Probability Of Slope Failure Research Articles

Instability analysis of jointed rock slope subject to rainfall using DEM strength reduction technique

Uncertain climatic factors like rainfall can induce the complex hydro-chemo mechanical processes within the rock mass, and thus substantially increase the failure probability of rock slope. This paper presents a numerical investigation into the rainfall-induced instability mechanism of jointed rock slope with two joint inclinations of dipping 45° and 60° and the corresponded safety factor using the two-dimensional Distinct Element Method (DEM), where the non-uniform strength reduction approach is employed. For this purpose, some crucial aspects were mainly discussed, i.e. the quantifications of water softening and chemical weathering effects in the micro bond contact model, the necessary fitted functional relationships used in the safety factor, and determinations on the intensities of water softening and chemical weathering. The results show that the proposed DEM strength reduction provides a feasible approach to analyze the rainfall-triggered instability of jointed rock slope. The significant rise of bond breakage and the accompanied large displacement of sliding block indicate the achieved critical infiltration depth of rainfall and the consequent destabilization of jointed rock slope. The jointed rock slope with steeper dipping joints has lower safety factor, and thus is more prone to instability under the same rainfall effect.

Stochastic seepage and slope stability analysis using vine-copula based multivariate random field approach: Consideration to non-Gaussian spatial and cross-dependence structure of hydraulic parameters

Stochastic seepage and slope stability analysis is conventionally performed in a random field framework. However, most of the studies are limited to Gaussian spatial and cross-dependence structure of hydraulic parameters. Using a well documented hydraulic conductivity (k) data from Borden aquifer, Canada (Sudicky, 1986), evidence of non-Gaussian spatial dependence is provided within a copula framework. It is shown that the non-Gaussian spatial dependence structure is a field reality for k. To handle the non-Gaussian spatial as well as cross-dependence structure, a multivariate random field framework based on vine copula theory is presented. It is shown that the vine-copula approach can efficiently model the non-Gaussian dependence structure of hydraulic parameters. For investigating the practical engineering importance of dependence structure, stochastic seepage and slope stability analysis under steady and transient seepage conditions is conducted. It is shown that the assumption of arbitrary spatial dependence structure, can significantly affect (by a factor of 100) the failure probability of slopes across the entire acceptable range (Salgado and Kim, 2014) of 10-4 to 10-2. It is also shown that the choice of spatial dependence structure is more crucial than the cross-dependence for stochastic seepage and slope stability analysis.

A two-dimensional limit equilibrium computer code for analysis of complex toppling slope failures

Evaluation of blocky or layered rock slopes against toppling failures has remained of great concern for engineers in various rock mechanics projects. Several step-by-step analytical solutions have been developed for analyzing these types of slope failures. However, manual application of these analytical solutions for real case studies can be time-consuming, complicated, and in certain cases even impossible. This study will first examine existing methods for toppling failure analyses that are reviewed, modified and generalized to consider the effects of a wide range of external and dead loads on slope stability. Next, based on the generalized presented formulae, a Windows form computer code is programmed using Visual C# for analysis of common types of toppling failures. Input parameters, including slope geometry, joint sets parameters, rock and soil properties, ground water level, dynamic loads, support anchor loads as well as magnitudes and forms of external forces, are first loaded into the code. The input data are then saved and used to graphically draw the slope model. This is followed by automatic identification of the toppling failure mode and a deterministic analysis of the slope stability against this failure mode. The results are presented using a graphical approach. The developed code allows probabilistic introduction of the input parameters via probability distribution functions (PDFs) and thus a probabilistic analysis of the toppling failure modes using Monte-Carlo simulation technique. This allows calculation of the probability of slope failure. Finally, several published case studies and typical examples are analyzed with the developed code. The outcomes are compared with those of the main references to assess the performance and robustness of the developed computer code. The comparisons demonstrate good agreement between the results.

Modeling multivariate cross-correlated geotechnical random fields using vine copulas for slope reliability analysis

Modeling multivariate cross-correlated random fields plays an important role in reliability analysis of geotechnical systems. The cross-correlation among random fields is commonly characterized by the Nataf transformation using a correlation coefficient matrix, which is equivalent to considering the Gaussian dependence structure from the perspective of the copula theory. In this study, a generic approach for modeling multivariate cross-correlated geotechnical random fields based on vine copulas is proposed. This approach can incorporate the diversity and non-Gaussianity of dependence structures in the cross-correlation characterization. A four-variate geotechnical dataset is used to verify the proposed approach and the results illustrate that the statistics of generated random field realizations are comparable with the predefined values. Furthermore, the application of the proposed approach to reliability analysis of soil slopes with spatially varying soil parameters (cohesion, friction angle, and unit weight) is presented. The results indicate that considerably different probabilities of slope failure are produced by different vine-copula models. The conventional Nataf transformation (i.e., vine-Gaussian copula model) may considerably underestimate the probability of slope failure. The difference of reliability results for different vine models is generally enlarged as the level of the failure probability becomes lower. The proposed approach provides a more flexible way for geotechnical practitioners to characterize the cross-correlation among geotechnical random fields compared with the Nataf transformation, and is applicable to reliability analysis of various geotechnical systems.

Hazard-Consistent Earthquake Scenario Selection for Seismic Slope Stability Assessment

Design ground shaking intensity, based on probabilistic seismic hazard analysis (PSHA) maps, is most commonly used as a triggering condition to analyze slope stability under seismic loading. Uncertainties that are associated with expected ground motion levels are often ignored. This study considers an improved, fully probabilistic approach for earthquake scenario selection. The given method suggests the determination of the occurrence probability of various ground motion levels and the probability of landsliding for these ground motion parameters, giving the total probability of slope failure under seismic loading in a certain time interval. The occurrence hazard deaggregation technique is proposed for the selection of the ground shaking level, as well as the magnitude and source-to-site distance of a design earthquake, as these factors most probably trigger slope failure within the time interval of interest. An example application of the approach is provided for a slope near the highway in the south of Sakhalin Island (Russia). The total probability of earthquake-induced slope failure in the next 50 years was computed to be in the order of 16%. The scenario peak ground acceleration value estimated from the disaggregated earthquake-induced landslide hazard is 0.15g, while the 475-year seismic hazard curve predicts 0.3g. The case study highlights the significant difference between ground shaking scenario levels in terms of the 475-year seismic hazard map and the considered fully probabilistic approach.

Probabilistic stability analyses of slope reinforced with piles in spatially variable soils

In this paper, deterministic stability analyses for soil slopes reinforced with pile of different locations and lengths were conducted firstly to calculate the factor of safety through limit equilibrium method (LEM). Since the effect of inherent uncertainties as well as the spatial variability of soils cannot be reflected via the deterministic factor of safety, probabilistic stability analyses of slopes reinforced with pile in spatially constant soils and spatially variable soils were successively carried out, respectively. The failure probability was determined by random limit equilibrium method (RLEM) considering the influence of different pile locations, pile length and soil statistical parameters. The optimal locations along slope and length of pile were analyzed based on the reliability analyses results in spatially constant soils and spatially variable soils, which were inconsistent with the results via the traditional deterministic methods, with a lower probability of sliding failure. Finally, method was proposed to determine the minimum samples of simulation iterations for investigating the convergence of failure probability of soil slope reinforced with piles. The results revealed that the multiple potential sliding surfaces introduced by the installations of pile would result in the increased uncertainty of slope failures.

Some Remarks on the Use of Deterministic and Probabilistic Approaches in the Evaluation of Rock Slope Stability

The rock slope stability assessment can be performed by means of deterministic and probabilistic approaches. As the deterministic analysis needs only representative values (generally, the mean value) for each physical and geo-mechanical parameter involved, it does not take into account the variability and uncertainty of geo-structural and geo-mechanical properties of joints. This analysis can be usually carried out using different methods, such as the Limit Equilibrium method or numerical modeling techniques sometimes implemented in graphical tests to identify different failure mechanisms (kinematic approach). Probabilistic methods (kinetic approach) aimed to calculate the slope failure probability, consider all orientations, physical characters and shear strength of joints and not only those recognized as kinematically possible. Consequently, the failure probability can be overestimated. It is, therefore, considered more realistic to perform both kinematic and kinetic analyses and to calculate a conditional probability given by the product of the kinematic and kinetic probabilities assuming that they are statistically independent variables. These approaches have been tested on two rock slopes in the Campanian region of Southern Italy affected by possible plane and wedge failures, respectively. Kinematic and kinetic probabilities have been evaluated both by means of the Markland’s test and the Monte Carlo simulation. Using the Eurocode 7, also a deterministic limit equilibrium analysis was performed. The obtained results were compared and commented on.

Efficient reliability analysis of earth dam slope stability using extreme gradient boosting method

Reliability analysis approach provides a rational means to quantitatively evaluate the safety of geotechnical structures from a probabilistic perspective. However, it suffers from a known criticism of extensive computational requirements and poor efficiency, which hinders its application in the reliability analysis of earth dam slope stability. Until now, the effects of spatially variable soil properties on the earth dam slope reliability remain unclear. This calls for a novel method to perform reliability analysis of earth dam slope stability accounting for the spatial variability of soil properties. This paper develops an efficient extreme gradient boosting (XGBoost)-based reliability analysis approach for evaluating the earth dam slope failure probability. With the aid of the proposed approach, the failure probability of earth dam slope can be evaluated rationally and efficiently. The proposed approach is illustrated using a practical case adapted from Ashigong earth dam. Results show that the XGBoost-based reliability analysis approach is able to predict the earth dam slope failure probability with reasonable accuracy and efficiency. The coefficient of variations and scale of fluctuations of soil properties affect the earth dam slope failure probability significantly. Moreover, the earth dam slope failure probability is highly dependent on the selection of auto-correlation function (ACF), and the widely used single exponential ACF tends to provide an unconservative estimate in this study.

System reliability analysis of geosynthetic reinforced soil slope considering local reinforcement failure

Abstract System reliability analyses are necessary for geosynthetic reinforced soil slopes because of the uncertainties associated with design parameters and complicated interaction between geosynthetic reinforcements and soil. This paper presents a new method for system reliability analysis of reinforced soil slopes considering local failures of reinforcements based on total probability rule with a typical example. The slope failure probability is calculated as the sum of the products of the local reinforcement failure probability and the conditional probability of the slope failure given the local reinforcement failure. An event tree is used to evaluate all possible mutually exclusive local reinforcement failure combinations. The present method avoids the assumption of different independent failure modes and is able to take the composite failure mode into account. The failure of local reinforcements incurs the redistribution of the forces in the other layers and increases the failure probability of the adjacent upper reinforcement layers, leading to cascading failure one after another. The failure probability of a reinforced slope is determined by both the probability of the local reinforcement failures and conditional probability of the slope given those events. It is not necessary to set the correlation coefficient between different failure modes in the present method.

Probabilistic stability analyses of multi-stage soil slopes by bivariate random fields and finite element methods

Abstract This study aimed to investigate the stability of multi-stage drained and undrained slopes considering the spatial variability in soil properties. A bivariate random field was adopted to characterize the spatial randomness in soil strength parameters of each stage of soil slopes. The random field was then incorporated with the finite element method to obtain the factor of safety (FS) and evaluate the slope failure mechanism. Monte Carlo simulations were conducted for slopes with random soils, resulting in histograms of the FS. The results indicated that around 65%–75% cases of a random slope under the drained condition had an FS being less than that of a uniform slope, and this comparison value reached about 92.6% under the undrained condition. As such, the deterministic analysis of a multi-stage slope may result in an overestimated value of the FS. Moreover, the influence of cross-correlation between cohesive strength and friction angle on the stability of drained slopes was also investigated. The findings demonstrated that the failure probability of multi-stage slope increases as the correlation coefficient increases.

Probabilistic characterization of the soil-water retention curve and hydraulic conductivity and its application to slope reliability analysis

Abstract Soil-water retention curve (SWRC) and hydraulic conductivity are two indispensable inputs in unsaturated seepage analysis for analyzing water flow in unsaturated soils, which can be obtained through direct measurements. Generally, the test data of the SWRC and unsaturated hydraulic conductivity obtained from direct measurements are limited because such measurements are time-consuming and costly. Thus, it is hard to determine an SWRC and hydraulic conductivity with certainty from a probabilistic perspective. How to quantify the uncertainty in them remains an unresolved question. This paper aims to propose a Bayesian approach to characterize the SWRC and hydraulic conductivity. The proposed approach is illustrated through a slope example. Results show that the proposed Bayesian approach is not only able to quantify the uncertainty in the estimated SWRC and hydraulic conductivity, but also capable of predicting the SWRC and hydraulic conductivity with reasonable accuracy. This facilitates the determination of both the SWRC and hydraulic conductivity in geotechnical applications for engineers by making use of the available test data. Moreover, the proposed approach offers a viable way to provide a robust estimate of slope failure probability by virtue of Bayesian model averaging, allowing SWRC parameter uncertainty and model selection uncertainty to be considered simultaneously in reliability analysis. This addresses the dilemma of over-reliance on a single SWRC model in geotechnical reliability analysis involving unsaturated soils. It is worthy to note that among the four candidate models, three of them belong to one category which may have similar abilities, other parametric models in different categories need to be considered in future research.

Probabilistic stability analysis of earth dam slope under transient seepage using multivariate adaptive regression splines

Earth dams are widespread throughout the world and their safety has gained increasing concern from geotechnical engineering societies. Although probabilistic stability analysis approach has been widely applied to the safety assessment of geotechnical structures, few studies have been performed to investigate the effects of water level fluctuations on earth dam slope stability considering uncertainties of soil parameters. This study proposes an efficient probabilistic stability analysis approach by integrating a soft computing algorithm of multivariate adaptive regression splines (MARS). The calibration of a MARS model generally requires a large number of training samples, which are obtained from repeated runs of deterministic seepage and slope stability analyses using the GeoStudio software. Based on the established MARS model, the earth dam slope failure probability can be conveniently evaluated. As an illustration, the proposed approach is applied to the probabilistic stability analysis of Ashigong earth dam under transient seepage. The effects of the uncertainties of soil parameters and water level fluctuation velocity on the earth dam slope failure probability are explored systematically. Results show that the MARS-based probabilistic stability analysis approach evaluates the earth slope failure probability with satisfactory accuracy and efficiency. The earth dam slope failure probability is significantly affected by the water level fluctuation velocity and the coefficient of variation of the effective friction angle.

Time-variant failure probability of critical slopes under strong rainfall hazard including mitigation effects

The time-variant failure probability for critical slopes under strong rainfalls, which cause reductions on the soil shear strength, is calculated and compared to the target failure probability. The soil properties and the rainfall characteristics are considered as random and the correlation between rainfall intensity and duration is included to assess the impact of water infiltration on the slope failure probability. The failure probability, defined as the probability that the safety factor is less than 1, is calculated through a Monte Carlo simulation process. The paper emphasizes the importance of the time during the water infiltration into the soil, as the rainfall sequence occurs. The target failure probability, derived from the minimum expected life-cycle cost, is compared to the slope failure probability to decide if the slope requires mitigation measures. If mitigation is required, the slope model is modified and a new annual failure probability is calculated. The slope annual failure probability, for three sites under strong rainfall hazard, is found to be around 0.78. However, by introducing mitigation actions, the failure probability reduces to 0.037. The slope failure probability allows for the risk-based prioritization of the attention for many slopes at several sites by stablishing basis for optimal resources allocation.

Copula-based approach coupling information diffusion distribution for slope reliability analysis

Uncertain probability distributions and interdependencies of geotechnical parameters have profound impacts on slope reliability analysis, especially under incomplete probabilistic information. In this paper, a copula-based approach coupling information diffusion (ID) distribution is proposed to reduce such uncertainties. Firstly, ID theory is introduced to establish marginal distribution of strength parameter. Copulas are subsequently performed to characterize the corresponding dependence structure and link the proposed ID margins. At last, equivalent samples are simulated and plugged into Monte Carlo simulation (MCS) to estimate slope reliability. The effect of the proposed method is validated by a slope case. Results show that the proposed ID algorithm holds remarkable superiority in estimating the marginal distribution with considering random volatility of geotechnical parameter. For slope reliability, both marginal distributions and interdependencies of geotechnical parameters barely affect the factor of safety (FS) but significantly impact failure probability (pf). Unreasonable estimation of probability distribution may lead to large deviation in calculation of slope failure probability. Comparably, the proposed copula-based approach coupling ID distribution can give a reasonable and robust reliability results with considering random volatility.

Probabilistic seismic slope stability analysis and design

Deterministic seismic slope stability design charts for cohesive–frictional ([Formula: see text]) soils are traditionally used by geotechnical engineers to include the effects of earthquakes on slopes. These charts identify the critical seismic load event that is sufficient to bring the slope to a state of limit equilibrium, but they do not specify the probability of this event. In this paper, the probabilistic seismic stability of slopes, modeled using a two-dimensional spatially random [Formula: see text] soil, is examined for the first time using the random finite element method (RFEM). Slope stability design aids for seismic loading, which consider spatial variability of the soil, are provided to allow informed geotechnical seismic design decisions in the face of geotechnical uncertainties. The paper also provides estimates of the probability of slope failure without requiring computer simulations. How the design aids may be used is demonstrated with an example of slope remediation cost analysis and risk-based design.

Subset simulation for efficient slope reliability analysis involving copula-based cross-correlated random fields

This study proposes a subset simulation (SS)-based approach for efficient slope reliability analysis involving copula-based cross-correlated random fields of cohesion (c) and friction angle (ϕ) of soils. First, the copula theory for modeling the cross-correlation between c and ϕ is briefly introduced. The algorithms for generating the copula-based cross-correlated random fields of c and ϕ are detailed. Then, the SS for efficient slope reliability analysis involving copula-based cross-correlated random fields of c and ϕ is explained. Finally, two slope examples with the same geometry but different sources of probability information are presented to illustrate and demonstrate the proposed approach. The results indicate that the proposed approach has both good accuracy and efficiency in slope reliability analysis involving the copula-based cross-correlated random fields of c and ϕ at low failure probability levels. The copula theory for characterizing the cross-correlated random fields can consider both the Gaussian and non-Gaussian dependence structures between c and ϕ. The copula selection has a significant impact on slope reliability with spatially variable c and ϕ. The probabilities of slope failure produced by different copulas differ considerably. This difference increases with decreasing probability of slope failure. The commonly-used Gaussian copula may lead to a significant underestimate of the probability of slope failure. The reasonable identification of the best-fit copula for characterizing the cross-correlated random fields of c and ϕ based on the test data is highlighted in practical slope reliability analysis.

Applicability of Two Newmark Models in the Assessment of Coseismic Landslide Hazard and Estimation of Slope-Failure Probability: An Example of the 2008 Wenchuan Mw 7.9 Earthquake Affected Area

This paper presents the landslide hazard assessment and slope-failure function using two Newmark displacement models regressed by regional and global station records. Taking the 2008 Wenchuan Mw 7.9 earthquake area as an example, based on the topographic and geological data of the study area, we prepared a factor-of-safety (Fs) map and a critical acceleration (ac) map, respectively. Then using these two simplified Newmark models, two displacement maps were compiled by combining the ac map and peak ground acceleration (PGA) map. By virtue of the actual landslide inventory of the W enchuan earthquake, we constructed the slope-failure probability curves of the two Newmark models. The results show that the abilities to predict landslide occurrence of the two simplified Newmark models are largely identical, by which the assessment results can well delineate the macroscopic distribution of coseismic landslides, and most predicted landslide cells are distributed on the two sides of the Beichuan-Yingxiu fault, especially Pengguan complex rock mass in the hanging wall of this fault. The probability equations of two Newmark models are roughly the same, though the parameters vary slightly. The probability equation proposed in this paper can be applied to the Wenchuan region and other areas with similar tectonic environments.

Probabilistic Assessment on Stability of Slopes Reinforced with Piles Considering Spatial Variability of Soil Properties

The spatial variability is an inherent property of soil materials, which heavily affected the failure probability of slope. In the present study, deterministic analysis with factor of safety and reliability analysis in uniform soil grounds and spatial variable soil conditions are successively carried out to investigate the effect of uncertainties and the spatial variability of soil on the stability of slope reinforced with piles using random limit equilibrium method (RLEM). The optimal location and length of pile are also analysed based on the calculation results of RLEM, which is inconsistent with the results of traditional deterministic method. The obtained results demonstrate the significant effect of the spatial variability on the failure probability of slope reinforced with pile.

Probabilistic stability analyses of layered excavated slopes

The random finite-element method (RFEM) is employed to study the effect of vertical spatial soil variability on the stability of layered excavated slopes. Particular emphasis of the paper is on the critical or ‘worst-case’ vertical spatial correlation length, at which the probability of slope failure reaches a maximum. The RFEM results indicate that layered slopes with a relatively low mean factor of safety or a relatively high coefficient of variation of soil strength are most likely to display the ‘worst-case’ phenomenon. The ‘worst-case’ phenomenon is explained by observing the failure mechanisms in layered soils where the critical spatial correlation length optimises the number of horizontal paths of weaker soil available for the mechanism to pass through.

Reliability analysis of Unsaturated Slope Stability Considering Spatial Variability in Hydraulic Parameters

Reliability analysis of slope stability provides a rational framework for slope safety evaluation, which plays a key role in geotechnical decision making for landslide disaster prevention. However, previous studies mainly focused on the slope reliability analysis accounting for uncertainties in shear strength parameters. How to perform reliability analysis of unsaturated slope stability considering the spatial variability of hydraulic parameters remains an open question. This paper aims to systematically investigate the effects of spatial variability of hydraulic parameters on the unsaturated slope reliability. The random fields of hydraulic parameters are derived from the random void ratio field, instead of direct generation, for considering the spatial variability of hydraulic parameters in a rational manner. It is found that the coefficient of variation (COV) and scale of fluctuation (SOF) of void ratio affects the unsaturated slope failure probability significantly. Additionally, the failure probability is sensitive to the selection of auto-correlation function (ACF) in the unsaturated slope reliability analysis.