Zi-Jun Cao

Efficient System Reliability Analysis of Slope Stability in Spatially Variable Soils Using Monte Carlo Simulation

Abstract Monte Carlo simulation (MCS) provides a conceptually simple and robust method to evaluate the system reliability of slope stability, particularly in spatially variable soils. However, it suffers from a lack of efficiency at small probability levels, which are of great interest in geotechnical design practice. To address this problem, this paper develops a MCS-based approach for efficient evaluation of the system failure probability P f , s of slope stability in spatially variable soils. The proposed approach allows explicit modeling of the inherent spatial variability of soil properties in a system reliability analysis of slope stability. It facilitates the slope system reliability analysis using representative slip surfaces (i.e., dominating slope failure modes) and multiple stochastic response surfaces. Based on the stochastic response surfaces, the values of P f , s are efficiently calculated using MCS with negligible computational effort. For illustration, the proposed MCS-based system reliab...

Bayesian Approach for Probabilistic Site Characterization Using Cone Penetration Tests

AbstractThis paper develops a Bayesian approach for probabilistic site characterization (i.e., on both stratigraphy and soil properties) using cone penetration tests (CPTs). The available site information prior to the project (e.g., existing geological maps, geotechnical reports, and local experience) is used in the Bayesian approach as prior knowledge, and it is integrated systematically with results of CPTs that are performed deliberately for the project. The inherent spatial variability of soil is modeled explicitly by random field theory. The proposed approach contains two major components: a Bayesian model class selection method to identify the most probable number of statistically homogenous layers of soil and a Bayesian system identification method to estimate the most probable layer thicknesses and soil properties probabilistically. Equations are derived for the Bayesian approach, and the proposed approach is illustrated using a set of real CPT data obtained from a site in Netherlands. It has been...

Bayesian Model Comparison and Characterization of Undrained Shear Strength

AbstractThis paper develops Bayesian approaches for facilitating the determination of characteristic (or nominal) values of geomaterial properties in geotechnical analysis and design when extensive testing cannot be performed, which is the case for a majority of geotechnical projects, particularly those of a small or medium size. These Bayesian approaches aim to characterize probabilistically the undrained shear strength, Su, of clay using a limited amount of liquidity index (LI) test data, and to provide a logical route to determine the characteristic values for analysis and design, particularly those using probability-based design codes. The proposed approaches include (1) a Bayesian model comparison approach that selects the most appropriate likelihood model, a key element in the Bayesian framework, using a limited number of LI data obtained from a specific project site, and (2) a Bayesian equivalent sample approach that uses the selected likelihood model, integrates the sound engineering judgment/loca...

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 Pf < 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 (Pf) and risk (R) of slope failure. These equations are illustrated using a soil slope example. It is shown that the Pf 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 Pf 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.

Bayesian Equivalent Sample Toolkit (BEST): an Excel VBA program for probabilistic characterisation of geotechnical properties from limited observation data

ABSTRACT In site investigation, the amount of observation data obtained for geotechnical property characterisation is often too sparse to obtain meaningful statistics and probability distributions of geotechnical properties. To address this problem, a Bayesian equivalent sample method was recently developed. This paper aims to generalize the Bayesian equivalent sample method to various geotechnical properties, when measured by different direct or indirect test procedures, and to implement the generalized method in Excel by developing an Excel VBA program called Bayesian Equivalent Sample Toolkit (BEST). The BEST program makes it possible for practitioners to apply the Bayesian equivalent sample method without being compromised by sophisticated algorithms in probability, statistics and simulation. The program is demonstrated and validated through examples of soil and rock property characterisations.

Full probabilistic design of slopes in spatially variable soils using simplified reliability analysis method

ABSTRACT A simplified reliability analysis method is proposed for efficient full probabilistic design of soil slopes in spatially variable soils. The soil slope is viewed as a series system comprised of numerous potential slip surfaces and the spatial variability of soil properties is modelled by the spatial averaging technique along potential slip surfaces. The proposed approach not only provides sufficiently accurate reliability estimates of slope stability, but also significantly improves the computational efficiency of soil slope design in comparison with simulation-based full probabilistic design. It is found that the spatial variability has considerable effects on the optimal slope design.

Probabilistic approaches for geotechnical site characterization and slope stability analysis

In the last few decades, reliability-based design (RBD) approaches/codes and probabilistic analysis methods, such as probabilistic slope stability analysis with Monte Carlo Simulation (MCS), have been developed for geotechnical structures to deal rationally with various uncertainties (e.g., inherent spatial variability of soils and uncertainties arising during geotechnical site characterization) in geotechnical engineering. Applications of the RBD approaches/codes and probabilistic analysis methods in turn call for the needs of probabilistic site characterization, which describes probabilistically soil properties and underground stratigraphy based on both prior knowledge (i.e., site information available prior to the project) and project-specific test results. How to combine systematically prior knowledge and project-specific test results in a probabilistic manner, however, is a challenging task. This problem is further complicated by the inherent spatial variability of soils, uncertainties arising during site characterization and the fact that geotechnical site characterization generally only provides a limited number of project-specific test data. This study aims to address these challenges in probabilistic site characterization. A Bayesian framework is first developed for geotechnical site characterization, which integrates systematically prior knowledge and project-specific test results to characterize probabilistically soil properties and underground stratigraphy. The Bayesian framework addresses explicitly the inherent spatial variability of soils and accounts rationally for uncertainties arising during site characterization. It is general and equally applicable for different types of prior knowledge and different amounts of project-specific test data. When the project-specific tests (e.g., standard penetration tests) only provide sparse data, the Bayesian framework is integrated with Markov Chain Monte Carlo Simulation (MCMCS) to develop an equivalent sample approach that generates a large number of equivalent samples

Slope stability analysis in the Three Gorges Reservoir Area considering effect of antecedent rainfall

ABSTRACT Effects of different initial conditions of pore water pressure distribution on slope stability are investigated based on rainfall data in the Three Gorges Reservoir Area. A method to incorporate the initial condition of pore water pressure distribution into the slope stability analysis is suggested. Then, sandy and clayey slopes are taken as examples to investigate the effect of antecedent rainfall on slope stability. Results indicate that the influence of antecedent rainfall on the slope stability increases as the saturated permeability coefficient of the soil decreases.

Auxiliary Random Finite Element Method for Risk Assessment of 3-D Slope

Spatial variability of soil properties is one of the major uncertainties in geotechnical properties that significantly affect slope reliability and risk. To account for the effect of three-dimensional (3-D) spatial variability, an efficient random finite element method (RFEM), named auxiliary RFEM (ARFEM), is proposed for 3-D slope reliability analysis and risk assessment. The ARFEM consists of two steps: the preliminary analysis using a relatively coarse 3-D finiteelement model and subset simulation, and the target analysis using a detailed 3-D finite-element model and response conditioning method. Compared with direct Monte Carlo simulation-based RFEM, ARFEM can provide consistent reliability and risk estimates with much less computational efforts. In addition, it is found that both the horizontal and vertical spatial variability have significant, but different, impacts on 3-D slope reliability, risk and failure mechanisms.

Reliability-based robust geotechnical design using Monte Carlo simulation

The reliability-based robust geotechnical design (RGD) approach provides an effective tool to deal with the uncertainty in the estimated statistics of geotechnical parameters in a reliability-based design. However, the existing reliability-based RGD approach is not straightforward to apply as it involves multiple concepts. In this paper, the applicability of the existing reliability-based RGD approach is improved by utilizing Monte Carlo simulation (MCS). Here, an MCS-based weighted technique is used to evaluate the failure probability of a geotechnical system. With the aid of this weighted technique, the variation in the failure probability, caused by the uncertainty in the estimated statistics of geotechnical parameters, is computed using MCS. To further improve the efficiency of the RGD method, a series of single-objective optimizations are used in lieu of a multi-objective optimization in the robust design optimization process. The proposed MCS-based RGD approach is illustrated through an example of rock slope design. Compared with the existing reliability-based RGD approach, the MCS-based RGD approach is not only more intuitive and easier to follow, but also more computationally efficient.