Transmission of Elastic P-waves across Single Fractures with a Nonlinear Normal Deformational Behavior |
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Authors: | J Zhao J G Cai |
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Affiliation: | (1) School of Civil and Structural Engineering, Nanyang Technological University, Singapore, SG |
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Abstract: | Summary This paper presents a theoretical study on normally incident elastic P-wave transmission across single dry fractures with
a nonlinear normal deformational behavior. The effects of nonlinear fracture normal behavior on P-wave transmission are examined
without the mixture of fracture shear behavior. The linear displacement discontinuity model for wave propagation across fractures
is extended to a nonlinear model – the hyperbolic elastic model (BB model). Numeric solutions of magnitudes of transmission
(|T
non|) and reflection (|R
non|) coefficients, for normally incident P-wave transmission across the nonlinear deformable fractures, are obtained and related
to the closure behavior of fractures. Parametric studies are conducted to acquire an insight into the effects of the nonlinear
fracture normal deformation on P-wave transmission, in terms of initial normal stiffness and the ratio of current maximum
closure to maximum allowable closure of the fractures, as well as the incident wave amplitude and frequency. Comparisons between
the linear 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 current maximum closure of fracture incurred
during the wave transmission is much smaller, relative to the maximum allowable closure. In addition, the nonlinear fracture
behavior gives rise to a phenomenon of higher harmonics during the wave transmission across the fracture. The higher harmonics
contribute to the increase of |T
non| from |T
lin|. |
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Keywords: | |
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