Slope Reliability Research Articles

Investigating the Impact of Random Field Element Size on Soil Slope Reliability Analysis

The determination of the optimal random field element (RFE) size is crucial in soil slope reliability analysis as it governs the trade-off between precision in failure probability calculations and computational efficiency. Given the substantial computational burden associated with smaller RFE sizes, studies on their impact on slope failure probability are scarce. This research examines the influence of RFE size on failure probability and safety factor, employing the Karhunen–Loève expansion to generate random fields and integrating the simplified Bishop method with particle swarm optimization (PSO) to assess slope stability. Through Monte Carlo Simulation (MCS), this study investigates the effects of the ratio of slope height to RFE size (H/De) on slope reliability metrics across two illustrative cases. Results reveal a notable influence of H/De on the distribution of safety factors (Fs) and failure probability (PF), with overestimation observed at smaller H/De ratios. When H/De exceeds 10 for Example 1 and 15 for Example 2, the Fs distribution patterns in both scenarios stabilize significantly, displaying minimal variability. The PF of Example 1 and Example 2 decreases with the increase of H/De and remains basically unchanged when H/De exceeds 10 and 15, respectively. Consequently, a recommended H/De ratio of 20 is proposed based on the analyzed cases, facilitating accurate calculations while mitigating computational overhead.

Impact of Random Field Simulations on FEM-Based Earth Slope Reliability

Impact of Random Field Simulations on FEM-Based Earth Slope Reliability

Probabilistic stability analysis of small-angle marine slopes considering hydrate decomposition and seismic excitation

The submarine massive mud transports of several seas around the world, including the Shenhu Sea, are thought to relate with hydrate decomposition, which occur even at small gradients. This article investigates the stability and reliability of marine slopes considering three factors related to hydrate decomposition and earthquake, namely decrease in sediment strength, increase in excess pore pressure, and activation by external seismic force. Taking the SH2 hole, implemented by the first Chinese offshore hydrate drilling mission (GMGS-1), as an example, the impacts of three factors mentioned above on marine slopes stability are analyzed with infinite slope theory. In addition, the space distribution of physical and mechanical parameters in hydrate deposits is under consideration. The cohesion, friction angle and buoyant unit weight in a non-stationary random field are treated as spatial random variables, where the means of the first two increase linearly with depth. Variation characteristics of the failure probability for various slope angles are analyzed under different scenarios. The outcomes reveal that the safety factor of the slopes at 30% potential for damage is around 1.25 within a given variant characterization. The proposed integrated stability and reliability analysis can effectively provide early warning for collapse of marine hydrate-bearing slopes.

Improved Bayesian model updating of geomaterial parameters for slope reliability assessment considering spatial variability

In engineering practice, Bayesian model updating using field data is often conducted to reduce the substantial inherent epistemic uncertainties in geomaterial properties resulting from complex geological processes. The Bayesian Updating with Subset simulation (BUS) method is commonly employed for this purpose. However, the wealth of field data available for engineers to interpret can lead to challenges associated with the “curse of dimensionality”. Specifically, the value of the likelihood function in the BUS method can become extremely small as the volume of field data increases, potentially falling below the accuracy threshold of computer floating-point operations. This undermines both the computational efficiency and accuracy of Bayesian model updating. To effectively address this technical challenge, this paper proposes an improved BUS method developed based on parallel system reliability analysis. Leveraging the Cholesky decomposition-based midpoint method, the total failure domain in the original BUS method, which involves a low acceptance rate, is subdivided into several sub-failure domains with a high acceptance rate. Facilitated with an improved Metropolis-Hastings algorithm, the improved BUS method enables the consideration of a large volume of field data and spatial variability of geomaterial properties in the probabilistic back analysis. The results of an illustrative soil slope, involving spatially variable undrained shear strength, demonstrate that the improved BUS method is effective in simultaneously incorporating a substantial volume of field measurements and observations in the model updating process. Through a comparison with the original BUS method, the improved BUS method is shown to be useful for Bayesian model updating of high-dimensional spatially variable geomaterial properties and slope reliability assessment.

An efficient method for calculating system reliability of soil slope with general shape slip surface

An efficient method for calculating system reliability of soil slope with general shape slip surface

Analyzing MSW Landfill Failures: Stability and Reliability Evaluations from Five International Case Studies

This study investigates five cases of municipal solid waste (MSW) landfill slope failures in the USA, China, Sri Lanka, and Greece, with the aim of assessing the safety margins and reliability of these slopes. The stability and reliability of the landfill slopes were evaluated under both static and seismic loading conditions, using pre-failure geometries and geotechnical data, with analyses conducted in accordance with Eurocode 7, employing all three design approaches. Under static loading, the factors of safety were close to unity, and reliability indexes ranged from 1.0 to 2.8, both falling below the recommended values set by Eurocode. The landfill slopes failed to meet the stability criteria in Design Approaches 2 and 3, while in Design Approach 1, four out of five landfills met the criteria. Under seismic conditions, safety factors and reliability indexes were significantly lower than the prescribed criteria in all analyses. Sensitivity analyses revealed that in two cases, unit weight and friction angle were the dominant parameters, while cohesion was the dominant parameter in one case. The findings of this study underscore the importance of establishing minimum design requirements for MSW landfill slope stability to mitigate potential risks to public health and the environment.

Modelling of slope reliability analysis methods based on random field and asymmetric CNNs

Modelling of slope reliability analysis methods based on random field and asymmetric CNNs

Rainfall Induced Slope Reliability Analysis Using Radial Degraded Random Fields

Rainfall Induced Slope Reliability Analysis Using Radial Degraded Random Fields

Slope displacement reliability analysis considering rock parameters spatial variability subjected to stochastic mainshock-aftershock earthquake

A new and efficient framework for analyzing the stochastic dynamic response and reliability of the rock slope was constructed based on the generalized probability density evolution method (GPDEM). The left bank slope of Jinping dam was taken as an illustrative example and the effects of mainshock-aftershock sequence randomness, spatial variability of geotechnical materials and coupled uncertainties on the slope dynamic response and reliability were compared and analyzed for the first time. Firstly, a series of mainshock-aftershock sequences and parameter random fields were generated as stochastic factors inputs. Then, the effectiveness of GPDEM was validated by comparing with Monte Carlo Simulation (MCS). The Newmark slip displacement method was combined with GPDEM to analyze the slope dynamic response and reliability subjected to single and coupled uncertainties from a probabilistic viewpoint. Finally, the fragility curves of three risk levels were established based on the reliabilities with different seismic intensities. The result suggests that parameter spatial variability affects the dynamic response and reliability of the slope to some extent, but this effect will be overshadowed by the uncertainty of mainshock-aftershock sequences when it is considered simultaneously. Besides, aftershocks will cause the decrease of slope reliability and the impact of aftershock cannot be overlooked.

Reliability and landslide consequence analysis of long heterogeneous soil infrastructure slopes: A parallel computing investigation

Long infrastructures, like flood defense levees, built upon diverse soils, often face complex landslide failures. Risk assessments for such structures involve evaluating slope stability reliability and potential landslide consequences. Historically, embankment slope reliability and failure assessments focused on shorter sections due to computational limitations. This study, however, delves into a longer 3D soil slope section, 100 times the height, using the random finite element method to analyse the size or length effect. It conducts a parametric study varying the soil strength’s horizontal correlation length to understand slope failure initiation in heterogeneous soils. In contrast to prior work, this paper emphasises several facets: the realised factor of safety (FOS) distribution, quantification of discrete unstable zones and failures, and the size impact on the reliability and landslide consequences of long embankment slopes. Findings indicate the Weibull distribution better fits the realised FOS, aiding in predicting long embankment slope system reliability when combined with the weakest link theory. While multiple failures are possible for very long soil embankment slopes, observations suggest a greater likelihood of a single localised failure despite this potential.

A Bayesian bootstrap-Copula coupled method for slope reliability analysis considering bivariate distribution of shear strength parameters

A Bayesian bootstrap-Copula coupled method for slope reliability analysis considering bivariate distribution of shear strength parameters

Efficient slope reliability and sensitivity analysis using quantile-based first-order second-moment method

This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method (QFOSM). The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids. Based on this geometric interpretation, the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system. The proposed method has the advantage of computational simplicity, akin to the conventional first-order second-moment method (FOSM), while providing estimation accuracy close to that of the first-order reliability method (FORM). Its performance is demonstrated with a numerical example and three slope examples. The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters. The proposed method does not involve complex optimization or iteration required by the FORM. It can provide a valuable complement to the existing approximate reliability analysis methods, offering rapid sensitivity evaluation and slope reliability analysis.

Analysis of slope stochastic fields using a novel deep learning model with attention mechanism

This paper proposes a novel deep learning model incorporating attention mechanisms for the analysis of slope stochastic fields. Initially, a deep learning model is designed to digitally image the stochastic field features of soil strength variability. This is achieved by discretizing the slope soil stochastic field using the Karhunen-Loeve expansion method and transforming the discrete results into digital images. These images are then used to establish a Convolutional Neural Network (CNN) surrogate model that maps the implicit relationship between stochastic field images and slope functional function values, thus calculating the probability of slope failure. The precision of the CNN surrogate model is enhanced through Bayesian optimization and five-fold cross-validation. Moreover, to overcome the limitations of existing data-driven landslide stability prediction models, this study also introduces a Spatial-Temporal Attention (STA) mechanism. By combining the CNN with Long Short-Term Memory (LSTM) networks, the model can accurately approximate the actual results of slope stability calculations in scenarios of high-dimensional representation imaging of stochastic fields and low-probability slope instability. Consequently, this significantly improves the computational efficiency of slope reliability analysis considering stochastic field simulations.

Study on Target Reliability of Mine Rock Slopes by Grey Fixed Weight Clustering and Analogy Method—Case Study of the Jinbao Iron Mine

Study on Target Reliability of Mine Rock Slopes by Grey Fixed Weight Clustering and Analogy Method—Case Study of the Jinbao Iron Mine

Probabilistic back-analysis of rainfall-induced landslides for slope reliability prediction with multi-source information

Probabilistic back-analysis is an important means to infer the statistics of uncertain soil parameters, making the slope reliability assessment closer to the engineering reality. However, multi-source information (including test data, monitored data, field observation and slope survival records) is rarely used in current probabilistic back-analysis. Conducting the probabilistic back-analysis of spatially varying soil parameters and slope reliability prediction under rainfalls by integrating multi-source information is a challenging task since thousands of random variables and high-dimensional likelihood function are usually involved. In this paper, a framework by integrating a modified Bayesian Updating with Subset simulation (mBUS) method with adaptive Conditional Sampling (aCS) algorithm is established for the probabilistic back-analysis of spatially varying soil parameters and slope reliability prediction. Within this framework, the high-dimensional probabilistic back-analysis problem can be easily tackled, and the multi-source information (e.g. monitored pressure heads and slope survival records) can be fully used in the back-analysis. A real Taoyuan landslide case in Taiwan, China is investigated to illustrate the effectiveness and performance of the established framework. The findings show that the posterior knowledge of soil parameters obtained from the established framework is in good agreement with the field observations. Furthermore, the updated knowledge of soil parameters can be utilized to reliably predict the occurrence probability of a landslide caused by the heavy rainfall event on September 12, 2004 or forecast the potential landslides under future rainfalls in the Fuhsing District of Taoyuan City, Taiwan, China.

Reliability analysis of vegetated slope considering spatial variability of soil and root properties

Vegetation acts as a natural engineering approach that can enhance the stability of shallow soil slopes. However, the intrinsic uncertainties of vegetation, particularly the randomness of root features, have rarely been considered in vegetated slope stability analysis. To address the issue, a modified random field model is proposed to simulate the spatial variability of root parameters (e.g., root volume ratio, Rv) with different root orientations and architectures. The proposed random field model, combined with the finite element method (FEM) and limit equilibrium method (LEM), is utilised to investigate the effects of root architecture, orientation, and depth on vegetated slope reliability, considering spatial variability of soil and root properties simultaneously under rainfall infiltration. It is found that the proposed model effectively characterises the spatial variability of root parameters with different root orientations and architectures, as validated against theoretical and field-measured data. Ignoring root orientation during simulation can lead to a misestimation of the slope reliability index by up to nearly 17.1%. Moreover, without considering the spatial variability of Rv within the root zone or spatially variable soil properties (i.e., void ratio, saturated water permeability, and soil water retention curve) beyond the root zone, the vegetated slope reliability index can be overestimated by up to 4.8 times. It is recommended to adopt a triangular root system, concentrating most of the roots in the shallow depth zone and extending horizontally, which can reduce slope stability uncertainty and improve overall slope reliability.

Probabilistic pile reinforced slope stability analysis using load transfer factor considering anisotropy of soil cohesion

AbstractA probabilistic limit equilibrium framework combining empirical load transfer factor and anisotropy of soil cohesion is developed to conduct pile‐reinforced slope reliability analysis. The anisotropy of soil cohesion is determined conditioned on that the thrust force direction is parallel to the major principal direction and it is easily combined with load transfer factor, which are related with soil parameters, and pile parameters. The proposed method is illustrated against a homogeneous soil slope. The sensitivity studies of pile parameters on factor of safety (FS; calculated at respective means of soil parameters) and β demonstrated that the anisotropy of soil cohesion tends to pose significant effect on reliability index β than on FS. The effect of anisotropy of soil cohesion on FS is found to be slightly different under different pile locations, whereas its effect on β is observed to be least if piles are drilled at the middle part of slope and more significant effect is observed when piles are drilled at the lower and upper part of slope. The plots from the sensitivity studies provide an alternative tool for pile designs aiming at the target reliability index β. The proposed method contributes to the pile‐reinforced slope stability within limit equilibrium framework.

Hybrid response surface method for system reliability analysis of pile-reinforced slopes

To consider the complex soil-structure interaction in a pile-slope system, it is necessary to analyze the performance of pile-slope systems based on a three-dimensional (3D) numerical model. Reliability analysis of a pile-slope system based on 3D numerical modeling is very challenging because it is computationally expensive and the performance function of the pile failure mode is only defined in the safe domain of soil stability. In this paper, an efficient hybrid response surface method is suggested to study the system reliability of pile-reinforced slopes, where the support vector machine and the Kriging model are used to approximate performance functions of soil failure and pile failure, respectively. The versatility of the suggested method is illustrated in detail with an example. For the example examined in this paper, it is found that the pile failure can significantly contribute to system failure, and the reinforcement ratio can effectively reduce the probability of pile failure. There exists a critical reinforcement ratio beyond which the system failure probability is not sensitive to the reinforcement ratio. The pile spacing affects both the probabilities of soil failure and pile failure of the pile-reinforced slope. There exists an optimal location and an optimal length for the stabilizing piles.

New Kriging methods for efficient system slope reliability analysis considering soil spatial variability

Recently, multiple Kriging (MK) metamodels have demonstrated their advantages in system slope reliability analysis. However, the inherent spatial variability of soil properties has not been considered due mainly to the ''curse of dimensionality''. This study aims to extend the application of MK metamodels to efficient slope reliability analysis with spatially variable soils via developing three different but related representative novel MK methods. The most complex among them is the representative active learning Kriging (RALK) method, which first proceeds with the simulation of random fields of soil properties with a small number of independent variables using Karhunen-Loève expansion method. Then, representative slip surfaces (RSSs) of a slope are identified to reduce the number of Kriging metamodels to be built, which is followed by using sliced inverse regression (SIR) to further reduce the number of independent variables. Thereafter, initial RALK metamodels are established for all RSSs with the dimension-reduced variables. Finally, a sequential sampling strategy is proposed to actively learn and update the RALK metamodels to further improve their efficiency. The other two methods are called MK-RSS and MK-RSS-SIR, which omit some steps compared with RALK method (MK-RSS-SIR omits active learning; MK-RSS omits active learning and SIR). The accuracy and efficiency of the three methods for slope reliability analysis are illustrated by considering two multi-layered soil slopes. The results show that RALK is suitable for slopes where the safety factor of one slip surface can be calculated separately, MK-RSS-SIR is suitable for slopes with simple conditions and more RSSs, and MK-RSS is suitable for slopes with complex conditions and fewer RSSs.

Reliability of Municipal Solid Waste Landfills within the Eurocode Framework

Municipal solid waste (MSW) landfill slope failures can have significant consequences for the economy, environment, and human health. One potential cause of slope failure is insufficient reliability, resulting from inadequate design. The usual practice in the design of MSW landfills involves utilizing established geotechnical codes, such as Eurocode 7 (EC7), to perform slope stability assessments. Considering the substantial heterogeneity of MSW relative to soil, questions arise regarding the justification of such an approach in the design of MSW landfills. This study examines the suitability of applying EC7 in MSW landfill design, analyzing the stability and reliability of landfill slopes across various heights, front slope angles, design approaches, and consequence classes. This study finds that, in most cases considered, EC7 does not ensure an adequate level of reliability for MSW landfill slopes. Therefore, it is suggested that EC7 should be complemented with specific guidelines for incorporating MSW in geotechnical analyses to achieve the desired structural reliability. Adopting this strategy will not only enhance the reliability of landfill design but also promote the development of solutions that are economically and environmentally sustainable.