Research of soil–water characteristics and shear

strength features of Nanyang expansive soil

Linchang Miao*, Songyu Liu, Yuanming Lai

College of Traffic Engineering, Institute of Geotechnical Engineering, Southeast University, Nanjing 210096, China

Received 8 December 2000; accepted 31 October 2001

Abstract

Nanyang expansive soil is investigated in its unsaturated state in this paper. The wetting–drying cycle tests of soil–water

characteristics of Nanyang expansive soil have been performed in the laboratory. The test results show that the soil–water

characteristic curve of the pre-load specimen can well reflect the soil property function of expansive soil. The strength features

of the different suction states of the unsaturated expansive soil are also investigated. The hyperbolic model of the suction

strength is presented and the parameters of this model are easily determined by tri-axial tests of unsaturated soils. The

hyperbolic model is conveniently applied to predict suction strength of an unsaturated soil. D 2002 Elsevier Science B.V. All

rights reserved.

Keywords: Expansive soil; Soil–water characteristic curve; Suction; Suction strength; Hyperbolic model

1. Introduction

The expansive soil is a particular clay that is of spe-

cial characteristics (i.e., swell–shrinking, crack and

over-consolidation characteristics). The characteristics

of the expansive soil are strongly related to the change

in suction.

The behavior of an unsaturated soil is strongly re-

lated to the pore size and pore geometrical distribution.

As a result, the soil–water characteristic curve defines

the degree of saturation corresponding to a particular

suction in the soil and becomes a dominant relationship

for understanding unsaturated soil behavior, but para-

meters of the equation of the soil–water characteristic

curve are difficult to determine. A number of equations

have been proposed to best-fit the soil–water charac-

teristic curve empirically. The following equation is the

one proposed by Fredlund and Xing (1994) to best-fit

the soil–water characteristic curve empirically:

hðua � uw,as,ns,msÞ

¼ Cðua � uwÞhs

fln½eððua � uwÞ=asÞns �gmsð1Þ

where: h = volumetric water content, hs = volumetric

water content at saturated, e = 2.718, ua = pore air

pressure, uw = pore water pressure, (ua� uw) =matric

suction, af = soil parameter related to the air entry of

the soil and equal to the inflection point on the curve,

nf = soil parameter related to the rate of desaturation,

mf = soil parameter related to residual water content,

and C(ua� uw) = correction factor to ensure that the

function goes through 1,000,000 kPa of suction at zero

0013-7952/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved.

PII: S0013 -7952 (01 )00136 -3

* Corresponding author.

E-mail addresses: lc.miao@jlonline.com (L. Miao),

lsong@public1.ptt.js.cn (S. Liu), ymlai@ns.lzbac.cn (Y. Lai).

www.elsevier.com/locate/enggeo

Engineering Geology 65 (2002) 261–267

water content. However, the conventional soil–water

characteristic curve does not consider the actual stress

state of soil mass in the field, and some parameters are

determined with difficulty.

The shear strength equation for an unsaturated soil

is presented by Fredlund et al. (1978) as:

sf ¼ cVþ ðr � uaÞtan/Vþ ðua � uwÞtan/b ð2Þ

where: sf = shear strength of an unsaturated soil, cV=effective cohesion of the soil, /V= effective angle of

shearing resistance for a saturated soil, (r� ua) = net

normal stress, (ua� uw) = soil suction, and /b = angle

of shearing resistance relative to an increase in suction,

but /b is difficult to determine.

Fredlund et al. (1994) and Vanapalli et al. (1996)

suggested several models for predicting the shear

strength of an unsaturated soil using the soil–water

characteristic curve and the saturated shear strength

parameters. Eq. (3) given below can be used for pre-

dicting the shear strength of unsaturated soil:

sf ¼ cVþ ðr � uaÞtan/Vþ ðua � uwÞtan/V

h � hrhs � hr

� �ð3Þ

where: hs = saturated volumetric water content, hr =volumetric water content at residual condition. The

second term of Eq. (3) is the shear strength contribution

due to suction. It can be expressed as

sus ¼ ðua � uwÞtan/Vh � hrhs � hr

� �ð4Þ

where sus is suction strength. It indicates that the soil–

water characteristic curve can be used to compute soil

property functions for unsaturated soils approximately.

However, soil–water characteristic curve is conven-

ientlymeasured in the laboratory, whereas the soil in the

field is usually subjected to certain stress. Thus, there

are some unestimated errors using Eq. (3) to compute

soil property function for unsaturated soils. For this

reason, the soil–water characteristic curve and shear

strength features of Nanyang expansive soils have been

studied in the paper.

2. Physical mechanical parameters of Nanyang

expansive soils

Nanyang is located in Henan Province, China. It is

a semi-arid region, and there is a lot of expansive soil

in Nanyang area. The canal of China Middle Route

South-to-North Water Transfer will cross through the

area. The canal is a typical cut and fill high slope in

expansive soils. In order to ensure the engineering

safety of this canal, the mechanical parameters, defor-

mation, soil–water characteristic curve, shear strength

feature and slope stability must be investigated.

The physical mechanical parameters of Nanyang

expansive soils are measured in the laboratory and

given in Table 1. The mineral components of Nanyang

expansive soils are given in Table 2. These parameters

show that Nanyang expansive soil is the middle grade

expansive soil and the content of illite and montmor-

illonite is higher.

3. The soil–water characteristic curve

The swell–shrinking deformation of expansive soil

is strongly related to the variation of water content. It

will be swelling as water content increases and

shrinkage as water content decreases. The soil–water

characteristic curve defines the relationship between

the soil suction and volumetric or gravimetric water

content, so the suction of the expansive soil should be

related to water content.

Table 1

The physical mechanics parameters of Nanyang expansive soils

Specific Dry density NMC WP (%) WL (%) IP Free cV(kPa) / (j) Granularity (%)gravity (g/cm3) W0 (%) sweling (%)

> 0.05

mm

0.05–0.005

mm

<0.005

mm

< 0.002

mm

2.7 1.63 21.4 26.5 58.3 31.8 74.0 32.0 21.3 6.7 48.6 44.7 24.8

L. Miao et al. / Engineering Geology 65 (2002) 261–267262

The soil–water characteristic curve of a soil is con-

ventionally measured by means of a pressure plate ex-

tractor in which any vertical or confining stress cannot

be applied and volume change of the soil specimen is

assumed to be zero. The soil in the field is usually

subjected to certain stress. Although it is theoretically

recognized that the stress state of a soil has some

influence on the soil–water characteristic curve (Fred-

lund and Raharjo, 1993), Vanapalli et al. (1996, 1998)

examined the influence of the total stress state on the

soil–water characteristic curve of a compacted fine-

grained soil indirectly. In this paper, the influence of

the stress state and wetting–drying cycles is studied for

the soil–water characteristic curve of Nanyang expan-

sive soil.

For Nanyang expansive soil, two group tests of the

soil–water characteristic curve are made using 15 bar

of the pressure plate. One group specimen is saturated

allowing volumetric change (i.e., no pre-load exerting

on the specimen). The other group specimen is satu-

rated maintaining constant volume (i.e., exerting a

pre-load on the specimen). The two group expansive

soil specimen are remolded specimen with a dry

density of 1.5 g/cm3. Three wetting–drying cycles

are measured for each group specimen in this test.

Fig. 1 is the soil–water characteristic curve of no

pre-load exerted on the specimen. Measured results

show that the wetting–drying cycles of the expansive

soil specimen are of obvious effect for the soil–water

characteristic curve of the no pre-load specimen.

There is a marked hysteresis between the drying and

wetting curve for all no pre-load expansive soil speci-

men. The hysteresis potential is reduced as the num-

ber of wetting–drying cycles increases, and will tend

to be stable. The soil–water characteristic curve of the

exerting pre-load expansive soil specimen is shown in

Fig. 2. From Fig. 2, it can be seen that the hysteresis

between the drying and wetting curve is more stable

as the number of wetting–drying cycles increases, and

the influence of the wetting–drying cycles of the pre-

load specimen is smaller than that of the no pre-load

specimen. So the soil–water characteristic curve of

the pre-load specimen can well reflect the soil prop-

erty function of expansive soil.

Comparing Fig. 1 with Fig. 2, the two soil–water

characteristic curves have obvious differences. This

phenomena is mainly caused by the arrangement in

different initial stress state. Further, the size of the

hysteresis loops of between the drying and wetting

curve seems to be dependent on the initial stress state

of soil specimen. Parameters hs, hr determined would

be stable and identical for one soil using the soil–

water characteristic curve of the pre-load specimen.

Fig. 3 is the soil–water characteristic curve of the pre-

Fig. 1. Soil–water characteristic curve of no pre-load exerted on the

specimen.

Fig. 2. Soil–water characteristic curve of pre-load exerted on the

specimen.

Table 2

The mineral components of Nanyang expansive soils (%)

Montmorillonite Illite Kaolinite Felspar Hydromic Chlorite Others

23.1 38.5 8.3 10.1 5.5 6.4 8.1

L. Miao et al. / Engineering Geology 65 (2002) 261–267 263

load Nanyang expansive soil specimen in total suction

range. The air entry value and the residual value of

Nanyang expansive soil are approximately 25 and

1500 kPa, and parameters hs = 33.7% and hr = 9.2%according to Fig. 3, respectively.

4. Shear strength test

4.1. Shear strength test of saturated expansive soil

The shear strength test of the saturated expansive

soil is measured by using conventional tri-axial. The

specimens are the remolded expansive soil specimen

and dry density is 1.5 g/cm3. The tri-axial test results

are shown in Fig. 4. Themeasured parameters of remol-

ded expansive soil specimen is cV= 32 kPa, /V= 21.3j.

4.2. Shear strength test of the unsaturated expansive

soils

The specimens have been prepared to predetermine

water content and density condition by static compac-

tion. The specimens are the remolded Nanyang expan-

sive soil. The dry density is 1.5 g/cm3, and the initial

water content is 17%. The tests of unsaturated soils are

performed by controlling suction in us = ua� uw = 50,

80, 120 and 200 kPa with unsaturated tri-axial. The

tests are made under the condition of draining water,

and the shear rate is 0.009 mm/min. Figs. 5–8 show

the stress–strain curve of the unsaturated soil tests in

us = 50, 80, 120 and 200 kPa, respectively. Tri-axial

test data are given in Table 3.

InTable3, ctotal = cV+ sus, cV is effective cohesive, susis suction strength and (/b = tan � 1(sus/us)) is the angleof shearing resistance relative to an increase in suction.

/b decreases with suction increase. It is a nonlinear

relationship between /b and suction.

4.3. Hyperbola model of suction strength

The tri-axial tests of the unsaturated expansive soils

demonstrate that cVand /Vare invariable, i.e., cV( = 32kPa) and /V( = 21.3j) are independent from suction.

Fig. 9 shows the relationship between us(us = ua� uw)

and sus, which is nonlinear. If sus and us are trans-

formed to 1/us and 1/sus, it becomes an approximate

linear relationship between 1/us and 1/sus. But when

Fig. 3. Soil–water characteristic curve of pre-load exerted on the specimen of Nanyang expansive soil.

L. Miao et al. / Engineering Geology 65 (2002) 261–267264

us = 0, 1/us will be singularity, so 1/us and 1/sus may be

transformed to 1/(us + pat) and 1/(sus + pat), where pat isatmospheric pressure. Fig. 10 shows the relationship

between 1/(us + pat) and 1/(sus + pat). We can use a

linear equation to describe that:

1

sus þ pat¼ a

us þ patþ b ð5Þ

where a and b are the test parameters and are deter-

mined by regressive analysis of test data of unsatura-

ted soil. For Nanyang expansive soil, a = 0.54 and b =

0.0046 kPa� 1. When us = 0, the soils are saturated

soils, so that sus = 0. If us = 0 and sus = 0 in Eq. (5), Eq.

(5) will become:

b ¼ 1� a

patð6Þ

Inserting Eq. (6) to Eq. (5), we can obtain:

sus ¼aus

1þ 1�apat

usð7Þ

Eq. (7) is a hyperbola equation. This is the hyperbola

model of the suction strength of unsaturated soils.

When us = 0 in Eq. (7), sus = 0; and us!l in Eq.

(7), sus! (a/(1/� a))pat. It indicates that the limit of

Fig. 6. Tri-axial test results of unsaturated expansive soil (us = 80

kPa).

Fig. 7. Tri-axial test results of unsaturated expansive soil (us = 120

kPa).

Fig. 5. Tri-axial test results of unsaturated expansive soils (us = 50

kPa).

Fig. 4. Tri-axial test results of saturated expansive soils.

L. Miao et al. / Engineering Geology 65 (2002) 261–267 265

sus is (a/(1� a))pat. This illustrates that the suction

strength is finite. Thus, equation of unsaturated soil

strength can be re-written as:

sf ¼ cVþ ðr � uaÞtan/Vþaus

1þ 1�apat

usð8Þ

When soil is saturated, i.e., us = 0, Eq. (8) will be

reduced as follows:

sf ¼ cVþ ðr � uaÞtan/V

We can apply the hyperbola model of suction strength

to the practical engineering and predict and calculate

the shear strength of unsaturated soils based on suction

data of unsaturated soils. However, parameter a in Eq.

(7) is constant for a certain range suction of unsatu-

rated soil tri-axial, i.e., it is relative to the range suction

of the test.

4.4. Suction strength analysis

Considering the soil–water characteristic curve of

pre-load expansive soil specimen and the hyperbolic

model of the suction strength, Eq. (4) (Vanapalli’s

(1996) model) and Eq. (7) (the hyperbola model of

this paper) could be used to calculate suction strength

of Nanyang expansive soils, respectively. The calcu-

lating suction strength are shown in Table 4. The

calculating results show that the calculating suction

strength of Vanapalli’s model is increased as us > 1000

kPa (i.e., water content of the soil specimen is higher)

and decreased as us > 1000 kPa (i.e., water content of

the soil specimen is lower). This phenomenon illus-

trates that Vanapalli’s model might be used to describe

the strength feature of an unsaturated soil in low

suction. But the suction strength of the hyperbola

model is increased as soil suction increases and there

is a limit suction strength, which accords with prac-

Fig. 9. The relationship curve between us and sus.

Fig. 10. The means of parameters a and b.

Fig. 8. Tri-axial test results of unsaturated expansive soil (us = 200

kPa).

Table 3

Shear strength data of Nanyang expansive soil

us (kPa) 50 80 120 200

Ctotal (kPa) 51.2 59 71 89.3

sus (kPa) 19.2 30.6 39 57.3

cV(kPa) 32.0 31.8 32.1 31.9

/V(j) 21.3 21.4 21.2 21.3

/b (j) 21.0 20.9 18.0 16.0

L. Miao et al. / Engineering Geology 65 (2002) 261–267266

tical condition. The hyperbola model of the suction

strength could be used to reflect the strength behavior

of an unsaturated soil. In Table 4, the calculating

suction strength of both Vanapalli’s model and the

hyperbola model are of basic agreement when soil

suction is smaller than 300 kPa, which illustrates that

the hyperbola model of suction strength is of reli-

ability to describe the strength feature of an unsatu-

rated soil.

5. Discussion

What we just discussed is the essential problem

that the engineering stability of the expansive soil

slope will be assured in the canal of Middle Route

South-to-North Water Transfer in China. The strength

of the expansive soil is a problem too. This is related

to the suction strength of expansive soil. Thus, the

following work must be done.

(1) Suction measure of the expansive soil. One

method is to directly measure soil suction with sensors

in the field. Another method will be to indirectly get

the soil suction from the soil–water characteristic

curve, but the method may produce some error. Our

research results illustrate that the soil–water charac-

teristic curve of pre-load specimen is better than that

without pre-load specimen.

(2) Stability research of expansive soil. If soil

suction has been obtained, we can use the hyperbola

model of suction strength presented in this paper to

calculate suction strength and total cohesion of expan-

sive soil and to predict the stability of expansive soil

slope.

6. Conclusions

(1) The soil–water characteristic curve and the size

of the hysteresis loops are influenced by the initial

stress state of the soil specimen. The hysteresis poten-

tial is reduced as the number of wetting–drying cycles

increases and will tend to stabilize at last for without

pre-load expansive soil specimen.

(2) The hysteresis loops between the drying and

wetting curve for pre-load expansive soil specimen

are more stable, and the influence of the number of

wetting–drying cycles is smaller, too. The soil–water

characteristic curve of the pre-load specimen could

well reflect the soil property function of expansive

soil. Using the soil–water characteristic curve of the

pre-load specimen, parameters hs, hr determined

would be stable and identical for an unsaturated soil,

and could predict the shear strength of unsaturated

soils with Eq. (3).

(3) The hyperbola model of suction strength pre-

sented by this paper could be used to reflect the

strength behavior of an unsaturated soil and is of

reliability to describe the strength feature of an unsa-

turated soil. The hyperbola model has an advantage in

that the model parameter might be easily determined

and has obvious meaning. The hyperbola model could

conveniently be applied to predict suction strength.

References

Fredlund, D.G., Raharjo, H., 1993. Soil Mechanics for Unsaturated

Soils. Wiley Interscience, New York.

Fredlund, D.G., Xing, A., 1994. Equations for the soil –water char-

acteristic curve. Can. Geotech. J. 31, 521–532.

Fredlund, D.G., Morgenstern, N.R., Widger, R.A., 1978. The shear

strength of unsaturated soil. Can. Geotech. J. 15, 313–321.

Fredlund, D.G., Xing, A., Huang, S., 1994. Predicting the perme-

ability functions for unsaturated soils using the soil–water char-

acteristic curve. Can. Geotech. J. 31, 533–546.

Vanapalli, S.K., Fredlund, D.G., Pufahl, D.E., Clifton, A.W., 1996.

Model for the prediction of shear strength with respect to soil

suction. Can. Geotech. J. 33, 379–392.

Vanapalli, S.K., Pufahl, D.E., Fredlund, D.G., 1998. The effect of

stress on the soil–water characteristic behavior of a compacted

sandy-clay till. 51st Canadian Geotechnical Conference, Ed-

monton, 81–86.

Table 4

Calculating suction strength of Nanyang expansive soils

us (kPa) 10 50 100 150 200 250 300 400 500 750 1000

h (%) 32.9 31.6 29.6 28.1 27.4 26.6 25.3 23.8 22.1 20.2 16.0

sus (kPa) in Eq. (4) 3.8 17.8 32.5 45.1 57.9 69.2 76.9 92.9 102.6 131.3 108.2

sus (kPa) in Eq. (7) 5.2 21.9 37.0 47.9 56.3 62.8 68.1 76.1 81.8 91.0 96.4

L. Miao et al. / Engineering Geology 65 (2002) 261–267 267