Ivan Depina

Cone penetration data classification with Bayesian Mixture Analysis

ABSTRACT This paper presents an application of the Bayesian Mixture Analysis (BMA) to deal with the classification of spatially variable soil data from the cone penetration test. The cone penetration data classification postulates a problem where a set of cone penetration measurements is used to identify “hidden or unobserved” soil classes. The problem is formulated as an incomplete-data Gaussian mixture where the observed data are defined by the natural logarithm-transformed values of the normalized friction and the normalized cone resistance, while the soil classes to be identified are considered as hidden data. The solution for the incomplete-data problem which consists of class-dependent mixture probabilities and Gaussian distribution parameters is defined in a Bayesian framework. The implementation of conjugate priors for the Gaussian mixtures enables an efficient sampling of the posterior parameters by the Gibbs algorithm of the Markov Chain Monte Carlo method. When compared to the well-established Robertson classification charts, the BMA formulation has an advantage due to the Bayesian framework which enables the definition of soil classes through mixture priors, class-dependent posterior parameter estimates, and a probabilistic soil classification. The presented approach is applied to the cone penetration data from the Sheringham Shoal Offshore Wind Farm site.

Bayesian Updating of Uncertainties in the Stability Analysis of Natural Slopes in Sensitive Clays

Safety assessment of natural slopes in sensitive clays is subjected to uncertainty due to the natural variation of soil properties, measurement and modelling errors. In order to ensure acceptable safety levels, geotechnical design codes (e.g., Eurocode 7) commonly provide frameworks for a systematic treatment of uncertainties in the safety assessment of a slope. The treatment of uncertainties in the design codes is primarily focused on the parameters directly involved in the analysis of the mechanical stability of a slope (e.g., soil strength parameters). Additional valuable contributions to the safety assessments of slopes can be also provided by information that relates indirectly to the mechanical stability of a slope (e.g., past slope performance). However, there is often a lack of systematic integration of indirect information in the existing design codes. This paper examines the integration of indirect information based on the observed past slope performance in the safety assessment of a slope. The integration is facilitated through the Bayesian framework because it provides a basis to update uncertainties in the slope stability and safety assessment, such that they are consistent to the observed slope performance. The paper examines the effects of slope survival and failure events on uncertainties in the slope stability analysis.

Estimation of Failure Probability by Limit State Sampling

This paper presents a novel approach, referred to as Limit State Sampling, for estimating failure probabilities of engineering structures. The majority of methods used to evaluate failure probabilities involve a large number of simulations of the structural model. In situations with low failure probability and numerically complex structural models this can become a computationally unpractical task. The Limit State Sampling approach is developed here with the intention of reducing the number of simulations of the structural model in the process of evaluation of the failure probability. This is performed by introducing a pseudo probabilistic density function with the purpose of sampling around the failure limit state. Samples from the pseudo probability density function are then used to construct a surrogate model of the structural behavior at the failure limit state. Finally, the failure probability is estimated by utilizing the efficiency of the surrogate model, with reduced computational expense. The novelty of the approach comes from the formulation of the pseudo probability density function and the application to the probabilistic analysis of structures.