A variable moduli probabilistic constitutive model for soils

Abstract

Measurement of stress - strain relationships in soil systems usually incorporate varying degrees of uncertainty. These uncertainties arise from laboratory testing mechanisms, sampling disturbances, errors performed by operators or technicians performing the tests, etc. Currently, deformation analyses have been modeled using several deterministic techniques. However, because of the uncertainties involved, there is a need to adapt these numerical methods into probabilistic models. This thesis develops a probabilistic constitutive model based on a variable moduli deterministic technique. First-order, second-moment stochastic methods are used to estimate a mean stress - strain curve and its ±1 standard deviation from raw data obtained on nearly identical, remolded sand samples. Probabilistic estimations for Bulk and Shear moduli are determined from the estimated mean curves and are used to develop a probabilistic constitutive model. Through the use of a probabilistic constitutive matrix, a stochastic equation is produced which can relate strains to any stress state imposed on a particular soil. This is verified through an example.