Constitutive modeling of idealized rock joints under quasi-static and cyclic loading.

A rather novel plasticity based constitutive model to describe the response of simulated (rock) joints under cyclic, quasi-static and static shear is developed. Development of the constitutive model includes both mathematical formalization based on the hierarchical approach and laboratory testing. The mathematical formulation is such that the model is basic and general and is capable of predicting observed behavior of joints. Laboratory test results are used for the determination of parameters for the model, and for comparison with model predictions. The constitutive model is based on the theory of incremental plasticity. A generalized three-dimensional plasticity model capable of predicting the behavior of geologic solid material such as soil and rock is specialized to describe the behavior of individual rock joints. At this time, the model allows for effects of initial normal stress, states of shear and normal stress, plastic hardening, nonassociativeness, volume changes at joints, and cycles of loading, unloading and reverse loading. The test program was conducted on simulated joints. The simulated specimens were cast in concrete with a variety of surface geometries (angles of asperities). Specimens were subjected to a series of quasi-static and fast cyclic direct shear tests. Tests were performed with a special device known as the Cyclic Multi-Degree-of-Freedom (CYMDOF) shear device; minor modifications of the device were necessary for the testing of joints. Quasi-static tests included shear loading, unloading and reverse loading, and fast cyclic tests repeated cycles of shear loading at the frequency of 1.0 Hz. Tests were conducted under different levels of normal stress and amplitudes of cyclic displacement. The constants for elastic and inelastic responses were found from the laboratory test data. Then typical observed results were predicted by integrating the incremental plasticity equations which were expressed in terms of the constants. The predictions, in general, were found to provide satisfactory correlation with the observations. The results of this research have demonstrated that the model described herein is capable of capturing many aspects of rock joint behavior during quasi-static and cyclic shear loading. The model is sufficiently simplified so that it can be easily implemented in numerical techniques such as the finite element method. Such computational procedures can be used to solve practical boundary value problems in rock mechanics involving static and dynamic loads