# SCEC TPV29¶

TPV 29 contains a vertical, right-lateral fault with **rough fault
interface** (Figure [fig:tpv29]). The fault surface has 3D stochastic
geometrical roughness (blue and red colors). In TPV 29, the surrounding
rocks respond elastically.

## Geometry¶

The roughed fault interface model is generated with Gmsh is complicated than planar faults in previous sections. There are 5 steps to generate the model.

- 1.Download fault topography data from SCEC. There are 2001 nodes
- along the strike and 1201 nodes along the downdip. The node files should contain:

```
Line 1: nx, ny
Line 2 to nx: positions of nodes along the strike (in meters)
Line nx+3 to ny+nx+3: positions of nodes along the downdip (in meters)
Line to the end: fault topography of each nodes (nx\*ny, in meters)
```

Save this file as *mytopo_tpv29*.

2.Make a model with plane fault as Figure [fig:tpv29geo]. The Gmsh tpv29.geo file can be found at

3.Use *gmsh_plane2topo.f90* and interpol_topo.in* to shift the planar
fault according to positions given in *mytopo_tpv29*.

```
$ ./gmsh_plane2topo interpol_topo.in
```

- This will generate a step1_modified.msh file which containing rough
- fault surface.

4.Make a new step2.geo file that contains the new rough fault and mesh following general Gmsh process.

5. Generate MSH mesh with the command line:

```
& gmsh tpv29_step2.geo -3 -optimize_netgen -o tpv29_step2.msh
```

option optimize_netgen is necessary for optimizing meshing with good quality.

## Material parameters¶

In TPV29, the entire model volume is a linear elastic material, with the following parameters listed in Table [table:tpv29material].

Parameter | Description | Value | Unit |
---|---|---|---|

\(\rho\) | density | 2670 | \(kg/m^{3}\) |

\(\lambda\) | Lame’s first parameter | 3.2044e10 | Pa |

\(\mu\) | shear module | 3.2038e10 | Pa |

\(h_{edge}\) | element edge length | 200 | m |

\(V_p\) | P wave velocity | 6000 | m/s |

\(V_s\) | S wave velocity | 3464 | m/s |

[table:tpv29material]

## Initial stress¶

The initial stress are listed in Table [table:tpv29fault].

Parameter | Description | Value | Unit |
---|---|---|---|

mu_s | static friction coefficient | 0.12 | |

mu_d | dynamic friction coefficient | 0.18 | |

d_c | critical distance | 0.30 | m |

s_zz | \(\sigma_{zz}\) | -2670*9.8*depth | Pa |

Pf | fluid pressure | 1000*9.8*depth | Pa |

s_xz,s_yz | \(\sigma_{xz}, \sigma_{yz}\) | 0 | Pa |

s_yy | \(\Omega * b33*(\sigma_{zz} + P_f) - P_f\) | Pa | |

s_xx | \(\Omega * b11*(\sigma_{zz} + P_f) - P_f\) | Pa | |

s_xy | \(\Omega * b13*(\sigma_{zz} + P_f)\) | Pa |

Table: Table of initial stress in TPV 29. \(b11, b33,b13\) are 1.025837, 0.974162, −0.158649, respectively.

\[\begin{split}\bar{\sigma}_{effective}= \begin{bmatrix} &\sigma_{xx} + P_f , & \sigma_{xy} ,& \sigma_{xz} \\ &\sigma_{xy}, &\sigma_{yy} +P_f , &\sigma_{yz} \\ &\sigma_{xz} ,&\sigma_{yz} , &\sigma_{zz} +P_f \end{bmatrix}\end{split}\]

where \(\Omega\) is defined as:

## Nucleation parameters¶

TPV29 uses a similar strategy for dynamic rupture nucleation.

The cohesion zone is defined as :

The friction parameters on the fault are listed in Table [table:tpv29fric].

Parameter | Description | Value | Unit |
---|---|---|---|

mu_s | static friction coefficient | 0.12 | |

mu_d | dynamic friction coefficient | 0.18 | |

d_c | critical distance | 0.30 | m |

t_0 | forced rupture delay time | 0.5 | s |

Table: Table of friction parameters in TPV 29.