Revisiting crown stability of tunnels deeply buried in non-uniform rock surrounds

A kinematic analysis procedure is presented to investigate the crown stability of deep-buried tunnels in non-uniform rock strata. The non-uniformity of rock properties is considered using the discretized approach with finite thickness layers. In the realm of upper bound theory, kinematic analysis is briefly presented for a single layer so as to provide basis for multi-layer analysis. A 2D collapse mechanism is postulated to depict the potential falling block with an arbitrary tunnel cross-section, although rectangular tunnels are considered in the 3D kinematic analysis for ease of calculation. An impending collapse is likely to occur, provided that the width of the excavation is no less than the collapse width. In order to reflect the nonlinear characteristics of rock materials at failure, the Hoek-Brown criterion is employed for tightly interlocked and very poor rock masses, with its form expressed by normal and shear stresses to facilitate calculations of internal energy dissipation rate. Based on the variational principle and power-based balance equation, the effective collapse mechanism is derived in closed form. Comparison is carried out to verify the robustness of the proposed approach. Sensitivity analysis is performed to depict the influence of each non-uniform rock strength parameter on crown stability. As expected, such a discretized approach incorporated into kinematic analysis enables one to account for non-uniformity of rock surrounds, which would fill the knowledge and design gap of similar tunnelling issues much needed at present state of practice.