Infinite Slope Stability Analysis for Unsaturated Granular Soils

Anuchit Uchaipichat Department of Civil Engineering, Vongchavalitkul University, Nakhon Ratchasima, 30000, Thailand e-mail: [email protected]

ABSTRACT This paper presents a derivation of expression for factor safety of infinite granular soil slope including the effect of matric suction. The derivation is based on effective stress concept. The simulation results show the variation in safety factor of infinite slope of granular soil with matric suction. The factor of safety increases with matric suction for the value of matric suction less than residual suction but decreases with increasing matric suction for the value of matric suction greater than residual suction. Moreover, the safety factor at very high value of suction is close to that at very low matric suction. Furthermore, the simulation results show the fluctuation of safety factor with matric suction becomes smaller with increasing value of thickness of sand layer.

KEYWORDS: Infinite slope; Suction; Granular soils; Partial saturation

INTRODUCTION The slope stability analysis is essential in geotechnical analysis and design of earth structures particularly for constructions of dam, road and other types of embankment. The slope must be stable through a lifetime of permanent earth structures or through particular period for temporary ones. To prevent losses of lives and properties, engineers need to check whether the safety factor of slope is appropriate for each type of structure for the worst condition of soil. However, the slope stability analysis is based on the classical soil mechanics assumption, in which fully saturated and completely dry conditions are assumed for soils below and above ground water level, respectively. The analysis without considering unsaturated soil condition is simple but can makes the increasing costs associated with construction. Moreover, the earth structures designed with the assumption of completely dry soil condition may encounter a reduction in factor of safety upon wetting after end of construction. In slope stability analysis, shear strength of soil is a very essential property. Since the shear strength of soil particularly under partially saturated condition can varies with the water content

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or the suction within the soils (e.g. Vanapalli et al. 1996; Khalili and Khabbaz 1998; Cunningham et al. 2003; Thu et at. 2006; Zhou and Sheng 2009; Uchaipichat 2010), the safety factor of the slope of earth structures varies with season change. Several elasto-plastic model have also been proposed to capture the mechanical behaviors of unsaturated soils (e.g. Kohgo et al. 1993; Wheeler and Sivakumar 1995; Gallipoli 2003; Tarantino 2007; Uchaipichat 2011). Moreover, Uchaipichat and Man-koksung (2011) recently found that the ultimate bearing capacity of foundation on granular soils can reduce upon drying at matric suction greater than the residual value. This implies that the effective stress of granular soils decreases upon drying in this range of suction. Therefore, similar behavior probably occurs for slope of earth structures consisting of granular materials. Therefore, the main purpose of this paper is to derive the expression for safety factor of infinite slope of granular soils including effect of matric suction. Simulations of factor safety for various values of matric suction and thickness of soil layer are performed. The results are presented and discussed.

EFFECTIVE STRESS IN UNSATURATED GRANULAR SOIL The effective stress, which is used to characterize the mechanical behavior of unsaturated soils, can be expressed as (Bishop and Blight 1963),

σ ′ = (σ − u a ) + χ s

(1)

in which, σ ′ is the effective stress, σ − u a is the total stress in excess of pore air pressure, referred to as mean total stress, s is the matric suction, defined as the difference between pore air pressure and pore water pressure (u a − u w ) , and χ is the effective stress parameter attaining a value of unity for a saturated soil and zero for a dry soil. The expression for parameter χ proposed by Uchaipichat and Man-koksung (2011) is written in terms of suction ratio ( s / s e ) as,

 1    s χ =   s e   s  s  e

for   

s ≤1 se

−Ω

 Ψ −Ω  s   r  se

for 1 <   

−Ψ

for

s  s  ≤  s e  s e  r

s  s > s e  s e

(2)

  r

in which, se is the suction value separating saturated from unsaturated state. For the values of (s / s e )r , Ω and Ψ equal to 25, 0.55 and 1.00 respectively, the expression becomes similar to that proposed by Russell and Khalili (2006). In this case, the value of χs increases with increasing suction for suction ratio less than 25 and constant at higher level of suction ratio. For Ψ > 1 , the values of χs decreases with increasing matric suction and becomes zero at s = ∞ .



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INFINITE SLOPE STABILITY FOR UNSATURATED GRANULAR SOILS The analysis for infinite slope can be carried out by considering a slice of soil with 1 unit width as shown in Fig.1. The forces on the slip plane are considered to be the weight of soil slice, the normal force ( N ), the resisting shear force ( T ), the matric suction ( s ) and the pore air pressure ( u a ). The forces P cancel each other out since any point on the slope is indistinguishable from any other.

1 unit

P W

Slip plane

P

T = Resisting shear force

z

β

N = Normal Force

Figure 1: Infinite slope stability analysis

Resolving an equilibrium of normal forces on the slip plane N = W cos β

(3)

From the definition of the normal stress ( σ ),

σ=

N 1 / cos β

(4)

Substituting the normal force N in Eq. (3) into Eq. (4) yields

σ = W cos 2 β

(5)

Then substituting the normal stress in Eq. (5) into the expressing for effective stress gives

σ ′ = W cos 2 β + χs − u a Now resolving an equilibrium of shear forces on the slip plane



(6)

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T = W sin β

(7)

From the definition of the shear stress ( τ ),

T 1 / cos β

τ=

(8)

Substituting the normal force T in Eq. (7) into Eq. (8) yields

τ = W sin β cos β

(9)

The factor safety, which is defined as shear strength to shear stress ration, can be expressed as,

FS =

s

τ

=

c + σ ′ tan φ

(10)

τ

Substituting σ ′ and τ into Eq. (10) yields

(

)

c + W cos 2 β + χs − u a tan φ FS = W sin β cos β

(11)

Eq. (11) can be rearranged as,

FS =

 χs − u a + 1 − W sin β cos β  W cos 2 β c

 tan φ   tan β

(12)

 tan φ   tan β

(13)

Substituting W = γz into Eq. (12) yields

FS =

 χs − u a + 1 − γz sin β cos β  γz cos 2 β c

In case of fully saturated condition, the matric suction becomes zero and pore air voids are replaced by water. Thus, replacing u a with u w and substituting s = 0 into in Eq. (13) yields

FS =

uw  + 1 − γz sin β cos β  γz cos 2 β c



 tan φ   tan β

(14)

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In case of completely dry condition, the effective stress parameter χ becomes zero. Therefore, Eq. (13) becomes

FS =

ua  + 1 − γz sin β cos β  γz cos 2 β c

 tan φ   tan β

(15)

SIMULATIONS OF SAFETY FACTOR OF INFINITE SLOPE WITH VARIOUS MATRIC SUCTIONS Material Properties The simulation of variation in safety factor of infinite slope is performed. The material used in simulations is compacted sand. The material properties reported by Uchaipichat and ManKoksung (2011) are given in Table 1. The soil-water characteristic curve obtained from filter paper technique suggested by ASTM D5298 is shown in Fig. 2.

Table 1: Properties of sand sample from Uchaipichat and Man-Koksung (2011) Property

Values

Cohesion ( c ) Internal angle of friction ( φ ) Maximum dry unit weight ( γ max ) Optimum moisture content ( OMC )

0 kPa 33.1o 16.6 kN/m3 7.0%

1.0

Degree of saturation

0.8 0.6 0.4 0.2 0.0 0.1

se

1

sr

10

100

1000

Matric suction (kPa)

Figure 2: Soil-water characteristic curve of compacted specimens



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Simulations and Discussions In this paper, the simulations are performed for an infinite slope of sand with various values of thickness. The pore air pressure is assumed to be atmospheric pressure ( u a = 0 ). Summary of parameter used in simulations is shown in Table 2.

Table 2: Summary of Parameters used in Simulations Parameter

Values

se sr (s / s e )r Ω

0.5 kPa 4.0 kPa 8.0 0

* Obtained from Uchaipichat and Man-koksung (2011)

Fig. 3 shows the variation of factor of safety with matric suction for various values of thickness. It is obvious that the factor of safety increases with matric suction for the value of matric suction less than residual suction ( s ≤ s r ). The factor of safety, however, decreases with increasing matric suction for the value of matric suction greater than residual suction ( s > s r ). It can be noticed that the safety factor at very high value of suction is close to that at very low matric suction. The simulation results also show that the fluctuation of safety factor with matric suction becomes smaller with increasing value of thickness of sand layer. The simulation results show the effect of matric suction on the safety factor of infinite slope with granular soil layer. Considering the granular soils with very low value of matric suction but greater than the air entry value ( se ), the state of the specimen enter the unsaturated conditions and the pores area is partially acted by matric suction. At this state, the stability of slope increases because of an increase in effective stress within the soil. This phenomenon can be found in both cohesive and cohesionless soils. At very high suction ration (s / s e ) , the amount of pore water is very small. At this the matric suction acting within the pores becomes insignificant and the behavior of soil is similar to that at very low suction. Thus, the safety factor at very high value of suction is close to that at very low matric suction.



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1.6 z =1 m z =2 m 1.5

z =4 m z =6 m z =8 m

Factor of safety

1.4

z = 10 m

1.3

1.2

1.1

1.0 0.1

1

sr

10

100

1000

10000

100000

Matric suction (kPa)

Figure 3: variation of factor of safety of infinite slope with matric suction for various values of thickness

CONCLUSIONS The expression for safety factor of infinite slope including effect of matric suction is derived. The effective stress parameter in the expression proposed by Uchaipichat and Man-koksung (2011) is used in this study. The simulation results show the variation in safety factor of infinite slope of granular soil with matric suction. The factor of safety increases with matric suction for the value of matric suction less than residual suction but decreases with increasing matric suction for the value of matric suction greater than residual suction. Moreover, the safety factor at very high value of suction is close to that at very low matric suction. Furthermore, the simulation results show the fluctuation of safety factor with matric suction becomes smaller with increasing value of thickness of sand layer.

ACKNOWLEDGEMENTS This work was supported by Vongchavalitkul University.

REFERENCES 1.

ASTM Standard D5298 (2010), Standard Test Method for Measurement of Soil Potential (Suction) Using Filter Paper, ASTM International, West Conshohocken, PA, 2003, DOI: 10.1520/D5298-10, www.astm.org.

2.

Bishop, A. W., and Blight, G. E. (1963). ‘‘Some aspects of effective stress in saturated and unsaturated soils.’’ Geotechnique, 13, 177–197.



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3.

Cunningham, M. R., Ridley, A. M., Dineen, K., and Burland, J. B. (2003). “The mechanical behaviour of a reconstituted unsaturated silty clay.” Geotechnique, 53(2), 183– 194.

4.

Gallipoli, G., Gens, A., Sharma, R., and Vaunat, J. (2003). “An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour.” Geotechnique, 53(1), 123–135.

5.

Khalili, N., and Khabbaz, M. H. (1998). “A unique relationship for the determination of the shear strength of unsaturated soils,” Geotechnique, 48(5), 681–687.

6.

Kohgo, Y., Nakano, M., and Mayazaki, T. (1993). “Theoretical aspects of constitutive modelling of unsaturated soils.” Soils. Found., 33(4), 49-63.

7.

Russell, A. R., and Khalili, N. (2006). “A unified bounding surface plasticity model for unsaturated soils.” International Journal for Numerical and Analytical Methods in Geomechanics, 30 (3), 181-212.

8.

Tarantino, A. (2007). “A possible critical state framework for unsaturated compacted soils.” Geotechnique, 57(4), 385–389.

9.

Thu, T. M., Rahardjo, H., and Leong, E. C. (2006). “Shear strength and pore water pressure characteristics during constant water content triaxial tests.” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 136(3), 411–419.

10.

Uchaipichat, A. (2010). “Prediction of shear strength for unsaturated soils under drying and wetting processes.” EJGE, 15(K), 1087-1102.

11.

Uchaipichat, A. (2011). “An elasto-plastic model for unsaturated soils including effect of drying and wetting on loading collapse curve.” EJGE, 16(E), 476–498.

12.

Uchaipichat, A. and Man-koksung, E. (2011). “Bearing capacity characteristic of unsaturated granular soils.” Advanced Material Research, Vol. 261-263, 989–993.

13.

Vanapalli, S. K., Fredlund, D. G., Pufahl, D. E, and Clifton, A. W. (1996). “Model for the prediction of shear strength with respect to soil suction.” Can. Geotech. J., 33, 379–392.

14.

Wheeler, S. J., and Sivakumar, V. (1995). “An elasto-plastic critical state framework for unsaturated soils.” Geotechnique, 45(1), 35–54.

15.

Zhou, A. N., and Sheng, D. (2009). “Yield stress, volume change and shear strength behaviour of unsaturated soils: validation of the SFG model.” Canadian Geotechnical Journal, 46(9), 1034–1045.

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