Relationship Between Padé Acoustoelastic Coefficients and Crack Parameters in Fractured Rocks Under Hydrostatic Condition

The response of elastic wave velocity to stress changes is critical for subsurface stress probing. While conventional acoustoelasticity is accurate at low stresses, it becomes unreliable at higher stresses. To address this, the Padé expansion is employed to approximate the strain energy function, with the resulting Padé acoustoelasticity theory providing improved accuracy in predicting velocity changes at higher effective stresses compared to conventional models. Using data from five artificial sandstones, we fitted the conventional model, calculated third-order elastic constants and the specific values of the two additional Padé coefficients introduced. Dual-pore models show that pressure affects pore distribution, which in turn influences velocity changes, correlating with the Padé coefficients. We established a relationship between these coefficients and crack parameters via effective pressure. The Padé acoustoelastic theory provides a more precise stress-velocity relationship by accounting for complex cracking behavior under prestress. Furthermore, the Padé coefficient serves as a valuable quantitative indicator of crack changes during pressurization, offering enhanced insight and broader applicability.