Nonlinear wave propagation in porous materials based on the Biot theory

Abstract

Nonlinearity must be considered with some porous granular media because of the large deformation under seismic waves. In this study, the propagation of nonlinear waves in porous media is studied based on the Biot theory and the governing equations are obtained by the Lagrangian formulation. Three new nonlinear parameters are introduced to consider the coupled nonlinearity between the solid and fluid components in porous media. It is shown that an additional nonlinear wave with a double frequency is generated by the coupling effect of linear fast and slow waves. When only a shear wave is applied at the source, no double-frequency nonlinear wave is predicted and three nonlinear longitudinal waves are generated. On the basis of the practical case studies, the effect of strong nonlinearity is computed under the influence of a one-dimensional single longitudinal wave source and a single shear wave source.

Nonlinear acceleration wave propagation in the DKM theory

“…where λ and µ are the Lamé coefficient and shear modulus and α, M are elastic coefficients of Biot, see Tong et al (2017). The constants c ij and d ij depend on parameters of the porous medium and are given explicitly in Donskoy et al (1997), equations (8) and (21), although we take the representations given in Tong et al (2017). The coefficient of the dissipation term is composed of η and κ which are the dynamic viscosity of the fluid and the permeability, respectively.…”

“…The subject of nonlinear acoustic wave propagation is one of intense recent interest as witnessed by the contributions of Christov (2016), Crighton (1979), Dazel and Tournat (2010), Donskoy et al (1997), Jordan (2005), Jordan (2016), Pushkina (2012), Tong et al (2017), and the many references therein.…”

“…For example, there are weakly nonlinear expansion techniques, see e.g. Dazel and Tournat (2010), Donskoy et al (1997), Pushkina (2012), Tong et al (2017). In addition, there are analyses for handling acoustic travelling waves, see e.g.…”

“…Biot (1962, 1972, 1973. Nonlinear wave motion in such media has been studied recently by Dazel and Tournat (2010), Donskoy et al (1997), Pushkina (2012), Tong et al (2017). We are particularly interested in an acceleration wave analysis.…”

Properties of Love Waves in Functional Graded Saturated Material

“…Deresiewics et al [4,5,6] derived the dispersion and attenuation equations of Love waves in the porous media. Wang, Tong, and Santos et al [7,8,9] used the iteration method to solve the dispersion equation of porous materials. In addition, Konezak [10] and Ba et al [11] gave a solution to the propagation of waves in porous layered half-space.…”