Frictional contact algorithm study on the numerical simulation of large deformations in deep soft rock tunnels

There exist three types of nonlinear problems in large deformation processes of deep softrock engineering, i.e., nonlinearity caused by material, geometrical and contact boundary. In this paper, the numerical method to tackle the nonlinear contact and large deformation problem in A Software on Large Deformation Analysis for Soft Rock Engineering at Great Depth was presented. In the software, based on Lagrange multiplier method and Coulomb friction law, kinematic constraints on contact boundaries were introduced in functional function, and the finite element equations was established for two incremental large deformation analyses models, polar decomposition model and additive decomposition model. For every incremental loading step, by searching for the contact points in the potential contact interfaces (the excavation boundaries), the Lagrange multipliers, i.e., contact forces are calculated iteratively by Gauss-Seidel method, and justified through satisfy the inequalities of static constraint on contact boundaries. With the software, large deformation and frictional contact of a transport roadway were analyzed numerically by the two models. The numerical examples demonstrated the efficiency of the method used in the software.