Three-Dimensional Analysis of Circular Tunnel Headings Using Broms and Bennermark’s Original Stability Number

Abstract

The stability of a tunnel face is described by the combined effects of surcharge load, self-weight of the soil, and internal supporting pressure. This combination can cause failure in either blowout or collapse. Since the plastic shearing in undrained soils is independent of loading directions in homogeneous soils, this paper studies Broms and Bennermark’s original stability number for the circular tunnel heading in cohesive soil using three-dimensional upper and lower bound finite-element limit analysis. Dimensionless ratios are used in this study to cover practical soil parameters and tunnel depths for collapse and blowout analyses. Numerical results of critical stability numbers are compared with two-dimensional and three-dimensional solutions available in the literature. Stability design charts and tables produced in this paper can be used to estimate safety factors for various design parameters.