Failure probability assessment and parameter sensitivity analysis of a contaminant’s transit time through a compacted clay liner

This paper presents failure probability assessment and parameter sensitivity analysis of a contaminant’s transit time through a compacted clay liner. Monte Carlo simulation (MCS) was used to assess failure probability, and the failure samples generated in the MCS were used to investigate the sensitivity of various uncertain parameters to the failure probability. To facilitate the MCS, a database on various transport parameters was developed by collecting and analyzing measurement data reported in literature. Failure probability assessment and parameter sensitivity analysis showed that the uncertainties in adsorption parameters, longitudinal dispersivity, and hydraulic conductivity have the most significant effects on failure probability.     

Evaluation of the Instability Risk of the Dam Slopes Simulated with Monte Carlo method (Case Study: Alborz Dam)

Embankment dams are one of the most important geotechnical structures that their failures can lead to disastrous damages. One of the main causes of dam failure is its slope instability. Slope Stability analysis has traditionally been performed using the deterministic approaches. These approaches show the safety of slope only with factor of safety that this factor cannot take into account the uncertainty in soil parameters. Hence, to investigate the impact of uncertainties in soil parameters on slope stability, probabilistic analysis by Monte Carlo Simulation (MCS) method was used in this research. MCS method is a computational algorithm that uses random sampling to compute the results. This method studies the probability of slope failure using the distribution function of soil parameters. Stability analysis of upstream and downstream slopes of Alborz dam in all different design modes was done in both static and quasi-static condition. Probability of failure and reliability index were investigated for critical failure surfaces. Based on the reliability index obtained in different conditions, it can be said that the downstream and upstream slope of the Alborz dam is stable. The results show that although the factor of safety for upstream slope in the state of earthquake loading was enough, but the results derived from probabilistic analysis indicate that the factor of safety is not adequate. Also the upstream slope of the Alborz dam is unstable under high and uncontrolled explosions conditions in steady seepage from different levels under quasi-static terms.

     

Efficient system reliability analysis of soil slopes using multivariate adaptive regression splines-based Monte Carlo simulation

System effects should be considered in the probabilistic analysis of a layered soil slope due to the potential existence of multiple failure modes. This paper presents a system reliability analysis approach for layered soil slopes based on multivariate adaptive regression splines (MARS) and Monte Carlo simulation (MCS). The proposed approach is achieved in a two-phase process. First, MARS is constructed based on a group of training samples that are generated by Latin hypercube sampling (LHS). MARS is validated by a specific number of testing samples which are randomly generated per the underlying distributions. Second, the established MARS is integrated with MCS to estimate the system failure probability of slopes. Two types of multi-layered soil slopes (cohesive slope and c–φ slope) are examined to assess the capability and validity of the proposed approach. Each type of slope includes two examples with different statistics and system failure probability levels. The proposed approach can provide an accurate estimation of the system failure probability of a soil slope. In addition, the proposed approach is more accurate than the quadratic response surface method (QRSM) and the second-order stochastic response surface method (SRSM) for slopes with highly nonlinear limit state functions (LSFs). The results show that the proposed MARS-based MCS is a favorable and useful tool for the system reliability analysis of soil slopes.     

Hazard analysis of seismic submarine slope instability

To assess the risk associated with a submarine landslide, one must estimate the probability of slope failure and its consequences. This paper proposes a procedure to estimate the probability of earthquake-induced submarine slope failure (hazard) based on probabilistic seismic hazard analyses, ground response analyses and advanced laboratory tests. The outcomes from these analyses are treated in a probabilistic framework, with analytical simulations using mathematical techniques such as the first-order reliability method, Monte Carlo simulation and Bayesian updating. Fragility curves of slope failure during the earthquake (co-seismic) and after the earthquake (post-seismic) were developed in this study, and were shown to provide a clear and well-organized procedure to estimate the annual failure probability of a submarine slope under earthquake loading.     

Probabilistic parameter estimation and predictive uncertainty based on field measurements for unsaturated soil slope

A key issue in assessment of rainfall-induced slope failure is a reliable evaluation of pore water pressure distribution and its variations during rainstorm, which in turn requires accurate estimation of soil hydraulic parameters. In this study, the uncertainties of soil hydraulic parameters and their effects on slope stability prediction are evaluated, within the Bayesian framework, using the field measured temporal pore-water pressure data. The probabilistic back analysis and parameter uncertainty estimation is conducted using the Markov Chain Monte Carlo simulation. A case study of a natural terrain site is presented to illustrate the proposed method. The 95% total uncertainty bounds for the calibration period are relatively narrow, indicating an overall good performance of the infiltration model for the calibration period. The posterior uncertainty bounds of slope safety factors are much narrower than the prior ones, implying that the reduction of uncertainty in soil hydraulic parameters significantly reduces the uncertainty of slope stability.     

Extension of subset simulation approach for uncertainty propagation and global sensitivity analysis

The subset simulation (SS) method is a probabilistic approach which is devoted to efficiently calculating a small failure probability. Contrary to Monte Carlo Simulation (MCS) methodology which is very time-expensive when evaluating a small failure probability, the SS method has the advantage of assessing the small failure probability in a much shorter time. However, this approach does not provide any information about the probability density function (PDF) of the system response. In addition, it does not provide any information about the contribution of each input uncertain parameter in the variability of this response. Finally, the SS approach cannot be used to calculate the partial safety factors which are generally obtained from a reliability analysis. To overcome these shortcomings, the SS approach is combined herein with the Collocation-based Stochastic Response Surface Method (CSRSM) to compute these outputs. This combination is carried out by using the different values of the system response obtained by the SS approach for the determination of the unknown coefficients of the polynomial chaos expansion in CSRSM. An example problem that involves the computation of the ultimate bearing capacity of a strip footing is presented to demonstrate the efficiency of the proposed procedure. The validation of the present method is performed by comparison with MCS methodology applied on the original deterministic model. Finally, a probabilistic parametric study is presented and discussed.     

Load-displacement uncertainty of vertically loaded shallow footings on sands and effects on probabilistic settlement estimation

This article focuses on the statistical characterisation and stochastic modelling of the load-displacement behaviour of shallow footings on cohesionless soils and on the probabilistic estimation of settlement for serviceability limit state design (LSD). The study relies on a field database of 30 full-scale footings subjected to vertical loading with cone penetration testing data available for each site. The performance of three load-displacement models in replicating field data is assessed comparatively through statistical analysis. Load-displacement uncertainty is subsequently modelled probabilistically to perform Monte Carlo Simulation (MCS)-based estimation of footing settlement using the best-performing power law model. The dependence among load-displacement model parameters is investigated and replicated using copula theory. Samples are generated to account for parametric uncertainties in model inputs. The simulation output samples of settlement are examined statistically in order to assess the relevance of parametric and load-displacement uncertainties in settlement estimation, as well as the importance of accounting for correlation between power law model parameters. A simple analytical model for the estimation of settlement at any target reliability level is obtained on the basis of the outputs of MCS. The model can be practically implemented in geotechnical LSD at serviceability limit states.     

Spatial risk analysis of Li-shan landslide in Taiwan

By coupling limit equilibrium analysis and Monte Carlo analysis with a geography information system (GIS), this study implements a method that can evaluate the risk (corresponding to probability of failure in this study) of landslide with consideration of spatial uncertainties. The GIS can adopt the three-dimensional information including surface topography, underground geomaterial distribution and groundwater level to determine slope profiles for analysis. Then the safety of defined slope can be evaluated by limit equilibrium analysis. In this study, the mechanical properties of geomaterial were considered as random variables instead of single values. The slope and groundwater profiles are also randomly adopted. Through a Monte Carlo sampling process, a distribution of safety factor and probability of failure can be determined. This probabilistic risk analysis approach was applied to Li-shan landslide in Central Taiwan.

Due to heavy rains, the sites near the highway 7A (mileage 73 k + 150) and the highway 8 (mileage 82 k) in the Li-shan Township began to subside in mid April 1990. Topography, geology, and groundwater condition of this area were first reviewed. Based on this review, together with field investigations and a series of limit equilibrium back analyses, a general hypothetic model was established to illustrate the failure mechanism of this landslide area. Then the developed probabilistic risk analysis model is applied to spatially evaluate the risk of this landslide area as well as the performance of the remediation treatment.     

Probabilistic stability analyses of slopes using the ANN-based response surface

Slope stability analysis is a geotechnical engineering problem characterized by many sources of uncertainty. Some of these sources are connected to the uncertainties of soil properties involved in the analysis. In this paper, a numerical procedure for integrating a commercial finite difference method into a probabilistic analysis of slope stability is presented. Given that the limit state function cannot be expressed in an explicit form, an artificial neural network (ANN)-based response surface is adopted to approximate the limit state function, thereby reducing the number of stability analysis calculations. A trained ANN model is used to calculate the probability of failure through the first- and second-order reliability methods and a Monte Carlo simulation technique. Probabilistic stability assessments for a hypothetical two-layer slope as well as for the Cannon Dam in Missouri, USA are performed to verify the application potential of the proposed method.     

Probabilistic and fuzzy reliability analysis of a sample slope near Aliano

Slope stability assessment is a geotechnical problem characterized by many sources of uncertainty. Some of them, e.g., are connected to the variability of soil parameters involved in the analysis. Beginning from a correct geotechnical characterization of the examined site, only a complete approach to uncertainty matter can lead to a significant result. The purpose of this paper is to demonstrate how to model data uncertainty in order to perform slope stability analysis with a good degree of significance.

Once the input data have been determined, a probabilistic stability assessment (first-order second moment and Monte Carlo analysis) is performed to obtain the variation of failure probability vs. correlation coefficient between soil parameters. A first result is the demonstration of the stability of first-order second moment (FOSM) (both with normal and lognormal distribution assumption) and Monte Carlo (MC) solutions, coming from a correct uncertainty modelling. The paper presents a simple algorithm (Fuzzy First Order Second Moment, FFOSM), which uses a fuzzy-based analysis applied to data processing.     

基于广义子集模拟的土坡系统可靠度分析

如何有效地评价边坡的系统可靠度并识别出对边坡稳定性具有重要影响的关键滑面一直是边坡稳定性分析的关键问题。提出了基于广义子集模拟的边坡系统可靠度分析方法及代表性滑面识别方法,并推导了基于广义子集模拟的边坡系统可靠度计算公式及边坡中滑面对边坡系统失效的相对贡献量化公式。基于广义子集模拟计算结果,采用概率网络评价方法识别边坡代表性滑面。以一个双层黏性土坡和芝加哥国会切坡算例验证了所提方法的有效性。结果表明：提出的基于广义子集模拟的边坡系统可靠度分析方法可有效地估计边坡系统及其单一滑面的失效概率,对于具有低失效概率水平边坡可靠度的求解,其计算效率明显优于传统蒙特卡洛模拟方法。此外,对于单个失效模式而言,广义子集模拟与子集模拟计算效率相当。对于多个失效模式的失效概率计算问题,广义子集模拟不需要重复对每个失效模式失效概率进行计算,计算效率明显优于子集模拟。提出的代表性滑面选择方法是在系统失效概率及单滑面失效概率的高效计算基础上实现的,代表性滑动面能够较好地代表边坡系统失效,从而有效地降低了边坡系统失效概率对代表性滑面数目及代表性滑面失效概率估计准确性的依赖性。     

考虑空间变异性条件下的边坡稳定可靠度高效敏感性分析

在有限数据条件下,可靠度敏感性分析是研究各种不确定性因素对边坡失稳概率影响规律的重要途径。基于直接蒙特卡洛模拟和概率密度加权分析方法提出了一种高效边坡稳定可靠度敏感性分析方法。所提出的方法通过随机场表征岩土体参数的空间变异性,并采用局部平均理论建立岩土体参数的缩维概率密度函数,用于概率密度加权分析中高效、准确地计算不同敏感性分析方案对应的边坡失稳概率。最后,通过一个工程案例--詹姆斯湾堤坝说明了所提出方法的有效性和准确性。结果表明：在敏感性分析过程中,所提出的方法只需要执行一次直接蒙特卡洛模拟,避免了针对不同敏感性分析方案重新产生随机样本和执行边坡稳定分析,节约了大量的计算时间和计算资源,显著提高了基于蒙特卡洛模拟的敏感性分析计算效率;在概率密度加权分析中采用岩土体参数的缩维概率密度函数能够准确地计算边坡失稳概率,避免了有偏估计,使概率密度加权分析方法适用于考虑空间变异性条件下的边坡稳定可靠度敏感性分析问题。     

Reliability analysis of soil liquefaction based on standard penetration test

A review of probabilistic and deterministic liquefaction evaluation procedures reveals that there is a need for a comprehensive approach that accounts for different sources of uncertainty in liquefaction evaluations. For the same set of input parameters, different models provide different factors of safety and/or probabilities of liquefaction. To account for the different uncertainties, including both the model and measurement uncertainties, reliability analysis is necessary. This paper presents a review and comparative study of such reliability approaches that can be used to obtain the probability of liquefaction and the corresponding factor of safety. Using a simplified deterministic Seed method, this reliability analysis has been performed. The probability of liquefaction along with the corresponding factor of safety have been determined based on a first order second moment (FOSM) method, an advanced FOSM (Hasofer–Lind) reliability method, a point estimation method (PEM) and a Monte Carlo simulation (MCS) method. A combined method that uses both FOSM and PEM is presented and found to be simple and reliable for liquefaction analysis. Based on the FOSM reliability approach, the minimum safety factor value to be adopted for soil liquefaction analysis (depending on the variability of soil resistance, shear stress parameters and acceptable risk) has been studied and a new design safety factor based on a reliability approach is proposed.     

Probabilistic back analysis of slope failure – A case study in Taiwan

In this paper, the authors present a probabilistic back-analysis of a recent slope failure at a site on Freeway No. 3 in northern Taiwan. Post-event investigations of this failure found uncertain strength parameters and deteriorating anchor systems as the most likely causes for failure. Field measurement after the event indicated an average slip surface of inclination 15°. To account for the uncertainties in input parameters, the probabilistic back analysis approach was adopted. First, the Markov Chain Monte Carlo (MCMC) simulation was used to back-calculate the geotechnical strength parameters and the anchor force. These inverse analysis results, which agreed closely with the findings of the post-event investigations, were then used to validate the maximum likelihood (ML) method, a computationally more efficient back-analysis approach. The improved knowledge of the geotechnical strength parameters and the anchor force gained through the probabilistic inverse analysis better elucidated the slope failure mechanism, which provides a basis for a more rational selection of remedial measures.     

基于随机响应面法的边坡系统可靠度分析

提出了一套基于随机响应面法的边坡系统可靠度分析方法。该方法首先从大量潜在滑动面中筛选出代表性滑动面。针对每条代表性滑动面,采用Hermite多项式展开建立其安全系数与土体参数间的非线性显式函数关系（即随机响应面）。然后,采用直接蒙特卡洛模拟计算边坡系统失效概率。在蒙特卡罗模拟中,采用所有代表性滑动面的随机响应面计算每一组样本所对应的边坡最小安全系数。最后,以两个典型多层边坡系统可靠度问题为例验证了该方法的有效性。结果表明：文中提出的边坡系统可靠度分析方法能够有效地识别边坡代表性滑动面,具有较高的计算精度和效率,并且确定代表性滑动面时无需计算滑动面间的相关系数。同时该方法可以有效地计算低失效概率水平的边坡系统可靠度,为含相关非正态参数的边坡系统可靠度问题提供了一条有效的分析途径。此外,多层边坡可能同时存在多条潜在滑动面,基于单一滑动面（如临界确定性滑动面）或者部分代表性滑动面进行边坡系统可靠度分析均会低估边坡失效概率。     

Assessment of shallow landslide susceptibility using the transient infiltration flow model and GIS-based probabilistic approach

This study proposes a probabilistic analysis method for modeling rainfall-induced shallow landslide susceptibility by combining a transient infiltration flow model and Monte Carlo simulations. The spatiotemporal change in pore water pressure over time caused by rainfall infiltration is one of the most important factors causing landslides. Therefore, the transient infiltration hydrogeological model was adopted to estimate the pore water pressure within the hill slope and to analyze landslide susceptibility. In addition, because of the inherent uncertainty and variability caused by complex geological conditions and the limited number of available soil samples over a large area, this study utilized probabilistic analysis based on Monte Carlo simulations to account for the variability in the input parameters. The analysis was performed in a geographic information system (GIS) environment because GIS can deal efficiently with a large volume of spatial data. To evaluate its effectiveness, the proposed analysis method was applied to a study area that had experienced a large number of landslides in July 2006. For the susceptibility analysis, a spatial database of input parameters and a landslide inventory map were constructed in a GIS environment. The results of the landslide susceptibility assessment were compared with the landslide inventory, and the proposed approach demonstrated good predictive performance. In addition, the probabilistic method exhibited better performance than the deterministic alternative. Thus, analysis methods that account for uncertainties in input parameters are more appropriate for analysis of an extensive area, for which uncertainties may significantly affect the predictions because of the large area and limited data.     

Locating the Multiple Failure Surfaces for Slope Stability Using Monte Carlo Technique

Owing to the complicated slope stratigraphy (e.g., multiple soil layers and multiple benches or gradients in side slopes), multiple failure surfaces for slope stability have been recognized in geotechnical discipline. This paper aims to develop a systematic and probabilistic approach to locate the multiple failure surfaces combining the traditional limit equilibrium method with Monte Carlo Simulation. Each of the multiple failure surfaces is selected from a large pool of failure surfaces and the correlation coefficient between two failure surfaces in factor of safety (FS) is adopted to characterize the extent to which two failure surfaces are correlated. After eliminating those highly correlated failure surfaces, the multiple failure surfaces can be gradually identified. The number of failure samples and the number of exclusive failure samples corresponding to each of multiple failure surfaces are determined within the proposed methodology. These data are reanalyzed to find the critical failure surface with the maximum failure probability, the critical failure surface with maximum simplified risk, and those failure surfaces dominating the risk of slope failure. The proposed approach is illustrated through two examples excerpted from the literature and validated against the results from the commercial software package and literature. The comparative study manifests that the critical failure surface with the minimum FS does not always coincide with that with the maximum failure probability and with the maximum simplified risk. In addition to FS, the failure surfaces should be received much attention. The proposed methodology provides an effective tool in decision making for slope stabilization and rehabilitation process.     

Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using Subset Simulation

Random finite element method (RFEM) provides a rigorous tool to incorporate spatial variability of soil properties into reliability analysis and risk assessment of slope stability. However, it suffers from a common criticism of requiring extensive computational efforts and a lack of efficiency, particularly at small probability levels (e.g., slope failure probability P _f ?<?0.001). To address this problem, this study integrates RFEM with an advanced Monte Carlo Simulation (MCS) method called “Subset Simulation (SS)” to develop an efficient RFEM (i.e., SS-based RFEM) for reliability analysis and risk assessment of soil slopes. The proposed SS-based RFEM expresses the overall risk of slope failure as a weighed aggregation of slope failure risk at different probability levels and quantifies the relative contributions of slope failure risk at different probability levels to the overall risk of slope failure. Equations are derived for integrating SS with RFEM to evaluate the probability (P _f ) and risk (R) of slope failure. These equations are illustrated using a soil slope example. It is shown that the P _f and R are evaluated properly using the proposed approach. Compared with the original RFEM with direct MCS, the SS-based RFEM improves, significantly, the computational efficiency of evaluating P _f and R. This enhances the applications of RFEM in the reliability analysis and risk assessment of slope stability. With the aid of improved computational efficiency, a sensitivity study is also performed to explore effects of vertical spatial variability of soil properties on R. It is found that the vertical spatial variability affects the slope failure risk significantly.     

Probabilistic analysis of strip footings resting on a spatially random soil using subset simulation approach

The failure probability of geotechnical structures with spatially varying soil properties is generally computed using Monte Carlo simulation (MCS) methodology. This approach is well known to be very time-consuming when dealing with small failure probabilities. One alternative to MCS is the subset simulation approach. This approach was mainly used in the literature in cases where the uncertain parameters are modelled by random variables. In this article, it is employed in the case where the uncertain parameters are modelled by random fields. This is illustrated through the probabilistic analysis at the serviceability limit state (SLS) of a strip footing resting on a soil with a spatially varying Young's modulus. The probabilistic numerical results have shown that the probability of exceeding a tolerable vertical displacement (P _e) calculated by subset simulation is very close to that computed by MCS methodology but with a significant reduction in the number of realisations. A parametric study to investigate the effect of the soil variability (coefficient of variation and the horizontal and vertical autocorrelation lengths of the Young's modulus) on P _e was presented and discussed. Finally, a reliability-based design of strip footings was presented. It allows one to obtain the probabilistic footing breadth for a given soil variability.     

Spatial probabilistic modeling of slope failure using an integrated GIS Monte Carlo simulation approach

Spatial probabilistic modeling of slope failure using a combined Geographic Information System (GIS), infinite-slope stability model and Monte Carlo simulation approach is proposed and applied in the landslide-prone area of Sasebo city, southern Japan. A digital elevation model (DEM) for the study area has been created at a scale of 1/2500. Calculated results of slope angle and slope aspect derived from the DEM are discussed. Through the spatial interpolation of the identified stream network, the thickness distribution of the colluvium above Tertiary strata is determined with precision. Finally, by integrating an infinite-slope stability model and Monte Carlo simulation with GIS, and applying spatial processing, a slope failure probability distribution map is obtained for the case of both low and high water levels.