13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- analytical results are in good agreement, indicating that the soil-water coupled scheme is effective in solving the consolidation and dissipation problems. Figure 1. 1D consolidation model setup 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 p/p0 z/h c v t/h2= 0.010 0.102 0.509 1.019 2.038 Simulation Analytical Figure 2. Normalized isochrones distribution of p Figure 3 present the change of relative error norm during the first 100 iterations. Every line represents the convergence behavior of the relative error norms of u and p during one time step. The error norms decrease linearly in a log scale until the prescribed tolerances values are satisfied, i.e., ( 1) ( ) ( 1) 1 1 1 3 10 i i i n n n p p p and ( 1) ( ) ( 1) 3 1 1 1 10 i i i n n n u u u . Figure 4 shows the number of iterations needed in each time step of the simulation. In general, convergence can be achieved in around 5 iterations. However, a varying number of iterations are needed in the later part of the simulation. 0 20 40 60 80 100 10-5 10-4 10-3 10-2 10-1 100 Iteration Numbers Relative Error Norm Pore Pressure Displacement Figure 3 Relative Error Norm 0 0.5 1 1.5 2 0 5 10 15 20 Dimensionless Time, C v t/h2 Iteration Number Sp = 1.5, avgIteration = 6.85 Figure 4. Comparison of iterations numbers 7. Conclusions A sequential hydro-mechanical coupling scheme using RKPM is presented in this paper. From the stability analysis and numerical simulations, the following conclusions can be drawn With a suitably chosen stabilization matrix S , the stabilization technique is proved to be able to effectively make the scheme unconditionally stable. Without the stabilization term, the scheme is proved to be conditionally stable.
RkJQdWJsaXNoZXIy MjM0NDE=