Effects of soil spatial variability, sampling strategy and field monitoring on geotechnical reliability

Abstract

This thesis develops several probabilistic tools to quantify and manage the geotechnical risk arising from spatial variability of soil properties. A robust simulation method for spatial variability is proposed, namely Latin hypercube sampling with dependence (LHSD), which is a stratified sampling technique that preserves the spatial autocorrelation characteristics. It can be applied for arbitrary spatial autocorrelation, and can incorporate soil sampling effect. LHSD is coupled with Polynomial Chaos expansion (PCE), a type of surrogate model, to evaluate the risk of the geotechnical system. LHSD-PCE approach is shown to be more robust than Monte Carlo simulation (MCS) through a failure probability analysis of c - φ slope. LHSD-PCE is also applied to strip footing displacement analysis to provide practical design guidelines for sampling depth and reliability assessment. Since the reliability of geotechnical system depends heavily on the spatial autocorrelation of soil properties, it is desirable to investigate the reliability subjected to a range of spatial autocorrelation features. This thesis proposes using a novel method named response function (RF). A simulation scheme for estimating RF is proposed, followed by analyses of strip footing displacement, Cu slope reliability, and pile group settlement. RF satisfactorily matches the result from MCS when the variance of the soil property is sufficiently small, while using a significantly smaller number of model evaluations. In an engineering project, information from soil samples can constrain the spatial variation of soil properties, which reduces the uncertainty of the geotechnical system. In principle, there exists an optimal sampling strategy which achieves the maximum uncertainty reduction. Such optimal strategy is identified by applying an extended formulation of Sobol' Sensitivity index, which is applicable for correlated soil properties. Sobol' index approach is efficient because extra model evaluations are not required. Through the extended Sobol' index approach, design charts are built for Cu slopes and c - φ slopes, which indicate the optimal sampling location. Based on the obtained sample value, the slope reliability can be readily assessed from the charts. Sobol' sensitivity index is also combined with an expected Type-I error criteria to decide the required amount of soil samples. Apart from soil sampling, field monitoring can also reduce the uncertainty when predicting the performance of geotechnical system. Through Bayesian updating, initial assumptions on soil property (prior probability) are updated to obtain the posterior probability, based on observations made during the construction process. Predictions for future performance are refined based on the updated property. This thesis attempts to Bayesian update the spatial variability of soil properties within soil layers. An adaptive Metropolis-Hastings algorithm is proposed for this purpose. The convergence of the algorithm is improved through a dimension reduction procedure. The algorithm is applied to a braced excavation project in Hong Kong, where the spatial variabilities of soil stiffness and strength are updated based on inclinometer measurements, and prediction for wall deflections and their uncertainty levels are subsequently refined.