Stability Analysis of Landslide Dam under Rainfall

Transcription

1 Stability Analysis of Landslide Dam under Rainfall Pei-Hsun Tsai, Zheng-Yi Feng 2, Fan-Chieh Yu 3 and Jian-Han Lin 4 Associate Professor, Department of Construction Engineering, Chaoyang University of Technology, 68 Jifong E. Rd., Wufong District, Taichung, 4349, Taiwan; phtsai@cyut.edu.tw 2 Professor, Department of Soil and Water Conservation, National Chung Hsing University, 250, Kuo- Kuang Rd. Taichung, 40227, Taiwan; tonyfeng@nchu.edu.tw 3 Professor, Department of Soil and Water Conservation, National Chung Hsing University, 250, Kuo- Kuang Rd. Taichung, 40227, Taiwan; fcyu@nchu.edu.tw 4 Graduate Student, Department of Construction Engineering, Chaoyang University of Technology, 68 Jifong E. Rd., Wufong District, Taichung, 4349, Taiwan; jonuslarry@yahoo.com.tw ABSTRACT: Failure of landslide dam may occur by river discharge and rainfall. A rise of water level in the upstream of landslide dam and rain infiltrate into the dam body will increase pore water pressure and weight of the dam. In this study, transient seepage analysis of rainfall infiltration and dam stability analysis is performed. The two-phase flow simulation using the finite difference code, FLAC, is adopted to analyze unsaturated seepage flow in transient fluid-mechanical calculations. The safety factor of dam stability is evaluated by the shear strength reduction technique. The parameters discussed in the study include the rising speed of water level, rain infiltrating and the hydraulic conductivity of soil. The results show that the slope failure time of the dam is about 22 minutes when only the effect of rising water level in the upstream is considered. The failure time becomes faster as 3 minutes when both the rain infiltration and rising water level in the upstream are considered. The results also indicate that the hydraulic conductivity of the dam influencing the failure time of the dam. INTRODUCTION Numerous landslides and debris flows occur after heavy rainfall. The wasting materials due to landslides and avalanches cound obstruct a river and create a landslide dam. Unlike manmade dams with compacting process and filtering materials, a landslide dam is formed by a mixture of unconsolidated soil/rock in a naturally unstable state. Water level uasually rises rapidly in the upstream side of a landslide dam due to continuous rainfall. The landslide dam is always unstable and dangerous because flash flood could occur in the downstream area due to failure of the landslide dam. Failure of landslide dam may occur in a number of processes which includes overtopping, sliding and piping, etc. The sliding failure could occurr in the dam body Page

2 due to the increase of pore water pressure. When rainfall or rising water level in upstream side occurs, the water infiltrating into dam causes the increase of water content and pore water pressure in the landslide dam. This is a transient seepage flow in unsaturated soils. The pore water pressure profile can be analyzed using a numerical transient analysis of saturated/unsaturated seepage flow model. For stability analysis of the landslide dams, the shear strength reduction technique is used to obtain the safety factor of the dams and to locate the corresponding critical slip surface. A number of studies including finite difference and finite element method performed 2D transient seepage flow analyses using saturated-unsaturated seepage theory (Ng et al., 998; Xu et al., 2003; Huang and Jia, 2009; Fu and Jin, 2009). Some experimental testing about the stability analysis of unsaturated slope has been studied by small-scale models (Orense et al., 2004; Tohari et al., 2007; Schnellmann et al., 200; Egeli and Pulat, 20). We examine the relationship between the safety factor of dam stability by transient analysis and the distribution of moisture inside the dam induced by influencing parameters. In addition, parametrical study was performed by varying the rising speed of water level and the saturated hydraulic conductivity of soil. NUMERICAL MODEL Landslide Dam Configuration The FLAC code with the two-phase flow model was adopted to analyze the timing of slope failure when water level rising in the upstream side. A typical configuration and finite difference mesh for the landslide dam is shown in Fig.. The dam with height H=4 m and length L=4 m was assumed to be situated above a riverbed. The slope angles of the upstream and downstream faces of the dam were assumed as 34, which is close to the angle of repose of the dam materials. 4m 2m saturated boundary 2m 6m 2m 6m 2m saturated boundary airy boundary airy boundary Impermeable boundary seepage boundary saturated boundary FIG.. A typical finite difference mesh for the landslide dam in this study To analyze the influence of the rising speed of water level in the upstream side on dam stability, three different rising speed of water level (v=20, 40 and 80 cm/min) were studied. To estimate the impacts of hydraulic conductivity of soil on stability of a Page 2

3 landslide dam, three different saturated hydraulic conductivity of soil (K= , and m/s) were used for analyses. Seepage Flow Modeling of Unsaturated Soil The transient seepage flow analysis of the dam after rising water level in the upstream side is described by Richards equation. C h h h K x (h ) K y (h ), t x x y y () where h is the water pressure head, Kx(h) and Ky(h) are the hydraulic conductivity in x and y direction, respectively. C is the specific moisture capacity, t is the time, x is horizontal coordinate and y is vertical coordinate. A model proposed by van Genuchten (980) is used as the relationship between water pressure head, moisture content and hydraulic conductivity. The relationship between soil moisture and water pressure head is expressed as: Se h m for h 0 (2) for h 0 where and are constant parameters related with matric potential of soil, m ( ), Se is the effective saturation, which is defined as: Se r, s r (3) where s and r are the saturated and residual moisture content, respectively. The relationship between effective saturation and unsaturated hydraulic conductivity is expressed as: 0.5 m m K K sse ( Se ) Ks 2 for h 0 for h 0 (4) where s is the saturated hydraulic conductivity. For the numerical analysis, the landslide dam and riverbed sediments were assumed to satisfy the Mohr-Coulomb failure criteria. The engineering properties of the landslide dam and riverbed sediment for the simulation are listed in Table. The landslide dam is assumed as an isotropic medium and the parametric values of unsaturated soil model are as follows: m=0.333, s=0.42, and r= Page 3

4 Table. The material parameters of the landslide dam and riverbed sediment Zone Density (kg/m 3 ) Bulk Modulus (MPa) Shear Modulus (MPa) Cohesion (kpa) Friction Angle ( ) Saturated Hydraulic Conductivity (m/sec) Dam Riverbed Procedures of the Simulation The initial values of water pressure head and moisture content in the dam were firstly specified. In the mechanical boundary condition, the bottom and two sides of the riverbed sediment were assumed to be fixed, i.e. the deformability is constrained and sliding will be prevented. The bottom of the riverbed sediment was assumed as a noflow boundary. The boundary condition on dam surface under water level in the upstream side and the upper, left and right side of riverbed sediment have to be specified for their pressure head and saturation. The seepage boundary is on the downstream side of the dam, which indicates the water leaves the soil and water pressure head is zero. The height of seepage face at the seepage boundary is not known initially. The upstream side over the water level and the upper side of the dam are airy boundaries. For rainfall infiltration case, the infiltration rates at the airy and seepage boundaries are assumed as the product of rainfall intensity and Cosine of the angle of the boundary regarding to a horizontal line. An initial static equilibrium in the dam body was carried out during the forming process of the landslide dam. An initial stress state in the dam can be obtained before the transient seepage flow analysis. The water level rises in the upstream side was simulated for river blockage by landslide materials. To estimate the failure time of the landslide dam, the safety factors of dam stability were calculated during the 0 water levels for the water retaining stage. The purpose of the various water levels simulation is to ensure a reasonable pressure head and saturation distribution in the dam. The boundary values of pressure head and saturation at the upstream boundary were will be re-specified during each water level raises. The various rates of the boundary values depend on the rising speed of water level. The transient seepage analysis with a time step of 0.5 s was performed and the analysis is decoupled with the mechanical analysis. The stress field of static equilibrium of the dam will be computed again after each transient seepage analysis. The shear strength reduction technique was used to obtain the safety factor of stability of dam and locate the corresponding critical slip surface during each water level raises. We assume safety factor of one to maintain the stability of the dam. RESULTS OF THE NUMERICAL ANALYSES Transient Results of Dam under Raising Water Level Process The rising speed of water level at the upstream was assumed as 40 cm/min. When Page 4

5 water level reached the top of dam (height = 4 m), i.e., 0 minutes after. The upstream water level was held at the level of the dam crest. The calculated saturation and pore water pressure profiles from the numerical analysis of the landslide dam when the time was 200 minutes are shown in Fig. 2. The computed saturated zone of soil occurred in the upstream side of dam and the range of saturation in the downstream side is between 0.5 and.0. Because the soil is in unsaturated state, the negative pore water pressure developed in the top portion of downstream side of the dam. Unit: N/m 2 (a) (b) FIG. 2. Contours when the time is 200 minutes: (a) saturation and (b) pore water pressure. Influence of the Rising Speed of Water Level on the Dam Stability To study the influence of rising speed of water level on the safety factor of dam stability, the saturated hydraulic conductivity of soil was fixed as K s = m/s and 3 rising speeds at 20, 40 and 80 cm/min were assumed. The simulated results under these rising speeds of water level are compared in Fig. 3. As can be seen in Fig. 4 Page 5

6 Factor of safety Factor of safety 3, the safety factors of dam stability decrease with increasing time when time is greater than 50 minutes. However, the influence of rising speed of water level on dam stability is insignificant because the variation is not obvious. The reason could be that the infiltrating time in dam body from upstream to downstream is more than that of water level rising, so that the pore water pressure profiles in these case are close v=20 cm/min v=40 cm/min v=80 cm/min Time (min) FIG. 3. Influence of rising speed of water level on dam stability K s = m/sec K s = m/sec K s = m/sec Time (min) FIG. 4. Influence of saturated hydraulic conductivity of soil on dam stability. Page 6

7 Factor of safety Influence of the Saturated Hydraulic Conductivity of Soil on Dam Stability To study the influence of saturated hydraulic conductivity on the safety factor of dam stability, two additional hydraulic conductivity were estimated, K s = and m/s. The simulated results under these hydraulic conductivities are compared in Fig. 4. In Fig. 4, it shows that the variation of safety factor is less before a threshold time, the safety factor of dam stability decreases with increasing time when time is more than the threshold time. The results imply that the threshold time and the dam failure time are almost proportional to the saturated hydraulic conductivity of dam. Influence of Adding Rain Infiltration on Dam Stability It can be observed from Fig. 5 that the slope failure time of the dam is about 22 minutes when the only effect of rising water level in the upstream is considered; however, it is 3 minutes in the case of rising water level adding the rain infiltration condition. The coupling with rainfall infiltration enlarges the zone of saturated soil and speeds up the wetting of unsaturated soil. Therefore, the timing of the dam failure of the case with both rain infiltration and water level rising comes earlier than the case of considering water level rising only without rain infiltration with rain infiltration CONCLUSIONS Time (min) FIG. 5. Influence of adding rain infiltration on dam stability. This study used FLAC to analyze stability of landslide dam assuming rising water level in upstream side. The influence parameters discussed include the rising speed of water level and the hydraulic conductivities of soils. Based on the numerical analyses presented in this paper, the following conclusions are made: Page 7

8 . The influence of rising speed of water level on safety factors of dam stability is less significant than varying hydraulic conductivities of soil. 2. The safety factors of dam stability decrease with increasing saturated hydraulic conductivity. 3. The timing of slope failure for the case of both with rainfall infiltration and rising water level is earlier than the case of considering rising water level alone. ACKNOWLEDGMENTS This study was supported by research funding from the National Science Council of Taiwan (NSC M MY3; NSC M MY3). Their support is gratefully appreciated. REFERENCES Egeli, I. and Pulat, H.F. (20). "Mechanism and modelling of shallow soil slope stability during high intensity and short duration rainfall." Scientia Iranica, Vol. 8(6): Fu, J.F. and Jin, S. (2009). "A study on unsteady seepage flow through dam." Journal of Hydrodynamics, Vol. 2(4): Huang, M. and Jia, C.Q. (2009). "Strength reduction FEM in stability analysis of soil slopes subjected to transient unsaturated seepage." Computes and Geotechnics, Vol. 36(): Ng, C.W.W. and Shi, Q. (998). "A numerical investigation of the stability of unsaturated soil slopes subjected to transient seepage." Computes and Geotechnics, Vol. 22(): 28. Orense, R.P., Shimoma, S., Maeda, K. and Towhata, I. (2004). "Instrumented model slope failure due to water seepage." J. Nat. Disaster Sci., Vol. 26 (): Schnellmann, R., Bussllinger, M., Schneider, H.R. and Rahardjo, H. (200). "Effect of rising water table in an unsaturated slope." Engineering Geology, Vol. 4: Tohari, A., Nishigaki, M. and Komatsu, M. (2007). "Laboratory rainfall-induced slope failure with moisture content measurement." Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 33 (5), van Genuchten, M.Th. (980). "A close-form equation for predicting the hydraulic conductivity of unsaturated soil." Soil Sci. Soc. Am. J., Vol. 44: Xu, Y.Q., Unami, K. and Kawachi, T. (2003). "Optimal hydraulic design of earth dam cross section using saturated unsaturated seepage flow model." Advances in Water Resources, Vol. 26(): 7. Page 8

9 Stability Analysis of Landslide Dam under Rainfall Pei-Hsun Tsai, Zheng-Yi Feng 2, Fan-Chieh Yu 3 and Jian-Han Lin 4 Associate Professor, Department of Construction Engineering, Chaoyang University of Technology, 68 Jifong E. Rd., Wufong District, Taichung, 4349, Taiwan; phtsai@cyut.edu.tw 2 Professor, Department of Soil and Water Conservation, National Chung Hsing University, 250, Kuo- Kuang Rd. Taichung, 40227, Taiwan; tonyfeng@nchu.edu.tw 3 Professor, Department of Soil and Water Conservation, National Chung Hsing University, 250, Kuo- Kuang Rd. Taichung, 40227, Taiwan; fcyu@nchu.edu.tw 4 Graduate Student, Department of Construction Engineering, Chaoyang University of Technology, 68 Jifong E. Rd., Wufong District, Taichung, 4349, Taiwan; jonuslarry@yahoo.com.tw ABSTRACT: Failure of a landslide dam might occur by river discharge or rainfall. A rise of the upstream water level of a landslide dam and rain infiltration into the dam body increase pore water pressure and the weight of the dam. In this study, transient seepage analysis of rainfall infiltration and dam stability analysis are performed. A two-phase flow simulation using the FLAC finite difference code is adopted to analyze unsaturated seepage flow in transient fluid-mechanical calculations. The safety factor of dam stability is evaluated using the shear strength reduction technique. The parameters discussed in this study include the rising speed of the water level, rain infiltration, and the hydraulic conductivity of soil. The results show that the time to slope failure of the dam is approximately 247 min when only the effect of the rising upstream water level of the dam is considered. The failure time decreases to 89 min when the rain infiltration and rising upstream water level of the dam are considered. The results also indicate that the hydraulic conductivity of the dam affects dam failure time. INTRODUCTION Landslides and debris flows commonly occur after heavy rainfall. Waste materials resulting from landslides and avalanches can obstruct a river and create a landslide dam. Unlike manmade dams with a compacting process and filtering materials, a landslide dam is formed by a mixture of unconsolidated soil and rock in a naturally unstable state. The water level typically rises rapidly upstream of a landslide dam because of continuous rainfall. Landslide dams are often unstable and dangerous because flash floods might occur downstream if the landslide dam fails. Sliding failure can occur in the dam body because of an increase in pore water pressure. When rainfall occurs or the water level rises upstream, the water infiltrating into the dam 55

10 56 IACGE 203 causes an increase in water content and pore water pressure, which is caused by transient seepage flow in unsaturated soils. The pore water pressure profile can be analyzed using a numerical transient analysis of a saturated-unsaturated seepage flow model. For stability analysis of landslide dams, the shear strength reduction technique is used to obtain the safety factor of the dams and to locate the corresponding critical slip surface. In numerous studies, the finite difference and finite element methods were used to perform 2D transient seepage flow analyses using the saturatedunsaturated seepage theory (Ng et al., 998; Xu et al., 2003; Huang and Jia, 2009; Fu and Jin, 2009). Experimental testing regarding the stability analysis of an unsaturated slope has been studied using small-scale models (Orense et al., 2004; Tohari et al., 2007; Schnellmann et al., 200; Egeli and Pulat, 20). The influence of the hydraulic conductivity of dam and rising speed of the water level on the dam failure time has not been fully examined. In this study, the relationship between the dam stability and the distribution of moisture inside the dam induced by influencing parameters was examined using a transient analysis. In addition, a parametric study was performed by varying the rising speed of the water level and the saturated hydraulic conductivity of soil. NUMERICAL MODEL Landslide Dam Configuration A FLAC code with a two-phase flow model was adopted to analyze the timing of the slope failure when the water level rose upstream of the dam. A typical configuration and finite difference mesh for the landslide dam is shown in Fig.. The dam, with a height of 4 m and a length of 4 m, was assumed to be situated above a riverbed. The slope angles of the upstream and downstream faces of the dam were set as 34, which is close to the angle of repose of the dam materials. To analyze the influence of the rising speed of the upstream water level on dam stability, three water level rising speeds (v = , and m/s) were studied. To estimate the effects of the hydraulic conductivity of soil on the stability of the landslide dam, three saturated hydraulic conductivities of soil (K s 4 5 = , and m/s) were used for analyses. 4m 6m 2m 6m 4m 4m 5m saturation boundary airy boundary airy boundary seepage boundary saturation boundary saturation boundary Impermeable boundary saturation boundary FIG.. Typical finite difference mesh for landslide dam. Seepage Flow Modeling of Unsaturated Soil The transient seepage flow analysis of the dam after the upstream water level rises is

11 IACGE described by Richards equation (93). C h h h K x (h ) K y (h ), t x x y y () where h is the water pressure head, and Kx(h) and Ky(h) are the hydraulic conductivity in the x and y directions, respectively. C is the specific moisture capacity, t is time, x is the horizontal coordinate, and y is the vertical coordinate. A model proposed by van Genuchten (980) is used to determine the relationship between water pressure head, moisture content, and hydraulic conductivity. The relationship between soil moisture and water pressure head is expressed as: Se h m for h 0 (2) for h 0 where and are constant parameters that express the matric potential of soil, m ( ), and Se is the effective saturation, which is defined as: Se r, s r (3) where s and r are the saturated and residual moisture content, respectively. The relationship between effective saturation and unsaturated hydraulic conductivity is expressed as: 0.5 m m K K sse ( Se ) Ks 2 for h 0 for h 0 (4) where s is the saturated hydraulic conductivity. For the numerical analysis, the landslide dam and riverbed sediments were assumed to satisfy the Mohr-Coulomb failure criteria. The engineering properties of the landslide dam and riverbed sediment for the simulation are listed in Table. The landslide dam is assumed to be an isotropic medium, and the parametric values of the unsaturated soil model are set as follows: m = 0.333, s = 0.42 and r = Simulation Procedures First, the initial values of the water pressure head and moisture content in the dam were specified in transient seepage flow analysis. The bottom of the riverbed sediment was assumed to be a no-flow boundary. The pressure head and saturation of the dam surface under the water level upstream and the upper, left, and right side of the riverbed sediment must be specified. The seepage boundary was on the downstream

12 58 IACGE 203 side of the dam, which indicated that water left the soil and that the water pressure head was zero. The height of the seepage face at the seepage boundary was not initially known. The upstream side above the water level and the upper side of the dam were airy boundaries. For the rainfall infiltration case, the infiltration rates at the airy and seepage boundaries were assumed to be the product of rainfall intensity and the cosine of the angle of the boundary face to the horizontal. This is because the direction of the discharge normal to the surface of the slope was specified on the boundaries, but the rainfall direction was assumed to be vertical. In mechanical analysis, the bottom and the 2 sides of the riverbed sediment were assumed to be fixed (i.e., the deformability was constrained and sliding was prevented). Table. The material parameters of the landslide dam and riverbed sediment Zone Density (kg/m 3 ) Bulk Modulus (MPa) Shear Modulus (MPa) Cohesion (kpa) Friction Angle ( ) Saturated Hydraulic Conductivity (m/s) Dam Riverbed The initial static equilibrium in the dam body was established during the forming process of the landslide dam. An initial stress state in the dam can be obtained before the transient seepage flow analysis is conducted. A rising water level upstream was simulated for the case in which the river was blocked by landslide materials. To estimate the failure time of the landslide dam, the safety factors of dam stability were calculated for 0 different water levels during the river blocked stage. The simulation of various water levels was conducted to ensure a reasonable pressure head and saturation distribution in the dam. The boundary values of the pressure head and saturation at the upstream boundary were re-specified for each water level. Transient seepage analysis with a time step of 0.5 s was performed separately from the mechanical analysis. The static equilibrium stress field of the dam was recomputed after each transient seepage analysis. The shear strength reduction technique was used to obtain the safety factor of dam stability and to locate the corresponding critical slip surface of each water level rise. To maintain the stability of the dam, a safety factor of one was assumed. NUMERICAL ANALYSES RESULTS Transient Seepage Results of a Dam Undergoing Rising Water Levels The rising speed of the water level upstream was assumed to be m/s. The water level reached the top of dam (height H = 4 m) after 0 min. The upstream water level was held constant at the level of the dam crest. The calculated saturation and pore water pressure profiles from the numerical analysis of the landslide dam at 200 min are shown in Fig. 2. The computed saturated zone of the soil occurring upstream of the dam and the range of saturation downstream is between 0.5 and.0. Fig. 2(a)

13 IACGE shows the wetting speed of the unsaturated soil is high in the bottom of the dam, possibly because of the effect of gravity. The positive pore water pressure is induced by rising water level upstream of dam, as shown in Fig. 2(b). Because the soil was in an unsaturated state, negative pore water pressure developed in the upper portion downstream of the dam. Saturation contours 6.00E E E E E E E E-0.00E+00 Flow vectors Max vector = 6.966E-04 Pore pressure contours 0.00E E E E E+04 Unit: N/m 2 (a) Flow vectors Max vector = 6.966E-04 Max. shear strain-rate 0.00E E E E-08.00E-07.25E-07.50E-07.75E-07 Exaggerated Grid Distortion Magnification = 2.864E+03 Max Disp =.64E-03m (b) FS=0.99 (c) FIG. 2. Contours when the time is 200 minutes: (a) saturation (b) pore water pressure and (c) maximum shear strain rate.

14 520 IACGE 203 Influence of the Rising Speed of the Water Level on Dam Stability To study the influence of the rising speed of the water level on the safety factor of dam stability, the saturated hydraulic conductivity of soil was fixed at K s = m/s, and the three rising speeds were assumed to be , , and m/s. The comparison of the simulated results under these water level rising speeds are shown in Fig. 3, which indicates that the safety factors of dam stability decrease with increasing time after 50 min. However, the influence of the water level rising speed on dam stability is insignificant because the variation is not obvious, possibly because the rain infiltration in the dam body from upstream to downstream is more rapid than the rise of the water level; therefore, the pore water pressure profiles under these water level rising speeds are similar. Factor of Safety v= m/s v= m/s v= m/s Time (min) FIG. 3. Influence of rising speed of water level on dam stability. Influence of the Saturated Hydraulic Conductivity of Soil on Dam Stability To study the influence of the saturated hydraulic conductivity on the safety factor of dam stability, two additional hydraulic conductivities were estimated, K s = and K s = m/s; Fig. 4 shows a comparison of the simulated results. The variation of the safety factor is small before a threshold time is reached, and, after the threshold time, the safety factor of dam stability decreases when the time increases. The threshold time indicates that the time is when seepage starts to affect the slope stability of the dam. The results also imply that the threshold time and the dam failure time increase when the saturated hydraulic conductivity of the dam is reduced. Influence of Rain Infiltration on Dam Stability Fig. 5 shows that the slope failure time of the dam is approximately 247 min when only the effect of rising water level upstream is considered; however, it is 89 min

15 IACGE when the rain infiltration condition is added to the rising water level. The coupling of the rising water level with rainfall infiltration enlarges the saturated soil zone and increases the wetting speed of the unsaturated soil. Therefore, the dam fails more quickly when both the rain infiltration and the rising water level are considered than when only the rising water level is considered. Factor of Safety Ks= m/s Ks= m/s Ks= m/s Time (min) FIG. 4. Influence of saturated hydraulic conductivity of soil on dam stability without rain infiltration with rain infiltration Factor of Safety Time (min) FIG. 5. Influence of adding rain infiltration on dam stability.

16 522 IACGE 203 CONCLUSIONS This study used FLAC to analyze the stability of a landslide dam assuming a rising water level upstream. The influencing parameters discussed include the rising speed of the water level and the hydraulic conductivity of the soil. Based on the numerical analyses presented in this study, the following conclusions are made:. The influence of the rising speed of the water level on the safety factors of dam stability is less significant than that of varying the hydraulic conductivity of the soil. 2. The dam stability is reduced when saturated hydraulic conductivity is increased. 3. The dam failure is more rapid when both rainfall infiltration and rising water level are considered than when rising water level alone is considered. ACKNOWLEDGMENTS This study was supported by research funding from the National Science Council of Taiwan (NSC M MY3; NSC M MY3). Their support is gratefully appreciated. REFERENCES Egeli, I. and Pulat, H.F. (20). "Mechanism and modelling of shallow soil slope stability during high intensity and short duration rainfall." Scientia Iranica, Vol. 8(6): Fu, J.F. and Jin, S. (2009). "A study on unsteady seepage flow through dam." Journal of Hydrodynamics, Vol. 2(4): Huang, M. and Jia, C.Q. (2009). "Strength reduction FEM in stability analysis of soil slopes subjected to transient unsaturated seepage." Computes and Geotechnics, Vol. 36(): Ng, C.W.W. and Shi, Q. (998). "A numerical investigation of the stability of unsaturated soil slopes subjected to transient seepage." Computes and Geotechnics, Vol. 22(): 28. Orense, R.P., Shimoma, S., Maeda, K. and Towhata, I. (2004). "Instrumented model slope failure due to water seepage." J. Nat. Disaster Sci., Vol. 26 (): Richards, L.A. (93). "Capillary conduction of liquids through porous mediums." Physics, Vol. : Schnellmann, R., Bussllinger, M., Schneider, H.R. and Rahardjo, H. (200). "Effect of rising water table in an unsaturated slope." Engineering Geology, Vol. 4: Tohari, A., Nishigaki, M. and Komatsu, M. (2007). "Laboratory rainfall-induced slope failure with moisture content measurement." Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 33 (5), van Genuchten, M.Th. (980). "A close-form equation for predicting the hydraulic conductivity of unsaturated soil." Soil Sci. Soc. Am. J., Vol. 44: Xu, Y.Q., Unami, K. and Kawachi, T. (2003). "Optimal hydraulic design of earth dam cross section using saturated unsaturated seepage flow model." Advances in Water Resources, Vol. 26(): 7.