Post-peak normalized displacement softening model for discontinuous rock joint

Usually, a negative slope of the stress-displacement curve characterizes the post-peak behavior, where the shear strength of a joint falls to a constant value that corresponds to the residual friction resistance of the joint; it means that the decay rate decreases until to ultimate strength. But for discontinuous joint, the curve follows a "S" shape; it means that strength decay rate increases at the initial stage, then decreases to zero; it means residual strength arrived. So, the constitutive model used by joints is not suitable for discontinuous joint. A new nonlinear normalized model is developed that takes a dimensionless form described by an exponential function. This function reflects the relationship between post-peak stress and displacement through normalized shear strength R and normalized displacement D. The post-peak shear strength reduction tau(p)-tau normalized by shear reduction from the peak to residual tau(p)-tau(r) is called normalized shear strength R:the post-peak shear displacement tau-tau(p) normalized by the difference from residual shear displacement to peak shear displacement tau(r)-tau(p) is called normalized shear displacement. At last, the model is used to fit experimental data for different types of discontinuous joints; and the high fitting accuracy shows its validity.