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Published online 8 March 2006
Published in Vadose Zone J 5:283-295 (2006)
DOI: 10.2136/vzj2005.0044
© 2006 Soil Science Society of America
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SPECIAL SECTION: FROM FIELD- TO LANDSCAPE-SCALE VADOSE ZONE PROCESSES

Effects of Soil Porosity on Slope Stability and Debris Flow Runout at a Weathered Granitic Hillslope

Muhammad Mukhlisina, Ken'ichirou Kosugib,*, Yoshifumi Satofukab and Takahisa Mizuyamab

a Dep. of Civil Engineering, Polytechnic Negeri Semarang, Indonesia
b Dep. of Forest Science, Graduate School of Agriculture, Kyoto Univ., Japan
* Corresponding author (kos{at}kais.kyoto-u.ac.jp)

Received 19 March 2005.



   ABSTRACT
TOP
 EXECUTIVE SUMMARY
 ABSTRACT
INTRODUCTION
 NUMERICAL STUDY
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Accurate models of rainfall infiltration are needed for analysis and prediction of slope failure induced by heavy rainfall. In this study, a numerical model was developed to simulate two-dimensional rainwater infiltration into an unsaturated hillslope, the formation of a saturated zone, and the resultant changes in slope stability. This model was subsequently used to analyze the effects of soil porosity parameters (i.e., saturated soil water content {theta}s and effective soil porosity [ESP]) on the occurrence of slope failure, the moisture conditions of the displaced material, and the movement of debris flow on weathered granitic hillslopes. We conducted the simulations by imposing various conditions of rainfall, initial wetness of the slope, soil thickness, and slope gradient. Results showed that when the surface soil of a slope has a relatively large ESP value, it has a greater capacity for holding water and therefore delays deeper water infiltration into the subsurface. Consequently, the increase in pore water pressure in the subsurface at a greater depth is also delayed. In this manner, the greater ESP value contributes to delaying slope failure. Under small storm conditions, slope failure tends not to occur when the surface soil has a relatively large ESP value. However, a greater ESP tends to increase the water content of the displaced matter, which results in faster and longer travel distances, and more deposition of debris flow, thus increasing the risk of damage in downstream regions.

Abbreviations: ESP, effective soil porosity • LN, lognormal [model]


   INTRODUCTION
TOP
 EXECUTIVE SUMMARY
 ABSTRACT
 INTRODUCTION
NUMERICAL STUDY
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
THE PREDICTION of slope failure and debris flow runoff is required to identify areas exposed to debris flow hazard and to establish evacuation protocols. Many studies (e.g., Anderson and Sitar, 1995; Wang and Sassa, 2003; Okura et al., 2002) have confirmed that pore pressure propagation and perched water table formation by rainwater infiltration can have a major effect on slope instability and landslide fluidization. For example, Okura et al. (2002) conducted laboratory flume experiments and found that the collapsing slope undergoes three distinct, but nearly simultaneous stages: (i) volumetric compaction of failing material as it shears, (ii) an increase in pore water pressure in the saturated zone, and (iii) rapid shearing along the slip surface. In another study, Wang and Sassa (2003) used a small flume (180 cm long, 24 cm wide, and 15 cm high) to conduct a series of tests by triggering rainfall-induced landslides. These test results support the conclusion that grain size and amounts of fine-particle content of slope material can both have a significant impact on the mobility of rainfall-induced landslides. Remarkable flume experiments conducted by Iverson et al. (1997, 2000) revealed mechanical effects of soil porosity on the mobility of a landslide. They found that initial soil porosity around slip surface affects pore water pressure changes during slope failure and controls the debris-flow mobilization. Field observations and modeling studies showed that rainstorm activity and antecedent rainfall also can have a large effect on slope stability (e.g., Rahardjo et al., 2001; Pasuto and Silvano, 1998; Terlien, 1998).

Modeling rainwater infiltration in hillslopes is needed for the analysis of slope failure induced by heavy rainfall. Numerical models have been used previously by Anderson and Howes (1985), Tsaparas et al. (2002), Cho and Lee (2001), Gasmo et al. (2000), Shakya and Chander (1998), and Wilkinson et al. (2002) to study the effect on slope stability of rainwater infiltration into unsaturated soils. To simulate infiltration, it is essential to know the relationship between volumetric water content, {theta} (cm3 cm–3), and soil matric pressure, {psi} (cm), and the relationship between unsaturated hydraulic conductivity, K (cm s–1), and {psi}. These relationships are known as the soil water retention curve and the hydraulic conductivity function, respectively.

Among soil hydraulic properties, the saturated hydraulic conductivity Ks, a measure of the rate of water movement in saturated soil, has been frequently analyzed for its effects on slope stability. Previous studies (e.g., Reid, 1997; Cai et al., 1998; Cho and Lee, 2001) reported that variations in Ks can modify the pore water pressure distribution, and therefore the shear stress and resistance of soil and slope stability during rainfall infiltration. Reid (1997) examined the destabilizing effects of small variations in Ks by using groundwater flow modeling, finite-element deformation analysis, and limit-equilibrium analysis. He concluded that destabilizing pressure changes induced by small Ks variations can be as great as those induced by the frictional strength variations typical of similarly textured materials. Cai et al. (1998) reported the effects of horizontal drains on groundwater levels during rainfall by applying a three-dimensional finite-element analysis of transient-water flow. They concluded that the effects of horizontal drains are mainly dependent on the ratio of rainfall intensity to Ks. A numerical study by Cho and Lee (2001) revealed that the stress field, which is closely related to slope stability, is modified by the pore water pressure distribution, which in turn is controlled by spatial variations in the hydraulic conductivity during rainfall infiltration. In addition, Reid et al. (1988) demonstrated that a small decrease in the downslope soil saturated hydraulic conductivity can influence the location of a landslide.

The water retention curve (i.e., the relationship between {theta} and {psi}) is the other fundamentally important hydraulic characteristic of soil (Assouline and Tessier, 1998). Most retention models (e.g., Brooks and Corey, 1964; van Genuchten, 1980; Kosugi, 1994) describe retention data in the range of {theta}r ≤ {theta} ≤ {theta}s, where {theta}r is the residual water content (cm3 cm–3) and {theta}s is the saturated water content (cm3 cm–3). The difference between {theta}s and {theta}r is the effective soil porosity (ESP), and represents the total volume of drainable soil pores per unit volume of soil. Hence, ESP is directly related to the water-holding capacity of a soil and can be an essential parameter in the characterization of rainwater infiltration and the occurrence of slope failure. Previous studies have pointed out that a large water-holding capacity of a soil delays the propagation of pore water pressure affecting the timing of slope failure (e.g., Haneberg, 1991; Reid, 1994; Iverson, 2000). At the same time, each of the soil porosity parameters can exert some control over a slope's soil moisture conditions and determine the water content of the displaced material, which is one of the key factors controlling the mobility of rainfall-induced landslides. To evaluate the effects of soil porosity on debris flow runout, these two hydrological aspects (i.e., the pressure propagation time and the moisture condition of displaced material) should be combined and analyzed simultaneously.

In this study, we developed a coupled hillslope hydrology and slope stability model, which numerically simulates the extent of infiltration into an unsaturated slope, the formation of a saturated zone, and the change in slope stability. The model is then used to analyze the effects of the soil porosity parameters on the occurrence of slope failure and the moisture conditions of the displaced material, as well as the movement of debris flow. We assumed typical properties for weathered granitic hillslopes because granite is known to be very sensitive to weathering and vulnerable to landslides. The effects of rainfall conditions, initial wetness of the slope, soil thickness, and slope gradient are also analyzed.


   NUMERICAL STUDY
TOP
 EXECUTIVE SUMMARY
 ABSTRACT
 INTRODUCTION
 NUMERICAL STUDY
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Infiltration Analysis
Two-Dimensional Unsaturated Flow Equation for Soil Water
According to the Darcy–Buckingham equation, the horizontal and vertical water flux (cm s–1) (qx and qz) in unsaturated soil are expressed as follows:

Formula 1[1]

Formula 2[2]
where K({psi}) is the hydraulic conductivity as a function of matric pressure {psi}. The equation of continuity for water is expressed as

Formula 3[3]
where t (s) is time. Substituting Eq. [1] and [2] into Eq. [3] yields the two-dimensional flow equation for soil water (the Richards equation):

Formula 4[4]
where C({psi}) = d{theta}/d{psi} (cm–1) is the water capacity function defined as the slope of the soil water retention curve.

Model for Soil Hydraulic Properties
The Lognormal (LN) model proposed by Kosugi (1996, 1999), which was developed by assuming a lognormal soil pore size distribution, is used in conjunction with Eq. [4]. Based on the LN model, the effective saturation Se({psi}) and the water capacity C({psi}) are expressed as follows:

Formula 5[5]

Formula 6[6]
where {sigma} is a dimensionless parameter corresponding to the standard deviation of log-transformed soil pore radius, {psi}m is the matric pressure head related to median pore radius (cm), and Q denotes the complementary normal distribution function defined as

Formula 7[7]

The expressions of K in terms of Se and {psi} are (Kosugi, 1999)

Formula 8[8]

Formula 9[9]
where Ks is the saturated hydraulic conductivity, and {alpha} and ß are dimensionless parameters that are used to characterize soil pore tortuosity. Applying the LN model, soil hydraulic properties are characterized by the seven parameters: {theta}s, {theta}r, {psi}m, {sigma}, Ks, {alpha}, and ß.

The LN model is used in this study because it has physically based parameters compared with empirical models (e.g., Brooks and Corey, 1964; van Genuchten, 1980), and it has been shown that the model produces adequate descriptions of measured hydraulic properties of various field soils (Kosugi, 1996, 1997; Tuli et al., 2001). Moreover, Kosugi (1999) showed that the general conductivity function expressed by Eq. [9] has more flexibility than the models proposed by Brooks and Corey (1964) and van Genuchten (1980), which use fixed {alpha} and ß values.

Soil Hydraulic Parameters
Granite soils are known to be very sensitive to weathering and vulnerable to landslides. In Japan, many disasters have occurred in granite soil areas following heavy rains, resulting in a total of more than 1000 casualties in the last 62 yr (Chigira, 2001). In all of these cases, the major disasters resulting from rainstorms were landslides that occurred on weathered granite slopes. Therefore, this study analyzed rainwater infiltration and slope stability by assuming typical weathered granite soil properties.

A number of data sets on the hydraulic properties of weathered granite soils have been collected from published (Ohta et al., 1985; Shinomiya et al., 1998; Hendrayanto et al., 1999) and unpublished studies (Shinomiya and Kosugi, personal communications, 2004). These data include measured values of Ks, K, {theta}s, and retention curves for undisturbed granitic forest soils collected from five sites situated in central to eastern Japan. The retention curves were measured using the vacuum method, the sand column method, and the pressure method. Values of K were measured during drying using the steady-state head control method and the instantaneous profile method. When we categorized the measured data according to their sampling depths, we found significant differences in hydraulic properties between soils taken from the 5- to 25-cm depths and from the 70- to 170-cm depths.

Figures 1a and 1b show the water capacity function [i.e., C({psi}) curve] of the surface (5–25 cm deep) and subsurface soils (70–170 cm deep), derived by numerically differentiating the observed retention data. The figures show that the surface soil layer had greater average C({psi}) values than those of the subsurface soil layer in the range of |{psi}| < 20 cm because of the presence of more macropores. The LN model expressed as Eq. [6] was fitted to the average curve of the observed data by using a nonlinear least-squares optimization procedure. When the model was applied, the {theta}s value was fixed at the observed average value shown in Table 1. The optimized parameter values are summarized in Table 1. It is evident that the surface soil has a larger ESP (= {theta}s – {theta}r) value than the subsurface soil, which indicates a greater water-holding capacity of the surface soil. Figure 1 shows that Eq. [6] successfully described the average C({psi}) curves.


Figure 1
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  		Fig. 1. Measured, averaged, and fitted C({psi}) curves for (a) surface and (b) subsurface soils. The fitted curve was used for Case 2. The blue line represents the C({psi}) curve when the average effective soil porosity (ESP) value is decreased by 50% (used for Case 1). The green line represents the C({psi}) curve when the average ESP value is increased by 50% (used for Case 3). Number of samples were 34 and 18 for surface and subsurface soils, respectively.

 

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  		Table 1. Fitted parameters of the Lognormal (LN) model for weathered granite forest soils.{dagger}

 
Figures 2a and 2b show the measured K({psi}) curves of the surface and subsurface soils. The figures show that the surface soil has greater average K values than the subsurface soil near saturation. However, in the dry region (|{psi}| > 100 cm), the surface soil has smaller K values than the subsurface soil. The LN model expressed as Eq. [9] was fitted to the average curve of the observed data by using the nonlinear least squares optimization procedure. When the model was applied, the Ks value was fixed at the observed average value shown in Table 1. The optimized parameter values (i.e., {alpha} and ß) are summarized in Table 1. Equation [9] successfully reproduces the average K({psi}) curves for both the surface and subsurface soils.


Figure 2
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  		Fig. 2. Measured, averaged, and fitted hydraulic conductivity curves for (a) the surface and (b) subsurface soils. Number of samples are 17 and 18 for surface and subsurface soils, respectively.

 
Soil Porosity
The effects of soil porosity were examined by assuming three different cases of ESP values (Cases 1 through 3) for the surface and subsurface layers. Among these cases, the ESP value for Case 2 was fixed at the fitted value shown in Table 1.

Compared with Case 2, the ESP value was decreased by 50% for Case 1 by decreasing the {theta}s value while the {theta}r value was fixed at the same value as in Case 2. Compared with Case 2, the ESP value was increased by 50% for Case 3 by increasing the {theta}s value while the {theta}r value was fixed at the same value as in Case 2 (see Fig. 1). These differences among Cases 1 through 3 were aimed at examining the effects of soil structure development on rainwater infiltration and slope stability since the {theta}s value of forest soil is expected to increase as the secondary pores are formed by biologic activities. Figure 1 shows that, if the ESP value is decreased or increased by 50%, the resulting C({psi}) functions are still within the range in which the measured data exist. Since we found no clear relationship between the measured Ks and {theta}s among surface or subsurface soils, Ks value was always fixed at the observed average values as summarized in Table 1.

Geometry and Boundary Conditions
The average slope assumed for the numerical simulation has two soil layers (i.e., the surface and subsurface layers) with a length of 20 m and a 40° slope gradient (Fig. 3 ). Total soil depth was 100 cm, and it was assumed that the thicknesses of surface and subsurface soil layers were the same. This thickness is typical of many of the granite areas (ranging between 50 and 300 cm) where landslides occur in Japan (e.g., Shimizu et al., 2002).


Figure 3
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  		Fig. 3. Geometry of the slope used for numerical analysis (average case with a soil depth of 100 cm and slope gradient of 40°).

 
Assuming an impermeable bedrock layer under the subsurface soil layer, a no-flux boundary condition was applied to the bottom of the soil layer. A no-flux condition was also applied to the top slope (a dividing ridge) boundary as well as to the bottom slope (hollow) boundary because we assumed the existence of the same slope as shown in Fig. 3 on the opposite side of the hollow (Sammori, 1994). Rainwater was applied to the soil surface, and when the groundwater table increased to the point of saturating the soil surface, discharge from that section was computed. That is, the seepage face boundary condition was applied to the soil surface. Richards' equation (Eq. [4]) was numerically solved by using the finite-element method with triangular elements (Istok, 1989). The discretizing system is shown in Fig. 3.

Hyetograph and Initial Conditions
On 20 July 2003, localized torrential rainfall in the mid-southern region of Kyushu in Japan triggered a large-scale debris flow along the Atsumari-gawa River in Hougawachi, Kumamoto Prefecture (Sidle and Chigira, 2004). Ten houses were destroyed instantly and 19 people were killed. The volume of sediment discharge was estimated at about 100 000 m3, making this one of the largest debris flows in recent years. This study used the Hougawachi rainstorm as the input data for a hyetograph. The total rainfall, peak rate, and event duration were established at 379 mm, 91 mm h–1, and 10 h, respectively.

To establish the initial conditions for the numerical simulations, a 50% reduced hyetograph of the Hougawachi rainstorm (i.e., the total rainfall, peak rate, and event duration of this hyetograph were 189.5 mm, 45.5 mm h–1, and 10 h, respectively) was initially applied. Next, a drainage duration of 48 h was simulated for the average case of the simulation, and the resulting matric pressure distribution within the whole slope was used for the initial condition for the main simulation. It was assumed that the whole slope had a constant matric pressure value, {psi}ini, just before the 50% reduced hyetograph was applied. The value of {psi}ini was fixed at –100 cm. The {psi}ini values of –50 and –200 cm were also tested, and it was found that the {psi}ini value did not cause significant differences in the matric pressure distribution within the whole slope at the end of the 48-h drainage.

Scenarios for Numerical Simulation
Five scenarios were simulated, and are summarized in Table 2. The first scenario used the average conditions discussed above. That is, a drainage period of 48 h for establishing the initial condition, a soil thickness of 100 cm, and a slope gradient of 40° were assumed. Effective soil porosity values were changed only for the surface layer, as in the three cases summarized in Fig. 1. For the subsurface layer, ESP was fixed at the measured value (Table 1).


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  		Table 2. Summary of parameters for each numerical simulation scenario.

 
In Scenario 2, ESP values were changed for both the surface and subsurface layers (Table 2). In Scenario 3, the slope gradient was changed from 40 to 35°. In Scenarios 4a and 4b, the effects of the initial soil moisture conditions were examined. That is, the drainage period after the antecedent rainfall was either shortened to 24 h to establish a wetter condition (Scenario 4a), or extended to 96 h to establish a dryer condition (Scenario 4b). In Scenarios 5a and 5b, the effects of soil thickness were examined. The total soil thickness was set to 50 cm in Scenario 5a and 150 cm in Scenario 5b. In both scenarios, the thicknesses of the surface and subsurface layers were the same, and the soil porosity parameters were changed for the surface layer.

Slope Stability Analysis
The Bishop method (Bishop, 1954) was used for the slope stability analysis. In this method, the safety factor (Fs) is computed based on the moment equilibrium among slices in a sliding circle:

Formula 10[10]
where I is the total number of slices in the sliding circle, ui (cm) is the positive pore water pressure at the bottom of the slice i, Wi (g) is the weight of the slice i, Gi (cm) is the horizontal length of the slice i, {delta}i (°) is the slope of the bottom of the slice i, {phi}i (°) is the internal friction, and ci is the cohesion (gf cm–2).

According to Sammori (1994), it was assumed that the cohesion ci depends on the negative pore water pressure, ui' (cm), and the degree of saturation, {theta}i/{theta}s,i:

Formula 11[11]

Formula 12[12]
where ci' (gf cm–2) is the cohesion under saturated conditions. In Sammori (1994), Eq. [11] was derived from Bishop et al. (1960), and Eq. [12] was developed based on the data by Jennings and Burland (1962). He checked the validity of Eq. [12] using measurements by Marui (1981).

The values of ci, Wi, and ui were computed for each time step from the pore water pressures and soil moisture contents estimated by the infiltration analysis. For the calculation of the Fs value, I was fixed at 20, and 4131 sliding circles were tested to determine the minimal Fs value. Furthermore, ci' = 20 gf cm–2 and {phi}i = 35° was assumed, values that were used by Suzuki (1991) as typical values for a weathered granite soil.

Analysis on Travel Distance and Deposition of Debris Flow
Takahashi (2000) proposed a model to analyze a motion of earth mass in which saturated soil underlies unsaturated soil. The model assumes that the saturated soil layer progressively turned into a liquefied layer, which supports the earth mass and makes it flow down along the channel as the front part of debris flow. The fundamental equations composing the model are an equation of momentum conservation for the earth mass, a volume conservation equation of the mass, an equation of thickness change in the liquefied layer, and an equation of liquefied layer production rate. The model was tested by laboratory experiments (Takahashi, 2000). Recently, Takahashi et al. (2003) modified the model to apply it to two-dimensional behaviors of earth mass and debris flow. In the modified model, the motion of debris flow is analyzed based on the Eulerian continuous fluid equation, while the motion of solid earth mass is analyzed based on a Lagrangian treatment. Detailed description of the model is found in Takahashi (2000) and Takahashi et al. (2003). In this study, we used the numerical code developed by Satofuka and Takahashi (2003).

The model calculation requires parameters such as sediment concentration Cs (cm3 cm–3) and viscosity µ of the whole earth mass and thicknesses of the saturated and unsaturated soil layers for each part of the earth mass. Here, Cs is defined as the ratio of solid-particle volume to the sum of solid-particle and water volumes. These parameter values were derived from the results of infiltration and slope stability analyses described above: Cs and thicknesses of saturated and unsaturated soil layers were computed based on the location and shape of the sliding circle, and distribution of soil porosity and volumetric water content within the sliding circle. The value of µ (Pa s) was computed from the Cs value by using the following experimentally derived function (Lorenzini and Mazza, 2004):

Formula 12[13]

To analyze the effect of ESP variation on the travel distance and extent of deposition of debris flow, two types of topography (Fig. 4a and 4b) were examined. Each consists of a channel and side slopes. A side slope at the top of channel corresponds to the slope for which the infiltration analysis and slope stability analysis are conducted (i.e., the slope shown in Fig. 3). The displaced matter from this slope drops into the channel, flows down along the channel, and deposits into the downstream region. For the travel distance analysis, the channel was divided into three sections with decreasing channel gradients toward the downstream direction (Fig. 4a). The side slope gradient was 40° in every section. Three channel sections were assumed for the analysis on extent of debris flow deposition (Fig. 4b). For the lowest section, we assumed a flat plain where the debris flow is expected to spread widely and stop.


Figure 4
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  		Fig. 4. Slope and channel systems for (a) debris flow travel distance simulation and (b) debris flow deposition extent simulation.

 

   RESULTS AND DISCUSSION
TOP
 EXECUTIVE SUMMARY
 ABSTRACT
 INTRODUCTION
 NUMERICAL STUDY
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
Effects of Surface Layer Effective Soil Porosity on Slope Stability
Figure 5a through 5c show the computed time series of the discharge, pore water pressure at 250 cm from the end of the slope (i.e., the pressure observation point in Fig. 3), and the safety factor, Fs. The figure shows that the occurrence of discharge and peak pore water pressure were controlled by the timing of the peak of the rainstorm event. During periods of intense rainfall, water infiltrated into the slope, increased the pore water pressure, and decreased the effective stress of the soil, resulting in slope failure (i.e., Fs < 1). These results are consistent with those of previous studies (e.g., Anderson and Sitar, 1995; Wang and Sassa, 2003) in that rainfall-induced landslides are caused by increased pore water pressure during periods of intense rainfall.


Figure 5
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  		Fig. 5. (a) Applied rainfall and computed discharge, computed (b) pore water pressure at the observation point, (c) safety factor, and (d) water content for Cases 1, 2, and 3. The numbers in each figure represent the numbers of cases. The observation point of pore water pressure is shown in Fig. 3. Black circles in Fig. 5 (c) and (d) indicate the times when Fs < 1.

 
The discharge and the pore water pressure increased earliest in Case 1, which had the smallest ESP value of the three cases (Fig. 1), because the smallest ESP value results in the surface layer with the smallest water-holding capacity. The rapid increase in pore water pressure in Case 1 between 2.5 and 3.1 h (Fig. 5b) resulted in a rapid decrease in the safety factor, and slope failure (i.e., Fs < 1) was estimated at 2.9 h (Fig. 5c). In Case 2, the rapid increase in the pore water pressure occurred from 3.3 to 3.6 h, which resulted in a slope failure estimated at 3.5 h. In Case 3, with the highest ESP value of the three, the discharge and pore water pressure increased latest, because a greater ESP value results in the surface layer with a larger water-holding capacity. The increase in the pore water pressure from 3.8 to 4.2 h resulted in the latest slope failure occurrence, computed at 4.1 h. These results demonstrate that ESP values have a significant effect on the timing of discharge and pore water pressure increases, and thus affect the time of the occurrence of slope failure.

On the basis of these results, we infer that a less intense storm event may cause failure of a slope with a small ESP value, whereas it would not cause the failure of a slope with a large ESP value. To illustrate this through numerical simulations, a less intense storm event, consisting of the a hyetograph of the first 3 h of the main Hougawachi rainstorm event, was applied (Fig. 6a ). Other conditions for these numerical simulations were the same as those used in Scenario 1. The results are presented in Fig. 6a, 6b, and 6c. Because the ESP value of Case 1 was smaller than that of Case 2, Case 1 had a greater peak discharge and greater pore water pressure (Fig. 6a and b). As a result, the safety factor of Case 1 decreased faster than that of Case 2 (Fig. 6c). In Case 3, which had a greater ESP than Case 2, the smallest peak discharge and the smallest pore water pressure were computed (Fig. 6a and 6b). The safety factor for Case 3 was always greater than those for Cases 1 and 2 (Fig. 6c). In Fig. 6c, slope failure was estimated only for Case 1, which had the smallest ESP value.


Figure 6
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  		Fig. 6. (a) Applied small rainfall and computed discharge, computed (b) pore water pressure at the observation point and (c) safety factor for Cases 1, 2, and 3. The observation point of pore water pressure is shown in Fig. 3.

 
To summarize the results shown in Fig. 5a through 5c and Fig. 6a through 6c, when the surface soil of a slope has a relatively large ESP value, it has a greater capacity for holding rainwater, which delays infiltration of the rainwater into the subsurface layer. Consequently, the increase in pore water pressure in the subsurface layer is delayed. In this manner, a greater ESP value of the surface layer contributes to a delay in the occurrence of slope failure. Under relatively weak storm conditions, slope failure tends not to occur when the surface soil has a larger ESP value.

Effects of Surface Layer ESP on Water Content of Displaced Slope
Figures 7a and 7b show distributions of pore water pressure and soil water content in the whole slope at the estimated time of slope failure. The sliding circle, groundwater table, and equi-hydraulic potential lines are shown in both figures. Figure 7a shows that the depths of the water table in the sliding circle are similar in each case, although the ESP value varies. However, Fig. 7b shows that Case 1 has drier soil and Case 3 has wetter soil than Case 2 when the estimated slope failure occurs. This is because the smaller ESP value in Case 1 and the larger ESP value in Case 3 result in either a decrease or an increase in the water-holding capacity of the surface layer.


Figure 7
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  		Fig. 7. Distributions of (a) pore water pressure and (b) soil water content in the whole slope at slope failure initiation time. The sliding circle (purple line), groundwater table (black line), and equi-hydraulic potential lines (green lines) are shown in both (a) and (b). The interval of the equi-hydraulic potential lines is 100 cm.

 
The moisture conditions of the sliding circle are an important factor in determining the mobility of the displaced debris because when the displaced debris contains a great deal of water, it can easily become a debris flow. Figure 5d shows the changes in water content (the ratio of water weight to solid weight) of the sliding circles shown in Fig. 7 for Cases 1 through 3. Compared with Case 2, the initial water content is smaller for Case 1 and greater for Case 3. During rainfall, the water content increase is greatest in Case 3 and smallest in Case 1. Moreover, Case 3 has the latest time of slope-failure occurrence, and the water content increases nearly 70% when Fs < 1. On the other hand, Case 1 is the first to experience slope failure, resulting in the smallest water content (<35%) when Fs < 1. The results shown in Fig. 7b and 5d imply that when the surface soil layer has a larger ESP value, the water-holding capacity is larger and the soil layer contains a great deal of water when slope failure occurs.

Figure 8 shows the weight of solid particles and water in the sliding circle at the estimated time of slope failure. Case 1 has the smallest {theta}s value, and so has the largest dry density of the surface layer. As a result, the solid weight is largest in Case 1. In contrast, Case 3 has the smallest solid weight because it has the largest {theta}s value. In Fig. 8, the water weight follows a contrary trend; it is the largest in Case 3 and the smallest in Case 1. As shown in Fig. 5d, the greater ESP value along with the higher initial water content result in a larger water amount in the sliding circle for Case 3.


Figure 8
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  		Fig. 8. Weight of solid particles and water in sliding circle at slope failure initiation time.

 
From the comparisons of Cases 1 through 3, it can be concluded that a greater surface soil layer ESP value delays the occurrence of slope failure and can increase slope stability against a shallow landslide. However, a greater ESP value tends to increase the water content of the displaced matter, which may result in the occurrence of debris flow, and contribute to the debris being transported further. Therefore, under greater ESP conditions, greater damage can be expected once slope failure occurs.

Influence of Soil Porosity of Both Surface and Subsurface Layers (Scenario 2)
In Scenario 2, the influence of variation in ESP in both the surface and subsurface layers was studied. When compared with the corresponding cases in Scenario 1, changes in the ESP values of both layers in Scenario 2 resulted in a diminished water-holding capacity in Case 1, the same water-holding capacity in Case 2, and an increased water-holding capacity in Case 3. Figure 9a shows that for Case 1 of Scenario 2, the slope failure was estimated at 2.6 h, which was earlier by about 0.3 h than the failure time for Case 1 in Scenario 1. On the other hand, Case 3 had a slower decrease in the safety factor. The estimated time of slope failure was 4.2 h, slower than that for Case 3 in Scenario 1, which had an estimated time of slope failure at 4.1 h.


Figure 9
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  		Fig. 9. (a) Slope failure initiation time and (b) weight of solid particles and water in sliding circle at slope failure initiation time.

 
Scenarios 1 and 2 showed the common trend that a greater ESP value tends to increase the water content of the displaced matter (Fig. 9b), although the difference was more pronounced in Scenario 2. That is, Case 1 in Scenario 2 had less water content than Case 1 in Scenario 1, and Case 3 in Scenario 2 had greater water content than Case 3 in Scenario 1.

Influence of Slope Gradient (Scenario 3)
As expected, the results of this analysis show that in Scenario 3, with a 35° slope gradient, the timings of estimated slope failure for all cases were later than those for the corresponding cases in Scenario 1, with a 40° slope gradient (Fig. 9a). The increased solid weight in sliding circle for Scenario 3 (Fig. 9b) suggests that the sliding circle became big as the slope gradient became small. Again, a greater ESP value tended to increase the water content of the displaced matter.

Influence of Initial Moisture Conditions (Scenario 4)
With 24- and 96-h drainage periods, Scenarios 4a and 4b had wetter and dryer initial conditions than Scenario 1, respectively. Slope failure was estimated to be earlier in Scenario 4a and later in Scenario 4b than in Scenario 1 (Fig. 9a). These results show that the initial soil moisture condition affects the timing of an increase in pore water pressure and a decrease in safety factor, which are consistent with results of similar analyses by Tsaparas et al. (2002), who studied the effect of antecedent rainfall on changes of pore water pressure during rainstorm events.

In spite of the difference in the slope failure timing, the water content of the displaced matter for all cases in Scenarios 4a and 4b were similar to those for the corresponding cases in Scenario 1, indicating that a greater ESP value increases the water content of the displaced matter.

Influence of Soil Depth (Scenario 5)
The results of the analysis for a 50-cm soil depth in Scenario 5a showed the safety factor in each case remained greater than 1. The results were attributable to the small soil thickness assumed in Scenario 5a, which resulted in a small soil weight reducing shearing forces. On the other hand, slope failure was estimated for the 150-cm soil depth (i.e., Scenario 5b) in every case. The deeper soil depth assumed in Scenario 5b, capable of absorbing much more water, showed a delayed decrease in the safety factor value compared with Scenario 1, for which the soil depth was 100 cm. The slope failure was estimated later than the cases in Scenario 1 (Fig. 9a).

After application of the Bishop equation, the greater soil thickness on the slope in Scenario 5b resulted in a increased weight of solids in the displaced matter compared with Scenario 1 (Fig. 9b). Comparisons among Cases 1 through 3 in Scenario 5b indicated the trend that a greater ESP value increases the water content of the displaced matter.

From Scenarios 2 through 5, we conclude that the effects of ESP on rainwater infiltration, slope stability, and debris flow runout found in Scenario 1 are true for every case regardless of soil layer, slope gradient, initial soil wetness, and soil thickness. That is, whereas a greater ESP value delays the occurrence of slope failure and can increase slope stability, a greater ESP value increases the water content of the displaced matter, which may result in the occurrence of debris flow, and contribute to further transportation of debris.

Influence of ESP on Travel Distance and Extent of Deposition of Debris Flow
Numerical analyses on the travel distance and extent of deposition of debris flow were conducted for Cases 1 through 3 in Scenario 1. The required parameters on the properties of the displaced matter were computed based on the results of infiltration and slope stability analyses shown in Fig. 7 and 8.

Travel Distance
Figure 10a through 10c show the motions of debris flow for Cases 1, 2, and 3 simulated by assuming the topography shown in Fig. 4a. It is clear that as the ESP value increased, debris flow moved faster and traveled longer. Figure 10b shows that in Case 2, the earth block of debris flow traveled about 87 m from the top of a channel at a time of 50 s. In Case 1, which has a smaller ESP value than Case 2, the motion of debris flow was very slow, and the earth block of debris flow traveled only about 50 m from the top of the channel at 50 s (Fig. 10a) because the smaller ESP value results in a small water content of the displaced matter (Fig. 8).


Figure 10
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  		Fig. 10. Simulation results on the travel distance of debris flow assuming the slope and channel system shown in Fig. 4a for (a) Case 1, (b) Case 2, and (c) Case 3 in Scenario 1. Each figure shows spread areas of the liquefied layer (cyan dots), saturated soil mass (blue dots), and unsaturated soil mass (black dots) at the time indicated by the number in each figure.

 
In Case 3, which had a greater ESP value than Case 2, the motion of debris flow was faster. At 50 s, the earth block of debris flow had traveled about 126 m from the top of the channel (Fig. 10c) because the relatively greater ESP value resulted in a large water content of the displaced matter (Fig. 8). These results agree with those of previous studies (e.g., Iverson et al., 1998; Chau et al., 2000; Legros, 2002), which concluded that an increase in the water content of the debris flow materials leads to an increase in the runout distance.

As a result, the ESP value had a significant effect on the runout distance of debris flow, in that a relatively larger ESP value results in a relatively larger water content in the sliding segment, resulting in a debris flow that travels faster and over a longer distance.

Extent of Deposition
Figure 11 shows the spread of debris flow deposition in response to ESP variations in the surface soil layer, simulated for the topography shown in Fig. 4b. In all cases, the earth mass descended quickly in the first 100 m due to the steepness of the channel gradient. In Case 1, which has a smaller ESP value than Case 2, the earth mass of debris flow is deposited approximately 120 m from the top of the channel at a time of 50 s, where the side slope gradient was 20° (Fig. 11a). However, in Case 3, which had a larger ESP than Case 2, the deposition of the earth block of debris flow spread farther and wider, with the deposit located more than 120 m from the top of the channel with a side slope gradient of 0° (see Fig. 11c). These results suggest that ESP values are also a dominant factor in determining the extent of debris flow deposition. In other words, relatively larger ESP values result in a broader area of debris flow deposition, which may cause greater levels of damage in the downstream area.


Figure 11
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  		Fig. 11. Simulation results on the extent deposition of debris flow assuming the slope and channel system shown in Fig. 4b for (a) Case 1, (b) Case 2, and (c) Case 3 in Scenario 1. Each figure shows the spread areas of the liquefied layer (cyan dots), saturated soil mass (blue dots), and unsaturated soil mass (black dots) at the time indicated by the number in each figure.

 
As summarized in Fig. 9, for all scenarios a similar trend was found for the effect of ESP on the water and solid content of the displaced matter. Therefore, we presume that the simulation results on the motion of debris flow found for Scenario 1 (i.e., Fig. 10 and 11) are true of every scenario.


   CONCLUSIONS
TOP
 EXECUTIVE SUMMARY
 ABSTRACT
 INTRODUCTION
 NUMERICAL STUDY
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
Numerical simulation models were used to investigate five scenarios to study the effects of effective soil porosity, ESP, on rainwater infiltration, slope stability, and the movement of debris flow at granitic hillslopes. The analyses yielded similar trends in each scenario on the effect of ESP values. In each scenario, Case 1 had a smaller ESP value than Case 2; the occurrence of discharge and the increase in pore water pressure started earlier in Case 1 because the smaller ESP value reduced the water-holding capacity of the soil layer. In contrast, Case 3 had a greater ESP value than Case 2; the occurrence of discharge and the increase in pore water pressure started at a later time in Case 3 because the greater ESP value increased the water-holding capacity of the soil layer. In summary, when the 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 ESP value of slope contributes to delaying slope failure. Under small storm conditions, slope failure tends not to occur when the soil has a relatively large ESP value. However, the greater ESP value tends to increase the water content of the displaced matter, which results in faster and longer travel distances and in a broader extent of deposition of debris flow. Therefore, a relatively large ESP value may lead to more severe damage in downstream region once slope failure occurs.


   REFERENCES
TOP
 EXECUTIVE SUMMARY
 ABSTRACT
 INTRODUCTION
 NUMERICAL STUDY
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 




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D. L. Corwin, J. Hopmans, and G. H. de Rooij
From Field- to Landscape-Scale Vadose Zone Processes: Scale Issues, Modeling, and Monitoring
Vadose Zone J., March 8, 2006; 5(1): 129 - 139.
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