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Swelling Behavior of Expansive Soils

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1. INTRODUCTION Volumetric changes (usually swell) of expansive soils in presence of water are undesirable from stability reasons. The consequence of swell leads to an increase in volume till suction pressure comes to equilibrium as determined by the environment. The amount of swell to satisfy the suction pressure depends on the magnitude of the vertical loading and soil properties that include soil composition, natural water content and density, and soil structure. The rate of swell depends on the coefficient of permeability (hydraulic conductivity), thickness, and soil properties. If a structure is founded on such expansive soils, then its presence along with the foundation prevents this volume increase (swell) and as a consequence, leads to swelling pressure. This swell- ing pressure has serious consequences in the form of cracks and distress on the structures founded on expansive soils. Lightweight structures are severely affected due to high swelling pressure exerted by these soils. These aspects of swelling and their consequences on building have been well documented in the literature (e.g., Gibbs and Holtz, 1956; Seed et al., 1962; Brackley, 1973; Chen, 1975; Katti et al., 1975; Sridharan et al., 1986). The first and essential step before any construction activ- ity on expansive soils is to assess the degree of expansiveness and the likely swelling pressure on the structure, so, as to adopt preventive measure to overcome the same. Hence, the study of swelling behavior and the associated parameters of expansive soils assume importance. To assess the degree of swell, many procedures, both simple and elaborate includ- ing laboratory methods of determining swell pressure have been developed by geotechnical researchers and engineers (e.g., Gibbs and Holtz, 1956; Ladd, 1960; Seed et al., 1962; Komornik and David, 1969; Ranganatham and Satyanarayan, 1969; Brackley, 1973; Chen, 1975; Sridharan et al., 1986). A number of factors influencing swelling behavior have been reported in the past (Ranganatham and Satyanarayan, 1969; Komorik and David, 1969; EI-Sohby and EI-Sayed, 1981, 1983; AL-Mhaidib, 1999; Azam and Abduljauwad, 2000). Among the iden tified factors that i nfluence the swell- ing behavior, type and amount of clay, initial placement conditions, stress history and stress path, nature of pore fluid, size and thickness of the sample are found to be more important. The swelling pressure of an expansive soil is primarily dependent on the initial dry unit weight or void ratio and also on the moisture content. The methods to determine swelling pressure influences the ultimate value of the same. H. B. Nagaraj, 1*  and M. Mohammed Munnas 2  and A. Sridharan 3  Swelling behavior of expansive soils ABSTRACT:  Volumetric changes (usuall y swell) of expansive soils in presence of water are undesirable from stability reas ons. Swell and Swelling pressure of an expansive soil is primarily dependent on the initial dry unit weight or void ratio and also on the moisture content. In this study, attempts have been made to study the effect of introducing varying number of vertical drains into the compacted soil at varying initial dry densities on the swell and swelling pressure behavior. Both percent swell and the swelling pressure are significantly influenced by the presence of vertical drains (facility of water availability). The percent swell versus time relationship could be identified as a rectangular hyperbola, facilitating the prediction of ultimate percent swell. This is advantageous to predict the swell from th e data obtained from the initial stages of the swell test and the experiment could be terminated without continuing till equilibrium conditions are reached. This concept was also extended to predict swelling pressure determined by constant volume meth od. Irrespective of the presenc e or absence of drains, the density effect on rate of secondary swelling and consolidation behavior of swollen sample was found to be almost the same for all testing conditions used in this study. KEYWORDS:  Clays, compaction, expan sive soils, swell, swelling press ure, vertical drains *Corresponding Author 1 Assistant Professor, Department of Civil Engineering, BMS College of Engineering, Bangalore 560 019, India. email: [email protected] 2 Post Graduate student, Department of Civil Engineering, BMS College of Engineering, Bangalore 560 019, India. email: [email protected] 3 Professor Emeritus, Department of Civil Engineering, Indian Institute of Science, Bangalore 560 012, India. email: [email protected] 99 International Journal of Geotechnical Engineering (2010) 4: (99-111) DOI 10.3328/IJGE.2010.04.11.99-111 J. Ross Publishing, Inc. © 2010
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1. INTRODUCTION

Volumetric changes (usually swell) of expansive soils in

presence of water are undesirable from stability reasons.

The consequence of swell leads to an increase in volume

till suction pressure comes to equilibrium as determined by

the environment. The amount of swell to satisfy the suctionpressure depends on the magnitude of the vertical loading

and soil properties that include soil composition, natural

water content and density, and soil structure. The rate of

swell depends on the coefficient of permeability (hydraulic

conductivity), thickness, and soil properties. If a structure

is founded on such expansive soils, then its presence along

with the foundation prevents this volume increase (swell)

and as a consequence, leads to swelling pressure. This swell-

ing pressure has serious consequences in the form of cracks

and distress on the structures founded on expansive soils.

Lightweight structures are severely affected due to high

swelling pressure exerted by these soils. These aspects ofswelling and their consequences on building have been well

documented in the literature (e.g., Gibbs and Holtz, 1956;

Seed et al., 1962; Brackley, 1973; Chen, 1975; Katti et al.,

1975; Sridharan et al., 1986).

The first and essential step before any construction activ-

ity on expansive soils is to assess the degree of expansiveness

and the likely swelling pressure on the structure, so, as to

adopt preventive measure to overcome the same. Hence, thestudy of swelling behavior and the associated parameters of

expansive soils assume importance. To assess the degree of

swell, many procedures, both simple and elaborate includ-

ing laboratory methods of determining swell pressure have

been developed by geotechnical researchers and engineers

(e.g., Gibbs and Holtz, 1956; Ladd, 1960; Seed et al., 1962;

Komornik and David, 1969; Ranganatham and Satyanarayan

1969; Brackley, 1973; Chen, 1975; Sridharan et al., 1986).

A number of factors influencing swelling behavior have

been reported in the past (Ranganatham and Satyanarayan

1969; Komorik and David, 1969; EI-Sohby and EI-Sayed,

1981, 1983; AL-Mhaidib, 1999; Azam and Abduljauwad2000). Among the identified factors that influence the swell-

ing behavior, type and amount of clay, initial placement

conditions, stress history and stress path, nature of pore

fluid, size and thickness of the sample are found to be more

important.

The swelling pressure of an expansive soil is primarily

dependent on the initial dry unit weight or void ratio and

also on the moisture content. The methods to determine

swelling pressure influences the ultimate value of the same.

H. B. Nagaraj,1*  and M. Mohammed Munnas2 and A. Sridharan3 

Swelling behavior of expansive soils

ABSTRACT:  Volumetric changes (usually swell) of expansive soils in presence of water are undesirable from stability reasons

Swell and Swelling pressure of an expansive soil is primarily dependent on the initial dry unit weight or void ratio and also

on the moisture content. In this study, attempts have been made to study the effect of introducing varying number of vertical

drains into the compacted soil at varying initial dry densities on the swell and swelling pressure behavior. Both percent swell

and the swelling pressure are significantly influenced by the presence of vertical drains (facility of water availability). The

percent swell versus time relationship could be identified as a rectangular hyperbola, facilitating the prediction of ultimate

percent swell. This is advantageous to predict the swell from the data obtained from the initial stages of the swell test and the

experiment could be terminated without continuing till equilibrium conditions are reached. This concept was also extended

to predict swelling pressure determined by constant volume method. Irrespective of the presence or absence of drains, the

density effect on rate of secondary swelling and consolidation behavior of swollen sample was found to be almost the same for

all testing conditions used in this study.

KEYWORDS:  Clays, compaction, expansive soils, swell, swelling pressure, vertical drains

*Corresponding Author

1Assistant Professor, Department of Civil Engineering, BMS College of

Engineering, Bangalore 560 019, India. email: [email protected]

2Post Graduate student, Department of Civil Engineering, BMS College of

Engineering, Bangalore 560 019, India. email: [email protected]

3Professor Emeritus, Department of Civil Engineering, Indian Institute of

Science, Bangalore 560 012, India. email: [email protected]

99

International Journal of Geotechnical Engineering (2010) 4: (99-111)

DOI 10.3328/IJGE.2010.04.11.99-111

J. Ross Publishing, Inc. © 2010

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In this study, attempts have been made to study the effect

of introducing vertical drains into the compacted soil on the

swell and swelling pressure behavior. The effect of varying

initial dry density without and with varying number of verti-

cal sand drains on time versus swell and also on time versus

swelling pressure determined by constant volume method is

also presented. The results of experiments that compare thetime required to attain the initial swell and primary swell

and also the rate of secondary swelling obtained without

and with introduction of vertical drains is presented in this

paper. The study also includes the comparison of predicted

ultimate swell and swelling pressure determined by constant

 volume method to the actual value obtained experimentally.

The consolidation behavior of swollen sample has also been

presented. Some useful conclusions have been drawn from

this study.

2. MATERIAL AND METHODS

One natural expansive soil, namely black cotton soil, which is

extensively involved in construction, with high value of liq-

uid limit obtained from Belgaum, Karnataka state, India was

selected and used in this study. The soil was characterized

for their physical properties according to ASTM Standards

and the results are summarized in Table 1. It may be seen

that it has a free swell ratio of 2 (Prakash, K. and Sridharan,

A., (2004)), and the primary clay mineral being montmoril-

lonite. (Free swell ratio is defined as the sediment volume in

water per gram of dry soil to the sediment volume in kero-

sene/carbon tetra chloride per gram of dry soil)

While other properties viz., liquid limit, plastic limit and

shrinkage limit and activity are presented in Table 1, they

no way reflect the swelling nature of the soil (Sridharan, A.

(2005)).

3. EXPERIMENTAL PROGRAM

The apparatus used in this study of swell and swelling pres-

sure is essentially the same as that of a laboratory one-dimen-

sional consolidation test with fixed type ring (oedometer).

The rings were of 60 mm in diameter and 20 mm in height.Smoothly ground porous stones have been used in the

oedometer to minimize seating displacements. Filter papers

are used to avoid intrusion of soil into the porous stones.

Porous stones used before placing inside the oedometer

are air dried and it fits close to the oedometer ring to avoid

extrusion or punching at high vertical pressures.

In this study an attempt has been made to introduce

 varying number of vertical sand drains to ensure complete

saturation with uniform moisture contents across the thick-

ness of the specimen in the swollen state. Also an attempt has

also been made to study the effect of initial dry density on the

swelling behavior and its associated parameters like, swell-

time behavior and swelling pressure-time behavior without

and with five and nine vertical drains.

3.1.  Preparation of Specimens

It was decided to maintain the height of the specimen

approximately two thirds the height of the ring to facilitateswelling of the soil on imbibing water. Hence, a height of 14

mm was used for all the tests in this study. Oven dried soil <

425 µm was used to prepare the soil specimens for the swell

test at three desired densities using static compaction. All

swell tests in this study were conducted at three selected dry

densities of 1.2 Mg/m3 (loose), 1.35 Mg/m3 (medium) and 1.5

(high) Mg/m3.

At each of the selected dry densities the requisite amount

of dry soil < 425 µm was calculated and placed in the oedom-

eter rings and statically compacted by placing a metal spacer

specially fabricated for the purpose to achieve a height of

14 mm on compaction. A plain paper (template) havingdiameter of 60 mm with the number and pattern of holes

to be drilled for making vertical drains was placed on top

of the compacted soil specimen. Using a manually operated

drill fitted with a drill bit of diameter 2.8 mm vertical holes

were made over the thickness of the statically compacted soil

specimen in the oedometer rings. Care was taken to drill

holes for vertical drains without disturbing the sides. The

required numbers of vertical holes were drilled in the similar

manner. At this stage, an air-dried, smoothly ground porous

100 International Journal of Geotechnical Engineering

Table1. Physical properties of soil used in the present study  

Sl. No. Item Values/Description

1 Soil Black Cotton Soil from

Belgaum

2 Specific Gravity, G 2.7

3 Liquid Limit (%) 87.9

4 Plastic Limit (%) 36.3

5 Plasticity Index (%) 51.6

6 Shrinkage Limit (%) 11.1

7Grain Size

Distribution

Gravel (%) 1

Sand (%) 3

Silt (Size) (%) 27

Clay (Size) (%) 69

8 Unified Soil Classification CH

9 Activity 0.75

10 Free Swell Index 100

11 Free Swell Ratio 2

12 Principal Clay Mineral Montmorillonite

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Swelling behavior of expansive soils 101

stone was positioned into the base of a dry oedometer. A

standard filter paper was placed on top of the porous stone.

The ring with the specimen having requisite number of verti-

cal holes was placed on top of the bottom porous stone and

filter paper. The vertical holes were carefully filled with sand

of particle size less than 425 µm by using a paper cone with

a small opening at the bottom. Sufficient care was taken tofill the sand into the vertical drains without spilling around

the top of the specimen. An air-dried filter paper was placed

on the top of the specimen with vertical sand drains, on top

of which a porous stone in dry condition and the loading

pad were placed. The oedometer was secured to the base by

means of screws. Thus the test specimen in the oedometer

were mounted and positioned on the loading frame with a

 vertical deflection dial gauge properly adjusted and fixed in

position to give proper dial reading. A seating load of 6.25

kPa was applied on the hanger. The initial dial gauge reading

was adjusted, so as to facilitate swell and later load the speci-

men to find the swelling pressure.

Figs. 1(a) and (b) are typical views of the compacted

specimen with five and nine vertical drains.

3.2.  Swell and Swelling pressure test

The swell and swelling pressure are generally determined in

the laboratory with the one-dimensional oedometer. Swell is

determined by subjecting the laterally confined soil specimen

to a seating pressure of 6.25 kPa and by giving both the top

and bottom of the prepared specimen access to free water

(usually distilled) to cause swell. The time-swell observations

were recorded.The swelling pressures were determined at various

densities by constant volume method/zero swell method.

Continuous loading was done in this method, allowing water

to be imbibed by the specimen and keeping the volume

change nearly zero.

After the completion of determination of swelling pres-

sure, unloading was done in stages until the seating load

was reached. Under the seating load the specimen was left

to reach equilibrium for sufficient time. Then the specimen

was completely unloaded and removed for determining the

equilibrium water content over the depth of the specimen.

3.3.  Water content Determination

In the routine practice of conducting swell test, it is not sure

that the specimen has reached uniform water content over

the thickness of the sample. To verify this it was planned

to determine the water content over the thickness of the

sample. Thus, after the completion of the swell pressure test,

the sample was removed from the oedometer ring, and sliced

horizontally into three portions namely top, middle and bot-

(a)

(b)

Figure 1.  Fig. 1(a) Solid 3-D view showing 5 vertical drains in specimen;

(b) Solid 3-D view showing 9 vertical drains in specimen; (c) See through

view of 9 vertical holes for vertical drains; (d) Final view of specimen

filled up with sand to make 9 vertical drains

(c)

(d)

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102 International Journal of Geotechnical Engineering

tom. The sliced portion of the samples were put into separate

containers for water content determinations taking care to

place the sliced sample from each portion into two contain-

ers, to obtain the average water content of each portion.

Water content was determined by oven drying method. Care

was taken to remove the sand being used for vertical drains

before slicing into three portions.

4. RESULTS AND DISCUSSION

4.1.  Results of Swell Tests

In this study, three dry densities i.e., 1.2 Mg/m3; 1.35 Mg/m3;

and 1.5 Mg/m3 were selected to study the influence of initial

dry density on swell behavior of expansive soils with a spe-

cific interest of studying the influence of introducing vertical

drains in combination with varied initial dry densities.

Fig. 2 (a) shows the swell-time behavior of the selectedsoil at three dry densities without vertical drains. It can be

seen from the figure that the amount of swell has increased

with an increase in the dry density. In order to have a check

on the reproducibility of the test results, swell tests were

repeated in the entire experimental program. One such

reproducibility test is shown in the figure at a dry density of

1.20 Mg/m3. It can be observed that there is good reproduc-

ibility on the swell-time behavior as well on the amount of

swell.

Since drilling holes to make vertical drains at lower

density of 1.2 Mg/m3  was not possible, further swell tests

at that density was not considered. Figs. 2 (b) and (c) showthe swell-time behavior having five and nine vertical drains

respectively at two dry densites namely 1.35 Mg/m3 and 1.5

Mg/m3. The amount of swell has shown to increase with

increase in density for the same number of vertical drains.

Also the tests have been shown to be reproducible.

Figs. 3 (a) and (b) show the influence of introducing

 vertical sand drains on the swell-time behavior at particular

densities of 1.35 Mg/m3 and 1.5 Mg/m3 respectively. It can

be observed from Fig. 3 (a) that both the swell-time behavior

and the amount of swell have increased with the introduc-

tion of vertical drains as compared to that of without vertical

drains; with very marginal variation in the behavior betweenfive and nine vertical drains. Similar swell-time behavior and

increased ultimate swell can be observed at higher density of

1.5 Mg/m3 with the introduction of vertical drains as shown

in Fig. 3 (b). However, there is marked influence both on the

swell and swell-time behavior between five and nine vertical

drains at this higher dry density of 1.5 Mg/m3. Table 2 sum-

marizes the amount of swell in divisions without and with

 vertical drains at varied dry densities.

4.2  Characterization of swell versus time plot

It could be seen from Figs. 2 and 3 that the shape of swell

 versus log time plot is a mirror image of the conventional

compression versus log time plot. One can indentify three

clear phases in swelling viz., the initial swelling, the primary

swelling and the secondary swelling (Sridharan and Gurtug,2004). Fig. 4 shows an idealized curve of swell versus log

time, which identifies three different phases of swelling.

The time taken for completion of initial (t i) and primary

swelling (t  p) for different testing conditions adopted in this

study has been read out from the Figs. 2 and 3, and the same

is been tabulated in Table 3. From Table 3 we can see that

as the density increases, the time taken to attain initial and

primary swelling has increased. At any density, introduction

of vertical drains has reduced the time required to attain

initial and primary swelling by nearly 50 % as compared to

that without vertical drains. However, the values are almost

similar for five and nine vertical drains.

4.3.  Prediction of Ultimate Swell

Fig. 5(a) is a typical plot of swell versus time on a natural

scale at a dry density of 1.5 Mg/m3  without and with five

and nine vertical drains. The shape of the curves resembles

the shape of a rectangular hyperbola. Similar observation

was found at various placement conditions i.e., various dry

densities; without and with vertical drains. It was earlier sug-

gested by Kondner (1963) that non linear stress-strain curves

of soils could be represented by a rectangular hyperbolic

equation. Later using this concept of linking non-linear rela-tionships to that of an hyperbolic equation, researchers have

made attempts to linearise the same by modifying the way of

the plotting the same results (Sridharan and Rao 1986). If one

can assume that the time versus swell relationship represents

a rectangular hyperbola, then the time versus time/swell

relationship is a straight line. Using this concept, attempts

have been made to predict the ultimate swelling using rect-

angular hyperbola concept (Dakshinamurthy, 1978; Rao

and Kondandaramaswamy, 1981; Sridharan et al., 1986,

Sridharan and Gurtug, 2004) from the reciprocal of the slope

of the straight line portion of (time/swell) versus time plot.

In the present study attempts have been made to seewhether prediction of the ultimate swelling for expansive soil

with vertical drains also holds good. Fig. 5(b) show the (time/

swell) versus time relationship for the plot presented in Fig

5(a), which is a straight line. The reciprocal of the slope of

the straight line portion have been calculated to predict the

ultimate swell and the same have been tabulated in Table 4

along with the actual experimental swell values. It can be seen

that the predicted values of swell matches well with experi-

mentally obtained values of swell, even for cases with vertical

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Swelling behavior of expansive soils 103

Figure 2.  Swell versus log time relationship for varying density with zero vertical drains; (b) Swell versus log time relationship for varying density

with five vertical drains; (c) Swell versus log time relationship for varying density with nine vertical drains

(a)

(b)

(c)

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104 International Journal of Geotechnical Engineering

Figure 3.  (a) Swell versus log time relationship for same density (=1.35 Mg/m3 ) with varying vertical drains;

(b) Swell versus log time relationship for same density (=1.50 Mg/m3 ) with varying vertical drain.

(a)

(b)

Table 2. Experimental values of Swell

Number

of VerticalDrains

Swell Values (mm)

Dry density 1.20 Mg/m3 1.35 Mg/m3 1.50 Mg/m3

zero2.015 (Trial - 1)

2.65 4.361.88 (Trial - 2)

five ...3.10 (Trial - 1)

4.823.14 (Trial - 2)

nine ...3.16 (Trial - 1)

5.083.16 (Trial - 2)

(Note: All tests also include Top and Bottom Drains)

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Swelling behavior of expansive soils 105

Table 3. Time taken for initial and primary swelling

Number

of

 Vertical

Drains

Time taken for initial and primary swelling (min)

Dry density 

1.20 Mg/m3 1.35 Mg/m3 1.50 Mg/m3

Initial Primary Initial Primary Initial Primary  

zero1.5 (Trial - 1) 17 (Trial - 1)

4 32 4 451.5 (Trial - 2) 18 (Trial - 2)

five ... ...18 (Trial - 1) 16 (Trial - 1)

2.6 301.8 (Trial - 2) 1.7 (Trial - 2)

nine ... ...1.6 (Trial - 1) 16 (Trial - 1)

2.6 301.8 (Trial - 2) 18 (Trial - 2)

(Note: All tests also include Top and Bottom Drains)

Figure 5.  (a) Swell versus Time relationship for same density (=1.50

Mg/m3 ) with varying vertical drains; (b) Time/swell versus Time relation-

ship for same density (=1.50 Mg/m3 ) with varying vertical drains.

(a)

(b)

Figure 4.  Schematic diagram showing the separation of initial, primary

and secondary swelling.

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106 International Journal of Geotechnical Engineering

drains also. From Fig.6, which is a plot of the experimentally

obtained swell values versus the predicted ultimate swell, it

can be observed that there is very good correlation between

the two as indicated by a good regression coefficient (r  = 1).The predicted percent swell is 1.002 times the experimental

percent swell. The predicted value ought to be more because

the predicted swell is the asymptotic value of the swell versus

time plot. Therefore the asymptotic value is more than the

 value obtained from the experimental results taken up to a

finite time. Theoretically, it takes infinite time to attain the

asymptotic value. Thus it is advantageous to predict the swell

from the data obtained from the initial stages of the swell test

and the experiment could be terminated without continuing

till equilibrium conditions are reached.

From Table 5, which summarizes the water content over

the thickness of the specimen for various placement condi-tions, it can be observed that for tests conducted without ver-

tical drains, the moisture content varied over the depth. The

 variation of water content is observed to be about 2% and

3% at 1.35 Mg/m3 and 1.5 Mg/m3 respectively. Introduction

of vertical drains has reduced the variations in moisture con-

tent over the thickness significantly. This variation in water

content over the thickness was observed to be almost the

same with five and nine vertical drains. Herein it is evident

that introducing vertical drains has improved the access for

the sample to imbibe water needed for swelling and in turn

has resulted in increase in the value of swell. Conventional

method determines reduced value of swell possibly resultingin unsafe values.

4.4.  Prediction of Swelling Pressure

Fig. 7 is a typical plot of void ratio versus swelling pressure by

constant volume method. The experimental values of swell-

ing pressure have been tabulated in Table 6. Similar to pre-

diction of swell, Sridharan et al. (1986) successfully extended

rectangular hyperbola concept to predict swelling pressureFigure 7.  Log pressure versus void ratio (Constant Volume Method)

relationship for density (=1.50 Mg/m3 ) with five vertical drains.

Figure 6.  Predicted swell versus Actual swell for the entire test results.

Table 4. Ultimate Percent Values – Predicted and Actual

Number

of

 Vertical

Drains

Ultimate Percent Swell Values (%)

Dry density 

1.20 Mg/m3 1.35 Mg/m3 1.50 Mg/m3

Predicted Actual Predicted Actual Predicted Actual

zero

14.44 (Trial - 1) 14.39 (Trial - 1)

19.02 18.93 31.27 31.1413.46 (Trial - 2) 13.43 (Trial - 2)

five ... ...22.19 (Trial - 1) 22.14 (Trial - 1)

34.50 34.4322.48 (Trial - 2) 22.43 (Trial - 2)

nine ... ...22.62 (Trial - 1) 22.57 (Trial - 1)

36.39 36.2922.62 (Trial - 2) 22.57 (Trial - 2)

(Note: All tests also include Top and Bottom Drains)

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Swelling behavior of expansive soils 107

in a constant volume method. In this study attempts have

been made to predict swelling pressure from the pressure-

time plots for the case of a soil sample compacted to a higher

initial dry density, without and with the introduction of both

five and nine vertical drains. Fig. 8(a) shows the pressure ver-

sus time relationship for samples compacted to an initial dry

density of 1.5 Mg/m3 without and with vertical drains. The

shape of curves for various placement conditions appears

to resemble the shape of a rectangular hyperbola. Fig. 8(b)

shows the transformed curves of (time/pressure) versus time.

The reciprocal of the slope of the straight line portions gives

the predicted swelling pressure, and the same has been tabu-

lated in Table 6 along with the experimentally obtained val-

ues of swelling pressure. From the good agreement between

the predicted and actual values of swelling pressure, it can

be advantageous to predict the swelling pressure with a care-

fully recorded time versus pressure data without continuing

the experiment until the equilibrium conditions are reached

From the data during the initial stages of the experiment,

once the straight line portion of the (time/pressure) versus

time is reached to obtain its slope, the swelling pressure could

be predicted from the reciprocal of the slope of the straight

line. It can be observed that the predicted values of swelling

pressures are slightly on the higher side which is safer. This is

acceptable because the predicted values of swelling pressure

ought to be more than the experimentally obtained value asthe predicted swelling pressure is the asymptotic value of the

swelling pressure versus time plot.

From Table 7, which summarizes the water content

over the depth of the specimen for various placement con-

ditions, it can be observed that for tests conducted without

 vertical drains, the moisture content varied over the depth

by the constant volume method and observed to be 11%. The

 variations are observed to be reduced significantly with the

introduction of the vertical drains, being 3% for five vertical

Figure 8.  (a) Pressure versus Time (Method – 2) relationship for density

(=1.50 Mg/m3 ) with varying vertical drains; (b) Time/Pressure versus

Time (Method – 2) relationship for density (=1.50 Mg/m3 ) with varying

vertical drains].

(a)

(b)

Table 5. Values of Moisture Content (%) determined over

the depth of the specimen

Number

of

 Vertical

Drains

Moisture Content (%) determined after consolidation

of swollen sample

Dry density 

Specimen

Portion 1.20 Mg/m3 1.35 Mg/m3 1.50 Mg/m3

zero

Top 47.10 45.36 36.44

Middle 46.92 43.54 33.47

Bottom 47.25 45.74 36.20

five

Top … 43.79 34.68

Middle … 43.18 33.32

Bottom … 43.42 34.56

nine

Top … 43.40 31.20

Middle … 43.18 31.08

Bottom … 43.37 31.27

(Note: All tests also include Top and Bottom Drains)

Table 6. Actual and Predicted Values of Swelling Pressure

for Density = 1.50 Mg/m3 (Constant volume method)

Number

of Vertical

Drains

Swelling Pressure (kPa) by constant volume

method for Dry density = 1.50 Mg/m3

 Actual Predicted

Predicted/ 

 Actual

zero 635.54 692.76 1.09

five 826.98 894.26 1.08

nine 970.85 1027.10 1.06

(Note: All tests also include Top and Bottom Drains)

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108 International Journal of Geotechnical Engineering

drains and about 2 % for nine vertical drains. Also, it can

be seen from the Table 6 that the ratio of (predicted/actual)

swelling pressure has reduced with the introduction of ver-

tical drains. It could be reasoned that vertical drains has

improved the access for the sample to imbibe water needed

for swelling as seen in the water content variation and in turn

has reflected in the value of swelling pressure.

Since, there is relatively better access for the sample to

imbibe water; the rate of swelling was more with the intro-

duction of vertical drains. Thus, in this method of swell test,

in order to keep the volume change nearly zero, frequent and

continuous loading was done to the specimen with vertical

drains compared the specimen without vertical drains where

the rate of swell was less. By frequently loading the specimen,

one gets more points on the curve during the initial portion

of the test. This can be advantageously used to predict the

swelling pressure by quickly terminating the test once the

straight line relationship is obtained (Fig. 8(b)). As observed

from Fig. 8(b), more the number of vertical drains, more

quickly, the straight line is obtained and hence reduced time

required for the test to predict the swelling pressure.

4.5.  Rate of Secondary SwellingThe three distinct phases of swelling i.e., the initial swelling,

the primary swelling and the secondary swelling as observed

through Figs 2 and 3, has been idealized as presented in Fig. 4.

Initial swelling is that portion of the swell time curve which is

almost parallel to the abscissa. The end of initial swell and the

beginning of primary swell is arbitrarily defined as the point

of intersection of the tangent to the initial portion of the

curve with the straight line portion of the curve representing

the primary swell. The completion of primary swell is arbi-

trarily defined as the intersection of the tangent to the curve

at the point of inflection, with the tangent to the straight line

portion representing a secondary time effect. Knowledge of

rate of secondary swelling will facilitate in long-term predic-

tion of swell, which may be a useful data for taking precau-

tionary measures for long term swell behavior when dealingwith expansive soils. The secondary swelling almost bears a

linear relationship in swell versus log of time plot. Similar

to what is known as rate of secondary compression, one can

call this as rate of secondary swelling (Sridharan and Gurtug,

2004). Similar to the definition of rate of secondary compres-

sion, one can define the rate of secondary swelling as:

  Rate of secondary swelling =Δ δH 

s

H  ∙Δlog

10t 

 

Table 8 shows the values of rate of secondary swelling

which can be used in predicting the long term swell. It can

be observed that the rate of secondary swelling is found to

be almost the same i.e., in the range of 0.022 for all the test-

ing conditions used in this study. Thus it can be seen that,

irrespective of the presence or absence of drains, the density

effect on rate of secondary swelling is around 0.022 for all

dry densities used in this study. Introduction of vertical

drains has not much influence on the rate of secondary swell.

Further, these values are comparable with the values reported

by Sridharan and Gurtug (2004).

4.6.  Consolidation behavior of swollensample

For the various testing conditions of dry density and verti-

cal drains, after the sample reached equilibrium, they were

loaded in stages keeping the load increment ratio (LIR) of

unity to study the consolidation behavior of swollen samples.

Next load increment was carried out when primary consoli-

dation was complete, indicated by the near constancy of the

dial gauge readings between two time intervals. Each load

Table 7. Values of Moisture Content (%) determined over

the depth of the specimen

Number

of Vertical

Drains

Specimen

Portion

Moisture Content (%) determined for

the sample used to determine swelling

pressure for dry density = 1.50 Mg/ 

m3 by constant volume method / zero

swell method

zero

Top 31.40

Middle 20.60

Bottom 31.56

five

Top 30.36

Middle 25.44

Bottom 30.66

nine

Top 29.30

Middle 27.29

Bottom 29.44

(Note: All tests also include Top and Bottom Drains)

Table 8. Rate of secondary Swell

Number

of Vertical

Drains

Swell Values (mm)

Dry density 

1.20 Mg/m3 1.35 Mg/m3 1.50 Mg/m3

zero0.020 (Trial - 1)

0.022 0.0230.019 (Trial – 2)

five ...0.024 (Trial - 1)

0.0230.022 (Trial - 2)

nine ...0.025 (Trial - 1)

0.0260.023 (Trial - 2)

(Note: All tests also include Top and Bottom Drains)

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Swelling behavior of expansive soils 109

increment lasted not more than 2 hours. Loading was con-

tinued till the sample compressed, so as to obtain the straight

line portion of e – log σ ʹυ curve. Fig. 9 shows the plot of the

 void ratio versus effective vertical consolidation pressure

for the swollen samples. From the figure, it can be seen that

the limb of the straight line portion of the e – log σ ʹυ curves

obtained from consolidating the swollen samples for vari-

ous testing conditions are almost parallel. The slope of thestraight line portion of e – log σ ʹυ curve (C 

c) is obtained and

tabulated in Table 9. These slopes which are similar to the

compression index of regular consolidation test appear to be

almost the same, being around 0.44. Thus it can be seen that,

irrespective of the presence or absence of drains, and also

with varied densities, it has no influence on the consolidation

behavior of swollen samples.

Sridharan et al., (1991) have proposed an improved

technique for estimation of pre-consolidation pressure (σ ʹc).

They suggested that pre-consolidation pressure could be

easily and accurately estimated from the plot of log (1 + e)

against log pressure. Fig. 10 (a) shows a typical plot of log (1+ e) versus log pressure without VDs for test conducted at

 varied densities. Fig. 10 (b) shows a typical plot of log (1 + e)

 versus log pressure at 1.50 Mg/m3 for zero VD, five VDs and

nine VDs respectively. The estimated σ ʹc have been summa-

rized in Table 10. It can be observed from the table that σ΄c

increases with the increase in the initial dry density for any

particular VDs. Further, at any particular dry density, σ ʹc has

decreased with the increase in the number of VDs. Also it can

be seen that the ratio of σ ʹc for ρ

d  = 1.5 Mg/m3 to 1.35 Mg/m3 

Figure 9.  Void ratio versus log pressure relationship for all testing conditions

Table 9. Compression index, Cc obtained from consolidation

of swollen sample

Number

of Vertical

Drains

Compression index, Cc obtained from consolidation

of swollen sample

Dry density 

1.20 Mg/m3 1.35 Mg/m3 1.50 Mg/m3

zero 0.44 0.43 0.44

five … 0.45 0.44

nine … 0.43 0.43

(Note: All tests also include Top and Bottom Drains)

Table 10. Pre-consolidation Pressure, σ΄ c obtained from con-

solidation of swollen sample

Number

of

 Vertical

Drains

Pre-consolidation Pressure, σ΄ c (kPa)

Dry density  Ratio of σ΄ c for

 ρd  = 1.50 to

1.35 Mg/m31.20 Mg/m3 1.35 Mg/m3 1.50 Mg/m3

zero 60 67 75 1.12

five … 50 55 1.10

nine … 45 47 1.04

(Note: All tests also include Top and Bottom Drains)

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110 International Journal of Geotechnical Engineering

has decreased with the increase in the number of VDs. This

may be because of better water accessibility with the increase

in VDs, the net attractive force has reduced and hence led

to the reduction in σ ʹc. The above observations indicate that

even for normal consolidation tests, vertical drains may

help to obtain better results. Conventional method without

any vertical drains determines higher σ ʹc. This needs furtherinvestigations.

CONCLUSIONS

The swelling behavior of expansive soil has been studied

without and with vertical drains. Attempts have been made

to study the effect of introducing five and nine vertical drains

with varied initial dry densities. The following conclusions

have been drawn.

Introducing vertical drains into the compacted soil is

found to have a marked influence on the swell and swelling

pressure behavior. The amount of swell has increased with

the introduction of vertical drains as compared to that of

without vertical drains. Introduction of vertical drains hasreduced the variations in moisture content over the thick-

ness significantly. The moisture content variation with the

thickness of sample is minimal with 5 or 9 vertical drains.

The conventional test results show the water content at the

middle portion of the sample to be much lower than the

one at the top and bottom of the samples. This results in

much lower value of percent swell as well as swelling pres-

sure. Herein, it is evident that introducing vertical drains has

improved the access for the sample to imbibe water needed

for swelling and in turn has reflected in the value of swell.

Percent swell versus log time relationship has essentially

three phases viz., initial, primary, and secondary portion. At

any density, introduction of vertical drains has reduced the

time required to attain initial and primary swelling by nearly

50 % as compared to that without vertical drains.

Prediction of both ultimate swell and also swelling pres-

sure with vertical drains using the concept of rectangular

hyperbola has found to agree well with the experimental

 values. The advantage of the prediction method is that it

could be done with only the data from the initial stages of

the swell test and the experiment could be terminated with-

out continuing till equilibrium conditions are reached. The

ratio of predicted / actual swelling pressure has reduced withthe introduction of vertical drains. It could be reasoned

that vertical drains has improved the access for the sample

to imbibe water needed for swelling as seen in the water

content variation and in turn has reflected in the value of

swelling pressure. More the number of vertical drains, more

quickly the linear relationship of time/pressure versus time

is obtained and hence reduced time of the test to predict the

swelling pressure.

Introduction of vertical drains has not much influ-

ence on the rate of secondary swell. Knowledge of rate of

secondary swelling will facilitate in long-term prediction of

swell, which may be a useful data for taking precautionarymeasures for long term swell behavior when dealing with

expansive soils. Preconsolidation (σ ʹc) pressure increases with

the increase in the initial dry density for any particular VDs.

Further, at any particular dry density,  pc has decreased with

the increase in the number of VDs. The precompression

pressure, σ ʹc determined without vertical drains can be more

because of lesser accessibility of water at the centre.

Figure 10.  (a) 1+e versus log pressure relationship for varying density

with zero vertical drains; (b) 1 + e versus log pressure relationship for

same density (=1.50 Mg/m3 ) with varying vertical drain

(a)

(b)

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Swelling behavior of expansive soils 111

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