The impact of the diameter to height ratio on the compressibility parameters of saturated fine grained soils

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 04 Issue: 06 | June-2015, Available @ http://www.ijret.org 8
THE IMPACT OF THE DIAMETER TO HEIGHT RATIO ON THE
COMPRESSIBILITY PARAMETERS OF SATURATED FINE-GRAINED
SOILS
T. Nguedia Rosine1
, T. Toma Sabbagh2
1
Ph.D. student, Civil Engineering Research Group, The University of Salford, School of Computing, Science and
Engineering, Newton Building, Salford, Greater Manchester, M5 4WT, UK
2
Lecturer, Civil Engineering, The University of Salford, School of Computing, Science and Engineering, Newton
Building, Salford, Greater Manchester, M5 4WT, UK
Abstract
Compressibility parameters of fine-grained soils are mainly influenced by soil mineralogy, moisture content and soil diameter to
height ratio (D/H). The British and American standards suggested that to obtain accurate engineering properties; it is necessary
to use D/H ratio of 4 and 2.5 respectively to eliminate friction between the soil and the structure. In the current study, various
D/H ratios were adopted ranging from 0.5 to 11. The D/H ratios effect on some compressibility parameters such as coefficient of
consolidation (cv), compression index (cc) and coefficient of volume compressibility (mv) were analysed. Additionally, the impact
of the D/H ratio on the acquire cv values were also presented where three methods were used namely: Casagrande, Taylor and
Inflection method. The scaling effects based on cv ratio [cv (√t) / cv (log t)] from Oedometer tests using different D/H ratios are
also presented. The results showed that Taylor’s method is the most appropriate way to achieve an accurate cv and an increase in
pressure leads to a reduction in cc and a gradual decrease in mv. The validation of the experimental results on a finite element
software package PLAXIS was completed.
Keywords: Compressibility, D/H ratio, Fine-grained soil, Friction
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1. INTRODUCTION
The diameter to height (D/H) ratio criteria is used to reduce
friction between the soil and structure. The American
Standard suggested a minimum value of 2.5 with a value
greater than four most suitable [5]. While the British
Standard proposed a value of 4 with a cell diameter of
75mm and height 20mm are mostly applicable [10]. No
available data were found to validate the D/H ratio proposed
by the American Standard. Morris and Lockington [21]
conducted a self-weight consolidation test on fine-grained
marine, riverine and lacustrine soils with a diameter to
height (D/H) ratio ranging from 1.9 to 4.1. The findings
showed that the final void ratio were relatively comparable
and was due to the sample particle sizes. Morris and
Lockington neglected the effect of D/H ratio from the self-
weight consolidation test. Berry and Reid [8] stated that the
greater the soil thickness, the more likely friction will occur,
and smaller soil sample have no friction.
During conventional consolidation test, the lateral pressure
acting on the side walls of the sample container produce
frictional resistance to the compression of the sample.
Taylor [26] investigated the effect of side friction in
consolidation tests and showed that the frictional force
varies from 12-22% of the applied pressure for remoulded
clay and 10-15% for undisturbed clay. Therefore, the thinner
the sample the less side friction due to the small lateral
surface area in contact with the wall of the Oedometer
apparatus. Leonards and Girault [19] used steel Oedometer
cell and show that friction can significantly alter the result.
Thus, by applying greased Teflon, it eliminates friction
provided the D/H ratios exceed six. Sivrikaya and Togrol
[25] investigated the effect of clay thickness on secondary
compression. Sivrikaya and Togrol [25] designed a new
Oedometer cell capable to measure the frictional effect
between the specimen and the cell. The outcomes revealed
that side friction does not remain constant with time but
slightly increases at a decreased rate. Kolay and
Bhattacharya [17] conducted consolidation tests on kaolin
soil with Teflon large diameter (120mm) with a D/H ratio
six. The comparison of the results of previous tests (D/H
ratio 3) with Kolay's investigation showed that cv is affected
by the apparatus side friction and a correction factor for
different consolidation characteristics was applied. The
correction factor derived by Kolay and Bhattacharya [17]
was to reduce side friction.
The effect of D/H ratio scale was not previously investigated
on cc and mv. The importance of cc is in the direct
calculation of settlement of structures from the relationship
of pressure and void ratio. It is used as its value does not
change with a change in confining pressure for normally
consolidated clays [1, 24]. On the other hand, mv is also the
most suitable compressibility parameters for direct
settlement calculation. Its variability with confining pressure
makes it less useful when correlating with some engineering
properties [24]. Hence, cc and mv have been studied to

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obtain a relationship with some design parameters. These
parameters include internal friction angle, recompression
index (cr), moisture content, liquid limit (LL) and specific
gravity (Gs).
On the other hand, the effect of D/H ratio on some
engineering properties such as shear strength (τ), modulus of
elasticity (E) and the stress-strain relationship was
previously investigated. These design parameters were
studied using Triaxial and Oedometer tests. Dirgeliene and
Stragys [14] proposed a reduction in the standard D/H ratio
in Triaxial test from 2 to 1 to eliminate friction. While
Grisso et al. [15] showed that the D/H ratio of a Triaxial soil
sample has little effect on the compacted soil as compared to
smaller D/H ratio. On the other hand, during Triaxial testing,
it was observed that at constant cell pressure, the modulus of
elasticity decreases with an increase in the D/H ratio [18].
In the current study, the effect of D/H ratios on
compressibility parameters is presented and it effect of cv
ratio [cv (√t) / cv (log t)]. More emphasis are employed in the
different method used to obtain cv and the how much impact
the D/H ratio has on the rate of consolidation of fine-grained
soils. Numerical simulation was also carried out to model
test results, using PLAXIS, to show the compatibility of the
numerical analysis with the test. During numerical
modelling, the Mohr-Coulomb (MC) model that is probably
the most used in the modelling of consolidation tests was
used. This model is mostly used due to their simplicity, and
specific parameters are easily obtained.
2. EXPERIMENTAL PROCEDURE
The sample preparation and test set up as described in the
British and American standard were adopted [9, 7]. A well-
known consolidation test was carried out using the
Oedometer apparatus. This test model the one-dimensional
consolidation of subsoil when pressed by structures only in a
vertical direction (the lateral strains are considered to be
negligible). The test was run over a period of 24 hours at
certain load increments under double drainage condition
under equal strain (where a porous stone was used for
uniform strain loading). Data were obtained using a
computerised system connected to each Oedometer test with
an accuracy of ±0.1%. The system was able to read data
from six channels simultaneously.
At each D/H ratio, the initial moisture content and void ratio
were calculated from the tested fine-grained soil. The
properties of the soils used (Table 1) were obtained as per
the standard methods [4, 9, 3, 7, 6]. In order to get the
undrained shear strength (cu), the soil was compacted at a
mould 100mm diameter and the vane size of 25mm was
used. The vane was inserted at a depth of 10mm within the
compacted soil with moisture content ranging from 35% to
61% with cu of 0.28 to 12kN/m2
respectively. The
mineralogy analysis of the soil was obtained using X-ray
diffraction (XRD), and the principal clay minerals present in
the clay is shown in Table1.
Table 1: Soil Properties summary
LL PL PI Gs cu
(kN/m2
)
Mineralog
y
Kaoli
n clay
63
%
32.4
%
30.6
%
2.
6
0.28 –
12
Kaolinite
and Quartz
Where; LL = liquid limit, PL = plastic limit, PI = plasticity
index, Gs is specific gravity and cu = undrained shear
strength (kN/m2
)
2.1 Diameter to Height Scale Range
A series of Oedometer tests were conducted at different D/H
ratio as shown in Table 2. For valid comparison in the D/H
ratio, the average of the initial moisture content was
considered
Table-2: Scale range Oedometer tests
D/H 0.5 1 1.5 2 (a) 2 (b) 3 4 5 6.5 11
Diameter (mm) 100 150 250 150 250 250 100 150 150 250
Height (mm) 200 130 200 80 130 80 23 30 23 23
Test T1 T2 T3 T4 T5 T6 T7 T8 T9 T10
Initial moisture
content
91% 74% 55% 65% 55% 55% 80% 60% 59% 64%
Average
moisture content
66%
2.2 Frictionless Boundary Condition
Previous researchers have shown that in order to reduce
friction, Telfon grease is applied to the wall of the
Oedometer apparatus by D/H ratio of 6. Kolay and
Bhattacharya [17] used Telfon with kaolin soil and found
that friction has an effect on cv. Moreover due to this side
friction in the consolidation test apparatus, the vertical
pressure on any horizontal plane will decrease with sample
depth. As side friction is a function of pressure, it is
expected that the e-log p graph becomes flatter with an
increase in side friction, thereby producing a small value of
the compression index [16]. In the current study, Vaseline
was applied to the Oedometer wall to reduce friction. Figure
1 shows the e – log p curve obtained in this study that
contradicts the statement by Healy and Ramanjaneya [16]
thus side friction was eliminated in this study. The e – log p
curve in Figure 1 shows a gradual decrease in void ratio
with an increase in pressure except at D/H 0.5 and 5 where
the graph becomes flatter. Thus, taking Healy’s statement,
friction was not reduced at D/H 0.5 and5.

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Fig-1: e-log p curve at different D/H ratios
2.3 Frictional Stress
Many studies have been performed to investigate the effect
of sample thickness on both primary and secondary
compression. Testing soil sample in the laboratory with
considerable great thickness will involve friction problem.
Sivrikaya and Togrol [25] revealed that the frictional stress
does not remain constant during the test and slightly
increases with a decrease in time for soil thickness of 60mm
and diameter 75mm (D/H 1.25). Friction was found to be
most significant at low stresses where the clay soil is still
over-consolidated [25]. In the current study, the clay is term
normally consolidated, and Figure 1 shows friction was
eliminated with reference to Healy and Ramanjaneya [16]
statement. Sivrikaya and Togrol [25] derived an expression
to obtain the frictional stress (τ) as shown in equation 1.
τ =
𝑇
𝜋𝐷𝐻
(1)
Where, D is soil diameter (mm); H is soil height (mm), and
T is the load transmitted to the ring (N).
Figure 2 shows the application of equation 1 in the current
study. It was observed that at a pressure less than 150kPa,
there is no significance difference in frictional stress. The
observation was at all scales except at D/H 2(b), 6.5 and 5,
where D/H 2(b) being greatly influenced. Figure 2 is
contradictory to Sivrikaya and Togrol [25], where it is
observed that the friction stress is most significant the high
stresses for normally consolidated soils under primary
consolidation. The difference in findings is due to D/H 1.25
used by Sivrikaya [25] on overconsolidated soils and 10
D/H ratios utilised in this study on normally consolidated
soils. Hence, the present study at D/H 1 and 1.5 normally
consolidated can directly be compared with D/H 1.25 over-
consolidated which shows the difference in findings is due
to the fine-grained soil state.
Fig-2: Frictional stresses at various D/H ratios
3. RESULTS
In this section, tests arise from the laboratory model, and
numerical analyses are shown. A discussion emphasised in
the response of fine-grained soils at different D/H ratio
scale. Furthermore, its effect on compressibility parameters
is presented.
3.1 Experimental Results
3.1.1 Stress-Strain Distribution
The vertical stress distribution within the soil matrix derived
from the finite element analysis corresponding to the
maximum loading and was normalized by the applied

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pressure. Figure 3 shows a variation in strain at different
D/H ratio under 55kPa and 110kPa. It displays the
fluctuation in strain with D/H ratio observed at both
loadings. The importance of D/H ratio, as stated in the
American standard, is confirmed. At D/H ratio less than 2.5,
the curve is difficult to construe, thus provide an uncertainty
in the curve fitting procedure in obtaining the coefficient of
consolidation (cv).
a)
b)
Fig-3: Time-deformation relationship at: a) 55kPa and b) 110kPa
3.1.2 Effect of D/H Ratio Scale on cc and mv
Compressibility parameters investigated were: coefficient of
consolidation (cv), compression index (cc) and coefficient of
volume compressibility (mv). The compressibility
parameters cc and mv are important in the calculation of
settlement of structures. cc is used to determine the primary
consolidation settlement of the normally consolidated soil.
Normally consolidated soils are a type of soil whose present
effective overburden pressure is the maximum pressure that
the soil was subjected to in the past [8]. Thus, the soil in this
study can normally be termed consolidated. A high cc value
indicates greater compressibility and higher consolidation
settlements (Figure 4a). A fluctuation in cc value was
observed with D/H scale, as the load increases, cc reduces to
a value less than 0.1 as depicted in Figure 4a. At 55kPa,
there was a sharp rise in cc and mv with the maximum value
observed at D/H 0.5 and D/H 11 respectively (Figure 4b).
The lowest value is discerned at D/H 2(a & b) for cc and mv.
It does show that D/H has an influence on the magnitude of
settlement and kaolin clay compressibility with correlation
factor 0.052 and 0.090 for cc and mv respectively.

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a)
b)
Fig-4: Effect of D/H ratio on some compressibility parameters: a) cc and b) mv
Data obtained shows a gradual drop in mv with pressure at
all D/H ratios except at D/H 0.5 and 5. mv was found to
reduce at 220kPa and increase at 276kPa by 72% and 60%
respectively (Figure 4b). The findings validate that by
Retnamony et al. [22], where mv was found to decrease with
an increase in pressure for kaolinite soil except at D/H 0.5
and 5 at 220 – 276kPa. Thus, D/H scale has an effect on soil
compressibility; nevertheless, the outcome is less significant
with the overall mv value being less than 0.006 m2
/MN
exhibiting a very low compressibility.
3.1.3 Effect of D/H Ratio on the Ratio of [cv (√t) / cv
(log t)]
The values of cv were determined using Casagrande, Taylor,
and Inflection methods. Statistical analysis was carried out
using SPSS for a total of 120 cv values at various D/H ratios.
The analysis demonstrates the statistical significance of the
value of cv obtained using different methods. The outcome
showed a normality in cv values at all scale except at D/H 5.
At D/H 5, the values of cv were abnormal due to an outlier
found, which is due to the experimental curve not matching
the theoretical curve. There is no substantial difference in cv
value attained using the different method with a sizeable

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difference of 0.003. Thus, the value of cv obtained using
either test method is not significantly different. Hence,
Taylor’s method was found to be precisely more adequate to
get cv where scale is a concern (Figure 5b) [26]. As
compared to Casagrande and Inflection method, cv was
affected by the curve fitting procedure [11, 13, 20]. The
relationship in cv with pressure obtained using the three
method are depicted in Figure 5. The √t curve fitting
process was a straightforward process as the primary
consolidation part of the curve was easily identified. The
issue with the remaining methods at D/H less than 2.5
especially at D/H 0.5 was that the secondary consolidation
was not clearly observed rendering difficulty in deriving cv
from curve fitting procedure.
a)
b)

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c)
Fig-5: Applied pressure against the coefficient of consolidation (cv) obtained at a) Casagrande method, b) Taylor’s method and c)
Inflection method
Previous researcher’s showed that cv obtained using
Taylor’s method is higher than that attained using
Casagrande method and Inflection method gives quite a
similar result to that of Casagrande method [2, 12, 20, 23].
The reason being; Taylor’s method is affected by the initial
compression (leading to an increase in cv) and in some cases
secondary compression (decrease in cv value). Casagrande
and Inflection method are mostly dependent on a certain
amount of secondary compression being observed on the
strain-deformation curve. In the current study, the opposite
was found where the highest value in cv was attained using
the Inflection method, and Taylor’s method produced the
lowest value. The cause of this is due to D/H scale at a
particular scale (D/H < 2.5). Figure 6 shows the ratio of cv
√t / log t50, cv √t / log t60 and cv log t50 / cv log t60 with D/H
ratio scale. The outliers in Figure 6 are observed at D/H less
than 2.5 and are due to the experimental curve not matching
the theoretical curve. The outliers present the uncertainty in
the curve fitting process at D/H < 2.5 and the validity of the
recommended value by the standard. Therefore, D/H > 2.5 is
adopted as per the standard and values showed to be closely
packed together. Despite the outliers, the inflection and
Casagrande method was found to correlate well as deduced
by previous researchers.
a)

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b)
c)
Fig-6: cv √t / log t ratio at various D/H ratio
3.2 Numerical Simulation
Finite element analyses were implemented to validate
experimental results on the validity of D/H ratio scale on
fine-grained soils. The D/H ratio model was completed
using the Mohr-Coulomb model (MC). The finite element
model (FEM) was firstly calibrated against the experimental
data.
3.2.1 Finite Element Model
A geotechnical finite element program PLAXIS was used
for the simulation of the fully saturated fine-grained soils at
diverse D/H ratios. The one-dimensional model was
axisymmetric and discretized using 16 nodes elements. The
young’s modulus was assumed to be 1000 kN/m2
, and a
default coefficient of permeability (k) was employed in
PLAXIS with value 5.5x10-7
m/s. The boundary conditions
were set as permeable at both the top and bottom of the soil
profile with the side being impermeable. In order to achieve
comparative curve to the experimental data, the vertical load
was applied in double increments.
3.2.2 Model Calibration
In order to establish the validity of the FEM, it was first
compared with the experimental data under hydraulic
loading at different D/H ratio scale with an average initial
moisture content of 66%. Figure 7 shows the comparison
between the experimental data and FEM, which shows that
the FEM can simulate the stress-strain deformation of fine-
grained soil with good accuracy with a maximum difference
of 2%. The properties of the studied fine-grained soil used to
calibrate the model as is as shown in Table 3.

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Table-3: Fine-grained soil used in calibration of model
Scale D/H 0.5 D/H 1 D/H 1.5 D/H 2(a) D/H 2(b) D/H 3 D/H 4 D/H 5 D/H 6.5 D/H 11
e 2.53 2.49 2.43 1.88 1.97 1.20 2.09 1.50 1.65 1.61
cu 12.00 12.00 12.00 12.00 12.00 12.00 12.00 12.00 12.00 12.00
γsat 14.33 15.00 14.40 15.20 15.40 17.00 17.30 15.90 15.70 15.8
Where; e is the void ratio, cu is the undrained shear strength (kN/m2
), and γsat is the saturated unit weight (kN/m3
).
a) b)
Fig-7: Comparison between experimental and numerical model at 110kPa for D/H 1; a) normalised FEM and b) experimental
model. Where; pexcess is the excess pore pressure and |u| is the soil deformation
3.2.3 Excess Pore Pressure Distribution
Practically, during consolidation under double drainage, an
excess pore water pressure (Pexcess) is observed at the mid-
height of the soil matrix. Figure 8 shows the difference in
excess pore pressure at various D/H ratios ranging from 0.5
to 11. It clearly shows that, as the D/H increases, Pexcess
concentration in the mid-height of the soil matrix increases.
At D/H 0.5, Pexcess is observed at the top of the soil, which is
mainly due to the scale and applied pressure proportion to
the soil profile. The proportion relates to the ratio of applied
pressure to scale on a fully saturated soil. Due to the
pressure being 55kPa at D/H 0.5 under 24hours, the ratio of
the pressure on the soil profile is trivial. However, as the
pressure increase, Pexcess was observed at the bottom of the
soil. Therefore, at D/H less than 2 fluctuations in behaviour
are found as compared to D/H greater than 2. Thus, the
minor difference in the recommended standard method is
not significant as the findings still validate that stated in the
British and American standard.

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Fig-8: Excess pore water pressure distribution under double drainage at different D/H ratio scale at 55kPa: a) D/H 0.5, b) D/H 1,
c) D/H 1.5, d) D/H 2(a), e) D/H 2(b), f) D/H 3, g) D/H 4, h) D/H 5, i) D/H 6.5 and j) D/H 11
In addition, from the trends discerned in Figure 8, D/H
yielded the highest excess pore pressure with the lowest
being observed at D/H 11. However, the value of D/H 0.5
can be deemed less accurate as the trend does not
correspond to the remaining scales. The flaws in trend at
D/H 0.5 was observed experimentally where the highest cv
and cc values were noted at this magnitude. Nevertheless,
D/H 1 and 2 (a&b) showed to produce adequate results that
are relatively comparable to the remaining scale. The
maximum values of Pexcess at D/H 1.5 and D/H 2(a&b) are
more or less analogous by 81% and 98% respectively.
4. CONCLUSION
A study of the influence of D/H ratio on compressibility
parameters was investigated. The significant influence of
D/H ratio was noticed on cv but was insignificant in cc and
mv. It was previously studied that scale has an impact on cv
but not taking D/H ratio into account. D/H ratio was
previously investigated at D/H 3 and 6 and showed it greatly
affect cv and D/H greater than 6 recommended. The
Standards suggested 2.5 and 4. The current study on Kaolin
clay showed that, at D/H greater than 1, adequate result in
the compressibility parameters are obtained. Previous
recommended D/H ratio values were in different soil sample
thus the difference D/H ratio values. D/H 0.5 showed to be
most problematic in obtaining the compressibility
parameters, and this was observed numerical where the
highest excess pore pressure was noted. In addition,
Casagrande and Inflection method were strenuous as the
experimental curve did not match the theoretical curve.
Therefore, in the absence of friction that is not usually
obtained in routine testing, it was observed that in terms of
D/H ratio, cv is easily attained using Taylor's method.
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