Characteristic Curves for Deep Circular Tunnels in Poroplastic Rock

Abstract

A complete analytical solution for an axisymmetric deep tunnel excavated in a saturated poroplastic rock is presented. Results are found for short- and long-term analyses and for different drainage conditions at the rock–liner interface. In the derivation, the following assumptions are made: (1) circular cross-section, (2) deep tunnel, (3) plane strain conditions on a cross-section perpendicular to the tunnel axis, (4) axisymmetric loading, (5) the rock is saturated, homogeneous and isotropic, and (6) the rock is elastic-perfectly plastic with brittle failure and non-associated flow rule. The results obtained indicate that, if the rock remains elastic during construction, the stresses of the liner and the tunnel deformations are the same for short- and long-term conditions and are independent of the drainage conditions at the rock–liner interface and on the magnitude of Biot’s parameter α. If the rock yields, the stresses in the liner and the tunnel deformations strongly depend on the type of analysis. Effective radial and tangential stresses inside the rock decrease with Biot’s parameter α, while radial displacements increase. The response of the liner in terms of stresses and deformations strongly depends on its stiffness relative to the rock, yielding of the rock, groundwater and drainage conditions, and construction operations, while it is somewhat less sensitive to the rock’s poroplastic properties. Stresses and deformations inside the rock, however, show a much stronger dependency.