Uniform Stresses in an Unjointed Medium: No Gravity

For an excavation deep underground, the gravitational variation of stress from top to bottom of the excavation may be neglected because the variation is small in comparison with the magnitude of stress acting on the volume of rock to be modeled. The model gravity command may be omitted, causing the gravitational acceleration to default to zero. The initial stresses are installed with the block insitu command – e.g.:

block insitu stress -5e6 -5e6 -1e7 0.0 0.0 0.0

The components \(\sigma_{11}\) (or \(\sigma_{xx}\)), \(\sigma_{22}\) (or \(\sigma_{yy}\)) and \(\sigma_{33}\) (or \(\sigma_{zz}\)) are set to compressive stresses of 5×10⁶, 5 × 10⁶ and 5 × 10⁷, respectively, throughout the model. Range parameters may be added if the stresses are to be restricted to a subregion of the model. The block insitu command sets all stresses to the given values, but there is no guarantee that the stresses will be in equilibrium. There are at least three possible problems. First, the stresses may violate the yield criterion of a nonlinear constitutive model assigned to deformable blocks. In this case, plastic flow of zones in the blocks will occur immediately after the model solve command is given, and the stresses will readjust; this possibility should be checked by doing one trial step and examining the response (e.g., plot block state). Second, the stress state may result in slip or separation along joints within the model. Plotting the subcontact state should indicate locations where joint movement is occurring. Third, the prescribed stresses at the model boundary may not equal the given initial stresses. In this case, the boundary gridpoints will start to move as soon as a model solve command is given; again, output should be checked (e.g., plotting veolcities) for this possibility.

The commands in the example below produce a single block with initial stresses that are in equilibrium with prescribed boundary stresses:

Initial and boundary stresses in equilibrium

model new
model random 10000
model large-strain on

block create brick 0,10  0,10  0,10
;
block zone generate edgelength 2.0
;
block zone cmodel assign el
block zone prop  dens 1000 bulk 8e9 shear 5e9
;
block gridpoint apply vel-z 0 range pos-z 0.0 
block face apply stress -5e6,0,0 0,0,0 range pos-x  0.0
block face apply stress -5e6,0,0 0,0,0 range pos-x 10.0
block face apply stress 0,-5e6,0 0,0,0 range pos-y  0.0
block face apply stress 0,-5e6,0 0,0,0 range pos-y  10.0
block face apply stress 0,0,-1e7 0,0,0 range pos-z 0.0
block face apply stress 0,0,-1e7 0,0,0 range pos-z 10.0

block insitu stress  -5e6  -5e6  -1e7  0,0,0
model step 1