, for each of which
the balance of forces is computed. The considered forces are usually the self-weight of the soil,
the top load on the crest of the structure, and the shear force along the slip plane. The self-weight
of the soil is both a driving and a resisting force. Near the crest of the structure the self-weight
acts in the same direction of the sliding of the slip plane, but near the toe it is possible that the soil

1 . Introduction
2
is pushed upwards. In this area the self-weight is a resisting force. The location of the most critical
slip plane is unknown beforehand, and therefore the stability has to be assessed for a large
number of slip planes in order to find the normative slip plane. For this reason a stability analysis
is usually performed using a computer program.
Figure 1.1: Illustration of macro-instability
The shear force that can be generated by the soil along the slip plane is an important factor in the
macro-stability. It is dependent on soil characteristics and on the effective stress in the soil. The
effective stress is the difference between the total stress resulting from the self-weight of the soil
and the load on top of it, and the pore water pressure caused by the groundwater. As long as the
volumetric weight of the soil and the top load do not change, an increase in pore pressure will
cause a decrease of the effective stress and consequently the shear resistance. The magnitude of
the pore pressure is therefore an important factor in the stability of the structure.
The magnitude of the pore pressures inside the structure is influenced by groundwater flow. In
the Netherlands the subsoil of a dike usually consists of a permeable Pleistocene sand layer,
covered by a less permeable Holocene top layer (TAW, 2004). In some cases intermediate sand
layers can be present in the Holocene layer. The groundwater flow in each of these layers has
different characteristics due to the differences in permeability.
In the dike profile and the Holocene layer a groundwater flow is present from the outside water
towards the inside water. Along the profile the pore pressures gradually decrease from the
outside water level to the inside water level. This gradient of the hydraulic head along the width
of the flood defence forms the phreatic surface. It is defined as the position where the water
pressure is equal to the atmospheric pressure. This definition is important, because above this
surface water is also present in the soil due to capillary forces. In this capillary zone the water
pressure is lower than the atmospheric pressure.
In the Pleistocene sand layer the situation is different. Due to the larger permeability the decrease
in pore pressure is less over the distance, which means the pore pressures are usually different
to those in the Holocene layer. Therefore in the lower part of the Holocene layer a transition zone
is present, where the pore pressure varies over the depth. Often the pore pressures in the
Pleistocene layer are higher than in the Holocene layer. Although this thesis is mainly concerned
with the pore pressures in the Holocene layers, the pore pressures in the lower layers also
influence the higher layers, and therefore these have to be considered as well.

1.2. Background
3
A schematic display of the soil layers and the phreatic surface is given in figure 1.2.
Figure 1.2: Schematic display of the soil layers and phreatic surface for a regional flood defence
The phreatic surface is more dependent on external circumstances than the hydraulic head of the
sand layer. The main influences are the water levels on each side of the flood defence, the internal
composition of the structure, and precipitation. Due to these factors it is difficult to predict the
exact position of the phreatic surface. It is therefore an important variable in stability analyses;
the uncertainties are high and the influence on the macro-stability is large.
All the factors involved make an accurate schematisation of the phreatic surface difficult when no
pore pressure measurements are available. Usually a schematisation is used. The water boards
managing regional flood defences often prescribe a schematisation, but differences exist between
the water boards. Moreover, the justification of these schematisations is not entirely clear. The
influence of precipitation is not based on soil characteristics or the amount of precipitation. Due
to these aspects it is unclear how accurate the schematisations are. If the schematisations are
inaccurate they result in a higher or lower calculated stability than in practice is the case.
For this reason research has been conducted on the phreatic surface in flood defences. From Ten
Bokkel Huinink (2016) it was found that the pore pressures are overestimated at larger depths
in the schematisation. In simulations the calculated phreatic surface is higher than the
schematisation, but because the pressure distribution is non-hydrostatic the actual pore
pressures are lower. In De Loor (2018) a similar result was found for a simulation in which a clay
dike is subjected to long-term precipitation. However, it is not clear what causes this non-
hydrostatic pressure and whether this actually occurs or whether it is a result of the used model.
Determining the position of the phreatic surface using a numerical model like in the mentioned
theses could be a method to obtain a more accurate result. In this way the influence of water
levels, precipitation and internal composition of the dike can be accounted for. However,
currently it is not clear whether such models accurately represent reality. In De Loor (2018) and
Ten Bokkel Huinink (2016) no pore pressure measurements were available to back up the results.
In 2012 a study was conducted where the position of the phreatic surface was modelled after a
field test with artificial precipitation, and the results were compared to measurements from this
field test (Alterra, 2013). It was concluded that a numerical model is able to accurately predict
the position of the phreatic surface. There are a few problems with this test, for example artificial
precipitation was applied to simulate an extreme event, no dry periods were included, the
simulated period was quite short and only a single cross-section was considered. Therefore the
results of this test do not conclusively show it is possible to determine the position of the phreatic
surface using this method for every situation.

1 . Introduction
4
The problems can be summarised in the following problem statement:
The position of the phreatic surface during extreme conditions is an important influence on the
macro-stability and therefore the safety of a regional flood defence. It is currently unclear whether
it is possible to determine this position of the phreatic surface more accurately using a numerical
model.
1.3 Objective
The objective of this thesis is to extend the knowledge of modelling the phreatic surface in
regional flood defences with the use of a numerical model.
1.4 Research questions
From the problem description and objective the main research question for this thesis was
composed:
Can a numerical model contribute to a more accurate estimation of the phreatic surface in a
regional flood defence during extreme conditions?
To answer this question the following sub-questions need to be answered:
1. What are the main influencing factors on the phreatic surface?
2. How is the phreatic surface currently schematised in regional flood defences?
3. What are the requirements for a numerical model to model the phreatic surface in a regional
flood defences?
4. How accurately can a numerical model simulate measured pore pressures in a regional
flood defence?
5. How does the phreatic surface in the numerical model respond to an extreme event?
6. What parameters and data are at least required for an accurate determination of the
phreatic surface using a numerical model?
1.5 Research method
To answer the research questions, a case study will be performed on a number of regional flood
defences for which pore pressures have been monitored during a long period. For these flood
defences a groundwater flow model will be set up in which the phreatic surface is simulated.
These simulated phreatic surfaces will be compared to the measurement data to analyse the
accuracy of the simulation.
Literature study
Starting point for the research is a literature study. This literature study is needed to answer the
first three research sub-questions and to obtain a better understanding of the subject. The
following subjects are researched:
• Currently used schematisation of the phreatic surface;
• Factors that influence the position of the phreatic surface;
• Theory on groundwater flow;
• Numerical models for groundwater flow.
In the literature study an investigation is made of the numerical models that can be used for the
research. Based on this a choice will be made. The chosen model is used to simulate the phreatic
surface for the research cases over the period for which measurement data of the phreatic surface
is available.

1.5. Research method
5
Research case
Regional flood defences exist in many shapes and sizes. Between cases there can be large
differences in geometry, soil composition, and water level difference. This makes it difficult to
provide a general answer to the research question. Therefore the research is focused on several
research cases. These research cases should fulfil the following requirements:
• Pore pressure measurements from monitoring wells or pressure sensors are available for
the case, so that the location of the phreatic surface over the cross-section is known. This
means several measurement points are needed per cross-section. Preferably the data
spans a period of least a year to have seasonal influences included.
• The case should be representative for a typical regional flood defence. What exactly
classifies as typical is hard to determine, as there can be large differences between
regional flood defences. At least a case should be chosen that is comparable to most other
flood defences. For example, no structural elements should be present in the cross-
section. Ideally the researched cases have some differences between them. If the same
conclusions are found for different situations, these conclusions are more general and
more likely to apply to other regional flood defences.
• Data regarding soil composition, water levels, precipitation and evapotranspiration is
available or can be acquired for the case.
Construction and calibration of the model
Using the model of choice, a model is constructed for each of the three research cases. In order to
do this, first a schematisation of the cross-section has to be constructed based on data from soil
borings and cone penetration tests. The load data (precipitation, water levels and evaporation)
are applied to the model as boundary conditions. The geotechnical parameters have to be
estimated based on the soil types in the cross-section. Using this input data the model is run to
simulate the period for which the measurement data is available.
To assess how accurate the model simulates the phreatic surface, the model results have to be
compared to the measurement sets. If large differences are found the model has to be calibrated
by adjusting the geotechnical parameters. To keep the model realistic, the parameters should be
variated within a realistic range. After each simulation the effect of the adjustment can be
analysed. This process should be continued until the best possible approximation of the measured
phreatic surface is reached.
The process of constructing and calibrating the model is illustrated in the flow chart in figure 1.3.
Geotechnical
parameters
Figure 1.3: Schematisation of the proposed research methodology
Geometry
(Schematisation of
the cross-section)
Numerical
model
Compare
results
Adjust
parameters
Measurement
data
Load data
(precipitation, water
levels, evaporation)

1 . Introduction
6
Extreme events
The fifth research sub-question aims to determine how the phreatic surface in the numerical
model responds to an extreme event. To answer this question, the extreme event first has to be
defined. Two types of extreme events can be of relevance: an extreme precipitation event and a
period of lasting drought. The extreme precipitation event will be analysed first, since this
situation is usually more relevant for the stability than the drought event.
First it is investigated whether any extreme events have occurred during the measurement
period, and it is determined what the return periods of those events are. For these events the
simulated and measured phreatic surface are compared to investigate how accurately extreme
events are simulated compared to normal conditions.
As a next step, a fictitious extreme event is simulated using the calibrated model. Regarding
precipitation many variations are possible. For a fixed return period various combinations of
durations and intensities can be tested. The effect of the way the precipitation is distributed over
time is also investigated.
Minimum requirements for an accurate model
The last research sub-question is aimed at determining what parameters and data are required
for an accurate determination of the phreatic surface using a numerical model. The way in which
the answering of this question is approached depends on the result of the main simulation. If the
model cannot accurately predict the position of the phreatic surface the sub-question becomes
irrelevant. If the model is able to model the phreatic surface with sufficient accuracy, it can be
investigated which parameters have the most influence on this result. Partly this is done already
during the calibration of the model. Additionally, it can be investigated how many monitoring
wells have to be placed in a cross-section, and how long these have to be monitored in order to
obtain enough measurements to create a sufficiently accurate model. This can be investigated by
calibrating the model for only a part of the measurement period (for example only the winter or
summer period) and analyse how this calibration compares to the main model. If a research case
is chosen for which measurements of the permeability are available, it can be analysed what the
influence of using a measured permeability is compared to using an estimate.

2.1. Schematisation of the phreatic surface
7
2 Literature
As starting point for the research a literature study has been conducted. The aim of this literature
study is to answer the first three research sub-questions, to obtain a better understanding of the
factors that influence the phreatic surface and to make an assessment of the numerical models
that could be used to conduct the research.
2.1 Schematisation of the phreatic surface
As described before, the phreatic surface is an important variable in the stability assessment of a
flood defence. Due to the large amount of influencing factors and the uncertainties, it is usually
schematised based on a number of points in the geometry. Since the stability has to be assessed
for high water situations and dry periods, schematisations exist for both situations.
2.1.1 Technical report pore pressures in dikes (TAW, 2004)
In the guideline for the assessment of the safety of regional flood defences (STOWA, 2015) the
approach given in the report ‘Pore pressures in dikes’ (TAW, 2004) is recommended for the high
water situation. This schematisation is mainly directed at primary flood defences. In principle,
the report only recommends this approach when no pore pressure measurements are available.
For the approach in this report four different types of dikes distinguished, based on whether the
subsoil is compressible or not, and whether the dike core is constructed out of clay or out of sand.
The schematisation of the phreatic surface for the types with a clay core is displayed in figure 2.1.
Figure 2.1: Schematisation of the phreatic surface in the report ‘Pore pressures in dikes’ (TAW, 2004)
The variables in this schematisation are defined as follows:
C: Point C represent the phreatic surface at the outer toe, and its location depends on the
presence of a drainage ditch. For dikes permanently loaded by water the point C1 on the
slope is used, which is the case for regional flood defences.
D: Point D1 is used in case of a drainage ditch near the inner toe, point D2 is used when no
drainage ditch is present.
L: Width of the dike base; dependent on the location of points C and D.
B: Dependent on the horizontal intrusion length I, which indicates how far into the dike the
influence of a water level raise reaches. Since water level fluctuations are smaller for
regional flood defences than primary flood defences, this parameter is of less relevance.
Point B should thus be located close the entry point.

2 . Literature
8
A: Represents the bulging of the phreatic surface due to precipitation. The horizontal
location is below the inner crest. The height is dependent on points C and D, the width of
the dike and the thickness of the clay sub-layer.
For types with a sand core a similar type of schematisation is used. This schematisation will not
be treated here, because these types are less relevant for the research.
Pleistocene sand layer
The pore pressure schematisation of the Pleistocene sand layer is dependent on whether or not
the compressible (Holocene) layer is pushed up by the water pressure. If this is not the case, the
hydraulic head according to the points C1, D1, E1, and G1 in figure 2.2 applies. If the compressible
layer is pushed up the points C2, D2, E2, and G2 are used instead.
Figure 2.2: Pore pressures in the Pleistocene sand layer. Source: TAW, 2004.
The horizontal location of point F is at the so-called entry point. This entry point is the point
where the outside water level is the boundary condition for the Pleistocene sand layer, i.e. the
point at which the head in the sand layer is equal to the outside water level. The location of this
point is dependent on the soil composition below the outside water and therefore the entry point
is hard to define. Considering the small dimensions of the canals that form the outside water of
regional flood defences, it is likely that this point often does not exist in reality. The height of point
F (as well as points C1, D1, E1, and G1) is the design high water level.
The horizontal location of points C1 and C2 is at the inner toe of the dike. From this point inwards
a push-up zone is defined with a length of 2*d, where d is again the thickness of the Holocene
layer. Points D1 and D2 are located at the end of this zone. The height of points C2 and D2 is at the
so-called boundary potential, which is the hydraulic head for which the water pressure below the
compressible layer is equal to the weight of this layer. Points E2 and G2 are at the average high
water level outside the dike. The head decline between points D2 and E2 is schematised as a
gradient of 1:50. This inclination determines the horizontal location of point E.
Since the heads in the top- and subsoil are different, somewhere a transition has to occur between
those heads. This transition zone is modelled as a so-called intrusion layer, in which the head
linearly transitions between the two heads. In the report ‘Pore pressures in dikes’ a formula is
provided to calculate the thickness of this intrusion layer, based on the permeability and
thickness of the compressible layer and the head in the sand layer. However, in practice usually
an intrusion layer thickness of 3,0 m us used for dikes in river and lake areas, and 1,0 m for sea
dikes.
The scientific basis for the schematisations in the report ‘Pore pressures in dikes’ is not entirely
clear. In an expert report from 2009 (Expertisenetwerk waterveiligheid, 2009) it is pointed out
that the report provides no information whether the schematisation is based on expert judgement
or on measurements. Furthermore, the bulging of the phreatic surface due to precipitation is

2.1. Schematisation of the phreatic surface
9
based on the geometry and the type of the dike and not on soil characteristics and the amount of
precipitation. Soil characteristics are used to calculate the intrusion length, but this only accounts
for water level variations and not for precipitation. For these reasons the accuracy of the
schematisation can be disputed.
Another potential problem is that these schematisations are mostly aimed at river dikes, for
which high water events have a water level several meters higher than the normally occurring
water level. In regional flood defences the outside water level is always close to the crest of the
dike, and the water level rise during high water events is no more than several decimetres.
This difference has only small consequences for the schematisation of the phreatic surface,
because that schematisation is mostly based on the geometry of the dike, except for the horizontal
intrusion length. However, for the transition between the phreatic surface and the head in the
Pleistocene sand layer the approach using an intrusion layer this difference may lead to problems.
This intrusion layer is based on the occurrence of a high-water wave, resulting in an increased
head in the Pleistocene sand layer. This higher head creeps in the compressible layer, which is a
slow process due to the low permeability of this layer. The thickness over which the head in the
compressible layer is influenced by the increased head in the Pleistocene layer is the intrusion
layer.
As mentioned, high water events for regional flood defences involve a much smaller water level
rise than for river dikes, resulting in a smaller or negligible increase of the head in the sand layer.
In addition to this, the head in the Pleistocene layer is often higher than the inside water levels.
This means that the use of an intrusion layer, which represent a transient state of the pore
pressures, is not valid for most regional flood defences. Instead, the transition between the two
head will occur over the entire thickness of the compressible layers. The exact course of this
transition is dependent on the conductivities of these layers.
2.1.2 Water boards
The water boards that manage regional flood defences often have their own guidelines for the
schematisations of the phreatic surface, usually based on pore pressure measurements and
expert judgement. Between water boards there are differences in these guidelines.
For the water board ‘Hoogheemraadschap van Delfland’ a schematisation was established in an
expert workshop (Delfland, 2008). However, based on field measurements the schematisation for
the high water situation was later adjusted to a more conservative approach. This more recently
established approach is described here. This information is taken from an assessment report of a
regional flood defence in the management area of this water board (RPS & Witteveen+Bos, 2016).
High water situation
In the high water situation the outside water level is the design water level with a return period
of 100 years. The phreatic surface below the inner crest is assumed to be at the intended water
level (the water level that is usually maintained in the boezem system). At the inner toe it is
assumed that seepage occurs, meaning the phreatic surface is at ground surface level. For the
inside water level it is assumed that the water level is 0,15 m above the intended water level.
Between these points a linear gradient of the phreatic surface is assumed. In some cases no
drainage ditch is present. If this is the case, and the polder water level is less than 0,5 m below
the ground surface, the phreatic surface inside of the flood defence is schematised at ground level.
When the polder water level is more than 0,5 m below the ground surface, the height of the
phreatic surface is schematised at 0,5 m above the polder water at 15 m from the toe. Between
this point and the toe again a linear course is used.
Dry situation
In the dry situation the intended outside water level is used. Below the outer crest a height of
1,5m below the outside water level is used. From this point onwards a slope with the same angle

2 . Literature
10
as the inner slope is schematised, up to the point where the intended inside water level is reached.
In case no drainage ditch is present, the inside water level is schematised at 0,7 m below the
intended polder water level.
The schematisations for both situations are displayed in figure 2.3.
Figure 2.3: Schematisation of the phreatic surface for a dry situation.
The schematisation is not applicable to every situation. An advisor has the obligation to interpret
whether or not the schematisation is realistic for a specific situation, for example when
intermediate sand layers are present. If the calculated stability of a flood defence is insufficient
using this schematisation, measurements of the phreatic surface are carried out over a period of
14 weeks. If the maximum measured height during this period is more than half a meter below
the schematised phreatic surface, the schematisation can be adjusted to a height of 0,5 m above
this maximum measured value, on the condition that precipitation has occurred during the
measurement period. If the maximum measured head at the inner crest is less than 0,1 m below
the intended water level, the schematisation at this location is adjusted to 0,1 m above the
intended water level.
A problem that occurs for these schematisations is the applicability in practice. Most regional
flood defences have an irregular geometry and have a much smoother shape than the dikes in the
schematisations. This means the exact boundaries between crest, slope and toe are hard to define.
Different interpretations can lead to a different schematised phreatic surface. In general it can be
concluded that the schematisation of the phreatic surface is fairly subjective.
2.2 Factors of influence on the phreatic surface
This section discusses the various factors that may be of influence on the height of the phreatic
surface. Various hydrological processes determine the in- and outflow of water in the dike, and
therefore determine the height of the phreatic surface. These processes are:
• Water level variations (in and outside water);
• Precipitation: partly infiltrates in the dike, and partly flows away as surface runoff;
• Evaporation and transpiration by plants (together evapotranspiration).
A schematic illustration of these factors of influence is given in figure 2.4.
Wet
Dry

2.2. Factors of influence on the phreatic surface
11
Figure 2.4: Illustration of the various hydrological processes influencing the height of the phreatic surface
2.2.1 Water level variations
One of the main influences on the position of the phreatic surface are the water levels on both
sides of the flood defence. For regional flood defences the situation regarding water levels is
different than for other types of flood defences. In primary flood defences the design water level
is usually much higher than the normally occurring water level, but in regional flood defences the
water level is at all time close to the crest.
In the technical report pore pressures in dikes (TAW, 2004) it is described that during a situation
with a higher water level the pore pressures inside a flood defence follow the outside water level
with a certain delay. When the high water level has passed the pore pressures will remain high
for some time. This lingering effect is mostly present in river dikes, where a high water event can
cause a water level raised by several meters for a multiple days. In a regional flood defence a
higher water level can also last for an extended period of time, but the difference compared to
normal water level is less than a meter. The rise of the phreatic surface is therefore also much
smaller, which means the lingering effect has only a small influence. The effect could be of
importance for a situation where the outside water level suddenly drops, which might occur when
another regional flood defence nearby breaches and causes the canal to drain.
The thesis of De Loor (2018) shows that the permeability has a very large influence on the
reaction of the phreatic surface to water level changes. It also shows that clay layers with soil
structure deterioration have a large influence due to their larger conductivity. Therefore the
conductivity and extent of clay layers with deterioration are an important factor in the change of
the phreatic surface due to water level differences. This influence could be even larger in regional
flood defences. These usually have smaller dimensions than primary flood defences and therefore
the deteriorated top layer forms a larger part of the total structure.
In 2012 a field test was conducted by the water board ‘Hoogheemraadschap Hollands
Noorderkwartier’ which was aimed at gaining insight in the influence of precipitation on peat
dikes (Alterra, 2013). In this field test both natural and artificial precipitation was applied to two
cross-sections on opposite sides of a boezem canal, and for both cross-sections the pore pressures
were monitored on several locations. Furthermore two reference cross-sections were monitored
to which no artificial precipitation was applied. After the first part of the test the water in the
boezem canal was raised about 30 cm, to investigate the influence of precipitation in combination
with a heightened outside water level. Although it was not the aim of the study, in the
measurements the effect of this raise of the water level can be observed. For both sides of the

2 . Literature
12
boezem canal and for both the irrigated and reference cross-sections the effect of the water level
raise can be observed. The rise of the phreatic surface occurs quite fast, within the same day a
more or less steady situation is reached. However, in the report it is mentioned that rubble is
present in the crest of the cross-section. Rubble has a large permeability and this might be the
cause for this fast rise of the phreatic surface.
Variation of water levels
In general, the variation of both the inside and outside water levels is relatively small for regional
flood defences. Both water levels are regulated by pumping stations, so water level rises can only
occur when the pumping capacity is temporarily lower than the inflow caused by precipitation
and seepage. Another possibility could be wind set-up in the system of boezem canals. The
variations that occur are small compared to the normal water level difference over the flood
defence.
An event that might cause a significantly lower water level could occur if the boezem canal is
drained due to a breach in another flood defence nearby.
It follows that the measure in which water level variations influence the phreatic surface is
dependent on the following factors:
• Water level difference variation;
• Duration of the water level variation;
• Soil characteristics (conductivity, porosity and composition)
Especially the soil characteristics and composition are important. In the study of De Loor (2018)
a homogeneous clay dike showed virtually no response to a flood wave, while a dike with a top
layer with higher permeability did show a response. The test described in Alterra (2013) show a
fast response to a relatively small water level rise, which is possibly caused by rubble in the crest.
The extent of soil structure deterioration is hard to determine, and also variable over time.
Inhomogeneity of the soil caused by for example rubble is also generally unknown. These factors
make it difficult to determine the effect of water levels on the phreatic surface. However, water
level differences for regional flood defences are usually small compared to difference between
the inside and outside water level. Therefore the changes they cause in the phreatic surface are
also comparatively small.
2.2.2 Influence of precipitation
Another main influence on the position of the phreatic surface is precipitation. Some of the
precipitation that falls on a flood defence flows away over the surface (run-off), but a part of it
infiltrates into the groundwater. This causes the groundwater table to rise, resulting in a flow
towards the edges of the structure, mostly towards the inner toe. This will cause the phreatic
surface to bulge, which in turn causes larger pore pressures and thus decreases the stability of
the dike.
According to the report ‘pore pressures in dikes’ (TAW, 2004), the type of cover of the flood
defence is an important factor in the influence of precipitation on the phreatic surface. A dike with
an impermeable asphalt cover is less influenced by precipitation than a dike with a grass cover. A
road on the crest of the flood defence causes less infiltration below the road, but near the
roadsides there is more infiltration due to the water flowing away over the road. The structure
below the road is also important. It usually consists of sand or other permeable materials, which
can cause an increased infiltration into the dike core.
The precipitation that falls on the slope of the structure is mostly absorbed by the unsaturated
zone above the phreatic surface. In clay soils, structures are present in this zone. These structures
are formed by mechanical and biological processes and can be divided in two types: a coarse
continuous system of cracks and tunnels and a finer, less continuous system of pores. These

13
structures influence the permeability of the unsaturated zone. The infiltrated water in the
unsaturated zone will partly infiltrate further into the core of the dike and partly evaporate or
transpire through plants.
For regional flood defences the internal structure of the dike determines the influence of
precipitation on the phreatic surface. A dike with a clay core responds slower to fluctuations than
a dike with a sandy core. The width is also important. For a regional flood defence with a small
width there is a risk that the groundwater exits the dike on the inner slope, which may cause
erosion.
TAW (2004) lists the following effects of precipitation on the phreatic surface:
• At the point of entry on the outer slope the height of the phreatic surface is equal to the
outside water level;
• At the inner crest the phreatic surface rises with 0,30 m compared to a regular situation,
but it never rises above the outside water level;
• At the inner toe the phreatic surface lies at ground level.
Many dikes are very dense due to traffic load over the years, which means the bulging of the
phreatic surface develops very slowly, but also is very insensitive to dry periods.
The thesis of Ten Bokkel Huinink (2016) is aimed at finding a method to assess the probability
distribution of the phreatic surface in regional flood defences. As a part of the research the
influence of precipitation on the phreatic surface was studied, by re-analysing the data from the
earlier mentioned field test described in Alterra (2013), and by using a finite element numerical
model.
From the analysis of the field test data it was found that both artificial and natural precipitation
have an effect on the phreatic surface, but no general method can be found to describe this
influence due to the variety in the results. The measured phreatic surface reacts to a precipitation
event within hours. The soil configuration has a large influence on this reaction speed.
Furthermore, it was found that the permeability of the soil is very uncertain, and shows a large
variability.
From the numerical study it was also found that precipitation can have a large influence on pore
pressures in a dike. The following conclusions were found:
• The toe of the dike responds first to a precipitation event, and the crest responds last.
• After an infinitely long precipitation event the position of the phreatic surface is solely
dependent on saturated permeability and not on the unsaturated characteristics.
• After a finite precipitation event the position of the phreatic surface depends on
precipitation duration and intensity and on both the saturated and unsaturated
characteristics of the soil;
• During a precipitation event pore pressures do not increase linearly with depth.
• The reaction speed of the pore pressures to a precipitation event is dependent on the
unsaturated permeability.
• The phreatic surface in a dike can rise to surface level as a result of a precipitation event;
this is in contradiction to the governing schematisation in (TAW, 2004).
• In the simulations, the calculated phreatic surface is higher than in the governing
schematisation of (TAW, 2004), but the pore pressures are lower due to their non-
hydrostatic nature. The schematisation therefore overestimates the pore pressures.
In the thesis of De Loor (2018) the effect of precipitation was also investigated for several dike
types. Furthermore, some extra tests were performed: a test where the dike was subjected to
measured long term precipitation for both a period of 26 years and of 52 years, and a test where
extreme events were added to this precipitation data.

2 . Literature
14
Regarding precipitation, the following conclusions were found (De Loor, 2018):
• In a homogeneous clay dike the phreatic surface shows no response to a precipitation
event, but a clay dike with soil deterioration in the top layer has a buffering effect in the
top layer. The top layer prevents run-off and slowly releases the water to the core.
However, most of this water flows through the top layer towards the toe.
• The sand dike shows more response to the load events than the clay dikes.
• In none of the simulations the rise of the phreatic surface was such that a dike failure
might occur.
• In clay dikes, small but regular events have a greater influence on the phreatic surface
than extreme events, since most precipitation runs off the slope due to the low
permeability.
• A uniform rainfall shape leads to the most infiltration; other shapes lead to more run-off.
• The core of the clay dikes becomes fully saturated when real precipitation data over a
period of 26 or 52 years is applied. However, the pore pressure in the subsoil barely
changes from the starting point. This means the pore pressure over the depth is not
hydrostatic.
When considering all sources discussed, it can be concluded that precipitation has a definite
influence on the position of the phreatic surface in a flood defence. The magnitude and speed of
the reaction are dependent on several factors, mainly the soil composition and characteristics.
From the studied reports the following aspects are of particular importance:
• A road on the crest of the flood defence;
• A deteriorated clay top layer with soil structures influences the infiltration;
• The distribution of pore pressures over the depth may not be hydrostatic.
Soil characteristics determine for a large amount of the influence of precipitation on the phreatic
surface.
2.2.3 Influence of evapotranspiration
Evaporation of water from the surface of the flood defence is a factor that can also be of influence
on the phreatic surface. Evaporation can occur directly from the surface, but loss of water also
occurs via transpiration through plants. The total outward flux from these two effects is called
evapotranspiration. The total evapotranspiration flux consists of three elements (GeoDelft,
2007): evaporation of interception water (precipitation stored by plants above the surface), soil
evaporation and transpiration through plant leaves.
The outward flux of evapotranspiration causes the phreatic surface to become lower. This means
evapotranspiration is of relevance for this research. If it is not taken into account the simulated
phreatic surface could be higher than the measurements, especially in the summer months. For
peat dikes evapotranspiration is also important for stability reasons. In most flood defences a
lower phreatic surface has a positive effect on the macro-stability, but this is not the case for peat
dikes. Peat decreases in weight and volume when it dries out, which has a negative effect on the
stability. Due to this effect several regional flood defences have failed in the past, for example in
Wilnis and Terbregge in 2003.
Several models exist to calculate the evapotranspiration flux, like the Penman-Monteith or the
Makkink methods. However, the flux calculated using these models represents the potential
evapotranspiration, which is the evapotranspiration that would occur with an unlimited water
supply. In reality evapotranspiration reduces the water content of the unsaturated zone, which
reduces the evapotranspiration rate. Therefore the actual amount of evapotranspiration is lower.
In 2014 a study was conducted using the model dgFlow in which the possible lowering of the
phreatic surface in a peat regional flood defence due to dry circumstances was analysed (Sman,
2014). For this analysis a particular case for which pore pressure measurements were available

15
was used. From the analysis it was concluded that the dry period result in a significantly lower
phreatic surface. The lowering mostly occurs near the toe of the structure, and remains limited
near the crest. Lowering the outside water level results in an even lower phreatic surface. Adding
a clay top layer has a smaller effect than expected. The clay layer seems to be diminishing the
desiccation, but also to be diminishing the infiltration. It is however remarked that it is uncertain
whether this effect accurately represents reality, because the model was calibrated for the
situation without the clay cover.
From the sources it is clear that dry periods play an important role in the stability of peat flood
defences. However, the influence of dry periods is caused by several factors apart from
evapotranspiration, like lack of precipitation and a lower outside water level. It is unclear how
large the influence of evapotranspiration itself is. Most likely the relative influence is smaller
during dry periods, because then the top layer is fully unsaturated which means no
evapotranspiration takes place.
2.2.4 Soil structures in the unsaturated zone
In clay the unsaturated zone is characterised by a soil structure, formed by cracks caused by
swelling and shrinking of the clay and by biological activity, like animal digging and plant rooting.
This soil structure has a large influence on the geotechnical characteristics of the soil. Clay itself
has a low permeability, but the soil structure can cause the permeability to be much larger.
The technical report ‘clay for dikes’ (TAW, 1996) describes how the soil structure in clay is
formed. Shrinking and swelling of clay is caused by drying and moisturising, which leads to
formation of cracks and tears in the unsaturated zone. Larger cracks usually form vertically, while
smaller tears may form in any direction. Besides cracking, the soil structure is also formed due to
burrow digging by worms and moles. Below a grass cover a soil structure is formed in several
years up to a depth of about 0,8 m. However, deeper in the flood defence a soil structure can also
be present. In case of a strengthened dike deeper layers may have been a top layer in the past,
and a soil structure can still be present. Plant and tree roots can also form structures deeper into
the flood defence.
These soil structures have a strong effect on the permeability of the soil. In an initially well-
compacted clay cover the permeability can increase from 10-6 m/s to 10-5 m/s in half a year due
to formation of a soil structure. The permeability of clay cover layers is rarely lower than 10-5 m/s
to 10-4 m/s due to soil structures.
In the earlier mentioned thesis of De Loor (2018) several simulations were performed using a top
layer with soil structures (described as soil structure deterioration). It was found that this top
layer is more influenced by water level changes due to the larger permeability. Furthermore, the
top layer acts as a buffer zone for precipitation. Water that would normally run off over the slope
is temporarily stored in the top layer and slowly released into the less permeable core of the dike.
For peat the same processes as for clay play a role, due to drying and moisturising cracks are
formed (GeoDelft, 2005). Cracks play a large role for infiltration, because water that would
normally run off the slope is collected in cracks and infiltrates at a larger depth. For evaporation
the effect of cracks is of small influence.
From the various sources it is clear that the soil structure of the top layer of the flood defence can
have a large influence on the phreatic surface. Because of its larger permeability and cracks, water
is stored in the top layer and slowly released to deeper layers. This increases the amount of
infiltration and therefore the rise of the phreatic surface. It is however difficult to determine the
permeability when a soil structure is present.

2 . Literature
16
2.3 Modelling the phreatic surface using numerical models
From literature it becomes clear that the height of the phreatic surface is mostly dependent on
water levels and precipitation. The extent in which precipitation and changes of the water level
influence the phreatic surface is largely determined by the soil composition and soil
characteristics. Factors like soil structure deterioration, rubble, the geometry of the dike, and a
road on the crest can have a large influence. This makes determining the height of the phreatic
surface difficult when no measurements are available. A possible method to include all the listed
factors of influences is the use of a numerical model. Several studies have been performed which
involved modelling of the phreatic surface using a numerical model.
The earlier mentioned study of the field test described in Alterra (2013) also involved modelling
the groundwater flow during this test, for which the model Hydrus-2D was used. For the set-up
of this model, a soil survey had been executed. Several samples were taken to determine the
saturated conductivity and retention characteristics of the unsaturated zone. The model showed
that initially the precipitation flows downwards, but soon changes to more horizontal. By adding
measurement points into the simulation at the same locations as the sensors in the field test it
was possible to compare the model results to the actual measurements. The main difference
occurs near the crest, near the toe the differences are smaller. At the start of the simulation the
simulated phreatic surface below the crest is higher than in the measurements. Later the
difference becomes smaller, but the simulated phreatic surface remains higher than the
measurements. Halfway the cross-section the opposite is true; the model shows a lower phreatic
surface than the measurements. In the report, the conclusion was drawn that a model like Hydrus-
2D can be used to model the effect of precipitation on dikes, but to generate reliable model results
it is necessary to have sufficient information about the soil. Furthermore reliable measurements
of ground water level are necessary to calibrate the model.
The report of this test shows that a model can approximate the influence of precipitation on the
phreatic surface, but several remarks can be made on this. In the model only extreme, artificially
applied precipitation was modelled, and no dry periods were included. Additionally, the
simulated period was relatively short and only one cross-section was modelled, so the
experiences with the model are limited. Due to these aspects it is not evident that the model can
be used in every situation. It is unclear how well the model approximates the location of the
phreatic surface during dry periods, or after a precipitation event following a dry period.
As mentioned before, in Ten Bokkel Huinink (2016) the model PlaxFlow was used to determine
the effect of precipitation on regional flood defences of three different soil types. However,
because of the theoretical nature of the research no real measurement data of the phreatic surface
was available to back up the results. Furthermore, the used models had a homogeneous cross-
section which is rarely the case in practice.
In De Loor (2018) a PlaxFlow model was used as well. In this case the cross-section was modelled
after a real flood defence, but no measurements of the phreatic surface were available and the
simulations were not based on actual events. Furthermore, the research was aimed at river dikes
and not regional flood defences. In most river dikes no continuous high water load is present, as
is the case for regional flood defences.
All in all, it is unclear how accurate a numerical model simulates the position of the phreatic
surface in a regional flood defence. In two of the mentioned studies (Ten Bokkel Huinink, 2016;
De Loor, 2018) no actual measurement data was available to verify the results. In another study
(Alterra, 2013) actual measurement data was present, but it is unclear whether the results can be
applied to a longer time period or to other cases.

3.1. Theory on groundwater flow
17
3 Numerical model
The central element in the research method presented in chapter 1 is a numerical model to
simulate the groundwater flow in a regional flood defence. There are many such models that
could potentially be used. In order to understand the theoretical background behind these
models, first the basic theory on groundwater flow is described. Next, an assessment is made of
the numerical models that are suitable and available for the research. Based on this assessment a
choice is made between these models.
3.1 Theory on groundwater flow
Groundwater flow can be separated into flow in the saturated zone and flow in the unsaturated
zone. The saturated zone is the area below the phreatic surface, where the pore water pressures
are higher than the atmospheric pressure. In the unsaturated or vadose zone water can also be
present due to capillary rise and infiltration of precipitation.
3.1.1 Saturated flow
The basis for calculation models of saturated flow is Darcy’s law and the law of conservation of
mass. According to (TAW, 2004), Darcy’s law is defined as follows for homogeneous and
incompressible fluids and isotropic permeability:
𝑞𝑥 = −𝐾
𝜕𝜑
𝜕𝑥
𝑞𝑦 = −𝐾
𝜕𝜑
𝜕𝑦
𝑞𝑧 = −𝐾
𝜕𝜑
𝜕𝑧
(3.1)
Where:
q = specific discharge (m/s)
K = hydraulic conductivity (m/s)
 = hydraulic head (m)
z = location height with respect to reference level (m)
ρ = water density (kg/m3)
g = gravitational acceleration (m/s2)
The hydraulic conductivity K represents the ability of the soil to transmit fluid. It is a property of
both the soil and the fluid. To exclude the effect of the viscosity of the fluid the intrinsic
permeability k is defined, which is independent on the fluid characteristics. The relation between
the hydraulic conductivity and intrinsic permeability is expressed as (Todd & Mays, 2005):
𝑘 =
𝐾𝜇
𝜌𝑔
(3.2)

3 . Numerical model
18
Where:
k = intrinsic permeability (m/s)
K = hydraulic conductivity (m/s)
 = dynamic viscosity (N s/m2)
ρ = fluid density (kg/m3)
g = gravitational acceleration (m/s2)
Since water is the only relevant fluid for the flow in regional flood defences, the hydraulic
conductivity is used in this thesis.
In the equations 3.1 it was also assumed that the hydraulic conductivity was isotropic, i.e. equal
in all directions. For anisotropic soils the conductivity can be divided in an x, y, and z direction.
Often the conductivity in vertical (z) direction is smaller than in the horizontal (x, y) directions.
Therefore often a horizontal (Kh) and (Kv) vertical conductivity are used to specify the hydraulic
properties of a soil.
Law of conservation of mass
For stationary flow the hydraulic conductivity and the geometry of the soil are sufficient to
calculate the groundwater flow. In these conditions the continuity equation applies (TAW, 2004):
𝜕𝑞𝑥
𝜕𝑥
+
𝜕𝑞𝑦
𝜕𝑦
+
𝜕𝑞𝑧
𝜕𝑧
= 0
(3.3)
This means the total amount of fluid in the soil does not change. The inflow of water is equal to
the outflow of water.
For non-stationary flow the amount of water changes and therefore equation 3.3 does not hold.
In order to comply to the law of conservation of mass storage has to occur. There are two types
of storage (TAW, 2004):
• Phreatic storage: occurs when the rising groundwater table fills the pore space in the soil.
The storage capacity is therefore dependent on the porosity.
• Elastic storage: occurs when the effective stress in the soil changes. This happens if the
pore pressure changes while the total stress remains the same. This changes the pore
space and therefore the amount of water that can be stored. The water itself may also be
compressed when gases are present in the pore space. The elastic storage capacity is
dependent on the stiffness of the soil. Clay and peat have a larger elastic storage capacity
than sand. The amount of elastic storage is significantly smaller than the phreatic storage.
For phreatic storage the continuity equation is defined as:
𝑛
𝜕ℎ
𝜕𝑡
+
𝜕(ℎ𝑞𝑥)
𝜕𝑥
+
𝜕(ℎ𝑞𝑦)
𝜕𝑦
= 𝑁
(3.4)
Where:
h = hydraulic head with respect to the base of the considered soil layer (m)
N = net infiltration due to precipitation (m/s)
n = effective phreatic porosity (-)

3.1. Theory on groundwater flow
19
For elastic storage the continuity equation is defined as:
(𝑚𝑣 + 𝑛𝛽)
𝜕𝑢
𝜕𝑡
=
𝜕𝑞𝑥
𝜕𝑥
+
𝜕𝑞𝑦
𝜕𝑦
+
𝜕𝑞𝑧
𝜕𝑧
(3.5)
Where:
mv = compressibility of the soil (m2/N)
β = compressibility of the water (m2/N)
Combining Darcy’s law and the continuity equation, a differential equation describing the ground
water follows. In order to solve this equation initial- and boundary conditions are required.
This equation can be solved using an analytical or a numerical model. Analytical models are more
transparent and need less input parameters than numerical models. However, a strong
schematisation of the geometry is necessary and therefore an analytical model is only suited for
relatively simple situations. This means an this type of model is not suited for this research, a
numerical model needs to be used.
Several types of numerical models can be distinguished (TAW, 2004):
• Finite difference method (implicit or explicit);
• Finite element method;
• Analytical function method;
• Boundary integral method.
The last two methods are not commonly used. Most models use the finite element method (FEM),
since it allows the most freedom in modelling complex geometry.
3.1.2 Flow in the unsaturated zone
Apart from the flow in the saturated zone, the flow in the unsaturated zone can also be important.
Groundwater recharge by precipitation first has to flow through the unsaturated zone before the
saturated zone is reached. The flow in the unsaturated zone has different characteristics than the
flow in the saturated zone. The pores are partially filled with air and therefore the permeability
is lower. The unsaturated permeability is dependent on the water content of the soil, and
therefore on the saturation. The saturation is in turn dependent on the pore pressure, which is
negative due to capillary rise (suction). The relation between this suction and the saturation is
described by a so-called water retention curve. The shape of this curve can be hysteretic. This
means that the curve follows a different path when the suction pressure increases than it does
when it decreases. Several models are available to describe the water retention curve. A
commonly used model is the Brooks and Corey model. However, the Van Genuchten model (1980)
includes more soil parameters and is therefore a more accurate representation of reality. The Van
Genuchten model defined as follow:
𝑆𝑒𝑓𝑓 = {
1,
[1 + (𝛼𝑝𝑐)𝑛]−𝑚
,
𝑝𝑐 ≤ 0
𝑝𝑐 > 0
(3.6)
Where:
𝑆𝑒𝑓𝑓 =
𝜃 − 𝜃𝑟𝑒𝑠
𝜃𝑠𝑎𝑡 − 𝜃𝑟𝑒𝑠
(3.7)

3 . Numerical model
20
Seff = effective saturation
θ = water content
θres = residual water content, the amount of water that always remains in the soil
θsat = saturated water content, water content in saturated conditions
pc = capillary suction pressure
α = parameter related to air entry suction
n = parameter related to pore size distribution
m = 1 – (1/n)
The parameters α and n are dependent on soil characteristics. From the effective permeability
the relative permeability can be calculated:
𝑘𝑟 = (𝑆𝑒𝑓𝑓)
1/2
[1 − (1 − (𝑆𝑒𝑓𝑓)
1
𝑚)
𝑚
]
2
(3.8)
The relative permeability is the ratio of the unsaturated permeability to the saturated
permeability:
𝑘𝑟 =
𝑘𝑢𝑛𝑠𝑎𝑡
𝑘𝑠𝑎𝑡
(3.9)
3.2 Possibly suitable models
Various groundwater flow models exist that might potentially be suitable for this research. In
order to be suitable the model has to fulfil at least the following requirements:
• It should be able to compute transient groundwater flow;
• It should be able to include precipitation and evapotranspiration;
• It should be able to model the sometimes complex geometry of the subsoil of regional
flood defences.
There are several models or programs that fulfil these requirements and therefore could be
suitable for the research. The models found to meet the requirements are described in the
following paragraphs.
3.2.1 D-Geo Flow
D-Geo Flow is a Deltares software module used to calculate 2D groundwater flow. It uses the finite
element model DgFlow, and also includes module for piping. Several types of boundary conditions
can be applied to the model: these are head, flux, seepage, submerging and no-flow boundary
conditions. Furthermore the program has the ability to model the unsaturated zone using the Van
Genuchten model to calculate the relative permeability (Deltares, 2018).
D-Geo Flow is a relatively new program, as of 2018 it has not been fully released yet. This means
not much experience in using the software has been gained yet, and some issues are still present
in the program. In addition to this, the user manual is relatively short and seems to be unfished.
These aspects could lead to some problems if D-Geo Flow is used for the research.

3.2. Possibly suitable models
21
3.2.2 COMSOL
COMSOL Multiphysics is a finite-element analysis simulation software for multiple fields in
physics. Several modules are available for electrical, mechanical, fluid and chemical applications.
One of these modules is the subsurface flow module, which is used to simulate flow in porous
media. This module allows for simulation of flow in unsaturated porous media and water
retention using the Van Genuchten and Brooks and Corey formulations. Additionally, it is possible
to simulate flow in fractures (COMSOL, 2013). COMSOL has the possibility to run models via
MATLAB files. A disadvantage is that it appears that no boundary condition can be applied to
include evapotranspiration dependent on the saturation of the soil.
3.2.3 PlaxFlow
PlaxFlow is an add-on module to the finite element program PLAXIS 2D. PLAXIS by default has
options to model stationary groundwater flow, but the PlaxFlow addon enables the option to
model transient groundwater flow. Several options are available to model the unsaturated soil
behaviour, like Mualem-Van Genuchten, approximate Van Genuchten and user-defined soil water
retention curves. Furthermore, various pre-defined data sets are included for common soil types.
The program allows for time dependent boundary conditions, which means precipitation can be
modelled. It is also possible to include an evaporation flux. The evaporation flux is only applied
when the top of the soil is not fully unsaturated (PLAXIS, 2018).
3.2.4 HYDRUS 2D/3D
Hydrus is a software package for simulating water, heat and solute movement in 2- and 3-
dimensional variably saturated media. The program can handle several types of boundaries,
which can vary over time. The unsaturated soil properties are described using various functions,
among which Van Genuchten, Durner, and Brooks and Corey. Hysteresis of the water retention
curve can also be implemented. Furthermore, add-on modules are available to model complicated
phenomena like dual permeability, which can be used when cracks are present in the soil.
However, these modules are only recommended for experienced users. Evapotranspiration can
be modelled by using input data for potential evapotranspiration. HYDRUS adds this as outward
flux dependent on water availability (Šimůnek, Van Genuchten, & Šejna, 2018).
3.2.5 MODFLOW + FloPy
MODFLOW is a modular finite-difference flow model from the U.S. Geological Survey. It is
considered an international standard in groundwater flow modelling. The source code is in the
public domain and therefore free to use (USGS, 2018). Due to this, numerous commercial and
non-commercial interfaces exist. FloPy is an interface that uses the programming language
Python to run MODFLOW models. It includes many of the available MODFLOW packages (Bakker,
et al., 2018).
Modflow also includes a package to model the flow in the unsaturated zone. However, this
package uses the Brook and Corey model and has no option to use the van Genuchten model,
which is more commonly used. However, this package does include options to model
groundwater recharge and evapotranspiration dependent on the saturation of the soil.
Furthermore, packages are included to include these effects without modelling the unsaturated
zone.
An advantage of using FloPy to write input for the model is that there are various Python packages
available to facilitate the input and output of the model. This means input and output can directly
be processed without transferring the data to another program.
The advantages and disadvantages of each program/model are summarised in table 3.1.

3 . Numerical model
22
Table 3.1: Advantages and disadvantages of several numerical models
Model Advantages Disadvantages
D-Geo
Flow
• Specifically aimed at flood defences
• Same software series as commonly
used software for stability analyses
• New program, so not much experience to
build on
• No possibility to run via scripting tool
• No possibility to include
evapotranspiration dependent on water
availability
COMSOL
• Two possible formulations for the
unsaturated zone
• Possibility to use with MATLAB
• No possibility to include
evapotranspiration dependent on water
availability
PlaxFlow
• Several formulations available for
the unsaturated zone, including
user defined
• Predefined data sets included
• Evaporation flux dependent on
water availability
HYDRUS
• Several formulations available for
the unsaturated zone
• Possibility to include hysteresis
water availability
MODFLOW
+ FloPy
• In Python, so broad possibilities to
facilitate in- and output
• MODFLOW is an international
standard
water availability
• Works with rectangular elements, so slope
cannot be modelled as smooth surface
• Unsaturated zone can only be modelled
using Brooks and Corey.
3.3 Model choice
From the models in table 3.1 the choice was made to use MODFLOW 6 in combination with FloPy.
This choice was made for the following reasons:
• With the use of FloPy the input and output of the Modflow model can be controlled using
Python. This means there are no limitations imposed by a graphical user interface, which
enables various possibilities, like reading the desired precipitation values from a csv file
for a specified period, to use Python libraries to plot the output of the models, and many
other options.
• Modflow is an international standard in groundwater modelling.
• Completely open source, so no licenses are required.
A disadvantage is that the unsaturated zone can only be modelled using the Brooks and Corey
formulation, which uses less parameters than the more recent Van Genuchten formulation. On
the other hand, modelling of the unsaturated zone also requires extra parameters to be specified,
which induces uncertainties to the input of the model. Therefore an option worth considering
could be to exclude the unsaturated zone in the model. Both these options will be investigated.
3.3.1 Model grid
In Modflow 6 there are two possible types of grid to construct the model (Langevin, et al., 2017):
• Regular grid: a rectilinear grid consisting of layers, rows and columns;
• Unstructured grid: The cells need not be rectangular in the horizontal direction, and the
number of connections between cells may vary per cell. Unstructured grids offer more
flexibility in constructing models with complex geometry.

3.3. Model choice
23
These grids only are different in the horizontal direction. Both grids use cells with a horizontal
top and bottom. Since the model is constructed in 2 dimensions, the grid choice is irrelevant. A
regular grid is easier to use because the cells in a regular grid are specified by the indices of the
layer, row, and column, which makes it easy to specify input and to obtain output for the cells. For
this reasons a regular grid is chosen for the model.
In a regular grid, the rows and columns represent the horizontal dimensions and the layers
represent the vertical dimension. The width and length of the cells has to be constant, but the
height can vary per cell. This makes it possible to specify one model layer for each layer of soil.
Another possibility is to keep the grid rectilinear in vertical direction, so that all cells in a layer
have the same top and bottom elevation. The soil type is then specified for each cell. These two
options are illustrated in figure 3.1.
It can be observed that the possibility to use different elevations for each layer allows for a much
finer resolution in vertical direction. The boundaries between layers are much smoother than
when strictly horizontal layers are utilised, while the number of columns in horizontal direction
is the same. Furthermore, the first option uses only 4 layers in the example, while the second
options uses 21 layers. The calculation times using option 1 are therefore shorter. A disadvantage
of using only one layer per soil type is that only one pore pressure is calculated for the entire
height of the layer, meaning a variation of the hydraulic head over the head of the layer cannot be
observed. However, this research considers the phreatic surface and therefore one head per layer
is sufficient. For this reason, and the comparatively faster computation time, the choice was made
to use the first option.
Using this method a difficulty arises for layers that do not extend along the entire width of the
model, like the intermediate (yellow) layer in figure 3.1. On the left boundary of the model 4 layers
exist, while on the right boundary only three layers exist. However, the number of layers cannot
vary in the horizontal directions of the model. To overcome this problem the following method
from the Modflow manual is used (Langevin, et al., 2017): The height of the cells on the locations
where the layer does not exist is set to a very small number, and these cells are specified to be
non-existent in the model. For a non-existent cell Modflow directly connects the cells above and
below the non-existent cell.
Another consequence of choosing this grid type is that layer boundaries under a steep angle have
to be treated with care. At steep angles the vertical shift between the cells is large, resulting in
vertical staggering of the grid. This concept is illustrated in figure 3.2. Due to the large vertical
shift combined with the small height of the middle layer, the cell of the middle layer in the right
column is not bordering the cell of the middle layer in the adjacent column. Since a Modflow cell
Figure 3.1: Options to construct a regular grid in Modflow. Left: using different elevations in a single layer.
Right: using strictly horizontal layers. The number of columns in horizontal direction is the same for both
options.

3 . Numerical model
24
only has horizontal connections to cells in the same layer, this
leads to inaccurate flows between the cells.
Since the research only a considers a cross-section, the model
is two dimensional. In longitudinal direction the model only
spans a single cell. For the resolution a row and column width
of 0,25 m is chosen. If the results show this is too small or too
large, this value can be adjusted.
Construction of the grid
The model grid has to be constructed based on a
schematisation of the profile of the flood defence. In order to
easily modify the resolution of the grid, the choice was made
to define the schematisation as a number of connected points,
and to write a Python script to construct a grid from these
points and a specified resolution. The script was built such that
a schematisation can be drawn in the program D-Geo stability.
This program, used for stability analyses of flood defences,
offers the option to export a schematisation. This export is written in the form of a text file and
can be read by a Python script. In this file the schematisation is defined in soil layers, which can
be converted to layers in Modflow. Layers that pinch-out in the cross-section are assigned a layer
height of 1 mm for the length along which the layer does not exist, and the cells along this length
are automatically specified as non-existent. This method using D-Geo Stability to draw a
schematisation makes it possible to easily adjust the schematisation, or to construct a new model.
3.3.2 Time discretisation
The timing of a simulation in Modflow is subdivided in two units: stress periods and time steps
(Langevin, et al., 2017). Stress periods are used to make a change in the boundary conditions of a
model. Stress periods are subdivided into time steps. The number of time steps can be specified
for each stress period separately, and it is also possible to vary the length of the time step over
the duration of the stress period. Parameters of the boundary conditions, for example water levels
and recharge rates, can be specified for each time step. Since the boundary conditions themselves
do not change, one single stress period is sufficient for the simulations in this research. The
measurement and precipitation data are available for hourly intervals, so a time step of hour is
used for the simulations.
3.3.3 Initial conditions
For the start of the model initial conditions have to be specified, in the form of a groundwater
head for each cell in the model. For the upper layers the measurements of the phreatic surface
could be used, but these only provide information at a few points along the cross-sections. This
means the initial conditions for the other cells have to be estimated by interpolation, which is
unlikely to represent an equilibrium situation of the model.
Another option is to start the simulation with a steady-state stress period. The results of this
stress period are than automatically used as initial conditions for the next, transient, stress
period, in which the actual simulation is performed. For the steady-state stress period initial
conditions still have to be provided, but these have no effect on the outcome because an
equilibrium situation is calculated. The initial conditions only determine the amount of time steps
required in the simulation to reach this equilibrium. The outcome of the steady-state simulation
will probably not match the first the first measurements of the monitoring wells. The first
measurements are influenced by the precipitation and evapotranspiration in the period before.
Therefore the transient part of the simulation has to start at an earlier point in time than the start
of the measurements, so that the model can adjust to the transient conditions.
Figure 3.2: Vertical staggering of a
Modflow grid. Source: Langevin, et
al., 2017

4.1. Vlaardingsekade (Delfland location 24)
25
4 Research cases
The research is centred around a number of case studies. In chapter 1 several requirements for
the research cases were listed:
• Pore pressure data is available from monitoring wells or pressure sensors;
• The case should be representative for a typical regional flood defence;
• Data for water levels, precipitation and evapotranspiration can be acquired for the case.
Three research cases from two different research projects were chosen to be analysed. Two of
these cases are located in the management area of the water board of Delfland, and the third
research case is located in the management area of the water board of Rijnland. In figure 4.1 the
geographical locations of the research cases are displayed.
4.1 Vlaardingsekade (Delfland location 24)
In the period 2010-2014 the water board of Delfland has conducted a programme in which
monitoring wells were placed in nine regional flood defences. The hydraulic head in these
monitoring wells was measured over a period of about 4 years (Delfland, 2016). Due to this long
measurement period the seasonal influences of several years are included.
From these nine locations two locations are chosen as research cases: the locations 24 and 25
near the village of Schipluiden, close to Delft. These locations are situated relatively close to each
other (about 500 m apart) on the same storage channel. The proximity of the two locations gives
the advantage that the same precipitation can be used for both research cases. At both locations
Figure 4.1: Locations of the research cases

4 . Research cases
26
three monitoring wells were installed, while at most other locations only two monitoring wells
were used. These considerations have led to the choice for these two locations.
Location 24, the Vlaardingsekade, is located on the eastern side of the Vlaardingsevaart, a canal
which is part of the boezem-system of Delfland. The dike contains two pavement structures: a
footpath on the crest and a road on the berm. At the toe of the dike formerly a drainage ditch was
located; however, this ditch was filled in sometime between 2005 and 2010. Enquiry at the water
board made clear that this ditch had been filled in before the monitoring wells were placed. A new
drainage ditch was excavated in 2017, which means during the measurements no drainage ditch
was present.
Three monitoring wells were installed in the
flood defence: one in the crest, one in the slope,
and one near the toe. However, the monitoring
well near the toe was placed on the opposite side
of the former drainage ditch. Since the ditch was
filled with sand, it can be expected that most of
the groundwater flow will take place through
this former ditch, in which case the monitoring
well provides no meaningful information about
the phreatic surface in the dike. On the other
hand it still provides information about the
groundwater table on the inside of the dike,
which is useful to determine the boundary
condition at the polder side of the model.
A drawing of the cross-section of location 24,
including the locations of the monitoring wells,
is included in appendix E. The locations of the
three monitoring wells are also indicated in
figure 4.2.
4.2 Duifkade (Delfland location 25)
The second research case within Delfland is
located about 500 m to the south of location 24,
on the western bank of the same
Vlaardingsevaart. The main difference between
the dike at this location and location 24 is the
lack of pavement: the dike is completely covered
with grass. This means the infiltration
characteristics are different to location 24,
which could result in a different response of the
phreatic surface to precipitation.
Inland of the dike a drainage ditch is present.
This ditch located about 5 m removed from the
toe. Three monitoring wells were placed in the
cross-section: one in the crest, one in the slope
near the toe and one near the drainage ditch.
The locations of the three monitoring wells are
indicated in figure 4.3. A drawing of the cross-
section of the dike is included in appendix E.
Figure 4.2: Location of the monitoring wells at
location 24.
Figure 4.3: Locations of the monitoring wells at
location 25.

4.3. Hogedijk (Rijnland)
27
4.3 Hogedijk (Rijnland)
The third research case in this thesis is located in the management area of the water board of
Rijnland. The companies Iv-Infra and Nectaerra are conducting a research project on several
regional flood defences of this water board with the aim to investigate whether it is possible to
determine the position of the phreatic surface by hydrological analysis and modelling based on
field measurements (Nectaerra, 2018). During the writing of this thesis, initially measurements
from August until October 2018 were available, but after a new readout this period was extended
to January 2019. In most of the cross-sections in this project four monitoring wells were placed,
and in addition to that field measurements of the conductivity were carried out. Although the
measurement period is much shorter than for the other two locations in Delfland, more
information is available thanks to the extra monitoring well and the conductivity measurements.
For this reason a case from this research project was used as the third research case for this thesis.
The research project involves four regional flood defences, in some of which monitoring wells
were placed in two cross-sections. The dike chosen for analysis in this thesis is the Hogedijk near
Aarlanderveen. This dike was chosen for the following reasons:
• The dike is also subject of a reinforcement project. The design for this reinforcement is
drafted by Iv-Infra, which means a lot of information on the dike can readily be obtained.
• In the measurement period a precipitation event has occurred with a volume of about 95
mm; at some of the other locations this occurred as well, but the precipitation volume at
the Hogedijk was the highest. It could be interesting to investigate how accurate this
extreme event can be simulated in the model.
A disadvantage of choosing this location is that the measurements started about a month later
than at the other locations. However, the amount of precipitation during that month was small,
so no interesting events are excluded due to the later start of the measurements.
Like Delfland, Rijnland has a boezem-system, but the Hogedijk is not located directly on this
boezem. The outside water is part of a polder with a much higher water level than the polder
behind the dike. This slightly different situation compared to the other research cases has no
influence on the modelling of the phreatic surface. The main difference between the Hogedijk and
the two cases in Delfland is the composition of the dike: the Hogedijk consists primarily of peat,
which is not present in the dike body for the two cases in Delfland, only in the subsoil.
Monitoring wells were placed in two cross-
sections of the Hogedijk. The main difference
between these cross-sections is the inside water
level; one of the cross-sections is located at an
area with a locally higher water level. This cross-
section was not chosen for this thesis. The locally
higher water level is not included in the
documentation of Rijnland, and therefore the
exact water level is unknown and it could also be
subject to fluctuations. Furthermore, the other
cross-section showed more interesting
fluctuations in the measured heads.
The chosen cross-section (indicated as HGD-1)
contains four monitoring wells. All are located on
the inner slope, with the furthest outward well
near the inner crest, and the furthest inward well
located about 10 m removed from the drainage
ditch. Furthermore, a rain gauge was installed
about 70 m removed from the cross-section. The
Figure 4.4: Location of the monitoring wells and
the rain gauge (blue square) at the Hogedijk.

4 . Research cases
28
locations of these objects are displayed in figure 4.4. A drawing of the cross-section of the dike is
included in appendix E.
4.4 Measurement data
4.4.1 Location 24
The cross-section of location 24 including the monitoring wells is displayed in figure 4.5. The
filters of the monitoring wells are indicated as a lighter colour.
Figure 4.5: Cross-section and location monitoring wells (MW) Delfland location 24
The head measurements of the three monitoring wells are displayed in figure 4.6. The total
measurement period for location 24 runs from 02-06-2010 until 07-07-2014, which is a period
of just over 4 years. Three manual measurements were carried out during the measurement
period, which are displayed as crosses. Larger plots of the measurements are included in
appendix D.
Figure 4.6: Monitoring well measurements Delfland location 24, from 01-06-2010 until 07-07-2014
For only a part of the total period measurements are available from all three monitoring wells.
Due to changes in the filters and errors of the data loggers large parts of the data are missing. At
some points shifts in the measurements can be observed, where the average level of the head
changes. An example of this can be seen in July 2011, in the monitoring well in the toe. The reason
is probably a readout of the logger. After a readout the baseline of the measurement has to be
reset based on a manual measurement. If this measurement is incorrect, this will lead to a shift of

4.4. Measurement data
29
the baseline of the data. In appendix D all holes and discrepancies in the measurement set are
listed.
4.4.2 Location 25
The cross-section and locations of the monitoring wells for location 25 are displayed in figure 4.7.
Figure 4.7: Cross-section and location monitoring wells (MW) Delfland location 25
The total measurement period for location 25 runs from 01-06-2010 until 22-10-2014. In this
period four manual measurements have been carried out. The measurements are displayed in
figure 4.8, larger plots are included in appendix D.
Figure 4.8: Monitoring well measurements Delfland location 25, from 01-06-2010 until 22-10-2014
The monitoring well in the crest was placed in an intermediate sand layer, which had the result
that the phreatic surface was not measured. Therefore later another monitoring well was placed
with a higher filter. The first monitoring well was not removed, and provides information on the
head in the intermediate sand layer. Several gaps are present in the data set, but these are smaller
than for location 24. Like location 24, several shifts in the baseline of the data can be observed. In
appendix D all holes and discrepancies in the measurement set are listed.
The several shifts recorded in the data for both locations indicate that not all parts of the data are
equally reliable. It is unclear how reliable the manual measurements are. Since the jumps in the
data have a magnitude of about 10 to 15 cm, it can be argued that on average the height of the

4 . Research cases
30
phreatic surface is known with an accuracy of about 15 cm. The magnitude of the fluctuations
compared to the baseline is likely to be more accurate.
Measurements Hogedijk
The locations of the four monitoring wells in the Hogedijk are displayed in the cross-section in
figure 4.9.
Figure 4.9: Cross-section and location monitoring wells Hogedijk
The research project including the Hogedijk was ongoing during the writing of this thesis. During
the set-up and calibration of the model only measurements from 23-08-2018 until 12-10-2018
were available. Later a new readout was performed, which extended the available measurement
set to 07-01-2019. This full measurement set is displayed in figure 4.10. No gaps are present in
the measurements. No failures have occurred during the so far relatively short measurement
period, and no measurements were removed from the data set. Notable is that the heads show a
gradual increase until about December 2018. This increase is caused by the dry summer of 2018,
after which it took several months for the phreatic surface to return to a more normal level. The
gradual increase is therefore not a discrepancy in the measurements.
Some other phenomena can be observed in the data for which no clear explanation could be
found. These phenomena were discussed in a meeting with Nectaerra, the company that carries
out the measurements. From this meeting more insights were obtained regarding the
discrepancies found in the data.
One of the phenomena can be observed in the measurements of the monitoring well at the inner
crest (HGD 1-1). For several periods, the head is at an increased level, after which it suddenly
drops back to baseline level. Outside of these periods the head fluctuations are quite small. The
elevated periods are caused by submerging of the pressure logger. When this occurs the air
pressure cannot be measured, and since the head is determined by subtracting the air pressure
from the water pressure this results in unreliable measurements. The measurements even exceed
the top of the monitoring well, which is physically impossible. The data was therefore topped off
at this level, which is at NAP -2,15 m, which results in the plateaus observed in figure 4.10. Due to
their unreliability, the elevated periods should be removed from the data when the
measurements are analysed.
Another remarkable observation is that the measurements of HGD 1-2 and HGD 1-3 show
different fluctuations, despite being placed relatively close to one another. HGD 1-2 shows a very
small and damped reaction to precipitation events, whereas HGD 1-3 shows much larger peaks,
which are more comparable to the peaks observed for the research locations in Delfland. This
difference is most likely a results of cracks in the dike. Many large cracks are present in the dike,
some of which are several centimetres wide. HGD 1-3 is probably connected to such a crack.
Runoff water from the surface can reach the monitoring well through the crack, resulting in a

4.5. Influence of precipitation on the phreatic surface
31
more direct and larger head rise. Another factor of influence causing large peaks is rise of the pore
pressures due to the increased weight of the topsoil when it becomes saturated by precipitation.
Figure 4.10: Monitoring well measurements Hogedijk, from 23-08-2018 until 12-10-2018
4.5 Influence of precipitation on the phreatic surface
To analyse the reaction of the phreatic surface to precipitation, the heads in the monitoring wells
were plotted together with the precipitation and potential evapotranspiration data. These plots
are included in appendix D. In chapter 5 the source of this evapotranspiration and precipitation
data is discussed.
In the plots of the measurements the precipitation events can easily be recognised: the heads
suddenly rise, and then slowly return towards the initial water level. To analyse the speed and
the magnitude of these responses of the heads, the precipitation events for the research locations
in Delfland were analysed. This analysis was not performed for the Hogedijk because of the small
number of precipitation events included in the dataset.
First the precipitation events had to be identified from the precipitation data. A period of
precipitation had to meet several criteria to be marked as a precipitation event in order to keep
the number of events at a manageable level. These criteria were the following:
• A minimal precipitation rate of 0,1 mm per hour to start the event; this criterion was
needed to exclude hours of very low intensity precipitation from the event.
• An event can have a maximum of 6 consecutive hours in which the precipitation is lower
than the specified minimal precipitation rate of 0.1 mm/hour.
• The total amount of precipitation over the event is more than 20 mm.
Using a Python script, the precipitation events were identified based on these criteria. Over the
period from 01-06-2010 until 22-10-2014 37 precipitation events were identified. To analyse the
effect of each event on the heads in the monitoring wells a plot was made for each event. These
plots included the precipitation and the head in each of the monitoring wells over the duration of
the precipitation event plus an additional 24 hours. For each event the time after which the
monitoring wells responded to the precipitation was determined manually, since this could not
be automated properly. The total rise of the head for each event was determined using the Python
script.

4 . Research cases
32
4.5.1 Location 24
For location 24, it was observed that the response of the heads is dependent on the shape of the
precipitation. If the event starts with a high intensity of several mm per hour, the response of the
heads can be observed quite clearly. However, if the event starts with several hours of lower
intensity the response time is much harder to define. When the event is preceded by another
precipitation event the heads can even still be declining for several hours after the start of the
new event, before a new rise is observed.
The heads at the crest, slope and toe show no clear order in the time between the start of the
precipitation and the response. Generally, the response starts in the same hour for all three
locations. If there is a consistent
sequence in which the monitoring
wells respond, this occurs on a
timescale smaller than an hour. On
average the three wells respond
after 4-5 hours after the start of the
precipitation.
For the peak of the head rise a more
clear sequence can be observed.
For most events the toe reaches the
peak of the head rise first, then the
slope, and finally the crest. An
example of this is given in figure
4.11. All three heads start to rise at
the same time, but the toe reaches
its peak earlier than the crest and
the slope.
To analyse whether the order in which the peaks are reached is related to the precipitation
intensity, several precipitation events are displayed in figure 4.12. On the x-axis the rank of the
events is displayed, where 1 corresponds to the event with the highest volume of precipitation.
The amount of precipitation is displayed on the y-axis. The colour of the bars indicates the
sequence order in which the peak head rise was reached. The bars of the events for which no data
was available for all three monitoring wells are left blank. For only 7 of the 33 events with a
volume larger than 20 mm the heads for all three monitoring wells were measured.
Figure 4.12: Order in which the peak head rise is reached after a precipitation event, for location 24
As was observed earlier, the most common sequence is toe-slope-crest. It appears that other
sequence orders only occur at lower intensity precipitation events, but since only seven events
are included no clear conclusions can be drawn. The precipitation amount of the included events
0
20
40
60
80
100
120
1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233
Precipitation
(mm)
Precipitation event rank
Crest - Slope - Toe
Slope - Crest - Toe
Toe - Slope - Crest
No data
Figure 4.11: Response of the heads in the monitoring wells at
location 24 for a precipitation event on

4.5. Influence of precipitation on the phreatic surface
33
only ranges from 20 to about 27 mm, so all events have approximately the same precipitation
volume. This makes it difficult to identify any relation between the precipitation volume and the
sequence order.
Another aspect that was analysed is the relation between the amount of precipitation and the
head rise in the monitoring wells. Again this was done by isolating the precipitation events using
the Python script. For each precipitation event the head rise compared to the head at the start of
the event was calculated. Since this analysis could be done automatically, more precipitation
events are included. The threshold to classify a precipitation event was lowered from 20 to 2 mm,
which resulted in 413 precipitation events. For these events the amount of precipitation was
plotted against the head rise; this plot is displayed in figure 4.13.
Figure 4.13: Head rise against amount of precipitation for location 24
As expected, a larger amount of precipitation leads to a larger head rise. The head rise at the crest
shows more spread than the slope and the toe. Furthermore the slope shows less head rise for
the same amount of precipitation compared to the other monitoring wells. This could be a result
of reduced infiltration caused by the road located on the slope. However, it must be noted that
the slope has less data points due to the large gap in the measurement series. Several of the largest
precipitation events of the total measurement period took place during this gap.
4.5.2 Location 25
The same analyses were conducted on the measurements from location 25. Just like at location
24 the heads respond 4 to 5 hours after the start of the precipitation, and all three respond at
approximately the same moment. However, regarding the peaks of the head rise no clear result
was found. For several precipitation periods the sequence in which the peak was reached was
exactly opposite to what was observed at location 24: the crest responded first, then the slope
and finally the toe. However, in some cases the slope responded last. To analyse this is the peak
sequence of the monitoring wells was analysed again. For location 25 the measurement data is
more complete, and therefore more events could be analysed, including the most extreme event.
The measurement period was also slightly longer, which means four more precipitation events
larger than 20 mm have occurred in the measurement period.

4 . Research cases
34
Figure 4.14: Order in which the peak head rise is reached after a precipitation event, for location 25
From figure 4.14 it is clear that for almost all events the crest responds first. Which monitoring
well responds second varies; for 10 of the 24 considered events the slope responds second, and
for 11 events the toe responds second. However, the four largest events all show the order crest
– slope –toe. Therefore it seems like the slope responds second for larger intensity precipitation.
On the other hand, this sequence also occurs for the lowest intensity events.
Another phenomenon that can be observed is a dip in the peak of the crest for some of the events.
First the head rises, then declines a little, and then rises again. This is probably caused by the so
called pre-draining of the boezem. When a large volume of precipitation is forecast, the water
board lowers the water level in anticipation of the water level rise caused by the precipitation.
This would also explain why this dip is not observed for every precipitation event.
Figure 4.15: Head rise against amount of precipitation for location 25
When the head rise is plotted against the amount of precipitation, again a different result is found
compared to location 24. In figure 4.15 it can be observed that that the head rise is smallest for
the toe, and largest for the slope. This difference may partially be caused by the measurements:
for location 24 the head at the slope was measured for a limited time, while at location 25 the
0
20
40
60
80
100
120
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37
Precipitation
(mm)
Precipitation event rank
Crest - Slope -Toe
Crest - Toe - Slope
Slope - Crest - Toe
Toe- Crest - Slope
No data

4.6. Histograms
35
head at the slope was measured almost continuously. Furthermore, the location of the monitoring
wells plays a role: the monitoring well at the toe is located quite close to the inside drainage ditch,
which might explain the smaller head rise.
4.5.3 Hogedijk
During the period for which measurements from the Hogedijk are available six precipitation
events of significance have occurred. The precipitation event of 05-09-2018 was the largest of
these, with a daily volume of 95,6 mm. Monitoring wells 1 , 3, and 4 showed a clear response to
this event, but monitoring well 2 showed only a very small and gradual increase in head. The
other precipitation events lead to very small responses in the monitoring wells: only monitoring
well 3 shows a clear response for the events, while the other wells only show a small and gradual
increase of the heads.
The more comprehensive analyses conducted on the cases from Delfland were not conducted for
the Hogedijk, since the amount of data is too limited to draw any meaningful conclusions.
4.6 Histograms
Another method to visualise the measurement data is the use of a histogram. In a histogram the
range between the minimum and maximum of the measurements is divided into a number of bins.
Each bin can then be plotted in a barplot, with the height of the bar representing the number of
measurements included in the bin. This provides a method to visualise how often a certain head
elevation has occurred in the measurement period.
Histograms with 25 bins were plotted for the measurements of the locations in Delfland. The
measurement period of the Hogedijk shows an upward trend due to the short measurement
period, which distorts the histogram.
The histogram for location 24 is displayed in figure 4.16. The three histograms show an
approximatly equal variation range of about 0,5 m. The histogram for the slope is much lower
than the other two; the reason for this is the large gap in the measurements for this location.
Figure 4.16: Histogram of the measurement data from location 24
The histograms for location 25 are displayed in figure 4.17. The difference between the three
monitoring wells is larger here: the variation range of the crest is relatively small, whereas it is
relatively large for the slope.

4 . Research cases
36
Figure 4.17: Histogram of the measurement data from location 25
Most histograms show a shape with a slightly heavier tail on the right-hand side. This indicates
that higher than average heads occur more frequently than lower than average heads.
The histograms only show the frequency of a certain head in the monitoring well, but provide no
information about the correlation between the monitoring wells. Therefore the correlation
coefficients are calculated for each combination of monitoring wells. The hours for which either
of the two monitoring wells considered had no measurement were excluded from the data. The
calculated correlation coefficients are displayed in table 4.1. The numbers for the two research
locations in Delfland are placed in separate columns, but no correlation coefficients between the
two cross-sections were calculated. A correlation coefficient of 1 means that both monitoring
wells show identical fluctuations; a value of 0 means that there is no correlation between the two
monitoring wells.
Table 4.1: Correlation coefficients between the monitoring wells for the locations in Delfland
Location Location 24 Location 25
Crest - Slope 0,831 0,007
Slope - Toe 0,204 0,716
Toe - Crest 0,416 0,230
For location 24, the fluctuations of the monitoring wells in the crest and slope are closely
correlated. The correlation coefficient of either of these two monitoring wells to the well in the
toe is smaller. Remarkable is that the correlation between the toe and crest is larger than the
correlation between the toe and the slope. However, it should be noted that the number of
measurements in the slope is much smaller than for the other two locations.
For location 25, the correlation between the crest and the two other monitoring wells is small,
whereas the correlation coefficient between the slope and the toe is relatively large. A possible
explanation is that the crest is more influenced by fluctuations of the outside water than the toe
and the slope.

5.1. Input data
37
5 Model set-up
This chapter describes the set-up of the Modflow models for the three research locations. This
involved determining or estimating the various required input parameters, and the
schematisation of the various soil layers in the cross-sections. Furthermore, a grid had to be
constructed from the soil schematisation, and the boundary conditions had to be applied to the
model. When the models were completed, calibration was required to fit the models to the
measurements.
5.1 Input data
The required input data for the model can be divided into two groups: hydraulic loads and
geotechnical parameters. The hydraulic loads consist of the in- and outside water levels,
precipitation and evapotranspiration. The geotechnical parameters encompass parameters of the
soil types, like the conductivity in horizontal and vertical direction, and storage parameters.
5.1.1 Precipitation and evapotranspiration data
At the Hogedijk a rain gauge was installed, so for this location precipitation data is directly
available. For the locations in Delfland this is not the case, so for those locations the data has to
be obtained via other means. One available source for precipitation data is the Dutch
meteorological institute (KNMI). However, for all of the research locations the closest weather
station is quite far away. For the evapotranspiration this is probably not a problem, but for the
precipitation data this could lead to large errors due to its large local variability. A better option
is the use of a service that combines data from radar images and weather stations to estimate
area-specific precipitation. One such service is the online archive Meteobase. This website is a
project of STOWA, the knowledge centre of the Dutch water boards. From Meteobase
precipitation and evapotranspiration data are available in grid format in a resolution of 1 by 1
km. The precipitation data is provided in hourly intervals, and is calculated by combining radar
imagery and precipitation measurements from the KNMI (STOWA, 2013). The
evapotranspiration data is available in daily intervals, and is calculated from weather station data
using both the Makkink and Penman-Monteith methods. The Makkink method is used by the
KNMI, but use of the Penman-Monteith method is more common internationally.
Due to the use of both precipitation measurements and radar imagery as well as its availability,
the use of Meteobase data is the best choice for this research. In appendix C it is described how
the data from Meteobase was downloaded and processed for use in the model. Because no actual
precipitation was measured at the research locations in Delfland, small differences may exist
between the data and the actual precipitation. However, there is no way to identify and quantify
these differences. These uncertainties are likely small compared to the uncertainties in soil
characteristics and are therefore disregarded.
For the location Hogedijk no Meteobase data could be obtained. The data was only available up
to the date of 31-12-2016, and for the Hogedijk data for 2018 was required. Precipitation data is
available from the rain gauge for the measurement period, but for the preceding period no data
is available. For the potential evapotranspiration no local data is available at all. The closest KNMI
weather stations to the Hogedijk are Schiphol (16,9 km), Valkenburg (21,1 km), and Cabauw (24,1
km) (KNMI, 2018). The potential evapotranspiration rate is calculated for each station, and the
average of the three stations weighted by distance is used as input data for the model. This
potential evapotranspiration rate was calculated using the Penman-Monteith formulation, using
the same method as used for the Meteobase data (STOWA, 2013) & (Schuurman & Droogers,
2010). This method is described more elaborately in appendix C.

5 . Model set-up
38
The locally measured precipitation was measured in 10-minute intervals. The recharge boundary
condition (described in paragraph 5.3.3) is calculated for hourly intervals. To maintain
consistency between the models the 10-minute data is converted to hourly data for use in the
model. In order to model the period preceding the measurements, precipitation data from the
weather station at Schiphol was used. Due to the local variability of precipitation, taking the
average of three stations for each hour could lead to underestimation of the precipitation
intensity.
5.1.2 Water levels
For each model two water levels have to be applied as boundary conditions: the outside water
level in the boezem canal and the inside water level in the polder.
Location 24
The boezem canal location 24 is located on, the Vlaardingsevaart, is part of the boezem-system of
Delfland, on which a water level of NAP -0,43 is maintained. (Delfland, 2018). This level is the
intended water level; during and after periods of heavy precipitation the actual water level may
vary. When heavy precipitation is forecast the water level is lowered in anticipation, with a
maximum of 20 cm below normal level. During dry periods water is let into the boezem-system
to keep the water at the intended level. This means the lowest possible water level is NAP -0,63
m. In extreme situations with heavy precipitation the water level might rise slightly above the
intended water level despite the lowering of the water level beforehand. The extreme water level
for these conditions was determined by the water board using a model of the boezem-system for
several return periods. For a return period of 100 years the water level rise is 0,06 m, which
means the water level would be NAP -0,35 m. This is the design water level used in stability
calculations.
It can be concluded that the outside water level variations are quite small. The water will usually
be at the intended level of NAP -0,43 m. It slightly varies in extreme situations and even then only
for a short period. In addition to that, the exact variations during the measurements period are
unknown. Therefore the choice is made to keep the outside water level in the model at the
intended level of NAP -0,43 m.
Similar to the outside water, the inside water levels also have an intended water level. This water
level is different for each polder. For location 24 the intended water level is NAP -3,63 m
(Delfland, 2018). This water level applies to a small part of the polder behind the flood defence:
the rest of the polder has a water level of NAP -3,42 m. Location 24 is located at an area where a
slightly lower water level is maintained. From communication with the waterboard it was found
that the variations in the polder water level are in the order of several centimetres. For this reason
the choice is made to also keep the inside water level constant in the model. However, the
drainage ditch at location 24 is filled in, meaning there is no direct inside water level present. This
has to be taken into account in the application of the boundary conditions to the model.
Another parameter of importance is the head in the Pleistocene sand layer, the bottom layer in
the model. The head in the layer was found in an assessment report for the flood defences along
the Vlaardingsevaart, which includes location 24 (RPS BCC B.V. & Witteveen + Bos, 2010). In this
report a head of NAP -1,61 m is given for location 24.
Location 25
Since location 25 is on the same boezem canal as location 24 the outside water level is the same,
so at NAP -0,43 m. For the inside water level the situation is slightly more complicated: the
drainage ditch has a flexible water level that can vary between NAP -3,00 m and -2,30 m. This
ditch is separated from the water system in the rest of the polder, and the water level is allowed
to fluctuate. However, when observing the measurement data of the monitoring well located
closest to this ditch it appears that the groundwater table at this point is on average around NAP
-3,15 m. This indicates that the water level in the ditch is very regularly below the intended -3,00

5.1. Input data
39
m. About 5 m inland of the drainage ditch is another drainage ditch, which has a water level of
NAP -3,10 in summer and NAP -3,15 in the winter. Probably the ditches are so close that the
groundwater flow causes the flexible water level to be constantly near the polder water level.
Therefore the polder water level is used for the inside water level. For this the winter water level
of NAP -3,15 m is used.
The head in the Pleistocene sand layer was obtained from the same report as for location 24 (RPS
BCC B.V. & Witteveen + Bos, 2010). For a location on the opposite the canal from location 25 a
head of NAP -1,55 m is given, so this head is used in the model.
Hogedijk
The water levels in- and outside of the dike are specified in the legger of Rijnland
(Hoogheemraadschap van Rijnland, 2018). The polder outside the dike has an intended water
level of NAP -1,54 m, and the polder inside the dike has an intended water level of NAP -5,98 m.
Again these water levels are assumed to be constant over time.
The head in the Pleistocene sand layer is taken from an Iv-Infra report concerning the Hogedijk
(Iv-Infra, 2018) and is NAP -5 m.
5.1.3 Soil parameters
For all three research locations soil borings at the locations the monitoring wells are available.
Using this information the soil composition can roughly be determined. For the location Hogedijk
measurements of the hydraulic conductivity are available as well. For the locations in Delfland
this is not the case, these soil parameters have to be estimated based on the type of soil. Water
boards usually have parameters sets of the local soil types based on laboratory analysis, but these
sets normally only include parameters concerning strength and settlement. Therefore
standardised conductivity values have to be used.
Hydraulic conductivity
For the locations in Delfland, the choice was made to use values from the Staring set as a first
estimate for the hydraulic conductivity. The Staring set is a data set from the research institute
Alterra containing geohydrological parameters for 36 soil types (Wösten, Veerman, De Groot, &
Stolte, 2001). These soil types are divided in two groups: top-soils and sub-soils. The top-soils are
soil near the surface, where the influence of plant roots is still noticeable, and the sub-soils are
the soils below this zone. Each of these two groups includes several types of sand, loam, clay and
peat.
Due to the nature of soils the conductivity can vary greatly, and therefore calibration is almost
always necessary for geohydrological models. Because of the large amount of samples (about
800) contained in it, the choice is made to use values from the Staring set as an initial estimate for
the hydraulic conductivity. During the calibration of the model these values will be altered to fit
the measurements. Care must be taken that the conductivity values remain within a realistic
range for the considered soil type. To define these ranges, conductivity values from several
sources are compared. This includes values found in literature, but also the measurements from
the research project in Rijnland. The measurements are included in appendix E. While they
provide some insight in the hydraulic conductivity in regional flood defences, the number of
samples is limited. Therefore literature was consulted to obtain information regarding common
conductivity values for clay, peat and sand.
Clay
Comparing the values of the hydraulic conductivity of clay in the Staring set values to the other
sources, the values appear to be quite large. The smallest value is larger than the largest value in
some of the other sources. However, these conductivity values apply to clay as a solid material.
As discussed in chapter 2 , clay soils often exhibit a soil structure which causes the conductivity
to be much larger. The values in the Staring set are aimed at geohydrological modelling of large

5 . Model set-up
40
areas of soil, and thus take this soil structure into account. This results in comparatively high
values. In a report assessing whether the Staring-values are applicable to dikes (Van den Akker,
2001), it was found that the Staring set actually even underestimates the conductivity of clay soils
in dikes. Compared to agricultural soils (which the Staring set is based on), soils in dikes are not
tilled or ploughed, which means the soil structure is more developed and therefore the
conductivity is higher.
The influence of the soil structure is also illustrated by the values given in Oosterbaan & Nijland
(1994). For well-structured clay and loam a range of 0,5 – 2 m/day is given, for poorly structured
clay a range of 0,002 – 0,2 m/day, and for dense clay a conductivity smaller than 0,002 m/day.
Since it was established in chapter 2 that soil structure has a significant influence on the phreatic
surface, the range of 0,002 to 2 m/day is considered the most realistic for use in the model, where
the values above 0,1 are only allowed for top layers.
Peat
The conductivity of peat is dependent on many factors, one of which is its degree of
decomposition. Decomposed (amorphous) peat has a lower conductivity than fibrous peat
(Wong, Hashim, & Ali, 2009). The compression of the peat also has a large influence on the
conductivity. The conductivity can vary from comparable to sand in its initial state to comparable
to soft intact clay. Due to this influence of compression the distinction must be made in the model
between peat layers near the surface and deeper peat layers. A similar range as for clay is used,
which was 0,002 to 2 m/day, and values above 0,2 are only applicable for top layers.
Sand
The conductivity range for sand in the Staring set is lower than the values found in other sources.
The sand types in the Staring set all contain loam in some measure, which probably causes this
lower conductivity. Since the sand found in the research cases also often contains loam and clay,
this lower range could be realistic. However, the largest Staring conductivity is just above 1
m/day, while other sources give values up to 50 m/day. Therefore a slightly larger range from 0,1
to 5 m/day is used for the calibration of the model.
The conductivity ranges for sand, clay and peat found in these sources are displayed in table 5.1.
Table 5.1: Values of the hydraulic conductivity for different soil types, found in literature
Conductivity
range
(m/day)
Staring Verruijt &
Broere
(2011)
Wong et
al.
(2009)
Morris &
Johnson
(1967)
Oosterbaan
& Nijland
(1994)
Nectaerra
(2018)
Clay
min 0,007 - 8,7*106 - - 8,15*10-6 < 0,002 0.22
max 0,14 8,7*10-4 - 1,22*10-3 2 31.2
Peat
min 0,011 - - 0,001 0,12 - 0,002
max 0,81 - 1 11,4 - 0,064
Sand
min 0,099 - 0,087 - 2,5 1 1.25
max 1,07 87 - 45 50
Hydraulic anisotropy
The conductivities discussed thus far are the conductivities in horizontal direction. Dependent on
the soil type, the vertical conductivity may vary considerably from the horizontal conductivity.
This anisotropy is especially present in clay and peat due to the orientation of the soil particles
or fibres. In general, the horizontal conductivity is larger than the vertical conductivity. The ratio
between the horizontal and vertical conductivity is called the hydraulic conductivity anisotropy
ratio and can be defined as:
𝑎 =
𝐾𝑣
𝐾ℎ
(5.1)

5.1. Input data
41
Where:
a = hydraulic conductivity anisotropy ratio (-)
Kv = vertical conductivity (m/day)
Kh = horizontal conductivity (m/day)
In order to make calibration of the model more straightforward, the anisotropy ratio is assumed
to be constant for a single soil type. In the calibration the horizontal conductivity is variated, and
the corresponding vertical conductivity is determined using the anisotropy ratio. Like the
conductivity itself, the anisotropy ratio has a large variability. Few sources could be found
regarding the relationship between the horizontal and vertical conductivity, but using the
information that was available an estimate could be made for each soil type.
Clay
In Morris & Johnson (1967) average conductivities for clay in both directions are given: 0,000204
m/day in horizontal direction and 0,0000815 in vertical direction. These values result in an
anisotropy ratio of 0,4. However, as said before these conductivities disregard the presence of a
soil structure. A soil structure may have a different effect on the vertical than on the horizontal
conductivity. The technical report ‘pore pressures in dikes’ (TAW, 2004) gives 0,33 as a
conventional anisotropy ratio for clay. De Loor (2018) uses different anisotropy ratios for the top
clay layer and the clay of the dike core in his research. For the core he uses a ratio of 0,33, which
is probably derived from TAW (2004). For the top layer he uses a ratio of 2, meaning the vertical
conductivity is higher than the horizontal conductivity. The explanation for this is that the soil
structure in the clay top layer mainly enlarges the vertical conductivity. Especially cracks are
vertically oriented, thus enlarging mainly the vertical conductivity.
As a first estimate, the value of 0,33 from TAW (2004) is used for the hydraulic anisotropy ratio.
This value might be altered in the calibration process. Especially for top layers it can be necessary
to use a larger value due to the soil structure.
Peat
The hydraulic anisotropy of peat is generally larger than for inorganic soil; values of about 300
have been found in tests (Wong, Hashim, & Ali, 2009). The technical report ‘pore pressures in
dikes’ (TAW, 2004) gives the same value as for clay (0,33) as a conventional value. In engineering
practice often a value of 0,1 is used; given the small number of sources and the differences
between them this value will be used in the model as well.
Sand
For sand TAW (2004) gives an anisotropy ratio of 0,66. Sand itself is relatively isotropic, but since
loam and clay is present in the sand of the research cases, the value of 0,66 will be used.
Specific yield
In steady-state simulations the groundwater flow is only determined by the hydraulic
conductivity. When transient conditions are considered storage of the groundwater occurs. As
described in paragraph 3.1, there are two storage mechanisms: elastic and phreatic storage.
Phreatic storage occurs when the soil is not fully saturated and is caused by a rise of the
groundwater table. The phreatic storage capacity is determined by the specific yield (Sy). The
specific yield is defined as the ratio of volume of water that can be drained by gravity from a
volume of soil (Todd & Mays, 2005). In the model, values from Todd & Mays (2005) will be used
as a first estimate. These values are specified in table 5.2.
Table 5.2: Specific yield. Source: (Todd & Mays, 2005)
Material Sy (-)
Clay 0,03
Peat 0,44
Sand 0,23

5 . Model set-up
42
Specific storage
The specific storage (Ss) determines the amount of elastic storage that occurs per unit of head rise
(Todd & Mays, 2005). Often the elastic storage is considered for the entire thickness of an aquifer,
and is then called the storativity (S). The storativity is equal to the specific storage multiplied by
the thickness of the soil layer. According TAW (2004), the specific storage of sand layers in the
Netherlands varies between 10-4 and 3*10-3. The specific storage is a property mainly applicable
to aquifers; for a small-scale model as used in this thesis the influence is probably small. As initial
value 10-4 will be used for all soils.
5.2 Model grid and soil composition
For all three locations soil borings and profiles of the cross-section were available, which are
included in appendix E. Based on this information the soil composition in the cross-section was
determined, from which the model grids were constructed. Sometimes assumptions had to be
made for the soil composition because of the limited information available, and sometimes
adjustments had to be made due to the limitations of the Modflow grid. For each soil type an
estimate of the conductivity was made based on the Staring set; the motivation for the chosen
Staring soil types is included in appendix F.
Location 24
In the provided profiles of the cross-sections, the geometry below the water line is not displayed,
which means the water depth is unknown. To determine the water depth the so-called ‘legger’
from the water board of Delfland is used (Delfland, 2018). In the legger all flood defences, canals,
and other structures within the management area of the water board are included. For all these
objects the required dimensions are defined, for instance the required depth for canals. For the
canal outside the flood defence two depths are defined: a minimum depth of 1,55 m and a legger-
depth of 1,9 m. This means that once the depth has become lower than the minimum depth, the
canal is dredged out to the legger-depth. For the schematisation of the cross-section the legger-
depth is used, because this is the largest depth. This gives the largest amount of interface area
between the flood defence and the water. Based on the chosen depth the profile was extended:
the outer slope was continued under the same angle as in the cross-section, until the legger depth
is reached. From this point further outwards the canal bottom is assumed to be horizontal.
For the construction of the schematisation of the subsoil the provided soil borings are used. At
the locations of each of the monitoring wells a soil boring was carried out. Additionally, several
extra borings and cone penetration tests were provided by Delfland for two cress sections close
to the research location. For these two cross-section soil schematisations were available as well.
Based on all the information a soil schematisation could be constructed, which is displayed in
figure 5.1. In this schematisation several vertical boundaries between the soil types can be
observed. This was necessary to prevent vertical staggering of the grid, as described in chapter 3
The cunets of the road and footpath, as well as the sand fill of the former drainage have layer
boundaries that cannot be directly translated into a grid. For this reason the top layer is split in
five parts, which are modelled as a single Modflow layer with different conductivities. Three of
these parts represent the clay cover of the dike, and the other two parts represent the cunets of
the footpath and the road on the dike. In reality the edges of these cunets are angled, but
modelling this using the chosen grid type would result in vertical staggering. The less permeable
asphalt cover of the road is not explicitly modelled in the schematisation, but is taken into account
in the boundary condition.
Furthermore, there are several uncertainties in the soil schematisation. The soil borings only
provide information for the exact location of the boring; between the borings an assumption has
to be made. This has the result that the soil composition is open to different interpretations, and
it is uncertain what interpretation is closest to reality. To account for this uncertainty several soil

5.2. Model grid and soil composition
43
scenarios were constructed, which are described in appendix F. The schematisation in figure 5.1
is the base scenario.
Figure 5.1: Model grid for location 24 with assigned Staring soil types
For each soil type in the schematisation a Staring soil type was chosen to make an estimation for
the conductivity. These soil types and the corresponding conductivity for each layer are also
included in appendix F.
Location 25
The canal on the outside of location 25 is the same as for location 24, and the depth of the outside
water is the same. The profile is extended outwards in similar fashion to location 24. There are
two drainage ditches located close to each other. Since it was decided to use a constant inside
water level, only the drainage ditch closest to the flood defence is considered in the model. For
the depth of this ditch a minimum depth of 0,25 m is defined, and a legger-depth of 0,15 m. Again,
the legger-depth is used for the schematisation. The schematisation is displayed in figure 5.2.
Figure 5.2: Model grid for location 25 with assigned Staring soil types
The composition of the subsoil is based on three soil borings performed at the locations of the
monitoring wells. The composition of the deeper soil layers is based on different soil borings close
to the cross-section obtained from DINOloket (TNO Geologische Dienst Nederland, 2018). These

5 . Model set-up
44
borings are also included in appendix E . Again, several soils scenarios were constructed. To each
soil layer a Staring soil type was assigned. These soil types and the soil scenarios are described in
appendix F.
Hogedijk
The required depth of the outside water at the measurement location is not specified in the legger
of Rijnland. However, it is specified for the same canal several hundreds of meters to the north
and to the south of the location as 1 m. This depth of 1 m is also assumed for the research location.
The legger-depth of the drainage ditch inside the dike is 0,50 m. The profile of this ditch is also
included in the drawing of the cross-section of this location, and this corresponds to the legger-
depth. Therefore the profile from drawing of the cross-section is used in the model.
Several soil borings as well as a cone penetration test were available at or close to the research
location. These are included in appendix E. At each of the four monitoring wells a soil boring was
executed, and in addition two borings and a cone penetration test were performed about 50 m to
the south. Compared to the other locations, this information gives a relatively consistent picture
of the soil composition. Therefore it was not necessary to construct soil scenarios.
Another difference with the other locations is that conductivity measurements are available.
These conductivities are measured using the monitoring wells, and therefore represent the
conductivity around the filters. These are located in a single peat layer, with the exception of
monitoring well 4, for which the filter is partly in the clay layer below the peat. Since the
conductivity was measured at those four locations, the peat layer is divided into four parts with
the separations halfway between the monitoring wells. For each of these four parts the
corresponding conductivity is assigned. For the remaining soil layers no measurements are
available, the conductivity of these layers is estimated using values from the Staring set. The
motivation for these values and a summary of the conductivities are included in appendix F. The
soil schematisation converted to the model grid is displayed in figure 5.3.
Figure 5.3: Model grid for Hogedijk with assigned conductivities
5.3 Boundary conditions
To model the inflow and outflow of water into and from the model boundary conditions need to
be applied. Boundary conditions in Modflow are applied by adding packages to the model, in
which the boundary conditions and the cells they are apply to are specified. Modflow includes a
large amount of packages to model various types of boundary conditions.
5.3.1 Water levels
To model the outside and inside water level the river (RIV) package is used. The purpose of this
package is to simulate the interaction between surface features like rivers and groundwater
systems (Langevin, et al., 2017). The package allows for both flow from the river to the

5.3. Boundary conditions
45
groundwater and vice versa. As input variables, the river package requires the cell index, water
level in the river, elevation of the river bed, and the conductance of the river bottom. The cells the
river package is applied to are the cells that directly border the outside or inside water. Only the
cells for which the top is above the water level are included. Since the water levels are assumed
to be constant, the number of cells to which the river package is applied remains constant
throughout the simulation. The water level is specified separately for each cell to which the river
package is applied. For the cells bordering the outside water the outside water level is used, and
for the cells bordering the inside water the inside water level. The elevation of the river bed is
more difficult to define. The river package is mostly aimed at modelling rivers in large-scale
regional models. For these models, often the entire width of the river is located in a single cell.
The bottom of the river is then below the top of the cell and is assumed to be horizontal. However,
for the model in this thesis the outside water spans several cells, and the bottom is not horizontal.
Since the river package is only applied to cells below the water surface, in this case the river
bottom corresponds to the cell top. The river bottom elevation for each cell is therefore specified
as the cell top elevation. Finally, the river bed conductance needs to be specified. In the river
package, the water in the river is separated from the groundwater system by a layer of riverbed
material with low permeability. The conductance of the layer can be computed with:
𝐶𝑟𝑖𝑣 = 𝐾 ∗
𝐴
𝑏
(5.2)
Where Criv is the riverbed conductance, A the area of the riverbed, b the thickness of the riverbed
and K the hydraulic conductivity of the riverbed material.
As discussed, in this model the cells are completely covered by the water. This makes the
modelling of a riverbed is unnecessary, so a large conductance value is chosen to obtain a head
equal to the water level in the cells. Test runs with the model have shown that a conductance of
0,2 produces the desired result.
At location 24 no inside water is present, which means the boundary condition had to be applied
to the sand fill of the former drainage ditch. This boundary is modelled using the general head
boundary (GHB) package. This package is similar to the river package, but no bottom elevation is
specified. The sand ditch is connected to the polder water at some distance from the research
location. This means the boundary should not always correspond to the polder level: during high
precipitation rates the water has to flow through the sand towards the polder water, which will
result in a head rise in the sand, and thus a higher head at the boundary. This can be modelled by
using a lower conductance of the GHB package. This value of the conductance has to be calibrated
to obtain a correct result.
5.3.2 Pleistocene sand layer
The head in the Pleistocene sand layer is simplified as being constant, which is modelled using
the constant head boundary (CHD) package in Modflow. This is one of the simpler packages: a
head is specified for a cell, and this head does not change throughout the simulation. This package
is applied to all cells of the Pleistocene sand layer.
5.3.3 Ground surface
The surface of the flood defence forms the most complex boundary of the model; on this boundary
the recharge by precipitation and loss by evapotranspiration has to be applied. Furthermore the
seepage through this boundary has to be considered: the heads in the topmost layer cannot be
higher than the ground surface, since the water seeps out of the surface if this were to occur. Since
under normal circumstances the phreatic surface is below the ground surface, the top layers of
the model are only partially saturated, which means precipitation has to travel through the
unsaturated zone before reaching the groundwater table. There are two options for the modelling
of the surface boundary: the use of the Modflow unsaturated zone flow (UZF) package, which

5 . Model set-up
46
accounts for the behaviour of the soil in the unsaturated zone, groundwater infiltration and
evaporation, and seepage. This means extra soil parameters are required for the unsaturated
zone.
The second option is to apply precipitation, evapotranspiration and seepage as separate
boundary conditions. The advantage of this option is that due to the simplification less
parameters are required, which makes calibration of the model more straightforward. On the
other hand, recharge is directly applied to the specified cells, which means the delay of the head
rise caused by the travel time through the unsaturated zone is not modelled.
Both options were applied to the model for location 25 in order to assess the differences in the
model results. It was found that the UZF package may cause the model to be unstable. The
simulation only converged when a relatively time period was simulated. The two options to
model the surface boundary could only be compared for a small portion of the total simulation
period. In this small period the response to precipitation in the model made a slightly better
match to the measurements when the UZF package was used, but the effect of evapotranspiration
could hardly be discerned. When using the separate packages the evapotranspiration was clearly
visible which also matched with the measurements. Considering the difficulties in the simulation
using the UZF package it was decided to apply the boundary conditions of the ground surface as
separate packages, and to not use the UZF package. This means the flow in the unsaturated zone
is not modelled.
Precipitation
The precipitation is applied to the model using the recharge (RCH) package. The input to this
package is relatively simple: the cells the package is applied to and the amount of recharge. The
package is only applied to the topmost layer. If the cell the recharge is applied to is dry, the
recharge is routed downwards until an active cell is reached (Langevin, et al., 2017). The amount
of recharge is more difficult to determine; it is not realistic to directly use the amount of
precipitation, since only part of the precipitation infiltrates into the soil and reaches the
groundwater. The exact amount of recharge is dependent on many factors: the hydraulic
conductivity of the topsoil, the amount of cracks and pores in the soil, the vegetation on the
ground surface, the geometry of the dike, etc. The recharge also varies along the cross-section: on
the slope water cannot collect in puddles, which leads to a smaller infiltration rate than near the
toe, where puddles can form. Al these unknown variables make an exact quantification of the
recharge impossible. For this reason a simplified method is used to estimate the recharge.
To include the variance of the recharge over the cross-section, the dike profile was split into four
sections: the outer slope, crest, inner slope and toe. This division applied to a generic dike profile
is displayed in figure 5.4. For each section a different recharge rate is applied.
Figure 5.4: Division of a dike profile into sections to estimate recharge
For location 24 two extra sections were added, since this cross-section has a berm. One section is
added to model the slope of the berm, and another to model the recharge in the hinterland. For
location 25 the hinterland was not considered, since the inner boundary condition had a fixed

47
water level as boundary condition. For location 24 the inner boundary condition is dependent on
precipitation, and therefore the recharge is also applied to the hinterland. The berm slope
(section 5) is treated the same as section 3, and the hinterland (section 6) the same as section 2.
The recharge capacity for a section is calculated based on a recharge threshold and a recharge
capacity. When the precipitation is below the threshold, no recharge is applied. This threshold
represents the absorption of small amounts of precipitation by the grass cover. The recharge
capacity poses an upper limit to the recharge: if the precipitation rate is higher than the recharge
capacity, this capacity is applied as the recharge. The remaining precipitation is assumed to run
off. To model the differences between the dike sections, the recharge capacity and the applied
precipitation are multiplied by a section-specific multiplier. The recharge threshold is not
multiplied by this multiplier so that the minimum required precipitation is the same for all
sections. Finally, the recharge for each section is multiplied by a general multiplier for calibration
purposes. The recharge is thus calculated as follows:
𝑅𝑠 = 0,024 ∗ 𝑚𝑡𝑜𝑡 {
0, 𝑝𝑠 < 𝑅𝑚𝑖𝑛
𝑚𝑠 ∗ 𝑝𝑠, 𝑅𝑚𝑖𝑛 ≤ 𝑝𝑠 < 𝑚𝑠 ∗ 𝑅𝑐𝑎𝑝
𝑚𝑠 ∗ 𝑅𝑐𝑎𝑝, 𝑝𝑠 ≥ 𝑚𝑠 ∗ 𝑅𝑐𝑎𝑝
(5.3)
Where:
Rs = recharge rate for section s (m/day)
Rcap = recharge capacity of the soil (mm/hour)
Rmin = recharge threshold (mm/hour)
ps = precipitation rate for section s (mm/hour)
ms = recharge multiplier for section s (-)
mtot = recharge multiplier for entire model (-)
The recharge is multiplied by a factor of 0,024 to convert the values from mm/hour to m/day.
This was done because the values are supplied in mm for each hour, whereas the model uses units
of days and meters.
For most sections the precipitation data is directly used as the precipitation rate ps. However, for
location 24 and the Hogedijk, the presence of the road on the berm and the footpath on the crest
must be taken into account. These structures have a low infiltration capacity. The water flows
over the structures towards the edges, where it infiltrates or runs off. The infiltration rate on the
surface is therefore nearly zero at the pavement of the road, and relatively high near the edges.
This infiltration behaviour is modelled by changing the precipitation rate for the sections
containing a road. The precipitation rate is set to zero for the largest part of the section, only on
the cells at the edges of the section precipitation is applied. The precipitation rate for these cells
is calculated by multiplying the input precipitation by the width of the road, dividing this by two
(since the precipitation flows towards both sides of the road) and finally dividing this by the width
of the cell. The width of the cell is dependent on the chosen grid resolution. This can be formulated
as follows:
𝑝𝑠,𝑟 =
𝑝 ∗ 𝑤
2 ∗ 𝑑𝑟𝑜𝑤
(5.4)

5 . Model set-up
48
Where:
ps,r = precipitation rate for section containing a road (mm/hour)
ps = input precipitation rate (mm/hour)
w = width of the section considered (m)
drow = width of the cell (dependent on grid resolution) (m)
This calculated precipitation rate is much higher than the input precipitation rate. For many of
the precipitation events the value will be higher than the recharge capacity. However, since the
substructure of the road consist of sand and/or rubble, the infiltration capacity is larger than for
the other sections. To model this, a large value is chosen for the multiplier mp,
As initial estimates a recharge capacity of 5 mm/hour and a recharge threshold of 0,2 mm/hour
are assumed. The total multiplier is set to 1, and the section multipliers are set to 0,5 for section
1 and 3 (the slopes), to 0,7 for section 2 (the crest) and to 1 for section 4 (the berm). For the
sections containing a road the multiplier is set at a value of 2, due to the mentioned larger
infiltration capacity.
For the crest and toe a larger multiplier is used, since these surfaces are nearly horizontal. If the
amount of precipitation is larger than the infiltration capacity, the excess water can store in
puddles, from which the infiltration can continue if the precipitation rate decreases. Because the
crest is less wide than the toe area, it is assumed that the puddles there are less developed than
near the toe. Therefore the multiplier for the crest is taken smaller than for the toe. The slope
infiltration also has to be corrected for the angle: assuming the precipitation is applied vertically,
the amount is dependent on the horizontal length of the slope. This precipitation is spread out
over the total length of the slope, meaning the precipitation per meter of slope is smaller than the
precipitation per meter on a horizontal surface. This correction was made by multiplying the
precipitation with the cosine of the slope angle.
The recharge is calculated for every hour; the data is only available in hourly intervals and for
simplicity it is assumed that the precipitation cannot be stored in puddles for longer than an hour.
For the inner slope (section 3) the amount of rejected precipitation is calculated and added to the
precipitation for the toe section (section 4). This intends to simulate the collection of slope run-
off water at the toe of the dike. The distribution of the precipitation over the dike is displayed in
figure 5.5.
Figure 5.5: Distribution of total precipitation volume over the cross-section

49
The blue arrows represent the total amount of precipitation, directly taken from the input data.
The green arrows represent the infiltration, and this amount is added as recharge rate for the
boundary condition. The red arrows represent the rejected precipitation, the runoff. This amount
is removed from the model. These calculated recharge rates are added to the model as a time
series. For this time series a stepwise interpolation mode is specified, meaning that between one
value and the next the value is kept constant. This ensures that the total amount of recharge over
the simulation period is correct, which is not the case if linear extrapolation would be used.
Evapotranspiration
For the modelling of water loss by evapotranspiration, Modflow includes the evapotranspiration
(EVT) package. This package is only used to model evapotranspiration from the saturated zone,
but since the unsaturated zone is not modelled this is no problem. The EVT package uses several
assumptions to calculate the evapotranspiration rate (Langevin, et al., 2017). Firstly, it is assumed
that when the water table is above a certain elevation, the evapotranspiration rate is equal to the
user specified rate. This elevation is called the ET surface. Secondly, when the water table is below
another certain elevation, the extinction depth, the evapotranspiration is zero. Between the
extinction depth and the ET surface the evapotranspiration rate is a fraction of the user specified
rate, dependent on the water level. The relation between the water level and the
evapotranspiration rate in this region can be specified using a curve consisting of several linear
segments. If the extinction depth is lower than the cell bottom, the evapotranspiration is extended
to the cell below. Therefore the package only has to be applied to the topmost layer.
Because these input parameters are a schematisation of the process for which no parameters are
known, assumptions have to be made. It is assumed that the evapotranspiration rate is equal to
the potential evapotranspiration rate if the water table is at the ground surface, and that it
decreases immediately when the water table becomes lower than the ground surface. This is
modelled by placing the ET surface at ground surface level. For the extinction depth a assumption
of 2 m is used as initial estimate. The interpolation between the extinction depth and the ET
surface is simply assumed to be linear. For the potential evapotranspiration input the daily values
from Meteobase are used.
Seepage
Modflow has no dedicated package to simulate seepage. To simulate seepage often the drain
(DRN) package is used which is used for modelling drainage pipes, but its functionality can also
be applied to seepage through the ground surface. For each cell the package is applied to, two
values need to be specified: the elevation of the drain and the drain conductance. If the water
table is above the drain elevation, water is discharged from the cell. The magnitude of the
discharge is proportional to the difference between the water table and the drain elevation, and
the constant of proportionality is defined be the drain conductance (Langevin, et al., 2017). This
conductance is similar to the conductance for the river package. To simulate seepage, the drain
elevation is simply defined as the surface elevation. The drain conductance is more difficult to
define. If the drain conductance is taken too low this might lead to a calculated water table above
the ground surface. The value should not be set too high either, since there is some resistance to
seepage caused by the vegetation on the surface. A value of 1 m2/day is used as an initial estimate.
5.3.4 Model edges
At the left and right edges of the model no flow should occur. Modflow automatically models the
edges of the model as no-flow boundaries, so no boundary conditions need to be applied.
5.3.5 Application to the model
With the exception of the boundary for the Pleistocene sand layer, all boundary conditions are
applied to the topmost active cells in the model. Since not all layers span the entire width of the
model, this means some boundary conditions are applied to multiple layers, albeit not in the same
rows. In figure 5.6 it can be seen which boundary conditions are applied to which cell.

5 . Model set-up
50
5.3.6 Processing of the output
The output of a Modflow model is written to a binary file, containing the head for each model cell
for each time step. When the simulation has finished, this file can be read using FloPy to access
the information. It is possible to extract more information from the model, for example flow
velocities, but since this research is concerned with the phreatic surface the heads are sufficient.
To interpret the output of the model, the data has to be visualised. Due to the large amount of data
choices have to be made: to show the variation of the head over the width of the flood defence for
a certain time step, or to show the variation of the head for a single point in the cross-section over
the duration of the simulation. Furthermore, there is variation over the depth in the cross-section.
The variation of the heads along the width of the model is different for each soil layer.
To assess the fit of the model to the measurements, a simple plot is used showing the head
fluctuations over time for the points in the cross-section corresponding to the monitoring wells.
The measurements are plotted in the same figure, to compare the results to the measurements.
When the heads in the cross-section have to be visualised, a plot can only be made for a single
time step simultaneously. Only by making an animation the heads in the cross-section varying
over time can be visualised. This was done to analyse the fluctuations, but these animations
cannot be included in this thesis report.
5.3.7 Tests
Before and during the calibration some tests were executed to assess the sensitivity of some of
the variables in the model. The following observations were made:
RIV
CHD
DRN, RCH, EVT
DRN, RCH, EVT, GHB
Figure 5.6: Applied boundary conditions to location 24 (top left), location 25 (top right) and the Hogedijk
(bottom). RIV = river package, used to model the in- and outside water, CHD = constant head boundary to
model the head in the Pleistocene sand layer, DRN = drain package, used to model seepage, RCH = recharge
package to model infiltration of precipitation, EVT = evapotranspiration package, GHB = general head
boundary package, used to model the inner boundary of location 24.

5.4. Calibration
51
• For time steps smaller than 24 hours, the time step has small influence on the shape and
magnitude of the precipitation peaks. Smaller time steps provide more detail in the peaks,
for instance smaller sub-peaks. For time steps larger than 24 hours errors can occur
sometimes, for instance the head may not return to base level after precipitation.
• Within a certain range, the grid resolution also has small influence. A finer resolution
provides a smoother, more detailed phreatic surface. However, for a column width
smaller than 10 cm the running times of the model increase drastically, errors occur and
in some cases the model becomes unstable. The initial column width of 0,25 m gives a
good balance between detail and stability, and is therefore maintained.
• After the start of the transient part of the simulation, the model needs less than two
simulated weeks to adjust to the precipitation. In these two weeks, the model might give
slightly lower or higher heads, dependent on how close the result of the steady-state is to
the phreatic surface at the start of the model. The steady-state simulation provides an
average level of the phreatic surface, so if the transient simulation starts shortly after a
dry or wet period the model needs to adjust.
• The influence of the specific storage is negligible. Values ranging between 10-2 and 10-6
were used, but no discernible difference could be observed in the resulting heads. The
initially assumed value of 10-4 is therefore used for all soil types. Most likely the specific
storage is more important for large models with thick aquifers.
• Another parameter that influences the results of the transient simulation is the specific
yield. The specific yield influences the phreatic storage and therefore only has an effect
on not fully saturated layers. A lower specific yield results in a larger response to
precipitation, and thus larger fluctuations of the heads. This can be explained by the
influence of the specific yield on the phreatic storage: a lower specific yield results in a
smaller phreatic storage capacity, which means that the same volume of recharge results
in a greater head rise.
• Changing the recharge parameters can lead to unexpected results. Increasing the recharge
capacity generally leads to larger peaks, but individual peaks sometimes decrease, and
increase again when the recharge capacity is increased further. Above about 15 to 20 mm
the influence of the parameter diminishes. The reason for this is that an hourly
precipitation volume of this magnitude rarely occurs, meaning the full recharge volume
is applied to the model for nearly every hour. The recharge threshold behaves similarly:
increasing the value leads to smaller peaks and less detail in the peaks, but individual
peaks may increase. The section multipliers only have a very small influence on the model.
The recharge is probably quickly redistributed in the cross-section, resulting in a small
influence of the initial distribution over the cross-section. The overall multiplier behaves
as expected: decreasing the value decreases the magnitude of all recharge peaks.
5.4 Calibration
For none of the three models the initially assumed parameters directly resulted in a well-fitting
model. Calibration of the models is therefore necessary . To adjust the model in a meaningful way,
an assessment was made of the variables that can be adjusted. Some of the variables have little
effect on the outcome, and can be neglected.
The adjustable variables can be divided in two groups: variables that can be adjusted for the
steady state simulation, and variables that can only be adjusted in the transient simulation. The
former group is easier to adjust, since a steady state simulation only takes several seconds to run.
In addition to that the result can directly be observed, since they are not variable in time. For
these reasons the choice is made to calibrate the variables for which it is possible under steady
state conditions, and to calibrate the other parameters subsequently in a transient simulation. In
the steady-state simulation a constant recharge rate is applied to the model, to represent the long-
term influence of precipitation. The rate of this recharge is set to 525 mm per year, which is
approximately a yearly average precipitation. The calibration is based on comparing the model

5 . Model set-up
52
to the average of the measurements. The measurement period of approximately 4 years is
considered to be long enough for the average to represent steady-state conditions.
Steady state
The variables that can be calibrated for steady state conditions are the following:
• Soil composition;
• Hydraulic conductivity;
• Conductance of the boundary conditions;
• Steady state recharge rate.
The conductance of the boundary conditions is for most situations set to a large value, since no
resistance is present in reality. This is with the exception of location 24, for which is the only
boundary condition that has to be calibrated.
Transient
Once the steady-state simulations match the measurements, transient conditions can be
considered. The steady-state parameters mainly influence the average height of the phreatic
surface, the parameters variated for the transient simulation influence the magnitude of the
fluctuations of the phreatic surface over time. Therefore the simulation results and the
measurements have to be compared for a time interval, preferably the entire measurement
period.
The variables that can be adjusted for transient conditions are:
• Hydraulic conductivity;
• Specific yield;
• Specific storage;
• Time period that has to be simulated before the start of the measurements;
• Infiltration parameters
It was already determined that the time period required before the start of the measurements is
about two weeks, and that the influence of the specific storage is negligible. These variables are
therefore not used in the calibration. The specific yield only has to be adjusted for the upper
layers, since the parameter has no influence on the storage in fully submerged cells.
The calibration of the transient part of the simulation is more complicated than the calibration
for the steady-state part for two reasons. Firstly, when the full measurement period is simulated
using a time step of one hour the total runtime of the simulation is about 5 minutes. This means
that changing a variable and assessing the influence is a lengthy process. Secondly, no clear
measure can be used to quantify how well the model results fit the measurements. Since the
simulation period spans multiple years the model may fit well for some parts of this period while
it does not for other parts.
There are two possible solutions to speed up the calibration process: simulate only a part of the
total period, or use a larger time step or grid resolution. Comparison between simulations using
a time step of 1 hour and of 12 hours shows that a time step of 12 hours is sufficient when the
total measurement period is considered. The use of this larger time step results in less detail, but
does not lead to large differences in the results. Therefore the choice was made to use a time step
of 12 hours to calibrate the model, and perform a simulation using the calibrated values
afterwards for which a time step of 1 hour is used. The difference between model and
measurements is assessed by plotting the measurements and the model results in a single plot.
The fit of the model can be determined by comparing the two graphs.
5.4.1 Location 25
The first research location that was modelled is Delfland location 25. The choice was made to
start with this location because the soil composition is simpler than for the other locations, which

5.4. Calibration
53
makes it easier to set up this model. In this paragraph the calibration process is summarised; a
more elaborate description and the resulting parameters are found in appendix F.
During the steady-state calibration some difficulties were encountered. A well-fitting model could
be obtained, but the resulting calibrated conductivities were not realistic. The values were within
the range of what is possible for the respective soil types, but relative to each other the values
were unrealistic. The intermediate sand layer in the cross-section was assigned a lower
conductivity than an adjacent peat layer. Since the conductivity is the only defining characteristic
of a soil type in this model, this means that in reality the sand layer is modelled as peat and vice
versa.
Further tests confirmed that the only soil composition resulting in a well-fitting model and
realistic parameters was a schematisation where the intermediate sand layer starts below the
slope of the dike, and extends inwards to the polder. The problem with this schematisation is that
it is in contradiction to the soil borings performed at the locations of the monitoring wells. Other
soil borings along the same flood defence were available, some of which contradict the other soil
borings. The borings show that the position of the sand layer varies along the length of the flood
defence. Two possible causes were identified to explain the contradiction between the model
calibration and the soil borings:
• Information uncertainty regarding the soil composition: available soil borings are in
contradiction to each other, and provide no information for locations between the
borings.
• Flow in the longitudinal direction occurs in the sand layer, which cannot be modelled
using the two-dimensional model.
Eventually the choice was made to use a model with the intermediate sand layer below the toe.
This was the only soil composition for which the measurements could be matched, and for which
the conductivities had realistic values. This position of the sand layer can be seen as a
simplification of the variation in longitudinal direction, which is not modelled.
This schematisation, along with the results of the calibrated steady-state simulation are displayed
in figure 5.7. The model calculates the head for each cell. These heads are visualised as a line
plotted for each model layer. To avoid clutter, only the heads of the topmost seven layers are
plotted. The monitoring wells are displayed as well, with the filter represented by a lighter colour.
The average head of the measurements for each monitoring well is indicated by a white bar.
Figure 5.7: Delfland location 25, results calibrated steady state simulation using the adjusted soil
schematisation.

5 . Model set-up
54
Using this updated schematisation the model was calibrated further in the transient simulation.
Regarding soil parameters, this mainly involved the two topmost layers. The sand layer was given
a larger conductivity and a smaller specific yield to increase the magnitude of the precipitation
peaks. The clay core was given a larger anisotropy ratio for the same reason. This ratio was set to
a value larger than 1, meaning the vertical conductivity is larger than the horizontal conductivity.
This is unusual, since in most soils the opposite is the case. The explanation for this is that the
cracks and pores in the clay mainly enlarge the vertical conductivity. De Loor (2018) also uses a
larger vertical than horizontal conductivity for the top part of clay layers in his research.
Additionally, some adjustments were made to the recharge parameters. These changes, the
calibrated soil parameters, and a more elaborate description of the calibration process can all be
found in appendix F.
The evapotranspiration parameters were left unchanged; changing these did not result in a better
fit. However, by varying the parameter it did become clear that evapotranspiration was a
necessary process to include for this model. When the evapotranspiration was set to zero, the
shape and magnitude of the dips in the head were not matched correctly. This means that for
location 25 evapotranspiration is a necessary boundary condition to include in the model.
5.4.2 Location 24
The next model that was calibrated was Delfland location 24. The full description of the
calibration process is included in appendix F.
Like location 25, the constructed soil scenarios were compared in a steady-state simulation to
determine the most probable of the six scenarios. Even though the results found in scenario 2
showed a slightly better fit to the measurements, scenario 1 was chosen for the soil
schematisation used for the further analyses. By changing the conductivity of the clay cover,
similar results to scenario 2 could be reached. The difference between the scenarios was
therefore too small to choose one over the other based on the model results. Scenario 1 is based
on soil borings directly at the measurement location, whereas scenario 2 is based on soil borings
further away. Scenario 1 is therefore preferable, and is used in the further calibration.
The steady-state calibration process was started by matching the measurements at the
monitoring well near the sand-filled drainage ditch. Although this monitoring well does not
provide information about the phreatic surface in the actual cross-section, it could be used to
calibrate the groundwater table inside of the dike. This was mainly done by varying the
conductance of the general head boundary package. Furthermore the conductivity of the deepest
clay layers had to be adjusted: the head in the Pleistocene resulted in too high heads near the toe.
The heads of the other two monitoring wells could easily be calibrated by changing the
conductivity of the rubble core of the dike and the clay cover.
The model still showed the phreatic surface exiting at the inner slope and the toe resulting in
seepage. Unfortunately no monitoring well was placed at the inner crest of the berm, so no
measurements are available to either prove or disprove whether this is correct. However, it is not
likely that seepage would continuously occur. With some further calibration a model could be
obtained with no seepage, and which still matched the measurements. The heads resulting from
this calibration are displayed in figure 5.8.
The transient calibration of the model was similar to location 25. The anisotropy ratio of the clay
top layer was increased to a value of 2, and the specific yields of the topmost layers was decreased
to increases the precipitation peak heights. The reaction of the recharge parameters was
different: the section multipliers had some influence, and this was used to increase the recharge
peaks near the toe.
Conversely to what was observed for location 25, the evapotranspiration for location 24 had a
negative effect on the fit of the model. The multiplier was reduced to 0,5 and the extinction depth

5.4. Calibration
55
from 2 m to 1 m, to reduce the dips in the head. Apparently evapotranspiration has a smaller
influence on this flood defence than on location 25.
Figure 5.8: Delfland location 24, results steady state simulation using calibrated values
5.4.3 Hogedijk
The calibration process for the Hogedijk was performed using a different method than the two
other research cases. Calibrating the model in a steady-state simulation is not meaningful in this
case, since only two months of measurements are available. This measurement period was
preceded by the dry summer of 2018, and the average of the measurements can therefore not be
said to represent the average position of the phreatic surface. For this reason the model was
calibrated directly in a transient simulation.
Running the model using the initially assumed parameters did not result in a good fit. For
monitoring wells 1, 2, and 3 the model result was lower than the measurements, while for
monitoring well 4 the simulated head was too high. For this monitoring well the head is almost
continuously lower than the polder water level, except for one peak caused by a precipitation
event. The monitoring well is placed in the slope 9 m removed from the drainage ditch, so a
measured head lower than the polder water level is unexpected. According to the available
information the polder water level is correct. Since there is no explanation why the measured
head is so low, the model is calibrated using the other three monitoring wells.
The modelled head at monitoring well 4 was slightly lowered by reducing the conductivity of the
deepest layers covering the Pleistocene sand layer. Due to the low elevation of the polder the
Pleistocene sand layer is relatively close to the surface, resulting in a large influence of its head.
To fit the model to the measurements, some changes were made to the schematisation:
• Below the crest, an extra section was created in the peat layer to obtain a correct head in
the monitoring well at the inner crest. This section was assigned a higher conductivity,
which can be explained by the sand and rubble of the road cunet.
• The transitions between the different sections of the peat layer were too sudden. At a
transition between two monitoring wells the phreatic surface was too close to the surface.
To prevent this, a linear gradient was assumed between the measured conductivities. This
is more in accordance to reality as well: the conductivity does not change from one value
to another at a vertical separation.
After these modifications the general height of the phreatic surface was in accordance to the
measurements, but the shape and magnitude of the precipitation peaks were not. One of the

5 . Model set-up
56
parameters that was of influence for this was the conductivity of layer 2, the loam top layer.
Assigning this layer a lower conductivity resulted in higher peaks near the crest. This is contrary
to the observations made in the other two models: a larger (vertical) conductivity of the top layer
resulted in higher peaks. The explanation for this is seepage. During precipitation events seepage
occurs near the toe through the loam layer, so a low conductivity of this layer provides more
resistance to seepage. Since the water cannot flow away as easily, the head upstream in the cross-
section will rise more. Since the loam layer does not extend fully towards the crest, the lower
conductivity has no influence on the resistance to recharge in the crest.
A strange phenomenon that could not be modelled properly was the difference in reaction
between monitoring wells 2 and 3. In the measurements, monitoring well 2 shows a damped
response to precipitation, whereas monitoring well 3 shows a much more peaked response. This
is strange, since these wells are located close to each other, and both are placed in the slope of the
dike. In the model this different response could not be reached. It was possible to approximately
match the damped response or the peaked response for both points simultaneously, but not for
each point individually. Changing recharge multipliers slightly increased the difference between
the two points, but not enough to match the measurements.
Eventually the model was calibrated by changing the specific yields such that both monitoring
wells 2 and 3 are matched approximately. At neither location the peaks could be matched exactly.
The fast, almost direct response of monitoring well 3 to a large precipitation event in early
September could not be modelled. The model responds more slowly, and reaches the peak after
a few days. The height of the peak could be matched, but if this was done the phreatic surface
remained too high for weeks after the precipitation. The choice was made to calibrate so that the
model result is close to the measurements most of the time, even though the peak height is not
matched.
In figure 5.9 the heads calculated in a steady-state simulation using the calibrated parameters are
displayed. The model was not calibrated using the steady-state simulation, the figure is only
intended to display the general position of the phreatic surface in the cross-section. Notable is
that for the steady-state to reach equilibrium, 100 time steps were required instead of the 20 that
were used in the other models.
Figure 5.9: Steady-state simulated heads in the Hogedijk

6.1. Main simulation
57
6 Results
In this chapter the results of the simulations are presented. The simulated heads from the model
are compared to the measurements to assess the accuracy of the model. To check the fit of the
model under extreme circumstances, and in order to compare the phreatic surface during these
circumstances to the schematisation, the highest and lowest simulated phreatic surfaces were
identified from the results and analysed. To further analyse extreme precipitation events,
precipitation with different combinations of duration and intensity were applied to the calibrated
models. An extra analysis was performed using the calibrated model from Delfland location 25.
In this analysis meteorological data from a longer period of 31 years was applied to the model to
analyse the long term fluctuations of the phreatic surface. Finally, some stability calculations were
carried out to assess the influence of variations of the phreatic surface on the macro-stability of
the flood defence.
In most of the analyses the model results are compared to a schematisation of the phreatic
surface, in order to assess whether the schematisation is a good approximation of the phreatic
surface under design conditions. For the two cases in Delfland, the schematisation from the water
board is used, which was described in paragraph 2.1.2. For the Hogedijk the schematisation
constructed by Iv-Infra was used (Iv-Infra, 2018). This schematisation was based on the
guidelines from the water board of Rijnland, which are nearly identical to those of Delfland.
6.1 Main simulation
The main simulation for this research is the simulation of the measurement period of the
monitoring wells. In chapter 5 the models were calibrated as good as possible for this period. To
analyse the fit of the model results, the measurements were plotted along with the head
fluctuations in the model cell closest to the corresponding monitoring well.
General
In all three models, it could be observed that the heads were different for each soil layer. When
looking at multiple soil layers, this means that the heads in the cross-section are non-hydrostatic.
This non-hydrostatic gradient of the pore pressures over the depth was also observed by Ten
Bokkel Huinink (2016) and De Loor (2018). For the models in this thesis, this gradient is related
to flow in vertical direction. Vertical flow occurs during precipitation events, but also in dry
conditions it is present due to the head in the Pleistocene sand layer. If this head is higher than
the phreatic surface, the vertical flow is upwards and the head increases with depth. When the
head in the Pleistocene layer is lower the opposite happens. Both situations can simultaneously
occur in the same flood defence, when the head in the Pleistocene layer is somewhere between
the inside and the outside water level.
The gradient of the of the pore pressures over depth is dependent on the relative conductivity of
the soil layers. In a multi-layered system, the head gradient over the less conductive layers is
larger than over the more conductive layers. In the models, the height of the phreatic surface
could sometimes be manipulated by changing the conductivity of the soil layers relative to each
other. This indicates that the conductivity of deeper soil layers, in conjunction with the head in
the Pleistocene sand layer, influences the height of the phreatic surface.
The response of the pore pressures is also variable over depth. The topmost (partially) saturated
layer shows the largest response, while deeper layers exhibit smaller and slower head
fluctuations.

6 . Results
58
The topmost layer in the models sometimes responded in an unexpected and unrealistic way.
During a precipitation event the layer was often filled up to the ground surface, while the layer
below still had a much lower head. During periods with a large evapotranspiration flux, the layer
was completely dry. In that case Modflow modelled the head of this layer as being on the level of
the extinction depth of the evapotranspiration package. This had the result that the head of this
layer in the model was often below the heads of the deeper layers. The cause of this is the way in
which the recharge and evapotranspiration are modelled. The choice was made to not take the
effect of the unsaturated zone of the model into account, which means said effects are modelled
in a simplified way. The top layer is normally unsaturated, and since unsaturated effects are not
modelled the heads in this layer are not accurate. This is not a problem, since the phreatic surface
is by definition the point where the saturated zone starts. However, it has the consequence that
the heads in this layer should not be used to determine the phreatic surface in the model as long
as the layer below it is not fully saturated.
6.1.1 Delfland 25
The model results and the measured heads for Delfland location 25 are displayed in figure 6.1.
The plot consists of four parts: the model results and measurements for each of the three
monitoring wells, and the daily precipitation and evapotranspiration volumes as bar plots in a
single graph.
Figure 6.1: Model results Delfland location 25
Differences can be observed in the fit of the model for the different locations in the cross-section:
in the crest the model fits better than for the other two locations. For a single monitoring well
differences can be observed between the peaks, some are modelled better than others.
In the crest, the fluctuations of the heads in the model are larger than what is observed in the
measurements. A possible explanation for this could be that the local conductivity is slightly
different than in the rest of the flood defence. In the model the dike core is schematised as one
homogeneous layer, while in reality the conductivity is probably more variable.

59
In the measurements long-term variations can be observed that are not present in the model. This
variation does not correspond to the seasonal variation caused by evapotranspiration, which can
be observed for the slope and the toe. A possible explanation could be variations of the outside
water level. From the water board of Delfland has water level measurements for the outside water
are available, but the overlap of these measurements with the measurements of the phreatic
surface only spans several months. This is not enough to determine whether water level
variations could be the origin of this long-term variation.
For the monitoring well in the slope the best fit between the model and the measurements is
observed. Most precipitation peaks reach the same height as in the model, but some peaks are
modelled too low. Comparing these peaks to the precipitation data, this mostly occurs for
precipitation events with a longer duration and lower intensity. This points to the model being
more suited to model high intensity precipitation than low intensity precipitation. Several dips in
the head caused by evapotranspiration can be observed that are not present in the
measurements. On the other hand, some of the dips in the measurements are not seen in the
model results.
For the toe some sections can be observed where the modelled head is lower or higher than the
measurements. This is mostly caused by the jumps in the measurements discussed in chapter 4 .
These jumps are probably errors in the measurements, which would explain the difference. When
the general height of the heads is disregarded and only the peaks are observed, the peaks match
the measurements quite well in shape, but are slightly smaller in magnitude.
To compare the frequency of occurrence of a certain head in the model and in the measurements,
histograms are plotted of the measurements and the model results. These are displayed in figure
6.2. On the horizontal axis the head elevation is displayed, and the vertical axis provides a
measure of the frequency of occurrence of a head elevation. Because the number of measurement
points is smaller than the number of time steps (due to gaps in the measurements), the
histograms are normalised to make comparison easier. Some of the histograms have a very
narrow tail which makes it unclear what the extreme values in the data are. For this reason the
extremes are indicated with a triangle. Furthermore, the height of the schematisation at the
locations of the monitoring wells is displayed in each of the plots.
Figure 6.2: Histograms of the measurements and model results of Delfland location 25
The histograms confirm the observation that the model is fitted best to the measurements in the
slope. The height of the schematisation in the slope is removed some distance from the highest
head in both model and measurements, indicating that the schematisation is not exceeded at this

6 . Results
60
point in the cross-section. For the head in the crest the histogram of the model is somewhat wider
on the right-hand side than it is for the measurements. This means relatively high heads occur
more often in the model than in the measurements. The heads are also closer to the
schematisation. In the model the schematisation height is exceeded for 10 consecutive hours on
13-10-2013, but in the measurements this is not the case. At the toe, the histogram for the model
is taller than for the measurements. This means the variation range of the modelled heads is
smaller. As discussed earlier, this can in part be explained by the shifted parts in the
measurements. This would also explain the second peak that can be observed in the histogram of
the measurements, which would be the mean of the shifted measurements in that case. In the
measurements the schematised phreatic surface is regularly exceeded, but in the model this does
not occur.
As a last assessment of the fit of the model, the difference between the measured head and the
modelled head was calculated for each time step, with the exclusion of time steps for which no
corresponding measurement existed. From these values the mean and standard deviations were
calculated.
Calculating the mean error is not necessarily a good indicator for the fit of the model; a mean
error close to zero only means that the model results are approximately equally often lower as
they are higher than the measurements. The mean only shows if the model consistently over- or
underestimates the heads. To provide another indication of the model fit, the Nash-Sutcliffe
model efficiency coefficient is calculated. This coefficient is used to determine the predictive
power of hydrological models, but can also be used for other types of models. The coefficient can
be calculated using (Nash & Sutcliffe, 1970):
𝑁𝑆𝐸 = 1 −
∑ (ℎ𝑚
𝑡
− ℎ𝑜
𝑡
)2
𝑇
𝑡=1
∑ (ℎ𝑜
𝑡
− ℎ𝑜
̅̅̅)2
𝑇
𝑡=1
(6.1)
Where:
NSE = Nash-Sutcliffe model efficiency coefficient (-)
T = number of timesteps (-)
ht
m = modelled head for timestep t (m NAP)
ht
o = observed (measured) head for timestep t (m NAP)
ho
̅̅̅ = mean of observed heads (m NAP)
A value of NSE smaller than 0 means the mean of the measurements is a better predictor of the
head than the model results. A value of 1 means the model results are identical to the
measurements.
Table 6.1: Errors between the model and the measurements per time step
Error Crest Slope Toe
Mean (m) 0,06 -0,04 0,03
Standard deviation (m) 0,12 0,13 0,1
Maximum error (m) 0,25 0,31 0,50
Minimum error (m) -0,45 -0,84 -0,27
Nash-Sutcliffe (-) -4,35 0,25 0,18
The mean error is relatively low for all three monitoring wells. The minima and maxima show
that large errors are present for some time steps. These are mostly caused by the dips and peaks
that are modelled too high or too low. The slope, which showed the best fit, remarkably has the
largest standard deviation for the error per time step. It also has the largest minimum error. The

61
cause of this is that for most time steps the model fits very well, but some of the largest errors
also occur at this location. The errors are mainly overestimations, underestimations are much
rarer and smaller. The overestimations are mainly caused by periods with large dips in the
measurements, which were not properly modelled.
The Nash-Sutcliffe model efficiency coefficients are above 0 for the slope and the toe, but for the
crest the value is below zero. This means that the fit of the model is less good in the crest, as was
observed earlier. The long-term variations in the measurement not being present in the model
has the result that the modelled head is almost always slightly higher or lower. This results in a
low model efficiency coefficient. On the other hand, many of the fluctuation patterns in the
measurements in the measurements can also be observed in the model, but at a slightly different
height. This shows that using a single indicator only shows limited information on the fit of the
model.
6.1.2 Delfland 24
For Delfland location 24, the model results are displayed in figure 6.3. The data for the monitoring
well in the toe is displayed as well, although it has no meaning for the phreatic surface in the
cross-section. As discussed earlier, this monitoring well is placed on the polder side of the sand
fill in the former drainage ditch, and the boundary condition is applied to this sand fill. The
measurements were only used to calibrate the boundary condition such that the inside
groundwater table was matched approximately.
Figure 6.3: Model results Delfland location 24
On first sight, the fit to the measurements is less good than for location 25. When taking a closer
look, it is mainly the dips in the model results that show a difference to the measurements. During
precipitation peaks the model fits quite well, but when the precipitation stops the modelled heads
decrease, whereas the measurements remain more stable.

6 . Results
62
This is illustrated in figure 6.4, which
shows one of these dips in more
detail. Up until the dry period of
several weeks, the model fits well, but
then the heads decrease while the
measured heads remain constant.
The measurements even show a head
rise in the middle of the dry period,
which does not correspond to any
precipitation event. This is probably
caused by fluctuations in the outside
water level. During dry periods water
is let into the boezem to maintain the
water level. This could be the
explanation for this head rise.
However, fluctuations do not fully
explain this difference between the
model and the measurements. The
outside water level is kept constant in the model, so if the outside water level slowly decreases
during a dry period, the measured heads would decrease whereas the model results would not.
The soil parameters could not be calibrated such that both the precipitation peaks and these dry
periods are modelled correctly. The explanation is probably found in the soil schematisation. The
rubble core is modelled as a single, homogeneous layer with a clear boundary, but in reality the
transition to the clay cover is probably more gradual.
This difference between the model and the measurements is reminiscent of the monitoring well
in the crest of location 25, which heads could also not be fully modelled. For location 24, the
monitoring wells are both in the crest, because of the permeable rubble core the heads of the two
locations are very close to each other. Both wells are therefore affected by the outside water level,
like the well in the crest of location 25. Neglecting the variation of the outside water level might
thus be part of the reason why the heads in the crest are modelled less accurately than in other
parts of the cross-section.
Again, histograms were plotted to compare the model results to the measurements. These are
displayed in figure 6.5.
Figure 6.5: Histograms of the measurements and model results of Delfland location 24
Figure 6.4: Detail of model results location 24

63
Large parts are missing in the measurements, especially for the slope. Some of the differences
between the histograms may be caused by these gaps rather than actual differences between the
model and measurements. For example, the two largest precipitation events are excluded from
the measurements which might partially explain why the higher heads in the slope occur more
regularly in the model than in the measurements. It can also be observed that lower heads are
also more present in the model, which corresponds to the observation that during dry periods
the modelled heads are too low.
In the slope, the schematisation is exceeded regularly, during 294 time steps. Many of these time
steps are consecutive and should be counted as single event. When this is done the schematisation
was exceeded during 9 events. The schematisation is never exceeded in the slope. In the toe the
schematisation is exceeded by the measurements a few times, but never by the model.
Once again, the error between the simulated and measured head was calculated for each time
step. The means, standard deviations, maxima and minima of these errors are displayed in table
6.2. The Nash-Sutcliffe model efficiency coefficient is also included.
Error Crest Slope Toe
Mean 0,05 0,1 0,05
Standard deviation 0,12 0,11 0,09
Maximum error 0,44 0,37 0,56
Minimum error -0,46 -0,22 -0,15
Nash-Sutcliffe -1,09 -3,34 -0,43
The mean error is in the same order as for location 25. The standard deviations are somewhat
smaller. Based on this information it would seem that the fit of this model is better than for
location 25. This is not the case, for location 25 the largest errors are larger, but the most common
magnitudes of error are smaller for location 25 than for 24. The Nash-Sutcliffe model efficiency
coefficient is below zero for all three locations, indicating a poor fit. The earlier discussed dips are
the main cause of this, since the errors are large for these sections.
6.1.3 Hogedijk
For the Hogedijk, the model results are displayed in figure 6.4. In contradiction to the other
models, the model for the Hogedijk was calibrated using only a part of the measurement period,
since this was the only part available at the time. In january 2019 new measurements became
available. Extending the precipitation and evapotranspiration data for this extended period the
model was runned again, without performing a new calibration. This way the fit of the model can
be assessed by comparing the results to measurements outside of the calibration set.
It can be observed that with the exception of the peaks, the model fits the measurements of
monitoring wells 1,2, and 3 quite well. As described in chapter 4, monitoring well 1 exhibits
several periods with unreliable measurements. For these periods the model does therefore not
match the measurements.
For monitoring well 2 the peaks in the model are too high compared to the measurements. It was
possible to calibrate the model such that the measurements were matched, but this resulted in a
less good fit for monitoring well 3. For that well the fit is quite good, except for the peaks: the
simulated head rises much slower. The fast response as observed in the measurements could not
be reproduced. However, after a meeting with Nectaerra, the company that executes the
measurements it was determined that the large fluctuations for monitoring well 3 are most likely
caused by cracks in the dike, which allow runoff water to flow into the well. This could explain
the inability to reproduce these measurements.

6 . Results
64
Figure 6.6: Model results Hogedijk. The black line indicates the end of the original measurement series the
model was calibrated on.
In the extended measurement period the modelled heads become about 10 cm higher than the
measurements, but the shape of the peaks still matched the measurements. It can be observed
that both the model and the measurements still show a gradual increase of the heads after the dry
summer period. In the model this increase is slightly larger than in the measurements, resulting
in a small deviation. Considering that the calibrationperiod was shorter than the extended period,
and directly following the dry summer months, this deviation of 10 cm is relatively small. With a
longer calibration period better results would probably be obtained.
As discussed earlier, the measurements of monitoring well 4 are rather remarkable since the
heads are lower than the polder water level, although the well is placed in the slope of the flood
defence 9 m removed from the drainage ditch. In the extended measurement period the head
approaches the polder level of NAP -5,98 m closer, but still remains below it. The model could not
be fitted to this head. A better match was possible by locally increasing the conductivity of the
peat layer greatly, but this would result in an unrealistic conductivity that would deviate
considerably from the conductivity in the rest of the peat layer and from the measured value.
During the meeting with Nectaerra no clear cause could be determined for these low
measurements. Possibly the polder level is different in reality, since many different water levels
are present along the dike.
For the Hogedijk no histogram is presented. Due to the short measurement period an upward
trend is observed in the heads, which distorts the histograms. The error per time step was
calculated, and the characteristics of these errors are displayed in table 6.3.

6.2. Extreme simulated phreatic surfaces
65
Error (m) HGD 1-1 HGD 1-2 HGD 1-3 HGD 1-4
Mean 0,01 -0,09 -0,06 -0,91
Standard deviation 0,11 0,06 0,08 0,13
Maximum error 0,38 0,05 0,74 -0,22
Minimum error -0,18 -0,28 -0,21 -1,13
Nash-Sutcliffe -0,19 -2,44 0,50 -108,58
As could be expected, the error for monitoring well 4 are very large. For the other three
monitoring wells the mean errors are slightly smaller than those observed for the other two
research locations in Delfland. The large maximum error for HGD 1-3 was caused by the large
peak that could not be matched by the model. The Nash-Sutcliffe coefficient is only above 0 for
HGD 1-3. The errors for HGD 1-1 and 1-2 are mainly caused by the structural difference in the
uncalibrated period. It is likely that a better fit would be obtained when the model were to be
calibrated over the entire measurement period.
6.2 Extreme simulated phreatic surfaces
The fifth research question established in chapter 1 was ‘How does the phreatic surface in the
numerical model respond to an extreme event?’. To answer this question, first the extreme events
that have occurred during the measurement period are investigated.
6.2.1 Extreme meteorological events in the simulation period
To assess the model results for the extreme events during the measurement period, the most
extreme precipitation events are identified. For the locations in Delfland, the precipitation events
during the measurement period were identified in chapter 4 . For the largest of those events an
estimate was made for the return period. These return periods are based on precipitation
statistics from STOWA (2015). These statistics are obtained from historical data, which was
corrected for changes in the measurement method. This data was detrended to represent the
climate around 2014. To include regional variations, the data was corrected for four different
precipitation regimes in the Netherlands. For each of these regimes a generalised extreme value
(GEV) distribution was fitted to the data, using which the relation between duration, intensity
and return period is described.
Statistics from the report are published on the website Meteobase.nl in the form of tables, from
which the return period can be obtained for a given duration and precipitation volume. These
tables are provided for each of the four precipitation regimes. All research locations are situated
in regime H. The exact values for the duration and volume of the precipitation events are not
included in the tables, but by interpolating between the given values the return periods could be
estimated. For the locations in Delfland three events with a return period larger than 10 years
have occurred during the measurement period: these are displayed in table 6.4.
Table 6.4: Three largest precipitation events during the measurement period in Delfland
Date Duration (hours) Volume (mm) Return period (years)
12-10-2013 19:00 22 102,8 250
13-7-2011 19:00 28 73,9 20
23-8-2010 1:00 9 42,4 10
At the Hogedijk, the measurement period was much shorter, so fewer extreme events have
occurred. Two events with a total volume larger than 20 mm have occurred, but by coincidence
one event with a very large return period of about 700 years was included. However, some
remarks need to be made for the large return period found for this event. The used statistics are
valid for precipitation events with durations of more than two hours. More recently the statistics

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66
were extended for durations as short as 10 minutes, but longer durations up to 12 hours were
included as well in this newer report (STOWA, 2018). Some large differences are found for these
longer durations between the new and the older statistics in STOWA (2015). The return period
for the event according to these newer statistics is 150 years. It is not entirely clear which of the
two statistics should be used for durations between 2 and 12 hours, and therefore both return
periods are displayed in table 6.5.
Table 6.5: Precipitation events with a volume larger than 20 mm during the measurements at the Hogedijk
Date Duration (hours) Volume (mm) Return period (years)
5-9-2018 6:00 8 95,6 700/150
24-8-2018 21:00 13 32,4 1
The STOWA report also provides a detrended evapotranspiration series. However, no
distribution was fitted to this series. Furthermore the series is based on the Makkink method
whereas in the models the Penman-Monteith method was used. To be able to identify the dry
periods the precipitation deficit was calculated for each year in the measurement period in
Delfland. This is the sum of the potential evapotranspiration rate minus the sum of the
precipitation, for the months April to September. For 2011 and 2012 there was a precipitation
surplus, and for the remaining years the precipitation deficit is displayed in table 6.7.
Table 6.6: Years with a precipitation deficit for Delfland
Year Precipitation deficit (mm)
2014 110,0
2013 73,6
2010 24,9
The measurement period of the Hogedijk was less than a year, so only one dry period is partially
included in the measurements. However, 2018 was one of the driest years on record which has
probably resulted in a lower than average phreatic surface at the start of the measurements.
6.2.2 Highest and lowest phreatic surface
As a next step, the highest and lowest simulated phreatic surfaces in the simulation were
identified. For each column in the cross-section the highest head was taken, for each time step. In
these columns the top layer was excluded, because as mentioned the simulated heads in this layer
do not represent reality. The deepest layers were also excluded because these are influenced by
the head in the Pleistocene sand layer. This maximum head represents the phreatic surface for
that slice. From all slices in the cross-section the mean was calculated, to obtain the average
height of the phreatic surface for the considered time step.
By identifying the peaks of this average head over time, the highest simulated phreatic surfaces
could be obtained. Between these peaks a minimum distance of 216 hours was specified, because
a single precipitation event may lead to multiple peaks.
Similarly, the lowest dips in the average head were identified to obtain the lowest phreatic
surface. Between the dips a minimum distance of 672 hours (4 weeks) was used, since dry periods
span a longer time period than precipitation events.
6.2.3 Delfland 25
The five highest simulated phreatic surfaces for location 25 are displayed in table 6.7. For
reference, the mean of the average phreatic surface over the simulation period is NAP -1,99 m.

67
Table 6.7: Five highest phreatic surfaces location 25
Rank model Date Average phreatic surface (m +NAP)
1 13-10-2013 -1,46
2 14-7-2011 -1,52
3 10-9-2013 -1,57
4 27-8-2011 -1,60
5 4-11-2013 -1,61
The highest and second highest phreatic surfaces correspond to the two most extreme
precipitation events. For rank 1 the model fits the measurements quite well. In the crest the model
is slightly higher than the measurements, but in the measurements a dip can be observed before
the precipitation peak. This dip could be the result of pre-pumping of the boezem, which is not
taken into account in the model. For rank 2 the heads in the model are slightly higher than the
measurements of all monitoring wells. For rank 3 the model fits well for the crest and toe, but in
the slope the heads are almost 0,5 m higher than the measurements. The peak in the
measurements is preceded by a gap and an inexplicable dip, so there might be an error in the
measurements for this precipitation event. For rank 4 and 5 the model fits the measurements
well.
The highest phreatic surface of the simulation is displayed in figure 6.7. In this figure the phreatic
surface is displayed, along with the measured heads in the monitoring wells which are displayed
as red crosses. Additionally, the schematisation of the phreatic surface is displayed for reference.
The schematisation is very similar to the simulated phreatic surface for this situation. Below the
inner slope the schematisation is slightly more conservative than the model, but near the crest
and the toe the simulated heads are a few centimetres higher than the schematisation.
Figure 6.7: Highest simulated phreatic surface for Delfland location 25
The five lowest phreatic surface are displayed in table 6.8.
Table 6.8: Five lowest phreatic surfaces location 25
1 10-7-2010 -2,27
2 24-7-2013 -2,25
3 28-5-2012 -2,25
4 8-5-2011 -2,25
5 5-6-2011 -2,23
It stands out that the average height of the phreatic surface is almost the same for all five dates.
This is the lowest phreatic surface that can be reached by the model, only a large peak in the

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68
evapotranspiration rate can lead to a slightly lower phreatic surface. There is no clear
correspondence to the years with the largest precipitation deficit; in fact 2014, the year with the
largest precipitation deficit, is not present in the lowest five phreatic surfaces.
For these five lowest phreatic surfaces, the measureed heads are about 5-10 cm higher than in
the model. However, there are some dips at different points in time where the measurements are
5-10 cm lower than the lowest heads in the model. This indicates the model is less accurate for
the prediction of low extremes than it is for high extremes.
In figure 6.8 the lowest simulated phreatic surface is displayed. For this point in time no
measurement in the crest was available, but the other four lowest phreatic surfaces are very
similar, and for those the measurement corresponds well to the model.
Figure 6.8: Lowest simulated phreatic surface for Delfland location 25
In the middle of the cross-section a strange dip in the heads of soil layers 2 and 3 can be observed.
This is most likely a result of the way the intermediate sand layer was schematised. In this area
the bottom of these two layers is slightly above the phreatic surface, which means the cells in
these layers are unsaturated. When the cells are unsaturated, the head is modelled at the
extinction depth of the evapotranspiration package, resulting in this dip. The phreatic surface in
this area is represented by the layer below, layer 4.
For this situation, the schematisation is lower than the simulated phreatic surface. The
schematisation accounts for the situation where the soil below the crest is more permeable, which
results in a lower phreatic surface. Both the measurements and the model point to this not being
the case for this particular flood defence.
6.2.4 Delfland 24
For the model of Delfland location 24, the five highest phreatic surfaces are displayed in table 6.9.
The mean of the average phreatic surface for all time steps is NAP -1,61 m.
Table 6.9: Five highest phreatic surfaces location 24
1 14-10-2013 -1,08
2 14-7-2011 -1,10
3 24-7-2011 -1,15
4 11-9-2013 -1,18
5 14-10-2012 -1,23
Again, the two highest phreatic surfaces correspond to the two largest precipitation events. The
third highest phreatic surface occurs only 10 days after the second highest phreatic surface.
Between these peaks some minor precipitation had occurred, and therefore the phreatic surface
was still raised when another precipitation event occurred on 23-07-2011. This shows that a

69
small precipitation event can still lead to a high phreatic surface, depending on the initial
situation.
The highest phreatic surface in the model corresponds well to the measurement, although no
measurement was available for the monitoring well in the slope. For the second and third highest
phreatic surfaces the model results are slightly higher, but a dip in the measurements seems to
point again to pre-pumping of the boezem being the cause of this. For the event with rank 4, the
simulated phreatic surface is almost 40 cm too high, for which no clear cause can be identified.
Remarkable is that the same precipitation event resulted in a similarly high phreatic surface for
location 25. This might mean that the model does not respond correctly to this particular
precipitation event, or that there is an error in the precipitation data for this event. For the event
of 14-10-2012 the model fits well. This is the only one of the five events for which measurements
were available for the monitoring well in the slope. In figure 6.9 the cross-section is displayed for
the time step with the highest phreatic surface.
Remarkable is the elevated plateau in the phreatic surface. This is a result of the way the rubble
core is schematised. At its right-hand edge, the core material continues below the clay of the berm.
During the extreme event, the head in the permeable core rises fast, which leads to overpressure
of the water below the berm material, which has a lower permeability. This causes the head in
the core to rise above the ground surface. In the model, the edge of the core material is sudden,
leading to a jump in the phreatic surface. In reality the change in conductivity from the core to the
berm is likely to be more gradual.
Figure 6.9: Highest simulated phreatic surface for Delfland location 24
In the crest, the phreatic surface remains below the schematisation. However, in the berm the
schematisation is exceeded by a large margin. The reason for this is that there is a second inner
crest at the berm. For a correct schematisation, below the crest of the berm a nearly horizontal
course of the phreatic surface should be schematised to take precipitation into account.
The five lowest phreatic surfaces in the simulation are ranked in table 6.10. Again, there is almost
no variation in the average height, indicating that these minima are at the lowest possible phreatic
surface for the model. It also stand out that the year with the largest precipitation deficit, 2014, is
not present in the top 5 for this location either.
Table 6.10: Five lowest phreatic surfaces location 24
1 8-5-2011 -1,83
2 10-7-2010 -1,83
3 26-7-2013 -1,83
4 4-4-2012 -1,81
5 9-4-2013 -1,81

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70
For most of these five events the phreatic surface in the model is about 10 cm lower than the
measured heads in the monitoring wells. The dips encountered in the model results are in general
less pronounced than in the measurements.
The lowest phreatic surface in the simulation is displayed in figure 6.10. The schematised phreatic
surface is much lower than the simulation. This is mainly caused by the head inside the dike,
which is schematised at 0,7 m below polder water level because no drainage ditch is present.
Figure 6.10: Lowest simulated phreatic surface for Delfland location 24
6.2.5 Hogedijk
For the Hogedijk the measurement period only spans several months, and therefore the highest
and lowest phreatic surfaces are statistically less relevant than for the other research cases.
However, by coincidence a large precipitation event has occurred in September 2018, which
makes it interesting to compare the head rise caused by this event to other maxima.
The five highest phreatic surfaces during the measurements are displayed in table 6.12. The total
period average of the average phreatic surface is NAP -4,16 m.
Table 6.11: Five highest phreatic surfaces Hogedijk
1 24-12-2018 -3,93
2 09-12-2018 -3,93
3 05-01-2019 -3,99
4 12-11-2018 -4,01
5 29-11-2018 -4,05
Remarkable in this top 5 is that the extreme precipitation event from 05-09-2018 is not present.
When looking at the results in figure 6.4 it can be seen why: although the event leads to one of the
largest peaks, the general level of the phreatic surface is still recovering from the dry summer.
Only around November the heads have stabilised. Because the general level of the heads is higher,
the top 5 peaks all have occurred in November or later. Furthermore the event had a very high
intensity, leading to a large run-off volume and a comparitively low infiltration.
When observing the measurements, the event of 05-09-2018 shows the largest measured head
for monitoring wells 3 and 4, but for monitoring well 1 and 2 higher heads are reached in
November and December, like in the model. The cause of this are the sharp peaks observed in
monitoring wells 3 and 4. It is unclear how accurate those peaks are: they might be caused by
filling of the wells by run-off water. The quick subsidence after the maximum is reached makes
the peaks different to the other peaks in the series.
In figure 6.11 the highest simulated phreatic surface is displayed.

6.3. Fictitious precipitation event
71
Figure 6.11: Highest simulated phreatic surface Hogedijk
At the toe and the lower regions of the slope the phreatic surface is at ground level, which
indicates seepage occurs. This is not only the case for this highest phreatic surface: from about
November onwards seepage nearly constantly occurs. Said region is also the region where the
schematised phreatic surface is exceeded: in the rest of the cross-section the phreatic surface
remains below the schematisation.
The lowest simulated phreatic surface in the measurement period is displayed in figure 6.12. The
minimum is taken from the part of the simulation for which measurements are available. A lower
phreatic surface might have occurred before the measurements started, but since the phreatic
surface is compared to the measurements only the measurement period is considered.
Figure 6.12: Lowest simulated phreatic surface Hogedijk
This lowest phreatic surface shows a good fit to the measurements. The low head of monitoring
well 4 is still not reached, although evapotranspiration has caused the phreatic surface to be
lower than the polder water level. This also means that in the regions near the toe the phreatic
surface is lower than the schematisation. In the rest of the cross-section the phreatic surface
remains above the schematisation.
6.3 Fictitious precipitation event
Regarding precipitation, only two events with a return period larger than 10 years have occurred
during the measurement period. An extreme precipitation event can be characterised by various
aspects, which may lead to a different responses of the model. To obtain a more complete picture
of the response of the model to precipitation, fictitious events are imposed on the model.

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72
6.3.1 Definition event
For the definition of the precipitation, the precipitation statistics from paragraph 6.2 (STOWA,
2015) are used again. A precipitation event for a given return period is defined by the duration of
the event and the total volume of precipitation. To investigate what combination of volume and
duration leads to the largest rise of the phreatic surface, several combinations are tested.
In general, the precipitation intensity is not constant over the duration of an event. Usually one
or more peaks are observed, and in the longer duration events short dry periods might even
occur. To model this variability of the intensity over time, STOWA has defined seven standard
patterns (STOWA, 2004). For a duration of 24 hours, these patterns are displayed in figure 6.13.
Figure 6.13: STOWA precipitation patterns
One pattern is nearly uniform with only a small peak, two patterns have two peaks, and the other
four patterns have one single peak with different intensities. The patterns for longer durations
are similar, but have more fluctuations. The precipitation patterns are only a for durations longer
than 24 hours. Since the information on precipitation patterns for durations shorter than 24
hours is limited, patterns were generated by scaling the 24 hours pattern to shorter durations.
Initially, a constant return period of 100 years is chosen to compare the different durations and
patterns. This return period is chosen based on the safety class of the flood defences. The return
period of the loads used for the safety assessment of regional flood defences is dependent on the
so-called IPO-class of the flood defence. This class is determined based on the economic damage
in case of failure (STOWA, 2015). All three research cases have the IPO-class III, which
corresponds to a return period of 100 years for the hydraulic loads.
Nine durations varying between 2 and 216 hours were simulated. Possibly the earlier mentioned
statistics from STOWA (2018) should be used for the durations between 2 and 12 hours, but since
this is unclear, and to maintain consistency, all data is taken from STOWA (2015). The response
of the model is assessed at four points in the cross-section. For location 25 the three locations of
the monitoring wells are used, with an additional point at the inner crest. For location 24 the
locations of the monitoring wells in the slope and crest are used, with two additional points in the
crest of the berm and at the toe. Due to its large width, six points are used for the Hogedijk. These
are the four points of the monitoring wells, plus to additional points in the inner and outer crest.
The phreatic surface is determined again by taking the maximum head of the upper layers, with
the exclusion of the topmost layer.
Another factor of influence is the starting point of the simulations. The initial height of the
phreatic surface determines the magnitude of the head rise. Several test simulations have shown

73
that this initial height has only a small on the maximum reached height of the phreatic surface.
The head rise compared to the situation before the precipitation event is therefore dependent on
the head in the initial situation. To prevent this, a steady-state simulation without precipitation
was used as initial condition. After the precipitation event the model will return to steady-state
conditions, and therefore the situation before and after the event are identical.
Evapotranspiration was not applied to the model.
6.3.2 Response for return period 100 years
Nine duration/volume combinations with each seven precipitation patterns were applied to the
models. For each duration the head variation at the four assessment points was plotted for the
seven patterns. These plots are included in appendix H. For each duration it was determined
which of the seven patterns resulted in the greatest head rise by calculating the maximum average
head over the width of the cross-section. The normative patterns are summarised in table 6.12.
Table 6.12: Normative pattern for event durations
Duration 2 4 8 12 24 48 96 192 216
Delfland
25
Uniform Uniform Uniform Uniform
Medium
High
Long High High High
Delfland
24
Uniform Uniform Uniform Low Uniform Uniform Uniform
Medium
High
Medium
High
Hogedijk Uniform Uniform Uniform Uniform Low
Medium
High
Medium
High
High High
Delfland 25
For location 25 there is a clear difference in the normative pattern between the shorter and longer
durations. For durations shorter than 24 hours the uniform pattern is normative, whereas for
longer durations the patterns including a peak lead to a larger head rise. The duration of 48 hours
is an outlier being the only duration for which a two-peaked pattern is normative. This indicates
that a certain intensity of precipitation is needed to reach the maximum head rise. The short
events have a large intensity for all patterns. Since the model is set up such that the soil has a
certain infiltration capacity, the largest infiltration is reached when this capacity is reached
during the entire event. This explain why the uniform pattern is normative for the short
durations. For the longer duration events the intensity is lower, especially when the uniform
pattern occurs. This results in a quick rise of the head shortly after the start of the event, after
which it remains approximately constant. An equilibrium situation is reached where the
infiltration of precipitation is equal to the outflow to the inside water and the seepage. A higher
head is only reached when the intensity increases, and therefore the peaked patterns are
normative for the longer durations. The occurrence of an equilibrium situation was also observed
by Ten Bokkel Huinink (2016).
To investigate the influence of the duration independent of the pattern, the response to the
normative pattern for each duration was plotted in a single figure, which is displayed as figure
6.14. The four subplots show the response at the four chosen points in the cross-section.

6 . Results
74
Figure 6.14: Response of the phreatic surface at location 25 to precipitation with various duration, using
normative patterns
It can be observed that the durations below 24 hours lead to a smaller head rise than the longer
durations, while the difference between the longer durations is very small. No larger head rise is
reached than about 70 cm. At the toe and the slope the difference in maximum head rise is smaller
between the durations than at the crest. At a certain height the head cannot rise any further at
these points, since seepage occurs. Near the toe the initial phreatic surface is relatively close to
the surface, and therefore the maximum head rise is limited.
Although the maximum head rise is nearly the same for the longer durations, a duration of 192
hours results in a slightly larger head rise than the other durations.
Delfland 24
For location 24 the relation between the normative pattern and the event duration was less clear.
All durations below 96 hours have the uniform as normative pattern, with the exception of the
duration of 12 hours. However, for that duration the response to the uniform pattern is almost
identical to that to the low pattern. The only real difference is observed for the two longest
durations, for which medium high is the normative pattern.
This difference compared to location 25 can be explained by the equilibrium situation. At location
25, an equilibrium was reached during the longer events preceding the peak of the event. Location
24 responds much slower: the equilibrium situation is not reached when the peak occurs. Only
for the longest durations the effect described at location 25 occurs. The slower response can also
be observed in the time it takes to return to the initial head: location 25 returns much faster. A
possible explanation for this is the intermediate sand layer at location 25, which allows the flood
defence to drain towards the polder.
Again the different durations with their normative patterns are displayed in a single graph, which
is displayed in figure 6.15.

75
Figure 6.15: Response of the phreatic surface at location 24 to precipitation with various duration, using
normative patterns
Compared to location 25, the difference in maximum head rise between the durations is more
pronounced. From 48 hours onwards, the maximum head rise reaches its limit. This limit is
probably an equilibrium situation where outflow and seepage balance the infiltration. In the berm
this can be observed for the durations of 192 and 216 hours: at 0,8 m the head rises no further
and remains constant. A duration of 96 hours results in the largest head rise, although the
difference to the other durations longer than 48 hours is small.
Hogedijk
The normative patterns for the Hogedijk show a similarity to location 25: the uniform pattern is
normative for the short durations, and a single-peaked pattern is normative for longer durations.
For the size of this peak a trend can be observed as well: the longer the duration, the higher the
peak of the normative pattern. This behaviour can be explained in similar way to location 25.
The different durations with their normative patterns are displayed in figure 6.16.
The equilibrium situation is reached quickly for the slope and the toe. As was observed earlier,
seepage occurs quickly in this region, since the phreatic surface is close to ground level. The crest
region of the flood defence show the opposite: the equilibrium situation is not even reached
during the longest precipitation event. The head rise is also much smaller, and it takes a longer
time for the head tor return to the original level. This difference in response between the higher
and lower regions is caused by the differences in properties of the different parts of the peat layer.
Near the toe the conductivity is larger, leading to a faster response. Another factor of influence is
the specific yield of part 3 of the peat layer. In an attempt to model the quick response of the
monitroing well in this section, the specific yield was set to a smaller value than the other parts
of the layer. This also results in a larger response for the slope of the model.

6 . Results
76
Figure 6.16: Response of the phreatic surface at the Hogedijk to precipitation with various duration, using
normative patterns
Like also observed at location 24, a relation between the event duration and the maximum head
rise is visible for most locations in the cross-section. Only for the toe the maximum head rise is
the same for all duration, but this is caused by seepage. The maximum head rise was observed for
a precipitation event with a duration of 192 hours.
6.3.3 Response for varying return periods
So far, all the precipitation events applied to the model were based on a return period of 100
years. To investigate the effect of events with a larger or smaller return period, simulations were
carried out for return periods between 1 and 1000 years. The maximum reached phreatic surface
for the duration and pattern resulting in the highest maximum are displayed for each return
period. Note that this is not the phreatic surface for the given return period: the pattern and
duration resulting in the greatest head rise are used, which have a probability of occurrence
themselves. Furthermore, only the influence of precipitation is taken into account, the water
levels are kept constant. The analysis is only intended to show the influence of precipitation
events with various probability of occurrence.
The highest phreatic phreatic surface was determined in a similar way as in paragraph 6.2, by
taking the highest head the columns of cells spanning the cross-section. The top layer is excluded
because it is affected by the boundary condition.
Delfland 25
For location 25, the results of this analysis are displayed in figure 6.17. For reference, the phreatic
surface in the initial situation and the schematisation are displayed as well. The difference
between the various return periods is small. Below the crest and near the toe the phreatic
surfaces are almost equal, and below the slope the difference between the highest and lowest is
about 30 cm. This corresponds to the equilibrium situation discussed earlier: at a certain level
the phreatic surface will not rise any further due to seepage. Near the toe this equilibrium

77
situation is reached earlier than in the slope, and therefore there is no difference between the
precipitation events.
Figure 6.17: Phreatic surfaces location 25 for precipitation events with various return periods
Near the outer crest, the phreatic surface rises to above the outer water level. For return periods
above 100 years, the schematisation is slightly exceeded. However, the schematisation assumes
a higher than normal water level occurs, while the model does not.
Delfland 24
The results for Delfland location 24 are displayed in figure 6.18. As was earlier discussed in
paragraph 6.2, the schematisation in the berm is lower than the simulated phreatic surface. The
difference between the return periods is small in the berm, and larger near the crest, which is in
accordance to the observations at location 25.
Figure 6.18: Phreatic surfaces location 24 for precipitation events with various return periods,
Hogedijk
The analysis was also performed for the Hogedijk. The results are displayed in figure 6.19.
Figure 6.19: Phreatic surfaces Hogedijk for precipitation events with various return periods

6 . Results
78
The difference between the different return periods is so small that it can hardly be discerned in
the figure. The maximum difference between the return periods of 1 year and 1000 years is about
10 cm. Below the berm and near the toe there is hardly even any head rise at all. Near the toe this
can be explained again by seepage. Below the crest the infiltration rate is reduced due to the road
on top. The small response reflects the measurements of the monitoring wells: apart from some
peaks the validity of which can be disputed, the head fluctuations are relatively small. The model
is calibrated to mirror this.
6.4 Long term precipitation
The simulations executed thus far had a simulation period of about 4,5 years. While this is a long
period for monitoring well measurements, from a statistics point of view it is a relatively short
period. By running a longer simulation using one of the calibrated models, an artificial dataset of
the phreatic surface over a much longer period can be generated, which is more suitable for a
statistical analysis. This simulation was performed for period of 31 years. The basis for this period
is the availability of meteorological data. The closest KNMI weather station with hourly data is at
Rotterdam, about 9 km removed from the locations in Delfland (KNMI, 2019). Because both
precipitation and evapotranspiration data are required for the model, radiation measurements
are needed. Radiation measurements at this station have started in December 1987. When the
data was downloaded it was available up to the 24th of January 2019, which gives a simulation
period of approximately 31 years. With this data, the daily Penman-Monteith potential
evapotranspiration rate was calculated using the same method as used for the Hogedijk
(described in appendix C).
Due to the simulation time and the large amount of output data, this long-term simulation was
performed using just one of the three research cases. The model of the Hogedijk was calibrated
on just a few months of data, and is therefore not considered reliable enough to simulate a period
of 31 years. Location Delfland 24 has a permeable core, which results in an atypical phreatic
surface for a regional flood defence. For location 25 some problems were encountered in
determining the correct soil composition, but of the three models it resulted in the best fit to the
measurements. For these reasons the choice was made to use this model for the long term
simulation.
To simplify the analysis of the model results, the phreatic surface was determined again by taking
for every time step the highest head of the layers for each grid column, with the exclusion of the
top layer and the deepest layer.
6.4.1 Exceedance of the schematisation
In order to investigate how often the phreatic surface exceeds the schematisation, the phreatic
surface for each time steps was compared to the schematisations for both the dry and the wet
situation. If the head in a single cell is below the dry schematisation, or above the wet
schematisation for a certain time step, the schematisation is exceeded. For the dry situation no
such events have occurred: in the 31 years the phreatic surface has never been below the dry
schematisation.
For the wet situation, the schematisation was exceeded for 1645 of the one-hour time steps. The
total number of time steps in the simulation was 272304, which means the schematisation was
exceeded for about 0,6% of the time. The 1645 exceedances are not all separate events,
sometimes the exceedance occurs for several consecutive time steps. When consecutive
exceedances are counted as a single event, 376 exceedances have occurred during the 31 years.

6.4. Long term precipitation
79
For each of the exceedances it was determined at which cell column in the cross-section it
occurred. This makes it possible to determine at what point in the cross-section the
schematisation is exceeded most frequently. To visualise this information, a histogram was
plotted over the cross-section. This histogram is displayed in figure 6.20.
Figure 6.20: Histogram of exceedances of the schematised phreatic surface
Each bar in the histogram represents a column of cells in the model grid. It stands out that all
exceedances have occurred near the toe, especially at the edge of the drainage ditch. No
exceedances have occurred at the crest or the slope. The exceedances probably have occurred
when seepage at the toe took place: in that situation the phreatic surface is locally at ground level,
while the schematisation is mostly below ground level. The schematisation and the highest found
phreatic surface are also displayed in the figure. This highest phreatic surface exceeds the
schematisation by just a few centimetres. Different interpretations of the guidelines for the
schematisation might therefore result in less or even no exceedances.
In addition to the histogram and the highest phreatic surface, the envelope of the found heads is
included. This indicates the area in which the phreatic surface varies. For the most part, the
highest phreatic surface lies on the upper boundary of the envelope. Only in the slope the
boundary of the envelope is slightly higher, which means in that area slightly higher heads have
occurred on some other point in time.
The highest phreatic surface was found by taking the time step with the highest average phreatic
surface over the cross-section. This maximum occurred on 13-10-2013. Notable is that this is also

6 . Results
80
the day with the highest phreatic surface during the main simulation of 4,5 years. When
examining the precipitation data it is found that this day indeed has the largest precipitation
volume in the 31 year period.
This raises another question: why was the schematised phreatic surface exceeded in the crest in
the main simulation, but not in this long-term simulation? The answer to this is the use of different
precipitation data. The localised Meteobase data shows that the precipitation event had a volume
of 103 mm, while in the data from the KNMI station the precipitation volume is only 63 mm. The
most extreme precipitation event is therefore less extreme in the long-term model, and therefore
the schematisation is not exceeded in this case. The cause for this difference in precipitation
volume is most likely local variation.
6.4.2 Histogram
For this long-term simulation again a histogram was plotted of the data. The long simulation
period has the result that a lot more data is included, leading to a more complete image of the
distribution of the heads.
In figure 6.21 these histograms are displayed. Like in paragraph 6.1, the histograms are plotted
for the locations of the three monitoring wells, but with an extra point added at the inner crest.
The maximum and minimum values are displayed as triangles. The heights of the schematised
phreatic surface at these points are included as vertical lines.
Figure 6.21: Histograms of the head at four points in the cross-section
It stands out that the shape of the histograms is smoother than of those in paragraph 6.1. The four
points show a similar shape with a convex shape on the left side, and a concave shape on the right
side. This shape is more pronounced near the crest than near the toe. At the toe, the histogram is
very narrow and tall, indicating that the head variations are relatively small. This is probably
caused by the proximity to the drainage ditch and the intermediate sand layer, which allows
precipitation to flow away easily. The largest variations are observed at the inner crest.
The schematisation is exceeded at the toe, which corresponds to the earlier observations. The
schematisation is almost reached at the crest, but no actual exceedances have occurred in this
model. In the slope the most common fluctuations are far removed from the crest, but the highest
heads are far removed from the mean and almost reach the schematisation. This histogram has a
very long and thin tail. At the inner crest the distance between the histogram and the
schematisation is the largest. Even the maximum value is about 30 cm removed from the
schematisation.

6.5. Uncalibrated model
81
The skewed shape of the histograms is reminiscent of the lognormal distribution. This
distribution was fit to the data, and the result is displayed in figure 6.22. The distribution fits the
data quite well, although the concave-convex shape of the histogram is not as pronounced in the
distribution.
Figure 6.22: Lognormal distribution fitted to model results
The means and standard deviations for the fitted distributions are displayed in table 6.13.
Table 6.13: Means and standard deviations of the fitted lognormal distributions
Location Crest Inner crest Slope Toe
Mean -0,797 -1,451 -2,954 -3,095
Standard deviation 0,097 0,184 0,067 0,027
These distributions could be used to calculate the probability of occurrence for the head at a
certain point in the cross-section. However, to calculate the probability of exceedance of a certain
value per year, an extreme value analysis would have to be conducted on the data. Furthermore,
a head with a certain probability at a single point in the cross-section does not necessarily
coincide with a head with the same probability in other points in the cross-section. As could be
observed in figure 6.20, the maximum simulated heads in the slope did not coincide with the
maximum phreatic surface on average. Although the difference was small this shows that the
maximum pore pressures do not occur simultaneously in the cross-section.
6.5 Uncalibrated model
During the set-up of the models, initial values were chosen for the soil parameters as a starting
point for the calibration. These values were immediately adjusted to calibrate the model for a
steady-state simulation, but the extreme phreatic surfaces resulting from an uncalibrated model
were not analysed. In this paragraph the results from uncalibrated models using estimated
parameters are compared to the results of the calibrated models. In this way the magnitude of the
error caused by using an uncalibrated model can be determined, and consequently the usefulness
of a model only using estimated parameters.
6.5.1 Parameters
For the soil parameters mostly the parameters used as starting point for the calibration were used
again. For location 25 a choice had to be made for the soil schematisation: the first schematisation
resulting in a poor fit of the model could be used, or the schematisation adjusted based on the
measurements. Eventually it was chosen to use the latter, so that the only difference between the
calibrated and uncalibrated model are the soil parameters. For the parameters themselves the

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82
initially chosen Staring types were used. For location 24 the initially chosen parameters were
used as well, and the schematisation was not changed. For the uncalibrated model of the Hogedijk
a Staring soil type was chosen instead of the conductivity measurements. The soil borings indicate
that the dike body consists of clayey peat, which corresponds to Staring type B18. This soil type
is used for the entire layer, no separations were made. For the other soil layers the Staring types
initially estimated for the calibration are used. Tables of the estimated Staring types in the models
are included in appendix G, paragraph G.2.1. For the anisotropy ratio and the specific yield the
estimates from paragraph 5.1.3 are used.
6.5.2 Results
For all three models a transient simulation using the estimated parameters was performed. The
results for location 25 are displayed in figure 6.23, the results for the other locations are included
in appendix G.
Figure 6.23: Model results location 25 for calibrated (green line) and uncalibrated model (blue line)
For the crest the fit of the uncalibrated and the calibrated model is almost the same, and at some
points the fit of the uncalibrated model is actually better that of the calibrated model. However,
in the slope and the toe the heads in the uncalibrated model are consistently much higher than
the measurements and the calibrated model. The fluctuations caused by precipitation are smaller
than in the measurements. The evapotranspiration dips are similar in size to those in the
measurements.
For location 24 the heads in the crest and the slope are also consistently about 30 cm higher than
the measurements and the calibrated model. In the toe the difference is smaller, but the heads are
also consistently higher than in the calibrated model. The head fluctuations are smaller than in
the measurements.
For the Hogedijk the difference between the calibrated and uncalibrated model is variable per
monitoring well. Near the crest (HGD 1-1) the uncalibrated heads are around 25 cm too low
compared to the measurements. For monitoring well HGD 1-2 the heads for calibrated and
uncalibrated model are almost the same, but for the other two locations the heads are too high.
For monitoring well 4 the heads in the calibrated model were much higher than the
measurements, and in the uncalibrated model the heads are even higher. The modelled
fluctuations are very small, smaller than those in the measurements. The reason is the high

6.6. Relation to macro-stability
83
specific yield of 0,44 estimated for peat; during the calibration this parameter was set to a much
lower value.
6.5.3 Extreme simulated phreatic surfaces
Using the same method as in paragraph 6.2, the highest and lowest simulated phreatic surfaces
were determined and plotted. In the plots the highest and lowest phreatic surface from the
calibrated model were included as well for comparison. The highest phreatic surface for location
25 are displayed in figure 6.24.
Figure 6.24: Highest phreatic surface of location 25 for the uncalibrated model (in blue) and the calibrated
model (in red). The red crosses represent the measured head at the moment the extreme in the
uncalibrated model was reached.
The moment at which the maximum or minimum was reached was not always the same as in the
calibrated model. For location 25 the maximum in the uncalibrated model occurred 2 days later
than in the calibrated model. In the crest, the maximum phreatic surface in the uncalibrated
model is lower than in the calibrated model, but in the slope and toe it is higher. The uncalibrated
model fits the measurements quite well for the maximum, but this is mainly because the phreatic
surface is very close to the ground surface. For the minimum phreatic surface the uncalibrated
phreatic surface is almost 0,5 m higher than both the model and the measurements.
For location 24 the differences between the highest phreatic surface in the calibrated and
uncalibrated model are small. Both are very close to the ground surface, which is probably the
reason why the difference for this maximum is small, whereas the uncalibrated model results in
higher heads during normal conditions.
The fluctuations in the uncalibrated model of the Hogedijk are very small, which has the result
that the difference between the maximum and the minimum phreatic surface is also small. The
use of a homogeneous layer has the result that the phreatic surface is an almost straight line from
the outer crest to the drainage ditch. In the crest this leads to a lower maximum phreatic surface
than in the calibrated model, and in the crest to a slightly higher phreatic surface. For the
minimum phreatic surface the situation is similar, but the differences are larger.
The results show that for the three research cases calibration was absolutely necessary to model
the head fluctuations. For the extreme phreatic surfaces the difference between the calibrated
and uncalibrated models is smaller, but this is mainly because the phreatic surface is closer to the
equilibrium height in these conditions, which is close to the ground surface in both situations.
6.6 Relation to macro-stability
In order to get a picture of the relation between the phreatic surface and the macro-stability of
the flood defence, several stability calculations were performed. For these calculations location
25 was used, since the long-term analysis was also performed on this case.

6 . Results
84
The parameters for the strength of the soil are taken from a stability calculation of the same flood
defence, which was provided by Delfland. These were included in the form of stress tables, which
relate the shear resistance to the effective stress. These stress tables are included in appendix E,
paragraph E.6. The calculations were carried out using the program D-Geo Stability (Deltares,
2017). This program includes several methods to model the slip plane. The most commonly used
methods in the Netherlands are the Bishop, Uplift-Van, and Spencer- van der Meij methods. When
there is a risk that the soil layers behind the flood defence are pushed up by the water pressure,
or when thin, weak soil layers are present, it is preferable to use Uplift-Van or Spencer- van der
Meij (STOWA, 2015). Considering a thin peat layer is present at location 25, one of these two
models should be used. The choice was made to use Uplift-Van, because it is easier to define the
slip planes in this model, which makes it easier to keep the slip planes consistent between the
calculations. Theoretically Spencer- van der Meij provides a better approximation of reality, but
this analysis is aimed at determining the influence of a different phreatic surface. The actual
calculated stability factor is of less importance. In the Uplift-Van model the slip plane consists of
two semi-circles, connected by a horizontal segment. The pore pressures are modelled by so-
called PL-lines, which indicate the course of the piezometric level over the cross-section. Multiple
PL-lines can be added and assigned to the soil layers.
For reference, first a calculation was performed in which the schematised phreatic surface was
used. For the schematisation of the soil layers the same schematisation as in the Modflow model
was used. Two PL-lines were used: one representing the schematised phreatic surface, and
another representing the head in the Pleistocene sand layer. The phreatic surface was used to
model the pore pressures in the top layers, including the intermediate sand layer and the clay
layer below the outside water. In the other layers, the pore pressures were linearly interpolated
between the phreatic surface and the head of the Pleistocene sand layer.
Using this schematisation a stability factor of 1,15 was calculated. The model and the normative
slip plane are displayed in figure 6.25.
Figure 6.25: Stability calculation Delfland location 25

6.6. Relation to macro-stability
85
6.6.1 Variation characteristic points schematisation
To obtain some comprehension on where in the cross-section fluctuations have the largest
influence on the stability, each of the characteristic points of the schematised phreatic surface
was shifted downwards and upwards if possible. The stability was then calculated again to assess
the change in stability factor.
The left- and rightmost points of the schematisation are placed at the fixed water levels, and can
therefore not be shifted. Instead, two extra points were added to the schematisation which were
variated. One point was added below the outer crest, about a meter removed from the entry point,
and another point was added about 1,5 m removed from the drainage ditch. The four variated
points are displayed in figure 6.26.
Figure 6.26: Variated points of the schematised phreatic surface
In table 6.14 the stability factors resulting from the changed schematisation points are displayed.
The point near the drainage ditch could not be shifted 0,25 m upwards, since that would place the
point above ground level. When all points were shifted, the individual points were shifted in the
range for which this was possible.
Table 6.14: Stability factors resulting from variation of four points in the schematised phreatic surface
Point/Shift -0,25 m -0,1 m 0 m +0,1 m +0,25 m
Outer crest 1,15 1,15 1,15 1,14 1,13
Inner crest 1,20 1,17 1,15 1,13 1,10
Toe 1,21 1,17 1,15 - -
Drainage ditch 1,18 1,16 1,15 1,13 -
All 1,30 1,21 1,15 1,11 1,05
From the resulting stability factors it can be observed that these changes of a single point have a
limited effect on the stability. The lowest stability factor is 1,10 and the highest is 1,20, so the
variation is relatively small. In the outer crest the effect of a variation is smallest: this is not
surprising, since in figure 6.25 it can be observed that the slip plane starts about halfway in the
crest. The largest influence is observed for the inner crest and the toe. In paragraph 6.4.2 it was
found that the inner crest also exhibits the largest variation of the phreatic surface, which means
that the inner crest is the most important location in the cross-section when regarding the
influence of precipitation on the macro-stability.
When all points are shifted, a change in the phreatic surface has a more significant influence on
the stability. For this flood defence the stability remains above 1, but for a flood defence with a
lower initial stability such a shift of the phreatic surface could cause instability.

6 . Results
86
6.6.2 Application of model results
As a second part of the stability analysis, some phreatic surfaces obtained from the simulations
are applied to the stability calculation. For these calculations, the following phreatic surfaces
were used:
• The highest phreatic surface from the main simulation of 4,5 years, on 13-10-2013;
• The heads from each separate layer applied as a PL-line for each layer, again for 13-10-
2013;
• The highest phreatic surface for the normative precipitation event with a return period of
100 years;
• The highest phreatic surface obtained from the uncalibrated model.
The highest simulated phreatic surface of 13-10-2013 is thus applied to the model in two ways.
In the first calculation, this phreatic surface simply replaces the schematised phreatic surface. In
the second calculation the heads calculated in Modflow are taken for each layer, and applied in D-
Geo Stability as a separate PL-line. This replaces the linear schematisation of the pore pressures
between the Pleistocene layer and the phreatic surface by the pore pressures calculated in the
model, which might lead to different results. In the third calculation the simulation of a 100 year
return period precipitation event is used. For this the normative duration and pattern are used,
which are a duration of 192 hours and the ‘High’ pattern. The highest average phreatic surface
was extracted from the simulation and applied as the phreatic line in the stability calculation.
The stability factors for these three calculations are displayed in table 6.15.
Table 6.15: Results of stability calculations using different phreatic surfaces
Situation Stability factor
Schematised phreatic surface 1,15
Phreatic surface 13-10-2013 1,17
PL line for every layer for 13-10-2013 1,18
100 year return period precipitation 1,17
Uncalibrated model 1,14
Again, the difference compared to the initial calculation is small. However, the calculation using
the highest simulated phreatic surface results in a slightly higher stability factor, even though the
schematisation is exceeded at some points in the cross-section. Taking into account that the
phreatic surface in question was the result of a precipitation event with a return period of about
250 years, this indicates that the schematisation is not necessarily unsafe, even though it is
exceeded in the simulations at some points.
Using the simulated heads for each soil layer resulted in a slightly higher stability factor than
when only the phreatic surface is used. This small difference indicates that a linear gradient
between the Pleistocene sand layer and the phreatic surface is a good enough approximation of
the pore pressure distribution. However, it should be noted that the slip plane only traverses
through the upper regions of the area for which the gradient applies, so for deeper slip planes the
difference could be of more importance.
The stability when using the 100 year return period precipitation is equal to the stability using
the phreatic surface of 13-10-2013. The phreatic surfaces for those situations are very similar,
and therefore lead to the same stability factor.
Using the highest phreatic surface simulated in the uncalibrated model results in a stability lower
than when using the schematisation. The heads at the toe and near the inner slope are at the
ground surface, which is higher than in the schematisation and the maximum phreatic surface of
the calibrated model. Even though the phreatic surface of the uncalibrated model is lower in the
crest, this results in a lower stability.

7.1. Conclusions
87
7 Conclusions
This chapter presents the conclusions from this thesis and answers the research questions.
Following the conclusions are the discussion and recommendations for further research.
The objective of this thesis, as presented in chapter 1 is to extend the knowledge of modelling the
phreatic surface in regional flood defences with the use of a numerical model.
The basis of the research consisted of the construction of numerical models for three regional
flood defences for which pore pressure measurements from monitoring wells were available. The
numerical models were calibrated to simulate the measured response of the phreatic surface to
precipitation and evapotranspiration.
7.1 Conclusions
The conclusions of this research are discussed based on the research questions presented in
chapter 1 . Each of the sub-questions is discussed, followed by the main research question.
1. What are the main influencing factors on the phreatic surface?
The main external influencing factors of influence are precipitation, evapotranspiration and
water levels. Precipitation is an important influence on the phreatic surface, as it can cause large
head rises of several tens of centimetres up to a metre. Various durations, volumes and patterns
of precipitation may lead to different reactions. Evapotranspiration can be a factor of influence,
but not in all situations. The three research cases suggest that a larger conductivity of the dike
core leads to a smaller influence of evapotranspiration. The mean in- and outside water level
determine the entry and exit point of the phreatic surface, and therefore are an important factor
for the phreatic surface. The fluctuations of these water levels were mostly omitted in this
research. For regional flood defences water levels on both sides are regulated which means the
fluctuations are relatively small compared to fluctuations due to precipitation. Only the mean
water levels are an important factor for the phreatic surface; the fluctuations are of smaller
importance.
The internal influencing factors on the phreatic surface are the soil characteristics. This includes
both the schematisation of the different soil types in the cross-section and the characteristics of
these soil types. The soil composition of the cross-section has a large influence on the baseline
position of the phreatic surface, especially when permeable layers are present. If the soil is
relatively homogeneous in the longitudinal direction of the dike, it is sufficient to know the soil
composition in the cross-section under consideration. However, when there are large variations
in this direction, information on the soil composition along the longitudinal direction is required
as well.
Regarding the soil types themselves, the conductivity is the most important parameter. It is often
anisotropic: the conductivity in vertical direction is different than in horizontal direction. The
flow from the outside towards the inside water is mainly horizontal, and therefore the horizontal
conductivity is mostly important for the baseline position of the phreatic surface. The vertical
conductivity has an influence on this baseline position as well, since flow also occurs to and from
the Pleistocene sand layer. The vertical conductivity is also an important influence on the reaction
of the phreatic surface to precipitation. A larger vertical conductivity leads to a quicker and larger
response. The response is also largely dependent on the specific yield, which determines the
storage capacity of the soil. A lower specific yield means less storage capacity and therefore also

7 . Conclusions
88
leads to a larger and quicker response. The vertical conductivity and the specific yield jointly
determine the reaction of the phreatic surface to precipitation.
2. How is the phreatic surface currently schematised in regional flood defences?
For stability analyses, the phreatic surface is usually schematised based on several points
determined by the geometry of the flood defence, and the water levels. Usually raised inside and
outside water levels are used, and it is assumed that seepage occurs at the toe.
In all three research cases, the schematisation was exceeded at some point during the simulation.
The exceedances were mainly observed between the toe and the drainage ditch, where the
modelled phreatic surface reached closer to the ground surface than the schematisation.
Additionally, the model result in the crest reached levels higher than the outside water level. Since
the schematisation uses a raised outside water level while the model did not, the schematisation
was usually not exceeded at this location. If a raised water level was taken into account, the
schematisation in the outer crest would be exceeded more often.
The fact that the simulated phreatic surface exceeded the schematisation at some points does not
necessarily mean that the schematisation overall is not sufficiently conservative. The
schematisation is exceeded near the toe and slightly at the outer crest, but at the inner crest the
schematisation is higher than the model results. Potential improvements to the schematisation
could thus be made by using a higher level at the outer crest, a lower level at the inner crest, and
placing the schematisation at ground level between the toe and the drainage ditch.
The model shows that the pore pressures do not increase hydrostatically with depth, which is
caused by vertical flow to and from the Pleistocene sand layer. When this non-hydrostatic
gradient was taken into account in the stability calculation, the difference in stability was small.
This indicates that using a linear gradient of the pore pressures between the phreatic surface and
the Pleistocene sand layer is a good schematisation.
3. What are the requirements for a numerical model to model the phreatic surface in a regional
flood defences?
In the literature study several requirements for a numerical model were listed. Based on the
experiences with the Modflow model the list of requirements to a numerical model can be
extended:
• The model needs to be able to simulate transient groundwater flow;
• Precipitation has to be included as a boundary condition;
• When simulating dry periods or calibrating using data from a dry period,
evapotranspiration should be included as a boundary condition;
• A boundary condition to allow seepage is necessary;
• The model needs to be able to model the sometimes complex geometry of the subsoil of
regional flood defences.
4. How accurately can a numerical model simulate measured pore pressures in a regional flood
defence?
The research models have shown that it is possible to model the phreatic surface with some
accuracy. The baseline position of the phreatic surface could be matched for all three models,
sometimes after adjusting the soil schematisation. The accuracy of the simulated fluctuations of
the phreatic surface varies between the research cases and between the locations in the cross-
section. In general, monitoring wells closer to the outside water were not simulated as accurately
as the monitoring wells further inward in the cross-section. A possible explanation for this could
be the influence of fluctuations of the outside water level, which were omitted in the models.

7.1. Conclusions
89
However, for the locations more inward in the cross-section not all peaks were matched correctly
either. The magnitude of the peaks was sometimes correct while the baseline phreatic surface
was higher or lower than the measurements. In part these differences may be explained by errors
in the measurements, but this does not explain all the differences. The other main causes are the
simplified geometry of the cross-section, the simplified method using which the infiltration is
modelled, using a non-variable water level, modelling the cross-section in 2 dimensions, and
errors in the measurement set. A certain degree of simplification is always required in a model
study, to keep the model manageable and because the available information is limited. Despite all
these simplifications it was possible to model the fluctuations quite well for most of the
measurement locations.
On average, the difference for each time step of one hour was around 10 cm. Analysis of the
highest simulated phreatic surfaces has shown that the deviation of the model for these extreme
events is smaller, being only several centimetres. Whether this accuracy is sufficient is open to
interpretation. An indication of the significance of the error can be obtained by assessing the
influence on the stability. A 10 cm raise of the entire phreatic surface leads to a small stability
decrease of 0,04 for research location 25, which does not lead to instability. For this research
location the average difference was smaller than for the other research locations, which means
that for research location 25 the error with regard to the macro-stability is sufficiently small.
For flood defences with a smaller initial stability the effect of rise of the phreatic surface can be
larger, possibly leading to instability. It can therefore not be concluded that the model is
sufficiently accurate for all situations. However, research location 25 has shown that it is at least
possible to construct a sufficiently accurate model, despite the necessary simplifications and
limited information. For models with a less good fit improvements can likely be made when more
information is available, for example with more monitoring wells for research location 24, and
with a longer calibration period without a dry period for the Hogedijk. It is therefore concluded
that a numerical model can simulate the measured pore pressure with sufficient accuracy with
regards the macro-stability, on the condition that sufficient information is available to construct
the model. The answer to research question 6 discusses what information is required.
5. How does the phreatic surface in the numerical model respond to an extreme event?
The fit of the three models for the highest occurring phreatic surfaces in the measurement set is
similar to the fit under normal conditions. For the lowest phreatic surface the models exhibits
heads about 10 cm lower than the measurements. This means the model performs similarly well
for extreme high conditions as for normal conditions, but slightly worse for extreme low
conditions.
More insight in the response to precipitation events was gained by adding various fictitious
precipitation events to the models. It was found that as a general rule, events with a longer
duration and lower intensity lead to larger head rises. After a certain duration a maximum head
rise is reached, after which the phreatic surface rises no further. At this point an equilibrium
situation is reached, in which the amount of infiltrated precipitation is equal to the outflow
towards the inside water and by seepage at the toe. The duration after which this equilibrium was
reached was different between the models, but for all models it was reached after at most 96
hours. The height of this equilibrium phreatic surface is dependent on the infiltration
characteristics and the conductivity of the soil.
The patterns determining the distribution of the precipitation over the duration of the events also
resulted in different responses. The pattern resulting in the largest head rise was different
between the various durations, but it could be observed that for shorter durations the pattern
with a mostly uniform distribution was normative, while for longer durations the patterns
including a single peak resulted in larger head rises. The reason for this is that for long durations
the equilibrium situation is reached for all patterns, while the peak results in an extra head rise

7 . Conclusions
90
above this for a short amount of time. Precipitation events with a duration longer than 96 hours
and including a single large peak therefore cause the highest phreatic surface in a regional flood
defence.
6. What parameters and data are at least required for an accurate determination of the phreatic
surface using a numerical model?
Comparison of the calibrated models and the uncalibrated models has shown that calibration is
required to accurately simulate the fluctuations of the phreatic surface. For extreme high phreatic
surfaces the fit of the uncalibrated model was comparable to that of the calibrated model.
However, when the normal fluctuations are not modelled properly it is uncertain that the reaction
to extreme events is always correct. To obtain reliable results calibration of the model is
necessary, and therefore pore pressure measurements are required to set up and calibrate a
geohydrological model of a regional flood defence.
The analyses have shown that the head variations in the inner crest are the largest. A
measurement point at the inner crest can therefore provide the most insight in the fluctuations
of the phreatic surface. To determine the course of the phreatic surface over the cross-section
measurement points near the outer crest and the toe are necessary as well, meaning a minimum
of three measurement points is required to calibrate the model. The required measurement time
is dependent on the situation. One of the models was calibrated using only two months of
measurement data, which was not sufficiently long. The calibration period was preceded by a dry
period, which influenced the calibration. Although two months was too short for this model, two
months of measurements conducted during more normal conditions is probably sufficiently long
to calibrate the model.
Precipitation data is also required for the calibration, even if the model is used to only model the
response to fictitious precipitation. The monitoring wells show the response to actual
precipitation, so to calibrate the response of the model the precipitation data has to be applied to
it. For two of the three models evapotranspiration had a noticeable effect on the fit of the model
to the measurements. When dry periods are included, or when the response to a dry period needs
to be modelled, evapotranspiration data is therefore required as well.
The models of locations 24 and 25 in Delfland have shown that measured conductivities are not
strictly necessary to construct a fitting model. However, the same head fluctuations could also be
modelled when using slightly different parameters. Only the hydraulic heads are considered for
the phreatic surface. This means several calibrations sets resulting in the same head fluctuations
may exist, but these different sets could result in different flow rates through the soil.
Measurements of the conductivity can provide an ‘anchor’ to the real values of the parameters. In
this way the values of the calibration parameters have more correspondence to their magnitude
in the real world, which gives more confidence that the model is accurate. Measured
conductivities can also provide a better understanding of the variation in the flood defence.
Perhaps the most important information required is the soil composition, especially the location
of permeable and less permeable layers in the cross-section. The conductivities can be adjusted
during the calibration, but if the soil schematisation is incorrect it is not possible to construct a
well-fitting model. This means sufficient knowledge of the subsoil from soil borings and cone
penetration tests is required. To obtain knowledge of the soil composition and the measuring
points, at least three soil borings at the locations of the monitoring wells are required. The
research cases have shown that this sometimes not even sufficient.

7.1. Conclusions
91
Main research question
The research sub-questions served to answer the main research question, which was defined as
follows:
Can a numerical model contribute to a more accurate estimation of the phreatic surface in a
regional flood defence during extreme conditions?
The research cases have shown that is possible to simulate the phreatic surface in a regional flood
defence using a numerical model with sufficient accuracy. Such model could theoretically be used
to estimate the phreatic surface during extreme conditions for usage in a stability calculation.
Provided sufficient information on the flood defence is available, a model can therefore contribute
to a more accurate estimation of the phreatic surface in a regional flood defence . However, the
sufficiently good fit of the models was only reached after extensive calibration of the model to the
measurement set. Pore pressure measurements are necessary to construct and calibrate an
accurate model. The calibration itself can be a long-drawn process, due to the large amount of
parameters that can be adjusted. The large amount of required data and the difficult calibration
process make it questionable whether it is always worthwhile to construct a numerical model to
determine the position of the phreatic surface. For stability assessments, construction of such a
model for every flood defence is not realistic. For these situations it is more reasonable to
continue improvement of the existing schematisations.
Numerical models could aid in further research regarding the pore pressures in flood defences. A
model provides insight in the height of the phreatic surface over the entire cross-section, whereas
pore pressure measurement only give information for a single point. The model can also be used
to estimate the phreatic surface in extreme conditions, even if the measurements only include
normal precipitation events. These characteristics make a numerical model useful for research
regarding the phreatic surface, for example to construct new schematisations.
Further conclusions and observations
The three models have shown that modelling the unsaturated zone is not strictly necessary to
model the phreatic surface. This makes setting up a geohydrological model for a flood defence
simpler, since no unsaturated soil parameters are required. Calibration of the boundary
conditions is necessary to construct a correct model, but this would also be necessary for the
unsaturated parameters. It is however possible that if the unsaturated zone were to be modelled
with correct parameters, some peaks would be matched better than in the models of this thesis.
The models also show that a 2-dimensional model is sufficient in many cases, but when large
variations exist in the longitudinal directions a 3-dimensional model might be required.
An extreme phreatic surface is not necessarily directly related to an extreme event. When the
phreatic surface is higher than normal due to precipitation, a relatively small precipitation event
can lead to an extreme phreatic surface. Conversely, an extreme event does not always lead to an
extreme phreatic surface. If the phreatic surface is lowered due to drought, and the event has a
short duration with a high intensity, the resulting height of the phreatic surface can be lower than
when a small event occurs during a wet period. This shows that a certain rise of the phreatic
surface is not only related to the event directly causing it, but also by the events of the preceding
weeks.
Performing a long-term simulation using one of the models has shown that the height of the
phreatic surface at a certain point in the cross-section can be described by a lognormal
distribution. The standard deviation of this distribution is variable over the cross-section, and is
largest at the inner crest.
Comparing the results of this long-term simulation to the schematisation, it was found that the
schematisation is exceeded regularly near the toe and the inside drainage ditch. In the other
simulations a slight exceedance in the outer crest was found as well, while in the inner crest the
schematisation remained well above the modelled phreatic surface. This suggests that the

7 . Conclusions
92
schematisation can potentially be improved. These potential improvements are using a higher
elevation at the inner crest, a lower elevation at the inner crest, and a higher elevation in the area
near the toe and the drainage ditch. More research is required to confirm this.
The results of an uncalibrated model show that for the three research cases calibration was
absolutely necessary to model the head fluctuations. For the extreme phreatic surfaces the
difference between the calibrated and uncalibrated models is smaller, but this is mainly because
the phreatic surface is closer to the equilibrium height in these conditions, which is close to the
ground surface in both situations.
7.2 Discussion
There are several assumptions and simplifications used in this research that have to be
considered when interpreting the results. This paragraph discusses the validity of the most
important of these assumptions.
7.2.1 Input data
First of all, it was assumed that the monitoring well measurements give a good representation of
the fluctuations of the pore pressure over time at a certain point in the cross-section. However,
all three measurement sets show discrepancies, shifts of a part of the set, or inexplicable peaks. It
is also not clear how accurate the measurements of monitoring wells are in general. The filter of
a monitoring well spans a certain vertical distance, and the head in the well is thus determined
by an equilibrium of the pore pressures over this distance. It seem likely that the highest pore
pressure over the filter determines the head, but this is not certain. Flow may occur through the
monitoring well to deeper parts of the soil, reducing the head in the well. Additionally, monitoring
wells provide storage of water. To measure a head rise, first water has to flow into the monitoring
well. This storage capacity can have an influence on the pore pressures around the well, and thus
distort the measurements. A further potential source of errors is the presence of cracks in the
dike. If such a crack is connected to a monitoring well, runoff water can flow via the crack directly
into the well. This loads to head fluctuations that do not correspond to the phreatic surface. Since
the models were calibrated on the measurements, a structural error in the measurements would
mean that the calibration is incorrect.
A potential problem not necessarily limited to monitoring wells, is the small number of
measurement points in the cross-section. For practical reasons, the number of monitoring wells
that can be placed in a flood defence is limited. It is also unknown whether the pore pressures
deeper in the soil are modelled correctly or not. If a model is calibrated to match the measurement
points, it can be assumed that the other points in the cross-section are correct too, but unexpected
variations in the soil composition and conductivity can lead to differences. The location of the
measurement points is also important: for example, at research location 24 not monitoring well
was placed at the inner crest of the berm, which means there is no measurement to verify the
phreatic surface in the berm.
7.2.2 Simplifications and schematisations
The soil structure in the top layers of the dikes had to be modelled in a simplified, unrealistic
manner. A higher conductivity was applied to the topmost layer in the model, and a larger
anisotropy ratio was used since cracks mainly increase the conductivity in vertical direction. With
this approach, only the average increase of conductivity caused by the soil structure is modelled.
In reality the pores and cracks form a network which forms preferential flow paths for the
precipitation to infiltrate. Cracks can intercept runoff water and transport it deeper into the dike.
This leads to a faster response of the phreatic surface compared to when the water has to travel
through the soil. Cracks can therefore cause different infiltration characteristics at different
locations in the dike, which are also variable in time due to formation and closing of cracks. The
soil structure might also have an influence on the specific yield and therefore the phreatic storage

7.3. Recommendations
93
capacity. All these processes cannot be simulated in the model. Some of the observed differences
between the model results might be explained by the exclusion of the soil structure.
Another simplification made to make the construction of the model manageable, was to model
the a cross-section as 2-dimensional. A 2-dimensional model was able to simulate the phreatic
surface sufficiently well for the three research cases, although for research location 25 it appeared
that flow in the third dimension had an influence on the results. This shows that schematising the
flow in the cross-section as 2-dimensional is not in all cases a valid assumption.
7.2.3 Calibration
The calibration of the model is a manual process and therefore prone to human error. Multiple
sets of calibration values can lead to similar results, which makes it unclear which is the best
calibration set. These different calibration sets can also lead to different pore pressures in the
parts of the cross-section for which there are no measurements. Although the differences are
small, this makes determination of the best calibration parameters difficult. Additionally, the
model was only aimed at determining the heads in the cross-section. The flow rate through the
dike was not calibrated, since this magnitude of the flow rate in reality is unknown. It is therefore
unclear whether the actual flow through the dikes was modelled correctly.
Extra information could help to make the calibration process easier. For the Hogedijk the soil
composition was less uncertain than for the other research locations, which reduced the number
of calibration variables. Measured conductivities can provide information on the variations in the
cross-section, which can also reduce the number of calibration variables.
7.3 Recommendations
Most information regarding the position of the phreatic surface in flood defences is obtained by
measurements using monitoring wells or pressure sensors. As mentioned in the discussion, the
validity of these measurements can be disputed. More research regarding the relation between
monitoring well measurements and the actual pore pressures in flood defences might provide
valuable insights on the validity of measurements, and thus indirectly on the validity of the
current schematisations and this research. For example, placing monitoring wells and a pressure
sensor in the single cross-section could provide more knowledge about the differences between
the measurement methods.
Another recommendation is to investigate different methods to determine the pore pressures in
flood defences than monitoring wells or pressure sensors. These methods only provide
information on the measurement location. If a measurement method existed that could provide
data of the pore pressures over the entire cross-section, a much more complete image of the
phreatic surface could be obtained. An interesting possibility could be the use of fibre optic cables.
These can be used to measure the temperature and therefore the presence of water. Several
cables on different elevations might be used to detect the position of the phreatic surface with a
finer resolution than when using separate sensors.
When measurements of the phreatic surface are being conducted, it is recommended to measure
at a sufficient number of locations. At least three measurement points are required to determine
the course of the phreatic surface. It is important that one of these points is placed at the inner
crest, since at that location the fluctuations of the phreatic surface caused by precipitation are the
largest. When the measurements are conducted with the aim to perform a model study, pore
pressure measurements at various depths can be useful to chart the gradient of the hydraulic
head. This makes it possible to calibrate the deeper soil layers more accurately. Conductivity
measurements can be useful to provide a reference value for the calibration, and to obtain insight
in the variation of the conductivity. It is preferable to use in-situ tests for these measurement, to
prevent disturbance of the soil. When monitoring wells are used to measure the pore pressures,
these can be also be used for in-situ conductivity tests. A disadvantage of these tests is that only

7 . Conclusions
94
a single conductivity is measured without direction. Laboratory tests are needed to determine
the anisotropy ratio. Laboratory research on samples taken at different depths and locations from
various flood defences can be useful to obtain a better comprehension of typical values of the
anisotropy ratio.
It was the intention to also analyse the differences between flood defences with different
geometry. For this reason a dike with a road on the crest and a dike without a road were chosen.
However, the soil compositions of the research cases were so different that no good comparison
regarding the mentioned characteristics could be made. It is therefore recommended to conduct
more research on the influence of the geometry of the dike on the phreatic surface. This concerns
differences in actual geometry, like the height, the angle of the slope or the presence of a berm,
but also the influence of a road on the crest.
As discussed in the conclusions, potential improvements to the currently used schematisation of
the phreatic surface could be made. The number of research cases in this thesis is too small to
conclude that this improvement could apply as a general rule. It is therefore recommended to
execute more research whether these changes could actually provide a more accurate and safe
schematisation.

References
95
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98
A Glossary
Boezem Network of regional canals which stores and transports excess water from
polders to the outside water.
Cunet Foundation of a road.
Evapotranspiration Combined flux of evaporation and plant transpiration from the soil to the
atmosphere.
Extinction depth MODFLOW parameter to model evapotranspiration. The maximum depth
from which evapotranspiration can take place.
Legger Document containing waterways, structures and other objects in the
management area of a water board and the properties of these objects.
KNMI Koninklijk Nederlands Meteorologisch Instituut. Dutch meteorological
institute.
MW Monitoring well
NAP Normaal Amsterdams Peil. Vertical reference level used in the
Netherlands.
Polder Low-lying area of land surrounded by dikes, in which a lower water level
is maintained than in the surrounding areas.
Recharge Downwards water flux from the ground surface to the groundwater table.
Runoff Flow of precipitation water over the ground surface, which does not
infiltrate in the subsoil.
STOWA Stichting Toegepast Onderzoek waterbeheer. Foundation for applied
water research.
Stress period Time subdivision in MODFLOW between which boundary conditions can
change.
TAW Technische Adviescommissie voor de Waterkeringen. Technical advisory
committee for flood defences.
Vertical staggering Distortion of a regular grid in MODFLOW due to steep layer separations.
Water board (Dutch: waterschap) Regional government responsible for the
management of flood defences, waterways, water levels and water quality.

B. List of symbols
99
B List of symbols
General parameters
a Hydraulic conductivity anisotropy ratio [-]
A Area m2
b Riverbed thickness m
Criv Conductance of riverbed m2/day
drow Width of cell in model grid m
g Gravitational acceleration m/s2
h Hydraulic head m
htm Modelled head for timestep t m NAP
ht
o Observed (measured) head for timestep t m NAP
ho
̅̅̅
̅̅̅ Mean of observed heads m NAP
k Intrinsic permeability m/s
K Hydraulic conductivity m/day
ms Recharge multiplier for section s [-]
mtot Recharge multiplier for entire model [-]
mv Compressibility of the soil m2/N
n Soil porosity [-]
N Net infiltration due to precipitation m/s
NSE Nash-Sutcliffe model efficiency coefficient -
ps Precipitation rate for section s mm/hour
q Specific discharge m/s
Rcap Recharge capacity of the soil mm/hour
Rmin Recharge threshold mm/hour
Rs Recharge rate for section s m/day
Ss Specific storage m-1
Sy Specific yield v
T Number of timesteps -
w Width of a recharge section m
β Compressibility of water m2/N
ρ Density kg/m3
ϕ Hydraulic head m
 Dynamic viscosity N s/m2
Van Genuchten
kr Relative permeability [-]
Seff Effective saturation [-]
θ Water content [-]
θres Residual water content [-]
θsat Saturated water content [-]
n Parameter related to pore size distribution [-]
m 1 – (1/n) [-]
pc Capillary suction pressure kN/m2
α Parameter related to air entry suction m-1

References
100
Penman-Monteith
dr Inverse relative distance earth-sun [-]
ETref Potential evapotranspiration rate mm/d
es Saturation vapour pressure kPa
ea Daily average vapour pressure kPa
G Soil heat flux density MJ/m2/d
Gsc Solar constant (= 118,08) MJ/m2/d
K
Incoming short-wave radiation MJ/m2/d
J Day number of the year [-]
K
Outgoing short-wave radiation MJ/m2/d
K0
Solar radiation MJ/m2/d
Kext Extra-terrestrial solar radiation MJ/m2/d
L
Incoming long-wave radiation MJ/m2/d
L
Outgoing long -wave radiation MJ/m2/d
Qnet Net radiation MJ/m2/d
RH Relative humidity [-]
Tmean Mean daily air temperature at 2 m height °C
uz Daily average wind speed at z m height m/s
z Height of weather station above sea level m
α Albedo [-]
γ Psychrometric constant kPa/°C
 Solar declination radians
 Latitude radians
s Solar time angle radians
σ Stefan-Boltzman constant (= 4,903*10-9) MJ/K4/m2/d

C. Meteorological data
101
C Meteorological data
C.1 Delfland
In this appendix it is described how the precipitation and evapotranspiration data used in the
model are attained from the online archive Meteobase.nl. The data was downloaded in grid
format. For this an area has to be selected on a map, which is displayed in Figure C.1. The locations
of the cases are displayed on this map as red squares. For this area both the hourly precipitation
data and daily evopotranspiration calculated using Penman-Monteith are downloaded for the
period 2010-2014.
Figure C.1: Selected area in Meteobase
For this area the data for several grid points was delivered. The nearest of these grid points is
displayed as a blue cross. The data for this grid point is used for the simulations.
The grid data from Meteobase is delivered in ASCII format, which means that every hourly or
daily data point is provided as a separate file. This file contains the number of selected grid points,
the coordinates of these points and the data for these points. Because of the large amount of files
(43801 for the total period) the data can only be requested for a period of 2 years at once, which
meant the data had to be downloaded in three parts. For the purposes of this research, the ASCII
format is not very useful to work with. For this reason a Python script was written, which reads
every file, extracts the data for the correct grid point, and writes this value along with the date
and time in a csv file which can be opened in Excel. In Excel the data was plotted to detect any
anomalies. One anomaly was found: The ASCII file for 1-1-2014 0:00 included a precipitation of
967 mm. This value is replaced with 0.1 mm, which is the average of the measurements of the
nearest KNMI weather stations at Hoek van Holland and Rotterdam for this hour.
To verify the precipitation data, the data from Meteobase was compared to precipitation data
from some weather stations nearby. This data was downloaded from the website of the Royal
Netherlands Meteorological Institute (KNMI, 2018). Data from the following weather stations was
used:

References
102
• Hoek van Holland (hourly data)
• Rotterdam (hourly data)
• Delft (daily data)
• Honselersdijk (daily data)
• Maasland (daily data)
The total precipitation over the research period from 01-06-2010 to 18-10-2014 for these
stations is compared for the total precipitation from this period in the Meteobase data. This is
displayed in Table C.1.
Table C.1: Comparison of Meteobase data and weather stations
Station Distance to cases (km) Cumulative precipitation (mm)
Hoek van Holland 11,6 3984,1
Rotterdam 8,9 3991,3
Delft 5,8 4432,0
Honselersdijk 5,9 4314,9
Maasland 4,1 4028,3
Meteobase - 4214,2
The cumulative precipitation for the weather stations and the Meteobase data is plotted in figure
D.2.
Figure D.2: Cumulative precipitation for Meteobase and weather station data.
It can be observed that there is some variance in the total precipitation over de considered
period. The stations at Hoek van Holland, Rotterdam and Maasland show very similar amounts
of about 4000 mm. The stations at Delft and Honselersdijk show significantly larger amounts of
respectively 4432 and 4315 mm. The Meteobase data shows a value in between those values of
4214 mm. This is not surprising, considering that this data is partially based on the weather
station data. However, by making this comparison it can be seen that the Meteobase data shows
anomalies caused by the processing. The Meteobase data is therefore considered realistic
enough to use for the simulations.
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
22-1-2010 10-8-2010 26-2-2011 14-9-2011 1-4-2012 18-10-2012 6-5-2013 22-11-2013 10-6-2014 27-12-2014
Cumulative
precipitation
(mm)
Date
Meteobase
Hoek van
Holland
Rotterdam
Maasland
Delft
Honselersdijk

103
C.2 Hogedijk
To calculate the Penman-Monteith potential evapotranspiration rate from KNMI weather station
data, the method described in Schuurman & Droogers (2010) was used. This method was largely
based on a report from the Food and Agriculture Organisation of the United Nations (Allen,
Pereira, Raes, & Smith, 1998). Since the KNMI stations do not measure al variables required for
the Penman-Monteith formulations, some of the variables have to be estimated. Said reports
provide a method for this.
The Penman-Monteith expression for the potential evapotranspiration rate is defined as:
𝐸𝑇𝑟𝑒𝑓 =
0,408 ∗ 𝑠 ∗ (𝑄𝑛𝑒𝑡 − 𝐺) + 𝛾 ∗
900
𝑇 ∗ 𝑢2 ∗ [𝑒𝑠 − 𝑒𝑎]
𝑠 + 𝛾( 1 + 0,34 ∗ 𝑢2)
(D.1)
Where:
ETref = potential evapotranspiration rate (mm/d)
Qnet = net radiation (MJ/m2/d)
G = soil heat flux density (MJ/m2/d)
γ = psychrometric constant (kPa/°C)
T = mean daily air temperature at 2 m height (°C)
u2 = daily average wind speed at 2 m height (m/s)
es = saturation vapour pressure (kPa)
ea = daily average vapour pressure (kPa)
es – ea = saturation vapour pressure deficit (kPa)
Slope of the vapour pressure curve (s)
The slope of the vapour pressure curve is calculated from the mean daily temperature using the
following expression (Allen, Pereira, Raes, & Smith, 1998):
𝑠 =
4098 ∗ [0,6108 ∗ exp (
17,27 ∗ 𝑇𝑚𝑒𝑎𝑛
𝑇𝑚𝑒𝑎𝑛 + 237,3)]
(𝑇𝑚𝑒𝑎𝑛 + 237.3)2
(D.2)
For standardization purposes the daily mean temperature Tmean is calculated as follows:
𝑇𝑚𝑒𝑎𝑛 =
𝑇𝑚𝑎𝑥 − 𝑇𝑚𝑖𝑛
2
(D.3)
Where:
Tmean = daily mean temperature (°C)
Tmax = daily maximum temperature (°C)
Tmin = daily minimum temperature (°C)
Net radiation (Qnet)
The net radiation consists of two components: the net short-wave and net long-wave radiation:
𝑄𝑛𝑒𝑡 = 𝐾↓
− 𝐾↑
+ 𝐿↓
− 𝐿↑
(D.4)
Where:

References
104
K
= incoming short-wave radiation (MJ/m2/d)
K
= outgoing short-wave radiation (MJ/m2/d)
L
= incoming long-wave radiation (MJ/m2/d)
L
= outgoing long-wave radiation (MJ/m2/d)
The incoming short-wave radiation is a quantity measured at the KNMI-stations. The outgoing
short-wave radiation can be estimated from this quantity using the albedo. The albedo is a
dimensionless number representing the ratio between the absorbed and reflected radiation.
Thus, the outgoing short-wave radiation is calculated as follows (Schuurman & Droogers, 2010):
𝐾↓
= 𝛼 ∗ 𝐾↑
(D.5)
α = albedo (-)
For the Penman-Monteith formulation a fixed value of 0,23 is used for the albedo.
For the long-wave radiation no measurements are available. It has to be estimated from other
meteorological measurements using the following empirical formulation (Allen, Pereira, Raes, &
Smith, 1998):
𝐿↓
− 𝐿↑
= 𝜎 [
𝑇𝑚𝑎𝑥
4
+ 𝑇𝑚𝑖𝑛
4
2
] (0,34 − 0,14 ∗ √𝑒𝑎)(1,35 ∗
𝐾↓
𝐾0
↓
− 0,35)
(D.6)
Where:
L
- L
= net outgoing long-wave radiation (MJ/m2/d)
σ = Stefan-Boltzman constant (= 4,903*10-9) (MJ/K4/m2/d)
Tmax = daily maximum temperature (°C)
Tmin = daily minimum temperature (°C)
K
= incoming short-wave radiation (MJ/m2/d)
K0
= solar radiation (MJ/m2/d)
The daily average vapour pressure is a quantity that is also directly required in the Penman-
Monteith equation, and will be discussed later. The solar radiation K0
is the radiation the earth
would receive without clouds. Based on the ratio between this value and the measured
incoming radiation the long-wave radiation is estimated. To calculate the solar radiation, the
extra-terrestrial radiation Kext is required, which is dependent on the time of year and the
geographical location on earth. The solar radiation is calculated using the following expressions
(Allen, Pereira, Raes, & Smith, 1998):
𝐾0
↓
= (0,75 + 2 ∗ 10−5
∗ 𝑧) ∗ 𝐾𝑒𝑥𝑡
(D.7)
𝐾𝑒𝑥𝑡 =
𝐺𝑠𝑐 ∗ 𝑑𝑟
𝜋
[𝜔𝑠 ∗ sin(𝜑) ∗ sin(𝛿) + cos(𝜑) ∗ sin(𝜔𝑠)]
(D.8)
𝑑𝑟 = 1 + 0,033 ∗ cos (
2𝜋
365
∗ 𝐽)

105
(D.9)
𝛿 = 0,409 ∗ sin(
2𝜋
365
∗ 𝐽 − 1,39)
(D.10)
𝜔𝑠 = arccos(− tan(𝜑) tan(𝛿))
(D.11)
Where:
K0
= solar radiation (MJ/m2/d)
z = height of weather station above sea level (m)
Kext = extra-terrestrial solar radiation (MJ/m2/d)
Gsc = solar constant (= 118,08) (MJ/m2/d)
dr = inverse relative distance earth-sun (-)
 = solar declination (rad)
 = latitude (rad)
s = solar time angle (rad)
J = day number of the year (-)
The height of the weather station is -2 m. The latitude is 52 degrees, or 0,911 radians.
Soil heat flux density (G)
The soil heat flux density is the energy required to heat up the soil. It can be negative when the
soil cools down. When calculating the evapotranspiration over an entire day, the soil heat flux
density is often set to zero, which is also done for this calculation.
Psychrometric constant (γ)
The psychrometric constant describes the relation between the partial pressure of the water in
air the air temperature. It is dependent on the air pressure and therefore height. This relation
between the constant and the height is small, and therefore usually a fixed value of 0,06 kPa/°C
is used.
Daily mean air temperature (T)
The air temperature is measured directly for every hour. For each day the mean of these
measurements is taken.
Daily average wind speed at 2 m height (u2)
The wind speed is also a quantity directly measured; however, these measurements are taken at
a height of 10 m. The wind speed close the ground surface increases logarithmically with height,
and therefore the wind speed at 10 m height can be approximated using the following equation
(Allen, Pereira, Raes, & Smith, 1998):
𝑢2 = 𝑢𝑧
4,87
ln( 67,8 ∗ 𝑧 − 5,42)
(D.12)
Where:
u2 = wind speed at 2 m height (m/s)
uz = wind speed at z m height (m/s)
z = height of the wind speed measurement (= 10 m) (m)
Saturation vapour pressure deficit (es – ea)

References
106
This quantity is the difference between the actual and the saturated vapour pressure, and
indicates the amount of water the air can absorb. A larger saturation vapour pressure deficit
means a larger evapotranspiration flux.
The actual vapour pressure ea cannot be measured directly, and is derived from the relative
humidty (RH), which is a measured quantity. The relative humidity is the ratio between the actual
and the saturated vapour pressure:
𝑅𝐻 =
𝑒𝑎
𝑒𝑠
(D.13)
Where:
RH = relative humidity (-)
es = saturation vapour pressure (kPa)
The saturation vapour pressure is dependent on the air temperature. It is calculated using the
following expressions (Allen, Pereira, Raes, & Smith, 1998):
𝑒°(𝑇) = 0,6108 ∗ exp [
17,27 𝑇
𝑇 + 237,3
]
(D.14)
𝑒𝑎 =
𝑒𝑠(0), 𝑇𝑚𝑎𝑥 + 𝑒𝑠(0), 𝑇𝑚𝑖𝑛
2
(D.15)
Where:
e°(T) = saturation vapour pressure at the air temperature T (kPa)
T = air temperature (°C)
Tmax = daily maximum air temperature (°C)
Tmin = daily minimum air temperature (°C)
The saturation vapour pressure is calculated for the daily maximum and minimum temperature,
and the average is taken to obtain the mean saturation vapour pressure. Using equation D.13, the
daily average vapour pressure can then be calculated using the relative humidty.
Using the equations D.2 –D.15 the input variables for the Penman-Monteith equation can be
calculated from the following measured parameters:
• Temperature: measured hourly, daily maximum, minimum and mean are taken;
• Incoming short-wave radiation;
• Relative humidity;
• Wind speed at 10 m height.
These quantities are available for the KNMI weather stations Schiphol, Valkenburg and Cabauw,
and were downloaded from the KNMI website (KNMI, 2018). For each station the Penman-
Monteith evapotransporation was calculated for each day with the use of an Excel sheet. From
these daily values the average of the three weather stations was taken, weighted by the distance
to the Hogedijk.

D. Measurement data
107
D Measurement data
D.1 Delfland location 24

References
110
D.2 Delfland location 25

D. Measurement data
113
D.3 Hogedijk

References
114
D.4 Discrepancies in the measurements
D.4.1 Delfland 24
The following holes and discrepancies were found in the measurements of location 24:
• Measurements at the slope start later, on 11-01-2012. This is due to several reasons: the filter
of the monitoring well was changed, for some time the settings of the data loggers were wrong
and later the monitoring well was damaged.
• There are no measurements for the crest and toe from 24-03-2011 until 12-04-2011 due to an
error in the settings of the data loggers.
• The crest shows a strange dip on 24-05-2015.
• There is a small gap in the data from 21-7-2011 until 24-7-2011 for the crest and toe.
• From 20-6-2012 until 29-10-2012 there are no measurements for the toe; no explanation is
reported for this.
• From 8-8-2013 until 16-03-2014 the measurements for the slope are removed due to
unrealistic fluctuations. On 8-8-2013 also a jump can be seen for the crest and slope, which
indicates a correction. However, no manual measurement is reported for this date.
• On 16-12-2013 the data for the slope is slightly shifted based on a manual measurement. The
crest is unchanged because the manual measurement is the same as the data logger.
• On 18-3-2014 another manual measurement was done, but the data is not changed based on
this measurement.
• The measurements ceased on 7-7-2014. A final manual measurement has taken place on this
day.
D.4.2 Delfland 25
The following remarks can be made on the measurements of location 25:
• The monitoring well at the crest was placed in an intermediate sand layer. Therefore an
additional monitoring well was placed for which measurements started on 30-09-2010.
The measurements at the slope show a strange peak downwards on the same date.
• There is a gap in the data from 24-03-2011 until 12-04-2011 caused by an error in the
settings of the data loggers.
• The toe and slope show a strange peak downwards on 24-05-2015.
• Around 21-07-2011 there is a small gap in the data for the toe and crest.
• From 20-6-2012 until 04-07-2012 there is a gap in the data for the toe. The data for the
first few hours when the measurements start again is not very meaningful. No explanation
is given for this gap.
• On 22-08-2012 the measurements for the slope stop, and at 04-10-2012 for the toe as
well. For both points the measurements restart on 19-10-2012. No explanation has been
found for this gap.
• The measurements for the intermediate sand layer cease on 13-09-2012. The data from
08-08-2013 until 07-11-2014 is removed due to unrealistic fluctuations. It is unclear why
the rest of the data is not present.
• On 08-08-2013 there is a small gap and a strange jump in the measurements for crest,
slope and toe. Probably the measurements before or after are shifted higher or lower. No
manual measurement is reported for this date.
• Another jump occurs on 16-12-2013. This corresponds to a manual measurement on this
date, so probably the data has been shifted to fit this.
• Another jump occurs on 18-03-2014. This corresponds to another manual measurement.
• A small jump occurs on 07-07-2014 at the toe, on the same day measurements for the
crest cease. This corresponds to a manual measurement.
• On 01-08-2014 measurements for the intermediate sand layer are restarted.
• On 22-10-2014 the measurements are stopped; a final manual measurement has taken
place on this date.

E. Cross-sections and soil data
115
E Cross-sections and soil data
E.1 Cross-sections
Location 24, Delfland

References
116
Location 25, Delfland

117
Location Hogedijk, Rijnland

References
118
E.2 Soil borings Delfland location 24
Soil borings taken at the research location
These soil borings were taken at the locations of the monitoring wells. The initial positions of the
filters of the monitoring wells also are displayed. The depths are indicated with respect to the
ground surface. The elevation of the ground surface for the three locations is as follows:
Crest: NAP +0,35 m
Slope: NAP -0,94 m
Toe: NAP -2,73 m
Crest Slope Toe
Source: (Delfland, 2010)

119
Other soil borings
The following borings were taken about 15 m to the south of the research cross-section, as a part
of a reinforcement program for the flood defence. Due to the proximity and similarity of this
cross-section these borings are considered relevant for the research location. The borings were
performed on two locations, comparable to the locations of the monitoring wells in the crest and
the slope in the research cross-section. Two manual borings and one mechanical boring are
available.
Manual boring crest
Manual boring toe

References
120
Mechanical boring crest
Source: (RPS BCC B.V. & Witteveen + Bos, 2010)

121
E.3 Soil borings Delfland location 25
These soil borings were taken at the locations of the monitoring wells. The initial positions of the
filters of the monitoring wells also are displayed. The depths are indicated with respect to the
ground surface. The elevation of the ground surface for the three locations is as follows:
Crest: NAP +0,006 m
Slope: NAP -1,79 m
Toe: NAP -2,65 m
Crest Slope Toe
Source: (Delfland, 2010)

References
122
Subsoil
The available soil borings only reach to a depth of about 5 m below the ground surface. To
determine the composition of the deeper soil layers two soil borings from the DINOloket (TNO
Geologische Dienst Nederland, 2018) were used, which are displayed below.

123
E.4 Soil borings Hogedijk
These soil borings were taken at the locations of the monitoring wells. The depths are displayed
with respect to NAP. The borings (and monitoring wells) are numbered 1 to 4 from the crest
towards the toe.
Boring 1
Boring 2
Boring 3
Boring 4
Source: (Nectaerra, 2018)

References
124
Other soil borings
About 50 m to the south two soil borings and a cone penetration test were conducted as a part
of the reinforcement project of the Hogedijk.
Soil borings

125
Cone penetration test

References
126
E.5 Conductivity measurements Nectaerra
Measured conductivity values Rijnland (Nectaerra, 2018)
The conductivity measured were performed at several depths and using several methods. The
measurements for which a depth is specified in Table E.1 were carried out using either
Amoozemeter or double-ring infiltration test. The double-ring test is used to measure the
infiltration of the soil, and is therefore only used for the top 10 cm of the soil. The amoozemeter
test were used up to a depth of about 70 cm. The remaining measurements were performed using
Slug tests. In this test the water level in a monitoring well is temporarily raised or lowered. Then
the time it takes to return to the initial water level is measured, and with this information the
hydraulic conductivity around the well can be calculated. It can be observed that the
measurements close the ground surface show a large conductivity, which is probably the result
of the soil structure. The measurements using the Slug test were all taken in peat, and show a
variation of about two orders of magnitude.
Table E.1: Conductivity measurements Nectaerra
Location
Location in dike
profile
Depth Soil type
Conductivity
(m/day)
HGD-1-1 Crest Monitoring well Peat 0.004
HGD-1-2 Slope Monitoring well Peat 0.01
HGD-1-4 Toe Monitoring well Peat 0.04
HGD-2-1 Crest Monitoring well Peat 0.001
HGD-2-4 Toe Monitoring well Peat 0.064
SKP-1-1 Crest Monitoring well Peat 0.0004
SKP-2-1 Slope Monitoring well Peat 0.0007
SKP-3-1 Toe Monitoring well Peat 0.0002
VEE-2-1 Crest 0 - 0.1 Sandy clay 8.64
VEE-2-2 Slope 0 - 0.1 Sandy clay 9
VEE-2-3 Toe 0 - 0.1 Sandy clay 11.52
VBK-2-1.5 Slope 0 - 0.1 Sandy clay 22.8
VBK-2-3 Slope 0 - 0.1 Sandy clay 31.2
VEE-2-1 Crest 0.26 - 0.46 Sandy clay 0.48
VEE-2-2 Slope 0.23 - 0.71 Sandy clay 0.22
VBK-2-4 Toe 0.2 - 0.4 Sandy clay 0.36
VEE-1-1 Crest 0.25 - 0.54 Silty clay 3.84
VEE-2-3 Toe 0.19 - 0.48 Organic clay 0.02
VBK-2-3 Slope 0.1 - 0.3 Sandy loam 3
VEE-1-1 Crest 0 - 0.1 Silty sand 1.25

127
E.6 Stress tables stability analysis
Three types of clay are present: anthropogenic clay (AP), Duinkerke clay (DK), and Calais clay
(CA). Sand is present as anthropogenic sand and Duinkerke sand. A single type of peat is used,
which is Hollandveen (HV). All the soil types are subdivided by location in the dike profile. Below
the dike is indicated as ‘o’, and adjacent to the dike as ‘n’. In the stress tables the effective stress
is indicated as sigma (σ), the shear stress as tau (τ). For the clay types, the same stress tables are
used multiple soil types with different volumetric weights. For example DK klei h1 and DK klei h2
use the same stress table, but have a different volumetric weight.
These values are taken from a stability calculation provided by Delfland.
Table E.2: Stress tables for clay (klei). All values are in kN/m2.
AP Klei (o) AP Klei (n) DK Klei (o) DK Klei (n) CA Klei (o)
σ τ σ τ σ τ σ τ σ τ
0 1,12 0 1,03 0 1,03 0 1,95 0 0,95
12 6,6 15,56 7,89 15,56 7,89 14,39 6,96 13,71 6,75
24 12,08 25,6 12,32 25,6 12,32 21,93 9,58 21,66 10,11
36 17,34 35,64 16,41 35,64 16,41 29,47 12,99 29,61 12,34
48 21,83 45,68 20,47 45,68 20,47 37 15,33 37,56 14,57
60 25,65 55,72 24,53 55,72 24,53 44,54 17,94 45,51 16,61
72 31,37 65,76 27,83 65,76 27,83 52,08 19,24 53,46 19,56
84 35,42 75,8 30,96 75,8 30,96 59,62 20,97 61,41 21,02
96 39,91 85,84 33,76 85,84 33,76 67,16 22,25 69,36 23,33
108 42,11 95,88 34,92 95,88 34,92 77,31 24.14
Table E.3: Stress tables for sand (zand) and peat (veen). All values are in kN/m2.
AP Zand (o) DK Zand HV Veen (o) HV Veen (n)
σ τ σ τ σ τ σ τ
0 0 0 0,12 0 0 0 0
7,69 3,33 18,77 8,52 9,18 5,62 7,38 3,87
15,39 7,71 25,65 11,59 13,77 8,44 11,06 5,87
23,08 10,99 32,52 14,55 18,36 10,85 14,75 7,72
30,77 14,41 39,39 17,12 22,95 12,49 18,44 9,42
38,46 17,41 46,26 19,44 27,54 14,9 22,13 11,31
46,15 19,86 53,14 21,51 32,13 15,59 25,81 13,24
53,85 22,76 60,01 23,93
61,54 27,48 66,88 25,26
69,23 29,4 73,76 27,85
Table_Apx E.4: Volumetric weight of the soil type used in the stability calculation
Soil type Volumetric weight dry (kN/m3) Volumetric weight wet (kN/m3)
AP Klei h2 (o) 14,10 14,10
AP Klei h1 (n) 16,20 16,20
DK Klei h1 (o) 16,20 16,20
DK Klei h2 (o) 14,10 14,10
DK Klei h1 (n) 16,20 16,20
CA Klei h1 (o) 14,90 14,90
AP Zand (o) 18,00 20,00
DK Zand 18,00 18,30
HV Veen (o) 10,00 10,50
HV Veen (n) 10,00 10,50

References
128
F Calibration of the models
This appendix describes the calibration of the models in more detail.
F.1 Initial values
As a starting point for the calibration process, assumptions were made for the conductivity of the
different soil types. For this the Staring set was used. Based on the composition of the soils found
in the borings a Staring type was assumed. The motivation for these chosen types is discussed for
each research case.
F.1.1 Delfland location 25
From the soil borings in appendix E a schematisation of the cross-section was constructed, which
is displayed in Figure F.1. In the soil borings the fractions of the different present soil types are
also indicated. Based on this information a soil type from the Staring set is chosen for each model
layer. The upper sand layer contains loam and peat fractions according to the soil borings, and
based on this Staring type B2 is chosen. Because the layer is on the surface, a top soil type is
chosen. The clay core of the dike is also considered to be close enough to the surface to be a top
soil type. For this layer B11 is chosen, which has an average permeability for clay. Layer 3, the
intermediate sand layer, contains more loam than the top sand layer and is located deeper. For
this reason the subsoil type O3 is assigned. The peat of layer 4 contains some clay, but no subsoil
peat types containing clay are included in the Staring set. Instead the top soil type B18 is used.
Since only the conductivity is used and not the unsaturated parameters, use of a topsoil type for
deeper layers is unlikely to lead to problems. Layer 5 is a clay layer containing loam. For this
reason the medium heavy clay subsoil type O12 is chosen.
For the layers 6 to 10 only the soil type is known, without any indication of fractions of different
soil types. Because no other information is available, the same Staring set types are used as for
the higher layers. The chosen soil types and motivation for the simulation are displayed in Table
F.1. These soil types will be adjusted later during the calibration of the model.
Table F.1: Assigned Staring soil types location 25 for each layer
Layer Soil type Staring set number Conductivity (m/day)
1 Sand B2 0,1252
2 Clay core B11 0,0453
3 Intermediate sand layer O3 0,1087
4 Peat B18 0,0667
5 Clay O12 0,0102
6 Peat B18 0,0667
7 Clay O12 0,0102
8 Peat B18 0,0667
9 Clay O12 0,0102
10 Pleistocene sand layer O1 0,1522

F. Calibration of the models
129
Figure F.1: Schematisation location 25
Soil scenarios
The soil schematisation is based on soil borings in the crest, slope and toe of the dike. Between
these borings the layers separations are interpolated linearly. In reality the soil composition
could differ from this schematisation. There is no way to determine this, and therefore soil
scenarios were constructed to assess the effect of variations on the model. Eight soil composition
scenarios were set up. Six of these scenarios are based on different interpretations of the soil
borings. In the scenarios the same Staring soil types were used as in the basis schematisation.
The following scenarios were constructed:
• Scenario 1: The constructed soil schematisation as described in this paragraph. This
scenario is used as a basis for the other scenarios. The layers between the borings were
linearly interpolated, and from the leftmost and rightmost borings to the model edges the
layers are assumed to be horizontal.
• Scenario 2: The intermediate sand layer is placed in direct contact to the outside water.
• Scenario 3: In scenario 1 the legger depth of the boezem was used for the bottom elevation
of the outside water. In scenario 3 the minimum depth is used instead.
• Scenario 4: In the soil boring located at the toe the intermediate sand layer cannot be
observed. In scenario 1 the thickness of this sand layer is assumed to linearly decrease
between the slope and toe, meaning the sand layer ends at the toe. However, the sand
layer could end anywhere between the two borings. In scenario 4 the sand layer is
assumed to end at about a third of the distance between the slope and the crest.
• Scenario 5: Left of the soil boring in the crest the intermediate sand layer is assumed to
continue with the same thickness towards the edge of the model, because it is unknown
where the layer ends. In scenario 5 it is assumed that the sand layer ends below the outer
toe of the dike.
• Scenario 6: The first peat layer is observed in the soil borings at the slope and the toe, but
since the soil boring at the crest ends in the intermediate sand layer the soil composition
below the sand layer is unknown. In scenario 1 it is assumed that the peat layer has the
same thickness below the crest as below the slope and continues with this thickness
towards the model edge. Scenario 6 assumes this peat layer ends at the soil boring in the
crest.
• Scenario 7: From preliminary runs of the model it became clear that the simulated
phreatic surface was too high at the slope and the toe. It appeared that a possible reason
for this was a too limited flow of the groundwater towards the inside water. In an attempt

References
130
to increase this, the peat layer below the inside water was given a greater thickness in
scenario 7. This scenario contradicts the soil boring at the toe.
• Scenario 8: In this scenario the intermediate sand layer is removed, in order to assess the
influence of this layer.
The drawings of these scenarios are included in paragraph F.3.1. During the calibration each of
these scenarios is tested, and based on this the most likely scenario will be chosen for use in
further analyses.
In Figure F.2 the constructed schematisation for location 24 is displayed. Several vertical layer
separations are used in this schematisation, which was necessary to prevent vertical staggering
of the model grid.
Figure F.2: Schematisation location 24
The top layer was cut in 5 parts, to model the cunets of the paths on the crest and the berm. For
the clay parts of this top layer Staring soil type B12 is chosen as an initial estimate, because it has
the largest permeability of the top soil types. The clay is the top soil and is therefore likely to
exhibit a soil structure, increasing the permeability. For the sand of the cunets Staring type B6 is
used.
One of the main problems in the schematisation is the core of the dike. At some point in the past
the dike was reinforced with rubble. This rubble is mixed with clay and sand, making it is difficult
to define the boundaries of the rubble layer. It can be identified in the soil borings in the crest and
in the slope. In the soil boring performed near the monitoring well in the crest, the rubble is
indicated as loamy sand, extending to a depth of 2,5 m below the surface (Delfland, 2010). Several
meters removed from this location another soil boring was performed in the crest. This soil
boring shows a rubble layer up to a depth of 4 m (Inpijn-Blokpoel, 2010). Apparently the core of
the dike is very inhomogeneous, containing rubble, sand , loam and clay. Because of this it is
difficult to assign a Staring soil type to the layer. Rubble by itself has a large conductivity, but the
conductivity is likely to be reduced due to the mixing with sand and clay. Staring type B4 is used
as an initial estimate, which corresponds to loamy sand.
The layer below the rubble core is subject to large uncertainties. The boring at the research
location shows a peat layer starting 2,5 m below the surface, but the other boring several meters
removed shows that the rubble extends to a depth of 4 m. Initially, it was assumed that the peat

131
layer below the rubble is the same layer as the peat layer found in the boring in the slope. This
would mean that the peat layer is located higher below the dike than it is next to the dike. This is
contrary to what would be expected: normally soil layers below the dike are located deeper due
to settlement. A second possibility is that the peat layer below the rubble is a separate, extra peat
layer. Whether this is truly the case cannot be verified, since the boring depth at the research
location is limited and does not show any deeper layers. For the initial schematisation the choice
is made to use the second option and model the peat as a separate layer. This separate layer also
extends below the outside water. For this layer the same peat type as for location 25 is chosen,
which is Staring B18.
Layer 2, the core of the berm, has an angled boundary with the rubble. The angle of this boundary
is considered gentle enough to model the soils as separate model layers. Staring type B11 is used
for this layer, since it is relatively close to the surface. This type has a slightly lower conductivity
than type B12 which was used for the top layer.
The clay layer 5 and the peat layer 6 are probably similar to the layers found at location 25;
therefore respectively Staring types O12 and B18 are chosen for these layers.
Layer 6 includes a section in which the peat is replaced by sand. This sand part (layer 6.2) intends
to model the sand fill of the former drainage ditch. The soil boring for the monitoring well at the
toe indicates that this sand fill has a thickness of more than a meter, which is much more than the
former depth of the ditch. This means that the peat below the ditch has settled due the weight of
the sand fill. Again, the edges of this sand fill should be sloped, but to prevent vertical staggering
the separation is modelled vertically.
For the remaining soil layers the soil borings and cone penetration test taken from a soil survey
(Inpijn-Blokpoel, 2010) are used. For the deeper layers the same soil types as for location 25 are
used. The chosen soil types and their conductivities are displayed in Table F.2.
Table F.2: Assigned Staring soil types location 25 for each layer
1.1 Clay B12 0,0537
1.2 Sand B6 1,069
1.3 Clay B12 0,0537
1.4 Sand B6 1,069
1.5 Clay B12 0,0537
2 Clay B11 0,0453
3 Rubble B4 0,2922
4 Peat B18 0,0667
5 Clay O12 0,0102
6.1 Peat B18 0,0667
6.2 Sand fill of drainage ditch O3 0,1087
6.3 Peat hinterland B18 0,0667
7 Clay O12 0,0102
8 Intermediate sand layer O3 0,1087
9 Clay O12 0,0102
10 Peat B18 0,0667
11 Clay O12 0,0102
12 Peat B18 0,0667
13 Clay O12 0,0102

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Soil scenarios
Similar to location 25, a number of soil scenarios was constructed for location 24. In the scenarios
for which new layers were added to the basis schematisation, the same Staring soil types were
used as in the basis schematisation.
• Scenario 1: The basis schematisation as displayed in figure 5.1.
• Scenario 2: As described earlier, there are some uncertainties regarding peat layer 4. In
scenario 2 this peat layer is removed and instead the rubble core is extended to a greater
depth, which corresponds to the soil boring several meters removed from the research
location. The peat below the water is replaced by clay.
• Scenario 3: In soil borings close to location a second intermediate sand layer can be
observed. This sand layer does not show up in the borings at location 24, but it may have
an effect on the research cross-section. Since the model is set-up in two dimensions this
cannot be modelled. Instead a scenario including the second sand layer is added.
• Scenario 4: Apart from soil borings, stability calculations of the dike were provided by
Delfland. In the schematisations for these calculations the clay cover of the rubble core is
only included on the crest. Because it was considered unlikely that the rubble directly
borders the outside water the clay cover was extended on the outer slope in the basis
schematisation. To analyse the effect of this choice scenario 4 was added, in which the
clay cover on the outer slope is removed.
• Scenario 5: Clay layer 4 slowly pinches out towards the toe in the basis schematisation. In
the mentioned schematisation provided by Delfland the clay layer ends below the berm.
This different schematisation is included in scenario 5.
• Scenario 6: In the basis schematisation the layers 1, 2, and 4 all pinch out towards the toe
of the dike. This could lead to inaccuracies near the toe. To analyse whether this is the
case, a scenario is added in which clay layer 4 ends in a vertical separation with the sand
fill of the drainage ditch. Because this sand fill now borders two layers, the sand fill layer
and the peat layer behind it had to be split in two parts.
Drawings of these scenarios are included in paragraph F.3.2.
F.1.3 Hogedijk
The modelling of the Hogedijk is approached in a different way than the other two research cases.
Not only are measurements of the conductivity available, the composition of the soil is less
ambiguous than for the other two locations. Therefore no soil scenarios are constructed. The
constructed soil schematisation is displayed in Figure F.3.
Figure F.3: Soil schematisation Hogedijk
Layer 3, the peat layer, is divided into four parts in order to apply the measured conductivities.
For the other layers no measurements are available, and therefore Staring types used again to

133
make an estimate. According to the soil borings, the sand top layer is moderately silty, and coarse
to moderately fine. Staring type B3 fits best to this description. Below the sand and at the surface
from halfway on the slope to the toe onwards a sandy loam layer is present. This corresponds
best to Staring type B13. For the peat layer the field measurements are used. For the silty clay
layer below the peat Staring type O11 is chosen, which is light clay. Below the clay is another peat
layer, which is rich in clay. Staring type O16 is assigned to this layer. For the Pleistocene sand
layer type O1 is used, which is the same as for the research cases in Delfland.
The assigned conductivities are summarised in Table F.3.
Table F.3: Assigned conductivity values for each soil layer Hogedijk
1 Sand B3 0,1542
2 Loam B13 0,1298
3.1 Peat (Measured) 0,004
4 Clay O11 0,1379
5 Peat O16 0,0107
F.2 Calibration
The calibration process was performed in two steps: first the models were calibrated using a
steady-state simulation to match the average position of the phreatic surface, and then the models
were calibrated in a transient simulation to calibrate the response to precipitation and
evapotranspiration.
Using the initially assumed soil composition and a steady state calculation was performed, for
which the resulting heads are displayed in Figure F.4. The heads are calculated for each cell. To
visualise this , the heads are displayed as a line for each model layer. To avoid clutter, only the
heads in the topmost five layers are plotted. The monitoring wells are displayed as well, with the
filter represented by a lighter colour. Furthermore the average head of the measurements is
indicated by a white bar for each monitoring well. The average of the monitoring well in the
intermediate sand layer is displayed as a yellow bar to the left of the monitoring well in the crest.
When comparing the heads to the average of the measurements it becomes clear that the
calculated head near the crest correspond quite well to the measurements, but the heads near the
slope and the toe deviate considerably. At these points the phreatic surface is so high that it exits
at the slope, meaning seepage occurs. In the deeper layers the head is even higher than the ground
surface.
Several attempts have been made to calibrate the model using this soil composition, but no set of
hydraulic conductivities could be found for which the model matched all three measurement
points. The cause of this lies with the subsoil, especially the topmost peat layer and the clay layer
below it. As is visible in Figure F.4, the head in these layers varies linearly from a high level below
the outside water to a lower level below the inside water. The monitoring wells at the toe and
slope are placed in these layers, and show that the heads at those points are close to the inside
water level. This means the linear variation as shown in the model is not correct. Changing the
conductivity of these layers has no influence on the heads: the heads at the boundaries of the
layers are constant, and therefore the conductivity has no influence on the variation of the heads

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over the width of the layer; it only influences the flow rate through the layer. Therefore it must
be concluded that the conductivity of these layers varies along the width of the dike.
Figure F.4: Steady-state results location 25
A physical explanation for this could be that in the subsoil below the dike settlement has taken
place due to the weight. The settled soil below the dike is more compacted than adjacent to the
dike, meaning the conductivity is lower.
To include this difference in conductivity, layers 4 and 5 are divided in two parts, with the
separation near the monitoring well in the slope. For the peat below the dike Staring type O17 is
applied, and for the clay below the dike Staring type O12 is used, which is the same as the initially
assumed type. The clay adjacent to the dike is changed to Staring type O11. These soil types are
chosen such that the conductivity below the dike is lower than adjacent to the dike.
Using this updated schematisation another steady-state simulation was performed. The results
are shown in Figure F.5. The differences compared to the first simulation are not directly obvious.
Upon closer inspection it can be seen that the heads show a kink at the slope, resulting in lower
heads. There is still some deviation from the measurements, but it is expected that this can be
solved by tweaking the conductivities below the dike and the berm.
Figure F.5: Steady-state results location 25 after splitting the subsoil layers

135
Calibration steady state
Earlier, several soil scenarios have been set up. These scenarios initially did not contain the layer
separation of layers 4 and 5, and were therefore altered to include this separation. A steady state
calculation was performed for each scenario, and the difference between the calculated and the
average of the measured heads was taken to compare the scenarios.
From this analysis it was observed that the difference between model and measurements is quite
large at the slope and the toe for all scenarios. This indicates that the conductivities of the subsoil
layers have to be adjusted. The difference between the different scenarios was small. At the slope
and at the toe the simulated heads are close to or on the ground surface, which means seepage
occurs. These heads therefore cannot rise higher than a certain height that is reached for all
scenarios. Since the heads are too high for all scenarios, a good comparison between the scenarios
is not possible for the used set of conductivities.
Since no optimum scenario could be identified, the model was calibrated for scenario 1. The
conductivities in the various layers were variated until an optimum was found. This was done for
each layer individually, which means this optimum does not necessarily yield the best possible
result for the entire model. Therefore the process was repeated several times: after a conductivity
was adjusted, the other layers were variated again. It was not possible to exactly fit the model to
the average of all of the measurements simultaneously. Therefore values were chosen such that
on average the difference was minimised. Using these values, the different scenarios were
analysed again. In Figure F.6 the difference between the model results and the measurements are
displayed for each scenario.
Figure F.6: Differences between model results and measurements using calibrated conductivities
The differences between the scenarios have become larger. The large differences for the
intermediate sand layer stand out. However, it should be noted that the monitoring well in this
layer was not specifically set up to measure the head in the sand layer; the filter also extended
into the clay core of the dike. In the model, the heads in the clay core are higher than in the sand
layer, which means that if the model is correct, the monitoring well would indicate the head in
the clay core rather than the head in the sand layer. It is therefore best to base the choice for a
scenario on the three other measurements.
Observing the total differences for each scenario, it appears that the scenarios 2 and 4 yield the
best results, but for different reasons: scenario 2 minimises the difference for the crest and the
sand layer, while scenario 4 minimises the difference for the slope and toe. Both scenarios involve
changes in the intermediate sand layer: scenario 2 directly connects the sand layer to the outside
water, while in scenario 4 the sand layer extends less far below the dike. Due to these differences
it is expected that a combination of the two scenarios leads to an even better fit of the model. This
combined scenario (scenario 9) is also included in Figure F.6. This scenario indeed further

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minimises the difference between the model and the measurements. Since scenario 9 does not
contradict the available soil information, this scenario will be used for further analyses.
The conductivity values have been calibrated for scenario 1, which means that these values are
not necessarily the best values for scenario 9 as well. Therefore the model was calibrated again.
For most of the layers no better values could be found than those from the first calibration, except
for the clay core for which a conductivity of 0,02 m/day yielded the best results. Since the
deviation for the three relevant monitoring wells is less than 10 cm no further calibration will be
done for the steady-state simulation. The calibrated conductivity values, along with the initially
assumed conductivities based on the Staring set, are displayed in Table F.4.
Table F.4: Original and calibrated conductivities Delfland location 25
Layer Soil type
Initially assumed
conductivity (m/day)
Conductivity after
calibration (m/day)
Anisotropy ratio
after calibration
1 Sand 0,1252 0,5 0,66
2 Clay 0,0453 0,02 2
3 Sand 0,1087 0,10 0,66
4.1 Peat dike 0,0293 0,01 0,01
4.2
Peat
berm
0,0667 0,80 0,1
5.1 Clay dike 0,0102 0,005 0,33
5.2
Clay
berm
0,1379 0,02 0,33
6 Peat 0,0667 0,01 0,1
7 Clay 0,0102 0,01 0,33
8 Peat 0,0667 0,01 0,1
9 Clay 0,0102 0,01 0,33
10 Sand 0,1522 0,15 1
For the deeper layers the difference between the original and calibrated values are relatively
small. The main differences are found for layers 2, 4 and 5; the conductivity for layer 2 is much
smaller than the assumed value, whereas the conductivity for layers 4 and 5 is an order of
magnitude higher. The conductivities for layers 4 and 5 are within the range of the Staring set,
but the conductivity of layer 2 is about 10 times smaller than the lowest value for clay in the
Staring set (B10). In Figure F.7 the results of a steady state simulation using these values are
displayed.

137
Figure F.7: Delfland location 25, results steady state simulation using calibrated values
Intermediate sand layer
In Figure F.7 it can be seen that the heads make a sharp bend at the division between the soil
below the dike and below the berm. The explanation for this is found in the conductivity values.
Peat layer 4.2 has a very large conductivity: 80 times larger than part 4.1, which is the same layer,
and 8 times larger than the intermediate sand layer. This calibration is therefore not realistic. The
conductivities may fall within the range of possibility for the soil types, but the relative values are
not realistic. Since the conductivity is the only defining characteristic of a soil type in this model,
these conductivities basically imply that layer 3 is peat instead of sand, and that layer 4.2 is a sand
layer instead.
Attempts were made to calibrate the model such that the intermediate sand layer has a larger
conductivity than the peat layer, but no satisfactory result were obtained. The same was true for
the other scenarios, even if the intermediate sand layer was not directly connected to the outside
water. The measurement from the middle monitoring well could only be matched when peat layer
4.2 had a larger conductivity than the intermediate sand layer.
There appears to be a contradiction between the soil borings and the measurements. The soil
borings show that the sand layer is present below the crest, but not below the toe. On the other
hand, the measurements in the slope and the toe are very close, while the difference between the
slope and the crest is large. This implies that the conductivity between the toe and slope is large,
while the conductivity between the slope and the crest is small. This points towards a sand layer
that extends from below the slope towards the polder.
More information regarding this sand layer was found in a report provided by Delfland, regarding
a safety assessment of the Duifkade, the flood defence location 25 is on (Tauw, 2009). For the
cross-sections along the flood defence, an assessment was made of the locations the sand layer
was present. This assessment is displayed in Table F.5. This was based on soil borings different
than those executed for the monitoring well research. Cross-section 4.1.36 corresponds to
location 25.
Table F.5: Locations along the Duifkade where the intermediate sand layer is present. o: sand layer present,
x: sand layer not present. Source: Tauw (2009)
Cross-section Crest Slope Toe
4.1.32 o x o
4.1.33 x o o
4.1.34 o o
4.1.35 x o
4.1.36a x x
4.1.36 x x o
4.1.36b o o
4.1.37 x o
4.1.38 o o
According to the report, the sand layer below location 25 is only present below the toe, which
contradicts the soil borings from the monitoring wells. Extra borings were performed 50 m to the
south and to the north of location 25 (4.1.36a and 4.1.36b). The borings to the north show a sand
layer present below the crest and the toe, while the borings to the south show no sand layer at
all. In the other cross-sections the presence of the sand layer varies as well. This information
therefore provides no clarity whether the sand layer at location 25 can be present below the toe.
On the other hand, it does show that there is a large variation in the longitudinal direction of the

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flood defence. This could lead to flow in the longitudinal, which is not simulated since the model
is two dimensional.
Summarising, two possible causes can be identified for the contradiction between the model
calibration and the soil borings:
• Information uncertainty regarding the soil composition: available soil borings are in
contradiction to each other, and provide no information for locations between the two
borings.
• Flow in the longitudinal direction occurs in the sand layer, which cannot be modelled
using the two-dimensional model.
Eventually the choice was made to use a model with the intermediate sand layer below the toe.
This was the only soil composition for which the measurements could be matched, and for which
the conductivities had realistic values. Another soil composition was tested in which the sand
layer extended from the polder to below the crest without being in contact with the boezem, but
this resulted in a head that was too low at the crest. The position of the sand layer can be
considered a simplification of the variation in longitudinal direction, which is not modelled. This
soil composition including the heads after steady-state calibration is displayed in Figure F.8.
Figure F.8: Delfland location 25, results calibrated steady state simulation using the adjusted soil
schematisation
The intermediate sand layer below the crest was replaced by clay. To make room for the new sand
layer, peat layer 5 was shifted downwards at the expense of clay layer 6. The geometry of the
other layers has not been changed.
Calibration transient
Conductivity
First the simulation was run using the values from the steady-state calibration. On average, the
simulated heads matched the measured heads quite well. However, the magnitude of the
fluctuations due to precipitation in the simulation is too small for the toe and slope, and too large
for the crest. Variation of the conductivities shows that a larger conductivity of the clay core leads
to more pronounced peaks of the heads in the slope and toe. However, this larger conductivity
also leads to a higher average level of the heads. This probably cannot be solved by varying the
other conductivities, since the used values are the optimum values from the steady-state
calibration. However, when only the vertical conductivity is changed, the magnitude of the
fluctuations increases without raising the average heads. Changing the vertical conductivity is

139
done by changing the anisotropy ratio of the soil type. To obtain fluctuations close to what is
observed in the measurements an anisotropy ratio larger than 1 is required, meaning the vertical
conductivity is larger than the horizontal conductivity. This is uncommon, in most soils the
opposite is the case. However, De Loor (2018) also uses a larger vertical than horizontal
conductivity for the top part of clay layers in his research. The explanation for this is that the
cracks and pores in the clay mainly enlarge the vertical conductivity.
Increasing the conductivity of the topmost sand layer also has a positive effect on the fluctuation
of the heads. This conductivity has a small influence on the steady-state simulation, and was
therefore assumed to be 0,50 m/day, based on the Staring set. This conductivity is changed to 3,5
m/day.
Specific yield
The specific yield only influences the partially submerged layers, which are in this case the sand
top layer and the clay core. For the clay core a change in the specific yield has a small influence.
The assumed value of 0,03 is relatively low and leaves small room for variation. Decreasing the
value to 0,015 has no significant effect on the peaks of the heads. Increasing the specific yield has
a negative effect on the size of the peaks. Because of its small influence, the specific yield of the
clay core is not changed.
For the sand top layer the effect of the specific yield is more prominent. Lowering the assumed
value of 0,23 again results in a larger response of the heads to precipitation. A value of 0,05 results
in the best approximation of the peaks in the model.
Recharge parameters
The initially assumed recharge parameters resulted in a reasonably well-fitting model. Only slight
adjustments were made to the assumed values. The difference between the largest peaks was too
small, and therefore the recharge capacity was increased. In general this resulted in more
differentiation between the larger peaks, but there were also peaks that actually decreased when
increasing the recharge capacity. The influence of the phreatic surface at the start of a
precipitation event can result in expected reactions in the model. A recharge capacity of 15 mm/h
resulted in the best approximation for most peaks. The recharge threshold was decreased to 0,1,
because this resulted in a slightly better fit of the smallest peaks. This means there is no actually
no threshold, since the precipitation data is supplied with an accuracy of 0,1 mm. The section
multipliers had a very small influence on the model, and were not changed from the original value.
The cause for this small influence is probably that the top sand layer, which has relatively large
conductivity compared to the clay below, redistributes the recharge over the cross-section. The
overall multiplier was decreased to 0,85, since overall the peaks were slightly too high. In Table
F.6 the original and the calibrated recharge parameters are summarised.
Table F.6: Recharge parameters location 25
Parameter Original value Calibrated value
Rcap 5 mm/h 15 mm/h
Rmin 0,2 mm/h 0,1 mm/h
m1 0,5 0,5
m2 0,7 0,7
m3 0,5 0,5
m4 1 1
mtot 1 0,85

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The soil parameters resulting from the calibration are displayed in Table F.7.
Table F.7: Calibrated parameters Delfland location 25
Layer Soil type Conductivity (m/day) Anisotropy ratio Specific yield (-)
1 Sand 3,5 0,66 0,05
2 Clay 0,015 2,5 0,02
3 Sand 3,5 0,66 0,23
4 Clay 0,003 0,33 0,03
5.1 Peat dike 0,008 0,01 0,03
5.2 Peat berm 0,06 0,5 0,03
6.1 Clay dike 0,007 0,1 0,03
6.2 Clay berm 0,005 0,66 0,03
7 Peat 0,1 0,3 0,03
8 Clay 0,01 0,1 0,03
9 Peat 0,005 0,02 0,03
10 Clay 0,005 0,1 0,03
11 Sand 0,15 1 0,23
Based on the experiences with location 25 the earlier soil schematisation of location 24 was
adjusted. The clay layer and the peat layer below it are divided in two parts: below the dike and
below the berm. The soil below the berm is probably less compacted and therefore has a higher
conductivity than the soil below the dike. Staring types O12 and O13 are used for the clay below
the dike and berm respectively, and for the peat the types O16 and B18. The other soil types and
the boundary conditions were applied to the model as described in chapter 5 . The results of the
steady-state simulation using these input parameters are displayed in Figure F.9.
Figure F.9: Steady-state results location 24
From these results it stands out that the heads nearly horizontal over the rubble core of the dike,
and only start to significantly decline in the clay berm. This is also observed in the measurements:
the average head in the slope is almost as high as the average head in the crest. However, the
simulated heads are about 20 cm higher than the measured values. Furthermore, the phreatic

141
surface exits the ground surface near the toe, and the simulated head in the sand fill of the
drainage ditch does not correspond to the measurements.
Calibration steady state
The fit of the model to the measurement in the steady state simulation is evaluated in the same
way as for location 25. The difference between the model and the measurements at the locations
of the monitoring wells is calculated for each scenario. For the model result at the crest and slope
the head in the rubble core (layer 3) is used. The filter of the monitoring well in the slope is mostly
located in clay layer 5.2, but a small part extends into the rubble core. Since the heads in the rubble
are much higher than in the clay, and the measurements show that the head is in fact relatively
high, the choice is made to use the head in the rubble. For the head in the monitoring well near
the sand fill the clay layer 7 is used. This monitoring well does not provide any information
regarding the phreatic surface in the dike, but still provides useful information regarding the
groundwater table in the polder.
The results of this analysis are displayed in Figure F.10.
Figure F.10: Difference between steady-state model results and measurements for 7 soil scenarios
In this analysis scenario 2 yields the best results. Compared to scenario 1, the heads in the rubble
core are higher because the soil below the outside water has a higher conductivity. However, it
should be noted that the same result could be reached by using a lower conductivity for the clay
cover. Scenario 3, which contains a second intermediate sand layer, gives slightly better results
than the basis scenario. This is probably also caused by the lowering of the heads in the rubble
core. Scenario 4, which excludes the clay cover, unsurprisingly shows unrealistically high heads
in the core. Therefore it can be concluded that a clay cover must be present, even though no
evidence was available for this at the moment of calibration. A later visual inspection has
confirmed this. Scenarios 5 concerns small changes in the geometry based on schematisations
provided by Delfland. It gives a slightly larger deviation compared to the measurements than
scenario 1, and it is therefore not considered in further analyses. Scenario 6 was aimed at
improving the model grid near the toe of the dike, since at this point three of the soil layers
pinched out. However, the difference compared to scenario 1 are small. Near the toe a small
difference can be observed in the heads compared to scenario 1. Therefore it is concluded that
the pinching out of the three layers has a negligible effect on the results.
Even though the results found in scenario 2 showed a slightly better fit to the measurements,
scenario 1 was chosen for the soil schematisation used for the further analyses. By changing the

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conductivity of the clay cover, similar results to scenario 2 could be reached. The difference
between the scenarios was therefore too small to prefer one over the other based on the model
results. Scenario 1 is based on soil borings directly at the measurement location, whereas
scenario 2 is based on soil borings further away. Scenario 1 is therefore preferable, and is used in
the further calibration.
The steady-state calibration process was started by matching the measurements at the
monitoring well near the sand-filled drainage ditch. This was mainly done by varying the
conductance of the general head boundary package. Increasing this conductance results in more
flow from the sand layer to the boundary condition, which results in a lower head and a smaller
head rise due to precipitation. However, the model could not be fitted well to the measurements
due to the high head in the lower soil layers. The monitoring well was placed in clay layer 7 and
this layer showed a higher head in the model than the sand layer above it, as can be observed in
Figure F.9. The cause of this is the influence of the head in the Pleistocene sand layer, which is
about 2 m higher than the polder water level. This means a head decline must occur from the sand
layer head towards the polder water level. The conductivities of the lower soil layers were such
that this resulted in heads that were too high in the layers closer to the surface. This was solved
by changing the conductivities of the deeper layers; the conductivity of the deepest clay layer was
decreased and the conductivity of the higher layers was slightly increased. The results of this
change was that the largest part of the decline of the heads over the depth occurred in the deeper
soil layers, resulting in a lower head near the surface. After this change the conductance of the
boundary could be changed such that a relatively good fit of the measurements could be reached.
Next, the heads at the other two monitoring wells were calibrated. Merely reducing the
conductivity of the clay cover at the outside water (layer 1.1) to 0,02 m/day was sufficient to
match the measurements. However, even when no recharge was applied to the model seepage
occurred. Under normal circumstances it is not desirable for a dike to show seepage at the toe, so
it is assumed that this does not occur in reality. Therefore an attempt was made to calibrate the
model such that no seepage occurs, but without contradicting the measurements. Changing the
conductivity of the clay berm, clay layer 5, and peat layer 6 yielded the desired results, which are
displayed in Figure F.11. The conductivities resulting from the calibration are displayed in Table
F.8.
Figure F.11: Delfland location 24, results steady state simulation using calibrated values

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Table F.8: Original and calibrated conductivities Delfland location 25
Layer Soil type
Estimated conductivity
(m/day)
Steady state calibrated
1.1 Clay 0,0537 0,012
1.2 Sand 1,069 1,0
1.3 Clay 0,0537 0,1
1.4 Sand 1,069 1,0
1.5 Clay 0,0537 0,1
2 Clay 0,0453 0,02
3 Rubble 0,2922 0,3
4 Peat 0,0667 0,05
5.1 Clay below dike 0,0102 0,02
5.2 Clay below berm 0,0437 0,04
6.1 Peat below dike 0,0446 0,1
6.2 Peat below berm 0,0667 0,1
6.3 Sand fill of drainage ditch 0,1087 1,0
6.4 Peat hinterland 0,0667 0,1
7 Clay 0,0102 0,03
8 Intermediate sand layer 0,1087 0,11
9 Clay 0,0102 0,03
10 Peat 0,0667 0,05
11 Clay 0,0102 0,005
12 Peat 0,0667 0,05
13 Clay 0,0102 0,005
14 Pleistocene sand layer 0,1522 1,0
Calibration transient
Performing a transient simulation using the values from the steady-state calibrated showed that
on average the measurements are matched relatively well. The magnitude of the fluctuations due
to precipitation at the crest and slope is approximately the same as in the measurements. At the
sand filled drainage ditch the simulated fluctuations are much smaller than in the measurements.
When observing longer term variations, it appears that the applied evapotranspiration rate is too
high. The simulated head in the slope is too high in the winter months and too low in the summer
months. This might be a result of the road on the berm and the footpath of the crest. These may
locally reduce or even prevent the occurrence of evapotranspiration. To model this the
evapotranspiration rate was set to zero for the locations of the footpath and the road. This gave a
better result, but the evapotranspiration influence was still too large. Therefore the
evapotranspiration multiplier was reduced to 0,5.
Similar to location 25, the vertical conductivity of the clay top layer was increased to increase the
magnitude of the head fluctuations due to precipitation. The anisotropy ratio was set to 2. This
was only done for the parts to which precipitation is applied, for the part of the top layer
bordering the outside water the conductivity was actually decreased slightly. Furthermore, the
conductivity of the peat in the hinterland was increased, which lead to more flow towards the
sand fill. In this way the magnitude of the head fluctuations in this sand was increased, which
matches the measurements better. The specific yield of the rubble core, the clay of the berm, and
of the sand fill in the drainage ditch were decreased, also to increase the magnitude of the head
fluctuations.
Several changes were made in the recharge parameters. The section multipliers had a more
noticeable influence for this model than for the model of location 25. These multipliers were

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slightly adjusted to increase the precipitation peaks near the toe. Like location 25, the recharge
threshold was set to 0,1 mm/h to obtain more detail in the smallest peaks. The recharge capacity
was kept at 5 mm/h; increasing the value did not lead to a better fit of the model. Finally, the
overall multiplier was decreased to 0,9 to fit the peaks better.
Table F.9: Changes in recharge parameters location 24
Parameter Initial value Calibrated value
Rcap 5 mm/h 5 mm/h
Rmin 0,2 mm/h 0,1 mm/h
m1 0,5 0,5
m2 2 1,5
m3 0,5 0,5
m4 2 1,5
m5 0,5 0,5
m6 0,7 0,8
mtot 1 0,9
The soil parameters resulting from the transient calibration are displayed in Table F.10.
Table F.10: Transient calibrated conductivities Delfland location 24
Layer Soil type
Transient calibrated
Hydraulic
anisotropy ratio (-
)
Specific
yield (-)
1.1 Clay 0,012 0,33 0,03
1.2 Sand 1,0 0,66 0,23
1.3 Clay 0,1 2 0,03
1.4 Sand 1,0 0,66 0,23
1.5 Clay 0,1 2 0,03
2 Clay 0,02 0,5 0,03
3 Rubble 0,3 0,66 0,06
4 Peat 0,05 0,1 0,44
5.1 Clay below dike 0,02 0,33 0,03
5.2 Clay below berm 0,04 0,33 0,03
6.1 Peat below dike 0,1 0,1 0,44
6.2 Peat below berm 0,1 0,1 0,44
6.3
Sand fill of
drainage ditch
1,0 0,66 0,1
6.4 Peat hinterland 0,2 0,1 0,44
7 Clay 0,01 0,33 0,03
8
Intermediate sand
layer
0,11 0,66 0,23
9 Clay 0,01 0,33 0,03
10 Peat 0,05 0,1 0,44
11 Clay 0,005 0,33 0,03
12 Peat 0,05 0,1 0,44
13 Clay 0,005 0,33 0,03
14
Pleistocene sand
layer
1,0 0,66 0,23

145
F.2.3 Hogedijk
Since the measurement period was too short to calibrate the model to the average of the
measurements, the model for the Hogedijk was calibrated in a transient simulation directly. The
initial condition of this simulation was still calculated using a steady state simulation, with the
assumed average recharge rate of 525 mm/year. To include the influence of the dry summer
months, the starting date of the transient simulation was set at 01-01-2018.
In Figure F.12 the results of the transient simulation using the initially assigned values are
displayed. Only the part of the simulation for which measurements are available is displayed.
Figure F.12: Model results Hogedijk using initial uncalibrated values
It appears that the simulated heads for monitoring wells 1, 2, and 3 are too low, whereas for
monitoring well 4 the head is too high. However, when looking at the heads of monitoring well 4
something strange can be observed: the head is almost continuously lower than the polder water
level, except for one peak caused by a precipitation event, The polder water level appears to be
correct, so possibly something is wrong with the measurements. Therefore the calibration was
mostly aimed at matching the model to the other three measurement points.
Even considering the low measured values for monitoring well 4, the head at this point in the
simulation is still quite high. Based on the experiences with the preceding models, a possible
solution could be to adjust the conductivities of the deeper soil layers, to diminish the influence
of the head in the Pleistocene sand layer. This head is between the inside and outside water level,
and thus lowers the phreatic surface in the crest and upper slope, while it raises the phreatic
surface at the lower slope and the toe of the dike. This change had some effect: heads 2 and 3
became higher and thus closer to the measurements, but head 1, while also becoming higher, did
not reach the level of the measurements. The effect on head 4 was small.
Another change that was made was the extinction depth of the evapotranspiration package. This
depth was set at 2 m, resulting in a low phreatic surface due to the dry summer months. By

References
146
changing this depth to 1 m, the phreatic surface became higher in this period and in the
measurement period. However, it is unknown whether this change is correct. It is unknown how
low the phreatic surface was during june and july 2018, and therefore it is unknown whether the
model is more correct using and extinction depth of 1 or 2 m. Using 1 m results in a better fit for
the measurement period, but might not result in as good a fit for later measurements.
Since changing the conductivities of the deeper layers did not result in a good enough fit of the
model, the conductivity of the peat layer has to be changed. Initially it was tried to keep the
horizontal conductivity constant on the measured values, while changing the anisotropy ratio and
thus the vertical conductivity. This had some effect, but still nog head could be reached at point 1
that approached the measured value. Lowering the horizontal conductivity of part 1 of the peat
layer resulted in a higher head, but this always raised the head at monitoring well 2.
This problem is probably a result of the chosen division of the peat layer, with divisions in the
middle between the monitoring wells. Disregarding precipitation, evapotranspiration and the
influence of the deeper soil layer, the head gradient in each part of the peat layer is approximately
linear. Calibrating one of these parts to a monitoring well means that the head in the middle of
the part is correct, but might be unrealistic near the separation. For example, lowering the
conductivity in part 1 to match the monitoring well results in a head close to the surface at the
layer separation.
There are two possible solutions for this:
• Place the layer separations at the monitoring wells. Between the wells the soil then
becomes homogeneous, resulting in a more linear course of the phreatic surface. A
disadvantage is that the separations are placed at the point where the head is evaluated,
meaning inaccuracies caused by the layer separation influence the model results.
• Varying the conductivities between the monitoring wells. This will result in a smoother
phreatic surface because the change in conductivity over the width is more gradual.
The choice was made to use the second option. The conductivity between the monitoring wells
was interpolated linearly. Using the measured values for the conductivity this resulted in a
reasonably good fit of monitoring wells 2 and 3, but still the measurements of monitoring well 1
were not matched. Changing the conductivity such that monitoring well 1 was matched resulted
in a deviation from monitoring wells 2 and 3. This could only be solved by making another cut in
the peat layer in the crest. The new section in the peat layer between the outside water and this
cut was assigned a higher conductivity, and in this way monitoring well 1 could be matched as
well. This higher conductivity zone could be present in reality as well, since this zone is located
below the road on the crest. Sand and rubble from the road cunet could result in a higher
conductivity.
After this modification the general height of the phreatic surface was in accordance to the
measurements, but the shape and magnitude of the precipitation peaks was not. One of the
parameters that was of influence for this was the conductivity of layer 2, the loam top layer.
Assigning this layer a lower conductivity resulted in higher peaks near the crest. This is contrary
to the observations made in the other two models: a larger (vertical) conductivity of the top layer
resulted in higher peaks. The explanation for this is seepage. During precipitation events seepage
occurs near the toe through the loam layer, so a low conductivity of this layer provides more
resistance to seepage. Since the water cannot flow away as easily, the head ‘upstream’ in the
cross-section will rise more. Since the loam layer does not extend fully towards the crest, the
lower conductivity has no influence on the resistance to recharge in the crest.
A strange phenomenon that could not be modelled properly was the difference in reaction
between monitoring wells 2 and 3. In the measurements, monitoring well 2 shows a damped
response to precipitation, whereas monitoring well 3 shows a much more peaked response. This
is strange, since these wells are located close to each other, and both are placed in the slope of the

147
dike. In the model this different response could not be reached. It was possible to approximately
match the damped response or the peaked response for both points simultaneously, but not for
each point individually. Changing recharge multipliers slightly increased the difference between
the two points, but not enough to match the measurements.
Eventually the model was calibrated by changing the specific yields such that both monitoring
wells 2 and 3 are matched approximately. At neither location the peaks could be matched exactly.
The fast, almost direct response of monitoring well 3 to the precipitation event in early September
could not be modelled. The model responds more slowly, and reaches the peak after a few days.
The height of the peak could be matched, but if this was done the phreatic surface remained too
high for weeks after the precipitation. The choice was made to calibrate so that the model result
is close to the measurements most of the time, even though the peak height is not matched.
The result of this calibration is displayed in Figure F.13.
Figure F.13: Calibration Hogedijk
It can be observed that excepting the peaks, the model fits the measurements of monitoring wells
1,2, and 3 quite well. As discussed earlier, monitoring well 1 shows a gradual rise of the head and
a sudden jump back to the original level. This is probably an error in the measurements, and it
could not be reproduced in the model. For monitoring well 2 the peaks in the model are too high
compared to the measurements. It was possible to calibrate the model such that the
measurements were matched, but this resulted in a less good fit for monitoring well 3. For that
well the fit is quite good, except for the peaks: the head rises much slower. The fast response as
observed in the measurements could not be reproduced.
The calibrated parameters are displayed in Table F.11. The measured conductivities in the peat
layer did not need to be changed. Altering the conductivities of the other layers and the anisotropy
ratio and specific yield was sufficient to calibrate the model.

References
148
Table F.11: Calibrated parameters Hogedijk
Layer Soil type Conductivity (m/day)
Anisotropy
ratio (-)
Specific yield (-)
1.1 Top layer 2,5 2 0,1
1.2
Rubble/sand from
road
2,5 2 0,1
2 Loam 1 3 0,01
3.0 Peat 0,012 0,2 0,05
3.1 Peat 0,004 0,2 0,05
3.2 Peat 0,01 0,3 0,05
3.3 Peat 0,005 0,2 0,006
3.4 Peat 0,04 0,2 0,05
4 Clay 0,001 0,2 0,01
5 Peat 0,002 0,01 0,03
6 Pleistocene sand layer 10 0,66 0,23

149
F.3 Scenarios

References
150

G. Model results
151
G Model results
G.1 Calibrated models

References
154
G.2 Uncalibrated models
G.2.1 Parameters
Table G.1: Parameters for the uncalibrated model of location 25
Layer Soil type
Staring
type
Conductivity
(m/day)
Anisotropy
ratio (-)
Specific yield (-)
1 Sand B2 0,1252 0,66 0,23
2 Clay B11 0,0453 0,33 0,03
3 Sand O3 0,1087 0,66 0,23
4 Clay B10 0,0070 0,33 0,03
5.1 Peat dike O17 0,0102 0,1 0,44
5.2 Peat berm B18 0,0667 0,1 0,44
6.1 Clay dike O12 0,0102 0,33 0,03
6.2 Clay berm O11 0,0667 0,33 0,03
7 Peat B18 0,0667 0,1 0,44
8 Clay O12 0,0102 0,33 0,03
9 Peat B18 0,0667 0,1 0,44
10 Clay O12 0,0102 0,33 0,03
11 Sand O1 0,1522 0,66 0,23
Table G.2: Parameters for the uncalibrated model of location 24
Layer Soil type
Staring
type
Conductivity
(m/day)
Anisotropy
ratio (-)
Specific
yield (-)
1.1 Clay B12 0,0537 0,33 0,03
1.2 Sand B6 1,069 0,66 0,23
1.3 Clay B12 0,0537 0,33 0,03
1.4 Sand B6 1,069 0,66 0,23
1.5 Clay B12 0,0537 0,33 0,03
2 Clay B11 0,0453 0,33 0,03
3 Rubble B4 0,2922 0,66 0,23
4 Peat O16 0,0107 0,1 0,44
5.1 Clay O12 0,0102 0,33 0,03
5.2 Clay O13 0,0437 0,33 0,03
6.1 Peat O16 0,0107 0,1 0,44
6.2 Peat B18 0,0667 0,1 0,44
6.3
Sand fill of
drainage ditch
O3 0,1087 0,66 0,23
6.4 Peat hinterland B18 0,0667 0,1 0,44
7 Clay O12 0,0102 0,33 0,03
8
Intermediate sand
layer
O3 0,1087 0,66 0,23
9 Clay O12 0,0102 0,33 0,03
10 Peat B18 0,0667 0,1 0,44
11 Clay O12 0,0102 0,33 0,03
12 Peat B18 0,0667 0,1 0,44
13 Clay O12 0,0102 0,33 0,03
14
Pleistocene sand
layer
O1 0,1522 0,66 0,23

G. Model results
155
Table G.3: Parameters for the uncalibrated model of the Hogedijk
Layer Soil type
Staring
type
Conductivity
(m/day)
Anisotropy
ratio (-)
Specific yield (-)
1 Sand B3 0,1542 0,66 0,23
2 Loam B13 0,1298 0,33 0,03
3.1 Peat B18 0,0667 0,1 0,44
3.2 Peat B18 0,0667 0,1 0,44
3.3 Peat B18 0,0667 0,1 0,44
3.4 Peat B18 0,0667 0,1 0,44
4 Clay O11 0,1379 0,33 0,03
5 Peat O16 0,0107 0,1 0,44
6
Pleistocene
sand layer
O1 0,1522 0,66 0,23
G.2.2 Results
Figure G.1: Heads calibrated and uncalibrated model location 25

References
156
Figure G.2: Heads calibrated and uncalibrated model location 24
Figure G.3: Heads calibrated and uncalibrated model Hogedijk

G. Model results
157
G.2.3 Highest and lowest simulated phreatic surfaces
Figure G.4: Highest and lowest phreatic surface for the uncalibrated model (in blue) and the calibrated
model (in red) of location 25.
model (in red) of location 25.

References
158
model (in red) of location Hogedijk

H. Extreme events
159
H Extreme events
H.1 Delfland 25 (Duifkade)

H. Extreme events
161
H.2 Delfland 24 (Vlaardingsekade)

H. Extreme events
163
H.3 Hogedijk

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