Stresses with Gradients in a Nonuniform Material

With the block insitu topography command, it is easy to install the initial stresses even when materials of different densities are present. Consider a layered system with a free surface, enclosed in a box with roller side boundaries and a fixed base. Suppose that the material has the following density distribution:

1600 kg/m³ from 0 to 10 m depth

2000 kg/m³ from 10 to 15 m

2200 kg/m³ from 15 to 25 m

Assume a horizontal stress ratio of 0.25. An equilibrium state is produced by the data file the following example.

Initial stress gradient in a nonuniform material

model new
model large-strain off

block create brick 0,20 0,20  0,25

block cut joint-set dip 0.0 origin 0,0,10 join
block cut joint-set dip 0.0 origin 0,0,15 join
block zone generate edgelength 2.0

block zone cmodel assign el
block zone prop  dens 1600 bulk 5e9 shear 3e9 range pos-z 0,10
block zone prop  dens 2000 bulk 5e9 shear 3e9 range pos-z 10,15
block zone prop  dens 2200 bulk 5e9 shear 3e9 range pos-z 15,25

model gravity 0 0 -10

block insitu topography ratio-x 0.25 ratio-y 0.25

block gridpoint apply vel-x = 0.0 range pos-x  0.0
block gridpoint apply vel-x = 0.0 range pos-x 20.0
block gridpoint apply vel-y = 0.0 range pos-y  0.0
block gridpoint apply vel-y = 0.0 range pos-y 20.0
block gridpoint apply vel-z = 0.0 range pos-z  0.0

model history mechanical unbalanced-maximum
model solve

An individual block is created for each material density; fictitious joints separate each block. The internal stress profile is calculated automatically for each block from the known overburden above it. In this case, it is assumed that all horizontal stress ratios are the same, but it would be possible to specify different horizontal stresses in different layers by giving multiple block insitu topography commands with different ratios specified over different ranges.

This example is not in equilibrium at one calculation step; approximately 500 steps are required. The presence of the fictitious joints also prevents the model from being in equilibrium when the initial stresses match the boundary stresses. A jointed model will often require more steps to equilibrate than an unjointed model.