# 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.

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)


Using generate_mytopo_tpv29.py to create the topography data.

2.Make a model with plane fault as Figure [fig:tpv29geo]. The Gmsh tpv29.geo file can be found at https://github.com/SeisSol/Examples/blob/master/tpv29/tpv29.geo.

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

$./gmsh_plane2topo interpol_topo.in  This will generate a step1_modified.msh file which containing rough fault surface. 4.Make a new step2.geo file that contains the new rough fault and mesh following general Gmsh process. 1. Generate MSH mesh with the command line: & gmsh tpv29_step2.geo -3 -optimize_netgen -o tpv29_step2.msh  option optimize_netgen is necessary for optimizing meshing with good quality. 6.Then convert the .msh file to 3D Gambit neutral file and PUML format as same as shown in TPV5 ::$ gmsh2gambit -i tpv29_step2.msh -o tpv29.neu \$ pumgen tpv29.neu tpv29

The mesh can be created by using the bash script https://github.com/SeisSol/Examples/blob/master/tpv29/generating_the_mesh.sh.

Here we show a fully opensource workflow which allows generating a mesh accounting for tpv29 rough fault geometry. This yields a mesh that does not properly account for the intersection between fault and the free-surface. We note that it is here not an important issue, as the tpv29 benchmark does not feature surface rupturing. Another drawback of this workflow is that the rate of mesh size coarsening is not easy parametrizable. A more straightforward and accurate way to generate a mesh would be to use simModeler.

## 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.

Note that the effective stress tensor is :

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

where $$\Omega$$ is defined as:

$\begin{split}\Omega = \left\{ \begin{array}{lr} &1, depth \leq 17000 m \\ & (22000 - depth)/5000 m, 17000 < depth < 22000 m \\ & 0, depth \geq 22000 m\\ \end{array} \right.\end{split}$

## Nucleation parameters¶

TPV29 uses a similar strategy for dynamic rupture nucleation.

$\begin{split}T = \left\{ \begin{array}{lr} & \frac{r}{0.7Vr} + \frac{0.081*r_{crit} }{0.7Vr} (\frac{1}{1-(r/r_{crit})^2} - 1), r \leq r_{crit} \\ & 1E+09, r > r_{crit}\\ \end{array} \right.\end{split}$

The cohesion zone is defined as :

$\begin{split}C_0 = \left\{ \begin{array}{lr} & 0.4 MPa + 0.000675 MPa * (4000- depth), depth < 4000 m \\ & 0.4 MPa, depth \geq 4000 m\\ \end{array} \right.\end{split}$

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.

## Results¶

The earthquake rupture is artificially nucleated in a circular zone on the fault surface.