EFFECT OF MATRIC SUCTION CHANGES ON UNSATURATED SOIL PARAMETER IN SLOPE STABILITY ANALYSIS DUE TO RAINFALL. Ahmad RIFA I 1

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1 EFFECT OF MATRIC SUCTION CHANGES ON UNSATURATED SOIL PARAMETER IN SLOPE STABILITY ANALYSIS DUE TO RAINFALL Ahmad RIFA I 1 1 Department of Civil and Environmental Engineering, Faculty of Engineering, Universitas Gadjah Mada, Indonesia ahmad.rifai@tsipil.ugm.ac.id ABSTRACT Matric suction has important role in shear strength changes of unsaturated soils. Loss of matric suction caused by increase of soil water content reduces shear strength, leading structural damages affected by soil movement. Slope stability analysis which ignoring matric suction leads to inaccuracy of safety factor calculation and slip surface determination. An understanding of unsaturated soil mechanics is very important to be studied. This research is focused in slope stability analysis involving matric suction parameter. Slope stability analysis integrated with seepage simulation in porous media were conducted and discussed. Soil water retention curve needed in unsaturated seepage analysis was selected based on grain size distribution obtained from knowledge database system. Rainfall models in seepage analysis are used to vary pore water distribution. There are several variations of rainfall model including one steady state analysis to represent the initial condition and transient analyses to represent climate changes. Results indicate that filter paper method can be used to provide soil water retention curve. High range in matric suction produces nonlinearity relationship between shear strength and matric suction. In low value of matric suction, a linear equation can approximate it. The results show that rainfall reduces negative pore water pressure in soil, causes decrease on shear strength, leading to instability. Saturated permeability of soil becomes an important parameter to predict critical rainfall intensity that significantly affecting slope stability. Rainfall with intensity near or surpass the saturated permeability of soil gives more significant effect in reducing safety factor. Keywords: matric suction, shear strength, infiltration, slope stability, rainfall model 1. INTRODUCTION Slope failure and landslide is frequently happened in Indonesia, especially at rainy season and is related to the decrease of soil strength caused by increasing of soil water content due to rainfall. Climate changes are prior phenomenon to cause instability at slope. Ground water table and soil moisture content of soil fluctuate due to precipitation and evaporation. Rainfall may occur seasonally, and the rain infiltration will change the initially unsaturated soil become more saturated or fully saturated. This condition may lead the reduction of shear strength of soil due to loss of suction. The soil resistance of an unsaturated soil is larger than in a saturated state. However, during wetting from a high level of precipitation, loss of shear strength of the unsaturated soils can be exhibited; so slope instability may occur. External loads do not only influence the mechanical behavior of soil, but changes of pore-water pressure and poreair pressure, namely is matric suction changes are also as governing factor. This is due to the unsaturated nature of the soil. Consequently, it can be easily admitted that any matric suction change will result in soil movement. Modeling the behavior of unsaturated soil requires the understanding of the solid-liquid-air phase s interaction. The unsaturated soil can be grouped into three (3) categories; first category is continuous water and discontinuous air phases. The air phase exists in an occluded form. This category is found in narrow transition zone in natural soil; above the saturated soil with lower degree of saturation and negative pore water pressure. The second category corresponds to continuous water and air phases. This phase has an intermediate degree of saturation and a negative pore water pressure. The pore air pressure may be zero if the continuous air phase is vented to the atmosphere. The last category corresponds to discontinuous water and continuous air phases. In this category, the soil has a very low degree of saturation. This situation is commonly found in the top layer at the ground surface in natural soil, but may be strongly influenced precipitation and evaporation. Due to precipitation, the moisture content become higher and will decrease the negative pore water pressure, while due to evaporation, the effect is at the vice versa. Conventional methods of slope stability analysis often ignore the negative pore water pressure above the ground water level. It assumes that soil is fully saturated below the ground water table and completely dry above the ground water table. This calculation results inaccurate safety factor and slip surface location. Recently, many literatures SEMINAR NASIONAL-1 BMPTTSSI - KoNTekS 5 G-15

2 discuss about the behavior of unsaturated soil, thus, simplification with ignoring the negative pore water pressure is no longer needed. This research is focused in slope stability analysis involving matric suction parameter. Slope stability analysis integrated with seepage simulation in porous media were conducted and discussed. Soil water retention curve needed in unsaturated seepage analysis was selected based on grain size distribution obtained from knowledge database system. Rainfall models in seepage analysis are used to vary pore water distribution. There are several variations of rainfall model including one steady state analysis to represent the initial condition and transient analyses to represent climate changes. 2. UNSATURATED SOIL PARAMETER Hydro-mechanical behavior of unsaturated soils has two main properties, hydric and mechanical properties. Hydric behavior means the constitutive response due to suction loading. The hydric behavior of unsaturated soils can be investigated as the soil samples are subjected to an isotropic hydric loading due to suction (Rifa i, 2002) and produce a curve of water content or degree of saturation and suction relationship, commonly known as Soil-Water Retention Curve (SWRC). Filter paper can be used to measure either matric suction when placed in contact with soil specimen or total suction when placed above the specimen with no contact. Filter paper will absorb moisture from soil and related to a suction value when it reaches equilibrium. Filter paper method can be used to measure almost the entire range of suctions (Fredlund and Rahardjo, 1993). Mechanical behavior means the constitutive response due to effective stress loading. The mechanical behavior of unsaturated soils can be investigated from isotropic and deviatoric loading paths (Rifa i 2002; Rifa i & Suhendro 2005). Measuring the unsaturated soil properties is difficult, time-consuming and costly. Therefore, many researchers for last few years to estimate the unsaturated soil properties from saturated soil properties. Fredlund et al. (1997) has proposed several procedures to determine unsaturated soil properties using laboratory test results and knowledge-based system. The prediction of SWRC from grain-size distribution for sands is found more accurate than silt. Clays, tills and loams were more difficult to predict although the accuracy is still in reasonable result (Fredlund, 1997). Fredlund et al. (1978) have proposed an equation to describe the strength of unsaturated soil, known as extended Mohr Coulomb failure criterion. The equation is presented in Equation (1). c ' u tan ' u u tan b (1) a a w where : shear strength kpa, c : cohesion kpa, σ : normal stress kpa, u a : pore air pressure kpa, u w : pore water pressure kpa, φ : angle of internal friction associated with the net normal stress variable degree, φ b : Angle of internal friction associated with matric suction that describes the rate of increase in shear strength relative to matric suction degree. Rifa i (2002) has proposed a non-linear relationship between cohesion and matric suction, expressed in equation (2). This proposed equation assumed that cohesion of soil below air entry value of matric suction is equal to saturated cohesion. While for matric suction higher than air entry value, cohesion of soil increases nonlinearly along with the increase of matric suction. c c ' r c s s e p a (2) where r c is a dimensionless evolution parameter of cohesion and determined using Equation (3), c is cohesion of soil at saturated state, s is matric suction, s e is the air-entry value, and p a is atmosphere pressure. 3 3 sin ' rc rk (3) 6cos ' where r k is a dimensionless evolution parameter and φ is internal friction angle of soil at saturated state. Evolution of cohesion due to matric suction from experimental data and equation (2) is plotted shown in Figure 1. G-16 SEMINAR NASIONAL-1 BMPTTSSI - KoNTekS 5

3 Figure 1. Evolution of cohesion due to increase of matric suction (Rifa i, 2002) 3. GREEN-AMPT INFILTRATION MODEL According to Chow et al. (1988), Green and Ampt (1911) have proposed an equation to model the infiltration by developing a more approximation physical theory that has an exact analytical solution. It assumes that as rain continues to fall and water infiltrates, the wetting front has penetrated to a depth L in time t. Soil below the wetting front has initial moisture content, θ i, and will increase to n (the porosity) as the wetting front passes. Figure 2 shows the parameter used in Green-Ampt infiltration model. Figure 2. Green-Ampt infiltration model Green-Ampt infiltration model was developed to model infiltration on horizontal ground surface. So that, the application on sloping ground surface needs modification. Chen and Young (2006) have proposed the modified Green-Ampt infiltration for sloping ground surface, presented in equation (4) and (5). é f ù f ( t) k sat êcos ú ê F t ú ë û (4) f é F t ln ê1 cos ê f cos ù F t k yt ú ú ë û (5) Parameter f(t) is potential infiltration mm/h, F(t) is cumulative infiltration mm/h, k sat is saturated hydraulic conductivity mm/h, β is inclination of the slope degree, ψ f is suction head mm, θ is volumetric water content deficit and t is time hour. SEMINAR NASIONAL-1 BMPTTSSI - KoNTekS 5 G-17

4 4. RAINFALL INDUCED IN SLOPE STABILITY Rainfall has a significant effect in the stability of slope through the change of soil water content. According to Abramson et al (1996), slope failures are often caused by processes that increase shear stresses or decrease shear strengths of the soil mass. Increasing in water content by rainfall will both reduce the soil suction and raise the unit weight of soil. Soil suction reduction will decrease shear strengths, and unit weight rising of soil will increase shear stresses. Rainfall characteristic that trigger slope failure is controlled by permeability of soil covering slope and generally defined into two types, heavy and antecedent rainfall. The intensity of heavy rainfall reaches 70 mm/hour or more than 100 mm/day. Heavy rainfall will effectively trigger landslide at slope which easily absorbs water, as in sandy clay and sand layer (Karnawati, 1997). Antecedent rainfall has intensity less than 20 mm/day. Table 1 shows classification of rainfall intensity (Sosrodarsono & Takeda, 1993). 5. MATERIAL AND METHOD Study area and material properties Table 1. Classification of rainfall intensity Rainfall Condition Rainfall Intensity (mm) 1 hour 24 hours Very low precipitation <1 <5 Low precipitation Normal precipitation Heavy precipitation Very heavy precipitation >20 >100 A slope located at km 13 Wonosari Highway, Sambipitu village, Special Region of Yogyakarta. The inclination of the slope is quite gentle, which is about 9 at the middle to the top side of the slope, while at the down side is about 20. The soil of the slope lies down at impermeable bedrock which has similar inclination with the ground surface. A sand-gravel mixture of embankment is constructed at the top side of the slope and supported by retaining wall. Physical properties of soil have been investigated and presented in Table 2. Input data for slope stability analysis involving matric suction parameter for strength parameter is shown in Table 3. The unit and total flux is used to model the rate of infiltration. In this research, modified Green-Ampt Equation is used to calculate the potential infiltration rate at the slope. The value of parameter used in modified Green-Ampt is provided in Table 4. Table 2. Physical properties of soil Parameters Silt Specific Gravity, G s Liquid limit, L L 87.69% Plasticity index, P I 44.95% Shrinkage limit, S L 16.92% Natural water content, w 58.20% Bulk density, γ b (g/cm 3 ) 1.6 Dry density, γ d (g/cm 3 ) 1.01 Void ratio, e 1.52 USCS classification MH Table 3. Input data of strength parameter Parameter Silt Concrete Wall Embankment γ (kn/m 3 ) c (kpa) φ ( ) φ b ( ) G-18 SEMINAR NASIONAL-1 BMPTTSSI - KoNTekS 5

5 Table 4. Value of parameter used in modified Green-Ampt Equation Modified Green-Ampt Parameter Value Saturated hydraulic conductivity, k sat mm/h Inclination of the slope, β 9 Suction head, ψ f mm Saturated volumetric water content, θ s Initial volumetric water content, θ i Volumetric water content deficit, θ Rainfall design Some considerations in determining the rainfall model are the hydraulic conductivity of the soil and the transition of the climate. Hydraulic conductivity has very important effect in seepage analysis. The soil has very low permeability, so the typical rainfall that effectively triggering the landslide based on literatures is normal rainfall with long duration. The normal intensity of rainfall according Sosrodarsono and Takeda (1993) is around 20-50mm/hour. Also, the transition of climate from the wet season to dry season, or on the contrary, will take different effect on slope stability. An existing rainfall data on November 2002 are also to be analyzed. The rainfall data of study area is predicted from rainfall data from 4 rain gauge stations around the study area using square distance method. The hourly rainfall data for a period from year 1993 to 2008 are used. Design of rainfall model used in this research are presented in Table 3. Numerical analysis Numerical simulation in seepage is conducted using SEEP/W and variation of rainfall models. There are seven models used, the first model is a steady state analysis where no rainfall. This simulation uses total head as a boundary condition to determine the location of initial ground water table. Another rainfall models are a transient analysis with rainfall as an input boundary condition at slope surface. Pore water pressure generated in SEEP/W is further used in slope stability analysis using SLOPE/W. Table 5. Design of rainfall model Rainfall model Typical of rainfall I No rainfall (initial condition) II Short duration of very heavy rainfall (4 hours) III Rainfall with normal intensity of 10mm/day for 10 days, continued by very heavy rainfall of 120.4mm/day for 2 days IV Very heavy rainfall of 120.4mm/day for 2days, continued by no rainfall for 3 days and normal rainfall of 40mm/day for 3 days V Normal rainfall of 30mm/day for 4 days followed by no rainfall for 3 days and 8 days of 10mm/day normal rainfall VI Normal rainfall of 10mm/days for 20 days VII Actual rainfall data recorded on November UNSATURATED HYDRO-MECHANICAL PROPERTIES Soil Water Retention Curve (SWRC) of soil and compared with database (Soilvision, 2004) are shown in Figure 2 (a). The results indicate that soils collected from database that have similar grain size distribution, show that they have similar Soil Water Retention Curve (SWRC). For silt soils, the SWRC from database are close with the estimation using Fredlund and Wilson equation, but experimental data obtained from filter paper method is relative still far enough. At the same value of degree of saturation, SWRC from filter paper method provides higher value of matric suction than SWRC of database, which has similar grain size distribution. The inaccuracy might be due to the effect of plasticity index values. Fredlund and Wilson estimation method only focuses on grain size distribution, without any review on consistency limit. Zapata et al. (2000) have researched that the SWRC of fine material is influenced by multiplication of finer fraction and plasticity index, the greater value of plasticity index, the higher value of soil suction. SEMINAR NASIONAL-1 BMPTTSSI - KoNTekS 5 G-19

6 DegreofSaturation(S), % Geoteknik Experimental (filter paper) Silt 1 (SoilVision Database) Silt 2 (SoilVision Database) Silt 3 (SoilVision Database) Fredlund and Wilson estimation Matric Suction (ua-uw), kpa Figure 2. (a) SWRC and (b) Unsaturated shear strength for silt soils Increase of shear strength due to suction is nonlinear for a large range of suction. In a short range, in this case from 0 to about 300kPa, the relationship between shear strength with matric suction can be considered as a linear function as shown in Figure 2 (b). The linearity of shear strength evolution in respect to both of net normal stress and matric suction is controlled by effective internal friction angle, φ and internal friction angle in respect with suction, φ b, respectively. In common practice, the effect of matric suction usually is under 80 kpa. Based on seepage simulation result, the maximum negative pore water pressure is no more than 50kPa. So, the justified value of φ b is 23.7 and used as input in stability analysis. 7. SLOPE STABILITY ANALYSIS Average rainfall duration that occurred at the study area is 4 hours. The rainfall intensity for four hour needs to be compared with the potential infiltration rate. If rainfall intensity exceeds the potential infiltration rate, then the excess rainfall will become surface runoff, but if the rainfall intensity is less than the potential infiltration, all rainwater will be infiltrated into the ground. Numerical simulation of slope stability at initial condition (rainfall model I) is ploted in Figure 3. The pore water pressure at the slip surface is below -20kPa, it indicates that the slip surface lies above the ground water table. Safety factor at initial condition is about Section A-A and B-B is used as point to observe the change of moisture in soil due to rainfall. Also, change of pore water pressure at base of slice is prior to influence the stability of the slope. From all simulation results, it is known that rainwater infiltration have a great contribution in changing the moisture of soil, meaning that it increases pore water pressure. The increase in pore water pressure can be observed clearly on section A-A, while at section B-B, the change is not significant. This is because the position of section A-A is directly below the surface where infiltration occurs, while at section B-B has no infiltration at the surface. At section A-A, simulation result on rainfall model VI has the greatest increment of pore water pressure at the end of simulation. From kPa of the minimum pore water pressure at initial condition, it increases become kP at rainfall model IV, followed by rainfall model V which is about kPa, rainfall model III is about kPa, rainfall model VI is about kPa and the smallest is in rainfall model II which is about kPa. These results show the same sequence that occurs in increasing of pore water pressure at base of slices and decreasing of safety factor. This indicates that there is a strong relationship between pore water pressure distribution and safety factor. Rainfall pattern in Model IV and V has interspersed by no rainfall for three days. Different result of pore water distribution at base of slices and safety factor change occurs between these two models after 3 days with no rainfall simulation. Both model IV and V, after no rainfall for three days, the minimum pore water pressure at section A-A and B-B decreases. However, different conditions occur in the average pore water pressure at the base of slice in silt soil. In Model IV, it experiences an increase in average pore water pressure at base of slices from kPa to kPa and a decrease in safety factor from to Whereas, in Model V, a decrease of pore water pressure occurs at the base of slices from kPa to kPa and an increase in safety factor from to 1.11safety factor of initial condition (no rainfall occurs) is about The greatest reduction in safety factor occurred in Model IV which is about The next sequence is held by Model V (SF=1.101), Model III (SF=1.115), Model VI (SF=1.134) and Model II (1.167). Evolution of safety factor for each model is shown in Figure 4. G-20 SEMINAR NASIONAL-1 BMPTTSSI - KoNTekS 5

7 Elevation, m SafetyFactor SafetyFactor Elevation, m Geoteknik Elavation (m) Initial ground water table Section A-A' Silt (MH) Silt (MH) Bedrock External Load (167 kpa) Sand-Gravel Mix A B Section B-B' A' B' Unstable zone Distance (m) Figure 3. Numerical simulation at initial condition (Rainfall model I). Infiltrated water due to rainfall reduces the negative pore water pressure and decrease safety factor. Very high intensity of rainfall for short duration (4 hours) in rainfall model II and low intensity of rainfall for long duration (rainfall model VI) do not provide significant effect in reducing safety factor. Saturated permeability of soil becomes an important parameter to predict critical rainfall intensity that significantly affecting slope stability. Rainfall with intensity near or surpass the saturated permeability of soil gives more significant effect in safety factor reducing than those with low intensity even though occur in long duration. The petrol station was opened at an early of November After approximately one month, the slope failed due to rainfall. An existing rainfall data for 30 days in November 2002 was used in analysis. Seven periods of time to be analyzed are 0, 5, 10, 15, 20, 25 and 30 days. Pore water distribution change is shown in Figure 5. Long duration of rainfall (30 days) using existing data gives an increase of ground water table about 130cm, from 4.3m become 3m below ground surface at section A-A, while at section B-B ground water table increase about 80cm. Evolution of safety factor evaluated every five days is shown in Figure 6. Rainfall is significantly decreasing the safety factor of the slope. Safety factor of the slope decrease from initial condition (SF = 1.186) until 10 days the safety factor become 1.1. No rainfall occurrence gives an increase of safety factor. The minimum safety factor for this analysis is about 1.07 after five days rainfall from day-15 up to day Hour- Model I Model II Days Model III Model IV Model V Model VI Figure 4. Safety factor of each rainfall model (a) initial condition (Model I) and hourly rainfall (Model II), (b) daily rainfall (from Model III to Model VI) Section A-A Section B-B Pore Water Pressure, kpa Pore Water Pressure, kpa (a) (b) Figure 5. Pore water pressure distribution for rainfall model VII (a) at section A-A and (b) at section B-B SEMINAR NASIONAL-1 BMPTTSSI - KoNTekS 5 G-21

8 Rainfal(m/h) SafetyFactor Geoteknik Day Hour- Figure 6. Evolution of safety factor due to existing rainfall data record on November 2002 (rainfall model VII). 8. CONCLUSION The rainfall data of study area is predicted from rainfall data from 4 rain gauge stations around the study area using square distance method. There are seven variations of rainfall model including one steady state analysis to represent the initial condition and six transient analyses to represent climate change. The results show that rainfall reduces matric suction in soil, causes decrease on shear strength, leading to instability. Filter paper method can be used to provide soil water retention curve (SWRC). For silt soils, the SWRC from database are close with the estimation using Fredlund and Wilson equation. Based on experimental data for high range in matric suction produces nonlinearity relationship between shear strength and matric suction, confirmed with non linear equation proposed by Rifa i (2002). In low value of matric suction, a linear equation can approximate it. The value of effective internal friction angle is relatively constant. Numerical simulation on seepage and stability analysis has also been presented. Infiltrated water due to rainfall reduces the negative pore water pressure and decrease safety factor. Very high intensity of rainfall for short duration and low intensity of rainfall for long duration do not provide significant effect in reducing safety factor. Saturated permeability of soil becomes an important parameter to predict critical rainfall intensity that significantly affecting slope stability. Rainfall with intensity near or surpass the saturated permeability of soil gives more significant effect in reducing safety factor than those with low intensity even though occur in long duration. 9. ACKNOWLEDGMENT The author expresses their thanks to DIKTI, National Education Department, Indonesia and Kyushu University, Japan for financial supporting by Competitive Grant of International Collaboration Research and Publication No. 425/SP2H/DP2M/VI/2010. REFERENCES Abramson, L.W., Lee S., Thomas, Sharma Sunil, Boyce M., Glenn, (1996) Slope Stability and Stabilization Methods, John and Wiley&Sonc, Inc, New York. Chen, L., & Young, M. H. (2006). Green-Ampt Infiltration Model for Sloping Surfaces. Water Resources Research Vol. 42. Chow, V. T., Maidment, M. R., & Mays, L. W. (1988). Applied Hydrology. New York: Mc Graw-Hill. Fredlund, D. G., & Raharjo, H. (1993). Soil Mechanics for Unsaturated Soills. New York: John Wiley & Sons. Fredlund, D. G., dan Xing A. (1994). Equation for the Soil-Water Characteristic Curve, Canadian Geotechnical Journal, 31: Fredlund, D.G., Morgenstern, N.R., and Widger, R.A. (1978). The shear strength of unsaturated soils. Proceedings of the 50th Canadian Geotechnical Conference. Ottawa. Fredlund, M. D., Fredlund, D. G., dan Wilson, G. W. (1997), Prediction of the Soil-Water Characteristic Curve from Grain-Size Distribution and Volume-Mass Properties, 3 rd Brazilian Symposium on Unsaturated Soils, Rio de Janeiro, Brazil, April 22-25, Vol. 1, pp Karnawati, D. (1997). Rain-Induced Landslides Problems in West Java Media Teknik, No. 3 XVIII November. Krahn, J. (2004). Seepage Modeling with SEEP/W. Calgary: GEO-SLOPE International. Lu, N., & Likos, W. J. (2004). Unsaturated Soil Mechanics, John Wiley & Sons, New Jersey. Rifa i, A. (2002). Mechanical Testing and Modelling of an Unsaturated Silt, with Engineering Applications. Lausanne: Doctoral Thesis, EPFL, 158 pp. G-22 SEMINAR NASIONAL-1 BMPTTSSI - KoNTekS 5

9 Rifa i, A., & Suhendro, B. (2005). Perilaku Tegangan Regangan Tanah Jenuh Sebagian Menggunakan Uji Triaksial Modifikasi, Forum Teknik Sipil, Vol. XV/1-Januari 2005, ISSN , pp , Yogyakarta. Soilvision manual (2004). A knowledge-based soils database. Saskatoon: SOILVISION System Ltd. Sosrodarsono, S., & Takeda, K. (1993) Analisis Hidrologi, PT. Pradnya Pramita, Jakarta. Zapata, C. E., Houston, W. N., Houston, S. L., & Walsh, K. D. (2000). Soil-Water Characteristic Curve Variability. Advances in Unsaturated Geotechnics. SEMINAR NASIONAL-1 BMPTTSSI - KoNTekS 5 G-23

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