Contribution of “Soils and Foundations” to Studies on Rainfall-Induced Slope Failure

SOILS AND FOUNDATIONS Japanese Geotechnical Society

Vol. 50, No. 6, 955–964, Dec. 2010

CONTRIBUTION OF ``SOILS AND FOUNDATIONS'' TO STUDIES ON RAINFALL-INDUCED SLOPE FAILURE RYOSUKE KITAMURAi) and KAZUNARI SAKOii) ABSTRACT The many recent slope failures due to heavy rainfall have been accompanied by signiˆcant loss of life, and massive damage to infrastructures and heritage. Many studies have been done to investigate the mechanism of rainfall-induced slope failures and establish a prevention system for slope disasters. In this paper, the state-of-the-art research works on slope failures due to rainfall published in the journal of Soils and Foundations (S&F) during the latest 50 years are reviewed and summarized. This report is written with the perspective that knowledge of unsaturated soil mechanics is necessary to elucidate the mechanism of rainfall-induced slope failure. Key words: rainfall, slope failure, slope stability analysis, unsaturated soil mechanics (IGC: E6/E7) the loss of many lives, and massive damage to existing infrastructure and local heritage. Basically, slope failure due to rainfall is mainly caused by 1) the increase in the weight of the soil mass, 2) the decrease in the suction of unsaturated soil with increasing

INTRODUCTION The greenhouse eŠect has brought change in climate all over the world. In Japan, slope failure due to rainfall has been increasingly frequent during the rainy season, with

Fig. 1. i) ii)

Mechanism of rainfall-induced slope failures

Professor, Kagoshima University, Kagoshima, Japan (kitamura＠oce.kagoshima-u.ac.jp). Associate Professor, Ritsumeikan University, Japan. The manuscript for this paper was received for review on May 24, 2010; approved on September 29, 2010.

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water content and 3) the rise in the groundwater level. Figure 1 shows the mechanism of rainfall-induced slope failures. In this ˆgure, the deformation of the soil mass followed by slope failure during rainfall is shown to be caused by the increase in water content in unsaturated soil. The ˆgure also indicates that the rise in groundwater level may cause deformation of the slope and lead to slope failure for deep slope failure. As such, the mechanical properties of unsaturated soils must be rigorously investigated to make the mechanism of slope failure due to rainfall clear. D. G. Fredlund (2006) reported in his paper that 1) the appearance of a high air entry ceramic disk at the end of the 1950s brought the gradual emergence of unsaturated

Fig. 2.

soil mechanics, i.e., numerous soil tests where the poreair pressure and pore-water pressure were measured independently using high air entry ceramic disks were conducted; 2) in the latter part of 1960s, independent stress state variables were proposed and applied to analyze the mechanical behaviors of unsaturated soil; 3) in the 1970s, the constitutive laws for saturated and unsaturated soils were actively investigated based on continuum mechanics; 4) in the 1980s, numerical methods such as Finite DiŠerence Method (FDM) and Finite Element Method (FEM) were applied to analyze seepage and deformation behaviors; 5) since the 1990s, unsaturated soil mechanics has been applied to practical geotechnical engineering to prove its validities. Kitamura et al. (2010) proposed a new

Research strategy of the prediction system for slope failure due to rainfall (Kitamura et al. (1993))

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unsaturated soil mechanics aided by the probability theory in order to understand various mechanical behaviors of unsaturated soil comprehensively. It has been recognized that the estimation of cyclic change in slope stability under both drying and wetting weather conditions is essential to predict when slope failure due to rainfall will occur, i.e., unsaturated soil mechanics, which comprehensively deals with various behaviors and properties, including water retention, poreair and pore-water permeability, and deformationstrength properties, needs to be further developed. Kitamura et al. (2003) proposed a research strategy for the prevention system of slope failure due to heavy rainfall where the seepage and strength properties of unsaturated soil depending on the water content (i.e., matric suction) were taken into account. The strategy is mainly composed of the ˆve methods shown in Fig. 2. These include: 1) laboratory soil tests on disturbed and undisturbed samples, 2) numerical simulations, 3) model tests of seepage and failure using soil box apparatus, 4) ˆeld measurements of suction and precipitation and 5) some in-situ tests for the identiˆcation of geological and geotechnical characteristics of the slope.

Detailed Explanations of These Five Methods Follows 1) The values of the input parameters are obtained from the laboratory tests on the soil samples to determine water retention, permeability and shear strength for use in numerical simulations designed to quantitatively estimate changes in slope stability with real time. 2) In the numerical simulations, the unsaturated seepage analysis and slope stability analysis are performed using one of the following: the Limit Equilibrium Method (LEM), FDM, FEM, or one of the particle methods (e.g., the Discrete Element Method (DEM), Smoothed Particle Hydrodynamics (SPH), Moving Particle Semi-implicit (MPS), and Particle-in-Cell (PIC) methods). 3) A model test to determine the initial and boundary conditions is carried out using the soil box apparatus in order to investigate the mechanism of slope failure due to rainfall. 4) In-situ slope pore-water pressure and the amount of rainfall with time are measured as the input data used to perform a 2D seepage analysis of the slope. 5) Some in-situ tests, such as the portable dynamic cone penetration test and boring, are carried out to determine the geological and geotechnical characteristics of the slope (i.e., the initial and boundary conditions for numerical analysis). The analytical domain is deˆned, and the structure of the layers and the potential slip plane are input into the computer code as inherent factors of the slope.

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THE TENDENCY OF STATE-OF-THE-ART RESEARCH ON RAINFALL INDUCED SLOPE FAILURE IN S&F AND OTHER JOURNALS

Research Work in the 1960s Typical of the research work on landslides performed during the 1960s was Taniguchi and Watari's (1965) investigation of the mechanism and countermeasure of the landslide which occurred at the Terao area in Yui-machi, Ihara-gun, Shizuoka. They carried out a case history, and proposed a perfect stabilization method for this landslide, as requested by the Japanese Government Agency. Ohhira et al. (1962) and Nakano (1967) investigated the mechanical properties of tertiary sedimentary rocks (mudstone or shale) sampled from the bed rock of the sliding area, tested the slaking behavior in the laboratory, and suggested that weathering was one of the main factors for landslides in the tertiary mudstone area. Matsuo (1962) investigated the landslide which occurred at Kashio near Nikawa Station of the Keihanshin Express Imazu line on 13 July, 1951 and suggested that a decrease in calcium ions in the pore water due to excessive rainfall resulted in a reduction in the safety factor of the slope. Kishimoto (1962) carried out an unconˆned compression test on undisturbed soils sampled from the potential slip plane to investigate the failure mechanism for the heterogeneous layered slope. Various research works on artiˆcial slopes were performed with a particular focus on ascertaining the base failure mechanism of the embankment. Muromachi (1964) published his measurement results of the displacement and strain on the ground surfaces obtained from the monitoring pile and ground surface strain-meter. Yamaguchi et al. (1962) investigated the deformation by consolidation, the change in stress distribution, the shear strength and pore-water pressure developed in the soil and the condition of the failure surface due to loading of the embankment by conducting model tests on the conˆguration of slip surface. Research on the shear strength properties of unsaturated sandy soils were carried out to gain a better understanding of slope failure due to rainfall. Haruyama (1969) described the eŠect of water content on the shearing characteristics of granular soils, such as Shirasu, by carrying out drained triaxial compression tests. In his paper, the eŠects of water content on the apparent cohesion and angle of shearing resistance were determined to be independent. Uchida et al. (1968) conducted triaxial compression tests on compacted partially saturated Masa-soil under both drained and undrained conditions, and found that the apparent cohesion and angle of shearing resistance decreased with an increase in the degree of saturation under the undrained condition, while the angle of shearing resistance did not decrease signiˆcantly even though the apparent cohesion decreased under the drained condition. They concluded that slope erosion and embankment failure may result from a decrease in the apparent cohesion with an increase in the degree of saturation due to rainfall.

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During the 1960s, the mainstream slope stability analysis method was the LEM proposed by such researchers as Fellenius (1936), Bishop (1955), Janbu (1957), and Morgenstern and Price (1965). Mizuno et al. (1960) proposed a calculation method to determine the bearing capacity of a cohesionless soil slope under horizontal loading along the top or berm. Chen et al. (1969) proposed a numerical method which utlilized the upper bound theorem of the generalized theory of perfect plasticity in order to obtain complete numerical solutions for the critical height of an embankment. In an overview published by Duncan (1996), it was noted that the widespread availability of microcomputers brought about a considerable change in the computational aspects of slope stability analysis. Indeed, computational methods have been employed for practical geoengineering problems since the late 1960s.

Research Work during the 1970s Slope failure due to heavy rainfall often occurred in regions where Shirasu and Masa-soil are predominant in Japan, which led to an interest in research work on the shear characteristic of Shirasu and Masa-soil. Haruyama (1973) investigated the formation and constituents of Shirasu ground, as well as the physical and mechanical properties of Shirasu soil in order to estimate the stability of slopes, and then proposed a method of classiˆcation from a geotechnical engineering perspective. Murata and Yamanouchi (1978) carried out unconˆned and triaxial compression tests on undisturbed Shirasu soil to investigate the eŠects of water content on the shear strength, and then investigated the mechanism of slope failure thought to be related to the change in water content from rainfall. Fukuda (1978) investigated the decrease in shear resistance of weathering soil, such as Masa-soil, using the improved direct shear testing apparatus in an eŠort to understand the change in slope stability of embankment due to submergence. The obtained test data were used to perform a numerical analysis for slope failure due to a rise in the groundwater table in the embankment. Roy (1976) proposed a method to analyze the stability sloped that experienced a drastic and sudden change due to the rapid drawdown of a wetting front which left residual porewater pressure in reservoirs and river embankments. Yoshida (1974) proposed a new concept for considering the seepage force generated in the quick sand and piping phenomena, which are the main factors that trigger the failure of earth dams and other embankments to derive a general equation for seepage force. In addition to these studies, many investigations in the seventies were carried out to estimate the computational accuracy of the LEM. The FEM has also been applied to studies on slope stability analysis since the 1970s. Several constitutive soil models, including those for linear elasticity, multilinear elasticity, hyperbolic elasticity and elastovisco-plasticity, were applied to perform deformation analyses of slopes using FEM (Duncan, 1996). In the journal of S&F, the following research on slope stability analysis were published. Matsuo and Kuroda

(1974) proposed a failure probability which took into account many of the variables and uncertainties in the slope stability analysis, where more than 0 in probability corresponded to more than 1 in safety factor. Moore (1970) discussed the additional pore pressure that may develop between the in-situ and failure states of the soil and redeˆned the safety factor of slopes under the undrained condition in terms of failure criterion. Chen and Snitbhan (1975) investigated the slip plane for uniform slopes with a horizontal top and found that the most critical surface is a logarithmic spiral surface with angle f. Ito et al. (1979) proposed a design method for the stability analysis of a slope with a landing pier in a harbor. Fukumoto (1972, 1976) investigated the pile behavior and its eŠects to prevent landslides in Niigata Prefecture in Japan. Nakamura (1977) discussed stability analysis methods to investigate the pile behavior for the prevention of landslides.

Research Work during the 1980s Many studies of rainfall-induced slope failure were done in the 1980s. Matsuo and Ueno (1981) developed a new prediction method of slope failure using the failure probability in which only the rainfall intensity was considered necessary data during a rainfall event. In this paper, the authors stated that there was a correlation between eŠective approaches to prevent or decrease the occurance of disasters due to rainfall and performing mechanical defensive works, such as constructing retaining walls (hard countermeasure) and ˆnding out good prediction method of slope failure (soft countermeasure) in order to minimize the damage. They also commented that taking measurements of deformation and pore-water pressure in a slope is very eŠective for predicting slope failure, but that it is practically impossible from both an economical and technical point of view to measure these factors in numerous steep slopes during heavy rainfall. Iseda et al. (1985) carried out a ˆeld investigation with saturated-unsaturated seepage analysis by FEM on a gentle slope failure of less than 309in inclination angle which occurred during the Nagasaki heavy rainfall event on 29 July, 1982 and found that the seepage force and the decrease in shear strength with an increase in the degree of saturation were the main causes of that slope failure. Suzuki and Matsuo (1988) proposed a linear regression analysis employing a Bayesian method where a new strength reduction parameter was used to evaluate the data obtained from ˆeld observations and past case records of slope failures due to rainfall. Kawamura and Sano (1989) proposed a design procedure for embankments in mountainous areas, making it possible to evaluate the safety factor and take into account the in‰uence of rainfall run-oŠ based on the ˆeld investigation at Noto Peninsula after heavy rainfall in July, 1985, where almost all the slides of road embankments were caused by the water run-oŠ from the surrounding valleys during/after the heavy rainfall. Nishida and Aoyama (1981) carried out laboratory tests on undisturbed decomposed granite soil to investigate the piping phenomenon, which is one

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of the main causes for slope failures due to rainfall. With slope design in mind, Yamanouchi et al. (1982) proposed an engineering classiˆcation of primary Shirasu soil at both natural and cut slopes by using the soil hardness tester, which is a simple portable device capable of qualitatively estimating the mechanical properties of soil. Gotoh et al. (1985) applied remote sensing technology to the estimate the slope stability to determine places where the potential of slope failure was high. In this method, the multispectral scanner data were used as the supervisor data obtained from sites where the slope failures had occurred previously. A large number of studies of 3D slope stability have been proposed since the late 1960s (Duncan, 1996). There was a special interest in 3D slope stability during the 1980s. In journal of S&F, Ugai (1985) and Baker and Leschensky (1987) proposed a 3D slope stability analysis using the limit equilibrium and variational analysis. Slope stability analysis using FEM were also proposed. Ugai (1989) proposed a method to calculate the total safety factor of a slope by elasto-plastic FEM. There was also an increase in the number of papers published in which uncertainties of slopes taken into consideration. Examples include the probabilistic slope stability models developed by Matsuo and Ueno (1981) and Bergado and Anderson (1985). Yasue (1984) proposed a design procedure for retaining walls for slope stability where the probabilistic factors were considered using a deterministic approach.

Research Work during the 1990s The research on rainfall-induced slope failure considering unsaturated soil mechanics dramatically increased from about 1990. Fredlund and Rahardjo (1993) published their text book on unsaturated soil mechanics. In this text book, a large number of experimental data on unsaturated soils were provided and the mechanism of rainfall-induced slope failure was described from a view point of unsaturated soil mechanics. Rahardjo et al. (1998) carried out ˆeld monitoring in order to investigate rainfall-induced slope failure. Pradel and Raad (1993) also conducted a study on the eŠect of rain inˆltration into a slope in terms of slope stability. Alonso et al. (1996) proposed a formulation for the coupled analysis of unsaturated soils and also proposed numerical solutions of combined seepage and deformation problems. In Japan, statistical methods for critical rainfall were developed for estimating slope stability and predicting slope failure during the 1990s, perhaps due to the increase in rainfall measuring sites. Okada et al. (1994) proposed a practical damage estimation method based on the statistical rainfall risk estimating method for the safety control operations for railway lines. This approach accurately predicts the hazard of slope collapse and can be used simply by railway workers. In this method, risk of a surface collapse of a cut slope during heavy rainfall was estimated using a multivariate analysis. In their paper, the authors noted that the amount of hourly rainfall has more in‰uence than the accumulated rainfall on the sur-

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face collapse of a cut slope. Sugiyama et al. (1995) proposed a discriminative method between a surface and a deep collapse for cut slope collapses, and a critical rainfall prediction method for the collapse of deep cut slopes during heavy rainfall. In their paper, they indicated that the accumulated rainfall has more in‰uence than the hourly rainfall on the deep collapse of cut slope. In the statistical approaches for slope stability, accurate ˆeld investigation data of failure and/or nonfailure slopes are essential. Okimura and Sugimoto (1979) reported that the eŠective factors for statistical analysis of slope failure were the slope angle and the degree of weathering from analysis results. Haruyama and Kitamura (1982) carried out statistical analyses for slope disaster in Kagoshima using a multiple classiˆcation analysis. Tajiri et al. (1992) performed a multiple classiˆcation analysis using the Geotechnical Information data base system and made a distribution map of the risk of slope failure. Kay (1998) discussed an alternative approach using measured Hong Kong slope performance to estimate the failure probabilities for a variety of conditions, and discussed the relationship between probabilities for the consequences of failure and the formal assessment of risk. Research work on chemical properties in the slopes was also carried out to investigate the slope failure mechanism due to rainfall. Mshana et al. (1993) reported that natural slopes in areas abundant in weathered soil and unwelded tuŠ were prone to catastrophic failure in periods of heavy rainfall. They showed the origin, the chemical and mineralogical composition of weathered soils of unwelded tuŠ and compared the data with other volcanic soils such as red and black volcanic soils, and Shirasu soil. They also discussed the eŠects of weathering on the stability of natural slopes with the help of actual case studies in north-central Kumamoto. The indeterminate problems for the LEM were discussed in the slope stability analysis. For example, Enoki et al. (1990) pointed out there was a problem in the slice methods of the limit equilibrium analysis in that it failed to assume the inter-slice forces, and they discussed appropriate techniques for determining these forces. They proposed an extended wedge method in which the equilibrium equations of forces acting on slices are directly presented and the safety factors on inter-slice planes are deˆned. Matsui and San (1990) developed a hybrid slope stability analysis method, in which the stress and strain that developed in a slope were determined by the FEM, while the basic concept of the LEM was adopted in the overall stability analysis. Zhang and Chowdhury (1995) developed an alternative method of tackling the limit equilibrium slope problem in which inter-slice forces were considered in a direct and realistic manner. Liang et al. (1997) proposed a direct method for determining the inter slice forces using the hypothesis of least resistance. Extended research work on strength was carried out, where the change in strength was regarded as a function of a variety of factors. Matsui and San (1992) proposed a shear strength reduction technique for ˆnite element

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slope stability analysis. In this paper, they tried to verify the shear strength reduction technique through their ˆeld test data taken from the Nose site, in Osaka Prefecture, Japan. Srbulov (1995) proposed the slope stability analysis using the LEM extended by adding a consideration of the possible kinematics of the chosen sliding bodies divided into rigid slices in order to predict progressive type failures. Yamagami and Jiang (1997) proposed a practical minimization approach for the 3D slope stability analysis in order to solve the problem of how to determine the minimum factor of safety and the corresponding critical slip surface. Case histories of slope failure due to rainfall were also studied. For example, Yamamoto et al. (1996) presented the characteristics of cut slopes consisting of Sangun metamorphic rocks which failed due to heavy rainfall in Yamaguchi Prefecture. The authors discussed the causes of the failure of cut slopes from the view points of geology, soil mechanics and petrology. Miwa et al. (1997) conducted an experiment in order to discuss the stability of Shirasu and its talus deposit due to the in‰ow and out‰ow of pore water normal to the slope. The authors concluded that the stabilities of the Shirasu and its talus deposit were in‰uenced by the slope angle, and the failure process due to outward-directed ‰ow was explained by the traditional continuum theory, and the failure mechanism due to in‰ow-directed ‰ow was analyzed by the single-grain theory.

Research Work during the 2000s Since the turn of the 21st century, there has been an increase in papers on slope failures due to rainfall because of the increase in the incidence of slope failures due to the green house eŠect. With regard to the inˆltration characteristics of slopes, a large number of studies have been conducted. Tsaparas et al. (2003) and Rahardjo et al. (2005) carried out in-situ ˆeld measurements, compiling rainfall and runoŠ data and pore-water pressure changes during inˆltration. In this paper, the relationship between the total rainfall and runoŠ, the in‰uence of the initial condition of slope on this relationship and the in‰uence of the rainfall patterns on the change in pore-water pressure were presented. Kitamura et al. (2000) and Sako et al. (2006a) used in-situ ˆeld monitoring to predict rainfall-induced slope failure and discussed the relationship between seepage behavior in unsaturated soil and rainfall intensity. Zhan et al. (2007) discussed the in‰uence of the natural grass cover on rainfall inˆltration into the slope. Notable laboratory examinations on rainfall-induced slope failure include those done by Tohari et al. (2007), Kitamura et al. (2007) and Sako et al. (2006b), all of whom conducted a series of laboratory experiments and discussed the relationship between the soil moisture content or negative pore-water pressure and slope failure. There have also been studies designed to experimentally investigate the mechanism of rainfall-induced slope failure. Chen et al. (2004) conducted the constant dead-

load tests on unsaturated completely decomposed granite and the anisotropically consolidated undrained triaxial tests on saturated specimens to simulate the ˆeld stress pass of rainfall-induced slope failure by reducing suction. Ng and Pang (2000) developed a new stress controllable pressure plate apparatus to investigate the in‰uence of the stress state on the soil-water characteristics and conducted a numerical analysis of transient seepage in unsaturated soil slopes using the measured stress dependent soil-water characteristic curves. Most notably, this ten year period was characterised by a large number of studies using numerical simulations. Zhang et al. (2004) developed a coupled hydro mechanical ˆnite element modeling program and a ˆnite element based slope stability analysis program in order to study the performance of an unsaturated soil during a rainstorm and to include the uncertainties of soil properties in the analyses. Also, certain uncertainties, particularly those pertaining to the soil hydraulic properties and shear strength properties that aŠect the stability and deformation of slopes were analyzed using the various methods developed. Collins and Znidaricic (2004) provided a procedural method for integrating rainfall into conventional slope stability analyses and provided a rational basis for explaining the various possible mechanisms of failure, whether in the saturated or unsaturated regimes, in order to develop an analytical formulation that incorporates the complete transient seepage and inˆltration analyses within a traditional slope stability framework. Slope stability analyses and deformation analyses of slopes using particle methods were proposed in the 2000s. Chen and Liu (2007) developed the LEM, incorporating an inter-particle adhesive force in order to account for the in‰uence of capillary menisci among particles. Maeda and Sakai (2004) employed SPH with a power-law nonlinear elastic constitutive model in order to predict the behavior of seepage-induced embankment failure. Bui et al. (2009) proposed that the SPH method, which employs the Drucker-Prager model with a non-associated plastic ‰ow rule, be used to evaluate the stability of a slope and to simulate the gross discontinuities after failure. In their work, the shear strength reduction method was also applied to estimate the safety factor of a slope, while critical slip surface was automatically determined from a contour plot of accumulated plastic strain. While all of this work was being done, the number of slope failures in Japan was increasing. In 2004, ten major typhoons hit Japan, with slope failures occurring in various places as a result. Toyota et al. (2006) investigated the failures of dikes and natural slopes induced by heavy rainfall in Niigata on 13 July 2004. In their paper, an outline of the sediment disaster was presented, and then the detailed results of their ˆeld investigation, and the series of direct and ring shear tests done in the laboratory were provided. Moreover, new but simpler analytical methods using unsaturated seepage were discussed with regard to analysing slope stability. Zhang and Chen (2006) discussed the failure mode and process of the 71-m high Gouhou con-

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crete-faced rockˆll dam in Qinghai Province, China, from the analysis of water inˆltration behavior, the ‰ow patterns and hydraulic head gradients in the rockˆll dam. Orense and Sapuay (2006) and Orense et al. (2006) published their report on their ˆeld investigations of a largescale landslide which occurred in Southern Leyte Province in the Philippines which was induced by heavy rainfall on February 17, 2006, and also on the sediment disasters in Quezon province in the Philippines, which were triggered by heavy rainfall from mid-November to early December 2004. Sehara et al. (2006) summarized the results of the investigations on the sediment disasters that occurred in Yamaguchi during the storm of Typhoon No. 14 on September 5 to 7, 2005. Mizuhashi et al. (2006) carried out an examination of slope hazard assessment using case studies of Earthquake- and Rainfall-induced landslides in the years 2004 and 2005. An emergency survey team of the Japanese Geotechnical Society (2006) reported ground damage resulting from torrential rains in Fukui Prefecture in July 2004. Sezaki et al. (2006) also reported the mechanisms of slope failure observed in the sediment disasters in the Kyushu district caused by typhoon No. 14 in September 2005 in relation to the rainfall characteristics and geological and mechanical aspects of the soil. Shibuya et al. (2007) showed the failure mechanism by discussing the causes of the slope failure based on the results of stability analysis performed using laboratory and ˆeld data, coupled with topological information and rainfall data. Nakai et al. (2006) proposed a new rainfall index designated as R?. In this paper the authors analyzed the rainfall data obtained during a serious disaster on June 29, 1999 and another on September 15, 1999 in Hiroshima Prefecture using the newlyproposed rainfall index R? which utilized the concept of eŠective rainfall in order to check the validity of the proposed method. Farooq et al. (2004) conducted drained triaxial tests on three sets of soil samples (normal sand, gravelly sand and silty sand) taken from natural slopes where large-scale landslides have occurred in the past under constant shear stress in order to understand the mechanism and conditions leading to failure of sandy slopes due to rainfall. In this paper, the eŠects of various parameters re‰ecting the initial condition, such as relative density, the principal stress ratio, the degree of saturation and the inˆltration rate on the development of deformation during the inˆltration process were investigated. Orense et al. (2004) conducted constant shear stress drained triaxial tests designed to mimic the ˆeld stress path on three sets of sandy samples obtained from sites of previous disastrous landslides in order to analyze the mechanism and conditions leading to slope failure due to rainfall. In this paper, the eŠects of various parameters, such as initial relative density and principal stress ratio, on the temporal development of deformation were examined. Tsuchida et al. (2002) proposed a new slip circle method with a slice method in order to address the challenge of how to determine the inter-slice forces. Jiang and Yamagami (2004) proposed a search procedure in

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order to locate 3D critical slip surfaces by combining dynamic programming with the column method from the Spencer safety factor equation for a 2D analysis. Cheng and Zhu (2004) developed a new uniˆed formulation of two dimensional limit equilibrium slope stability analysis method. Ye et al. (2005) proposed 2D and 3D soil-water coupled ˆnite element analysis based on a modiˆed elasto-plastic model with Matsuoka-Nakai failure criterion. The authors discussed the characteristics of slope failure using the proposed analysis method and investigated the eŠectiveness of this method in simulating the progressive failure of a slope. Moriguchi et al. (2005) developed a numerical method using the Constrained Interpolated Proˆle Scheme in order to predict large deformations associated with a geomaterial ‰ow during the occurrences of such geo-disasters as landslides and slope failures. The eŠect of vegetation on rainfall inˆltration into a slope and shear strength were discussed by some researchers. Ng and Zhan (2007) conducted a ˆeld monitoring on an unsaturated expansive soil slope in China in order to improve our understanding of the vegetation eŠect on rainfall inˆltration and on slope stability. Ali and Osman (2008) investigated the reinforcing eŠect of the soil-root matrix in the laboratory using a modiˆed large shear box apparatus. Their results indicated that shear strength was in‰uenced by the roof proˆle and, to some extent, the physiological parameters of the plants. CONCLUSIONS In this paper, we have brie‰y reviewed the state-of-theart research work on slope failure due to rainfall over the course of the last 50 years. Most of the reports referred to in this paper were published in Soils and Foundations (S&F). A look back over the research trends over this half century reinforced our belief that unsaturated soil mechanics is key to investigating the mechanism of rainfall-induced slope failure and also to predicting such failure. In our review of Soils and Foundations, Journal of Geotechnical, Geoenvironmental Engineering (ASCE), Geotechnique, and Canadian Geotechnical Journal, it is clear that the vast majority of studies into rainfall-induced slope failure have been focussed on unsaturated soil mechanics since the 1990s. Finally, the tendencies of the research on slope failure due to rainfall in Soils and Foundations is summarzed as follows. 1) A large number of studies of case studies of rainfallinduced slope failure were done in 2004 and 2005. In these studies, the mechanism of slope failures was discussed using ˆeld investigation results. 2) The decrease in shear strength of unsaturated soil with the increase in water content is one of the causes of rainfall-induced slope failure. Studies on the eŠect of the change in water content for shear strength of unsaturated Shirasu and Masa-soil were conducted during 1960s. However, most of the

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research on rainfall-induced slope failure taking unsaturated soil mechanics into consideration has been done since 1990. 3) Studies into critical rainfall prediction methods and statistical methods for estimating the risk of slope failure were developed during the 1990s. Only in the Journal of Soils and Foundations can these studies be found. 4) Computational engineering methods have been employed for practical geoengineering problems since the late 1960s. There were many studies of slope stability analysis with the Limit Equilibrium Method put forward during the 1960s. A large number of slope stability analyses were done to estimate the computational accuracy of the LEM in the 1970s. The Finite Element Analyses of slopes also became a regular feature of discussions into slope failure due to rainfall since the 1970s. In Japan, the studies into the probability of slope failure considering the the uncertainties of soil materials have been developed since the late 1970s. During the 1980s, many 3D slope stability analyses using the LEM and FEM were proposed. In the 1990s, there were more studies done combining an analysis of unsaturated soils and numerical solutions of combined seepage and deformation problems. At present, the trend appears to be the use of particle methods in order to simulate slope stability and the large deformation of slope. REFERENCES 1) Ali, F. H. and Osman, N. (2008): Shear strength of a soil containing vegetation roots, Soils and Foundations, 48(4), 587–596. 2) Alonso, E., Gens, A. and Delahaye, C. (1996): EŠect of rain inˆltration on the stability of slopes, Proc. 1st Int. Conf. on Unsaturated Soils, Unsat '95, 241–249. 3) Baker, R. and Leshchinsky, D. (1987): Stability analysis of conical heaps, Soils and Foundations, 27(4), 99–110. 4) Bergado, D. T. and Anderson, L. R. (1985): Stochastic analysis of pore pressure uncertainty for the probabilistic assessment of the safety of earth slopes, Soils and Foundations, 25(2), 87–105. 5) Bishop, A. W. (1955): The use of the slip circle in stability analysis of slopes, Geotechnique, 5, 7–17. 6) Bui, H. H., Sako, K. and Fukagawa, R. (2009): Slope stability analysis and slope failure simulation by SPH, 17th Int. Conference on Soil Mechanics and Geotechnical Engineering (ICSMGE), 1578–1581. 7) Chen, H., Lee, C. F. and Law, K. T. (2004): Causative mechanisms of rainfall-induced ˆll slope failures, ASCE Journal of Geotechnical and Geoenvironmental Engineering, 130(6), 593–602. 8) Chen, H. J. and Liu, S. H. (2007): Slope failure characteristics and stabilization methods, Canadian Geotechnical Journal, 44(4), 377–391. 9) Chen, W. F., Giger, M. W. and Fang, H. Y. (1969): On the limit analysis of stability of slopes, Soils and Foundations, 9(4), 23–32. 10) Chen, W. F. and Snitbhan, N. (1975): On slip surface and slope stability analysis, Soils and Foundations, 15(3), 41–49. 11) Cheng, Y. M. and Zhu, L. J. (2004): Uniˆed formulation for two dimensional slope stability analysis and limitations in factor of safety determination, Soils and Foundations, 44(6), 121–127. 12) Collins, B. D. and Znidarcic, D. (2004): Stability analyses of rainfall induced landslides, ASCE Journal of Geotechnical and Geoenvironmental Engineering, 130(4), 362–372.

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22(1), 109–115 (in Japanese). 91) Yasue, T. (1984): Reliability-based design for resistant force against slope failure, Domestic Edition of Soils and Foundations, 24(3), 168–176 (in Japanese). 92) Ye, G., Zhang, F., Yashima, A., Sumi, T. and Ikemura, T. (2005): Numerical analyses on progressive failure of slope due to heavy rain with 2D and 3D FEM, Soils and Foundations, 45(2), 1–15. 93) Yoshida, S. (1974): The force of percolation water through porous media, Domestic Edition of Soils and Foundations, 14(1), 89–94 (in Japanese). 94) Zhan, T. L. T., Ng, C. W. W. and Fredlund, D. G. (2007): Field study of rainfall inˆltration into a grassed unsaturated expansive soil slope, Canadian Geotechnical Journal, 44(4), 392–408. 95) Zhang, L. L., Fredlund, D. G., Zhang, L. M. and Tang, W. H. (2004): Numerical study of soil conditions under which matric suction can be maintained. Canadian Geotechnical Journal, 41(4), 569–582. 96) Zhang, L. L., Zhang, L. M. and Tang, W. H. (2005): Rainfall-induced slope failure considering variability of soil properties, Geotechnique, 55(2), 183–188. 97) Zhang, L. M. and Chen, Q. (2006): Seepage failure mechanism of the Gouhou rockˆll dam during reservoir water inˆltration, Soils and Foundations, 46(5), 557–568. 98) Zhang, S. and Chowdhury, R. N. (1995): Interslice shear forces in slope stability analysis—A new approach—, Soils and Foundations, 35(1), 65–74.