Simulation of random fields of soil properties by the local average subdivision method and engineering applications

The seismic performance of oil and natural gas pipelines founded or embedded in earth slopes encompasses great uncertainty related both to the earthquake shaking characteristics and to the natural heterogeneity of geomaterials. Regarding the latter, the parameters of shear strength, stiffness, density, etc., may vary indeed from point to point even within the same soil layer as a result of the natural formation process. Apart from their cross-correlation, such random variables exhibit autocorrelation, in which the soil properties at a given point appear to be spatially correlated with the properties of neighbouring points. Therefore, there is a need to use stochastic methods in the safety evaluation of such systems. Aiming at the reliability assessment of such soil-pipeline systems under seismic shaking, this paper introduces an automated methodology for generating random fields using the Local Average Subdivision (LAS) method by Fenton and Vanmarcke (J Eng Mech 116(8):1733–1749, 1990). Subsequently, it performs rigorous nonlinear dynamic analysis of a given slope using the finite difference method. The automated procedure is used in a Monte-Carlo simulation scheme for computing the probability of exceeding different levels of anticipated permanent slope movement for different levels of shaking intensity. The results demonstrate that the effect of the spatial variability of the soil properties on the permanent displacements of natural slopes is important, leading to a range of variation of about ± 60%.