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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).

Rainfall infiltration test under one dimensional condition is conducted to evaluate the effect of rainfall intensity on seepage velocity and infiltration characteristics for initial unsaturated sediment. Experimental results are compared with those numerical simulations with respect to variations of pore water pressure, degree of saturation and discharge velocity with time, and both results give good agreement. High rainfall intensity tends to increase seepage velocity almost linearly.But it shows rapid increase as rainfall intensity approaches saturated hydraulic conductivity of the sediment. In addition, the upper part of wetting front depth is partially saturated, not fully. Therefore, actual wetting front depth is considered to advance faster than theoretical prediction, which leads to slope instability of unsaturated slope due to surface rainfall.

According to an exhibition of clay soils consisting of not only elastic but also viscous properties, we present Kelvin-Voigt model combined by an elastic spring and a damper in parallel to investigate the dynamics of crack opening. The equation of motion of crack opening is derived mathematically from the equilibrium equation; that means the frictional shear stress is equal to the tension in the soil. After obtaining the equation of motion, the experiments were carried out in laboratory on Kaolin to validate the proposed model through cracks. The obtained experimental data were fitted by the dynamical equation of motion using curve-fitting method. The results indicate that the proposed model yields a good correlation between the experiment data and the computed values with the fairly high coefficient of regression (=0.98). Therefore, it is concluded that the proposed Kelvin-Voigt model can be used appropriately for describing the dynamics of crack opening in clays.