# Benchmark 4

Viscoelastic (Maxwell) relaxation of stresses from a single, finite, strike-slip earthquake.

Benchmark #4a: A 2D anti-plane analysis on a finite domain (± 400 km laterally, 400 km deep). If the code allows, also test using infinite elements in both directions.

Benchmark #4b: A 3D analysis without gravity. Evaluate results with fixed boundary conditions on a cube with sides of length 24, 48, 96, and 192 km. If the code allows, also test using infinite elements in all directions.

Benchmark #4c: A 3D analysis with gravity. Evaluate results with fixed boundary conditions on a cube with sides of length 24, 48, 96, and 192 km. 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.

### Goals

• Benchmark #4a: Test far-field viscoelastic relaxation.
• Benchmark #4a & 4b: Code comparison, particularly near fault tips.
• Benchmark #4a & 4b: Test the effect of boundaries in the finite element mesh for strike-slip faulting.
• Benchmark #4c: Test the implementation of gravity for strike-slip faulting.

### Detailed Description

• Model size: see dimensions given above; (-X km ≤ ≤ x ≤ X km; 0 km ≤ y ≤ Y km; -Z ≤ z ≤ 0 km)
Top layer: -12 km ≤ z ≤ 0 km;
Bottom layer: -Z ≤ z ≤ -12 km
Where X, Y and Z = 12, 24, 48 and 96 km.
• Elastic material properties: Poisson solid, G = 30 GPa
• Maxwell viscoelastic material properties:
Top layer: η = 1025 Pa-s (essentially elastic)
Bottom layer: η = 1018 Pa-s
• Density and Gravity: when applicable: ρ = 3000 kg/m3; g = 10 m/s2
• 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 in 3D and dx = dz = 2 km in 2D
• Fault specifications:
Type: vertical strike-slip fault
Location: Strike parallel to y-direction at center of model (x = 0km)
0 km ≤ y £lle; 16 km; -16 km ≤ z ≤ 0 km
Slip distribution: 1 m of uniform strike slip motion 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 (all components) and displacements along three lines parallel to the y-axis at x = 0, 1, and 5 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 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.