On three-stage temperature dependence of elastic wave velocities for rocks

Abstract

For most rocks, the typical temperature behavior of elastic wave velocities generally features a three-stage nonlinear characteristic that could be expressed by a reverse S-shape curve with two inflexion points. The mechanism regulating the slow-to-fast transition of elastic constants remains elusive. The physics of critical points seems related to the multimineral composition of rocks with differentiated thermodynamic properties. Based on laboratory experiments for several rocks with different levels of heterogeneity in compositions, we conduct theoretical and empirical simulations by nonlinear thermoelasticity methods and a S-shape model, respectively. The classical theory of linear thermoelasticity based on the Taylor expansion of strain energy functions has been widely used for crystals, but suffers from a deficiency in describing thermal-associated velocity variations for rocks as a polycrystal mixture. Current nonlinear thermoelasticity theory describes the third-order temperature dependence of velocity variations by incorporating the fourth-order elastic constants. It improves the description of temperature-induced three-stage velocity variations in rocks, but involves with some divergences around two inflexion points, especially at high temperatures. The S-shape model for empirical simulations demonstrates a more accurate depiction of thermal-associated three-stage variations of P-wave velocities. We investigate the physics of the parameters ${a_1}$ and ${b_1}$ in the S-shape model. These fitting parameters are closely related to thermophysical properties by being proportional to the specific heat and thermal conductivity of rocks. We discuss the mechanism that regulates the slow-to-fast transition in the three-stage nonlinear behavior for various rocks.

Experimental Study on Acoustic Emission Characteristics of Granite and Sandstone under Uniaxial Compression

“…Literature [35] combined the acoustic emission test index with the integrated machine learning model and revealed the internal relationship between rock acoustic emission and rock fracture instability. Literatures [36,37] believed that the acoustic emission phenomenon is caused by the release of the energy generated by the sudden rupture of some microelements in the rock in the form of elastic waves. Literatures [38][39][40] explored the relationship between rock failure mechanism and acoustic emission signal under uniaxial and triaxial compression tests at different temperatures by studying the change of acoustic emission elastic wave signal of granite.…”

Third‐Order Padé Thermoelastic Constants of Solid Rocks

“…It should be noted that the nonlinear temperature‐dependent velocities of elastic waves occur at lower temperatures for solid rocks than for crystals. In such cases, the higher‐order thermoelastic constants (Yang, Fu, Fu, et al., 2019) could be applicable but have more unknown elastic constants that have difficulty for physical interpretation (N. Li et al., 2021).…”