Quasi-static modeling with explicit numerical manifold method via timestep scaling technique and velocity-based viscous damping model

An explicit numerical manifold method (NMM) is developed to solve quasi-static continuous and discontinuous geotechnical engineering problems. However, due to the small timestep size for explicit time integration scheme, the number of calculation steps is usually very large, and the analysis process may be very time-consuming, especially for large-scale rock and soil masses. As the extension to the mass-scaling technique, a timestep-based mass-scaling technique (timestep scaling technique) is introduced to explicit NMM in this study to model quasi-static geotechnical problems more effectively. This technique scales the lumped mass matrix through the formula of critical timestep size $\Delta t_c$ directly, and $\Delta t_c$ can be increased to be larger than the required timestep size $\Delta t$. In addition, to dissipate the kinetic energy of the system, a velocity-based viscous damping model is used to weaken the dynamic response and accelerate the convergence speed to reach the final state of the quasi-static problem. Through a series of verification and application examples, it has been proven that the timestep scaling technique and velocity-based viscous damping model in the context of the explicit NMM can efficiently solve quasi-static problems.