Vertical S waves in soil stratum over halfspace

An analytical model of a soil layer resting on a halfspace with vertically propagating shear waves is studied under a harmonic excitation on the surface. The soil is treated as a Kelvin-Voigt continuum, using the one-dimensional wave equation. The material parameters can be strain dependent. A hyperbolic model proposed by Hardin & Drnevich is used for describing the nonlinear stress-strain relationship. Based on this, a solution to a problem where thirty thousand people were jumping to the rhythm of rock music on the field in a stadium is given. The soil stratum is a 5-60m thick uniform soft high-plastic clay. The particle velocity was estimated to range from 22·5 mm/s to 45 mm/s in the first overtone. These velocity values exceeded the critical value, of 20 mm/s, of the German building code DIN 4150 which may explain the occurence of damages.