Artificial Boundaries

Artificial boundaries fall into two categories: planes of symmetry and planes of truncation. Symmetry planes take advantage of symmetry conditions in a physical system; truncation planes are needed when modeling an infinite or very large system.

Symmetry Planes

Sometimes it is possible to take advantage of the fact that the geometry and loading in a system are symmetrical about one or more planes. For example, if everything is symmetrical about a vertical (\(yz\)) plane, then the horizontal displacements on that plane will be zero. Therefore, we can make that plane a boundary, and fix all gridpoints in the horizontal direction, using the command block gridpoint apply velocity-x 0. If velocities on the plane of symmetry are not already zero, they will be set to zero with this command. In the case considered, the \(y\)-component and \(z\)-component of velocity on the vertical plane of symmetry are not affected; they should not be fixed. Similar considerations apply to a horizontal plane of symmetry. The command block gridpoint apply velocity-normal 0 can be used to set planes of symmetry that lie at angles to the coordinate axes.

The presence of discontinuities makes the application of symmetry planes more difficult. When using symmetry planes in 3DEC, the modeler should always be careful to consider the effect of joint orientation.

Boundary Truncation – Location of the Far-Field Boundary

When modeling infinite bodies (e.g., tunnels underground) or very large bodies, it may not be possible to cover the whole body with zones, due to constraints on memory and computer time. Artificial boundaries are placed sufficiently far away from the area of interest that the behavior in that area is not greatly affected. It helps to know how far away to place these boundaries, and what errors might be expected in the stresses and displacements computed for the area of interest.

Several points should be considered when selecting the location for artificial boundaries:

  1. A fixed boundary causes both stresses and displacements to be underestimated, while a stress boundary does the opposite.
  2. The two types of boundary condition “bracket” the true solution, so that it is possible to do two tests with small boundaries and get a reasonable estimate of the true solution by averaging the two results.
  3. The effect of boundary location is most noticeable for elastic bodies because the displacements and stress changes are more confined when plastic behavior is present; there is a natural cut-off distance within which most of the action occurs. The artificial boundary may be placed slightly closer without serious error. However, any artificial boundary must not be sufficiently close that it attracts plastic flow and thereby invalidates the solution.

It is always best to run several (coarse) models first, with different boundary locations, to evaluate the potential influence of the boundary on the calculated response, before performing the detailed analysis.