Curved Beam Analog for Tunnel Design in Massive Rock

A curved-beam analog is shown to be valid for tunnel design in massive rock. A mechanics of materials analysis is used that retains a physical model of the dominant stress action by assuming an experimentally verifiable deformation, thus radically simplifying the mathematics, and providing a continued insight as complexity is added to the fundamental problem. The specific technique, curves-beam analysis isolates some of the material immediately surrounding the opening in the mass, and bordering on the uniform stress field, as a uniformly loaded ring, for which there is precedent. Qualitative and quantitative studies give an orientation into the mechanisms involved, particularly the deformation-controlled loading along the outer boundary of the ring, which was most simply handled by postulating a degenerate beam action.