An engineering mechanics of unsaturated porous rock was proposed in order to consider the nonlinear and irreversible deformations of both rock material and porous rock. Firstly, with using the volume fraction concept and mixture theory, the equation of energy balance in terms of five state variables was obtained in virtue of the mixture homogenous response principle, which were called void strain tensor, degree of saturation and the material volume strain of each constituent. The five elastic equations which were determined by free energy and the one equation that the sum of all volume fractions was equal to unity compose six constitutive equations. Based on these equations, all six unknown variables (three displace vectors and three volume fractions) could be solved in the constitutive model of unsaturated rock. Secondly, according to the irreversible thermodynamics, the potential of dissipative rate in terms of internal variables was proposed on the basis of entropy production formula. Thus, the dissipative constitutive equations were derived to describe the irreversible deformation behaviors such as viscosity or plasticity. Results show that, the two potential functions of free energy and dissipative rate can depict the discipline of elastic and inelastic deformations, respectively, which both form the constitutive theoretical framework of unsaturated porous rock.
HU Ya yuan. Thermodynamics-based constitutive theory for unsaturated porous rock. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2017, 51(2): 255-263.
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