A damage constitutive model for intermittent jointed rocks under cyclic uniaxial compression

A damage constitutive model is proposed to describe the deformation and strength characteristics of intermittent jointed rocks under cyclic uniaxial compression. First, a coupled damage tensor for intermittent jointed rocks is derived based on the Lemaitre strain equivalence hypothesis, which combines the Weibull statistical damage model for micro-flaws and the fracture mechanics model for macro-joints. Second, a fatigue constitutive model with an internal variable (i.e., irreversible plastic strain) is proposed to reproduce the degradation behaviors in fatigue deformation and strength of rocks under cyclic loading. Finally, a damage constitutive model with a definite physical significance is constructed for the intermittent jointed rocks under cyclic uniaxial compression. Our new model comprehensively reflects the coupled damage induced by micro-flaws and macro-joints, in which the geometric parameters and the mechanical properties of intermittent joints are considered simultaneously. Moreover, this model is able to reproduce the hysteretic stress-strain curves and the cumulative fatigue plastic deformation of rock materials under cyclic loading. In addition, a compaction coefficient, which is defined as the ratio of the secant modulus to the Young's modulus, is proposed to reflect the compaction stage of rock materials during the first loading process. To validate this new model, nine cyclic uniaxial compression tests are conducted on both intact and jointed rock samples prepared with synthetic rock-like materials. A reasonable consistency is observed between the theoretical and experimental results for the cyclic stress-strain curves and the fatigue deformation modulus.