FIELD AND THEORETICAL ANALYSIS OF ACCELERATED CONSOLIDATION USING VERTICAL DRAINS

International Journal of Advances in Engineering & Technology, June, 2017.
©IJAET ISSN: 22311963
318 Vol. 10, Issue 3, pp. 318-329
FIELD AND THEORETICAL ANALYSIS OF ACCELERATED
CONSOLIDATION USING VERTICAL DRAINS
Chinmay Joshi and Anand Katti
Department of Civil Engineering,
Datta Meghe College of Engineering, Airoli, Navi Mumbai, India
ABSTRACT
Mumbai is the region consisting of soft compressible marine clay deposits. There are several construction
problems on such soils and thus ground improvement is need to be carried out. Vertical drains is generally
preferred technique as accelerated settlement is achieved during the construction phase itself if planned
accordingly. The concept of vertical drains is based on the theory of three dimensional consolidation as described
by Terzaghi (1943). Based on this concept, a consolidation programme is developed and an attempt is made to
determine the field to laboratory coefficient of vertical consolidation ratio by Taylor’s Square Root of Time
Method and Casagrande’s Logarithm of Time Fitting Method for this region by considering the case study of
Bhandup Lagoon Works Embankment. Based on this ratio, the rate of consolidation and time required for
consolidation in the field can be determined knowing the consolidation parameters. Equations are developed by
using output of the programme and it is explained.
KEYWORDS: Soft Compressible Clay, Vertical Drains, Consolidation
I. INTRODUCTION
In the early times before the advancement in the geotechnical engineering, the only alternate for the
foundation engineers was to design the foundation matching to the sub-soil conditions at the provided
site. But now a days, due to the advancement in geotechnical techniques and with the help of latest
technology it is possible for us to alter the engineering characteristics of weak founding soil to suit the
foundation of our choice. This geotechnical processes of improving the quality of the founding soil to
our desired requirements are called as ‘Ground Improving’.
Terzaghi [10] (1943) defined consolidation as “Every process involving a decrease in water content of
saturated soil without replacement of water by air is called a process of consolidation”. In general it is
the process in which reduction in volume takes place by expulsion of water under long term static loads.
It occurs when stress is applied to a soil that causes the soil particles to pack together more tightly,
therefore reducing its bulk volume. When this occurs in a soil that is saturated with water, water will be
squeezed out of the soil.
In case of highly compressible saturated soft clay, imposition of load generates excess pore water
pressure in soft layer. This excess pore water pressure may trigger both shear and settlement failures if
not monitored and altered. This paper presents analysis and monitoring of ground improvement of soft
saturated marine clays.
II. LITERATURE REVIEW
To address settlement issues, literature review has been carried out for the theories related to three
dimensional consolidation, and methods related to evaluation of consolidation parameters.
Terzaghi (1943) [10], proposed one dimensional consolidation model and developed the corresponding
analytical solution to explain, its mechanism and the phenomenon of the settlement of soil under
surcharge, which triggered the study of the consolidation theory. Terzaghi [10], proposed piston and
spring analogy for understanding the process of consolidation.

319 Vol. 10, Issue 3, pp. 318-329
The basic differential equation proposed by Terzaghi is:
𝜕𝑢
𝜕𝑡
=
𝑘
𝛾 𝑤 𝑚 𝑣 𝜕𝑧2
= 𝑐 𝑣𝑧
𝜕2
𝑢
𝜕𝑧2
(1)
Where ‘cvz’ is coefficient of vertical consolidation, ‘k’ is the coefficient of permeability, ‘γw’ is the unit
weight of water and ‘mv’ is coefficient of volume change:
𝑐 𝑣𝑧 =
𝑘
𝛾 𝑤 𝑚 𝑣
(2)
The solution for the above differential equation can be obtained by considering proper boundary
conditions and by solving Fourier series as:
𝑢 = ∑
2∆𝑝
𝑚
[sin
𝑚𝑧
𝐻
]
𝑁=∞
𝑁=0
𝑒(−𝑚2 𝑐 𝑣𝑧 𝑡)/𝐻2
(3)
Wherein, ‘m’ is an integer, ‘t’ is time, ‘H’ is the thickness of the clay layer, ‘Δp’ is increment in pressure
and z gives the variation in depth.
To arrive at a solution, use of two non-dimensional parameters are introduced. The first non-
dimensional group is the time factor Tv where:
𝑇𝑣 =
𝑐 𝑣𝑧 ∗ 𝑡
𝐻2 (4)
The second non-dimensional group is the degree of consolidation ‘U’. The term ‘U’ is expressed as the
ratio of the amount of consolidation which has already taken place to the total amount which is to take
place under the load increment and is represented as:
𝑈% = 100 (1 − ∑
2
𝑚2
𝑒−𝑚2 𝑇𝑣
𝑁=∞
𝑁=0
)
(5)
For the values of U% between 0 and 52.6%, Tv can be represented as:
𝑇𝑣 =
𝜋
4
(
𝑈%
100
)2
(6)
For the values of U% greater than 52.6%, Tv can be represented as:
𝑇𝑣 = 1.781 − 0.933 𝑙𝑜𝑔(100 − 𝑈%) (7)
Barron (1948) [1], presented an analytical solution for combined vertical and radial drainage by
decoupling the radial and vertical drainage at first and then attaining a product of the contribution from
the radial and vertical drainage. Formulas for consolidation by vertical and radial flow to wells, for free
strain and equal strain with or without peripheral smear and drain well resistance were also analyzed.
The differential equation for consolidation for equal strain case without smear and well resistance is
given as:
∂u̅
∂t
=ch (
1
r
∂u
∂r
+
𝜕2
𝑢
∂r2 ) +cvz
𝜕2
𝑢
∂z2 (8)
Wherein, ‘ch’ is the co-efficient of consolidation for horizontal flow, ‘ 𝑢̅’ is excess pore water pressure
and ‘r’ is radial distance.
For radial flow only, ‘cvz’ will be zero.

320 Vol. 10, Issue 3, pp. 318-329
A solution for this second order expression is:
𝑢 𝑟 =
4𝑢̅
𝑑𝑒2 ∗ F(n)
[𝑟𝑒2
∗ 𝐿𝑛 (
𝑟
𝑟𝑤
) −
𝑟2
− 𝑟2
𝑤
2
]
(9)
In which,
𝑢̅ = 𝑢0 𝑒 𝜆
(10)
Wherein, ‘e’ is the base of natural logarithm,
𝜆 =
−8𝑇ℎ
𝐹(𝑛) (11)
And,
𝐹(𝑛) =
𝑛2
𝑛2 − 1
𝑙𝑛(𝑛) −
3𝑛2
− 1
4𝑛2 (12)
Whereas the solution for same differential equation for equal strain case with smear zone at periphery
is:
𝑢 𝑟 = 𝑢̅ 𝑟
[𝑙𝑛 (
𝑟
𝑟𝑠
) −
𝑟2
− 𝑟𝑠
2
2𝑟𝑠
2 +
𝑘ℎ
𝑘 𝑠
(
𝑛2
− 𝑠2
𝑛2 )ln(𝑠)]
𝑣
(13)
In which,
v = F(n, S, kh, ks)
(14)
𝑚 =
𝑘ℎ
𝑘 𝑠
(
𝑛2
− 𝑆2
𝑛2 ) ln(𝑆) −
3
4
+
𝑆2
4𝑛2
+
𝑛2
𝑛2 − 𝑆2
ln (
𝑛
𝑆
)
(15)
And,
𝑢̅ 𝑟 = 𝑢0 𝜀 𝜉 (16)
In which,
𝜉 =
−8𝑇ℎ
𝑚 (17)

321 Vol. 10, Issue 3, pp. 318-329
Figure 1. Plan of drain well pattern and
fundamental concepts of flow within zone of
influence of each well
Figure 2. Average degree of consolidation for
various values of ‘n’ under ‘equal strain’ condition at
any given time
Figure 3. Effect of smear and well resistance on
‘equal strain’ consolidation by radial flow to drain
wells
Figure 4. Comparison of equal strain and free strain
Biot (1941) [2], extended the classical reviews of Terzaghi’s [10] one dimensional problem of column
under a constant load to three dimensional case and established equations valid for any arbitrary load
variable with time. In this theory, Biot interpreted the mathematical formulation of the physical
properties of soil and number of constants used to describe this property. Johnson (1970) [7], gave the
detailed use of vertical drains as a pre-compression technique for improving the properties of
compressible soils. Richart (1959) [9], presented diagrams for quantitative evaluation of equivalent
“ideal well” of reduced diameter. The theories for consolidation due to vertical flow and radial flow of
water to drain well was also reviewed. Hansbo (1979) [5], made extensive sand drain study involving
large scale field tests and observations of sand drain in soft clays. The consolidation process of clay by
band shaped prefabricated drains was also studied and considered the design considerations.
Various case records for ‘cvz (field)/cvz (lab)’ ratio have also been recorded for vertical drains by
different methods. Bergado (1991) [3], studied the effectiveness of Mebra prefabricated drains inside
the AIT campus by constructing 4m high embankment. Bergado (1991) [3], analysed time-settlement
data for Bangna-Bangpakong highway and the coefficient of consolidation ‘cvz’ was back-figured from
the field performance of the highway embankment and the following correlations was found ‘cvz
(field)/cvz (lab)’ = 26. Leroueil (1987) [8], showcased the ‘cvz (field)/cvz (lab)’ ratio for more than 15
sites.

322 Vol. 10, Issue 3, pp. 318-329
2.1. Analysis
As per Terzaghi’s [10] theory of one dimensional consolidation, it was assumed that the soil is laterally
confined and the strains are in vertical direction only. In most of the actual problems surface loadings
cause excess pore pressure which will vary both radially and vertically. The resulting consolidation will
involve radial as well as vertical flow. Such a process is called ‘Three Dimensional Consolidation’.
The basic differential three dimensional consolidation equation in polar coordinates can be expressed
as:
𝑐 𝑣𝑟 (
𝜕2
𝑢
𝜕𝑟2
+
1
𝑟
𝜕𝑢
𝜕𝑟
) + 𝑐 𝑣𝑧
𝜕2
𝑢
𝜕𝑧2
=
𝜕𝑢
𝜕𝑡 (18)
The general solution for the above equation can be given by the combination of the one dimensional
flow and radial flow as:
(1 − 𝑈) = (1 − 𝑈𝑧) (1 − 𝑈𝑟) (19)
Wherein, U = degree of consolidation for three dimensional flow
Uz = degree of consolidation for one dimensional flow (in vertical direction)
Ur = degree of consolidation for radial flow.
2.2. Methods to determine the laboratory cvz
Two methods, namely the logarithm of time (Casagrande) and the square root of time (Taylor), is used
for evaluating coefficients of consolidation of clayey soils are adopted.
Casagrande’s logarithm of time fitting method
In this method, the determination of the coefficient of consolidation normally requires that compression
readings be carried out at least for 24 hours so that the slope of the compression curve attributed to the
secondary compression of the soil can accurately be evaluated on a curve of compression versus
logarithm of time. The procedure for determination of cvz is as follows:
𝑐 𝑣𝑧 =
0.197 ∗ 𝐻2
𝑡50
(20)
Figure 5. Log of time fitting method Figure 6. Square root of time fitting method
Taylor’s method of time fitting
The procedure for determination of cvz is as follows:
𝑐 𝑣𝑧 =
0.848 ∗ 𝐻2
𝑡90
(21)

323 Vol. 10, Issue 3, pp. 318-329
2.3. Instrumentation
Instrumentation can be defined as the set of techniques employed which gives the behaviour of
soil/structure under the applied load/stress. In our case we will be adopting deep settlement markers to
measure settlement of soft marine clay with time under the construction load. Pore pressure
measurement devices such as piezometers are used to measure the development and dissipation of pore
water pressure with time.
Importance of Instrumentation
Instrumentation for marine clay with ground improvement is intended in following aspects of design
and construction.
i) In the design for stability analysis, factor of safety can be adopted just near to unity, for economy in
embankment cross section by providing instrumentation, which helps in monitoring of embankment
during construction.
ii) The sequence of construction and time gaps particularly during surcharge laying operation can be
monitored with instrumentation with reference to stability of embankment.
iii) The pavement construction can be done after ensuring that no appreciable settlement will take place
further.
iv) Construction period is expected to practically reduce by use of settlement data, since there maybe
vast difference between estimated and observed settlement time. Further it may be possible to reduce
the estimated settlement time in further projects with the experience that double drainage condition is
prevailing or not.
v) The instrumentation process provides a valuable experience and a reliable and vast data bank which
can be used for guiding into subsequent designs.
2.4. Programme developed for evaluation of consolidation
Based on the procedures suggested by Barron (1948), rigorous analysis has been carried out to
understand the behaviour of coefficient of consolidation with time for different ‘kv’ (coefficient of
permeability in vertical direction) and ‘kh’ (coefficient of permeability in horizontal direction)
parameters. For evaluation of consolidation, a programme is developed in which, basic parameters
which are obtained from soil exploration programme, field and laboratory tests are used as input
parameters.
In short, for analysis of 11 m Depth of clay layer; by keeping depth of clay layer constant and using
each ‘ch to cv’ ratio for analysis of 4 different ratios, we get the results for different centre to centre
spacing of Vertical Drains, and for varying Percent Consolidation and Time. This procedure is carried
out for any depth of clay layer.
Figure 7. Schematic Description of Legends Figure 8. Description of treated and untreated layer

324 Vol. 10, Issue 3, pp. 318-329
Table 1. Various Input Parameters for the Programme
Description Legends Units Value
Depth of clay layer H m 11.00
Bulk Density of clay layer 2 g/cm3
1.40
Coefficient of consolidation in Vertical Direction Cvz cm2
/sec 4.00E-04
Relation between Cvz and Cvr 1
Coefficient of consolidation in Horizontal Direction Cvr cm2
/sec 4.00E-04
Height of working platform Hwp m 1.00
Density of working platform  g/cm3
1.80
Height of embankment He m 2.00
Density of embankment material  g/cm3
1.80
INPUT FOR TREATED LAYER
Height of band drain Hsd m 10.50
Value of CVZ Cvz cm2
/sec 4.00E-04
Value of CVR Cvr cm2
/sec 4.00E-04
Drainage condition Double as SD
Sand Drain Diameter d cm 6.50
Spacing of Sand Drain s m 0.50
cm 50.00
Drain Layout
Triangular 3
Square 4
Pattern of sand drain 3
INPUT FOR SMEAR ZONE
Radius of Drain well rw cm 3.25
Relation between rw and rs 1
Radius of Smear Zone rs cm 3.25
Permeability of soil in horizontal direction Kh 1.00
Relation between Kh and Ks 1
Permeability of smear zone Ks 1.00
INPUT FOR UNTREATED LAYER
Thickness of Untreated Clay Layer Hcl m 0.50
CV of Untreated clay layer Cv cm2
/sec 4.00E-04
Drainage Condition
Single 1
Double 2
Drainage Condition 1
Based on the above input parameters, typical output from the programme will be as under:
After executing the programme using equal strain condition the output is presented pictorially in Figure
9 and Figure 10. Figure 9 presents the variation of pore water pressure with respect to time for varying
spacing of vertical drain varying from 0.25 m to 3.0 m. The variation of spacing with respect to time
for different degrees of consolidation is presented in Figure 10.
From Figure 9 it is observed for spacing of 2.0 m, the percent consolidation varies from 30% at time
around 1 month and reaches to 100% by the time it reaches 15 month. Similar variations are observed
for spacing varying between 3.0 m to 0.25 m. From Figure 10, it is seen that for 90% consolidation time
required is less than a month when spacing is 0.25 m and it takes 10 months when the spacing increases
to 2.0 m.

325 Vol. 10, Issue 3, pp. 318-329
Figure 9. Schematic Variation of Percent
Consolidation with Time for varying Spacing
(cvz=4x10-04
cm2
/sec, cvr=1.0 cvz)
Figure 10. Schematic Variation of Spacing with
Time for Varying Percent Consolidation (U%)
(cvz=4x10-04
cm2
/sec, cvr=1.0 cvz)
The cvz values proposed here is based on the field values observed in Mumbai region. Hence, the cvz
values considered are 1x10-01
cm2
/sec to 1x10-09
cm2
/sec. The ratio between the vertical and horizontal
consolidation considered is for 0.5, 1.0, 1.5 and 2.0. From the plot of U% versus ‘cvz’ it is seen that the
U% falls from 100% to 0% where the cvz varies from 1 x 10-02
cm2
/sec to 1 x 10-06
cm2
/sec as can be
seen in Figure 11. Hence, it can also be seen that as the time increases the gradient of the drop also
decreases, i.e. the curve flattens out.
To understand this behaviour in depth it was decided to plot time vs cvz (cm2
/sec) on log10-log10 scale.
Here a unique relation is observed where the relation between time and cvz is straight line for all the
cases and these lines are parallel to one another as seen in Figure 12. Analysis is in progress to
understand this phenomenon.
Figure 11. Variation of coefficient of consolidation
with percent consolidation for varying time,
constant spacing (S=1.0m)
Figure 12. Variation of coefficient of consolidation
with time for varying spacing, constant percent
consolidation (U%=90%)
It is proposed to compare the theoretical calculation with the field observations, and to understand the
behaviour of soft saturated clay when under the application of the applied stress. For this purpose we
are proposing to compare theoretical results with the field observation. To understand this behaviour of
vertical band drain in the field, a case studies have been considered namely:
i. Bhandup Lagoon Works Embankment.
0
10
20
30
40
50
60
70
80
90
100
0 3 6 9 12 15 18 21 24
PercentConsolidation'U(%)'
Time (Months)
0.25m 0.5m 0.75m 1.0m
1.25m 1.5m 1.75m 2.0m
2.25m 2.5m 2.75m 3.0m
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
0 20 40 60 80
Spacing(m)
Time (Months)
% consolidation
"U%"
10%
20%
30%
40%
50%
60%
70%
80%
90%

326 Vol. 10, Issue 3, pp. 318-329
2.5. Case Study: Bhandup Lagoon Works Embankment
Figure 13. Bhandup Lagoon Works Embankement Location
The entry to the BMC lagoons at the Bhandup end is located at the busy suburb of Mumbai which is
approximately 25 kms from Mumbai down town on the North East end of Mumbai. The plant is located
1.5 kms from the junction of the Eastern Expressway Highway, and 3 kms from Bhandup Railway
Station. The approach embankment stretched from the 9 chainages. This entire length is located on
marine clay/ salt pan deposits on the banks of Thane creek.
Table 2. Typical soil properties adopted for design based on laboratory and field tests
Sr. no Soil Properties Value Unit
1. Bulk Density of clay 1550 kg/m3
2. Natural Moisture content 43-77 %
3. Specific Gravity 2.6
4. Liquid Limit 59-115 %
5. Plastic Limit 18-41 %
6. Unconfined compressive strength 3000 kg/m2
7. Compression index 0.99
8. Coefficient of consolidation 2.79 x 10-04
cm2
/sec
Figure 14. Variation Modified settlement curve/
Taylor’s Method (Sett. marker) (A-1)
Figure 15. Variation Casagrande’s Method
(Settlement Marker) (A-1)
The field instrumentation was done with the help of settlement and piezometer markers and the analysis
is done considering the time-settlement and time-pore pressure data for chainage A-1, A-2, A-3, A-4,
A-2/A-3 Jn., B-1/B-2 Jn., N-W Curve, E-1 and E-V. The stage loading is calculated for given
embankment height keeping in mind the bearing capacity aspect.

327 Vol. 10, Issue 3, pp. 318-329
Figure 14 shows the modified time-settlement curve obtained as per IS code 2720-Part 15 [6] used for
Taylor’s Square Root of Time method. Figure 15 is modified time settlement curve on log10 of time
scale used for Casagrande’s Logarithm of Time Fitting method.
Taylor’s Method
Here, H= 5.0 m = 500 cm, Tv = T90 = 0.848, t = t90 = 10454400 sec
𝑐 𝑣𝑧 =
0.848 ∗ (500)2
10454400
Based on above parameters, cvz (field) = 2.03 x 10-02
cm2
/sec
• Casagrande’s Method
Here, H= 5.0 m = 500 cm, Tv = T50 = 0.197, t = t50 = 3283200 sec
𝑐 𝑣𝑧 =
0.197 ∗ (500)2
3283200
Based on above parameters, cvz (field) = 1.50 x 10-02
cm2
/sec
2.6. Summary
Based on the work carried out an attempt is made to determine rate of settlement which is likely to take
place in field based on these ratios. The ratio of cvz(field)/cvz(lab) for various cases is presented in Table
4. This data can be useful to estimate the rate of consolidation and time required for consolidation in
the field in this vicinity.
Table 3. Coefficient of Consolidation Field (cvz) in cm2
/sec
Sr.
No.
Marker Chainage Laboratory
Taylor Method
(cvt)
Casagrande Method
(cvc)
1 Settlement A-1 2.79 x 10-04
2.03 x 10-02
1.50 x 10-02
1.96 x 10-02
1.58 x 10-02
3 Settlement A-3/L1 5.14 x 10-04
1.70 x 10-02
1.27 x 10-02
1.45 x 10-02
1.04 x 10-02
5 Settlement A2/A3 JN 3.90 x 10-04
2.14 x 10-02
1.63 x 10-02
6 Settlement B1/B2 JN/L1 5.14 x 10-04
2.03 x 10-02
1.63 x 10-02
7 Settlement N-W CURVE 3.90 x 10-04
2.03 x 10-02
1.54 x 10-02
8 Settlement E-1 2.79 x 10-04
1.70 x 10-02
1.43 x 10-02
9 Settlement E-V/L1 5.14 x 10-04
2.10 x 10-02
1.63 x 10-02
10 Piezometer A-1 2.79 x 10-04
1.65 x 10-02
1.14 x 10-02
1.65 x 10-02
1.14 x 10-02
12 Piezometer A-3/L1 5.14 x 10-04
1.41 x 10-02
1.08 x 10-02
13 Piezometer A-4/L1 5.14 x 10-04
1.45 x 10-02
1.21 x 10-02
14 Piezometer A2/A3 JN 3.90 x 10-04
1.12 x 10-02
8.38 x 10-03
15 Piezometer B1/B2 JN/L1 5.14 x 10-04
1.57 x 10-02
1.27 x 10-02
16 Piezometer N-W CURVE 3.90 x 10-04
1.25 x 10-02
1.04 x 10-02
17 Piezometer E-1 2.79 x 10-04
1.25 x 10-02
1.04 x 10-02
18 Piezometer E-V/L1 5.14 x 10-04
1.70 x 10-02
1.43 x 10-02
Table 4. Ratio of Coefficient of Consolidation by Taylor’s & Casagrande’s Methods (cvt , cvc) to Coefficient of
Consolidation of lab (cvz lab)
Sr.
No.
Marker Chainage
Laboratory
(cvlab)
Taylor Method
(cvt/cvlab)
Casagrande Method
(cvc/cvlab)
72.68 53.77
70.11 56.75

328 Vol. 10, Issue 3, pp. 318-329
33.15 24.64
28.25 20.16
5 Settlement A2/A3 JN 3.90 x 10-04
54.95 41.76
6 Settlement B1/B2 JN/L1 5.14 x 10-04
39.45 31.69
7 Settlement N-W CURVE 3.90 x 10-04
52.00 39.50
8 Settlement E-1 2.79 x 10-04
61.07 51.08
9 Settlement E-V/L1 5.14 x 10-04
40.93 31.69
59.09 40.86
59.09 40.86
12 Piezometer A-3/L1 5.14 x 10-04
27.40 20.92
13 Piezometer A-4/L1 5.14 x 10-04
28.25 23.60
14 Piezometer A2/A3 JN 3.90 x 10-04
28.72 21.49
15 Piezometer B1/B2 JN/L1 5.14 x 10-04
30.55 24.64
16 Piezometer N-W CURVE 3.90 x 10-04
32.10 26.57
17 Piezometer E-1 2.79 x 10-04
44.87 37.15
18 Piezometer E-V/L1 5.14 x 10-04
33.15 27.72
So for the given property of soil, which are measured in laboratory multiplied by this ratio would give
us the rate of consolidation which is likely to take place in the field. The same could be used as a
multiplication factor with laboratory test data for all cases in this particular region to determine rate of
consolidation, which is likely to occur thus giving us a brief idea of how the soil is going to be behaving
under the stress conditions.
Thus, from the above ratio, knowing the laboratory coefficient of consolidation the field coefficient of
consolidation can be found out for that region. Now from the programme developed for evaluation of
Rate of Consolidation, with proper consolidation parameters from the case study, time required for 70%
consolidation for the given spacing of 1.0 m can be obtained from Figure 9 as around 3 months.
Similarly for time of 2.93 months with spacing 1.0 m the percent consolidation works out to 70% from
Figure 10.
Based on the output generated after running the programme, relation is plotted on a log10 – log10 scale
between coefficient of consolidation and time for 50%, 70% and 90% consolidation. On the log10/log10
scale, it is seen that for different spacing (S), these relations are all straight lines and parallel to one
another. It is observed that, as cvz reduces (from 1 x 10-01
cm2
/sec to 1 x 10-09
cm2
/sec) the time increases
at higher rate. As per the study of Curve Fitting/ Regression Analysis, the best fit curve by least square
method is attempted. On taking log10 cv and log10 t, the graph obtained was a set of straight lines and
hence the best fit curve to the obtained observations is t=A*Cv^B. But from our analysis it is observed
that, the B value works out to -1. Hence the equation reduces to, t=A/Cv. So it can be written as,
A=Cv*t.
For determining time for 90% consolidation of 11 m depth of clay layer, for ch = 1.0 cv and for double
drainage condition we get the following equation,
𝐶𝑣 ∙ 𝑡 = 2.45𝐸−03
𝑆2
+ 6.69𝐸−04
S – 5.04𝐸−04
(22)
Now, if we know any of two parameters from 1) coefficient of consolidation ‘cv’, 2) time ‘t’ required
for 50% consolidation, 70% consolidation or 90% consolidation or 3) spacing of vertical drain ‘S’, we’ll
be able to determine the remaining parameter.
For example, in the project report of Bhandup case study, they have mentioned cvLaboratory to be taken as
2.79 x 10-04
cm2
/sec, and Spacing taken for project is 1.25 m. By putting these values in the above
equation, we get the time required for 90% consolidation is 137506.71 days.
III. CONCLUSIONS
Thus, this data will be useful in planning of the given project i.e.

329 Vol. 10, Issue 3, pp. 318-329
• In deciding the various factors such as time required for the stage loading,
• Time when the future activities can be started when a considerable amount of consolidation has taken
place.
• Time taken to complete the project.
• Spacing required for the project to complete the consolidation process in desired time.
ACKNOWLEDGEMENTS
This journal was made possible by the contribution of my supervisor Dr. Anand Katti, Professor,
Department of Civil Engineering. I am deeply indebted to him for his outstanding supervision,
encouragement and guidance throughout the period of my candidature.
REFERENCES
[1]. Barron R.A., (1948), “Consolidation of Fine Grained Soils by Drain Wells,” Transactions of American
Society of Civil Engineers, Volume 113, pp.718-742.
[2]. Biot M.A. (1941), “General Theory of Three Dimensional Consolidation,” Journal of Applied Physics,
Volume 12, pp.155-164.
[3]. Bergado, D. T., Asakami, H., Alfaro, M.C. & Balasubramaniam, A.S. (1991), “Smear Effects of
Vertical Drains on Soft Bangkok Clay”. J. Geotech. Eng. Div. ASCE, 117, 1509-29.
[4]. Chinmay Joshi, (2017), M. Tech thesis titled “Critically Study the Load-Settlement and Load-Pore
Pressure Characteristics of Soft Saturated Clays in the Field to Arrive at Equations for Spacing/Time
Required for Accelerated Consolidation” submitted to University of Mumbai in Partial fulfilment of
Master’s Degree in Civil Engineering. (Unpublished)
[5]. Hansbo. S. (1979), “Consolidation of Clay by Band shaped Prefabricated Drains”. Ground
Engineering, Volume 12, No.5, pp. 16-25.
[6]. IS: 2720-Part 15-1986, “Determination of Consolidation Properties”.
[7]. Johnson S. J., (1970), “Pre-compression for Improving Foundation Soils,” Journal of Soil Mechanics
and Foundation Division, American Society of Civil Engineers, Volume 96, No. 1, pp.111-144.
[8]. Leroueil, S. (1987). “Tenth Canadian geotechnical colloquium: recent developments in consolidation
of natural clays.” Canadian Geotechnical Journal, 25, 85-107.
[9]. Richart F.E., (1959), “Review of the Theories for Sand Drains,” Transactions of ASCE, pp.709-736.
[10]. Terzaghi K., (1943), “Theoretical Soil Mechanics” Published By John Wiley and Sons Inclusive, New
York.
Authors
Chinmay Joshi is a Post Graduate Student in Datta Meghe College of Engineering, Navi
Mumbai, India. He received B.E. (Civil) Degree in 2014 from Mumbai University.
Dr. A. R. Katti is a Professor for Geotechnical Engineering in Datta Meghe College of
Engineering, Navi Mumbai, India.

FIELD AND THEORETICAL ANALYSIS OF ACCELERATED CONSOLIDATION USING VERTICAL DRAINS

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FIELD AND THEORETICAL ANALYSIS OF ACCELERATED CONSOLIDATION USING VERTICAL DRAINS