Dynamic Binary-Medium Model for Jointed Rock Subjected to Cyclic Loading

Revealing the damage mechanism of jointed rocks under a cyclic loading and formulating the corresponding dynamic constitutive model to meet the requirements for the evaluation of anti-vibration safety for critical engineering construction and operation is an essential, urgent and basic subject. Based on the breakage mechanics for geological material, jointed rock is considered as a binary-medium material composed of the bonded elements and frictional elements. The bonded elements are regarded as elastic-brittle elements, and the frictional elements are regarded as elastic-plastic elements. Firstly, the static binary-medium model for jointed rock is established based on the homogenization method and by introducing the breakage ratio and the strain concentration coefficient. Then, the dynamic binary-medium model for jointed rock under cyclic loads is established considering the nonlinear damage effect resulting from cyclic loads. The breakage ratio formula is improved, and the Drucker–Prager criterion is introduced. During the unloading stage, it is supposed that the breakage ratios and strain concentration coefficients remain unchanged and the stress–strain ratios of both bonded elements and frictional elements are constant. The model is verified by static and dynamic triaxial tests of jointed rock samples with an interpenetrated joint. It is found that the model can describe the nonlinear stress–strain characteristics of a jointed rock subjected to cyclic loads relatively well and can reflect the effects of cyclic loading on the deformation and damage, including the lateral deformation characteristics. Meanwhile, the typical three-stage (varying from sparse to dense to sparse) evolution laws of the stress–strain curves are also reflected relatively well.