Abstract：A theoretical study is presented on normally incident elastic P-wave transmission across single dry fracture with nonlinear normal deformation behavior. The effects of nonlinear normal deformation on P-wave normal incidence are studied without the shear deformation considered. The linear displacement discontinuity model for wave propagation across fracture is extended to nonlinear model，the hyperbolic elastic model(BB model). Numeric solutions of transmission and reflecton coefficients for normally incident P-wave transmission across the nonlinear deformable fracture are obtained and related to the closure behavior of fracture. Parameter studies are conducted to get an insight into the effects of the nonlinear normal deformation of fracture on P-wave transmission，in terms of initial normal stiffness and the ratio of given closure to maximum allowable closure of the fracture，as well as the incident wave amplitude and frequency. Comparisons between the linear and nonlinear models are presented. It is shown that，the transmission and reflecton coefficients for the linear model are special solutions of those for the nonlinear model，when the incident wave amplitude is so low that the maximum closure of fracture incurred during the wave transmission is much smaller relative to the maximum allowable closure. In addition，the nonlinear behavior of fracture gives rise to the phenomenon of higher harmonics during the wave transmission across the fracture.
