Stochastic Variability of Soil Properties: Data Analysis, Digital Simulation, Effects on System Behavior

by Radu Popescu

A disertation presented to the faculty of Princeton University
in candidacy for the degree of Doctor of Philosophy

November, 1995

Aside from the measurement induced bias and even within assumed homogeneous soil strata, natural soils are variable in their properties. The scarcity in field test results, characteristic to geotechnical engineering, and a sufficiently large degree of disorder exhibited by soil properties leads to the use of statistical methods in describing the distribution of those properties within a ``statistically homogeneous'' soil zone.

In this context, it is proposed to model relevant soil parameters as the components of a multi-dimensional, multi-variate (nD-mV) stochastic field. The characteristics of the stochastic field (cross-spectral density matrix, probability distribution of each component) are evaluated by nonlinear regression analysis based on sample functions derived from statistically significant sets of ``in-situ'' measurement results. Sample functions of an nD-mV non-Gaussian stochastic field are then simulated using an extension of the spectral representation method. A methodology for evaluating traditional soil parameters from the results of conventional field tests is proposed and employed to derive the spatial distribution of soil parameters which are relevant for dynamic analyses. Monte Carlo simulations of the behavior of horizontally layered soil deposits, as well as of structures founded on liquefiable soil and subjected to seismic loads are performed by combining vector field simulations with nonlinear dynamic finite element analyses.

The numerical simulation results (predicting excess pore-pressure build-up, liquefaction index, and liquefaction induced deformations) obtained using stochastic input constitutive parameters are compared to deterministic input simulation results. It is concluded that, for the case of dynamically induced pore water pressure build-up, the results of classical deterministic analyses are on the non-conservative side. Selection of the optimum discretization mesh size for stochastic analyses, as well as influence on the computational results of assumed spatial correlation distances and probability distribution functions are also discussed.

The theoretical developments are illustrated with numerical examples conducted in terms of traditional soil parameters, and based on data obtained from extensive field measurement programs. Therefore, the study will provide a basis for characterization of spatial variability of soil properties and for liquefaction risk assessment.

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