Damping,convergence criterion and excavation simulation algorithm for numerical manifold method

The dynamic relaxation algorithm is used to solve quasi-static problems in numerical manifold method(NMM).However,the mechanism of energy dissipation of NMM is unclear.In this paper,the viscous-type and self-adaptive dampings are adopted to absorb the kinetic energy caused by the oscillation of system.The equilibrium equations containing damping term are derived by minimizing the total potential energy.A new algorithm for simulation of sequential excavation in rock masses is proposed.The excavation faces are considered as the special kind of discontinuity,and the phased excavation process is simulated through setting contact states of excavation faces according to excavation sequences.The convergence criterion including displacement and acceleration criteria are defined to determine whether the system reaches new equilibrium or not.The numerical results show that the improved NMM has good convergence performance and that the results from NMM agree with those from UDEC and analytical solutions.