Ground Response Curves for Rock Tunnels

TLDR

Ground response curves relate support pressure to tunnel convergence, aiding understanding of rock‑support interaction and support design. The authors present two analytical solutions for a circular tunnel in hydrostatic stress: a closed‑form elastic‑brittle‑plastic model with constant dilatancy and a stepwise elastic‑strain softening‑plastic model with reduced dilatancy, both assuming plane strain. Both solutions, based on nonlinear peak and residual strength criteria, are demonstrated through illustrative examples.

Abstract

Calculations of support pressure—tunnel convergence relationships, or ground response curves are used to improve understanding or rocksupport interaction and to aid in the dimensioning of tunnel support elements. Methods of response curve calculation are presented for a tunnel of circular cross‐section excavated in a rock mass initially subjected to a hydrostatic in situ stress field. Plane strain conditions are assumed. The two solutions presented use nonlinear peak and residual rock mass strength criteria. Particular consideration is given to the influence of plastic volumetric strains in the rock mass surrounding the tunnel. A closed‐form solution is presented for an elastic‐brittle‐plastic material behavior model in which post‐peak dilatancy occurs at a constant rate with major principal strain. A second solution is presented as a stepwise sequence of calculations for an elastic‐strain, softening‐plastic model in which post‐peak dilatancy occurs at a lower rate with major principal strain in the constant strength plastic zone than in the strain softening zone. These two solutions are applied in illustrative examples.