Theoretical investigation of large-amplitude waves in granular soils

A theoretical investigation of plane waves in granular soils is presented. Dynamic equations are derived with the use of the hypoplasticity theory for granular materials. For numerical calculations the material parameters of Karlsruhe sand are used. Wave speeds as slopes of characteristics of the dynamic equations are calculated for various stresses and densities. It is shown that under certain conditions the dynamic equations lose hyperbolicity and the initial boundary value problem thus becomes ill-posed. Two types of ill-posedness are found, known as flutter ill-posedness and stationary discontinuity. The latter is shown to arise at higher shear stress than the former. A comparison is made between dynamic ill-posedness and stability of static equilibrium. With the use of the second-order work stability criterion it is found that the dynamic equations lose hyperbolicity when the static equilibrium under a dead load is still stable. Numerical solutions to the problem of propagation of boundary disturbance in a half-space are obtained. Owing to dilatancy and contractancy of the granular material, a purely transverse disturbance induces a longitudinal component of velocity in the wave, and vice versa.