COOLING PRIZE PAPER Numerical analysis of the effect of rainfall infiltration on slope stability Esteban Litvin, geotechnical engineer, Atkins Introduction Landslides constitute a major threat to both lives and property worldwide, especially in tropical and subtropical areas such as South America, Africa and the Far East. These regions are characterised by periods of prolonged dry weather with periods of intense rainfall. During dry periods negative negative pore-water pressures develop in the soils, which have a stabilising effect. When dry periods are followed by intense rainfall events, rainfall infiltration leads to an increase in positive pore-water pressures (a decrease in suctions) and a reduction in the shear s trength on the potential failure surface – and slope failure is common. To account account for the influence influence of negative pore-water pressure on soil strength and hence on the factor of safety (FoS), Fredlund et al, 1978 developed a modified form of the Mohr-Coulomb failure criterion for unsaturated soils, which is as follows:
τ = c ´ + σ n − u a ta tan ´ +
u a− u w
tan
b
(Equation 1)
where, σn is the normal stress and φb is an angle defining the increase in shear strength for an increase in matric suction and varies between 0˚ and φ’. Equation 1 is graphically presented in Figure 1. The understanding of the influence of the transient seepage in unsaturated soils on slope stability is still quite poor in comparison to other ) τ ( s s e r t s r a e h S
Extended Mohr-Coulomb failure envelope
elements of geotechnical engineering. Finite element software like SEEP/ W or VADOSE/W provide a means to improve understanding of the destabilisation mechanism of soil slopes under transient seepage analysis. However, using such software does not guarantee that the obtained obtained solution is representative of the real process. To achieve an acceptable degree of accuracy in the solution, t he experience of the engineer plays a significant role. The aim of this project was twofold – to study the the effect of suction loss due to rainfall infiltration on slope stability and to study the ability of SEEP/ W and SLOPE/W to predict pore-water pressures and sl ope failure. The project used a real landslide as a case study. The finite element software SEEP/W modelled both steady state and transient seepage analysis and the limit equilibrium software SLOPE/W carried out the slope stability analysis.
Case Study: Shek Kip Mei slope failure (Hong Kong) Information about the landslide was obtained from the Report on the Shek Kip Mei landslide of the 25 of August 1999 prepared by the Fugro Maunsell Scott Wilson joint venture for the Hong Kong Geotechnical Engineering Office in 2000 (FMSW, 2000). This report indicates that the failure took place after a five-day storm – during which 641mm of rainfall was recorded in the nearest raingauge (No K06) located 1km away from the slope. The Monitoring data
φb
n i o t c u s ) i c - u w t r a u a M (
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Steady state analysis (initial condition)
φb
Rainfall data
(ua - uw)f tan φb c‘
Transient analysis φ‘
PWP (To be used in SLOPE/W) Variation Variatio n of F0S with time
c‘
Figure 3
0
Net normal stress ( σ - ua)
Figure 1: Extended Mohr-Coulomb Mohr-Coulomb failure criterion ) r h / m m ( l l a f n i a r y l r u o H
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Time of instability first noted at the northern portion of the slope
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Location of shotcrete
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Completely decomposed granite
Slip surface (FMSW, 2000)
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Fig Fi gure 2: Hou Hourl rly y ra rain infa fall ll re reco cord rde ed at ra rain ing gau aug ge No K06 38
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Figu Fi gure re 4: Ge Geom omet etry ry of th the Shek Kip Mei sl slop ope e GROUND ENGINEERING MAY 2008
hourly rainfall record between the 21-25 August is presented in Figure 2. Steady state and transient seepage analyses modelled the effect of the rainstorm on the stability of the slope. The steady state analysis modelled the initial groundwater level. The results of this analysis, in terms of pore-water pressures, were compared to the insitu pore-water pressure readings and used as the initial condition in the transient analysis. The transient analysis modelled the effects of the rainstorm. The results of the transient analysis were used to study the effect of the rainstorm on the stability of the slope. The methodology followed during this study is presented in Figure 3.
Geometry Prior to failure, the slope consisted of an upper and lower slope. The upper slope was 35m in height and was at an angle of 35˚. The lower slope was 21m in height, had an average slope of 55˚ and comprised five batters separated by between 1m and 2m wide berms. The lower slope surface had a hard cover consisting of sprayed concrete and between the slopes there was a drain. However, the drain was poorly maintained and the hard cover had deteriorated – together these were proposed to be strong contributing factors to the slope failure (FMSW, 2000). The slope geometry prior to failure can be seen in Figure 4 A simplified model was used to study the effect of the rainfall infiltration on the slope stability as shown in Figure 5. A sensitivity analysis was undertaken to determine the effect of the upper slope on the results. The upper slope was found to have minimal effect on the results and therefore was not included in the model.
Geology and soil parameters The FMSW report indicates that the geology of the site consists of completely decomposed granite (CDG) overlying fresh granite. The slope consists of CDG with fresh granite at the base. Typical shear strength parameters of the CDG are presented in Table 1 (FMSW, 2000). Two additional soil parameters are required for each soil when undertaking seepage analysis: the water retention curve (WRC) and the permeability function (PC). The former describes the ability of the soil to store water under changes of pore-water pressures, while the latter controls the soil’s ability to transport water under both saturated and unsaturated conditions. Typical WRC and PF for the CDG are presented in Figures 6 and 7 (FMSW, 2000).
Groundwater Post-landslide monitoring data recovered from tensiometers and piezometers
Soil
c’(kPa)
ϕ’(˚)
ϕb(˚)
γ (kN/m3)
8
38
15
20
CDG
Table 1: CDG Shear strength parameters
Completely decomposed granite Bedrock
installed at the crest of the slope provided the pre-failure groundwater conditions. This information indicates that the groundwater at the site is located within, or close to, the fresh granite bedrock and that the measured suctions were 85kPa at 5.5m below the crest level.
Boundary conditions Different boundary conditions were used for the steady and the transient analyses. In the steady state analysis, the side boundaries were specified as a constant head boundary. On the right side, a head boundary was specified at 15mPD and on the left side at 26mPD (FMSW, 2000). In the transient analysis, the top boundary was specified as a flux (recharge) boundary (q). The degree of deterioration of t he hard cover was modelled using a flux boundary condition, which was a percentage (100%, 90%, 80% and 75%) of the precipitation recorded by the raingauge (Hsu et al, 1983). The simplified daily rainfall distributions used in the analyses are presented in Figure 8.
Mesh and time step refinement Karthikeyan et al, 2000 and Tan et al, 2004 found that, when analysing groundwater flow in unsaturated soils, oscillatory results are often observed in the finite element solution. To avoid this problem, a mesh and time step refinement was undertaken. The aim of this analysis was to identify the size of the mesh elements and time steps for which a convergent solution was achieved. For this study, a flux boundary 10 times larger than the real rainstorm was used. The minimum FoS found in the transient analysis and the ratio between this and t he steady state FoS are presented in Figure 9. A mesh having elements with an area of 0.5m by 0.5m and time steps of 360s gave the minimum FoS and was selected for the analysis. Finer meshes were considered, but these took several days to compute the results and therefore the 0.5m by 0.5m mesh was considered the most practical (Figure 10).
Steady state results The pore-water pressures generated by the steady state analysis were determined using SEEP/W along two vertical sections located at crest and 3m behind it. These profiles are shown in Figure 11. The profile at the slope crest indicates that at depths between 5m and 6m below the surface, suctions vary between 82kPa and 89kPa, while the profile 3m behind the crest shows the suctions vary between 72kPa and 81kPa. The agreement between the predicted values and those measured ) y t i v i t c u d n o c ( 0 1 g o L
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Figure 6: CDG permeability function Elevation (m) 40
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Figure 5: Shek Kip Mei model Geometry and slip surface definition GROUND ENGINEERING MAY 2008
Figure 7: CDG water retention curve 39
COOLING PRIZE PAPER ) h / m m ( l l a f n i a r y l i a D
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Figure 8: Rainfall scenarios ) S 0.8 o F S S0.75 / S o F n 0.7 i M ( o i t 0.65 a R
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insitu (85kPa) demonstrates the ability of SEEP/W to predict the correct pore-water pressures when the proper mesh and boundary conditions are used. In addition, the FoS of the slope in steady state conditions was calculated in two different ways – the difference being that in one of the analyses the contribution of the negative pore-water pressures was not taken into account. The aim was to prove that suction distribution within the ground played an important role in keeping the Shek Kip Mei stable. In SLOPE/W, if φb is undefined, any negative pore-water pressure is ignored. If a non-zero value of φb is specified, then Equation 1 is used in SLOPE/W and an extra strength component dependent on the suctions is added to the slice base shear strength. When suctions were not included in the slope stability calculations (φb=0˚), the FoS was found to be 0.964, which indicated that the slope was unstable. However, when the suctions were included in the calculations (φb=15˚), the FoS was 1.197, confirming the importance of the negative pore-water pressure on the slope stability.
Transient analysis results The results from this analysis are shown in Figures 12 and 13. The suction profiles presented on Figure 13 were taken along a vertical section at the crest of the slope. To take into account the effect of suction on the slope stability, a φb=15˚ was used in SLOPE/W. The variation of pore-water pressures and the slope’s FoS followed the same pattern. During modelling for rainfall, a drop in suction was predicted within the slope, which in turn led to a decrease in the computed FoS. When
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Figure 9: Mesh and time step refinement result
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Figure 11: SEEP/W pore-water pressure predictions Variation of FoS:
S o F
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h 2 h 4 h 8 h 6 h h y s y s y s y s y s y s S F 1 F 2 F 2 F 3 F 4 R S R S 1 S R B R A R A R A R B A 1 2 4 d a d a d a d a d a d a A 2 4 8 1 6 2 4 3 8 Time
Figure 10: 0.5m by 0.5m and 1m by 1m meshes 40
Figure 12: Variation of FoS with time for the four rainfall scenarios GROUND ENGINEERING MAY 2008
modelling for dry periods, an increase in negative pore-water pressured was observed which led to an increase in the slope’s FoS. The results indicate that the slope failure took place after the fourth day of rainfall. This is in agreement with the FMSW report, which indicates that the slope failure took place between the fourth and the fifth day of the rainstorm. The SEEP/W and SLOPE/W predictions agree with the FMSW report not only on the time, but also on the type of failure. According to the numerical analysis results, it was a deep rotational failure passing through the slope’s toe. The maximum depth at which the soil was mobilised was 7.5m and the slide volume was found to be 2700m3. These values were in accordance with the slope failure diagnosis described in the FMSW report, which indicates that the displaced mass was about 2500m 3, having a maximum depth of approximately 8m. Conclusions
Numerical analysis has been used to enhance the understanding of the effect of suction loss due to rainfall infiltration on slope stability. The results confirm that soil suction can have an important contributory effect on the stability of slopes. If the designer intends to include for the beneficial effect of the negative pore-water pressures in the slope stability analysis, it is imperative that the appropriate drainage system is in place and that it is properly maintained during the design life of the slope. SEEP/W proved to be a valuable tool for predicting pore-water pressures when the soil properties and the ground conditions are known. Nevertheless, such accuracy in the results would not have been achievable without carrying
) 40 m ( n o 35 i t a v e l E 30
out a mesh and time step refinement prior to performing the numerical analysis. In addition, it has been proved that, when combined with SEEP/ W, SLOPE/W is a reliable tool for slope stability analysis in unsaturated conditions. Numerical analysis can be a very reliable means of determining the effect of rainfall infiltration on slope stability. However, the use of finite element software should always be combined with engineering judgment in order to achieve better understanding of both the problem and the solution. References
1. Fugro Maunsell Scott Wilson Joint Venture for the geotechnical Engineering Office, Government of Hong Kong. FMSW (2000) Report on the Shek Kip Mei landslide of the 25 of August 1999 . 2. Geo-Slope International, 1998a. SEEP/W for Finite Element Seepage Analy sis Vol. 4, Users Manual . Calgary, Alberta, Canada. 3. Geo-Slope International, 1998b. SLOPE/W for Slope Stability Analysis Vol. 4, Users Manual . Calgary, Alberta, Canada. 4. Hsu, S.I., Lam, K.C. & Chan, K.S., 1983. A Study of Soil Moisture and Runoff Variation in Hillslopes . Occasional paper No. 45, Department of Geography, Chinese University of Hong Kong, 57p. 5. Karthikeyan, M., Tan, T.S. & Phoon K.K., 2001. Numerical Oscillations in Seepage Analysis of Unsaturated Soils . Canadian Geotechnical Journal, Vol.38, pp.639-651. 6. Tan, T.S., Phoon, K.K & Chong, P.C., 2004. Numerical Study of Finite Element Method Based-Solutions for Propagation of Wetting Fronts in Unsaturated Soil . Journal of Geotechnical and Geoenviromental Engineering, Vol. 130(3), pp.254-263.
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Figure 13: Pore-water pressure variation
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