Depth and spacing of tension cracks

Abstract

Contraction cracks in basalt, permafrost, and mud, and crevasses in glaciers are examples of geological phenomena that might be studied by reference to a theoretical model of tension cracks in a semi-infinite solid. The effect of the crack in relieving stress at the ground surface bears on the problem of crack spacing, and the rate of energy dissipation at the advancing crack tip bears on the problem of crack depth. Even though the stresses that cause cracking develop slowly, an elastic model of the stress near a crack can be useful as long as the cracks, once initiated, propagate rapidly. Results are presented for the elastic stress perturbation caused by a crack in an infinite or semi-infinite medium in which the initial stress is a step function or a linear function of depth. Tables and graphs are presented which can be applied directly to problems in which the variation of stress with depth is arbitrary. These results, used with the modified Griffith theory of macroscopic fracture introduced by Irwin [1948] and Orowan [1950], suggest a means of predicting depth and spacing of tension cracks in terms of the stress field and measurable properties. The method is illustrated with a discussion of cooling joints in basalt, and other problems of tension fracture in geology.