Random Isogeometric Analysis for Modeling Seepage in Unsaturated Soils

Abstract

This study proposes a new probabilistic framework, random isogeometric analysis (RIGA), combining isogeometric analysis (IGA) and random fields to numerically simulate seepage in unsaturated soils. The proposed framework benefits from computationally efficient IGA solutions and properly accounts for the variability of unsaturated soil parameters by using random field theory. Two constitutive models commonly used to describe the behavior of unsaturated soils, the soil water retention curve (SWRC) and hydraulic conductivity function (HCF), are considered under the proposed RIGA method. A database of unsaturated hydraulic properties is used to investigate the variability of SWRC and HCF model parameters for different soils. Random field concepts with statistical homogeneity (fixed mean, standard deviation, and spatial correlation) are implemented to generate SWRC and HCF model properties considering a joint lognormal distribution function among the model parameters. The joint lognormal distribution function is used with IGA to perform Monte Carlo simulations. The number of realizations in the Monte Carlo simulation accounts for the effect of stochastic soil parameters in unsaturated soil analysis. The application of the proposed RIGA is illustrated by simulating unsaturated seepage in two example problems, a one-dimensional flow in a rectangular domain and a two-dimensional infiltration problem in a semicircular furrow. The results of these problems depict the statistical outputs relating to seepage quantities and negative pore water pressure with respect to standard deviation and correlation between SWRC and HCF model parameters. In all cases, the results are compared with those obtained from an alternative deterministic analysis and it is shown that negative pore water pressure, flow rate, and other quantities of interest change considerably with respect to standard deviation and correlation of the model parameters.