Spherical Wave Propagation In Brittle Materials

In the past year or two, considerable effort has been expended to calculate the spherical wave propagation phenomena associated with explosions in a "hard rock" medium (Godfrey, 1969; McKay and Godfrey, 1969; Burford, et al, 1970). This effort was stimulated primarily by the recognition that early calculations predicted peak particle displacements which seriouly disagreed with field data. In most of the calculations mentioned above, rock was modeled as an inelastic continuum (see for example Isenberg, et al, 1970 for some recent results using "classical" elastic-plastic material property models). However, several investigators (Handin, et al, 1967; Cherry, et al, 1967) have shown that the simple classical yield surface models cannot simultaneously account for the observed brittle failures of intact materials under compression, extension and torsion. One approach to more correct modeling of dynamic rock behavior is to make the inelastic model more and more sophisticated. For ex- ample, recent experiments at the University of Utah (Swanson, 1969) have suggested possible modifications to the yield surface model that could better account for the ductile behavior of intact granite sam- ples under various states of stress. The approach followed in this paper proceeds in an entirely different direction. We want the physics which is built into our conception of rock to be as simple as possible while at the same time reproducing the most important features of rock's behavior. Therefore, we abandon the requirement that rock be treated strictly as a continuum. Instead we consider a "discontinuous" model in which one of the most significant characteristics of rock is treated..