Stress wave penetration into non-linear granular materials

Abstract

A one-dimensional normal stress wave propagation equation applicable to non-linear, compressible, granular, dry materials at a large interval of stress intensities is developed. The paper analyses the evolution of the wave profile and the possible development of a shock profile when a normal stress wave penetrates these materials. The approach consists of integrating a system of two coupled balance equations and applying the method of characteristics. The results include the development of a stress-dependent propagation velocity function and a normal stress–particle velocity relationship, which is an implicit function of the stress. The results are applicable to the fields of seismology, protective shelter design, impact studies and the design of instrumentation to sense high-intensity stresses and particle velocities. They can also be used to interpret various phenomena associated with normal stress wave and shock wave actions in some granular ground materials.