Two-Dimensional Elastic Analysis and Distinct Element Modeling for Characteristic Curves of Tunneling

Abstract

Active mobilization of bearing capacity of rock mass surrounding an underground opening characterizes the NATM (New Austrian Tunneling Method) concept of supporting. There have been many attempts to give quantitative expressions for this capacity but no one has ever completely solved the question. In the first part of this paper the theoretical relations between support pressure and tunnel wall displacements are briefly discussed. We derive a simplified solution of a circular lined-tunnel in an elastic ground under the plain strain for full-slip and no-slip conditions. These two conditions at the ground-lining interface make it possible to explain the effects of shear stress transmission and relative shear displacement. The lateral free-field ground stresses for this solution are restricted to a fixed value of the vertical stresses (σ_V^*=-p, σ_H^*=-kp). An actual tunnel opening is excavated and supported after the load corresponding to the free-field stresses. We introduce an assumption of the actual “excavation unloading” conditions that occur during tunneling. By advancing this derivation, the strict solution is utilized successfully to construct a theoretical characteristic curve of tunneling. The characteristic curve shows clearly the bearing capacities of a tunnel lining, the surrounding ground and the total by using an index, “relative-support-stiffness”.
The elastic theory of the stress distribution around tunnels demonstrates that the deviatoric stresses are maximum at the periphery of the excavation. Therefore, the rock mass may yield in the overstressed zone surrounding the excavation. Discussion here should include the dependence of the characteristic curve on the zone of yielded ground and the discontinuity in the ground. We have carried out numerical simulations for a discontinuous ground with Distinct Element Modeling. The realistic ground reaction curves by the analyses are examined with the theoretical solution derived above. We will learn that while the ground may work, more or less, as a load bearing structural component to the load corresponding to the free-field stresses, overestimation must be avoided.