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|Title:||The influence of out-of-plane stress on a plane strain problem in rock mechanics|
|Authors:||Reed, M B|
|Citation:||Maths Technical Papers (Brunel University). February 1987, pp 1-17|
|Abstract:||This paper analyses the stresses and displacements in a uniformly prestressed Mohr-Coulomb continuum, caused by the excavation of an infinitely long cylindrical cavity. It is shown that the solution to this axisymmetric problem passes through three stages as the pressure at the cavity wall is progressively reduced. In the first two stages it is possible to determine the stresses and displacements in the rθ-plane without consideration of the out-of plane stress . In the third stage it is shown that an inner plastic zone develops in whichzσzσ=σθ, so that the stress states lie on a singularity of the plastic yield surface. Using the correct flow rule for this situation, an analytic solution for the radial displacements is obtained. Numerical examples are given to demonstrate that a proper consideration of this third stage can have a significant effect on the cavity wall displacements.|
|Appears in Collections:||Mathematical Science|
Dept of Mathematics Research Papers
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