# SCEC TPV12¶

TPV12 and 13 are recommended by SCEC for elastic/plastic wave
propagation code validation. TPV 12 describes spontaneous rupture on a
**60-degree dipping normal fault** in a homogeneous half-space. Material
properties are linear **elastic**. Initial stress conditions are
dependent on depth. Strongly super-shear rupture conditions.

## Geometry¶

The model volume is a half-space. The fault is a 60-degree dipping, planar, normal fault. The fault reaches the Earth’s surface. Rupture is allowed within a rectangular area measuring 30000 m along-strike and 15000 m down-dip.

Note that 15000 m down-dip corresponds to a depth of 12990.38 m. A node which lies exactly on the border of the 30000 m \(\times\) 15000 m rectangle is considered to be inside the rectangle, and so should be permitted to rupture.

The portions of the fault below, to the left of, and to the right of the 30000 m \(\times\) 15000 m rectangle are a strength barrier, within which the fault is not allowed to rupture.

The nucleation zone is a square measuring 3000 m × 3000 m. The center of the square is located 12000 m down-dip (at a depth of 10392.30 m), and is centered along-strike.

The geometry is generated with Gmsh. All the files that are needed for the simulation are provided at https://github.com/SeisSol/Examples/tree/master/tpv12_13.

The geometry and mesh generation process is similar to TPV5. The planar-fault geometry is built with Gmsh (Figure [fig:tpv12geo]).

## Nucleation¶

In previous benchmarks, nucleation was achieved by imposing a higher initial shear stress within a nucleation zone. In TPV12 and TPV13, nucleation is achieved by selecting a lower static coefficient of friction within a nucleation zone, so that the initial shear stress (which is implied by the initial stress tensor) is greater than the yield stress.

Outside the 30000 m * 15000 m rectangular rupture area there is a strength barrier, where nodes are not allowed to slip. Some codes implement the strength barrier by setting the static coefficient of friction and frictional cohesion to very large values. Other codes implement the strength barrier in other ways.

## Parameters¶

### LSR parameters¶

TPV12 uses a linear slip weakening law on the fault with different parameters inside and outside the nucleation zone. The parameters are listed in Table [table:tpv12lsr].

Parameter | inside the nucleation zone | Value | Unit |
---|---|---|---|

inside the nucleation zone | |||

mu_s | static friction coefficient | 0.54 | |

mu_d | dynamic friction coefficient | 0.10 | |

d_c | critical distance | 0.50 | m |

cohesion | shear stress cohesion | -200 000 | Pa |

outside the nucleation zone | |||

mu_s | static friction coefficient | 0.70 | |

mu_d | dynamic friction coefficient | 0.10 | |

d_c | critical distance | 0.50 | m |

cohesion | shear stress cohesion | -200 000 | Pa |

Table: Table of LSR parameters on the fault.

## Initial stress¶

The initial stress on the fault is depth-dependent in TPV12/13. In the shallower portion above 11951.15 m, the stress field is optimal orientated while the other is isotropic.

Parameter | Value |
---|---|

above 11951.15 m | |

\(\sigma_1\) | 26460 Pa/m * H |

\(\sigma_3\) | 15624.3 Pa/m * H |

\(\sigma_2\) | \((\sigma_1+\sigma_3)/2\) |

\(P_f\) | \(1000 kg/m^3 *9.8 m/s^2 *H\) |

below 11951.15 m | |

\(\sigma_1,\sigma_2,\sigma_3\) | \(2700 kg/m^3 *9.8 m/s^2 *H\) |

## Results¶

SeisSol output xdmf file that can be loaded in Paraview directly. The wave field and fault output files have the same format as in TPV5.