With regards to the composition of natural rocks including voids or pores, deformation behavior is strongly affected by variation in porosity. By using a statistical damage-based approach, the characteristics of strain softening and hardening under the influence of voids and volume changes are investigated in the present paper. Suppose that a rock consists of three parts: voids, a damaged part, and an undamaged part. The effects of voids and volume changes on rock behavior are first analyzed through determination of the porosity and an associated damage model is then developed. Later, a statistical evolution equation describing the influence of the damage threshold on the propagation condition of rock damage is formulated based on measurement of the mesoscopic element strength. A statistical damage constitutive model reflecting strain softening and hardening behavior for rocks loaded in conventional triaxial compression is further developed and a corresponding method for determining the model parameters is also provided. Theoretical results of this proposed model are then compared with those observed experimentally. Finally, several aspects of the present constitutive model, which affect the relevant behavior of rocks, are particularly discussed.

A constitutive model with capacity to simulate the full deformation and failure process for rocks considering initial compression and residual strength behaviors is discussed in this paper. The rock was assumed to consist of the initial voids portion and the solid skeleton portion. The full deformation model of rocks can be established by the consideration of the macroscopic deformation of rocks and the microscopic deformations of the two different portions based on the statistical damage theory. Comparisons between the experimental data from triaxial compression tests and calculated results show that the proposed constitutive model provided a good prediction of the full deformation and failure process, including the effects of initial void compression, stiffness degradation, strain hardening–softening, and residual strength.

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Considering the nonlinear rheological properties of saturated clay, the modified unified hardening (UH) constitutive relation was introduced to describe the nonlinear rheological deformation. Meanwhile, Swartzendruber's flow law was used to simulate the non-Darcian flow of pore water in the progress of rheological consolidation. Consequently, a nonlinear rheological consolidation model (NRCM), for one-dimensional consolidation, that simultaneously incorporates nonlinear stress-strain-time relationship, Swartzendruber's flow, self-weight stress, and variable permeability coefficient has been developed here. The finite volume method (FVM) was utilized to solve the NRCM system, and its effectiveness was verified by comparing with the existing consolidation data. The parametric analysis results indicate that the soil's nonlinear rheological effect induced the excess pore water pressure (EPWP)'s accumulation in the initial loading. This phenomenon became more significant when considering the self-weight stress or as the initial overconsolidated parameter, soil thickness, and seepage parameter increased. In contrast, it weakened with the increase of external loading. Additionally, considering the self-weight stress slowed down the whole dissipation of EPWP in the initial period of loading. Nevertheless, it accelerated the nonlinear consolidation process in the middle and late loading stages.