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La

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a

ARRA

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t(tfttiteiw1olo

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Journal of Rock Mechanics and Geotechnical Engineering 5 (2013) 162–167

Journal of Rock Mechanics and GeotechnicalEngineering

Journal of Rock Mechanics and GeotechnicalEngineering

journa l homepage: www.rockgeotech.org

reep model for unsaturated soils in sliding zone of Qianjiangping landslide�

iangchao Zoua, Shimei Wanga,∗, Xiaoling Laib

Key Laboratory of Geological Hazards of Three Gorges Reservoir Area of Ministry of Education, China Three Gorges University, Yichang 443002, ChinaDepartment of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China

r t i c l e i n f o

rticle history:eceived 16 May 2011eceived in revised form 16 February 2012ccepted 28 May 2012

eywords:liding zonensaturated soilsatric suction

a b s t r a c t

The mechanical behavior of sliding zone soils plays a significant role in landslide. In general, the slidingzone soils are basically in unsaturated state due to rainfall infiltration and reservoir water level fluctuation.Meanwhile, a large number of examples show that the deformation processes of landslides always take along period of time, indicating that landslides exhibit a time-dependent property. Therefore, the deforma-tion of unsaturated soils of landslide involves creep behaviors. In this paper, the Burgers creep model forunsaturated soils under triaxial stress state is considered based on the unsaturated soil mechanics. Then,by curve fitting using the least squares method, creep parameters in different matric suction states areobtained based on the creep test data of unsaturated soils in the sliding zones of Qianjiangping landslide.

reep behaviorurgers model

Results show that the predicted results are in good agreement with the experimental data. Finally, to fur-ther explore the creep characteristics of the unsaturated soils in sliding zones, the relationships betweenparameters of the model and matric suction are analyzed and a revised Burgers creep model is developedcorrespondingly. Simulations on another group of test data are performed by using the modified Burgerscreep model and reasonable results are observed.

© 2013 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

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cmmlippme

. Introduction

Landslide is a major geological disaster, which poses a greathreat to human life and property in most parts of the worldYang and Lu, 1993). Sliding zone, one of the significant struc-ural elements of a landslide, records the detailed informationor physical changes and dynamic developments in the evolu-ion process of a landslide. In terms of sliding belt formed inhe development of a landslide, the creep behaviors of the soilsn sliding zone can reveal the mechanism of landslide forma-ion, and serves as an important index for the prediction andvaluation of a landslide (He, 2005). On the one hand, soils in slid-ng zone are basically unsaturated due to rainfall infiltration or

ater level fluctuation of reservoir (Riemer, 1992; Furuya et al.,999; Wang et al., 2008); on the other hand, a large number

f cases show that the deformation of landslides always takes aong period of time, which means that time-dependent propertiesf landslide soils are observed. According to this understanding,

� Supported by the National Natural Science Foundation of China (50879044)nd Master’s Degree Thesis Excellent Training Funds of Three Gorges University2011PY008).∗ Corresponding author. Tel.: +86 717 6393044.

E-mail address: wwsm3044@yahoo.com.cn (S. Wang).

atw

utubl

674-7755/$ – see front matter © 2013 Institute of Rock and Soil Mechanics, Chinese Acattp://dx.doi.org/10.1016/j.jrmge.2013.03.001

series of triaxial creep tests on unsaturated sliding zone soilsere performed (Lai, 2010; Lai et al., 2010). To investigate andescribe the creep behaviors of the unsaturated soils, an appro-riate creep model needs to be constructed on the basis of creepest data.

At present, creep models for the saturated soils can be roughlylassified into four categories: component model, integrationodel, empirical model and semi-empirical model. Among theseodels, component model, which is constructed on the basis of

inear visco-elastoplastic theorem, is featured with clear phys-cal meaning, visual concept and good reflection of rheologicalroperties of geotechnical materials (Sun, 1999). For this pur-ose, numerous researches have been conducted using componentodels (Liingaard et al., 2004; Wang et al., 2004; Sun, 2007; Yan

t al., 2008; Dey and Basudhar, 2010; Zhang et al., 2012). Most ofbove-mentioned researches using creep models took the satura-ion condition into consideration, but the unsaturated conditionas rarely considered.

In this paper, a revised Burgers creep model for unsat-rated soils in triaxial stress state is constructed. Then, all

he parameters are obtained by the self-developed FSR-6nsaturated triaxial creep apparatus. Finally, the relationshipsetween parameters of the model and matric suction are ana-

yzed.

demy of Sciences. Production and hosting by Elsevier B.V. All rights reserved.

L. Zou et al. / Journal of Rock Mechanics and Geotechnical Engineering 5 (2013) 162–167 163

Table 1Physico-mechanical parameters of soils in the sliding zone of Qianjiangping landslide (Chen, 2005; Lai, 2010).

3 mit (%) Plastic limit (%) Cohesion (kPa) Internal friction angle (◦)

17 28.3 18

2

2

ibYlts

Qi

2

duaisomsa

is

2

gtwdTthi

2

tae

TS

Specific gravity Water content (%) Density (g/cm ) Liquid li

2.71 19 2.02 40.5

. Creep test and results

.1. Soil samples

The soils used in laboratory test were sampled from the slid-ng zone of Qianjiangping landslide, which is located at the southank of Qinggan River, a branch of Yangtze River in Zigui County,ichang, China. In this test, the sliding zone soils with particle size

ess than 2 mm were used to make remolded samples for labora-ory test, because it is very difficult to obtain field undisturbed soilamples from the sliding zone of landslides.

Some basic laboratory indices of soils in the sliding zone ofianjiangping landslide (Chen, 2005; Lai, 2010) are summarized

n Table 1.

.2. Creep test apparatus

The FSR-6 unsaturated triaxial creep apparatus has beeneveloped based on conventional triaxial creep apparatus andnsaturated triaxial apparatus. It consists of loading system andir pressure controlling system (Guan and Wang, 2008). Hence, its capable of applying constant shear stress and constant air pres-ure. The FSR-6 unsaturated triaxial creep apparatus is composedf several parts, including confining pressure controlling system,atric suction controlling system, pore water pressure measuring

ystem, axial loading system, cell pressure chamber, measurementnd data acquisition system (see Fig. 1).

The axial load was exerted in a conventional way by apply-ng deadweights in the axial direction. The dimensions of the soilpecimens are 120 mm in length and 60 mm in diameter.

.3. Test scheme

The scheme of creep test is listed in Table 2. In order to investi-ate the effect of matric suction on soil creep characteristics underhe unsaturated condition, the net confining pressure � ′

3(= �3 − ua)as kept at 100 kPa, and the deviator stress level (the ratio of theeviator stress, q, to the drained shear strength, qf) was kept at 0.55.he matric suction, s, was controlled at 50–250 kPa by adjustinghe pore air pressure ua. Five groups of drained triaxial creep testsave been conducted considering drainage condition of landslide

n a long period of time.

.4. Creep test results

According to the test scheme shown in Table 2, each group ofest was performed within about one week. The creep test resultsre shown in Fig. 2, in which simulated curves were obtained usingxtended Burgers creep model (see Section 3.2).

able 2cheme of creep test.

Group � ′3 (kPa) s (kPa) qf (kPa) q (kPa) q/qf

1 100 50 187 103 0.552 100 100 225 124 0.553 100 150 256 141 0.554 100 200 341 188 0.555 100 250 347 191 0.55

sasrtrs

Fig. 1. FSR-6 unsaturated triaxial creep apparatus.

It can be observed from Fig. 2 that the creep behaviors of theliding zone soils are evident under different matric suctions. Inddition, it can be found that the higher the matric suction is, themaller the creep strain is, which exhibits the impact of unsatu-ated conditions on soil creep behaviors. It is also worth noting that

he acceleration creep behavior was not measured because of theelatively low deviator stress level. Actually, even in high deviatortress level, it is difficult to obtain the acceleration creep behavior in

164 L. Zou et al. / Journal of Rock Mechanics and Geotechnical Engineering 5 (2013) 162–167

thc

3

3

a

scsum

mtiKcdficdc

at

p

w

p

p

p

p

q

q

q

wttrHKb

ε

Fig. 2. Results of creep test under different matric suctions.

he laboratory tests. Because the sliding zone soils usually presentigh plasticity and large plastic strain properties, the accelerationreep behavior will not be considered in this paper.

. Creep model for unsaturated soils

.1. Burgers creep model

Burgers creep model is mainly composed of Maxwell bodynd Kelvin body (Fig. 3a). The Maxwell body can be employed to w

Fig. 3. Sketch of component creep models.

imulate the instantaneous and stationary creep strains of the creepurves under shear stress, and the decreasing creep strain can beimulated by the Kelvin body. Thus, the Burgers model is oftensed to simulate the visco-elastoplastic creep process of geologicalaterials (Sun, 1999).Practically, several Kelvin bodies are used in series in the Burgers

odel, which is known as the extended Burgers model. It exhibitshe same creep law as the Burgers model but is more accuraten predicting experimental creep curves. Theoretically, the moreelvin bodies are put in series into the model, the more precise thereep characteristics of soils can be reflected, whereas the moreifficult to determine model parameters for use (Sun, 1999). There-ore, the extended Burgers model with two Kelvin bodies in series,.e. M-2K creep model, is adopted to fit the experimental creepurves (Fig. 3b). It should be noted that the extended Burgers modeloes not account for the stage of acceleration creep, which is moreomplicated and will not be discussed in this paper.

The extended Burgers creep model is developed by insertingnother Kelvin body into the Burgers model. The constitutive equa-ion (Sun, 1999) can be written as

1� + p2�̇ + p3�̈ + p4 �� = q1ε̇ + q2ε̈ + q3�ε (1a)

here

1 = El1El2 (1b)

2 = ˇ1El1 + ˇ3El1 + ˇ1El2 + ˇ2El2 + El1El2

EH(1c)

3 = ˇ1ˇ2 + ˇ1ˇ3 + ˇ2ˇ3 + ˇ1ˇ3El1

EH+ ˇ1ˇ2El2

EH(1d)

4 = ˇ1ˇ2ˇ3

EH(1e)

1 = El1El2ˇ1 (1f)

2 = El1ˇ1ˇ3 + El2ˇ1ˇ2 (1g)

3 = ˇ1ˇ2ˇ3 (1h)

here EH, El1 and El2 are the elastic moduli of the Maxwell body,he first and second Kelvin bodies, respectively; ˇ1, ˇ2 and ˇ3 arehe viscosity of Maxwell body, the first and second Kelvin bodies,espectively (see Fig. 3); �, �̇, �̈ and �� are the stresses exerted on theook body and Newton body of Maxwell body, the first and secondelvin bodies, respectively; ε̇, ε̈ and �ε are the strains of Maxwellody, the first and second Kelvin bodies, respectively.

The creep equation of this model can thus be obtained as

(t) = �{

1EH

+ t

ˇ1+ 1

El1

[1 − exp

(−El1t

ˇ2

)]

+ 1El2

[1 − exp

(−El2t

ˇ3

)]}(2)

here t is the time.

nd Geo

3

s

oe

s

w

s

s

wsp

�

s

w

s

s

ipsaa

s

wd

s

w

s

(tm(od

ε

wttKb

K

w

3

oifo(

gt

Britm

etb1

eswsGds

vGvt

Glviw

3

m

ε3K 3GH 3�1 3Gl1 �2

L. Zou et al. / Journal of Rock Mechanics a

.2. Extended Burgers creep model for unsaturated soils

To extend Burgers creep model for unsaturated soils, the stresstate in unsaturated soils needs to be analyzed.

According to the theory of elasticity mechanics, the stress statef one point can be expressed by stress tensor (sij) as follows (Xiet al., 2008):

ij = s′ij + s′′

ij (3a)

here

′ij = �mıij = 1

3�kkıij (k = 1, 2, 3) (3b)

′′ij = sij − �mıij (3c)

here s′ij

is the spherical stress tensor, s′′ij

is the deviator stress ten-or, �m is the mean stress, ıij is the Kronecker delta, and �kk is therincipal stress.

In the triaxial stress state, by using three invariable stresses �1,2, �3, the stress state can be written as follows:

ij = s′ij + s′′

ij =

⎡⎢⎣

�1 0 0

0 �2 0

0 0 �3

⎤⎥⎦ (4a)

here

′ij = �mıij = 1

3(�1 + �2 + �3) (4b)

′′ij = sij − �mıij =

⎡⎢⎣

�1 − �m 0 0

0 �2 − �m 0

0 0 �3 − �m

⎤⎥⎦ (4c)

Practically, in conventional triaxial creep tests, the axial stresss �1 and the confining stress is �2 = �3. Fredlund et al. (1978) pro-osed that the pore air pressure should be added to describe thetress state of one point, which is known as double stress state vari-bles: matric suction and net stress. The matric suction is expresseds

= ua − uw (5)

here uw is the pore water pressure. It can be valued as zero in therained shear test.

Consequently, the net stress tensor is changed to

ij = s′ij + s′′

ij =

⎡⎢⎣

�1 − ua 0 0

0 �2 − ua 0

0 0 �3 − ua

⎤⎥⎦ (6a)

here

′ij = �mıij − ua (6b)

According to the matric suction tensor described in Eq. (5), Eq.2) can be written in three-dimensional state based on the assump-ions (Yan et al., 2010) as follows: (1) the volumetric deformation of

aterials is flexible, linear, invariable and completed in an instant;2) the creep deformation is caused by deviator stress tensor, inther words, the spherical stress tensor has no contribution to creepeformation; and (3) the Poisson’s ratio does not vary with time.

Therefore, Eq. (2) can be rewritten as

ij =s′

ij

3K+

s′′ij

3GH+

s′′ij

3�1t +

s′′ij

3G

[1 − exp

(−Gl1t

�2

)]

l1

+s′′

ij

3Gl2

[1 − exp

(−Gl2t

�3

)](7)

technical Engineering 5 (2013) 162–167 165

here GH, Gl1 and Gl2 are the shear moduli of the Maxwell body,he first and second Kelvin bodies, respectively; �1, �2 and �3 arehe viscous coefficients of the Maxwell body, the first and secondelvin bodies, respectively; and K is the bulk modulus, which cane determined by

= 2GH(1 + �)3(1 − 2�)

(8)

here � is the Poisson’s ratio.

.3. Parametric study

Parameters of the extended Burgers creep model can bebtained by using nonlinear least squares method, which can bemplemented by MATLAB, and details of using this method can beound in Zou and Wang (2010). As the value of � has minor effect onther parameters, it is assumed as 0.4 herein based on experienceSun, 1999).

Parameters of the extended Burgers creep model under eachroup of matric suction, as well as the correlation coefficient R2 ofhe fitting curves, are summarized in Table 3.

As shown in Table 3, the predicted results using the extendedurgers creep model are in good agreement with the experimentalesults shown in Fig. 2, with correlation coefficients above 0.98. Itndicates that the reasonable predication of the creep behaviors ofhe unsaturated soils can be given by the extended Burgers creep

odel.In order to further investigate the relationship between param-

ters of the extended Burgers creep model and matric suction,he plots of model parameters versus matric suction (normalizedy dividing the standard atmospheric pressure Pa, which equals01.325 kPa) are presented in Fig. 4.

As it can be seen from Fig. 4, the obvious linear relationshipxists between the model parameters (GH, Gl1, Gl2, �1) and matricuction (s); and it can be expressed by the linear function y = ax + b,here a and b are the correlation coefficients. When the matric

uction is increased, GH and �1 show a linear increasing trend, butl1 and Gl2 display a linear decreasing trend, i.e. the elasto-plasticeformation of the samples decreases with the increasing matricuction.

In Eqs. (6a) and (6b), we can see that the maximum value ofisco-elastic deformation depends on the values of Gl1/�2 andl2/�3, thus the values of Gl1/�2 and Gl2/�3 were considered asariables, and the relationships with the matric suction are illus-rated in Fig. 5.

In Fig. 5, a linear relation also exists between the values ofl1/�2, Gl2/�3 and matric suction s, which can also be written by the

inear function y = ax + b. When the matric suction is increased, thealues of Gl1/�2 and Gl2/�3 show a linear decreasing trend, indicat-ng that the maximum value of visco-elastic deformation decreases

ith the increasing matric suction.

.4. Modified Burgers creep model

Given the parameters of the Burgers creep model vary withatric suction, the Burgers creep model is modified as follows:

ij =s′

ij′ +

s′′ij′ +

s′′ij′ t +

s′′ij′

[1 − exp

(−G′l1t′

)]

+s′′

ij

3G′l2

[1 − exp

(−G′l2t

�′3

)](9a)

166 L. Zou et al. / Journal of Rock Mechanics and Geotechnical Engineering 5 (2013) 162–167

Table 3Parameters of the extended Burgers creep model.

Group GH (MPa) Gl1 (GPa) Gl2 (kPa) �1 (MPa min) �2 (kPa min) �3 (kPa min) R2

1 139 439 33.8 65.2 98.2 169 0.992 151 531 29.6 75.9 88.8 260 0.993 155 551 28.5 14 162 595 27 15 167 602 27.4 1

Fig. 4. Normalized relations between parameters of the extended Burgers modeland matric suction.

w

K

G

G

G

�

Geac

gapt

06 61.1 271 0.9955 33 122 0.9871 30.4 225 0.98

here

′ = 2(1 + �)3(1 − 2�)

GH (9b)

′H = aGH

s

Pa+ G0

H (9c)

′11 = aGl1

s

Pa+ G0

l1 (9d)

′l2 = aGl2

s

Pa+ G0

l2 (9e)

′1 = a�1

s

Pa+ �0

1 (9f)

G′l1

�′2

= aGl1/�2

s

Pa+

(Gl1

�2

)0

(9g)

G′l2

�′3

= aGl2/�3

s

Pa+

(Gl2

�3

)0

(9h)

In saturated soils, the matric suction s is considered to be 0, thus0H, G0

l1, G0l2, �0

1, (Gl1/�2)0, (Gl2/�3)0 can be considered as the param-ters under saturated condition; and aGH , aGl1

, aGl2, a�1 , aGl1/�2

,

Gl2/�3can be considered as the influence coefficients of parameters

orresponding to the matric suction.In order to calibrate the modified Burgers creep model, another

roup of test data is employed. This group of test soils is the sames other several groups, which can be considered that their creeparameters are alike. Keeping the net confining pressure and devia-or stress level of this group of experiment as same as other several

Fig. 5. Normalized relations of Gl1/�2 and Gl2/�3 with matric suction s.

L. Zou et al. / Journal of Rock Mechanics and Geo

0 2,000 4,000 6,000 8,000 10,000

0

2

4

Cre

ep s

trai

n (

%)

Test data

Simulated curve

6

gs

dt

4

bd

(

(

(

cc

oud

R

C

D

F

F

G

H

L

L

L

R

S

S

W

W

X

Y

Y

Y

Z

Time (min)

Fig. 6. Results of creep test under matric suction of 300 kPa.

roups, and the matric suction of 300 kPa, the simulated results arehown in Fig. 6.

It can be seen from Fig. 6 that the simulated curve also fits testata well with the correlation coefficient of 0.93, which proves thathis modified Burgers creep model is reasonable and effective.

. Conclusions

The unsaturated soils in the sliding zone exhibit evident creepehaviors. Based on detailed analysis, some conclusions can berawn as follows:

1) The extended Burgers creep model for unsaturated soils intriaxial stress state was derived, and all of parameters undervarious matric suctions were obtained. The simulated resultsare in good agreement with the experimental results, with cor-relation coefficients above 0.98.

2) Relations between parameters of the extended Burgers creepmodel and matric suctions were discussed, and a linear rela-tion was found between them. The elasto-plastic deformationand the maximum value of visco-elastic deformation of the soilsamples decrease with the increasing matric suction.

3) Considering the relations between parameters of the extendedBurgers creep model and matric suction, a modified Burgerscreep model was developed and calibrated by another groupof creep test. The test results show that the modified Burgerscreep model is reasonable and effective.

Creep behaviors of sliding zone soils are rather complex, espe-ially in unsaturated situation. In this paper, just one level of netonfining pressure and deviator stress was discussed. However, in

Z

technical Engineering 5 (2013) 162–167 167

rder to better understand and model the creep behavior of unsat-rated sliding zone soils, more levels of net confining pressures andeviator stresses should be considered in further studies.

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