Reliability assessment of slopes considering sampling influence and spatial variability by Sobol’ sensitivity index

Abstract

This paper presents an extended formulation of the Sobol' sensitivity index for geotechnical reliability assessments involving spatially variable soil properties. It incorporates the subsurface spatial correlation structure with the response surface method, which is then assimilated into the context of the Sobol' index approach. A Sobol' index map can be generated for the entire subsurface domain, identifying the sensitive zones that also represent the optimal sampling locations. In addition, the approach allows the derivation of the mean and variance of system response conditional to any sample value, without the need to conduct separate conditional random field simulations. This is adopted for the assessment of the reliability of slopes, where design charts are established for cases in which a single sample is obtained within slopes of cu or c - ϕ soils, with various conditions of geometries and spatial variability. The approach can also be applied to multiple sampling points, thereby facilitating a feedback mechanism where the planning of geotechnical investigation and evaluation of performance uncertainty can be considered in a holistic manner.