Closed-form solutions for collapse mechanisms of tunnel crown in saturated non-uniform rock surrounds

The crown stability of a deep-buried metro tunnel or station is evaluated by means of a kinematic analysis procedure, with considerations of non-uniform rock surrounds and pore water effects. Non-uniform rock strata are discretized to several layers with finite thickness, with varying rock parameters assigned to different layers and constant parameters within each layer. Pore water effect is considered as an external loading acting on rock mass and boundaries. Employing the nonlinear Hoek-Brown criterion, a preliminary study is presented to analyse tunnel crown stability in a uniform rock medium, in the realm of upper bound theory. After having obtained general solutions of 2D and 3D collapse mechanisms, non-uniformity of rock masses is considered and investigated in crown stability analyses. 2D and 3D closed-form solution are formulated based on variational principle and work rate balance equation. Apart from the collapse shape and dimension, the weight of collapsing block is calculated, which gives a quick estimate of the average overburden pressure and hence guides the design of tunnel lining. Some examples related to circular and rectangular (square) tunnels are provided to offer insights of the implication of influential factors on the crown stability of a tunnel deeply excavated in saturated non-uniform rock strata.