### Benchmark 6

Viscoelastic (Maxwell) relaxation of stresses from a single, finite, dip-slip earthquake in 3D with body forces.

#### GOALS

Test implementation of gravity for thrust faults.

#### DETAILED DESCRIPTION

- Model size: same dimensions as Benchmark 5.
- Elastic material properties: Poisson solid, G = 30 GPa
- Maxwell viscoelastic material properties:

Top layer: η = 10^{25}Pa-s (essentially elastic)

Bottom layer: η = 10^{18}Pa-s

- Density and Gravity: when applicable ρ = 3000 kg/m
^{3}; g = 10 m/s^{2} - Boundary conditions:

Bottom pinned

Sides with normals in the x-direction pinned

Side at y = max(y) km pinned

Side at y = 0 km has 0 y-displacement (i.e., symmetry condition applied)

Top free

- Coarse mesh node spacing: dx = dy = dz = 2 km
- Fault specifications:

Type: 45° dipping fault

Location: Strike parallel to y-direction ; Top edge at x = mean(x) – 8 km; Bottom edge at x = mean(x) + 8 km; 0 km ≤ y ≤ 16 km; -16 km ≤ z ≤ 0 km

Slip distribution: 1 m of uniform thrust slip (0.707 m in the z-direction and -0.707 m in the x-direction) for 0 km ≤ y ≤ 12 km and -12 km ≤ z ≤ 0 km with a linear taper to 0 slip at y = 16 km and z = -16 km.

#### REQUESTED OUTPUT AND RESULTS

Mesh Variations: As memory, time, and patience allow, run models at 1/2, 1/4, and 1/8, etc. the original coarse mesh spacing, investigate variable mesh spacing, and/or employ a variety of element types. For All Benchmark Variations:

- Stresses and displacements along three lines parallel to the y-axis at 0, 1, and 5 km from the fault plane at the depths of 0, 12, 16, 17, and 21 km (e.g. at the surface x=4, 5, and 9 km, at z = -12, x=16, 17, and 20 km); and three lines parallel to the x-axis at y = 12, 17, and 21, at depths of 0, 12, 16, 17 and 21 below the surface, all results at times of 0, 1, 5 and 10 years.
- CPU time, wallclock time, memory usage info, compiler info, and platform info

#### TRUTH

Okada will be used to generate an elastic solution. The ‘best’ viscoelastic answer will be derived via mesh refinement and increasing the distance to the model boundaries. Analytical solutions to the viscoelastic solution are being sought if anyone has information.

#### ADDITIONAL NOTES

Always run the same meshes both with and without gravity so that the magnitude of the gravitational effect with distance from the fault can be estimated. The effects of gravitational loading (as in BM2) should be relaxed before the fault slip is imposed. Alternatively, Winkler nodes could be used to calculate the gravitational restoring forces resulting from the deformed upper surface.