Transmission of elastic P-waves across single fractures with a nonlinear normal deformational behavior

This paper presents a theoretical study on normally incident elastic P-wave transmission across single dry fractures with a nonlinear normal deformati onal behavior. The effects of nonlinear fracture normal behavior on P-wave transmission are examined without the mixture of fracture shear behavior. T he linear displacement discontinuity model for wave propagation across frac tures is extended to a nonlinear model - the hyperbolic elastic model (BB m odel). Numeric solutions of magnitudes of transmission (\T-non\) and reflec tion (\R-non\) coefficients, for normally incident P-wave transmission acro ss the nonlinear deformable fractures, are obtained and related to the clos ure behavior of fractures. Parametric studies are conducted to acquire an i nsight into the effects of the nonlinear fracture normal deformation on P-w ave transmission, in terms of initial normal stiffness and the ratio of cur rent maximum closure to maximum allowable closure of the fractures, as well as the incident wave amplitude and frequency. Comparisons between the line ar and nonlinear models are presented. It is shown that, \T-lin\ and \R-lin \ for the linear model are special solutions of \T-non\ and \R-non\ for the nonlinear model, when the incident wave amplitude is so low that the curre nt maximum closure of fracture incurred during the wave transmission is muc h smaller, relative to the maximum allowable closure. In addition, the nonl inear fracture behavior gives rise to a phenomenon of higher harmonics duri ng the wave transmission across the fracture. The higher harmonics contribu te to the increase of \T-non\ from \T-lin\.