Analysis of tunnel-support interaction using an equivalent boundary beam

The convergence-confinement method used for tunnel analysis is based on the simplifying assumption of axisymmetric conditions. This paper presents a method for tunnel support design which is not limited to the hydrostatic loading simplification. With knowledge of the unsupported tunnel displacements, a circular beam equivalent to the plane strain tunnel boundary is found. Then, the distribution of field stresses between the ground and support system can be readily computed. The proposed method allows utilizing existing solutions for plastic deformations around excavations under non-hydrostatic loading, such as the solution derived by Detournay (1986), in order to compute the non-uniform support response. Significantly less computational resources are required compared to the finite-element method; hence, this method is well suited at the preliminary stage of a project to conduct extensive sensitivity analyses and identify critical support scenarios.