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Benchmark 2

Various tests on the implementation of gravity in viscoelastic finite element models. All analyses are 2D plane strain and assume uniaxial strain boundary conditions.

Benchmark #2a : Relaxation of deviatoric stresses following application of body forces in a viscoelastic block. Lateral and vertical density homogeneity is assumed ( ρ = ρ1).

Benchmark #2b : Relaxation of deviatoric stresses following application of body forces in a viscoelastic block. Lateral variations in density are included with a region of lower density located in the upper, +x-direction quadrant of the model (see Figure 1; low density material in x > 12 km, d z > -8 km). The block has uniform viscosity.

Benchmark #2c : Relaxation of deviatoric stresses following application and removal of a surface load in a block containing an elastic layer overlying a viscoelastic layer (see Figure 2). Lateral and vertical density homogeneity assumed ( ρ = ρ1).

Goals

  • All benchmarks: Test the implementation of gravity and confirm an approach toward an isostatic response.
  • All benchmarks: Test the effects of different meshes, e.g., optimizing the mesh based on expected strain energy distributions, the effect of free form meshes, etc.
  • Benchmark #2c: Test the viscoelastic gravitational response to surface loads during both loading and unloading. 

Detailed Description

  • Model size: 24 km by 24 km (0 km ≤ x ≤ 24 km; -24 km ≤ z ≤ 0 km) 
  • Top layer: -12 km ≤ z ≤ 0 km; Bottom layer: -24 ≤ z ≤ -12 km 
  • (Note: Top and bottom layers only necessary in benchmarks #2b and 2c)
  • Elastic material properties: Poisson solid, G = 30 GPa
  • Maxwell viscoelastic material properties: Top layer (if elastic): η = 1025 Pa-s 
  • Rest of model: η = 1018 Pa-s
  • Power-law material properties: ηref = 1018 Pa-s and σref = 10Pa. (Note: This value is chosen because the maximum intial elastic stress is of order 10Pa, only a fraction of that is deviatoric, and the deviatoric stress decreases with time.)
  • Density and Gravity: ρ= 3000 kg/m3; ρ= 2700 kg/m3; g = 10 m/s2 
  • Boundary conditions: Bottom pinned 
  • Sides pinned in x and y; free in z
  • Top free (except 2c) 
  • Coarse mesh node spacing: dx = dz = 2 km 
  • Surface loading (Benchmark #2c only): Sinusoidal surface load defined by TBD.

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 along a path through (0,0,-24) and (24,24,0) at t = 0, 1, 5, and 10 years.
  • Displacements along a path through (0,0,-24) and (24,24,0) at t = 0, 1, 5, and 10 years.
  • CPU time, wallclock time, memory usage info, compiler info, and platform info

Truth

Analytical solutions for each benchmark will be posted at  geoweb.mit.edu/fe

Additional Notes

None.
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