# Strain-Softening Analyses of a Circular Bore under the Influence of Axial Stress
## Nomenclature  
\(A=-Y_{r}/(\alpha_{r}-1)\) constant  
\(B=p_{in}+Y_{r}/(\alpha_{r}-1)\) constant  
\(c\) cohesion  
\(c_{p}\) peak cohesion  
\(c_{r}\) residual cohesion  
\(E\) elastic modulus  
\(G\) shear modulus  
\(q\) axial in situ stress  
\(r_{0}\) radius of the circular bore  
\(r\) radial coordinate in the cylindrical polar coordinate system  
\(r_{i}\) the radius of the \(i\)th plastic annulus  
\(\overline{R}\) radius of the interface of the inner plastic zone and the outer plastic zone  
\(R_{s}\) radius between softening and residual zones  
\(R\) plastic radius  
\(p_{c\,i}\) the critical internal pressure. The out-of-plane in situ stress is the major principle stress for \(i=1\), it is the intermediate principle stress for \(i=2\) and the minor principle stress for \(i=3\)  
\(p_{in}\) the internal pressure  
\(\Delta p_{k}\) the kth pressure decrease  
\(u_{c\,i}\) the displacement at the interface of the plastic zone and the elastic zone. The out-of-plane in situ stress is the major principle stress for \(i=1\), it is the intermediate principle stress for \(i=2\) and the minor principle stress for \(i=3\). \(u_{c\,i}=R(\sigma_{0}-p_{c\,i})/(2G)\)  
\(u_{\overline{R}}\) the displacement at the interface of the inner plastic zone and the outer plastic zone  
\(u\) radial displacement  
\(\Delta u_{(i)}\) incremental radial displacementat the ith load increment  
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