Three-Dimensional Numerical Manifold Method Based on Viscoelastic Constitutive Relation

In order to accurately and efficiently simulate the dynamic processes of coupled phenomena with viscoelastic, continuous and discontinuous deformations, a three-dimensional (3D) numerical manifold method combining Maxwell's viscoelasticity (3D-VisNMM) is proposed and implemented in this study. First, the matrix formulas of 3D-VisNMM are derived, and then its technique flowchart is presented. Second, four viscoelastic models, which represent creep characteristics, stress relaxation features, stress accumulation, and frictional deceleration, respectively, are used to verify the feasibility of 3D-VisNMM. The creep model shows that the simulated deformation at each time step is highly consistent with the analytical solution. The stress relaxation model shows that the accuracy of simulated stress mainly depends on the time step, that is, the range of the Relative Standard Deviation (RSD) is 0.3%-4.8%, which corresponds to a time length of 0.1-2.0 years. The gravity-driven stress accumulation model shows that the RSD between the simulated results and analytical solutions is less than 0.004%. The frictional deceleration simulation shows that the RSD of cumulative displacements and accelerations are less than 0.65% and 2.4%, respectively. All these numerical simulations show that 3D-VisNMM is suitable for analyzing viscoelastic deformations, stress relaxation, and frictional sliding issues in multitemporal scale (second-century) and multispatial scale (meter-hundred kilometers). Therefore, 3D-VisNMM has a good application prospect in Geoscience research.