effect of soil hydraulic properties on slope stability

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JOUR.GEOL.SOC.INDIA, VOL.83,MAY 2014

586 MUHAMMAD MUKHLISIN AND OTHERS

Effect of Soil Hydraulic Properties Model on Slope StabilityAnalysis Based on Strength Reduction Method

MUHAMMAD MUKHLISIN1,2, MARLIN R AMADHAN BAIDILLAH

1, A NIZA IBRAHIM1,3

and MOHD. R AIHAN TAHA1

1Dept. of Civil & Structural Engineering, Universiti Kebangsaan Malaysia, Bangi, Malaysia2Dept. of Civil Engineering, Polytechnic Negeri Semarang, Semarang, Indonesia

3Dept. of Civil Engineering, Universiti Pertahanan Nasional Malaysia, Malaysia

Email: [email protected] and [email protected]

Abstract: Soil hydraulic properties models which have been proposed were derived based on the empirical fitting curve

such as Brooks-Corey model (BC) and Van Genuchten model (VG), or based on soil pore radius distribution such as

Lognormal model (LN). Each model has different accuracy for predicting soil moisture distribution. In the analysis of

rainfall-induced slope failure, the soil hydraulic properties model was needed to describe the physical phenomena of

behavior characteristic of water in unsaturated soil. As moisture content has an effect on soil strength, it is vital to select

the suitable soil hydraulic properties model for predicting Factor of Safety (FOS) especially in forecasting landslide

hazard. In this study, a numerical model of seepage finite element analysis using BC, VG, and LN model were used and

compared in order to analyze the soil moisture distribution, water movement phenomenon, and slope stability characteristic

in unsaturated soil slope based on the strength reduction method (SRM). The results showed that the variations of the

parameters predicting the moisture content of soil leads to differences of FOS in some cases. The parametric study

showed that for the unsaturated soil condition, BC model has the greatest FOS value than the other model, while VG

model has the lowest. On the other hand, the FOS of all models have the same result for the saturated condition. Other

than that, it was found that the increasing of ESP value in the surface layer has significant effect in the sub-surface layer.

Keywords: Hydraulic conductivity, Rainfall-induced slope failure, Stability analysis, Numerical model.

hydraulic properties is needed to describe the physical

phenomenon of water behavior characteristic in unsaturated

soil (Mukhlisin et al., 2011a). Soil hydraulic properties

include the soil water retention curve (the relationship

between volumetric water content θ and soil capillary

pressure ψ ) and the hydraulic conductivity function (the

relationship between unsaturated hydraulic conductivity K

andψ ). Generally, the soil hydraulic properties models which

have been proposed is derived based on the empirical fittingcurve or soil pore radius distribution. Some of the models

are based on the empirical fitting curve such as: Brooks-

Corey (BC) (Brooks and Corey, 1964) and van Genuchten

(VG) (van Genuchten, 1980) . Other than that, Lognormal

(LN) is based on the soil pore radius distribution (Kosugi,

1996). These models are intended to obtain prediction value

corresponding to the observed data. However, each model

has different accuracy of prediction of the soil moisture

distribution. van Genuchten and Nielsen (1985) concluded

that VG model was better than BC model with regard to the

accuracy of prediction of the moisture content for saturated

INTRODUCTION

Recently, due to the rapid development, slope failure

due to the high intensity rainfall each year, rainfall-induced

landslide has become an essential topic in geotechnical

engineering in tropical regions. The mechanism of rain-

water infiltration resulting in instability of soil slope has

been widely analyzed and reviewed. This is due to the

fact that rainwater infiltration is capable of changing soil

strength, and thus increases the probability of slope failure.In other words, the increase of saturation value or decrease

of the negative pore water pressure of the soil consequently

will decrease its shear strength values. There are several

factors that contribute to the slope failure such as soil

thickness (Mukhlisin and Taha, 2009), soil porosity

(Mukhlisin et al., 2006), hydraulic properties (Rahimi et

al., 2010) and characteristics of infiltrated water (Gasmo et

al., 2000, Mukhlisin et al., 2011b; Mukhlisin and Taha,

2012). However, the effect of hydraulic properties on soil

instability has not been dealt so far.

In the analysis of rainfall-induced slope failure, the soil

JOURNAL GEOLOGICAL SOCIETY OF INDIA

Vol.83, May 2014, pp.586-594

0016-7622/2014-83-5-586/$ 1.00 © GEOL. SOC. INDIA




SLOPE STABILITY ANALYSIS BASED ON STRENGTH REDUCTION METHOD 587

soil. This is due to the θ −ψ curve that has an inflection

point on it . Kosugi (1996) also concluded that the

models which are not derived based on soil pore radius

distribution are not effective enough to analyze moisture

characteristics. As the property of soil strength has

relationship with soil moisture distribution, it is necessary

to select the compatible soil hydraulic properties model.

In addition, the lack prediction of factor of safety (FOS)

leads to serious problem that might occur in landslide

hazard management.

In this study, a numerical model of seepage finite element

analysis using BC, VG and LN model were compared to

the analyzed soil moisture distribution, water movement

phenomena and slope stability characteristic in unsaturated

soil slope, based on strength reduction method. The study

was performed in two steps; pressure-head analysis, andstatic analysis. These two analyses were conducted by

employing a commercial software product, COMSOL

Multiphysics. Pressure-head analysis was conducted to solve

the Richard’s equation by calculating the pore water

pressures distribution, while static analysis was used to

compute the FOS by solving the distribution of the effective

stress of a slope.

DESCRIPTION OF THE NUMERICAL MODELS

Two-dimensional Unsaturated Flow Equation for Soil Water

In COMSOL Multiphysics, Richard’s equation is used

to solve the two-dimensional unsaturated flow problem.

The equation for soil water is as follow:

(1)

where p is pressure, δ ts is a scale time, C is the specific

capacity [1/cm], S e is the effective saturation, S is the storage

coefficient [1/cm], k s is the saturated hydraulic conductivity

[cm/s], η is the fluid viscosity, k r is the relative hydraulicconductivity, ρ

f is the fluid density, g is gravitational

acceleration, D is the vertical coordinate, and Q s is the fluid

source (COMSOL Multiphysics, 2007). It is noted that

all variables in this equation are constant except the

pressure, p.

Soil Hydraulic Properties Models

The three soil hydraulic properties models that were

used in this study to solve Eq. (1) are Brooks-Corey, Van

Genuchten, and Lognormal model. These equations will be

defining variables such as θ , C , S e and K r .

Brooks-Corey Model

Brooks and Corey (1964) proposed that the effective

saturation, S e is expressed as a power function with respect

to the matric pressure head y: The equations are as follows:

S e = (ψ

BC / ψ )λ for ψ < ψ

BC(2)

S e

= 1 for ψ ≥ ψ BC

(3)

where ψ BC

[cm] is the bubbling pressure and λ [-] is

dimensionless soil characteristic parameter. Based on

Mualem model for relative hydraulic conductivity model

K r

[-]= K/K s where K

s [cm/s] is saturated hydraulic

conductivity. The relationship of K r - ψ for BC model is

written as

K r (ψ ) = (ψ

BC / ψ )2+(2+l)λ for ψ < ψ

BC(4)

K r (ψ ) = 1 for ψ ≥ ψ

BC(5)

Van Genuchten Model

This widely used model (Van Genuchten, 1980)

suggested that the effective saturation is expressed by

S e = { 1 + (a

v |ψ |n ) } –m (6)

where av [cm] and n [-] represent the empirical

parameters, andm is related to n where m=1-1/n. Therefore

the relative hydraulic conductivity for VG model is written

as

(7)

Lognormal Model

In 1994, Kosugi proposed a new model of soil water

retention known as the Lognormal model (LN) which was

developed by assuming a lognormal distribution of soil poresize . But then, this model was modified in 1996. Kosugi

(1996) suggested that the effective saturation of LN model

is expressed as:

(8)

where s is a dimensionless parameter corresponding to the

standard deviation of log-transformed soil pore radius, ψ m

[cm] is the matric pressure head related to median pore

radius. Q denotes the complementary normal distribution

function which defined as:

( ) sts e r f s

f

k C pS S k p gD Q

g t δ ρ

ρ η

∂+ + ∇ ⋅ − ∇ + = ∂

( )( ) ( ){ }

( ){ }

21

1 1

1

mn n

v v

r ml n

n

v

a a

K

a

ψ ψ

ψ

ψ

−− − +

=

+

( ) ( )lne mS Qψ ψ ψ σ =





(9)

Then, the expression of K in term of S e and y are

(10)

(11)

It is suggested that COMSOL Multiphysics can be

used to solve equations by using VG and BC model in the

earth science module. By using these equations mentioned

earlier, parameters such as ψ BC , g, and l for BC parametersor a

v, m and l for VG parameters are needed. Even though

COMSOL Multiphysics is using VG and BC model in the

analysis, other equations from other models also can

be used by applying the additional option to define the

equations.

STRENGTH REDUCTION METHOD (SRM)

Strength Reduction Method (SRM) is used to analyze

the effect of negative pore water pressure changes to the

stability of a slope. SRM can be used as an alternative

method to the previous method, the Limit Equilibrium

Method (LEM). By using SRM, there will be no assumptions

about the shape of failure surface is needed compared to

the LEM. On the other hand, by using SRM, the calculation

is time consuming and more soil properties are needed.

Other than that, the value of FOS for SRM depends on the

parameter convergence (Hammah et al., 2005), mesh size

and the number of mesh.

Study on slope stability using the SRM covers the

determination of stress-strain parameters of the medium, the

influence of negative pore water pressure distribution,

determination of material failure and yield surface modeland a sequence of reduction of shear strength parameters

algorithm.

There are five soil’s strength parameters in analysing

slope stability with SRM; friction angle f , cohesion C ,

Young’s modulus E , Poisson’s ratio n ,and unit weight g .

The basic idea of this analysis is the reduction of shear

strength parameters of soil until the solution of computation

stress distribution is non-convergence.

The soil strength parameters C f and f

f used in FEM

procedures are defined as the actual shear strength

parameters C i and f divided by a shear strength reduction

factor F t .

C f = C

i / F

t (12)

φ f = arctan (tan (φ ) / F t ) (13)

In this case, material used is assumed to be highly

nonlinear stress-strain behavior. In this study, the material

failure model is studied using Drucker-Prager model (a

smooth approximation of the Mohr-Coulomb yield surface).

The yield surface form of Drucker-Prager is as follows:

(14)

where I 1 and J

2 I

2 is invariant of the Cauchy stress and

deviatoric part of the Cauchy stress respectively. The

equation of I 1 and J

2are as follow:

I 1 = σ

1 + σ

2 + σ

3(15)

J2 = [(σ1 – σ

2)2 + (σ

1 – σ

3)2 + (σ

2 – σ

3)2]/6 (16)

where:

(17)

The FOS using SRM can be determined by searching

the value of the reduction factor that caused the slope failure

when the computation of shear strength distribution is

leading to non-convergence (Griffiths and Lane, 1999),

with FOS equal to shear strength reduction factor, F S = F

t . In

order to find F S the constant parameter of C and f need to

be changed so that negative pore water pressure is also

changed.

SOIL PROPERTIES AND INITIAL CONDITION

In this study, the geometry of the soil’s slope is assumed

to be in two layers; surface layer and sub-surface layer. The

soil slope has 45o of inclination and each layer has 50 cm

thickness.The geometry was discretized by triangular meshwith 3280 number of elements. For the analysis of pore water

pressure and water content, the data were evaluated at point

evaluation of 7, 7.2 (Fig.1).

Pressure-head Analysis

In solving pressure-head analysis using Richard’s

equation in the seepage face boundary (top surface

geometry) in COMSOL Multiphysics was defined as a

general mixed boundary condition (Chui and Freyberg,

2009). The right and bottom boundary was defined as

Zero flux/symmetry. While, the left boundary was defined

( ) ( )2

0.52 exp

2 x

xQ x dxπ

∞− −=

( ) ( )1a

r e e e K S S Q Q S βσ − = +

( )1 1

ln lna

r

m m

K Q Qψ ψ

ψ βσ σ ψ σ ψ

= +

( ) 1 2 f I J k σ α = + =

( )

( )2

sin

3 3 sin

φ α

φ =

+

( )

( )2

3 cos

3 sin

C k

φ

φ =

+





as the pressure head condition that interface with a head of

1 m.

The hyetograph data which was used in this study was

based on localized torrential rainfall in the mid-southern

region of Kyushu in Japan. This area suffered a large-scale

debris flow along the Atsumari-gawa river in Hougawachi,Kumamoto Prefecture on July 20, 2003. The total rainfall,

peak rate, and event duration were established as 379 mm,

91 mm/h, and 10 h, respectively (Fig. 2). To establish the

initial conditions for the numerical simulation, an antecedent

rainfall which is the reduction of 50% from the main

hyetograph as indicated in Fig. 2, was applied and the whole

slope has a constant matric pressure value, yini

at -100 cm.

Drainage duration was set as 48 hours and resulting matric

pressure distribution within the whole slope was used for

initial condition for the main simulation. A number of data

set on the hydraulic properties of weathered granite soilswas obtained from Mukhlisin et al (2006). The soil hydraulic

parameter and fit parameters value for BC, VG and LN are

described in Table 1.

Static Analysis Elasto Plastic Material

The analysis of soil slope stability was done by assuming

that the dependency of cohesion C i [Pa] to the negative pore

water pressure ui [Pa] using an equation by Sammori

(Sammori, 1994). The equations are as follows:

C i = C'

i – χ u

i tan φ (18)

χ = MIN (1,11.25(θ /θ s)) (19)

where C i' is cohesion under saturated condition. In

Sammori (1994), Eq. [18] was derived from Bishop et al.

(1960), and Eq. [19] was developed based on the data by

Jennings and Burland (1962). He checked the validity of

Eq. [19] using measurements by Marui (1981). The value

of C i' and f is assumed as 2 kPa and 35o, respectively.

These values were used by Suzuki (1991) as typical values

for weathered granite soils. Another material properties for

soil slope stability analysis that used in this study were E , v,

and g with the value of 20 MPa, 0.3, and 10.5 kN/m3

respectively.

SCENARIOS FOR NUMERICAL MODELING

Three scenarios were performed for simulations in this

study; scenario 1, scenario 2, and scenario 3.

Scenario 1

Numerical modelling for scenario 1 was conducted by

assuming six different cases of θ s values as summarized in

Table 2. The difference between θ s and θ r is the effective

Fig.1. The schematic geometry of slope.

Table 1. Soil hydraulic parameters

Subsurface Surface

q s [cm3/cm3] 0.456 0.621

qr [cm3/cm3] 0.242 0.370

ESP 0.214 0.251 K

s [cm/s] 7.9e-3 32.2e-3

VG av [1/cm] 0.051 0.113

m 0.465 0.49

BC ψ BC

[cm] -12.936 -6.134

λ 0.869 0.9607

LN ψ m [cm] -33.8 -14.3

σ 0.98 0.92

Fig.2. Rainfall intensity.





soil porosity (ESP), and represents the total volume of

drainable soil pores per unit volume of soil. Case 1a, 1b

and 1c were simulation cases for q s variation on subsurface

layer. While, case 1d, 1e and 1f were simulation cases for q s

variation on surface layer. Case 1b and case 1e were the

observed data that was described previously. In case 1a, theESP value was increased by 53.27% from the case 1b. Other

than that, the ESP value of case 1c was decreased by 53.27%.

While in case 1d, the ESP value was 25% higher than case

1e. Other than that, case 1f is 25% lower than the case 1e.

These variation of parameter were based on the plotted

SWRC is shown in Fig.3 and Fig.4.

Scenario 2

In this scenario, there were three variations in hydraulic

conductivity parameters of VG, BC, and LN models. The

variations of parameters were av

, y BC ,

and ym

for VG, BC,

and LN respectively for sub-surface and surface. These

variation of parameter were based on the plotted

SWRC shown in Fig.3, and Fig.4. These variations of

assumption for simulation is also summarized in

Table 3.

Scenario 3

In this scenario, the analyses was done by differences

of soil slope angle. The slope angles in this scenario were

35o and 45o.

RESULTS AND DISCUSSION

Effect of Soil Water Retention Curve (SWRC) Model

Figure 6 shows that the pore water pressure distribution

in the whole soil slope was dissimilar among the three

models. It can be seen that the BC model predicts that the

unsaturated zone condition is wider than the LN and VG

models. It indicates that the results of VG model are almost

similar to the LN model.

Figure 7 shows the calculation of FOS when soil slope

experienced rainstorm. After 48 hours of rainfall the result

Table 2. The values of θsand θ

r for surface and subsurface layer assumed

for simulation cases

Case Subsurface Surface

θ s

θ r

θ s

- θ r

θ s

θ r

θ s

- θ r

1a 0.57 0.242 0.328 0.621 0.370 0.251

1b 0.456 0.242 0.214 0.621 0.370 0.251

1c 0.342 0.242 0.1 0.621 0.370 0.251

1d 0.456 0.242 0.214 0.77625 0.370 0.40625

1e 0.456 0.242 0.214 0.621 0.370 0.251

1f 0.456 0.242 0.214 0.46575 0.370 0.09575

Fig.3.SWRC BC model of (a) (c) subsurface and (b) (d) surface

layer.

Fig.4. SWRC VG model of (a) (c) subsurface and (b) (d) surface

layer.

Table 3. The values of av , ψ

BC and ψ

m for surface and subsurface layer

assumed for simulation cases

Case VG BC LN

Sub- Surface Sub- Surface Sub- Surface

surface surface surface

av

[1/m] av [1/m] ψ

BC [m] ψ

BC [m] ψ

m[m] ψ

m[m]

2a -0.5 -0.143 -0.2 -0.06134 -0.5 -0.143

2b -0.338 -0.143 -0.12937 -0.06134 -0.338 -0.143

2c -0.2 -0.143 -0.07 -0.06134 -0.2 -0.143

2d -0.338 -0.3 -0.12937 -0.11 -0.338 -0.3

2e -0.338 -0.143 -0.12937 -0.06134 -0.338 -0.143

2f -0.338 -0.12 -0.12937 -0.02 -0.338 -0.11





shows a significant difference in soil water content and pore

water pressure along the slope (see point evaluation in

Fig. 1). Curve in Fig.7 shows that the increasing of time

corresponds to the increasing rainfall intensity. At the

initial time, the soil slope changes from unsaturated to

saturated condition.

Figure 7 also shows the result of volumetric water

content, pore water pressure and FOS for the three models.

Figure 7(a) and (b) shows that during the initial stage of

rainfall, the soil water content and the pore water pressure

value for VG model were greatest compared to the other

models. On the other hand, when saturated condition

approaches, the LN and VG result is similar than in the BC

model.

All three models show different FOS when the slope is

in unsaturated condition. BC model shows a higher value of

0.0035 than LN model. For the VG model it is lower than

LN model by a value of 0.035. The results show that

approaching to the saturated condition, slope failure for VG

model is faster than the other two models.

Fig.5. SWRC LN model of (a) (c) subsurface and (b) (d) surface

layer.

Fig.6. Distributions of pore water pressure [Pa] for initial

conditions after 48 hours drainage.

Fig.7. Comparisons of the three soil-hydraulic models (a)

volumetric water content and (b) pore water pressure and

(c) safety factor value at point evaluation (see Fig. 1).





It can be seen that all models have similar result in the

timing of slope failure. Although BC model has greater

safety factor in the initial condition, it has similar value

during decreasing of FOS with the other models. The results

also show that rainstorm has a significant effect on the

increase of pore water pressure and decrease of FOS of

the slope.

On the other hand, all models show the same FOS at the

saturated soil condition. After the occurrence of the highest

rainfall intensity, the soil slope is still in the saturated

condition. At some point, although the pore water pressure

has been decreased, the cohesion value in the slope is still

remaining constant which is 2 kPa. This explains the fact

that after 8 hours of the highest rainfall, the FOS has not

decreased significantly.

Scenario 1

Figure 8 shows the results of case 1a, 1b and 1c. All

models have a consistent result at the saturated condition

as mentioned above and BC model has a highest FOS while

VG model has lowest FOS. The result proved that for all

models, the greater value of ESP will trigger longer slope

failure event. This shows the consistent result obtained

(Mukhlisin et al., 2006). On the other hand, Fig.9 shows the

comparison of FOS for the case 1d, 1e, and 1f. Similar with

case 1a, 1b, and 1c, the BC model has the highest FOS

compared to other models. It is noted that the increasing of

ESP in the surface layer has greater effect than increase of

ESP value in the sub-surface layer. It is also observed

that the result shown in Figure 7, 8, and 9, indicate that the

BC model has the highest and VG model has lowest FOS.

Scenario 2

For the effect of relative hydraulic conductivity, K r,

it is

observed from the result that only in case 2c the VG model

shows that the slope failure is faster than other models

(Fig.10). The simulation results show that in the case 2a,BC model has greatest FOS value compared to the other

cases. Case 2c experienced the lowest FOS value in VG

model.

Figure 11 indicates that all cases 2d, 2e and 2f have

similar result of FOS from all models, with BC model

Fig.8.Comparison of safety factor between VG, BC, and LN results for case 1a, 1b and 1c.

Fig.9. Comparison of safety factor between VG, BC, and LN results for case 1d, 1e and 1f.





Fig.10. Comparison of safety factor between VG, BC, and LN results for case 2a, 2b and 2c.

Fig.11. Comparison of safety factor between VG, BC, and LN results for case 2d, 2e and 2f.

Fig.12. Comparison of safety factor as effect of 35o and 45o slope

angle.

having greatest FOS value and the VG model has the lowest

FOS value. Therefore, Figure 11 shows that different K r

at the surface layer has no significant effect on the FOS

value.

Scenario 3

Result for the effect of slope angle shows that BC model

has the highest FOS value and VG model has the lowest

FOS for both slope of 35o and 45o. This indicates that byincreasing the slope angle, the value of FOS is getting lower.

Therefore, it is proved that the inclination of the slope has

significant effect on the FOS value.

CONCLUSION

In this study, the effect of different of parameters for

SWRC, and soil hydraulic properties model was analyzed.

The results showed that the variation of these parameters

will affect the FOS value, based on the models. In the

unsaturated condition, the results show that BC model





gives the greatest FOS than other models, while the VG

model the lowest.

On the other hand, the FOS of all model are almost

similar for the saturated soil condition. This study has also

analyzed the effect of ESP on the FOS value. It is believed

that the increasing of ESP value in the surface layer has

significant effect than in the subsurface layer.

It is observed from the result that all models have high

FOS value with the variations of K r while different K

r values

at the surface layer has no significant effect on the FOS

value. Lastly, the variations of soil hydraulic properties

affect the FOS value with increasing slope inclination. It is

proved that the higher the slope angle, the lower the FOS

value for the soil slope.

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(Received: 16 July 2012; Revised form accepted: 23 January 2013)

effect of soil hydraulic properties on slope stability

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