Constitutive modelling of state-dependent behaviour of unsaturated soils: an overview
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REVIEW PAPER
Constitutive modelling of state-dependent behaviour of unsaturated soils: an overview C. W. W. Ng1 • C. Zhou2
•
C. F. Chiu3
Received: 12 December 2019 / Accepted: 19 June 2020 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract An unsaturated soil is a three-phase material that is ubiquitous on the earth’s surface. The fully saturated and completely dry states are just two limiting conditions of an unsaturated soil. The state and properties of unsaturated soils can change significantly with external loads, weather conditions and groundwater level. Proper modelling of the state-dependent behaviour of unsaturated soils is crucial for analysing the performance of almost all civil engineering structures. So far, there are many unsaturated soil models and several relevant review papers in the literature. None of the existing review papers, however, focused on the state dependency of unsaturated soil behaviour. Moreover, some aspects of soil behaviour have not been reviewed, including small strain stiffness, dilatancy and stress-dependence of water retention curve. In the current review paper, the state dependency of unsaturated soil behaviour is reviewed, with a particular attention to the three missing parts. The review is carried out in a unified and relatively simple constitutive framework, which adopts a three-bythree compliance matrix to link incremental volumetric strain, deviator strain and degree of saturation to incremental mean net stress, deviator stress and suction. All of the nine variables in the proposed three-by-three compliance matrix have clear physical meanings and can be measured through compression, shearing and water retention tests. Theoretical models based on other constitutive stress variables can be also converted to this framework by matrix transformation. Keywords Constitutive modelling Hydromechanical coupling State dependency Unsaturated soil
1 Introduction Soil is a porous medium in which the pores between solid grains play an important role in governing its mechanical and hydraulic behaviour. The pores can be filled up with liquid and/or gas. Many classical theories of soil mechanics & C. Zhou [email protected] C. W. W. Ng [email protected] C. F. Chiu [email protected] 1
Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong
2
Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
3
Department of Civil and Environmental Engineering, Shantou University, Shantou, China
have been developed based on the assumptions that the pores are filled up with either liquid (i.e. fully saturated) or gas (i.e. completely dry), e.g. Terzaghi’s theory of onedimensional consolidation, Rankine’s theory of earth pressure, among others. However, fully saturated and completely dry states are only two limiting conditions of soils [57]. In many geotechnical engineering applications, the degree
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