Effects of Single Joint with Different Nonlinear Normal Deformationalbehaviors on P-Wave Propagation
The classical exponential elastic model and the BB hyperbolic elastic model are used to investigate the effects of nonlinear normal deformation on elastic P-wave normal incidence without the shear deformation considered. A theoretical research is presente
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EFFECTS OF SINGLE JOINT WITH DIFFERENT NONLINEAR NORMAL DEFORMATIONALBEHAVIORS ON P-WAVE PROPAGATION J. Yu Geotechnical Engineering Department, Nanjing Hydraulic Research Institute Nanjing 210024, China
The classical exponential elastic model and the BB hyperbolic elastic model are used to investigate the effects of nonlinear normal deformation on elastic P-wave normal incidence without the shear deformation considered. A theoretical research is presented on normally incident P-wave transmission across single dry joint with these different nonlinear normal deformation behaviors. Based on the classical and the BB nonlinear models, the different nonlinear displacement discontinuity models are established. Numeric difference resolution and analytic resolution of reflected and transmitted coefficients for normally incident P-wave propagates across single joint with different nonlinear normal deformation behaviors are obtained. Then parametric studies are conducted, in terms ofthe quantitative ratio of the joint current maximum closure to the joint maximum allowable closure, the joint initial normal stiffness and the incident wave frequency. Comparisons between the results of different nonlinear behaviors are drawn and the conclusions have theoretical meaning.
PREFACE Extensive studies have been conducted to investigate the effects of joints on stress wave propagation in fractured media, for such effects are important subjects in solving problems of rock mass dynamics and shelter engineering. The theories of wave scattering at cracks have been developed with the considerations of linear contact conditions of crack faces (e.g., Hudson, 1981, Angle and Achenbach, 1985) and nonlinear contact conditions of crack faces (Achenbatch and Norris, 1982, Smyshlyaev and Willis, 1994). The objects investigated are mainly cracks of small size relative to wavelength. In comparison with the micro-cracks, the macro-joints may be more dominant in a fractured rock mass on most occasions (Zhao, 2001). A planar macro-joint, which is assumed to be large in extent and very thin in thickness relative to a wavelength (hereafter termed simply as joint), can be physically viewed as a planar collection of collinear micro-voids and asperities in contact. When waves propagate across such a joint, the stress field is continuous, but the displacement field is discontinuous due to the joint deformation. To account for the effects of joints on wave propagation, the joint deformational behaviors are treated as displacement discontinuity boundary conditions in the wave equation, which is termed as displacement discontinuity theory. Linear elastic displacement discontinuity models for dry joints have been established by Schoenberg (1980) and Kitsunezaki (1983). The linear elastic displacement discontinuity models for dry joints
are valid, provided that the magnitude of the seismic stress is insufficient. However, it has been found that the complete deformational behaviors of rock joints are generally nonlinear. Zhao (2001) promote the famous static norm
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