Nonlinear surface waves in soil

Abstract

Nonlinear effects in surface waves propagating in soil are investigated theoretically. Analytic solutions are derived for the second harmonics and difference frequency waves generated by a bifrequency primary wave propagating at moderate amplitude. The soil is modeled as an isotropic solid. As such, its elastic properties are described by five elastic constants, two at second order in the strain energy density (the shear and bulk moduli) and three at third order. Nonlinear propagation of the surface waves is based on a theory developed previously [Zabolotskaya, J. Acoust. Soc. Am. 91, 2569–2575 (1992)]. Elements of the nonlinearity matrix associated with the interacting spectral components are expressed in terms of the five elastic constants. It was found convenient to express the nonlinearity matrix for soil as a function of a nonlinearity parameter corresponding to B/A for liquids, particularly for saturated soils exhibiting liquidlike properties. This nonlinearity parameter can vary by several orders of magnitude. For soils with shear wave speeds less than 20% of the compressional wave speeds, the nonlinearity of surfaces waves is found to be independent of the third-order elastic constants and dependent only on the shear modulus. [Work supported by ONR.]