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 = 0 km)
• 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.

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

For benchmark 4a, some codes may need to use 1-2 layers of 3D elements constrained to be anti-plane. For benchmark 4b & 4c, 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.

Created on 03 Mar 2022, Last modified on 03 Mar 2022