SCEC TPV12
TPV12 and 13 are verification benchmarks for a 60 degree dipping normal fault embedded in a homogeneous halfspace. The rheology is linear elastic in TPV12 and nonassociative DruckerPrager viscoplastic in TPV13. Initial stress conditions are dependent on depth. Strongly supershear rupture conditions are assumed.
Geometry
A halfspace domain is assumed. The fault is a 60degree dipping, 30 km \(\times\) 15 km planar, normal fault. It reaches the Earth’s surface, and extends up to 12.99038 km depth. A square nucleation area of 3 \(\times\) 3 km is assumed. In fault coordinates, it is centered at (0, 12) km, that is at a depth of 10.3923 km. The CAD model (see Figure 2) and mesh are generated with Gmsh. All the files that are needed for the simulation are provided here. The geometry and mesh generation process is similar to TPV5.
Nucleation strategy
In previous benchmarks, nucleation is achieved by imposing higher initial shear stress within the nucleation zone. In TPV12 and TPV13, nucleation is achieved by decreasing the static friction coefficient, leading the initial shear stress to exceed fault strength.
Parameters
friction parameters
TPV12 uses a linear slip weakening law with different parameters inside and outside the nucleation zone. The parameters are listed in the table below:
Parameter 
description 
Value 
Unit 

d_c 
critical distance 
0.50 
m 
cohesion 
shear stress cohesion 
200 000 
Pa 
inside the nucleation zone 

mu_s 
static friction coefficient 
0.54 

mu_d 
dynamic friction coefficient 
0.10 

outside the nucleation zone 

mu_s 
static friction coefficient 
0.70 

mu_d 
dynamic friction coefficient 
0.10 
Table 1: frictions parameters used in TPV12/13.
Initial stress
The initial stress is assumed depthdependent in TPV12/13. Above 11951.15 m depth, deviatoric stresses are nonzero, and the stress field is well orientated for rupture of the normal fault. Below, the stress is isotropic.
Parameter 
Value 

above 11951.15 m depth 

\(\sigma_1\) 
26460 Pa/m \(\times\) H 
\(\sigma_3\) 
15624.3 Pa/m \(\times\) H 
\(\sigma_2\) 
\((\sigma_1+\sigma_3)/2\) 
\(P_f\) 
\(1000 \mathrm{kg/m}^3 \times 9.8 \mathrm{m/s}^2 \times H\) 
below 11951.15 m depth 

\(\sigma_1,\sigma_2,\sigma_3\) 
\(2700 \mathrm{kg/m}^3 \times 9.8 \mathrm{m/s}^2 \times H\) 
Results
SeisSol output can be visualized directly in Paraview by loading their xdmf files.