The present work is focused on the details of a fuzzy set plasticity theory that was used to model the hysteresis loops in the SoilWater 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.

This paper presents how the elasto-plastic constitutive relations have been used to predict the hysteretic behavior in unsaturated sands. An efficient method was selected to represent the relation, and the predicted capabilities were assessed on many scanning curves. The proposed method is derived from Gajo and Wood's evolution equation for the plastic modulus to evaluate the suction change during wetting/drying processes. The study proposes the simple formulas for the relationship between the boundary curves and the scanning curves. The results obtained from the proposed formulas were verified through a comparison with the existing experimental data in the literature. The comparison indicates that the elasto-plastic constitutive relations during cyclic loading can be utilized to describe the scanning behavior of Soil Water Characteristic Curves (SWCCs).