Probabilistic Slope Stability Analysis Research Articles

Fragility curves for rainfall-induced shallow landslides on transport networks

Many of the earthworks assets on rail transport networks were constructed in the 1800s and have thus operated for periods far in excess of their expected service life. Incidences of failure — particularly shallow planar landslides — are increasing, in part due to the effect of more intense and longer duration rainfall events. Network owners have difficulty in targeting scarce resources to reduce risk across networks. This paper proposes a methodology for developing fragility curves for rainfall-induced landslides on transport networks. Fragility curves provide the probability of exceedance of different limit states for a given hazard considering a range of magnitudes. In this paper, the vulnerability of slopes as expressed by a loss of performance is quantified for rainfall events of various intensities and duration. The approach expands upon probabilistic slope stability analysis and provides a rational logical framework for considering how vulnerable a slope is to rainfall-induced failure.

Probabilistic stability analysis of an earth dam by Stochastic Finite Element Method based on field data

This paper performs a probabilistic stability analysis for an existing earthfill dam using a Stochastic Finite Element Method (SFEM) and considering the spatial variability of soil properties based on field data. Previous works on probabilistic slope stability analysis are generally based on hypothetical data while using data from existing earth structures is not widespread.A probabilistic procedure based on field data is here implemented to analyze the stability of an existing embankment dam. The spatial variability of several soil properties is modeled from the geostatistical analysis of the available dataset of the dam studied. Random variables and random fields representing the variability of dam materials are integrated into an FE model by performing Monte Carlo simulations (MCS). This probabilistic analysis based on field data allowed to characterize the variability of the sliding safety factor for the case study of an existing dam.

System reliability analysis of soil slopes stabilized with piles

Piles are widely used to increase the stability of piles. Probabilistic methods can be used to explicitly consider the uncertainties involved in a slope stability analysis. Currently, most probabilistic slope stability analyses focus on the reliability of slopes without reinforcement. In this paper, an existing method for system reliability analysis of unreinforced slopes is extended to slopes reinforced with piles. The described procedure may potentially be used to convert other methods for reliability analysis of slopes without reinforcement to slopes reinforced with piles. Two examples are used to illustrate the suggested method. It is found that the location of the most critical slip surface of the reinforced slope generally differs from that of the unreinforced slope, and may change with the pile location and the pile spacing. The optimal locations of the piles with and without considering the uncertainties in the soil property are different. For slopes in layered soils, the system failure probability may be governed by several representative slip surfaces even when piles are installed. The system effect is more obvious when the pile spacing increases. To maximize the effectiveness of slope stabilization, the stabilizing piles should intersect with all representative slip surfaces with significant failure probabilities.

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This work focuses on the probabilistic analysis of slope stability and rigid shallow footing problems. For this purpose, mathematical models based on the Finite Element Method (FEM), Montecarlo (MC) method and Local Average Subdivision (LAS) procedure are studied. The LAS procedure is used to generate random fields, which properly represent the associated uncertainties in the properties of the materials. The FEM focuses on the numerical response of the problem in terms of displacements and stresses. The plasticity of the soil can be included via a visco-plastic algorithm beside a Mohr-Coulomb law. The LAS and MEF procedures are implemented in the framework of a MC analysis, where each MC execution requires several simulations of the problem at hand. This permits to quantify the failure probability of the system and report the most probable settlement to occur in the case of shallow foundations. After many executions of the numerical model, it is suggested that at least 4000 and 500 simulations are needed for the slope stability and shallow foundation problems, respectively, in order to obtain stable and reliable values. The obtained results show that the failure probability of the slope is relatively low and equal to 0.18, while the expected settlement of a shallow rigid foundation is around 1.96 cm.

Deterministic and probabilistic failure analysis of simple geosynthetic reinforced soil slopes

Reinforced slopes with horizontal layers of geosynthetic reinforcement can have different mechanisms of failure. In this paper two major mechanisms of failure of reinforced slopes are investigated. External mechanisms occur when the critical slip surface passes beyond the reinforced zone. Internal mechanisms are characterised by failure surfaces that intersect all of the reinforcement layers. For a target value of the factor of safety and a specific value of the reinforcement length, there is a minimum value of the reinforcement tensile strength that will generate only external mechanism types. For greater reinforcement strength values, there is no change in the mechanism of failure and the value of the factor of safety. On the other hand, increasing the minimum reinforcement length, while keeping the reinforcement tensile strength equal to or less than the minimum value obtained for an external failure mechanism, will generate an internal mechanism type with the same mean value of factor of safety. In this study, probabilistic slope stability analysis of these two mechanisms is carried out using Monte Carlo simulation of slopes with different purely frictional and cohesive-frictional (c − ϕ) soils and different slope angles. Margins of safety are expressed in terms of a conventional factor of safety and in terms of maximum probability of failure. Cross correlation between soil strength parameters is also considered in this paper. It is shown that considering practical values of cross correlation coefficient reduces the maximum probability of failure for both internal and external failure mechanisms.

Identification of representative slip surfaces for reliability analysis of soil slopes based on shear strength reduction

Although a slope may have numerous potential slip surfaces, its failure probability is often governed by several representative slip surfaces (RSSs). Previous efforts mainly focus on the identification of circular RSSs based on limit equilibrium methods. In this paper, a method is suggested to identify RSSs of arbitrary shape based on the shear strength reduction method. Monte Carlo simulation is used to generate a large number potential slip surfaces. The RSSs are identified through analyzing the failure domains represented by these samples. A kriging-based response surface model is employed to enhance the computational efficiency. These examples shows that the RSSs may not always be circular, and that the suggested method can effectively locate the RSSs without making prior assumptions about the shape of the slip surfaces. For the examples investigated, the system failure probabilities computed based on the shear strength reduction method are comparable to, but not the same as those computed based on the limit equilibrium methods. The suggested method significantly extends our capability for identifying non-circular RSSs and hence probabilistic slope stability analysis involving non-circular slip surfaces.

APPLICATION OF THE PROBABILISTIC SLOPE STABILITY ANALYSIS

Slope stability analysis in the middle part of the Mzymta-river valley was implemented. Several approaches were used to solve this problem. The first — traditional — is based on average value of the properties of soils. The second approach presents probabilistic slope stability analysis based on probabilistic distribution functions of the factors of landslide activity. It’s shown that the results of the probabilistic slope stability analysis agreed better with field observations. This type of analysis was added by sensitivity slope stability analysis, which is oriented on the dependence of the safety factor from the variability of parameters of landslide activity.

A Study on Landslide Risk Management by Applying Fault Tree Logics

Slope stability is one of the focal areas of curiosity to geotechnical designers and also appears logical for the application of probabilistic approaches since the analysis lead to a “probability of failure”. Assessment of the existing slopes in relation with risks seems to be more meaningful when concerning with landslides. Probabilistic slope stability analysis (PSSA) is the best option in covering the landslides events. The intent here is to bid a probabilistic framework for quantified risk analysis with human uncertainties. In this regard, Fault Tree Analysis is utilized and for prediction of risk levels, consequences of the failures of the reference landslides have been taken. It is concluded that logics of fault trees is best fit, to clinch additional categories of uncertainty; like human, organizational, and knowledge related. In actual, the approach has been used in bringing together engineering and management performances and personnel, to produce reliability in slope engineering practices.

CST-based first order second moment method for probabilistic slope stability analysis

Correlated random variables are commonly involved in probabilistic slope stability analysis, such as reliability analysis of slopes with spatially variable soil properties. This paper proposes a simple Correlated Sampling Technique (CST) for generating samples of correlated random variables. The CST firstly produces correlated standard-normally distributed samples through linear combinations of independent standard-normally distributed samples. Correlated arbitrarily distributed samples can then be obtained by the Nataf transformation. The CST was combined with FOSM (named CST-based FOSM) for probabilistic slope stability analysis. The slope reliabilities of a single-layered cohesive soil slope and a high earth and rockfill dam were analyzed to illustrate the CST-based FOSM. These illustrative examples indicated that the CST-based FOSM can accurately estimate the slope reliability indices with considerably fewer simulations (especially in the case of low failure probability) compared with direct MCS, and the slope reliability was sensitive to the correlation of the strength parameters.

Sensitivity Study of Local Average Size on the Failure Probability of Spatially Variable Slope Stability

This paper explores the influence of local average size, Δz, on the failure probability, pf, of spatially variable slope failure along a given slip surface and along a combination of two slip surfaces. The spatial variability of statistical geotechnical property with depth is modeled by a lognormal random field with an exponentially decaying correlation structure. The probabilistic slope stability analysis incorporating random field theory with Monte Carlo simulation is adopted to conduct the sensitivity study. The variance reduction due to local averaging and the correlations between local averages are considered (denoted M1), and a simplified approach (denoted M2) neglecting the variance reduction and simulating correlations between local averages at the mid-points of local averages is compared with M1. The results of sensitivity study on an undrained slope have shown that the influence of Δz on pf of slope failure along a given slip surface hinges on the given slip surface. As the ratio of Δz to the scale of fluctuation, λ, varies in the range of 0.0 to 0.4, M1 and M2 can predict the results within 10% normalized discrepancy for the pf of slope failure along a given slip surface. As Δz/λ is greater than 0.4, the performance of M1 is superior to that of M2. As Δz increases, a larger value of Δz cannot identify the additional contribution to pf if slope failure along more than one slip surface is taken into account.

Probabilistic stability analysis of simple reinforced slopes by finite element method

Probabilistic slope stability analyses of simple geosynthetic reinforced soil slopes were carried out using the shear strength reduction method in combination with the finite element method (FEM). An existing open-source FEM code was modified to include bar elements to model horizontal layers of geosynthetic reinforcement. Analysis results using the modified code (mFEM) demonstrate that large reductions in probability of failure can be realized by adding geosynthetic reinforcement layers to constructed slopes. The modified code was also used to investigate the effect of variability of soil friction angle on probabilistic outcomes for constructed unreinforced and reinforced purely frictional soil slopes.

Shear band propagation analysis of submarine slope stability

The paper summarises recent developments in the shear band propagation approach, which enables simplified submarine slope stability analysis to account for catastrophic and progressive failure. This approach covers a wide variety of potential failure mechanisms, such as slab failures, spreadings, ploughings and run-outs, and provides analytical energy balance criteria for predicting their occurrence. The simple form of the resulting criteria enabled their incorporation into deterministic and probabilistic slope stability analysis of offshore developments within the geographical information system. In contrast to conventional limiting equilibrium approaches used in such analysis, the shear band propagation approach is capable of explaining enormous dimensions of observed palaeo-landslides and predicting annual probabilities of failure that are orders of magnitude higher, as validated by reconstructed historical frequencies.

Multi-modal Reliability Analysis of Slope Stability

Probabilistic slope stability analysis typically requires an optimisation technique to locate the most probable slip surface. However, for many slopes particularly those containing many different soil layers or benches several distinct critical slip surfaces may exist. Furthermore, in large slopes these critical slip surfaces may be located at significant distances from each other. In such circumstances, finding and rehabilitating the most probable failure surface is of little merit, as rehabilitating that surface does not improve the safety of the slope as a whole. Unfortunately, existing slip surface search techniques were developed to converge on one global minimum. Therefore, to implement such methods to evaluate the stability of a slope with multiple failure mechanisms requires the user to define probable slip locations prior to calculation. This requires extensive engineering experience and places undue responsibility on the engineer in question. This paper proposes the use of a locally informed particle swarm optimisation method which is able to simultaneously converge to multiple critical slip surfaces. This optimisation model when combined with a reliability analysis is able to define all areas of concern within a slope. A case study of a railway slope is presented which highlights the benefits of the model over single objective optimisation models. The approach is of particular benefit when evaluating the stability of large existing slopes with complicated stratigraphy as these slopes are likely to contain multiple viable slip surfaces.

AN ANALYTICAL SOLUTION FOR RELIABILITY ASSESSMENT OF PSEUDO-STATIC STABILITY OF ROCK SLOPES USING JOINTLY DISTRIBUTED RANDOM VARIABLES METHOD

Reliability analysis of rock slope stability has received considerable attention in the literature. It has been used as an effective tool to evaluate uncertainty so prevalent in variables. In this research the application of the jointly distributed random variables method for probabilistic analysis and reliability assessment of rock slope stability with plane sliding is investigated. In a recently published paper, the authors showed the dependency of the numerator and denominator of the safety factor relationship and argued that, as a result of this dependency, the method could not assess the reliability correctly. In the current research the authors present a new approach to solve this problem. In this approach, using the basic relations in this method, the safety factor relationship is obtained directly without separation of its numerator and denominator. Furthermore, in addition to friction angle of sliding surface, apparent cohesion, depth of water in tension crack, and earthquake acceleration ratio, in the present work the unit weight of rock is also considered as a stochastic parameter. The results are compared with the Monte Carlo simulation. Comparison of the results indicates good performance of the proposed approach for assessment of reliability. The new results of parametric analysis using the jointly distributed random variables method show that the friction angle of sliding surface is the most effective parameter in rock slope stability with plane sliding.

Effects of anisotropy in correlation structure on the stability of an undrained clay slope

Slopes are mainly naturally occurred deposits, so slope stability is highly affected by inherent uncertainty. In this paper, the influence of heterogeneity of undrained shear strength on the performance of a clay slope is investigated. A numerical procedure for a probabilistic slope stability analysis based on a Monte Carlo simulation that considers the spatial variability of the soil properties is presented to assess the influence of randomly distributed undrained shear strength and to compute reliability as a function of safety factor. In the proposed method, commercially available finite difference numerical code FLAC 5.0 is merged with random field theory. The results obtained in this study are useful to understand the effect of undrained shear strength variations in slope stability analysis under different slope conditions and material properties. Coefficient of variation and heterogeneity anisotropy of undrained shear strength were proven to have significant effect on the reliability of safety factor calculations. However, it is shown that anisotropy of the heterogeneity has a dual effect on reliability index depending on the level of safety factor adopted.

Effects of the spatial variability of permeability on rainfall-induced landslides

The saturated hydraulic conductivity (Ks) of soil is characterized by strong spatial variability and often decreases with depth. The main objective of this paper is to investigate how the trend function of the mean of saturated hydraulic conductivity (μKs) and its spatial variability affect the distribution of critical failure surfaces and the probability of slope failure during a period of rainfall. A random field method is used to simulate the spatial variability structure in the numerical analysis of a slope, and a numerical procedure for a probabilistic slope stability analysis based on Monte Carlo simulations is presented, in which Ks is modeled as a non-stationary lognormal random field. For a hypothetical weathered soil slope subjected to rainfall, a deterministic analysis and a sequence of probabilistic analyses are conducted using an infinite unsaturated slope model. The results show that these shallow failures are attributed to the reduction of matric suction and the development of positive pore pressure. The probability of slope failure increases with an increase in the variation of the trend component (Δk), but the rate of increase levels off at the later stage of rainfall. Ignoring the trend component of μKs would lead to less conservative estimates of the failure probability. The coefficient of variability has a more significant influence on the distribution of the critical failure surfaces and the probability of failure than does the correlation length of Ks.

Deterministic and probabilistic multi-modal analysis of slope stability

Traditional slope stability analysis involves predicting the location of the critical slip surface for a given slope and computing a safety factor at that location. However, for some slopes with complicated stratigraphy several distinct critical slip surfaces can exist. Furthermore, the global minimum safety factor in some cases can be less important than potential failure zones when rehabilitating or reinforcing a slope. Existing search techniques used in slope stability analysis cannot find all areas of concern, but instead converge exclusively on the critical slip surface. This paper therefore proposes the use of a holistic multi modal optimisation technique which is able to locate and converge to multiple failure modes simultaneously. The search technique has been demonstrated on a number of benchmark examples using both deterministic and probabilistic analysis to find all possible failure mechanisms, and their respective factors of safety and reliability indices. The results from both the deterministic and probabilistic models show that the search technique is effective in locating the known critical slip surface while also establishing the locations of any other distinct critical slip surfaces within the slope. The approach is of particular relevance for investigating the stability of large slopes with complicated stratigraphy, as these slopes are likely to contain multiple failure mechanisms.

Probabilistic slope stability analysis considering the variability of hydraulic conductivity under rainfall infiltration–redistribution conditions

Many soil parameters are highly variable, especially saturated hydraulic conductivity, which is bound to significantly influence the stability of unsaturated soil slopes that are subjected to rainfall infiltration and redistribution. A random variable model is used to characterize the variability of saturated hydraulic conductivity. Random number sequences of saturated hydraulic conductivity are generated following a lognormal distribution using the Monte Carlo Simulation method. Then the closed form of the limit state function is established, based on the combination of the extension of the Green-Ampt model and the infinite slope stability model. The suggested probabilistic method can calculate the time-dependent failure probability of the slope during a process of rainfall infiltration and redistribution. For a hypothetical slope that is subjected to steady-state rainfall infiltration, a series of parameter analyses are conducted and the results indicate that there exists a critical rainfall duration. At different stages of rainwater infiltration–redistribution, the trends between the failure probability of the soil slope and the coefficient of variation of the saturated hydraulic conductivity have a different form. The coefficient of variation of the saturated hydraulic conductivity does not affect the failure time of the slope that is most likely to occur. This paper figures out why some landslides occur after a rainfall event from the perspective of rainwater redistribution, and the corresponding lag times generally depend on the duration of antecedent rainfall. It is very risky to adopt mean safety factors to assess their stabilities for rainfall-induced landslides when the variability of the hydraulic conductivity is considered.

Probabilistic slope stability analysis by risk aggregation

This paper develops a probabilistic slope stability analysis approach that formulates the slope failure event as a series of mutually exclusive and collectively exhaustive events using conditional probability and utilizes Monte Carlo Simulation (MCS) to determine the occurrence probability for each of the mutually exclusive and collectively exhaustive events in a progressive manner. Then, these probabilities are aggregated to represent the overall slope failure probability pf. Equations are derived for the proposed approach, and the implementation procedures are illustrated using a cohesive slope example. The pf values obtained from the proposed approach are shown to agree well with those pf values that have been obtained by searching a large number of potential slip surfaces for the minimum factor of safety (FS) in each MCS sample. The computational time, however, is shown to reduce by, at least, an order of magnitude. In addition, a sensitivity study is performed to explore the effect of a key parameter in the proposed approach, i.e., the correlation coefficient threshold ρ0, on both the accuracy of pf and computational cost. When the spatial variability is significant, the effect of ρ0 on the accuracy of pf is significant, and a relatively large ρ0 value is needed to ensure the accuracy of pf. On the other hand, the computational time reduces substantially as the ρ0 value decreases. At an extreme case of ρ0=1.0, the risk aggregation approach becomes equivalent to an approach where a large number of potential slip surfaces are searched for the minimum FS in each MCS sample. In contrast, at the other extreme case of ρ0=0, the risk aggregation approach is the same as an approach that has been used in many previous studies and relies on only one slip surface. The risk aggregation approach deals rationally with the possibility of slope failure along more than one distinct slip surface (i.e., multiple failure modes) with significantly reduced computational efforts.

Risk de-aggregation and system reliability analysis of slope stability using representative slip surfaces

This paper develops a risk de-aggregation and system reliability approach to evaluate the slope failure probability, pf, using representative slip surfaces together with MCS. An efficient procedure is developed to strategically select the candidate representative slip surfaces, and a risk de-aggregation approach is proposed to quantify contribution of each candidate representative slip surface to the pf, identify the representative slip surfaces, and determine how many representative slip surfaces are needed for estimating the pf with reasonable accuracy. Risk de-aggregation is performed by collecting the failure samples generated in MCS and analyzing them statistically. The proposed methodology is illustrated through a cohesive soil slope example and validated against results from previous studies. When compared with the previous studies, the proposed approach substantially improves the computational efficiency in probabilistic slope stability analysis. The proposed approach is used to explore the effect of spatial variability on the pf. It is found that, when spatial variability is ignored or perfect correlation assumed, the pf of the whole slope system can be solely attributed to a single representative slip surface. In this case, it is theoretically appropriate to use only one slip surface in the reliability analysis. As the spatial variability becomes growingly significant, the number of representative slip surfaces increases, and all representative slip surfaces (i.e., failure modes) contribute more equally to the overall system risk. The variation of failure modes has substantial effect on the pf, and all representative surfaces have to be incorporated properly in the reliability analysis. The risk de-aggregation and system reliability approach developed in this paper provides a practical and efficient means to incorporate such a variation of failure modes in probabilistic slope stability analysis.