Tunnel closure calculations

When a deeply penetrating munition explodes above the roof of a tunnel, the amount of rubble that falls inside the tunnel is primarily a function of three parameters: first the cube-root scaled distance from the center of the explosive to the roof of the tunnel. Second the material properties of the rock around the tunnel, and in particular the shear strength of that rock, its RQD (Rock Quality Designator), and the extent and orientation of joints. And third the ratio of the tunnel diameter to the standoff distance (distance between the center of explosive and the tunnel roof). The authors have used CALE, a well-established 2-D hydrodynamic computer code, to calculate the amount of rubble that falls inside a tunnel as a function of standoff distance for two different tunnel diameters. In particular they calculated three of the tunnel collapse experiments conducted in an iron ore mine near Kirkeness, Norway in the summer of 1994. The failure model that they used in their calculations combines an equivalent plastic strain criterion with a maximum tensile strength criterion and can be calibrated for different rocks using cratering data as well as laboratory experiments. These calculations are intended to test and improve the understanding of both the Norway Experiments and the ACE (Array of conventional Explosive) phenomenology