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Infiltration effects on stability of a residual soil slope
Computers and Geotechnics 26 (2000) 145±165 www.elsevier.com/locate/compgeo
In®ltration eects on stability of a residual soil slope J.M. Gasmo *, H. Rahardjo, E.C. Leong Nanyang Technological University, NTU-PWD Geotechnical Research Centre, c/o School of Civil and Structural Engineering, Blk N1, #1A-37, Nanyang Avenue, 639798, Singapore Received 11 January 1999; received in revised form 8 June 1999; accepted 15 November 1999
Abstract Many slope stability studies have indicated that the in®ltration of rainwater into a slope decreases the stability of the slope. However, the diculty of quantifying the eect of rainwater in®ltration on slope stability still exists. It would be advantageous to know what percentage of rainfall enters a slope as in®ltration and how much this in®ltration decreases the stability of a slope. Numerical models were used to study how in®ltration into a slope varied with respect to rainfall intensity and how this in®ltration aected the stability of the slope. A numerical study revealed that the amount of in®ltration was highest at the crest of a slope. A case study revealed that it was dicult to quantify the amount of in®ltration occurring in a slope with the numerical model. The numerical model was, however, able to illustrate the eect of in®ltration on slope stability through the combined use of seepage and slope stability analyses. # 2000 Published by Elsevier Science Ltd. All rights reserved.
1. Introduction Research in the area of slope stability has brought about the realisation that most slope failures are caused by the in®ltration of rainwater into a slope. Studies performed by Sweeney and Robertson [1], Chipp et al. [2], Pitts [3,4], Brand et al. [5], Brand [6], Tan et al. [7], and Johnson and Sitar [8] all con®rmed that the in®ltration of rainwater into a slope has an adverse eect on its stability. However, the amount of rainfall that becomes in®ltration and the in®ltration eects on the stability of a slope have yet to be con®rmed. It would be advantageous to be able to quantify the in®ltration into a slope and the corresponding change in the factor of safety to gain * Corresponding author. E-mail address: jason_ [email protected] (J.M. Gasmo). 0266-352X/00/$ - see front matter # 2000 Published by Elsevier Science Ltd. All rights reserved. PII: S0266-352X(99)00035-X
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a better understanding of how much the stability of a slope can vary. One way to achieve this objective would be through the use of numerical models. Numerical models have been used previously by Alonso et al. [9], OÈberg [10], Fredlund and Rahardjo [11], and Shimada et al. [12] to study the interaction between in®ltration and unsaturated soils with respect to slope stability. This paper describes how numerical models were used to further study the eect of in®ltration on the stability of unsaturated residual soil slopes in Singapore. The objective was to make use of seepage and slope stability software that are currently available to engineers to determine how in®ltration in a slope varied with respect to rainfall intensity, and how in®ltration aected the stability of a slope. Emphasis was placed on quantifying the amount of in®ltration that occurred in a slope and quantifying the factor of safety (FOS) change during in®ltration. A numerical study and a case study were performed to obtain these results. 2. Relevant theory Unsaturated soil mechanics theory was utilised by the numerical models used in this study. The ®nite element seepage model, SEEP/W [13], made use of the soilwater characteristic (SWC) curve and permeability function to simulate the ¯ow of water through an unsaturated soil. The limit equilibrium slope stability model, SLOPE/W [14], made use of unsaturated shear strength parameters to determine the factor of safety for a slope. The SWC curve represents the volumetric water content of a soil at various matrix suction values. Matric suction can be de®ned as a negative pore±water pressure referenced to the pore±air pressure. As matric suction increases, the volumetric water content of the soil decreases. This aects the movement of water through the soil because there are less water ®lled spaces available for water ¯ow. As matric suction increases, the permeability of the soil decreases. The permeability of a soil at various matric suction values is represented by the permeability function. The seepage model makes use of the governing equation for water ¯ow through a soil to calculate the results. The basic equation that governs the ¯ow of water in an isotropic soil is given as follows: @ @hw @ @hw @hw kw kw 1 mw 2 w g @x @y @x @y @t The left-hand side of Eq. (1) represents the ¯ow of water through a soil element in the x- and y-directions based on Darcy's law. This water ¯ow is equal to the change in the volume of water in the soil element per unit time as given on the right-hand side of the equation. The term refers to the slope of the SWC curve for a speci®c change in pore±water pressure. The pore±water pressure change multiplied by the slope of the curve equals the change in the volume of water for that change in pore± water pressure, per unit time. The kw term represents the coecient of soil permeability with respect to water and the hw term represents the hydraulic head available
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for ¯ow. The governing equation for water ¯ow incorporates all the parameters necessary to de®ne the ¯ow of water. As water is removed from the void spaces of a saturated soil, negative pore±water pressures develop between the particles of soil. As more water is removed, the matric suction increases and the air/water interface exerts a tension force on the soil particles giving the soil an added value of shear strength. When in®ltration occurs, the matric suction decreases, and the shear strength of the soil is reduced. In this way, in®ltration has an adverse eect on the shear strength of the soil. The slope stability model makes use of the shear strength equation for unsaturated soils to determine the factor of safety. The shear strength equation for unsaturated soils is an extension of the Mohr±Coulomb failure criterion into the third dimension as shown in Fig. 1 [15]. The shear strength for an unsaturated soil consists of an eective cohesion, c, and independent strength contributions from the stress state variables of net normal stress, ÿ ua , and matrix suction, ua ÿ uw . The shear strength equation making use of the stress state variables is given as follows: ff c0 f ÿ ua f tan 0 ua ÿ uw f tan b where ff c0
f ÿ ua f ff uaf
= shear stress on the failure plane at failure = intercept of the ``extended'' Mohr±Coulomb failure envelope on the shear stress axis where the net normal stress and the matrix suction at failure are equal to zero; also referred to as ``eective cohesion'' = Net normal stress state on the failure plane at failure = total normal stress on the failure plane at failure = pore-air pressure on the failure plane at failure
Fig. 1. Failure envelope for unsaturated soils.
2
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0 ua ÿ uw f uwf b
= angle of internal friction associated with the net normal stress state variable, f ÿ ua f = matric suction on the failure plane at failure = pore-water pressure on the failure plane at failure = angle indicating the rate of increase in shear strength relative to the matric suction, ua ÿ uw f .
It can be seen that Eq. (2) provides a smooth transition into the shear strength equation for saturated soils. When the soil becomes saturated, the pore-water pressure equals the pore±air pressure and Eq. (2) takes on the form of the shear strength equation for saturated soils as shown below in Eq. (3). ff c0 f ÿ uw f tan 0
3
3. Numerical study of slope in®ltration The numerical study of rainwater in®ltration into a slope was performed using the ®nite element program SEEP/W [13]. The purpose of the numerical study was to determine what portion of an applied rainfall became in®ltration, and how the in®ltration rate in the model varied with rainfall intensity, time and location on the slope. A typical pro®le of a homogeneous soil slope was used in this study. The soil type was speci®ed as a silty clay with a saturated permeability, ks , of 8.310ÿ7 m/s. The SWC curve for the silty clay, shown in Fig. 2, was obtained from Lim et al. [16] and the permeability function, shown in Fig. 3, was generated based on this SWC curve
Fig. 2. Soil±water characteristic curve for soil used in the numerical study.
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and the above value of ks . Fig. 4 shows the numerical model representation of the typical slope. To calculate the in®ltration into the slope, the seepage model makes use of ¯ux sections. A ¯ux section is simply a line which de®nes a group of elements across which moisture movement is calculated. Flux sections were drawn just below the ground surface through the ®rst row of elements to calculate the in®ltration into the slope. Three separate ¯ux sections were drawn for the crest, face and toe of the slope (arrows in Fig. 4) to study how the in®ltration varied at dierent parts of the slope.
Fig. 3. Permeability function for soil used in the numerical study.
Fig. 4. Numerical model representation of typical slope for numerical study.
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Steady-state and transient conditions were analysed in this study. Realistically, the steady-state condition seldom exists in the ®eld. This condition was used to understand what the long term ¯ow conditions in the slope would be. If the transient analysis was performed for a sucient length of time, it would lead to the same results as the steady-state solution. Therefore, the steady state solution was used to check if the results from the transient analyses were reasonable. 3.1. Steady state analyses 3.1.1. Finite element model The boundary conditions for the steady state condition in the seepage model were de®ned as shown in Fig. 4. The side boundaries, FA and CB, were de®ned as head boundaries equal to the speci®ed groundwater level. The bottom boundary, AB, was speci®ed as a no ¯ow boundary, and the top boundary, FEDC, was speci®ed as a ¯ux boundary. The side and bottom boundary conditions were kept constant while the ¯ux at the top boundary was changed to simulate various intensities of rainfall. The ¯ux was varied from values lower than ks to values higher than ks of the soil. Ponding was not allowed to occur at the ground surface (FEDC). This meant that when a ¯ux greater than the permeability of the soil was applied to the top boundary, the seepage model would not allow pore±water pressures at the ground surface to build up greater than 0 kPa. This simulated the actual ®eld conditions where excess rainfall at the ground surface is removed from the slope as runo. The ¯ux applied at the ground surface (rainfall) was compared with the computed ¯ux into the soil (in®ltration) to quantify the amount of in®ltration for the crest (FE), face (ED) and toe (DC) of the slope. 3.1.2. Results Rainfall intensities between 1.010ÿ8 m/s (0.036 mm/h) and 1.010ÿ3 m/s (3600 mm/h) were applied to the top boundary of the slope. Fig. 5 shows the calculated ¯ux plotted with respect to the applied ¯ux. The four curves represent the ¯ux across the crest, face, toe, and overall surface of the slope. The diagonal reference line represents the condition where all the applied ¯ux in®ltrates completely into the slope (i.e. calculated ¯ux equals the applied ¯ux). The horizontal reference line is the saturated permeability of the soil, which would be the maximum rate at which water can enter the soil when the soil is fully saturated (with a hydraulic gradient equal to one). The applied and calculated ¯uxes were similar for the crest, face, and toe of the slope at low in®ltration rates of 1.010ÿ8 and 1.010ÿ7 m/s (1±2 orders of magnitude less than ks ). When a ¯ux within one order of magnitude of ks was applied, the calculated ¯ux becomes less than the applied ¯ux (Fig. 5). The calculated ¯ux at the crest of the slope is found to be closest to the ks line with a steady state value of 55% of ks (4.610ÿ7 m/s). The ¯ux at the face of the slope reached a steady state value of 9% of ks (7.210ÿ8 m/s). The ¯ux at the toe of the slope reached the lowest steady state value of 0.5% of ks (4.510ÿ9 m/s). The overall ¯ux for the slope reached a steady state value of 16% of ks (1.310ÿ7 m/s). Comparison between the steady
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Fig. 5. Results from the steady-state analysis.
state ¯ux values shows that the largest in®ltration occurs at the crest of the slope, followed by the face, and then the toe of the slope. The above results are reasonable for the steady state conditions. In the model, the crest of the slope allowed the largest amount of in®ltration because most of the in®ltration at the crest ¯owed vertically downwards. This in®ltration then became inter¯ow within the slope and ¯owed down towards the toe. Since the in®ltration ¯owed downward and away from the crest of the slope, the crest could continue to accept more rainfall. The in®ltration at the crest increased the water content of the soil throughout the rest of the slope. The increase in water content at the slope face from within the slope meant that there were less void spaces available to accept in®ltration. This resulted in less water entering the slope face as in®ltration. The portion of water that did enter the face of the slope was combined with the inter¯ow from the crest and ¯owed down towards the toe. This resulted in even less water being able to in®ltrate the slope at the toe. As a result, the largest amount of in®ltration occurred at the crest. 3.2. Transient analyses 3.2.1. Finite element model To study the transient conditions, the same ®nite element mesh, soil properties, and boundary conditions were used as for the steady state conditions. Flux values for the top boundary (ground surface FEDC) were varied from lower than ks to higher than ks of the soil. The computed ¯uxes across the ¯ux sections were recorded
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with respect to the elapsed time. This analysis was used to study how in®ltration varied over time with respect to the applied rainfall and the part of the slope on which it occurred. 3.2.2. Results Rainfall intensities from 1.010ÿ7 m/s (0.36 mm/h) to 1.010ÿ5 m/s (36.0mm/h) were applied to the overall surface of the slope for the transient analyses. The ¯ux calculated across the ¯ux sections in the model were recorded with respect to time and then divided by the saturated permeability of the soil. This resulted in a dimensionless quantity, termed the relative in®ltration value (RIV), which allowed for easier comparison of the results. The RIV versus elapsed time for the crest of the slope is shown in Fig. 6. A line representing the saturated permeability of the soil (RIV equal to 1.0) is also plotted on the graph. Fig. 6 shows that for a low rainfall rate of less than 1.010ÿ7 m/s (1±2 orders of magnitude less than ks ), the initial in®ltration rate at the crest was low (RIV less than 1.0). As the soil became wet, the permeability increased and the in®ltration rate gradually increased over time to the steady-state condition. For rainfall rates greater than ks , the initial in®ltration rate was higher than the ks value by as much as 3.5 times (RIV of 3.5). Then the in®ltration rate decreased over time towards the steady-state
Fig. 6. Results from the transient analysis at the crest of the slope.
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condition. Because ponding was not allowed to occur, the same in®ltration curve was calculated for any rainfall intensity greater than ks (Fig. 6). The results of the transient analyses for the face, toe, and overall surface of the slope show a trend similar to the results for the crest, with the exception of their magnitudes. The magnitude of the RIVs at the face, toe and overall slope surface were less than the RIV at the crest for the same given time. This is in agreement with the results shown by the steady-state analysis where the largest amount of in®ltration occurred at the crest of the slope. The possibility of having an RIV greater than 1.0 can be explained using Darcy's law, ki. An in®ltration rate, , greater than ks was possible because the hydraulic head gradient available for the ¯ow, i, was high enough that it compensated for the low value of permeability, k. In this way, rainwater can in®ltrate the soil at a higher rate than what the saturated permeability indicates. The results from the transient analyses (Fig. 6) are also in agreement with the results reported by Premchitt et al. [17]. Fig. 7 shows the general trend for runo rates and in®ltration rates for a residual soil slope in Hong Kong over time. By comparing the shape of the in®ltration curve in Fig. 7 with the in®ltration curve in Fig. 6, it can be seen that they are similar for the modelled condition where the rainfall intensities are greater than the ks of the soil. As shown in Fig. 6, the initial in®ltration rate is high (RIV greater than 1.0) and as the ground saturates, the in®ltration rate starts to decrease towards a steady state condition. An in®ltration rate that is greater than the saturated permeability is an important consideration because it can also cause a rapid decrease in the shear strength of the soil, which can reduce the stability of the slope and possibly result in a landslide. 3.3. Summary The results from the numerical study showed that the largest amount of in®ltration occurred at the crest of the slope and that in®ltration rates greater than ks are possible for high intensity rainfalls. This is in agreement with observations made by
Fig. 7. Variation of runo and in®ltration rates over time (from Premchitt et al. [16]).
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Johnson and Sitar [8] where it was reported from observations of debris ¯ow source areas that landslides were initiated high on the slope face. A large amount of in®ltration at the crest would increase the pore±water pressures in the soil and decrease the stability of the slope at that location. If the increase in pore±water pressures were large enough, failure of the slope might then occur. 4. Case study Based on the information gained from the numerical study, an instrumented slope was used to study rainwater in®ltration and its eect on slope stability. The speci®c goals of the case study were to quantify the in®ltration rate for the slope, check/ verify the ®ndings of the numerical study, and quantify the eect in®ltration has on the factor of safety of a slope. The numerical seepage model (SEEP/W) was used to simulate the pore±water pressure changes that were measured in the ®eld. Flux sections were used to determine the in®ltration rate in the modelled slope. The limit equilibrium slope stability analysis (SLOPE/W) was used to quantify how the change in pore-water pressures aected the factor of safety of the slope. Data collected from the instrumented slope were used to verify the results of the numerical analyses. 4.1. Collected ®eld data The soil pro®le of the case study slope is shown in Fig. 8. A detailed description of the slope and its instrumentation are presented by Gasmo et al. [18]. The slope is well turfed and stands at an angle of approximately 26 . The slope consists of residual soils, the weathering product from the sedimentary rock of the Jurong formation. The
Fig. 8. Idealised pro®le of case study slope.
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site investigation revealed that the slope consisted of a weathered bedrock layer overlain by purple silty clay, and orange silty clay [19]. Data collected from the slope during a three week period were used for the case study. Fig. 9 shows the pore±water pressures measured by the tensiometers in the ®rst row at the crest (Row A), from 21 July 1996 to 10 August 1996, in combination with the hourly rainfall. The ®ve lines shown on the graph represent readings from the ®ve tensiometers as indicated in the legend. The bar graph represents the rainfall data and shows that a rainfall occurred on 3 August 1996 and 8 August 1996. The eect of evaporation and in®ltration on pore-water pressures in the slope can be seen in Fig. 9. From 21 July 1996 to 2 August 1996 the matric suction increased (or the pore±water pressure decreased) as moisture was removed from the soil via evaporation or evapotranspiration. This is shown by the downward trend of the lines. The matric suction at 0.5 m reached approximately 80 kPa, while the matrix suction at 1.1 m and below reached only approximately 10 kPa. This dierence in pore±water pressure changes is probably due to dierences in the soil characteristics caused by uneven weathering. The rainfall on 3 August 1996 provided in®ltration to the slope. The in®ltration caused a decrease in the matrix suction as shown by the sudden upward shift of the lines. The change in matric suction at 0.5 m was approximately 70 kPa while the matric suction at the other depths decreased by 10±20 kPa due to the in®ltration. From Fig. 9 it can be seen that all ®ve tensiometers responded to the in®ltration which shows that the zone of in¯uence for in®ltration at the slope is greater than the 3.2 m. The ®eld data shown in Fig. 9 were plotted as pore±water pressure pro®les with respect to depth to allow easier comparison between the ®eld data and model results. Fig. 10(a) shows the pore-water pressure pro®les at speci®c times from 21 July 1996 to 3 August 1996. As the matric suction increases over time, the curves shift to the left. Fig. 10(b) shows the pore±water pressure pro®les during in®ltration on 3 August
Fig. 9. Pore±water pressures at dierent depths of Row A from 21 July 1996 to 10 August 1996.
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Fig. 10. Variation of pore-water pressure pro®les for Row A.(a) From 21 July 1996 to 3 August 1996, as a result of evaporation.(b) From 00:19 to 02:19 on 3 August 1996, as a result of in®ltration.
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1996. As the matric suction decreases over time, the curves shift to the right. It took approximately 2 weeks for the matric suction to increase due to evaporation and less than one day for the matric suctions to decrease due to in®ltration. The pore±water pressure at the 0.5 m depth took approximately 12 h to increase completely where the pore±water pressures below this depth increased within approximately 2 h. The slow response of the 0.5 m tensiometer was likely due to poor contact between the instrument tip and the surrounding soil (caused by shrinkage of the soil during the previous dry period). 4.2. In®ltration analyses 4.2.1. Seepage model The seepage model was used to simulate movement of water through the soil in two dimensions and to predict the change in pore±water pressures throughout the slope pro®le. The inputs required by the seepage model were the geometry and soil pro®le of the slope, the SWC curve and the permeability function of each soil layer in the pro®le and the boundary conditions of the slope. The geometry and pro®le of the case study slope were de®ned in the seepage model as shown in Fig. 8. The SWC curve, permeability function, and shear strength parameters were determined by performing laboratory tests on soil specimens obtained from block samples. A block sample was taken at the ground surface from each of the two silty clay layers of the slope. The SWC curve for each of the silty clay soil layers was determined from volumetric pressure plate tests. The saturated permeability for each soil layer was determined from triaxial permeameter tests. The permeability functions for the soil layers were determined indirectly using the computer program ACUPIM 1.0 [20] with the SWC curves and the ks values as input. The results of the laboratory tests are summarised in Table 1. These results were used to specify the input parameters required by the numerical models. It was not possible to get soil samples for the weathered bedrock layer of the case study slope. It was assumed that this layer would have a lower saturated permeability than the two silty clay soil layers, and was, therefore, assigned a ks value of 1.010ÿ10 m/s in the numerical model. This caused most of the groundwater ¯ow to occur in the upper two silty clay layers. This assumption is acceptable because the bedrock layer
Table 1 Permeability and shear strength parameters for soil of the case study slope Orange silty clay[19] ks c fb
ÿ6
1.010 m/s 20 kPa 26.5 23.0 21.0 kN/m3
Purple silty clay[21] 3.010ÿ9 m/s 90 kPa 35.0 35.0 22.6 kN/m3
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was located suciently far away from the top 3 m of the slope where this study was being concentrated. The boundary conditions for the seepage model (Fig. 8) were de®ned in the same manner as the boundary conditions de®ned in Fig. 4. The side boundaries were de®ned as head boundaries with a hydraulic head equal to the groundwater level, the bottom boundary was de®ned as a no ¯ow boundary, and the top boundary was speci®ed as a ¯ux boundary. The boundary conditions for the side and bottom boundaries were kept constant throughout the analyses. Only the ¯ux speci®ed for the top boundary was changed during the transient analyses in order to simulate the conditions measured in the ®eld. The in®ltration rate in the model was calculated by drawing ¯ux sections at the ground surface of the slope. To perform the transient analysis of in®ltration, the initial conditions recorded on 3 August 1996 needed to be input into the model. This could only be done by performing two separate analyses which adjusted the results in the model to be similar to the porewater pressure distribution on 3 August 1996. The ®rst analysis was required to adjust the initial hydrostatic results from the steady state solution to the transient condition recorded for 21 July 1996, 00:02 [Fig. 10(a)]. This was achieved by specifying a rainfall intensity in the model which was greater than the saturated permeability of the orange silty clay. As a result, the pore±water pressures in the slope increased to values close to the pore±water pressures measured in the slope on 21 July 1996. The second analysis was needed to simulate the increase in matrix suction from 21 July 1996 to 3 August 1996 [Fig. 10(a)] caused by evaporation. The seepage model was not designed to model evaporation, but it could be manipulated to generate pore-water pressure distributions similar to those measured in the ®eld. To increase the matrix suction, a negative ¯ux was applied to the ground surface which acted like evaporation. The value for the negative ¯ux was estimated from the ®eld data collected at his slope by applying a method similar to that described by Sattler [22]. A negative surface ¯ux of 2.010ÿ7 m/s (17.0 mm/day) and 4.410ÿ11 m/s (0.004 mm/day ) was applied to the ground surface of Rows A±E (orange silty clay) and Rows F±G (purple silty clay) respectively. These ¯uxes were applied over a sucient time period to generate pore-water pressures that were similar to those from the ®eld conditions on 3 August 1996. After achieving the ®eld pore-water pressure conditions on 3 August 1996, then the transient analysis of in®ltration was performed. The rainfall that occurred on August 3, 1996, lasted for 7 h. It had an initial intensity of 57.5 mm/h (1.610ÿ5 m/ s) for the ®rst hour and then an average intensity of 4.0 mm/h (1.110ÿ6 m/s) for the remaining 6 h. This rainfall was averaged to a daily rainfall value of 81.5 mm/day (1.010ÿ6 m/s). The ¯ux speci®ed at the surface of the slope was 1.010ÿ6 m/s. 4.2.2. Results The pore±water pressure pro®les from the numerical model are shown in Figs. 11(a) and (b). The model pro®les have the same trend as the pore±water pressure pro®les in the ®eld [Fig. 10(a) and (b)]. The model results show that the matrix suction increased over time due to the applied negative ¯ux, and then decreased over time due to the applied rainfall (in®ltration).
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Fig. 11. Numerical model results for Row A.(a) Matric suction increase. (b) In®ltration (matric suction decrease).
Veri®cation of the model results was performed by plotting the model pore±water pressure distributions together with the ®eld data as shown in Fig. 12. The results from the in®ltration analysis show that the model results follow the general trend of the ®eld data, with the matric suctions being lost near the ground surface ®rst, and then the pore-water pressures gradually increased at deeper depths. The gradual
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shifting of the curves to the right over time shows the downward progression of the in®ltration. Note that in the model the pore-water pressure at the ground surface was equal to zero when the rainfall was applied. This occurred because the speci®ed rainfall intensity (1.010ÿ6 m/s) was equal to the saturated permeability of the soil. As a result the soil became saturated at the ground surface and the pore-water pressures increased to zero. No ®eld instrumentation was installed at exactly the ground surface depth so the ®eld data do not show this information. Comparison between the elapsed times of the ®eld and the model (Fig. 12) shows that the model did not accurately represent the elapsed time in the ®eld. For the in®ltration analysis, the elapsed time in the model was greater than the actual elapsed time in the ®eld. It appears that the in®ltration rate in the model was lower than the in®ltration rate that occurred in the ®eld. Therefore, since the elapsed time for the model in®ltration does not match the elapsed time in the ®eld, the in®ltration rate calculated by the ¯ux sections does not accurately represent the in®ltration rate in the ®eld, and the numerical model was not able to accurately quantify the in®ltration for this case study. Even though the seepage model results were unable to quantify the in®ltration for this case study, the pore±water pressure distributions could still be used in the slope
Fig. 12. Comparison of ®eld and model pore±water pressure pro®les for Row A from 00:19 to 02:19 on 3 August 1996, as a result of in®ltration.
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stability analyses. The pore±water pressure distributions in the model were an acceptable match with the pore±water pressure pro®les from the ®eld. By using the model pore±water pressure distribution at the appropriate times in the ®eld, the change in the factor of safety could still be determined. 4.3. Slope stability analyses 4.3.1. Stability model The inputs required by the slope stability model (SLOPE/W) were the geometry and soil pro®le of the slope, the shear strength parameters and density of soil layers in the slope, the pore±water pressure distribution throughout the slope. The geometry and soil pro®le were input from the idealised soil pro®le shown in Fig. 8. The shear strength parameters for the soil layers (Table 1) were determined from laboratory tests. The pore±water pressure distributions for the slope stability model were de®ned using two methods. The ®rst method utilised the pore±water pressure distribution from the seepage model as a mesh of pore±water pressure heads. The second method utilised the actual ®eld pore-water pressures as a grid of points at their respective depths. An area of possible slip surface locations was de®ned in the model by specifying a grid of possible centres of rotation and a series of slip circle radii. The factor of safety was calculated for each time step in the transient analyses [Fig. 11(a) and (b)] as well as for each time corresponding to the respective ®eld data [Fig. 10(a) and (b)]. The factor of safety determined by the slope stability model was plotted with respect to the elapsed time that occurred in the ®eld. The results from the slope stability in combination with the rainfall data are shown in Fig. 13. The factor of safety was calculated only up to August 3, 1996, for the SEEP/W pore-water pressure heads. The factors of safety for the grid of measured ®eld pore±water pressures were calculated up to August 10, 1996, to include the occurrence of a second rainfall.
Fig. 13. Factor of safety for the case study slope from 21 July 1996 to 10 August 1996.
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4.3.2. Results The results of the numerical analyses illustrate the eect of evaporation and in®ltration on the factor of safety of the slope. From the stability analyses using the SEEP/W pore-water pressure distributions, the factor of safety increased by 34% over 13 days due to evaporation. When the rainfall occurred, the factor of safety decreased by 27% over 2 h. From the stability analyses using the measured porewater pressures, the factor of safety increased by 32% over 13 days due to evaporation. When the rainfall occurred, the factor of safety decreased by 16% over 2 h. The factor of safety then continued to decrease by another 10% over the next 7 h as the pore-water pressures in the ®eld continued to increase due to the downward movement of in®ltration. These results show that the factor of safety increases slowly due to evaporation and then decreases rapidly due to in®ltration. The two methods of de®ning pore-water pressures resulted in dierent values of factors of safety. The factors of safety calculated using the SEEP/W pore±water pressures were less than the factors of safety calculated using the actual pore±water pressures in the ®eld. This was because of the dierence between the model and the ®eld pore±water pressure pro®les. Large positive pore-water pressures were present in the slope stability analysis when the SEEP/W pore±water pressure distribution was used. From Fig. 12 it can be seen that large positive pore±water pressures were present below a depth of 2.0 m. As a result, the overall shear strength of the soil in the slope was reduced and therefore the calculated factor of safety also decreased. The results of the stability analyses using the measured pore-water pressures in the ®eld also show the eect of antecedent moisture conditions on the stability of a slope. Johnson and Sitar [8] stated that a high antecedent moisture condition allowed a rainfall of lower intensity and duration to initiate a failure and from Fig. 13 it can be seen how this is possible. The ®rst rainfall on 3 August 1996 caused the factor of safety to decrease by 26% from 4.81 to 3.57. The second rainfall had a lower intensity and caused the factor of safety to decrease even further by 12% to 3.38. This shows that the antecedent moisture condition may be an important factor to consider when determining the stability of a slope. From the factor of safety in Fig. 13 it can be seen that the case study slope has little risk of failure. A factor of safety greater than 3.0 indicates that the slope is quite stable. However, the factor of safety of the slope will still vary over time due to changes in the pore-water pressure distribution caused by changes in climate. This range of variation in the factor of safety quanti®es the eect of evaporation and in®ltration on slope stability. For the case study slope, 2 weeks of dry weather increased the stability of the slope by approximately 30%. A rainfall intensity of 80 mm/day decreased the stability of a slope by approximately 25%. 4.4. Numerical model limitations The numerical seepage model was unable to quantify the in®ltration rate for the case study slope because the elapsed times in the model did not match the elapsed times in the ®eld. The reason that the elapsed times did not match is because the numerical model was given a simpli®ed representation of a complex residual soil
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slope. Residual soils are highly variable in their layering and characteristics, as can be seen by the shape of the pore±water pressure pro®les in Figs. 10(a) and (b). Overall, the model pro®les [Figs. 11(a) and (b)] are a good approximation of the ®eld data. However, the discrepancies between the ®eld and model pro®les at various depths would suggest that the soil layers idealised in the model may not exactly match those in the ®eld. Similarly, the permeability functions that were speci®ed in the numerical model for each soil layer may not be representative. The permeability function for a soil layer can vary with depth. The permeability function speci®ed in the numerical model for the in®ltration stage did not accurately represent the permeability of the soil in the ®eld. The in®ltration stage of the model required 21 days to achieve the pore±water pressure pro®le that existed in the ®eld after 2 h. It appears that the saturated permeability used in the model was too low and needs to be increased in order to allow the elapsed time in the model to match the elapsed time in the ®eld. The time that elapses in the numerical model is controlled by the saturated permeability that is speci®ed in the model. By increasing the value of ks by one order of magnitude, the time over which pore-water pressure changes occur is decreased by one order of magnitude, and vice versa. Therefore to get the elapsed time in the model to match the elapsed time in the ®eld, the permeability function needs to be increased. It would be reasonable to increase the ks of the soil because of the method that was used to determine the value of ks . The ks value used in the numerical model was determined in the laboratory using the triaxial permeameter. The permeability test was performed on a specimen of soil from a depth of 30 cm. The eective con®ning pressure of the triaxial permeameter (a minimum of 10 kPa) would cancel out the eects of the cracks and ®ssures in the soil by compressing the cracks closer together. Therefore, the ks determined in the laboratory would be lower when compared to what may actually exist in the ®eld. The eective ks for the slope is actually higher because of the cracks and ®ssures that exist in the soil. Another reason for the discrepancy between the ®eld data and the computed results for the in®ltration process is due to the speci®ed boundary conditions. The average value of rainfall that was speci®ed as a ¯ux at the ground surface was not an accurate representation of conditions in the ®eld. The actual rainfall intensity varies over time, and therefore the in®ltration will also vary over time. This will result in the pore-water pressures that will also change at dierent rates over time. 5. Conclusions The numerical study and the case study were used successfully to study in®ltration and its eect on slope stability. The results of the numerical study show that most in®ltration occurs at the crest of the slope. For the steady-state condition, the applied ¯ux and the calculated ¯ux will be approximately the same for rainfall intensities that are 1 or more orders of magnitude less than ks . Within one order of magnitude of ks , the calculated ¯ux is a portion of the applied ¯ux with the largest portion occurring at the crest. For the transient condition with a rainfall intensity
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less than ks , the initial in®ltration rate is much less than ks and then the in®ltration rate gradually increases towards ks . For a rainfall intensity greater than ks , the initial in®ltration rate is greater than ks and then it decreases towards ks . The results from the case study were unable to quantify the in®ltration rates for the instrumented slope because the permeability functions that were input into the model did not accurately represent the ®eld conditions. The numerical model of slope stability was, however, able to quantify the eect of in®ltration on the stability of the slope. Two weeks of evaporation without any rain increased the stability of the slope by approximately 30%. A rainfall with an intensity of 80 mm/day decreased the stability of the slope by approximately 25% in approximately half a day. This shows that it is possible to quantify the eects of evaporation and in®ltration on the stability of a residual soil slope. The results from the numerical models indicate that further research is warranted to improve the accuracy of the numerical analyses. The models themselves worked properly, but the input parameters speci®ed in the models need to be re®ned. The case study provided valuable information in regards to improving the accuracy of unsaturated slope stability analysis. To improve the accuracy of the numerical model representations, better de®nition of the soil parameters such as the soil pro®le, ks , SWC curves, and permeability functions are required. For the in®ltration stage, the saturated permeability should be measured in the ®eld at the ground surface to account for the eect of cracks and ®ssures in the soil. For the evaporation stage, further research is required to develop a ®nite element numerical model that can handle seepage ¯ow and evaporative ¯ow in 2-dimensions. A more detailed representation of the slope in the numerical models would improve the accuracy of the analyses. If conditions in the ®eld are highly variable, it becomes increasingly dicult to accurately model the slope. Accurate representations of the ®eld conditions are necessary to achieve accurate model results. Slopes that have a high degree of variation in their pro®le and soil properties will be dicult to model accurately using the simpli®ed model representation. More case studies are required to build up a knowledge base of quanti®ed ®eld in®ltration rates and changes in factors of safety. Acknowledgements This work is funded by the Nanyang Technological University (RP15/91 and RG22/94) Academic Research Funds. Special thanks to Professor Del Fredlund for initiating the collaboration between the University of Saskatchewan and Nanyang Technological University which allowed the ®rst author to be on this research programme. References [1] Sweeney DJ, Robertson PK. A fundamental approach to slope stability problems in Hong Kong. Hong Kong Engineer October 1979: 35±44.
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[2] Chipp PN, Henkel DJ, Clare DG, Pope RG. Field measurement of suction in colluvium covered slopes in Hong Kong. In: Proceedings of the Seventh Southeast Asian Geotechnical Conference, November 22±26 Hong Kong, 1982. p. 49±62. [3] Pitts J. The form and causes of slope failures in an area of West Singapore Island. Singapore Journal of Tropical Geography 1983;4(2):162±8. [4] Pitts J. An investigation of slope stability on the NTI campus, Singapore. Nanyang Technological Institute, Applied Research Project, March, 1985. [5] Brand EW, Premchitt J, Phillipson HB. Relationship between rainfall and landslides in Hong Kong. In: Proceedings of the 4th International Symposium on Landslides, Toronto, Canada, 1984. Vol. 1, p. 377±384. [6] Brand EW. Landslides in southeast Asia: a state-of-the-art report. In: Proceedings of the 4th International Symposium on Landslides, Toronto, Canada, 1984. Vol. 1, p. 17±59. [7] Tan SB, Lim TL, Tan SL, Yang KS. Landslide problems and their control in Singapore. In: 9th Southeast Asian Geotechnical Conference, Bangkok, Thailand, 1987. p. 1±25, 1±36. [8] Johnson KA, Sitar N. Hydrologic conditions leading to debris-¯ow initiation. Canadian Geotechnical Journal 27:789±801 [9] Alonso E, Gens A, Lloret A, Delahaye C. Eect of rain in®ltration on the stability of slopes. In: Proceedings of the First International Conference on Unsaturated Soils, UNSAT'95, Paris, France, 1995. Vol. 1, p. 241±9. [10] OÈberg AL. Negative pore pressures Ð seasonal variance and importance in slope stability analysis. In: Proceedings of the First International Conference on Unsaturated Soils, UNSAT'95, Paris, France, 1995. Vol. 2, p. 907±13. [11] Fredlund DG, Rahardjo H. Hillside slope stability assessment in unsaturated residual soils. In: IKRAM Seminar on the Geotechnical Aspects of Hillside Development, Kuala Lumpur, Malaysia, 1994. p.1±41. [12] Shimada K, Fujii H, Nishimura S, Morii T. Stability analysis of unsaturated slopes considering changes of matrix suction. In: Proceedings of the First International Conference on Unsaturated Soils, UNSAT'95, Paris, France, 1995. Vol. 2, p. 907±13. [13] GEO-SLOPE. SEEP/W v3.0. GEO-SLOPE International Ltd., Calgary, Alberta, Canada, 1994. [14] GEO-SLOPE. SLOPE/W. GEO-SLOPE International Ltd., Calgary, Alberta, Canada, 1991. [15] Fredlund DG, Rahardjo H. Soil mechanics for unsaturated soils. New York: John Wiley & Sons, 1993. [16] Lim TT, Rahardjo H, Chang MF, Fredlund DG. Eect of rainfall on matrix suction in a residual soil slope. Canadian Geotechnical Journal 33: 618±628 [17] Premchitt J, Lam HF, Shen JM. Rainstorm runo on slopes. 1986. GEO Report No. 12, p. 5±104. [18] Gasmo JM, Hritzuk KJ, Rahardjo H, Leong EC. Instrumentation of an unsaturated residual soil slope. Geotechnical Testing Journal 22 (2): June, 128±137 [19] Gasmo JM. Stability of unsaturated residual soil slopes as aected by rainfall. Master of Engineering Thesis, School of Civil & Structural Engineering, Nanyang Technological University, 1997. [20] Leong EC. ACUPIM 1.0. Automated computation of unsaturated permeability from indirect measurements, Nanyang Technological University, 1993. [21] Hritzuk KH. Eectiveness of drainage systems in maintaining soil suctions. Master of Engineering Thesis, School of Civil & Structural Engineering, Nanyang Technological University, 1997. [22] Sattler PJ. Numerical modelling of vertical ground movements. Master of Science Thesis, University of Saskatchewan, 1989.
In®ltration eects on stability of a residual soil slope J.M. Gasmo *, H. Rahardjo, E.C. Leong Nanyang Technological University, NTU-PWD Geotechnical Research Centre, c/o School of Civil and Structural Engineering, Blk N1, #1A-37, Nanyang Avenue, 639798, Singapore Received 11 January 1999; received in revised form 8 June 1999; accepted 15 November 1999
Abstract Many slope stability studies have indicated that the in®ltration of rainwater into a slope decreases the stability of the slope. However, the diculty of quantifying the eect of rainwater in®ltration on slope stability still exists. It would be advantageous to know what percentage of rainfall enters a slope as in®ltration and how much this in®ltration decreases the stability of a slope. Numerical models were used to study how in®ltration into a slope varied with respect to rainfall intensity and how this in®ltration aected the stability of the slope. A numerical study revealed that the amount of in®ltration was highest at the crest of a slope. A case study revealed that it was dicult to quantify the amount of in®ltration occurring in a slope with the numerical model. The numerical model was, however, able to illustrate the eect of in®ltration on slope stability through the combined use of seepage and slope stability analyses. # 2000 Published by Elsevier Science Ltd. All rights reserved.
1. Introduction Research in the area of slope stability has brought about the realisation that most slope failures are caused by the in®ltration of rainwater into a slope. Studies performed by Sweeney and Robertson [1], Chipp et al. [2], Pitts [3,4], Brand et al. [5], Brand [6], Tan et al. [7], and Johnson and Sitar [8] all con®rmed that the in®ltration of rainwater into a slope has an adverse eect on its stability. However, the amount of rainfall that becomes in®ltration and the in®ltration eects on the stability of a slope have yet to be con®rmed. It would be advantageous to be able to quantify the in®ltration into a slope and the corresponding change in the factor of safety to gain * Corresponding author. E-mail address: jason_ [email protected] (J.M. Gasmo). 0266-352X/00/$ - see front matter # 2000 Published by Elsevier Science Ltd. All rights reserved. PII: S0266-352X(99)00035-X
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a better understanding of how much the stability of a slope can vary. One way to achieve this objective would be through the use of numerical models. Numerical models have been used previously by Alonso et al. [9], OÈberg [10], Fredlund and Rahardjo [11], and Shimada et al. [12] to study the interaction between in®ltration and unsaturated soils with respect to slope stability. This paper describes how numerical models were used to further study the eect of in®ltration on the stability of unsaturated residual soil slopes in Singapore. The objective was to make use of seepage and slope stability software that are currently available to engineers to determine how in®ltration in a slope varied with respect to rainfall intensity, and how in®ltration aected the stability of a slope. Emphasis was placed on quantifying the amount of in®ltration that occurred in a slope and quantifying the factor of safety (FOS) change during in®ltration. A numerical study and a case study were performed to obtain these results. 2. Relevant theory Unsaturated soil mechanics theory was utilised by the numerical models used in this study. The ®nite element seepage model, SEEP/W [13], made use of the soilwater characteristic (SWC) curve and permeability function to simulate the ¯ow of water through an unsaturated soil. The limit equilibrium slope stability model, SLOPE/W [14], made use of unsaturated shear strength parameters to determine the factor of safety for a slope. The SWC curve represents the volumetric water content of a soil at various matrix suction values. Matric suction can be de®ned as a negative pore±water pressure referenced to the pore±air pressure. As matric suction increases, the volumetric water content of the soil decreases. This aects the movement of water through the soil because there are less water ®lled spaces available for water ¯ow. As matric suction increases, the permeability of the soil decreases. The permeability of a soil at various matric suction values is represented by the permeability function. The seepage model makes use of the governing equation for water ¯ow through a soil to calculate the results. The basic equation that governs the ¯ow of water in an isotropic soil is given as follows: @ @hw @ @hw @hw kw kw 1 mw 2 w g @x @y @x @y @t The left-hand side of Eq. (1) represents the ¯ow of water through a soil element in the x- and y-directions based on Darcy's law. This water ¯ow is equal to the change in the volume of water in the soil element per unit time as given on the right-hand side of the equation. The term refers to the slope of the SWC curve for a speci®c change in pore±water pressure. The pore±water pressure change multiplied by the slope of the curve equals the change in the volume of water for that change in pore± water pressure, per unit time. The kw term represents the coecient of soil permeability with respect to water and the hw term represents the hydraulic head available
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for ¯ow. The governing equation for water ¯ow incorporates all the parameters necessary to de®ne the ¯ow of water. As water is removed from the void spaces of a saturated soil, negative pore±water pressures develop between the particles of soil. As more water is removed, the matric suction increases and the air/water interface exerts a tension force on the soil particles giving the soil an added value of shear strength. When in®ltration occurs, the matric suction decreases, and the shear strength of the soil is reduced. In this way, in®ltration has an adverse eect on the shear strength of the soil. The slope stability model makes use of the shear strength equation for unsaturated soils to determine the factor of safety. The shear strength equation for unsaturated soils is an extension of the Mohr±Coulomb failure criterion into the third dimension as shown in Fig. 1 [15]. The shear strength for an unsaturated soil consists of an eective cohesion, c, and independent strength contributions from the stress state variables of net normal stress, ÿ ua , and matrix suction, ua ÿ uw . The shear strength equation making use of the stress state variables is given as follows: ff c0 f ÿ ua f tan 0 ua ÿ uw f tan b where ff c0
f ÿ ua f ff uaf
= shear stress on the failure plane at failure = intercept of the ``extended'' Mohr±Coulomb failure envelope on the shear stress axis where the net normal stress and the matrix suction at failure are equal to zero; also referred to as ``eective cohesion'' = Net normal stress state on the failure plane at failure = total normal stress on the failure plane at failure = pore-air pressure on the failure plane at failure
Fig. 1. Failure envelope for unsaturated soils.
2
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0 ua ÿ uw f uwf b
= angle of internal friction associated with the net normal stress state variable, f ÿ ua f = matric suction on the failure plane at failure = pore-water pressure on the failure plane at failure = angle indicating the rate of increase in shear strength relative to the matric suction, ua ÿ uw f .
It can be seen that Eq. (2) provides a smooth transition into the shear strength equation for saturated soils. When the soil becomes saturated, the pore-water pressure equals the pore±air pressure and Eq. (2) takes on the form of the shear strength equation for saturated soils as shown below in Eq. (3). ff c0 f ÿ uw f tan 0
3
3. Numerical study of slope in®ltration The numerical study of rainwater in®ltration into a slope was performed using the ®nite element program SEEP/W [13]. The purpose of the numerical study was to determine what portion of an applied rainfall became in®ltration, and how the in®ltration rate in the model varied with rainfall intensity, time and location on the slope. A typical pro®le of a homogeneous soil slope was used in this study. The soil type was speci®ed as a silty clay with a saturated permeability, ks , of 8.310ÿ7 m/s. The SWC curve for the silty clay, shown in Fig. 2, was obtained from Lim et al. [16] and the permeability function, shown in Fig. 3, was generated based on this SWC curve
Fig. 2. Soil±water characteristic curve for soil used in the numerical study.
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and the above value of ks . Fig. 4 shows the numerical model representation of the typical slope. To calculate the in®ltration into the slope, the seepage model makes use of ¯ux sections. A ¯ux section is simply a line which de®nes a group of elements across which moisture movement is calculated. Flux sections were drawn just below the ground surface through the ®rst row of elements to calculate the in®ltration into the slope. Three separate ¯ux sections were drawn for the crest, face and toe of the slope (arrows in Fig. 4) to study how the in®ltration varied at dierent parts of the slope.
Fig. 3. Permeability function for soil used in the numerical study.
Fig. 4. Numerical model representation of typical slope for numerical study.
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Steady-state and transient conditions were analysed in this study. Realistically, the steady-state condition seldom exists in the ®eld. This condition was used to understand what the long term ¯ow conditions in the slope would be. If the transient analysis was performed for a sucient length of time, it would lead to the same results as the steady-state solution. Therefore, the steady state solution was used to check if the results from the transient analyses were reasonable. 3.1. Steady state analyses 3.1.1. Finite element model The boundary conditions for the steady state condition in the seepage model were de®ned as shown in Fig. 4. The side boundaries, FA and CB, were de®ned as head boundaries equal to the speci®ed groundwater level. The bottom boundary, AB, was speci®ed as a no ¯ow boundary, and the top boundary, FEDC, was speci®ed as a ¯ux boundary. The side and bottom boundary conditions were kept constant while the ¯ux at the top boundary was changed to simulate various intensities of rainfall. The ¯ux was varied from values lower than ks to values higher than ks of the soil. Ponding was not allowed to occur at the ground surface (FEDC). This meant that when a ¯ux greater than the permeability of the soil was applied to the top boundary, the seepage model would not allow pore±water pressures at the ground surface to build up greater than 0 kPa. This simulated the actual ®eld conditions where excess rainfall at the ground surface is removed from the slope as runo. The ¯ux applied at the ground surface (rainfall) was compared with the computed ¯ux into the soil (in®ltration) to quantify the amount of in®ltration for the crest (FE), face (ED) and toe (DC) of the slope. 3.1.2. Results Rainfall intensities between 1.010ÿ8 m/s (0.036 mm/h) and 1.010ÿ3 m/s (3600 mm/h) were applied to the top boundary of the slope. Fig. 5 shows the calculated ¯ux plotted with respect to the applied ¯ux. The four curves represent the ¯ux across the crest, face, toe, and overall surface of the slope. The diagonal reference line represents the condition where all the applied ¯ux in®ltrates completely into the slope (i.e. calculated ¯ux equals the applied ¯ux). The horizontal reference line is the saturated permeability of the soil, which would be the maximum rate at which water can enter the soil when the soil is fully saturated (with a hydraulic gradient equal to one). The applied and calculated ¯uxes were similar for the crest, face, and toe of the slope at low in®ltration rates of 1.010ÿ8 and 1.010ÿ7 m/s (1±2 orders of magnitude less than ks ). When a ¯ux within one order of magnitude of ks was applied, the calculated ¯ux becomes less than the applied ¯ux (Fig. 5). The calculated ¯ux at the crest of the slope is found to be closest to the ks line with a steady state value of 55% of ks (4.610ÿ7 m/s). The ¯ux at the face of the slope reached a steady state value of 9% of ks (7.210ÿ8 m/s). The ¯ux at the toe of the slope reached the lowest steady state value of 0.5% of ks (4.510ÿ9 m/s). The overall ¯ux for the slope reached a steady state value of 16% of ks (1.310ÿ7 m/s). Comparison between the steady
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Fig. 5. Results from the steady-state analysis.
state ¯ux values shows that the largest in®ltration occurs at the crest of the slope, followed by the face, and then the toe of the slope. The above results are reasonable for the steady state conditions. In the model, the crest of the slope allowed the largest amount of in®ltration because most of the in®ltration at the crest ¯owed vertically downwards. This in®ltration then became inter¯ow within the slope and ¯owed down towards the toe. Since the in®ltration ¯owed downward and away from the crest of the slope, the crest could continue to accept more rainfall. The in®ltration at the crest increased the water content of the soil throughout the rest of the slope. The increase in water content at the slope face from within the slope meant that there were less void spaces available to accept in®ltration. This resulted in less water entering the slope face as in®ltration. The portion of water that did enter the face of the slope was combined with the inter¯ow from the crest and ¯owed down towards the toe. This resulted in even less water being able to in®ltrate the slope at the toe. As a result, the largest amount of in®ltration occurred at the crest. 3.2. Transient analyses 3.2.1. Finite element model To study the transient conditions, the same ®nite element mesh, soil properties, and boundary conditions were used as for the steady state conditions. Flux values for the top boundary (ground surface FEDC) were varied from lower than ks to higher than ks of the soil. The computed ¯uxes across the ¯ux sections were recorded
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with respect to the elapsed time. This analysis was used to study how in®ltration varied over time with respect to the applied rainfall and the part of the slope on which it occurred. 3.2.2. Results Rainfall intensities from 1.010ÿ7 m/s (0.36 mm/h) to 1.010ÿ5 m/s (36.0mm/h) were applied to the overall surface of the slope for the transient analyses. The ¯ux calculated across the ¯ux sections in the model were recorded with respect to time and then divided by the saturated permeability of the soil. This resulted in a dimensionless quantity, termed the relative in®ltration value (RIV), which allowed for easier comparison of the results. The RIV versus elapsed time for the crest of the slope is shown in Fig. 6. A line representing the saturated permeability of the soil (RIV equal to 1.0) is also plotted on the graph. Fig. 6 shows that for a low rainfall rate of less than 1.010ÿ7 m/s (1±2 orders of magnitude less than ks ), the initial in®ltration rate at the crest was low (RIV less than 1.0). As the soil became wet, the permeability increased and the in®ltration rate gradually increased over time to the steady-state condition. For rainfall rates greater than ks , the initial in®ltration rate was higher than the ks value by as much as 3.5 times (RIV of 3.5). Then the in®ltration rate decreased over time towards the steady-state
Fig. 6. Results from the transient analysis at the crest of the slope.
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condition. Because ponding was not allowed to occur, the same in®ltration curve was calculated for any rainfall intensity greater than ks (Fig. 6). The results of the transient analyses for the face, toe, and overall surface of the slope show a trend similar to the results for the crest, with the exception of their magnitudes. The magnitude of the RIVs at the face, toe and overall slope surface were less than the RIV at the crest for the same given time. This is in agreement with the results shown by the steady-state analysis where the largest amount of in®ltration occurred at the crest of the slope. The possibility of having an RIV greater than 1.0 can be explained using Darcy's law, ki. An in®ltration rate, , greater than ks was possible because the hydraulic head gradient available for the ¯ow, i, was high enough that it compensated for the low value of permeability, k. In this way, rainwater can in®ltrate the soil at a higher rate than what the saturated permeability indicates. The results from the transient analyses (Fig. 6) are also in agreement with the results reported by Premchitt et al. [17]. Fig. 7 shows the general trend for runo rates and in®ltration rates for a residual soil slope in Hong Kong over time. By comparing the shape of the in®ltration curve in Fig. 7 with the in®ltration curve in Fig. 6, it can be seen that they are similar for the modelled condition where the rainfall intensities are greater than the ks of the soil. As shown in Fig. 6, the initial in®ltration rate is high (RIV greater than 1.0) and as the ground saturates, the in®ltration rate starts to decrease towards a steady state condition. An in®ltration rate that is greater than the saturated permeability is an important consideration because it can also cause a rapid decrease in the shear strength of the soil, which can reduce the stability of the slope and possibly result in a landslide. 3.3. Summary The results from the numerical study showed that the largest amount of in®ltration occurred at the crest of the slope and that in®ltration rates greater than ks are possible for high intensity rainfalls. This is in agreement with observations made by
Fig. 7. Variation of runo and in®ltration rates over time (from Premchitt et al. [16]).
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Johnson and Sitar [8] where it was reported from observations of debris ¯ow source areas that landslides were initiated high on the slope face. A large amount of in®ltration at the crest would increase the pore±water pressures in the soil and decrease the stability of the slope at that location. If the increase in pore±water pressures were large enough, failure of the slope might then occur. 4. Case study Based on the information gained from the numerical study, an instrumented slope was used to study rainwater in®ltration and its eect on slope stability. The speci®c goals of the case study were to quantify the in®ltration rate for the slope, check/ verify the ®ndings of the numerical study, and quantify the eect in®ltration has on the factor of safety of a slope. The numerical seepage model (SEEP/W) was used to simulate the pore±water pressure changes that were measured in the ®eld. Flux sections were used to determine the in®ltration rate in the modelled slope. The limit equilibrium slope stability analysis (SLOPE/W) was used to quantify how the change in pore-water pressures aected the factor of safety of the slope. Data collected from the instrumented slope were used to verify the results of the numerical analyses. 4.1. Collected ®eld data The soil pro®le of the case study slope is shown in Fig. 8. A detailed description of the slope and its instrumentation are presented by Gasmo et al. [18]. The slope is well turfed and stands at an angle of approximately 26 . The slope consists of residual soils, the weathering product from the sedimentary rock of the Jurong formation. The
Fig. 8. Idealised pro®le of case study slope.
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site investigation revealed that the slope consisted of a weathered bedrock layer overlain by purple silty clay, and orange silty clay [19]. Data collected from the slope during a three week period were used for the case study. Fig. 9 shows the pore±water pressures measured by the tensiometers in the ®rst row at the crest (Row A), from 21 July 1996 to 10 August 1996, in combination with the hourly rainfall. The ®ve lines shown on the graph represent readings from the ®ve tensiometers as indicated in the legend. The bar graph represents the rainfall data and shows that a rainfall occurred on 3 August 1996 and 8 August 1996. The eect of evaporation and in®ltration on pore-water pressures in the slope can be seen in Fig. 9. From 21 July 1996 to 2 August 1996 the matric suction increased (or the pore±water pressure decreased) as moisture was removed from the soil via evaporation or evapotranspiration. This is shown by the downward trend of the lines. The matric suction at 0.5 m reached approximately 80 kPa, while the matrix suction at 1.1 m and below reached only approximately 10 kPa. This dierence in pore±water pressure changes is probably due to dierences in the soil characteristics caused by uneven weathering. The rainfall on 3 August 1996 provided in®ltration to the slope. The in®ltration caused a decrease in the matrix suction as shown by the sudden upward shift of the lines. The change in matric suction at 0.5 m was approximately 70 kPa while the matric suction at the other depths decreased by 10±20 kPa due to the in®ltration. From Fig. 9 it can be seen that all ®ve tensiometers responded to the in®ltration which shows that the zone of in¯uence for in®ltration at the slope is greater than the 3.2 m. The ®eld data shown in Fig. 9 were plotted as pore±water pressure pro®les with respect to depth to allow easier comparison between the ®eld data and model results. Fig. 10(a) shows the pore-water pressure pro®les at speci®c times from 21 July 1996 to 3 August 1996. As the matric suction increases over time, the curves shift to the left. Fig. 10(b) shows the pore±water pressure pro®les during in®ltration on 3 August
Fig. 9. Pore±water pressures at dierent depths of Row A from 21 July 1996 to 10 August 1996.
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Fig. 10. Variation of pore-water pressure pro®les for Row A.(a) From 21 July 1996 to 3 August 1996, as a result of evaporation.(b) From 00:19 to 02:19 on 3 August 1996, as a result of in®ltration.
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1996. As the matric suction decreases over time, the curves shift to the right. It took approximately 2 weeks for the matric suction to increase due to evaporation and less than one day for the matric suctions to decrease due to in®ltration. The pore±water pressure at the 0.5 m depth took approximately 12 h to increase completely where the pore±water pressures below this depth increased within approximately 2 h. The slow response of the 0.5 m tensiometer was likely due to poor contact between the instrument tip and the surrounding soil (caused by shrinkage of the soil during the previous dry period). 4.2. In®ltration analyses 4.2.1. Seepage model The seepage model was used to simulate movement of water through the soil in two dimensions and to predict the change in pore±water pressures throughout the slope pro®le. The inputs required by the seepage model were the geometry and soil pro®le of the slope, the SWC curve and the permeability function of each soil layer in the pro®le and the boundary conditions of the slope. The geometry and pro®le of the case study slope were de®ned in the seepage model as shown in Fig. 8. The SWC curve, permeability function, and shear strength parameters were determined by performing laboratory tests on soil specimens obtained from block samples. A block sample was taken at the ground surface from each of the two silty clay layers of the slope. The SWC curve for each of the silty clay soil layers was determined from volumetric pressure plate tests. The saturated permeability for each soil layer was determined from triaxial permeameter tests. The permeability functions for the soil layers were determined indirectly using the computer program ACUPIM 1.0 [20] with the SWC curves and the ks values as input. The results of the laboratory tests are summarised in Table 1. These results were used to specify the input parameters required by the numerical models. It was not possible to get soil samples for the weathered bedrock layer of the case study slope. It was assumed that this layer would have a lower saturated permeability than the two silty clay soil layers, and was, therefore, assigned a ks value of 1.010ÿ10 m/s in the numerical model. This caused most of the groundwater ¯ow to occur in the upper two silty clay layers. This assumption is acceptable because the bedrock layer
Table 1 Permeability and shear strength parameters for soil of the case study slope Orange silty clay[19] ks c fb
ÿ6
1.010 m/s 20 kPa 26.5 23.0 21.0 kN/m3
Purple silty clay[21] 3.010ÿ9 m/s 90 kPa 35.0 35.0 22.6 kN/m3
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was located suciently far away from the top 3 m of the slope where this study was being concentrated. The boundary conditions for the seepage model (Fig. 8) were de®ned in the same manner as the boundary conditions de®ned in Fig. 4. The side boundaries were de®ned as head boundaries with a hydraulic head equal to the groundwater level, the bottom boundary was de®ned as a no ¯ow boundary, and the top boundary was speci®ed as a ¯ux boundary. The boundary conditions for the side and bottom boundaries were kept constant throughout the analyses. Only the ¯ux speci®ed for the top boundary was changed during the transient analyses in order to simulate the conditions measured in the ®eld. The in®ltration rate in the model was calculated by drawing ¯ux sections at the ground surface of the slope. To perform the transient analysis of in®ltration, the initial conditions recorded on 3 August 1996 needed to be input into the model. This could only be done by performing two separate analyses which adjusted the results in the model to be similar to the porewater pressure distribution on 3 August 1996. The ®rst analysis was required to adjust the initial hydrostatic results from the steady state solution to the transient condition recorded for 21 July 1996, 00:02 [Fig. 10(a)]. This was achieved by specifying a rainfall intensity in the model which was greater than the saturated permeability of the orange silty clay. As a result, the pore±water pressures in the slope increased to values close to the pore±water pressures measured in the slope on 21 July 1996. The second analysis was needed to simulate the increase in matrix suction from 21 July 1996 to 3 August 1996 [Fig. 10(a)] caused by evaporation. The seepage model was not designed to model evaporation, but it could be manipulated to generate pore-water pressure distributions similar to those measured in the ®eld. To increase the matrix suction, a negative ¯ux was applied to the ground surface which acted like evaporation. The value for the negative ¯ux was estimated from the ®eld data collected at his slope by applying a method similar to that described by Sattler [22]. A negative surface ¯ux of 2.010ÿ7 m/s (17.0 mm/day) and 4.410ÿ11 m/s (0.004 mm/day ) was applied to the ground surface of Rows A±E (orange silty clay) and Rows F±G (purple silty clay) respectively. These ¯uxes were applied over a sucient time period to generate pore-water pressures that were similar to those from the ®eld conditions on 3 August 1996. After achieving the ®eld pore-water pressure conditions on 3 August 1996, then the transient analysis of in®ltration was performed. The rainfall that occurred on August 3, 1996, lasted for 7 h. It had an initial intensity of 57.5 mm/h (1.610ÿ5 m/ s) for the ®rst hour and then an average intensity of 4.0 mm/h (1.110ÿ6 m/s) for the remaining 6 h. This rainfall was averaged to a daily rainfall value of 81.5 mm/day (1.010ÿ6 m/s). The ¯ux speci®ed at the surface of the slope was 1.010ÿ6 m/s. 4.2.2. Results The pore±water pressure pro®les from the numerical model are shown in Figs. 11(a) and (b). The model pro®les have the same trend as the pore±water pressure pro®les in the ®eld [Fig. 10(a) and (b)]. The model results show that the matrix suction increased over time due to the applied negative ¯ux, and then decreased over time due to the applied rainfall (in®ltration).
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Fig. 11. Numerical model results for Row A.(a) Matric suction increase. (b) In®ltration (matric suction decrease).
Veri®cation of the model results was performed by plotting the model pore±water pressure distributions together with the ®eld data as shown in Fig. 12. The results from the in®ltration analysis show that the model results follow the general trend of the ®eld data, with the matric suctions being lost near the ground surface ®rst, and then the pore-water pressures gradually increased at deeper depths. The gradual
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shifting of the curves to the right over time shows the downward progression of the in®ltration. Note that in the model the pore-water pressure at the ground surface was equal to zero when the rainfall was applied. This occurred because the speci®ed rainfall intensity (1.010ÿ6 m/s) was equal to the saturated permeability of the soil. As a result the soil became saturated at the ground surface and the pore-water pressures increased to zero. No ®eld instrumentation was installed at exactly the ground surface depth so the ®eld data do not show this information. Comparison between the elapsed times of the ®eld and the model (Fig. 12) shows that the model did not accurately represent the elapsed time in the ®eld. For the in®ltration analysis, the elapsed time in the model was greater than the actual elapsed time in the ®eld. It appears that the in®ltration rate in the model was lower than the in®ltration rate that occurred in the ®eld. Therefore, since the elapsed time for the model in®ltration does not match the elapsed time in the ®eld, the in®ltration rate calculated by the ¯ux sections does not accurately represent the in®ltration rate in the ®eld, and the numerical model was not able to accurately quantify the in®ltration for this case study. Even though the seepage model results were unable to quantify the in®ltration for this case study, the pore±water pressure distributions could still be used in the slope
Fig. 12. Comparison of ®eld and model pore±water pressure pro®les for Row A from 00:19 to 02:19 on 3 August 1996, as a result of in®ltration.
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stability analyses. The pore±water pressure distributions in the model were an acceptable match with the pore±water pressure pro®les from the ®eld. By using the model pore±water pressure distribution at the appropriate times in the ®eld, the change in the factor of safety could still be determined. 4.3. Slope stability analyses 4.3.1. Stability model The inputs required by the slope stability model (SLOPE/W) were the geometry and soil pro®le of the slope, the shear strength parameters and density of soil layers in the slope, the pore±water pressure distribution throughout the slope. The geometry and soil pro®le were input from the idealised soil pro®le shown in Fig. 8. The shear strength parameters for the soil layers (Table 1) were determined from laboratory tests. The pore±water pressure distributions for the slope stability model were de®ned using two methods. The ®rst method utilised the pore±water pressure distribution from the seepage model as a mesh of pore±water pressure heads. The second method utilised the actual ®eld pore-water pressures as a grid of points at their respective depths. An area of possible slip surface locations was de®ned in the model by specifying a grid of possible centres of rotation and a series of slip circle radii. The factor of safety was calculated for each time step in the transient analyses [Fig. 11(a) and (b)] as well as for each time corresponding to the respective ®eld data [Fig. 10(a) and (b)]. The factor of safety determined by the slope stability model was plotted with respect to the elapsed time that occurred in the ®eld. The results from the slope stability in combination with the rainfall data are shown in Fig. 13. The factor of safety was calculated only up to August 3, 1996, for the SEEP/W pore-water pressure heads. The factors of safety for the grid of measured ®eld pore±water pressures were calculated up to August 10, 1996, to include the occurrence of a second rainfall.
Fig. 13. Factor of safety for the case study slope from 21 July 1996 to 10 August 1996.
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4.3.2. Results The results of the numerical analyses illustrate the eect of evaporation and in®ltration on the factor of safety of the slope. From the stability analyses using the SEEP/W pore-water pressure distributions, the factor of safety increased by 34% over 13 days due to evaporation. When the rainfall occurred, the factor of safety decreased by 27% over 2 h. From the stability analyses using the measured porewater pressures, the factor of safety increased by 32% over 13 days due to evaporation. When the rainfall occurred, the factor of safety decreased by 16% over 2 h. The factor of safety then continued to decrease by another 10% over the next 7 h as the pore-water pressures in the ®eld continued to increase due to the downward movement of in®ltration. These results show that the factor of safety increases slowly due to evaporation and then decreases rapidly due to in®ltration. The two methods of de®ning pore-water pressures resulted in dierent values of factors of safety. The factors of safety calculated using the SEEP/W pore±water pressures were less than the factors of safety calculated using the actual pore±water pressures in the ®eld. This was because of the dierence between the model and the ®eld pore±water pressure pro®les. Large positive pore-water pressures were present in the slope stability analysis when the SEEP/W pore±water pressure distribution was used. From Fig. 12 it can be seen that large positive pore±water pressures were present below a depth of 2.0 m. As a result, the overall shear strength of the soil in the slope was reduced and therefore the calculated factor of safety also decreased. The results of the stability analyses using the measured pore-water pressures in the ®eld also show the eect of antecedent moisture conditions on the stability of a slope. Johnson and Sitar [8] stated that a high antecedent moisture condition allowed a rainfall of lower intensity and duration to initiate a failure and from Fig. 13 it can be seen how this is possible. The ®rst rainfall on 3 August 1996 caused the factor of safety to decrease by 26% from 4.81 to 3.57. The second rainfall had a lower intensity and caused the factor of safety to decrease even further by 12% to 3.38. This shows that the antecedent moisture condition may be an important factor to consider when determining the stability of a slope. From the factor of safety in Fig. 13 it can be seen that the case study slope has little risk of failure. A factor of safety greater than 3.0 indicates that the slope is quite stable. However, the factor of safety of the slope will still vary over time due to changes in the pore-water pressure distribution caused by changes in climate. This range of variation in the factor of safety quanti®es the eect of evaporation and in®ltration on slope stability. For the case study slope, 2 weeks of dry weather increased the stability of the slope by approximately 30%. A rainfall intensity of 80 mm/day decreased the stability of a slope by approximately 25%. 4.4. Numerical model limitations The numerical seepage model was unable to quantify the in®ltration rate for the case study slope because the elapsed times in the model did not match the elapsed times in the ®eld. The reason that the elapsed times did not match is because the numerical model was given a simpli®ed representation of a complex residual soil
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slope. Residual soils are highly variable in their layering and characteristics, as can be seen by the shape of the pore±water pressure pro®les in Figs. 10(a) and (b). Overall, the model pro®les [Figs. 11(a) and (b)] are a good approximation of the ®eld data. However, the discrepancies between the ®eld and model pro®les at various depths would suggest that the soil layers idealised in the model may not exactly match those in the ®eld. Similarly, the permeability functions that were speci®ed in the numerical model for each soil layer may not be representative. The permeability function for a soil layer can vary with depth. The permeability function speci®ed in the numerical model for the in®ltration stage did not accurately represent the permeability of the soil in the ®eld. The in®ltration stage of the model required 21 days to achieve the pore±water pressure pro®le that existed in the ®eld after 2 h. It appears that the saturated permeability used in the model was too low and needs to be increased in order to allow the elapsed time in the model to match the elapsed time in the ®eld. The time that elapses in the numerical model is controlled by the saturated permeability that is speci®ed in the model. By increasing the value of ks by one order of magnitude, the time over which pore-water pressure changes occur is decreased by one order of magnitude, and vice versa. Therefore to get the elapsed time in the model to match the elapsed time in the ®eld, the permeability function needs to be increased. It would be reasonable to increase the ks of the soil because of the method that was used to determine the value of ks . The ks value used in the numerical model was determined in the laboratory using the triaxial permeameter. The permeability test was performed on a specimen of soil from a depth of 30 cm. The eective con®ning pressure of the triaxial permeameter (a minimum of 10 kPa) would cancel out the eects of the cracks and ®ssures in the soil by compressing the cracks closer together. Therefore, the ks determined in the laboratory would be lower when compared to what may actually exist in the ®eld. The eective ks for the slope is actually higher because of the cracks and ®ssures that exist in the soil. Another reason for the discrepancy between the ®eld data and the computed results for the in®ltration process is due to the speci®ed boundary conditions. The average value of rainfall that was speci®ed as a ¯ux at the ground surface was not an accurate representation of conditions in the ®eld. The actual rainfall intensity varies over time, and therefore the in®ltration will also vary over time. This will result in the pore-water pressures that will also change at dierent rates over time. 5. Conclusions The numerical study and the case study were used successfully to study in®ltration and its eect on slope stability. The results of the numerical study show that most in®ltration occurs at the crest of the slope. For the steady-state condition, the applied ¯ux and the calculated ¯ux will be approximately the same for rainfall intensities that are 1 or more orders of magnitude less than ks . Within one order of magnitude of ks , the calculated ¯ux is a portion of the applied ¯ux with the largest portion occurring at the crest. For the transient condition with a rainfall intensity
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less than ks , the initial in®ltration rate is much less than ks and then the in®ltration rate gradually increases towards ks . For a rainfall intensity greater than ks , the initial in®ltration rate is greater than ks and then it decreases towards ks . The results from the case study were unable to quantify the in®ltration rates for the instrumented slope because the permeability functions that were input into the model did not accurately represent the ®eld conditions. The numerical model of slope stability was, however, able to quantify the eect of in®ltration on the stability of the slope. Two weeks of evaporation without any rain increased the stability of the slope by approximately 30%. A rainfall with an intensity of 80 mm/day decreased the stability of the slope by approximately 25% in approximately half a day. This shows that it is possible to quantify the eects of evaporation and in®ltration on the stability of a residual soil slope. The results from the numerical models indicate that further research is warranted to improve the accuracy of the numerical analyses. The models themselves worked properly, but the input parameters speci®ed in the models need to be re®ned. The case study provided valuable information in regards to improving the accuracy of unsaturated slope stability analysis. To improve the accuracy of the numerical model representations, better de®nition of the soil parameters such as the soil pro®le, ks , SWC curves, and permeability functions are required. For the in®ltration stage, the saturated permeability should be measured in the ®eld at the ground surface to account for the eect of cracks and ®ssures in the soil. For the evaporation stage, further research is required to develop a ®nite element numerical model that can handle seepage ¯ow and evaporative ¯ow in 2-dimensions. A more detailed representation of the slope in the numerical models would improve the accuracy of the analyses. If conditions in the ®eld are highly variable, it becomes increasingly dicult to accurately model the slope. Accurate representations of the ®eld conditions are necessary to achieve accurate model results. Slopes that have a high degree of variation in their pro®le and soil properties will be dicult to model accurately using the simpli®ed model representation. More case studies are required to build up a knowledge base of quanti®ed ®eld in®ltration rates and changes in factors of safety. Acknowledgements This work is funded by the Nanyang Technological University (RP15/91 and RG22/94) Academic Research Funds. Special thanks to Professor Del Fredlund for initiating the collaboration between the University of Saskatchewan and Nanyang Technological University which allowed the ®rst author to be on this research programme. References [1] Sweeney DJ, Robertson PK. A fundamental approach to slope stability problems in Hong Kong. Hong Kong Engineer October 1979: 35±44.
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[2] Chipp PN, Henkel DJ, Clare DG, Pope RG. Field measurement of suction in colluvium covered slopes in Hong Kong. In: Proceedings of the Seventh Southeast Asian Geotechnical Conference, November 22±26 Hong Kong, 1982. p. 49±62. [3] Pitts J. The form and causes of slope failures in an area of West Singapore Island. Singapore Journal of Tropical Geography 1983;4(2):162±8. [4] Pitts J. An investigation of slope stability on the NTI campus, Singapore. Nanyang Technological Institute, Applied Research Project, March, 1985. [5] Brand EW, Premchitt J, Phillipson HB. Relationship between rainfall and landslides in Hong Kong. In: Proceedings of the 4th International Symposium on Landslides, Toronto, Canada, 1984. Vol. 1, p. 377±384. [6] Brand EW. Landslides in southeast Asia: a state-of-the-art report. In: Proceedings of the 4th International Symposium on Landslides, Toronto, Canada, 1984. Vol. 1, p. 17±59. [7] Tan SB, Lim TL, Tan SL, Yang KS. Landslide problems and their control in Singapore. In: 9th Southeast Asian Geotechnical Conference, Bangkok, Thailand, 1987. p. 1±25, 1±36. [8] Johnson KA, Sitar N. Hydrologic conditions leading to debris-¯ow initiation. Canadian Geotechnical Journal 27:789±801 [9] Alonso E, Gens A, Lloret A, Delahaye C. Eect of rain in®ltration on the stability of slopes. In: Proceedings of the First International Conference on Unsaturated Soils, UNSAT'95, Paris, France, 1995. Vol. 1, p. 241±9. [10] OÈberg AL. Negative pore pressures Ð seasonal variance and importance in slope stability analysis. In: Proceedings of the First International Conference on Unsaturated Soils, UNSAT'95, Paris, France, 1995. Vol. 2, p. 907±13. [11] Fredlund DG, Rahardjo H. Hillside slope stability assessment in unsaturated residual soils. In: IKRAM Seminar on the Geotechnical Aspects of Hillside Development, Kuala Lumpur, Malaysia, 1994. p.1±41. [12] Shimada K, Fujii H, Nishimura S, Morii T. Stability analysis of unsaturated slopes considering changes of matrix suction. In: Proceedings of the First International Conference on Unsaturated Soils, UNSAT'95, Paris, France, 1995. Vol. 2, p. 907±13. [13] GEO-SLOPE. SEEP/W v3.0. GEO-SLOPE International Ltd., Calgary, Alberta, Canada, 1994. [14] GEO-SLOPE. SLOPE/W. GEO-SLOPE International Ltd., Calgary, Alberta, Canada, 1991. [15] Fredlund DG, Rahardjo H. Soil mechanics for unsaturated soils. New York: John Wiley & Sons, 1993. [16] Lim TT, Rahardjo H, Chang MF, Fredlund DG. Eect of rainfall on matrix suction in a residual soil slope. Canadian Geotechnical Journal 33: 618±628 [17] Premchitt J, Lam HF, Shen JM. Rainstorm runo on slopes. 1986. GEO Report No. 12, p. 5±104. [18] Gasmo JM, Hritzuk KJ, Rahardjo H, Leong EC. Instrumentation of an unsaturated residual soil slope. Geotechnical Testing Journal 22 (2): June, 128±137 [19] Gasmo JM. Stability of unsaturated residual soil slopes as aected by rainfall. Master of Engineering Thesis, School of Civil & Structural Engineering, Nanyang Technological University, 1997. [20] Leong EC. ACUPIM 1.0. Automated computation of unsaturated permeability from indirect measurements, Nanyang Technological University, 1993. [21] Hritzuk KH. Eectiveness of drainage systems in maintaining soil suctions. Master of Engineering Thesis, School of Civil & Structural Engineering, Nanyang Technological University, 1997. [22] Sattler PJ. Numerical modelling of vertical ground movements. Master of Science Thesis, University of Saskatchewan, 1989.