This paper develops a Monte Carlo simulation (MCS)-based reliability analysis approach for slope stability problems and utilizes an advanced MCS method called “subset simulation” for improving efficiency and resolution of the MCS at relatively small probability levels. Reliability analysis is operationally decoupled from deterministic slope stability analysis and implemented using a commonly available spreadsheet software, Microsoft Excel. The reliability analysis spreadsheet package is validated through comparison with other reliability analysis methods and commercial software. The spreadsheet package is then used to explore the effect of spatial variability of the soil properties and critical slip surface. It is found that, when spatial variability of soil properties is ignored by assuming perfect correlation, the variance of the factor of safety (FS) is overestimated, which may result in either over (conservative) or under (unconservative) estimation of the probability of failure (P_f = P(FS < 1)). When the spatial variability of soil properties is considered, the critical slip surface varies spatially and such spatial variability should be properly accounted for. Otherwise, the probability of failure can be significantly underestimated and unconservative.

In geotechnical engineering, the number of measurement data obtained from in situ or laboratory tests is usually sparse, especially for projects of small or medium size. Interpretation from such sparse measurement data is challenging and may result in significant statistical uncertainty, which refers to inaccuracy of the statistical inference results caused by a limited number of data used in the statistical inferences. Consider, for example, a soil property profile (i.e. variation of a soil property with depths), which is usually interpreted from sparse measurement data and unavoidably contains significant uncertainty. Geotechnical design and analysis results are greatly affected by the interpreted soil property profile and its uncertainty. Quantification of the uncertainty contained in the interpreted soil property profile is therefore essential, especially for probability-based design and analysis. This paper aims to address this problem using a Bayesian compressive sampling (BCS) method. The proposed approach is able not only to provide a rational and objective interpretation of the soil property profile from a relatively limited number of measurement data, but also to quantify the associated statistical uncertainty simultaneously. The quantified uncertainty provides an objective and explicit measure on the accuracy and reliability of the interpreted soil property profile. An important novelty of the proposed approach is that it depicts the quantitative evolution of statistical uncertainty in the interpreted profile as the number of measurement data increases. The proposed approach is illustrated using two sets of real cone penetration test data (i.e. tip resistance, q_c). The q_cprofile and the associated uncertainty are reasonably reconstructed and quantified from sparse q_cdata points. Furthermore, as the number of measured q_cpoints increases, the statistical uncertainty in the interpreted q_cprofile reduces substantially. When all q_cpoints are measured, the associated statistical uncertainty reduces to almost zero.

This 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...