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Axisymmetric Analysis

In the Project Settings dialog, two different types of analysis can be selected - Plane Strain or Axisymmetric analysis.

The Axisymmetric option allows you to analyze a 3-dimensional excavation which is rotationally symmetric about an axis. The input is 2-dimensional, but because of the rotational symmetry, you are in fact analyzing a symmetric 3-dimensional problem.

A typical use of the Axisymmetric modeling option is to analyze the stress state around the end of a circular tunnel. See the RS2 Tutorials section for a tutorial on Axisymmetric modeling.

Some simple Axisymmetric models are shown below. Only an External boundary is required, the shape of the External boundary implicitly defines the excavation.

Examples of Axisymmetric models: if the left edge of each mesh is coincident with the X = 0 axis, then the model on the left represents a SPHERE and the model on the right represents a CYLINDER, in three dimensions.

image\axi1_wmf.gif image\axi2_wmf.gif

The mathematical formulation of an Axisymmetric finite element is actually similar to Plane Strain (and plane stress) problems. By symmetry, the two components of displacement in any plane section of the excavation through its axis of symmetry define completely the state of strain, and therefore, the state of stress. Instead of analyzing a unit out-of-plane depth, the analysis is performed on a unit radian.

Restrictions on Axisymmetric Modeling

There are several restrictions on the use of Axisymmetric modeling in RS2:

  1. The Field Stress must be axisymmetric i.e. aligned in the axial and radial directions. Out-of-plane (or circumferential) field stress exists, but is equal to the radial stress, and cannot be independently varied.
  2. Cannot be used with Bolts (however Liners are permitted).
  3. All materials must have Isotropic elastic properties (cannot use Transversely Isotropic or Orthotropic elastic properties).
  4. The true orientation of your excavation can be arbitrary (i.e. it could be horizontal, vertical or at any inclination). However, for the purposes of the RS2 Axisymmetric analysis, you will have to map your coordinates so that the model is symmetric about the X = 0 axis (i.e. a vertical axis located at X = 0), since all finite elements are rotated about this axis.
  5. To form a closed excavation, one edge of your mesh must be coincident with the X = 0 (vertical) axis. If this is not the case, the excavation will be "open-ended".
  6. Most other RS2 modeling options can be used with an Axisymmetric model, however, always keep in mind the nature of an Axisymmetric model (for example, when defining loads, boundary conditions, etc.)

NOTE: As of RS2 version 9, joints can be used with Axisymmetric models. This includes joint boundaries, as well as joints associated with Composite liners or structural interfaces.

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