A Soil-Water Hysteresis Model for Unsaturated Sands Based on Fuzzy Set Plasticity Theory

The present work is focused on the details of a fuzzy set plasticity theory that was used to model the hysteresis loops in the Soil-Water Characteristic Curves (SWCCs). This study first presents an elasto-plastic stress-strain relationships of capillary hysteresis behavior in unsaturated conditions. The linear evolution equation for the elasto-plastic modulus and the membership function in the fuzzy set plasticity theory are introduced. An implicit integration method is then applied to develop the full set of incremental equations. Experimental and literature-cited data were used to evaluate model accuracy. Qualitative predictions of the proposed model show that incorporating soil-water characteristic equation and membership function into the fuzzy set plasticity model opens a full range of possibilities in modeling hysteretic behavior in unsaturated sands.