Tunnel Closure for Nonlinear Mohr-Coulomb Functions

A closed-form analysis for elastic-plastic response of a cylindrical tunnel in rock under axisymmetric loading at infinity shows the effect of yielding according to a nonlinear Mohr-Coulomb-type function in which the angle of internal friction decreases with increasing mean normal stress. Explicit expressions for stresses and deformation are obtained by approximating the nonlinear function by a series of straight line segments. Comparisons of tunnel closures calculated with nonlinear functions with those from single straight line approximations show that tunnel closure is sensitive to plastic behavior nearest the tunnel. This means that the low-stress part of the yield function, where nonlinearity is usually greatest, should be modeled as accurately as possible.