Modified contact model with rock joint constitutive in numerical manifold method

In the classical numerical manifold method (NMM), contact conditions are enforced by applying or releasing contact springs repeatedly. Penalty spring stiffness is constant during the calculation process. In this study, a modified contact model describing joint mechanical behavior is proposed using the NMM. Two rock joint constitutive models, namely the BB model and hyperbolic model, are used to modify normal and shear stiffness, respectively. In the modified contact model, stiffness varies with normal and shear inter-penetration distance in each iteration step. Therefore, stiffness varies for different contact points. With increasing inter-penetration distance, the normal stiffness increases and shear stiffness decreases. As a result, the force needed for trigger sliding along the joint increased. Finally, three example simulations are conducted to validate the effectiveness of the modified contact model.