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Journal of Applied Mathematics
Volume 2013, Article ID 537185, 15 pages
Research Article

A Unified Elastoplastic Model of Unsaturated Soils Considering Capillary Hysteresis

1State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Xiaohongshan, Wuchang, Wuhan, Hubei 430071, China
2College of Civil and Architectural Engineering, Guilin University of Technology, Guilin, Guangxi 541004, China
3Department of Civil Engineering, Shanghai University, Shanghai 200072, China

Received 14 May 2013; Accepted 26 July 2013

Academic Editor: Pengcheng Fu

Copyright © 2013 Tiantian Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Unlike its saturated counterparts, the mechanical behavior of an unsaturated soil depends not only upon its stress history but also upon its hydraulic history. In this paper, a soil-water characteristic relationship which is capable of describing the effect of capillary hysteresis is introduced to characterize the influence of hydraulic history on the skeletal deformation. The capillary hysteresis is viewed as a phenomenon associated with the internal structural rearrangements in unsaturated soils, which can be characterized by using a set of internal state variables. It is shown that both capillary hysteresis and plastic deformation can be consistently addressed in a unified theoretical framework. Within this context, a constitutive model of unsaturated soils is developed by generalizing the modified Cam-Clay model. A hardening function is introduced, in which both the matric suction and the degree of saturation are explicitly included as hardening variables, so that the effect of hydraulic history on the mechanical response can be properly addressed. The proposed model is capable of capturing the main features of the unsaturated soil behavior. The new model has a hierarchical structure, and, depending upon application, it can describe the stress-strain relation and the soil-water characteristics in a coupled or uncoupled manner.