Abstract
The theories of thermoelasticity and acoustoelasticity are widely employed to characterize the effects between temperature and stress fields on elastic wave propagation in preheated and prestressed isotropic solid rocks, respectively. However, the Earth’s depth rocks experience high temperature and high pressure simultaneously, which are governed by coupling thermoelastic and acoustoelastic effects (i.e., thermoacoustoelasticity). Previous studies on this coupling effect have been conducted under the acoustoelastic framework with the preheat-induced strain to capture changes in wave velocity with temperature, but ignoring the preheat-induced stress and the prestress-induced thermoelastic effects (thermal stress/strain). We address this gap by formulating the theory of thermoacoustoelasticity under the framework of the total energy function of both preheat- and prestress-induced strains incorporated with the equation of heat conduction. This framework considers the cross-coupling effects between temperature and stress fields, and therefore couples preheat-induced acoustoelastic and prestress-induced thermoelastic effects. We unify third-order thermoelastic and acoustoelastic constants based on their equivalence in isotropic media. The proposed thermoacoustoelastic model predicts the presence of two slow modes, thermal slow P (T wave) and slow S waves, along with two classical modes (fast P and fast S waves). The four propagation modes show dependencies on temperature and stress at varying levels. The T wave is coupled with two fast modes and presents diffusive behavior, while the slow S wave remains frequency independent. The predicted wave velocities for saturated Berea sandstone show reasonable agreement with ultrasonic measurements at different temperatures.
Paper Information
Yang J., Fu L.-Y., Han T., Deng W., Fu B.-Y. Thermoacoustoelasticity for Elastic Wave Propagation in Preheated and Prestressed Solid Rocks[J]. Rock Mechanics and Rock Engineering, 2025. https://link.springer.com/article/10.1007/s00603-024-04361-z.
