School of Civil Engineering High Performance Computing Laboratory “Dynamic Simulation of Shear Rupture in Planar Faults Using XFEM” by : M. Parchei, S. Mohammadi, and H. Zafarani Anti-plane Shear (Mode III) In plane Shear (Mode I/II) Out of plane mesh deformation In plane mesh deformation Computation of anti-plane rupture parameters Computation of in plane rupture parameters Numerical calculation of SV wave front evolution by XFEM (using C elements) 0 Lr = 32.1875 Lr = 24.1875 Lr = 16.1875 Lr = 8.1875 u z τ yz Snapshots of SH wave propagation at different rupture lengths (L ) r u x τ xy σ xx Lr = 24.1875 Lr = 16.1875 Lr = 8.1875 Lr = 4.1875 Snapshots of coupled P-SV wave propagation at different rupture lengths (L ) r Schematic of LATIN method for imposing non-linear contact boundary conditions E AI E IA S A 0 S A n S A n+1 S I 0 S I n S AI A I A : Linear Equation of Motion I : Non-linear Boundary Conditions 0.4 6.8 13.2 19.6 26 32.4 38.8 45.2 51.6 58 64.4 -1 0 1 2 3 4 5 6 -35.0 -32.2 -29.4 -26.6 -23.8 -21.0 -18.2 -15.4 -12.6 -9.8 -7.0 -4.2 -1.4 1.0 3.8 6.6 9.4 12.2 15.0 17.8 20.6 23.4 26.2 29.0 31.8 34.6 X time Shear stress 0.4 6.8 13.2 19.6 26 32.4 38.8 45.2 51.6 58 64.4 0 5 10 15 20 25 30 35 40 45 -35.0 -32.2 -29.4 -26.6 -23.8 -21.0 -18.2 -15.4 -12.6 -9.8 -7.0 -4.2 -1.4 1.0 3.8 6.6 9.4 12.2 15.0 17.8 20.6 23.4 26.2 29.0 31.8 34.6 X time Slip 0.4 6.8 13.2 19.6 26 32.4 38.8 45.2 51.6 58 64.4 0 2 4 6 8 10 12 -35.0 -32.2 -29.4 -26.6 -23.8 -21.0 -18.2 -15.4 -12.6 -9.8 -7.0 -4.2 -1.4 1.0 3.8 6.6 9.4 12.2 15.0 17.8 20.6 23.4 26.2 29.0 31.8 34.6 X time Slip Rate A Detailed view of A: Shear Deformation of a Split Element in a LATIN-based Contact Model 0.4 6.8 13.2 19.6 26 32.4 38.8 45.2 51.6 58 64.4 0 2 4 6 8 10 12 14 16 -35.37 -32.57 -29.77 -26.97 -24.17 -21.37 -18.57 -15.77 -12.97 -10.17 -7.37 -4.57 -1.77 0.57 3.37 6.17 8.97 11.77 14.57 17.37 20.17 22.97 25.77 28.57 31.37 34.17 Slip Rate X time 0.4 6.8 13.2 19.6 26 32.4 38.8 45.2 51.6 58 64.4 -1 4 9 14 19 24 29 34 39 44 49 -35.37 -32.57 -29.77 -26.97 -24.17 -21.37 -18.57 -15.77 -12.97 -10.17 -7.37 -4.57 -1.77 0.57 3.37 6.17 8.97 11.77 14.57 17.37 20.17 22.97 25.77 28.57 31.37 34.17 Slip X time 0.4 6.8 13.2 19.6 26 32.4 38.8 45.2 51.6 58 64.4 -1 -0.5 0 0.5 1 1.5 2 2.5 -35.4 -32.6 -29.8 -27.0 -24.2 -21.4 -18.6 -15.8 -13.0 -10.2 -7.4 -4.6 -1.8 0.6 3.4 6.2 9.0 11.8 14.6 17.4 20.2 23.0 25.8 28.6 31.4 34.2 Shear stress X time -1.5 -1 -0.5 0 0.5 1 -36 -27 -18 -9 0 9 18 27 36 Shear Stress x t = 16 -1.5 -1 -0.5 0 0.5 1 1.5 -36 -27 -18 -9 0 9 18 27 36 Shear Stress x t = 32 -1.5 -1 -0.5 0 0.5 1 1.5 -36 -27 -18 -9 0 9 18 27 36 Shear Stress x t = 48 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 -36 -27 -18 -9 0 9 18 27 36 Shear Stress x t = 64 0 2 4 6 8 10 12 -36 -27 -18 -9 0 9 18 27 36 Slip x t = 16 0 5 10 15 20 25 -36 -27 -18 -9 0 9 18 27 36 Slip x t = 32 0 5 10 15 20 25 30 35 -36 -27 -18 -9 0 9 18 27 36 Slip x t = 48 0 5 10 15 20 25 30 35 40 45 50 -36 -27 -18 -9 0 9 18 27 36 Slip x t = 64 0 1 2 3 4 -36 -27 -18 -9 0 9 18 27 36 Slip Rate x t = 16 0 1 2 3 4 -36 -27 -18 -9 0 9 18 27 36 Slip Rate x t = 32 0 1 2 3 4 5 6 7 -36 -27 -18 -9 0 9 18 27 36 Slip Rate x t = 48 0 2 4 6 8 10 12 -36 -27 -18 -9 0 9 18 27 36 Slip Rate x t = 64 -1 -0.5 0 0.5 1 1.5 2 2.5 3 0 10 20 30 40 50 60 70 Shear Stress Time Analytical (Kastrov 1964) XFEM without Artificial Damping XFEM with Artificial Damping x = 10 x = 20 x = 30 -1.5 -1 -0.5 0 0.5 1 -36 -27 -18 -9 0 9 18 27 36 Shear Stress x t = 12 -1.5 -1 -0.5 0 0.5 1 -36 -27 -18 -9 0 9 18 27 36 Shear Stress x t = 24 -1.5 -1 -0.5 0 0.5 1 -36 -27 -18 -9 0 9 18 27 36 Shear Stress x t = 36 -1.5 -1 -0.5 0 0.5 1 -36 -27 -18 -9 0 9 18 27 36 Shear Stress x t = 48 0 0.5 1 1.5 2 2.5 3 3.5 -36 -27 -18 -9 0 9 18 27 36 Slip Rate x t = 12 0 0.5 1 1.5 2 2.5 3 3.5 -36 -27 -18 -9 0 9 18 27 36 Slip Rate x t = 24 0 0.5 1 1.5 2 2.5 3 3.5 4 -36 -27 -18 -9 0 9 18 27 36 Slip Rate x t = 36 0 0.5 1 1.5 2 2.5 3 3.5 4 -36 -27 -18 -9 0 9 18 27 36 Slip Rate x t = 48 0 1 2 3 4 5 6 7 8 -36 -27 -18 -9 0 9 18 27 36 Slip x t = 12 0 2 4 6 8 10 12 14 16 -36 -27 -18 -9 0 9 18 27 36 Slip x t = 24 0 2 4 6 8 10 12 14 16 18 20 -36 -27 -18 -9 0 9 18 27 36 Slip x t = 36 0 5 10 15 20 25 30 -36 -27 -18 -9 0 9 18 27 36 Slip x t = 48