Infinite Slope Stability Research Articles

Lateral strength and critical depth in infinite slope stability analysis

Infinite slope (IS) method is the simplest limit equilibrium method for slope stability analysis. It gives reliable results for slides where the longitudinal dimension prevails on the depth of the landslide. Usually results are conservative since ignoring the effects of the strength along lateral bounds. Here, starting from the assumption of considering the effects of the shear strength along lateral bounds by a rectangular cross section, a new expression of the safety factor is investigated, based first on an elliptical and then on a parabolic cross section of the landslide mass. The safety factor evaluated in this way can be quite different from those returned by the classic formula of IS model, in particular when the width of the landslide is narrow with respect to its depth and the ratio between the width and the depth of the landslide is lower than 5. An interesting implication of the proposed model is that if cohesion differs from zero, there is a ‘critical depth’, where the safety factor has a minimum value. Copyright © 2013 John Wiley & Sons, Ltd.

GIS기반 토석류 산사태 대응공법 설계 프로그램 개발

We developed a computer program (CDFlow v. 1.0) to design countermeasures against debris flows in natural terrain. The program can predict the probability of landslides occurring in natural terrain and can estimate the zone of damage caused by a debris flow. It can also be used to design the location and size of countermeasures against the debris flow. The program is run using the ArcGIS Engine, which is one of the most well-known Geographic Information System (GIS) tools for developers. The quasi-dynamic wetness index and the infinite slope stability equation were applied to predict landslide probability as a type of slope safety factor. The calculated safety factor was compared with the required safety factor, and areas of high probable potential for landslides were then selected and represented on the digital map. The volume of debris flow was estimated using these areas of high probable potential for landslides and soil depth. The accumulated volume of debris flow can be calculated along the flow channel. To assess the accuracy of the program, it was applied to a real landslide site at Deoksan-ri, Inje-gun, Kangwon-Province, where four debris barriers have been installed in the watershed of the site. The results of soil tests and a field survey indicate that the program has great potential for estimating probable landslide areas and the trajectory of debris flows. Calculation of the capacity volume of existing debris barriers revealed that they had insufficient capacity to store the calculated amount of debris flow. Therefore, this program enables a rational estimation of the optimal location and size of debris barriers.

Landslide model performance in a high resolution small-scale landscape

The frequency and severity of shallow landslides in New Zealand threatens life and property, both on- and off-site. The physically-based shallow landslide model LAPSUS-LS is tested for its performance in simulating shallow landslide locations induced by a high intensity rain event in a small-scale landscape. Furthermore, the effect of high resolution digital elevation models on the performance was tested. The performance of the model was optimised by calibrating different parameter values. A satisfactory result was achieved with a high resolution (1m) DEM. Landslides, however, were generally predicted lower on the slope than mapped erosion scars. This discrepancy could be due to i) inaccuracies in the DEM or in other model input data such as soil strength properties; ii) relevant processes for this environmental context that are not included in the model; or iii) the limited validity of the infinite length assumption in the infinite slope stability model embedded in the LAPSUS-LS. The trade-off between a correct prediction of landslides versus stable cells becomes increasingly worse with coarser resolutions; and model performance decreases mainly due to altering slope characteristics. The optimal parameter combinations differ per resolution. In this environmental context the 1m resolution topography resembles actual topography most closely and landslide locations are better distinguished from stable areas than for coarser resolutions. More gain in model performance could be achieved by adding landslide process complexities and parameter heterogeneity of the catchment.

Role of Vegetation on Slope Stability under Transient Unsaturated Conditions

We examine the role of vegetation on the stability of shallow soils under unsaturated transient regime. Two main positive effects of the vegetation on slope stability are discussed: i) a geo-mechanical effect, i.e., the reinforcement of soil by plant roots; ii) a soil-hydrological effect, i.e., the soil suction regime affected by root water uptake. The root distribution is assessed by an eco-hydrological model, which predicts the root density as function of local climatic conditions in growing season and soil hydrological properties. The predicted root distribution is employed for assessing the vertical variability of both the apparent soil cohesion provided by roots and the root water uptake. A one-dimensional model of vertical soil water dynamics is employed for simulating soil suction regime, assumed representative of well-drained soils on steep forested plane slopes. The geo-mechanical and the soil-hydrological effects on slope stability are examined with an infinite slope stability model, generalized for unsaturated conditions. We show that in the case of a loamy-sand soil under a Mediterranean climatic regime, the geo-mechanical effect tends to be more relevant than the soil-hydrological effect during the rainy season, within depths up to twice the average root depth.

Physically-based approach to analyze rainfall-triggered landslide using hydraulic gradient as slide direction

An infinite slope stability numerical model driven by the comprehensive physically-based integrated hydrology model (InHM) is presented. In this approach, the failure plane is assumed to be parallel to the hydraulic gradient instead of the slope surface. The method helps with irregularities in complex terrain since depressions and flat areas are allowed in the model. The present model has been tested for two synthetic single slopes and a small catchment in the Mettman Ridge study area in Oregon, United States, to estimate the shallow landslide susceptibility. The results show that the present approach can reduce the simulation error of hydrological factors caused by the rolling topography and depressions, and is capable of estimating spatial-temporal variations for landslide susceptibilities at simple slopes as well as at catchment scale, providing a valuable tool for the prediction of shallow landslides.

Modelling shallow landslide susceptibility by means of a subsurface flow path connectivity index and estimates of soil depth spatial distribution

Abstract. Topographic index-based hydrological models have gained wide use to describe the hydrological control on the triggering of rainfall-induced shallow landslides at the catchment scale. A common assumption in these models is that a spatially continuous water table occurs simultaneously across the catchment. However, during a rainfall event isolated patches of subsurface saturation form above an impeding layer and their hydrological connectivity is a necessary condition for lateral flow initiation at a point on the hillslope. Here, a new hydrological model is presented, which allows us to account for the concept of hydrological connectivity while keeping the simplicity of the topographic index approach. A dynamic topographic index is used to describe the transient lateral flow that is established at a hillslope element when the rainfall amount exceeds a threshold value allowing for (a) development of a perched water table above an impeding layer, and (b) hydrological connectivity between the hillslope element and its own upslope contributing area. A spatially variable soil depth is the main control of hydrological connectivity in the model. The hydrological model is coupled with the infinite slope stability model and with a scaling model for the rainfall frequency–duration relationship to determine the return period of the critical rainfall needed to cause instability on three catchments located in the Italian Alps, where a survey of soil depth spatial distribution is available. The model is compared with a quasi-dynamic model in which the dynamic nature of the hydrological connectivity is neglected. The results show a better performance of the new model in predicting observed shallow landslides, implying that soil depth spatial variability and connectivity bear a significant control on shallow landsliding.

비 집수면적 산정기법에 따른 사면 안정성 비교·분석

최근 기후변화에 따른 집중호우의 증가 및 무분별한 유역개발에 의한 산사태 발생빈도 및 재해복구비용이 증가하고 있는 추세이다. 본 연구에서는 2011년 7월에 발생한 서울시 우면산 지역을 대상으로 뿌리 점착력을 고려한 GIS기반의 무한사면안정모형을 이용하여 사면안정해석을 수행하였다. 무한사면안정모형의 중요 매개변수인 습윤지수의 공간분포화를 위해 비 집수면적 개념을 도입하였으며, 세가지 기법(일방향 흐름기법, 다방향 흐름기법, 무한방향 흐름기법)를 이용하여 비 집수면적을 산정하고, 각 기법에 따른 대상유역내의 격자별 사면안전율의 변화양상을 분석하였다. 또한, 기존의 무한사면안정모형을 이용한 사면안정 해석에 일반적으로 적용되고 있는 공간집중형 습윤지수 결과와의 비교를 통하여 우면산 지역의 사면안정 해석의 차이점을 비교 분석하였다. 무한사면안정모형을 이용하여 산정된 사면안전율 분석결과, 거주지 주변의 절개지 부근과 산지정상부근의 급경사지에서 불안정 지역이 집중적으로 분포하고 있음을 확인하였으며, IFD와 집중형 습윤지수에 의한 불안정지역은 유사하게 나타난 반면, SFD와 MFD에 의한 불안정지역은 앞선 두 가지기법에 비해 작게 산정되었다. There has been an increase for the landslide areas and restoration expenses due, in large part, to the increased locally heavy rains caused by recent climate change as well as the reckless development. This study carried out a slope stability analysis by the application of distributed wetness index, using the GIS-based infinite slope stability model, which took the root cohesion effect into consideration, for part of Mt. Umyeon in Seoul, where landslide occurred in July 2011, in order to compensate the defects of existing analysis method, and subsequently compared its result with the case on the exploitation of lumped wetness index. In addition, this study estimated the distributed wetness index by methodology, applying three methods of specific catchment area calculation: single flow direction (SFD), multiple flow direction (MFD), and infinity flow direction (IFD), for catchment area, one of the variables of distributed wetness indices, and finally implemented a series of comparative analysis for slope stability by methodology. The simulation results showed that most unstable areas within the study site were dominantly located in cutting-area surroundings along with the residential area and the mountaintop and unstable areas of IFD and lumped wetness index method were similar while SFD and MFD provided smaller unstable areas than the two former methods.

Modeling of layered infinite slope failure triggered by rainfall

The infinite slope is typically regarded as composed of a single-layered soil with a uniform property in various physical-based models used for modeling rainfall-induced shallow landslides. This study extends the physical-based model to consider the layered infinite slope to examine the importance of soil layer distribution for rainfall-induced shallow landslides. Hypothetical scenarios of infinite slope composed of soil layers with different thicknesses and parameters are employed to conduct this examination. The results show that pressure heads caused by rainfall infiltration are strongly related to soil layer distribution. This shows the significant influence of soil layer distribution in assessing infinite slope stability. Failure of a layered infinite slope does not necessarily occur at the impervious bottom of the hillslope soil, but may also occur at the interface between two soil layers. This result shows that a neglect of soil layer distribution could misestimate failure depth. Hence, soil layer distribution must be considered to reliably analyze infinite slope failure induced by rainfall.

An analytical solution for rainfall infiltration into an unsaturated infinite slope and its application to slope stability analysis

SUMMARYSurficial slope failures in residual soils are common in tropical and subtropical regions as a result of rainfall infiltration. This study develops an analytical solution for simulating rainfall infiltration into an infinite unsaturated soil slope. The analytical solution is based on the general partial differential equation for water flow through unsaturated soils. It can accept soil–water characteristic curve and unsaturated permeability function of the exponential form into account. Numerical simulations are conducted to verify the assumptions of the analytical solution and demonstrate that the proposed analytical solution is acceptable for the coarse soils with low air entry values. The pore‐water pressure (pwp) distributions obtained from the analytical solution can be incorporated into a limit equilibrium method to do infinite slope stability analysis for a rain‐induced shallow slip. The analysis method takes into account the influence of the water content change on unit weight and hence on factor of safety. A series of analytical parametric analyses have been performed using the developed model. The analyses indicate that when the residual soil slope, consisting of a completely decomposed granite layer underlain by a less permeable layer, is subjected to a continuous heavy rainfall, the loss of negative pwp and the reduction in factor of safety were found to be most significant for the shallow soil layer and during the first 12 h. The antecedent and subsequent rainfall intensity, depth of a less permeable layer and slope angle all have a significant influence on the pwp response and hence the slope stability. Copyright © 2012 John Wiley & Sons, Ltd.

Stability of infinite slopes under transient partially saturated seepage conditions

Prediction of the location and timing of rainfall‐induced shallow landslides is desired by organizations responsible for hazard management and warnings. However, hydrologic and mechanical processes in the vadose zone complicate such predictions. Infiltrating rainfall must typically pass through an unsaturated layer before reaching the irregular and usually discontinuous shallow water table. This process is dynamic and a function of precipitation intensity and duration, the initial moisture conditions and hydrologic properties of the hillside materials, and the geometry, stratigraphy, and vegetation of the hillslope. As a result, pore water pressures, volumetric water content, effective stress, and thus the propensity for landsliding vary over seasonal and shorter time scales. We apply a general framework for assessing the stability of infinite slopes under transient variably saturated conditions. The framework includes profiles of pressure head and volumetric water content combined with a general effective stress for slope stability analysis. The general effective stress, or suction stress, provides a means for rigorous quantification of stress changes due to rainfall and infiltration and thus the analysis of slope stability over the range of volumetric water contents and pressure heads relevant to shallow landslide initiation. We present results using an analytical solution for transient infiltration for a range of soil texture and hydrological properties typical of landslide‐prone hillslopes and show the effect of these properties on the timing and depth of slope failure. We follow by analyzing field‐monitoring data acquired prior to shallow landslide failure of a hillside near Seattle, Washington, and show that the timing of the slide was predictable using measured pressure head and volumetric water content and show how the approach can be used in a forward manner using a numerical model for transient infiltration.

Reliability assessment of infinite slope stability using the jointly distributed random variables method

Slope stability analysis is a branch of geotechnical engineering that is highly amenable to probabilistic treatment. Probabilistic analysis of slope stability has received considerable attention in the literature, and has been used as an effective tool to evaluate uncertainty that is so prevalent in variables. In this research, the jointly distributed random variables method is used for probabilistic analysis and reliability assessment of the stability of infinite slopes without seepage. The selected stochastic parameters are internal friction angle, cohesion and unit weight, which are modeled using a truncated normal probability distribution function. The geometric parameters, such as height of slope and angle of slope relative to horizontal, are regarded as constant parameters. The results are compared with the Monte Carlo, Point Estimated, and First Order Second Moment methods. Comparison of the results indicates the superior performance of the proposed approach for assessment of reliability.

Limits on the validity of infinite length assumptions for modelling shallow landslides

ABSTRACTThe infinite slope method is widely used as the geotechnical component of geomorphic and landscape evolution models. Its assumption that shallow landslides are infinitely long (in a downslope direction) is usually considered valid for natural landslides on the basis that they are generally long relative to their depth. However, this is rarely justified, because the critical length/depth (L/H) ratio below which edge effects become important is unknown. We establish this critical L/H ratio by benchmarking infinite slope stability predictions against finite element predictions for a set of synthetic two‐dimensional slopes, assuming that the difference between the predictions is due to error in the infinite slope method. We test the infinite slope method for six different L/H ratios to find the critical ratio at which its predictions fall within 5% of those from the finite element method. We repeat these tests for 5000 synthetic slopes with a range of failure plane depths, pore water pressures, friction angles, soil cohesions, soil unit weights and slope angles characteristic of natural slopes. We find that: (1) infinite slope stability predictions are consistently too conservative for small L/H ratios; (2) the predictions always converge to within 5% of the finite element benchmarks by a L/H ratio of 25 (i.e. the infinite slope assumption is reasonable for landslides 25 times longer than they are deep); but (3) they can converge at much lower ratios depending on slope properties, particularly for low cohesion soils. The implication for catchment scale stability models is that the infinite length assumption is reasonable if their grid resolution is coarse (e.g. >25 m). However, it may also be valid even at much finer grid resolutions (e.g. 1 m), because spatial organization in the predicted pore water pressure field reduces the probability of short landslides and minimizes the risk that predicted landslides will have L/H ratios less than 25. Copyright © 2012 John Wiley & Sons, Ltd.

확률론적 해석기법을 이용한 보은지역의 사면재해 안정성분석

본 연구는 사면재해 취약성 평가를 위해 사면모델 중 하나인 무한사면 해석모델을 적용하였다. 그러나 무한사면 해석모델은 광역적인 연구지역에 적용하는데 있어서 데이터획득 및 처리과정에 어려움이 있고 데이터 획득과정에서 불가피하게 불확실성이 개입되는 문제가 있다. 이러한 불확실성을 최소화하기 위해 확률론적 해석기법인 몬테카를로 시뮬레이션을 적용하였으며, 광역적인 연구지역에 무한사면 해석모델을 적용하기 위하여 GIS를 활용한 무한사면 안정해석법으로 파괴확률을 획득하였다. 연구지역으로는 사면재해가 집중적으로 발생한 보은지역을 선정하였고 사면의 기하학적인 특성과 점착력 및 내부마찰각 등의 강도정수를 획득하였다. 또한 불확실성의 효과를 평가하기 위해 강도정수의 변동계수를 10%에서 30%로 고려하였고 이러한 과정을 통하여 확률론적 해석기법은 자료의 불확실성을 감쇠시킬 수 있다는 결과를 도출하였다. In this study the infinite slope model, one of the physical landslide models has been suggested to evaluate the susceptibility of the landslide. However, applying the infinite slope model in regional study area can be difficult or impossible because of the difficulties in obtaining and processing of large spatial data sets. With limited site investigation data, uncertainties were inevitably involved with. Therefore, the probabilistic analysis method such as Monte Carlo simulation and the GIS based infinite slope stability model have been used to evaluate the probability of failure. The proposed approach has been applied to practical example. The study area in Boeun area been selected since the area has been experienced tremendous amount of landslide occurrence. The geometric characteristics of the slope and the mechanical properties of soils like to friction angle and cohesion were obtained. In addition, coefficient of variation (COV) values in the uncertain parameters were varied from 10% to 30% in order to evaluate the effect of the uncertainty. The analysis results showed that the probabilistic analysis method can reduce the effect of uncertainty involved in input parameters.

Estimating the effects of heavy rainfall conditions on shallow landslides using a distributed landslide conceptual model

This study used a distributed landslide conceptual model to examine the effects of variable, heavy-rainfall conditions on shallow landslides. A digital terrain model with 50-m resolution was used to calculate the regional potential for shallow landslides based on the distribution of shallow infiltration water, Darcy’s law, and a safety factor estimated by infinite slope stability analysis. The model was applied to the upper Miyagawa River basin at Odai-cho in Mie Prefecture, Japan. In 2004, Typhoon Meari caused severe landslides in areas adjacent to the study area, whereas other heavy-rainfall events in the same year did not cause severe landslides. Response analysis of data collected hourly during heavy-rainfall events revealed that temporal changes in shallow landslide potentials were influenced by both temporal rainfall patterns and effective soil cohesion. Two indices obtained from the model were found to be useful for discriminating between rainstorms with and without sediment-related disasters.

Mapping basin-wide subaquatic slope failure susceptibility as a tool to assess regional seismic and tsunami hazards

This study of subaquatic slope failures in Lake Lucerne, central Switzerland, presents a new concept for evaluating basin-wide slope stability through time as a potential tool for regional seismic and tsunami hazard assessments. Previously acquired high-resolution bathymetry and reflection seismic data, as well as sedimentological and in situ geotechnical data, provide a comprehensive data base to use this lake as a “model basin” to investigate subaquatic landslides and related geohazards. Available data are implemented into a basin-wide slope model. In a Geographic Information System (GIS)-framework, a pseudo-static limit equilibrium infinite slope stability equation is solved for each model point representing reconstructed slope conditions at different times in the past, during which earthquake-triggered landslides occurred. Comparison of reconstructed critical stability conditions with the known distribution of landslide deposits reveals minimum and maximum threshold conditions for slopes that failed or remained stable, respectively. The resulting correlations reveal good agreements and suggest that the slope stability model generally succeeds in reproducing past events. The basin-wide mapping of subaquatic slope failure susceptibility through time thus can also be considered as a promising paleoseismologic tool. Furthermore, it can be used to assess the present-day slope failure susceptibility, allowing for identification of location and estimation of size of future, potentially tsunamigenic subaquatic landslides.

A distributed hydrological–geotechnical model using satellite-derived rainfall estimates for shallow landslide prediction system at a catchment scale

This paper describes the potential applicability of a hydrological–geotechnical modeling system using satellite-based rainfall estimates for a shallow landslide prediction system. The physically based distributed model has been developed by integrating a grid-based distributed kinematic wave rainfall-runoff model with an infinite slope stability approach. The model was forced by the satellite-based near real-time half-hourly CMORPH global rainfall product prepared by NOAA-CPC. The method combines the following two model outputs necessary for identifying where and when shallow landslides may potentially occur in the catchment: (1) the time-invariant spatial distribution of areas susceptible to slope instability map, for which the river catchment is divided into stability classes according to the critical relative soil saturation; this output is designed to portray the effect of quasi-static land surface variables and soil strength properties on slope instability and (2) a produced map linked with spatiotemporally varying hydrologic properties to provide a time-varying estimate of susceptibility to slope movement in response to rainfall. The proposed hydrological model predicts the dynamic of soil saturation in each grid element. The stored water in each grid element is then used for updating the relative soil saturation and analyzing the slope stability. A grid of slope is defined to be unstable when the relative soil saturation becomes higher than the critical level and is the basis for issuing a shallow landslide warning. The method was applied to past landslides in the upper Citarum River catchment (2,310 km2), Indonesia; the resulting time-invariant landslide susceptibility map shows good agreement with the spatial patterns of documented historical landslides (1985–2008). Application of the model to two recent shallow landslides shows that the model can successfully predict the effect of rainfall movement and intensity on the spatiotemporal dynamic of hydrological variables that trigger shallow landslides. Several hours before the landslides, the model predicted unstable conditions in some grids over and near the grids at which the actual shallow landslides occurred. Overall, the results demonstrate the potential applicability of the modeling system for shallow landslide disaster predictions and warnings.

Rainfall infiltration: infinite slope model for landslides triggering by rainstorm

Shallow slope failure due to heavy rainfall during rainstorm and typhoon is common in mountain areas. Among the models used for analyzing the slope stability, the rainwater infiltration model integrated with slope stability model can be an effective way to evaluate the stability of slopes during rainstorm. This paper will propose an integrated Green-Ampt infiltration model and infinite slope stability model for the analysis of shallow type slope failure. To verify the suitability of the proposed model, seven landslide cases occurred in Italy and Hong Kong are adopted in this paper. The results indicate that the proposed model can be used to distinguish failed and not-yet failed slopes. In addition, the proposed model can be used as the first approximation for estimating the occurrence time of a rainfall-induced shallow landslide and its depth of sliding.

Impacts of Unsaturated Zone Soil Moisture and Groundwater Table on Slope Instability

The combined effect of soil moisture in unsaturated soil layers and pore-water pressure in saturated soil layers is critical to predict landslides. An improved infinite slope stability model, that directly includes unsaturated zone soil moisture and groundwater, is derived and used to analyze the factor of safety’s sensitivity to unsaturated zone soil moisture. This sensitivity, the change in the factor of safety with respect to variable unsaturated zone soil moisture, was studied at local and regional scales using an active landslide region as a case study. Factors of safety have the greatest sensitivity to unsaturated zone soil moisture dynamics for shallow soil layers (<2 m) and comparatively deep groundwater tables (1 m). For an identical groundwater table, the factor of safety for a 1 m thick soil mantle was four times more sensitive to soil moisture changes than a 3-m thick soil. At a regional scale, the number of unstable areas increases nonlinearly with increasing unsaturated zone soil moisture and with moderately wet slopes exhibiting the greatest sensitivity.

Unsaturated Infinite Slope Stability Considering Surface Flux Conditions

A slope stability model is derived for an infinite slope subjected to unsaturated infiltration flow above a phreatic surface. Closed form steady state solutions are derived for the matric suction and degree of saturation profiles. Soil unit weight, consistent with the degree of saturation profile, is also directly calculated and introduced into the analyzes, resulting in closed-form solutions for typical soil parameters and an infinite series solution for arbitrary soil parameters. The solutions are coupled with the infinite slope stability equations to establish a fully realized safety factor function. In general, consideration of soil suction results in higher factor of safety. The increase in shear strength due to the inclusion of soil suction is analogous to making an addition to the cohesion, which, of course, increases the factor of safety against sliding. However, for cohesive soils, the results show lower safety factors for slip surfaces approaching the phreatic surface compared to those produced by common safety factor calculations. The lower factor of safety is due to the increased soil unit weight considered in the matric suction model but not usually accounted for in practice wherein the soil is treated as dry above the phreatic surface. The developed model is verified with a published case study, correctly predicting stability under dry conditions and correctly predicting failure for a particular storm.

Effects of degree of saturation on shallow landslides triggered by rainfall

The empirical rainfall threshold concept and the physical-based model are two commonly used approaches for the assessment of shallow landslides triggered by rainfall. To investigate in detail the rainfall-triggered shallow landslides, many physical-based models coupling the infinite slope stability analysis with the rainfall infiltration modeling in variably saturated soil were developed. However, in those physical-based shallow landslide models, the unit weight and the unsaturated shear strength were assumed constant rather than depending on the degree of saturation. In this study, the effects of the unit weight and the unsaturated shear strength as function of degree of saturation on rainfall-triggered shallow landslides are examined. Several designed scenarios and a real case scenario are used to conduct the examinations. The results show that not only the occurrence of shallow landslides but also the failure depth and the time to failure could be misassessed if the influences of degree of saturation on the unit weight and the unsaturated shear strength are neglected.