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.

Statistical damage constitutive models (SDCMs) have been widely employed to describe the mechanical response of strain-softening rock, especially in brittle failure under moderate confining pressure. The residual strength, referring to the strength of strain-softening rock in the postpeak region, has not been accurately considered in present works. In this study, an extended definition of damage was proposed based on the fact that the intact material gradually evolves into another damaged material, and these two parts are mixed together to carry external loads. Accordingly, a modified damage mechanical model was established. Then, the evolution equation of the damage variable was formulated based on the well-known Weibull distribution. Furthermore, a modified SDCM reflecting strain-softening and residual strength behavior for rocks loaded in conventional triaxial compression (CTC) was developed. The model parameters were estimated based on the extremum method. Finally, validation indicated that the calculated results from the modified SDCM had good agreement with the experimental observation and were much better than the calculated results from other models. Issues related to the lateral deformation of this model were also examined.

Finite element limit analysis (FELA) was used to investigate the bearing capacity of strip footing on a rock mass with single or multiple continuous voids. The underlying rock mass was assumed to have perfect plasticity and obey the modified Hoek–Brown criterion. A sensitivity study relevant to the material constants, such as intact rock strength, unit weight, and geological strength index, was also conducted; in addition, some other geometric parameters, including the location, size, width, height, and quantity of voids, were addressed. The results include presentations of a series of design charts and descriptions of the failure mechanisms.

This study employed finite element limit analysis (FELA) to investigate the influence of eccentric loads on the bearing capacity of footings above single and double continuous voids. Upper bound theorem (UB), lower bound theorem (LB), and adaptive meshing techniques were used in a parametric study to investigate the influence of some factors, including the relative distance between double voids, the depth of voids, the geometry of voids, the variation of soil shear strength, and the eccentricity of loadings on the bearing capacity of footings. The results indicated that, for the footings inclined above a single void, the bearing capacity with a void located on the same side of the eccentric load was less than that in an opposite position. In addition, the failure mechanisms were summarized and analyzed in this study.