Effect of Soil Porosity and Slope Gradient on the Stability of Weathered Granitic Hillslope

Jurnal Kejuruteraan 23(2011): 57-68

(Kesan Keliangan Tanah dan Kecerunan Cerun pada Kestabilan Cerun Bukit Granit Terluluhawa)

Muhammad Mukhlisin & Mohd Raihan Taha

ABSTRACT

Modeling rainwater infiltration in slopes is vital to the analysis of rainfall induced slope failure. Amongst the soil hydraulic properties, the hydraulic conductivity K and considered as the most dominant factor affecting the slope stability. Of less prominent was the effect of water retention characteristics. In this study, a numerical model was developed to estimate the extent of rainwater infiltration into an unsaturated slope, the formation of a saturated zone, and the change in slope stability. This model is then used to analyze the effects of the soil porosity parameters (i.e., saturated soil water content qs and effective soil porosity (ESP)) and slope gradient on the occurrence of slope failure. Results showed that when the surface soil of a slope has a relatively large ESP value, it has a greater capacity for holding rainwater, and therefore delays rainwater infiltration into the subsurface layer. Consequently, the increase in pore water pressure in the subsurface layer is also delayed. In this manner, a relatively large surface layer ESP value contributes to delaying slope failure. In addition, the slope gradient of slope is also a significant parameter in slope stability analysis. The time taken for gentle slope to reach failure is longer compared to similar cases with 40o slope gradient.

Keywords: Effective soil porosity; slope gradient; slope stability; granite soil

ABSTRAK

Pemodelan penyusupan air hujan dalam cerun adalah penting untuk analisis hujan yang menyebabkan kegagalan cerun. Antara ciri-ciri hidraulik tanah, konduktiviti hidraulik K dianggap sebagai faktor yang paling dominan yang mempengaruhi kestabilan cerun. Ciri yang kurang penting adalah kesan ciri-ciri pengekalan air. Dalam kajian ini, model berangka telah dibangunkan untuk mengira sejauh manakah penyusupan air hujan ke dalam cerun tidak tepu, pembentukan zon tepu, dan perubahan dalam kestabilan cerun. Model ini kemudiannya digunakan untuk menganalisis kesan parameter keliangan tanah (iaitu kandungan air tanah tepu qs dan keliangan berkesan tanah (ESP)) dan kecerunan apabila berlaku kegagalan cerun. Hasilnya menunjukkan bahawa apabila tanah permukaan cerun mempunyai nilai ESP yang agak besar, ia mempunyai kapasiti yang lebih besar untuk memegang air hujan, dan oleh itu menunda penyusupan air hujan ke dalam lapisan bawah permukaan. Oleh itu, kenaikan tekanan air liang di lapisan bawah permukaan juga ditangguhkan. Dengan cara ini, nilai ESP yang agak besar bagi lapisan permukaan menyumbang kepada melambatkan kegagalan cerun. Di samping itu, kecerunan cerun juga merupakan parameter penting dalam analisis kestabilan cerun. Masa yang diambil untuk cerun yang landai untuk mencapai kegagalan adalah lebih lama berbanding dengan kes-kes yang serupa dengan kecerunan cerun 40o.

Kata kunci: Keliangan berkesan tanah; kecerunan cerun; kestabilan cerun; tanah granit

INTRODUCTION particular the relationship between volumetric water content Modeling rainwater infiltration in slopes is vital to the θ (cm3 cm-3) and soil capillary pressure ψ (cm), and the analysis of slope failure induced by heavy rainfall. relationship between unsaturated hydraulic conductivity K Numerical models have been used previously by Tsaparas (cm s-1), and ψ. These relationships are known as the water et al. (2002), Cho and Lee (2001), Gasmo et al. (2000), retention curve and the hydraulic conductivity function, Wilkinson et al. (2002), Mukhlisin et al. (2006), Gofar respectively. and Lee (2008) to study the effect on slope stability of Among soil hydraulic properties, the hydraulic rainwater infiltration into unsaturated soils. In order analyze conductivity K, a measure of the ability for water rainwater infiltration into soil, it is important to have an movement in soil, has been frequently analyzed for its understanding of the hydraulic properties of the soil, in effects on slope stability. Previous studies (e.g., Reid 58

1997; Cai et al. 1998; Cho and Lee 2001) reported that unsaturated slope, the formation of a saturated zone, the variation in hydraulic conductivity K, can modify pore change in slope stability. This model is then used to analyze water pressure distribution, and therefore the effective the effects of the soil porosity parameters and slope gradient stress of soil and slope stability during rainfall infiltration. on the occurrence of slope failure. Reid (1997) examined the destabilizing effects of small variations in hydraulic conductivity by using groundwater flow modeling, finite-element deformation analysis, NUMERICAL STUDY and limit-equilibrium analysis. The author concluded that earth materials with similar textures can have hydraulic INFILTRATION ANALYSIS conductivity variations of several orders of magnitude and frictional strength variations of about 4-8o. The TWO-DIMENSIONAL UNSATURATED FLOW EQUATION FOR SOIL WATER destabilizing pore pressure effects induced by small hydraulic conductivity variations can be as great as those According to the Darcy-Buckingham equation, induced by these frictional strength variations. Cai et al. horizontal and vertical water flux (qx and qz) in unsaturated (1998) reported the effects of horizontal drains on ground soil are expressed as follows: water levels during rainfall by applying three-dimensional finite element analysis of transient water flow through unsaturated to saturated soils. The authors concluded (1) that the effects of horizontal drains are mainly dependent on the ratio of rainfall intensity to saturated hydraulic conductivity. In another study, Cho and Lee (2001) used (2) numerical methods to examine the mechanisms of slope failure within a soil mass during rainfall infiltration. The where K(ψ) is the hydraulic conductivity as a function of authors concluded that the stress field, which is closely capillary pressure ψ. The equation for continuity of water related to slope stability, is modified by pore water pressure is expressed as distribution, which is controlled by the spatial variation of hydraulic conductivity during rainfall infiltration. In ∂θ  ∂q ∂q  addition, Reid et al. (1998) demonstrated that a small down = − x + z  ∂t  ∂x ∂z  (3) slope decrease in soil hydraulic conductivity can decide the location of a landslide. In contrast, few studies have been published on the effects of water retention characteristics where t is time. Substituting Eq. (1) and Eq. (2) into Eq. (i.e., the relationship between volumetric water content θ (3) yields the two-dimensional, vertical and horizontal flow and soil capillary pressure ψ) on slope stability. equation for soil water (Richard’s Equation): The water retention curve is considered one of the most fundamentally important hydraulic characteristics ∂ψ ∂  ∂ψ  ∂  ∂ψ  ∂ C(ψ ) = K(ψ ) + K(ψ ) + K(ψ ) of soil (Assouline and Tessier 1998). On the water ∂t ∂x  ∂x  ∂z  ∂z  ∂z (4) retention curve, the volumetric water content θ is equal 3 -3 to the saturated water content θs (cm cm ) when the soil capillary pressure ψ is equal to zero. As ψ decreases below where C (ψ ) = dθ / d ψ (cm-1) is the water capacity function zero, θ usually decreases according to an S-shaped curve defined as the slope of the soil water retention curve. with an inflection point. Asψ decreases further, θ decreases Solving Eq. [4] requires the use of models for soil water seemingly asymptotically toward a soil-specific minimum retention and hydraulic conductivity. 3 water content known as the residual water content θr (cm cm-3). As a result, most retention models (e.g., Brooks and Corey 1964; van Genuchten 1980; Kosugi 1994) described MODEL FOR SOIL HYDRAULIC PROPERTIES retention curves in the range of θr ≤ θ ≤ θs. The difference The Lognormal (LN) model proposed by Kosugi (1996, between θs and θr is the effective soil porosity (ESP), and represents the total volume of drainable soil pores per unit 1999), which was developed by assuming a lognormal soil- volume of soil. Hence, ESP is directly related to the water- pore size distribution, is used to solve Eq. [4]. Based on holding capacity of a soil and can be a dominant parameter the LN model, the effective saturation Se(ψ) and the water in the characterization of rainwater infiltration and the capacity C(ψ) are expressed as follows: occurrence of slope failure. Moreover, each of the soil porosity parameters exerts some control over a slope’s soil (5) moisture conditions, and therefore determines the water content of the disturbed material which is one of key factors controlling the mobility of rainfall-induced landslides. In this study, numerical models are developed to estimate the extent of rainwater infiltration into an (6) 59

where θs and θr are the saturated and residual water A number of data sets on the hydraulic properties contents, respectively, σ is a dimensionless parameter, of weathered granite soils were collected from published ψm is the capillary pressure head related to median pore (Ohta et al. 1985; Shinomiya et al. 1998; Hendrayanto et radius (cm), and Q denotes the complementary normal al. 1999) and unpublished studies (Shinomiya and Kosugi, distribution function defined as personal communications). These data sets include the observed values of saturated and unsaturated hydraulic (7) conductivities, saturated water contents, and retention curves. Observations were divided into surface and subsurface

The expression of K with respect to Se and with respect soil layers, and comprised two sample sets of 34 and 18 to ψ are (Kosugi 1999) samples of soil that were taken from 5- to 25-cm depths and from 70- to 170-cm depths, respectively. Figures 1a and b show the water capacity function (i.e., (8) C(ψ) curve) of the surface and subsurface soils, derived by numerically differentiating the observed retention data. The figures show that the surface soil layer has greater (9) average C(ψ) values than those of the subsurface soil layer in the range of |ψ| < 20 cm. The LN model expressed as Eq. [6] was fitted to the average curve of the observed data. where Ks is the saturated hydraulic conductivity, and α and When the model was applied, the θs value was fixed at the β are dimensionless parameters that are used to characterize observed average value shown in Table 1. The optimized soil pore tortuosity. Applying the LN model, soil hydraulic parameter values are summarized in Table 1. It is evident properties are characterized by the seven parameters θs, θr, that the surface soil has a larger ESP (= θs-θr) value than the

ψm, σ, Ks, α, and β. subsurface soil, which indicates the greater water-holding

capacity of the surface soil. Figure 1 shows that Eq. [6] successfully describes the average C(ψ) curves. SOIL HYDRAULIC PARAMETERS Figures 2a and b show the observed K-ψ curves of the surface and subsurface soils. The figures show that Granite soils are known to be very sensitive to the surface soil has greater average K values than the weathering and vulnerable to landslides. In Japan, many subsurface soil near saturation. However, in the dry region disasters have occurred in granite soil areas following heavy (|ψ| > 100 cm), the surface soil has smaller K values than rains, resulting in a total of more than 1000 casualties over the subsurface soil. The LN model expressed as Eq. [9] was the last 62 years. In all of these cases, the major disasters fitted to the average curve of the observed data. When the resulting from these rainstorms were owing to landslides model was applied, the Ks value was fixed at the observed that occurred on weathered granite slopes (Chigira 1999). average value shown in Table 1. The optimized parameter Therefore, this study analyzed rainwater infiltration values (i.e.,α and β) are summarized in Table 1. Equation and slope stability by assuming weathered granite soil [9] successfully reproduces the average K-ψ curves for properties. both the surface and subsurface soils.

TABLE 1. Fitted parameters of the Lognormal (LN) model for weathered granite forest soils† Data Layer θ θ θ -θ ψm σ K α β number s r s r s cm cm/s Surface 34 0.621 0.370 0.251 -14.3 0.92 0.0322 -0.747 2.899 Sub-surface 18 0.456 0.242 0.214 -33.8 0.98 0.0079 -1.258 2.964

† θs, saturated water content; θr , residual water content; ESP, effective soil porosity; ψm and σ, parameters in the retention and conductivity models expressed

as Eq. [5] through [9]; Ks, saturated hydraulic conductivity; α and β, parameters in the conductivity model expressed as Eq. [8] and [9].

SOIL POROSITY by 50% for case 1 by decreasing the θs value while the θr The effects of soil porosity were examined by assuming value was fixed at the same value as in case 2. Compared three different cases of ESP values (Cases 1 through 3) for with case 2, the ESP value was increased by 50% for case the surface and subsurface layers. Among these cases, 3 by increasing the θs value, while the θr value was fixed at observed ESP values were used for case 2. the same value as in case 2 (see Figure 1). Variation among Compared with case 2, the ESP value was decreased cases 1 through 3 was aimed at examining the effects of 60 soil structure development on rainwater infiltration and resulting C(ψ) functions are still within the range in which slope stability, since the θs value of forest soil is expected the observed data exist. Since it was found that there was to increase as the secondary pores are formed by forest no clear relationship between the observed Ks and θs among ecosystem (plant and animal) activities. Figure 1 shows surface or subsurface soils, Ks value was always fixed at the that, if the ESP value is decreased or increased by 50%, the observed average values as summarized in Table 1.

0.025 (a) (b) observed observed 0.020 averaged averaged case 2 case 2 case 3 case 3 )

-1 0.015 case 1 case 1 ) (cm ψ ( 0.010 C

0.005

0.000 1 10 100 1000 1 10 100 1000 |ψ| (cm) |ψ| (cm)

FIGURE 1. Observed, averaged, and fittedC (ψ) curves for (a) the surface and (b) subsurface soils. The fitted curve was

used for case 2. The dotted line represents the C(ψ) curve when the average (θs-θr) value is decreased by

50% (used for case 1). The thick line represents the C(ψ) curve when the average (θs-θr) value is increased by 50% (used for case 3).

0 (a) (b) -1 K observed K observed K averaged K averaged -2 K fitted K fitted -3 -4

(cm/s) -5 K -6 -7 -8 -9 0 50 100 150 200 250 0 50 100 150 200 250

|ψ| (cm) |ψ| (cm)

FIGURE 2. Observed, averaged, and fitted hydraulic conductivity curves for (a) the surface and (b) subsurface soils.

TABLE 2. The value of θs, θr, and (θs-θr) for the surface layer assumed for the seven simulation cases

Layer Case 1 2 3 1’ 3’ 2a 2b

Surface θs 0.495 0.621 0.747 0.621 0.621 0.747 0.495

θr 0.370 0.370 0.370 0.495 0.244 0.495 0.244

θs-θr 0.125 0.251 0.377 0.126 0.377 0.252 0.252 The parameters used in case 2 correspond to the average observed values summarized in Table 1. 61

Figure 3 illustrates the relationship between the θ - ψ The effects of soil porosity were examined by assuming curve and the water capacity function C(ψ). The C(ψ) function seven different cases of θs, θr, and (θs-θr) values for the is derived by differentiating the θ - ψ curve. On the θ - ψ surface layer as summarized in Table 2. The changes in θ- curve, θ changes are in the range of θr ≤ θ ≤ θs. Therefore, the ψ curve resulting from these seven different combinations whole area surrounded by the C(ψ) function and the x-axis are illustrated in Figure 4. In Table 2 and Figure 4, case should be equal to the effective porosity (θs-θr). 2 corresponds to the average observed retention curve expressed by the parameters summarized in Table 1 and 2. θ θ or or CC(ψψ)) In addition to cases 1 through 3, four additional cases (i.e., cases 1’, 3’, 2a, and 2b in Table 2 and Figure 4) were θ - ψ θ −ψ curvecurve analyzed to clarify the effects of the soil porosity parameters θ (i.e., θ , θ , and (θ -θ )) on rainwater infiltration and slope s CC(ψ(ψ)) curve s r s r stability. For case 1’, the (θs-θr) value was decreased by 50% compared with case 2 by increasing the θr value, while

θ s − θ r the θs value was fixed at the same value as case 2 (Figure 4b). Compared with case 2, the (θs-θr) value was increased

by 50% for case 3’ by decreasing the θr value (Figure 4b). θ r Both cases 2a and 2b have the same (θs-θr) value as case 2, although case 2a has greater θ and θ values than case 2, ψ s r and case 2b has smaller θs and θr values than case 2 (Figure FIGURE 3. Curves for C(ψ ) and θ −ψ 4c).

θ θ θ θ (a) (b) (c) 3 θ θ θs 2a θ s ss s s 2 1’ 2 1 2 θ θ θ r θrr rr 2b θr 3’ ψ ψ ψ

FIGURE 4. θ - ψ curve with ESP (θs-θr) variation, (a) variable θs and fixedθ r, (b) fixed θs and variable θr,

GEOMETRY AND BOUNDARY CONDITIONS 100 cm

The standard slope assumed for the numerical simulation had two soil layers (i.e., the surface and subsurface layers) with a length of 20 m and a 40o slope gradient (Figure 5). Total soil depth was 100 cm, and it was assumed that the depths of surface and subsurface soil for Bedrock each layer were the same. This depth is typical of many of the granite areas (ranging between 50 and 300 cm) where landslides occurred in Japan (e.g., Shimizu et al. 2002). Assuming an impermeable bedrock layer under the 2000 cm subsurface soil layer, a no-flux boundary condition was applied to the bottom of the soil layer. A no-flux condition Surface layer was also applied to the top slope (a dividing ridge) and bottom slope (hollow) boundaries. Rainwater was applied to the soil surface, and when the soil surface was saturated, Sub-surface layer 40o discharge from that section was computed. That is, the Point of the pressure observation seepage face boundary condition was applied to the soil surface. Richards Equation (Eq. [4]) was numerically solved by using the finite element method (Istok 1989). The FIGURE 5. Geometry of the slope used for numerical analysis discretizing system are shown in Figure 5. As shown in the (standard case with a soil depth of 100 cm and slope figure, triangular elements were used. gradient of 40o). 62

HYETOGRAPH AND INITIAL CONDITIONS where I is the total number of slices in the sliding circle,

ui (cm) is the positive pore water pressure at the bottom On July 20, 2003, localized torrential rainfall in the mid- of the slice i, Wi (g) is the weight of the slice i, Gi (cm) is southern region of Kyushu in Japan triggered a large-scale o the horizontal length of the slice i, δi ( ) is the slope of the debris flow along the Atsumari-gawa River in Hougawachi, o bottom of the slice i, φi ( ) is the internal friction and ci is Kumamoto Prefecture. Ten houses were destroyed instantly the cohesion (gf cm-2). and nineteen people were killed. The volume of sediment According to Sammori (1994), it was assumed that discharge was estimated at about 100,000 cubic meters, the cohesion ci change depends on the negative pore water making this one of the largest debris flows in recent years. pressure, ui’ (cm), and the degree of saturation, θi/θs,i: This study used the Hougawachi rainstorm as the input data for a hyetograph. The total rainfall, peak rate, and event c = c '−χ u ' tanφ (11) duration were established at 379 mm, 91 mm/h, and 10 h, i i i i respectively. To establish the initial conditions for the numerical  θ  χ = MIN 1, 1.25 i  simulations, a 50%-reduced hyetograph of the Hougawachi  θ  (12) rainstorm (the total rainfall, peak rate, and event duration  s,i  of this hyetograph were 189.5 mm, 45.5 mm/h, and 10 -2 h, respectively) was initially applied. Next, a drainage where ci’ (gf cm ) is the cohesion under saturated duration of 48 h was simulated for the standard case of the conditions. simulation, and the resulting capillary pressure distribution The values of ci, Wi, ui were computed for each time within the whole slope was used for the initial condition for step from the pore water pressures and soil moisture the main simulation. contents estimated by the infiltration analysis. For the It was assumed that the whole slope had a constant calculation of the Fs value, I was fixed at 20, and 4,131 sliding circles were tested to determine the minimal Fs capillary pressure value, ψini, just before the 50%-reduced value. Furthermore, c ’ = 20 gf cm-2 and φ = 35o was hyetograph was applied. The value of ψini was fixed at -100 i c assumed, values that were used by Suzuki (1991) as typical cm. The ψini values of -50 and -200 cm were also tested, values for a weathered granite soil. and it was found that the ψini value did not cause significant differences in the capillary pressure distribution within the whole slope at the end of the 48-h drainage. RESULTS AND DISCUSSION

SCENARIOS FOR NUMERICAL SIMULATION EFFECTS OF SURFACE LAYER ESP ON SLOPE STABILITY

Two scenarios were used for numerical simulation, Figure 6a-c shows the computed time series of the discharge, summarized in Table 2. The first scenario (scenario 1) used pore water pressure at 250 cm from the end of the slope the standard conditions discussed previously. That is, a (i.e., the pressure observation point in Figure 5), and the drainage period of 48 h, a soil thickness of 100 cm, and safety factor, Fs. The figure shows that the occurrence of o a slope gradient of 40 were assumed. The soil porosity discharge and peak pore water pressures were affected parameters were changed only for the surface layer, as in by the timing of the peak of the rainstorm event. During the seven cases summarized in Table 2 and Figure 4. For periods of intense rainfall, rainwater infiltrated into the the subsurface layer, the soil porosity value was fixed at the slope, increased the pore water pressure, and decreased the same value as case 2. effective stress of the soil, which resulted in slope failure o In scenario 2, the slope gradient was changed from 40 (i.e., Fs < 1). These results are consistent with those of o to 35 , while the other parameters remained the same as previous studies (e.g., Anderson and Sitar, 1995; Wang in scenario 1. The seven cases of soil porosity parameter and Sassa, 2003), in that rainfall-induced landslides were sets were examined by changing the retention curves of the caused by increased pore water pressure during periods of surface layer. intense rainfall. The results are presented in Figures 6a, b, and c. Because the ESP value of case 1 was smaller than that of SLOPE STABILITY ANALYSIS case 2, case 1 had a greater peak discharge and greater pore water pressure (Figures 6a and b). As a result, the Following Sammori (1994), the Bishop method safety factor of case 1 decreased faster than that of case (Bishop 1954) was used in conducting the slope stability 2 (Figure 6c). In case 3, which had a greater ESP than case analysis. In this method, the safety factor (Fs) is computed 2, the smallest peak discharge and the smallest pore water based on the moment equilibrium among slices in a sliding pressure were computed (Figures 6a and b). The safety circle: factor for case 3 was always greater than those for cases 1 1 I c G + (W − u G )tanφ  = i i i i i i and 2 (Figure 6c). In Figure 6c, slope failure was estimated Fs I ∑   i=1  cosδ i + sinδ i tanφi / Fs  (10) only for case 1, which had the smallest ESP value. ∑Wi sinδ i i=1 63 Time (h) ESP value varies. However, Figure 7b shows that case 1 has 0 1 2 3 4 5 6 7 8 drier soil and case 3 has wetter soil than case 2 when the 20000 0 estimated slope failure occurs. This is because the smaller (a) 50 17500 ESP value in case 1 and the larger ESP value in case 3 result

/h) 15000 100 2 in either a decrease or an increase in the water holding 12500 150 capacity of the surface layer. 10000 200 The moisture conditions of the sliding circle are an 7500 250 1 2 3 important factor in determining the mobility of the affected 5000 300 Discharge (cm Discharge debris, because when the affected debris contains a great 2500 350 Rainfall intensity (mm/h) intensity Rainfall deal of water, it can easily become a debris flow. Figure 0 400 6d shows the changes in water content (the ratio of water 70 O) 2 (b) weight to solid weight) of the sliding circles shown in 60 Figure 7 for cases 1 through 3. Compared with case 2, 50 the initial water content is smaller for case 1 and greater 40 for case 3. During rainfall, the water content increase is 30 1 2 3 greatest in case 3 and smallest in case 1. Moreover, case 20 3 has the latest time of slope-failure occurrence, and the 10 water content increases nearly 70% when Fs < 1. On the 0 other hand, case 1 is the first to experience slope-failure, Pore water pressure (cm H (cm pressure Pore water -10 resulting in the smallest water content (< 35 %) when Fs < 1.8 (c) 1. The results shown in Figures 7b and 6d imply that, when ) 1.6 the surface soil layer has a larger ESP value, the water- Fs 1.4 holding capacity is larger and the soil layer contains a great deal of water when slope failure occurs. 1.2 1 2 3 1.0 -30 cmH2O case 1 -20 In 3 Factor of Safety ( Safety of Factor 0.8 -10 0.6 0 In 3 case 2 90 10 (d) 80 20 In 3 case 3 70 3 30 40 60 50 2 50 60 In 2 case 1 40 1 In 3 30 In 2 Water content (%) Water content 20 In 3 case 2 In 2 10 (a) 0 1 2 3 4 5 6 7 8 In 3 case 3 Time (h) In 1 FIGURE 6. (a) Applied rainfall and computed discharge, computed (b) pore water pressure at the observation point, (c) In 1 safety factor and (d) water content for cases 1, 2, and 0.325 3. The numbers in each figure represent the numbers of In 1 0.350 cases. The observation point of pore water pressure is (b) 0.375 shown in Figure 5. Black circles in Figure 6 (c) and (d) 0.400 indicate the times when Fs <1. 0.425 0.450 In 1 0.475 0.500 EFFECTS OF SURFACE LAYER ESP ON WATER CONTENT OF In 1 0.525 0.550 CORRUPTED SLOPE In 1 Figures 7a and b show distributions of pore water pressure FIGURE 7. Distributions of (a) pore water pressure and (b) soil water and soil water content in the whole slope at the estimated content in the whole slope at the estimated time of slope time of slope failure. The sliding circle, groundwater failure. The sliding circle (line ln 1), groundwater table table, and equi-hydraulic potential lines are shown in both (line ln 2), and equi-hydraulic potential lines (lines ln 3) figures. Figure 7a shows that the depths of the water table are shown in both (a) and (b).The interval of the equi- in the sliding circle are similar in each case, although the hydraulic potential lines is 100 cm

1e+5 Time (h) solid water 0 1 2 3 4 5 6 7 8 8e+4 1.8 0 (a) 1.6 3 100 6e+4 3' 1.4 1 200 4e+4 1' Weight (g) 1.2 300 2 2e+4 1.0 400 0.8 500 Factor of Safety (FoS)Factor Safety of

0 (mm/h) intensity Rainfall 1 2 3 0.6 600 90 Case (b) 80 FIGURE 8. Weight of solid particles and water in sliding circle at 70 3 estimated time of slope failure 60 50 Figure 8 shows the weight of solid particles and water 1' 40 3' 1 in the sliding circle at the estimated time of slope failure. 2 30 Case 1 has the smallest θs value, thus it has the largest dry (%) Water content 20 density of the surface layer. As a result, the solid weight is largest in case 1. In contrast, case 3 has the smallest solid 10 0 1 2 3 4 5 6 7 8 weight because it has the largest θs value. In Figure 8, the water weight follows a contrary trend; it is the largest in Time (h) case 3 and the smallest in case 1. As shown in Figure 6d, the greater ESP value along with the higher initial water FIGURE 9. (a) Applied rainfall and computed safety factor, Fs, and content result in a larger water amount in the sliding circle (b) computed water content for cases 1, 2, 3, 1’, and 3’. for case 3. Black circles in Figure 9 (a) and (b) indicate the times From the comparisons between cases 1 through 3, it when Fs <1. can be concluded that a greater surface soil layer ESP value delays the occurrence of slope failure and can increase hand, case 3 has the greatest Fs value, resulting in the slope stability against a shallow landslide. However, a lightest overall slope weight and the largest Fs value during greater ESP value tends to increase the water content of the the initial stage of rainfall. disturbed matter, which may result in the occurrence of However, Figure 9 clearly indicates that the times of debris flow, and contribute to the debris being transported both the rapid decrease in the Fs value and slope failure further. Therefore, under greater ESP conditions, greater (i.e., when Fs < 1) are controlled by the ESP value. When damage can be expected once slope failure occurs. cases 1 and 1’, and 3 and 3’ are compared, it is clear that

the differences in θs and θr values have no effect on the time of slope failure. CASES 1’ AND 3’ Figure 9b shows the increase in water content in the sliding segment of the slope for cases 1, 2, 3, 1’, and 3’. In case 1’, the ESP value of the surface layer was decreased Each case displays a peculiar increase pattern. Although by 50% as compared to the observed average value (i.e., the initial water content value was smaller in case 3’ than case 2) by increasing the θr value. In case 3’, the ESP value in case 2, the two cases have a similar water content at the of the surface layer was increased by 50% by decreasing estimated time of slope failure (i.e., Fs < 1). Case 3’ has a the θr value (Figure 4b, Table 2). greater ESP value, resulting in a greater increase in water Figure 9a shows the Fs values for variations in soil content from the initial condition to the time when Fs < 1. porosity for cases 1, 1’, 2, 3, and 3’. Cases 1’ and 3’ have On the other hand, a smaller ESP value in case 1’ results in a similar Fs values to case 2 in the initial stage of rainfall, smaller increase in the water content. When Fs < 1, case 1’ and under relatively dry conditions θs is the dominant has a similar water content to cases 2 and 3’. factor in determining the Fs value. During the initial stage The similar water moisture content in the sliding circle of rainfall, case 1 has the smallest Fs value, and has the of slope failure for cases 1’, 2, and 3’ are presented in Figure smallest θs value, resulting in the greatest dry density of 10. Figure 10 shows clearly that cases 1’, 2, and 3’ have soil and an increased overall slope weight. This explains similar weights of solids and water in sliding segments at why the Fs value is the smallest for case 1. On the other the estimated time of slope failure. 65

1e+5 CASE 2a AND 2b solid water 8e+4 The ESP values of cases 2a and 2b are the same as that of the observed average value (i.e., case 2), although the absolute 6e+4 values of θs and θr in cases 2a and 2b differ. In case 2a, 4e+4 both the θ and θ values of the surface layer were increased Weight (g) s r from that of the observed average value. In case 2b, both 2e+4 the θs and θr values of the surface layer were decreased from that of the observed average value (Figure 4c, Table 0 1' 2 3' 2). Moreover, the θr value of case 2a was equal to the θs Case value of Case 2b. Figure 11a shows the Fs values with respect to the soil FIGURE 10. Weight of solid particles and water in a sliding circle on the slope at estimated time of slope failure. porosity variation for cases 1, 2, 3, 2a, and 2b. During the initial stage of rainfall, the Fs value of case 2b was smaller than that of case 2 and similar to that of case 1. In the initial

Time (h) stage of rainfall, the Fs value of case 2a was greater than that of case 2 and similar to that of case 3. That is, under 0 1 2 3 4 5 6 7 8 1.8 0 relatively dry conditions, the θs value is one of the dominant (a) factors in determining the Fs value. 1.6 100 However, cases 2, 2a, and 2b share similar times of 2 2a 1.4 200 rapid decrease in Fs value and timing of slope failure (i.e., 2b when Fs < 1). Therefore, the ESP value is the dominant 1.2 300 factor in determining the Fs value under heavy rainfall 1 3 1.0 400 conditions. The different θs and θr values have no effect on the timing of slope failure. 0.8 500 Factor of Safety (FoS)Factor Safety of The increase in water content in the sliding circle of Rainfall intensity (mm/h) intensity Rainfall 0.6 600 the slope for cases 1, 2, 3, 2a, and 2b is presented in Figure 11b. During the initial stage of rainfall, the water content 90 (b) value was affected by a combination of θ and θ values. 80 s r Case 2a had the same θs value and a greater θr value than 70 case 3, resulting in a greater water content value during the 60 2a initial stage of rainfall. Furthermore, case 2b had the same 3 50 θs value and a smaller θr value than case 1, and the water 40 2 content value for case 2b was smaller during the initial 30 1 stage of rainfall. Although the initial water content value Water content (%) Water content 20 2b differed between cases 1 and 2b, and between cases 2a and 3, the water content was similar between these cases at the 10 estimated time of slope failure (i.e., Fs < 1), because of 0 1 2 3 4 5 6 7 8 the determining effect of the θs value. Figure 12 shows that Time (h) these sets of cases (1 and 2b, 2a and 3) had similar weights of solid particles and water in the sliding segment of slope FIGURE 11. (a) Applied rainfall and computed safety factor, Fs, and (b) computed water content for cases 1, 2b, 2, 2a, and failure.

3. Black circles in Figure 11 (a) and (b) indicate the These results demonstrate that θs is the dominant factor times when Fs <1. in determining the soil moisture conditions on a slope and the water content of the corrupted matter at the estimated 1e+5 time of slope failure. solid water 8e+4

INFLUENCE OF THE SLOPE GRADIENT (SCENARIO 2) 6e+4

4e+4 Weight (g) Next, the effects of soil porosity variations in the surface layer with fixed values of ESP in the subsurface 2e+4 layer when the slope gradient was 35o were analyzed. The 0 antecedent rainfall drainage, length and depth of slope soil, 1 2b 2 2a 3 and the major rainfall event were the same as those used in Case scenario 1. FIGURE 12. Weight of solid particles and water in sliding circle of The results of this analysis show that scenario 3, slope at estimated time of slope failure. with a 35o slope gradient, and scenario 1, with a 40o slope 66

Time (h) failure was at about 3.076 h for case 1, 3.648 h for case 0 1 2 3 4 5 6 7 8 2, and 4.206 h for case 3, all of which are longer times of 20000 0 slope failure than those of the 40o slope gradient used in (a) 17500 50 scenario 1.

/h) 15000 100 2 Furthermore, the general trend of a rapid decrease in 12500 150 the Fs value for cases 1, 2, 3, 1’, 3’, 2a, and 2b as shown in 10000 200 Figure 13c-d was also similar to those shown in scenarios 7500 1 2 3 250 1. While the estimated times of slope failure were similar 5000 300

Discharge (cm Discharge in cases 1 and 1’, cases 3 and 3’, and cases 2, 2a, and 2b, 2500 350 ESP Rainfall intensity (mm/h) intensity Rainfall owing to the effect of the value, the differences in the 0 400 absolute values of θs and θr had no effect on the timing of 70 O) slope failure. These results showed that the change in slope 2 60 gradient does not cause any changes in the effect of soil (b) 50 porosity on slope stability. 40 1 2 3 30 90 (a) (b) 20 80 10 70 3 0 60 2a

Pore water pressure (cm H (cm pressure Pore water -10 50 3 2.0 1' 3' (c) 40 1 2 1.8 3 2 3' 30 1 1.6 1 (%) Water content 20 2b 1.4 1' 2 10 1.2 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 1.0 Time (h) Time (h)

Factor of Safety (FoS)Factor Safety of 0.8 0.6 90 90 2.0 (a) (b)(a) (b) (d) 80 80 3 1.8 70 70 3 2 2a 1.6 60 60 2a 2b 2a 1.4 50 50 3 3 1 3 1' 3' 1' 3' 1.2 40 1 40 2 1 2 2 2 1.0 30 30 1 1 Water content (%) Water content Water content (%) Water content 2b Factor of Safety (FoS)Factor Safety of 0.8 20 20 2b 0.6 10 10 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 Time (h) Time (h) Time (h) Time (h) FIGURE 13. (a) Applied rainfall and computed discharge, computed FIGURE 14. Computed water content for cases 1, 2, 3, 1’, 3’, 2a, (b) pore water pressure at the observation point, and and 2b. The black circles indicate the times when Fs (c), (d) safety factor, Fs, for cases 1, 2, 3, 1’, 3’, 2a, <1. and 2b. The observation point of pore water pressure is shown 1.2e+5 in Figure 5 The black circles in Figure 13 (c) and (d) solid indicate the times when Fs <1. water 1.0e+5

8.0e+4 gradient, shared a similar overall trend. Changing the slope 6.0e+4 gradient from 40o to 35o had the effect of increasing the peak discharge, the pore water pressure, and the safety Weight (g) 4.0e+4 factor value during the initial stage of the rainfall event. 2.0e+4 The increase in the safety factor value during the initial stage of the rainfall indicates that a 35o slope was more 0.0 stable than a 40o slope. Although the slope was more stable 1 2b 1' 2 3' 2a 3 in the initial stage rainfall, the more rapid increase of pore Case water pressure (Figure 13b) caused a more rapid decrease FIGURE 15. Weight of solid particles and water in sliding circle of (Figure 13c) in the Fs value. The timing of estimated slope slope at the estimated time of slope failure. 67

The deeper water table in scenario 2 resulted in a Gasmo, J. M., Rahardjo, H. and Leong, E. C. 2000. heavier weight of solid particles and water (Figure 15) in Infiltration effects on stability of a residual soil slope. all cases as compared to scenario 1 (Figures 8, 10 and 12). Computers and Geotechnics 26:145–165. The heavier weight of solid particles and water resulted in Gofar N and Lee M. L. 2008. Extreme Rainfall a more rapid increase of pore water pressure, causing slope Characteristics for Surface Slope Stability in the failure, even though the slope gradient was decreased from Malaysian Peninsular. GEORISK: Assessment & 40o to 35o. Management Risk for Engineering Systems & Geohazards 2 (2): 65-78 Hendrayanto, Kosugi, K., Uchida, T., Matsuda, S. and CONCLUSIONS Mizuyama, T. 1999. Spatial variability of soil hydraulic properties in a forested hillslope. Journal of A numerical simulation model was used to investigate Forest Research 4:107–114. two scenarios to study the effects of effective soil porosity Istok, J. 1989. Groundwater modeling by the finite element (ESP) and slope gradient on rain-water infiltration induced method. Water resources monograph 13. American slope stability. In summary, when the soil of a slope Geophysical Union (AGU). has a relatively large ESP value, it has a greater capacity Kosugi, K. 1994. Three-parameter lognormal distribution for holding rainwater, and therefore delays rainwater model for soil water retention. Water Resour. Res. infiltration into the subsurface layer. Consequently, the 32:2697–2703. increase in pore water pressure in the subsurface layer is Kosugi, K. 1996. Lognormal distribution model for also delayed. In this manner, a relatively large ESP value of unsaturated soil hydraulic properties. Water Resour. slope contributes to delaying slope failure. Under weaker Res. 30:891–901. storm conditions, slope failure tends not to occur when Kosugi, K. 1999. General model for unsaturated hydraulic the soil has a relatively large ESP value. However, the conductivity for soils with Lognormal pore-size greater ESP value tends to increase the water content of the distribution. Soil Sci. Soc. Am. J. 63:270–277. disturbed matter. In addition, the slope gradient of slope is Mukhlisin, M., Kosugi, K., Satofuka, Y., and Mizuyama, T. also a significant parameter in slope stability analysis. The 2006. Effects of Soil Porosity on Slope Stability and timings of estimated slope failure with a 35o slope gradient Debris Flow Runout at a Weathered Granitic Hillslope. for all cases were longer than those for the corresponding Vadoze Zone Journal 5:283-295 cases with a 40o slope gradient. The increased solid weight Ohta, T., Tsukamoto, Y. and Hiruma, M. 1985. The behavior in sliding suggests that the sliding circle became deeper as of rainwater on a forested hillslope, I, The properties the slope gradient became small. These results showed that of vertical infiltration and the influence of bedrock on the change in slope gradient does not cause any changes in it (in Japanese, with English summary.) J. Jpn. For. the effect of soil porosity on slope stability Soc. 67:311–321. Reid, M. E. 1997. Slope instability caused by small variations in hydraulic conductivity. Journal of REFERENCES Geotechnical and Geoenviromental Engineering 123:717–725. Anderson, S. A. and Sitar, N. 1995. Analysis of rainfall- Reid, M. E., Nielsen, H. P., and Dreiss, S. J. 1988. induced debris flows. Journal of Geotechnical Eng. Hydrologic factors triggering a shallow hillslope ASCE. 121:544–552. failure. Bull. Assoc. Engrg. Geol. 25:349–361. Assouline, S. and Tessier, D. 1998. A conceptual of the soil Sammori, T. 1994. Sensitivity analyses of factors affecting water retention curve. Water Resour. Res. 34:223–231. landslide occurrences. (In Japanese with translator Bishop, A. W. 1954. The use of the slip circle in the stability in English.) Dr. Dissertation. of Kyoto University, analysis of slopes. Geotechnique 5:7–17 Kyoto, Japan. Brooks, R. H. and Corey, A. T. 1964. Hydraulic properties Shimizu, Y., Tokashiki, N. and Okada, F. 2002. The of porous media. Hydrol. Pap. 3. Civil Eng. Dept. September 2000 torrential rain disaster in the Tokai Colo. State Univ. Fort Collins. region: Investigation of a mountain disaster caused Cai, F., Ugai, K., Wakai, A. and Li, Q. 1998. Effect of by heavy rain in three prefectures; Aichi, Gifu and horizontal drains on slope stability under rainfall by Nagano. Journal of Natural Disaster Science 24:51– three-dimensional finite element analysis. Computers 59. and Geotechnics 23:255–275. Shinomiya, Y., Kobiyama, M. and Kubota, J. 1998. Cho, S. E. and Lee, S. R. 2001. Instability of unsaturated soil Influences of Soil Pore Connection Properties and Soil slopes due to infiltration. Computers and Geotechnics Pore Distribution Properties on the Vertical Variation 28:185–208. of Unsaturated Hydraulic Properties of Forest Slopes. Chigira, M. 2001. Micro-sheeting of granite and its J. Jpn. For. Soc. 80:105–111. relationship with landsliding specifically after the Suzuki, M. 1991. Functional relationship on the critical heavy rainstorm in June 1999, Hiroshima prefecture, rainfall triggering slope failures. (In Japanese with Japan. Engineering Geology 59:219–231. translation in English). Journal of Japan Society 68

Erosion Control Engineering, JSECE 43:3 – 8. Muhammad Mukhlisin* Tsaparas, I., Rahardjo, H., Toll. D. G. and Leong, E. C. Department of Civil Engineering 2002. Controlling parameters for rainfall-induced Polytechnic Negeri Semarang landslides. Computers and Geotechnics 29:1–27. Jl. Prof. H. Sudarto, SH Tembalang Semarang 50275 Wang, G. and Sassa, K. 2003. Pore-pressure generation Indonesia and movement of rainfall-induced landslide: effect of grain size and fine-particle content. Engineering Mohd Raihan Taha Geology 69:109–125. Department of Civil and Structural Engineering Wilkinson, P. L., Anderson, M. G. and Lloyd, D. M. 2002. Faculty of Engineering & Built Environment An Integrated hydrological model for rain-induced Universiti Kebangsaan Malaysia landslide prediction. Earth Surface Processes and 43600 UKM Bangi, Sleangor, Malaysia Landforms 27:1285–1297. Universiti Kebangsaan Malaysia van Genuchten, M. Th. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated *Corresponding author ([email protected]) soils. Soil Sci. Soc. Am. J. 44:615–628.