A new acoustoelastic model for velocity-hydrostatic-pressure in rocks based on general acoustoelastic theory for elastic solids

Abstract

Acoustoelastic model based on classic acoustoelastic theory of solids fails to describe rock acoustoelasticity, where wave velocities in rocks has complex non-linear relations with the applied hydrostatic pressure. In order to extend acoustoelastic model into better prediction for rock acoustoelasticity, a new acoustoelastic model is presented based on general acoustoelasticity of elastic solids having complicated constitutive law of rocks, which combines third-order elastic constants of compact rocks with the exponential terms for the influence of pore/cracks in rocks. The data for P- and S-wave velocities of diabase and greywacke samples subjected to the pressure up to 400 MPa are taken as examples to validate the presented model. The results show that the presented model could not only predict rock acoustoelasticity but also be linked with frequently-used empirical model and meso-mechanical model. The intrinsic connection among mechanical parameters, acoustical parameters, and meso-mechanical parameters could be established clearly, which will benefit the determination of high-resolution constitutive law and the compliant porosity by the measured ultrasonic-wave velocities of rock samples.

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