Benchmark Description

Summary

Viscoelastic (Maxwell) relaxation of stresses from a single, finite, reverse-slip earthquake in 3D with gravity. Evaluate results with imposed displacement boundary conditions on a cube with sides of length 24 km. The displacements imposed are the analytic elastic solutions. Symmetry boundary conditions are imposed at y = 0, so the solution is equivalent to that for a domain with a 48 km length in the y direction.

The effects of gravitational loading 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.

Problem Specification

Model size

0 km ≤ x ≤ 24 km; 0 km ≤ y ≤ 24 km; -24 ≤ z ≤ 0 km

Top layer

-12 km ≤ z ≤ 0 km

Bottom layer

-24 km ≤ z ≤ -12 km

Material properties

The top layer is nearly elastic whereas the bottom layer is viscoelastic.

Elastic

Poisson solid, G = 30 GPa; ρ = 3000 kg/m^3; g = 9.80665 m/s^2

Maxwell viscoelastic material properties

Top layer

η = 1.0e+25 Pa-s (essentially elastic)

Bottom layer

η = 1.0e+18 Pa-s

Boundary conditions

Bottom and side displacements set to analytic solution. (Note: the side at y = 0 km has zero y- displacements because of the symmetry.) Top of the model is a free surface.

Discretization

The model should be discretized with nominal spatial resolutions of 1000 m, 500 m, and 250 m. If possible, also run the models with a nominal spatial resolution of 125 m. Optionally, use meshes with variable (optimal) spatial resolution with the same number of nodes as the uniform resolution meshes.

Element types

Linear and/or quadratic and tetrahedral and/or hexahedral.

Fault specifications

Type

45 degree dipping reverse fault.

Location

Strike parallel to y-direction with top edge at x = 4 km and bottom edge at x = -12 km. 0 km ≤ y ≤ 16 km; -16 km ≤ z ≤ 0 km

Slip distribution

1 m of uniform thrust 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. In the region where the two tapers overlap, each slip value is the minimum of the two tapers (so that the taper remains linear).

Boundary conditions

Lateral and bottom displacements are set to analytic elastic solution. Note that the side at y = 0 km has zero y-displacements because of the imposed symmetry at y = 0 km.

Requested Output

Solution

Displacements at all nodes at times of 0, 1, 5, and 10 years as well as the mesh topology (i.e., element connectivity arrays and coordinates of vertices) and basis functions.

June 30, 2006

Use ASCII output for now. In the future we will switch to using HDF5 files.

Performance

• CPU time
• Wallclock time
• Memory usage
• Compiler and platform info

"Truth"

Okada routines are available to generate an elastic solution. The ‘best’ viscoelastic answer will be derived via mesh refinement. Analytical solutions to the viscoelastic solution are being sought if anyone has information.