Tunnel intersection mechanics: Closed-form pseudo-3D approximations for deformation modeling and shear-failure prediction

Deformation modeling of underground tunnel intersections attempts to provide answers on the occurrence of localized structural instabilities under different, and possibly dynamically-changing, in-situ conditions. Design decisions hinge on these findings; since much of the stresses underground are compressive, shear-failure predictions provide outlines for maintaining structural stability on the intersections of underground tunnel excavations in anisotropic rock masses, such as those made using tunnel-boring machines (TBMs).

Three-dimensional (3D) deformations around the circumference of the orthogonal intersection plane of two tunnels are modeled using a pseudo-3D approximation approach established in petroleum engineering, which adjusts for stress interferences coming from each tunnel. The rationale for such approach is that the normal stresses on the circumference of the primary “Tunnel A” are used as inputs to evaluate the stresses on the base of a smaller, secondary “Tunnel B” which approximates the two tunnels’ intersection plane.

The resultant closed-form expressions are used as a boundary condition in a Mohr-Coulomb-type model for shear failures, in a cylindrical coordinate system. Dimensionless plots (“allowable stress diagrams”) provide the means to visually recognize whether the induced stresses on the tunnel intersection can trigger shear failure, or not. The dynamic impact of sediment settling is quantitatively assessed and non-orthogonal tunnel intersections are discussed.