The importance of distribution types on finite element analyses of foundation settlement

We investigate the effects of using different types of statistical distributions (lognormal, gamma, and beta) to characterize the variability of Young’s modulus of soils in random finite element analyses of shallow foundation settlement. We use a two-dimensional linear elastic, plane-strain, finite element model with a rigid footing founded on elastic soil. Poisson’s ratio of the soil is considered constant, and Young’s modulus is characterized using random fields with extreme values of the scale of fluctuation. We perform an extensive sensitivity analysis to compare the distributions of computed settlements when different types of statistical distributions of Young’s modulus, different coefficients of variation of Young’s modulus, and different scales of fluctuation of the random field of Young’s modulus are considered. A large number of realizations are employed in the Monte Carlo simulations to investigate the influence of the tails of the statistical distributions under study. Results indicate the type of distribution considered for characterization of the random field of Young’s modulus can have a significant impact on computed settlement results. In particular, considering different types of distributions of Young’s modulus can lead to more than 600% differences on computed mean settlements for cases with high coefficient of variation and large scale of fluctuation of Young’s modulus. The effect of considering different types of distributions is reduced, but not completely eliminated, for smaller coefficients of variation of Young’s modulus (because the differences between distributions decrease) and for small values of the scale of fluctuation of Young’s modulus (because of an identified “averaging effect”).