The generalized Zhang-Zhu (GZZ) criterion successfully extends the widely used Hoek-Brown criterion to a three-dimensional (3D) version by considering the intermediate principal stress. Based on the GZZ criterion, a constitutive model within the elastic-perfectly plastic framework has already been developed. In this paper, a general strain-softening/hardening constitutive model is proposed aiming to enhance the performance with respect to post-failure behavior prediction. The plastic deviatoric strain is taken as the fundamental variable in a series of exponential functions to control the softening/hardening behavior of rock. The same type of exponential function but with different parameters is used to describe the evolution of the plastic potential function. The constitutive model has been implemented in a 3D finite-difference code and used to analyze two types of rock tested under a true triaxial condition. The results indicate that the calculated stress versus strain and lateral strain versus axial strain relations based on the constitutive model are in good agreement with those from the experiments. A systematic parametric study is also performed to explore the effect of the strain-softening/hardening parameters on the post-failure behavior of rock.


The Hoek-Brown strength criterion (Hoek and Brown, 1980; Hoek, 1983; Hoek and Brown, 1997; Hoek et al., 2002), which considers the effects of rock mass structure and discontinuity surface conditions, is the most popular strength criterion for rock masses and has been applied to a wide range of rock engineering problems over the past decades. Continuous work (Martin et al., 1999; Marinos et al., 2005; Hoek and Diederichs, 2006; Cai, 2010) has been carried out to expand its framework to tackle with different engineering problems and versatile application scenarios.

As for the constitutive models for rock, most of the current finite-element (FE) and finite-difference (FD) codes employ the elastic-perfectly plastic framework to model the post-failure behavior. Plenty of efforts have been made to adopt the perfectly plastic framework to theoretically analyze rock engineering problems (e.g., Serrano and Olalla, 1998a, b; Carranza-Torres and Fairhurst, 1999; Shen et al., 2013). However, the strain-softening/hardening behavior of rock, which can be observed in both field and laboratory tests, cannot be properly described by the existing perfectly plastic constitutive models. Ignoring the strength degradation could lead to overestimation of the residual strength of rock masses and the potential failure of rock engineering structures. To overcome this limitation, many researchers (e.g., Lee and Pietruszczak, 2008; Zou et al., 2016; Wang and Qian, 2018) have proposed analytical and/or numerical solutions based on the concept of strain-softening, where a piecewise linear function is commonly adopted to capture the degradation of strength after failure. However, this type of function may result in a sharp transition between the peak strength and the residual strength.

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