Acoustoelasticity is a non-linear acoustical phenomenon that describes the influence of stress or deformation states of rocks on wave velocities. Assumed that a wave motion is superimposed on rocks under the predeformation and introduction of third-order elastic constants, classic acoustoelastic theory of rocks has been provided to describe acoustoelastic phenomenon of rocks under the infinitesimal static deformation. Because rocks have complex constitutive relation, especially under the large static deformation, there is evident discrepancy between the predicted result by the classic acoustoelastic theory and experimental results. In order to solve this discrepancy, incremental theory for acoustoelasticity in rocks with arbitrary constitutive relation is investigated in this paper by incremental loading method based on classic acoustoelastic theory of rocks and compared with ultrasonic wave velocity measurement in diabase under hydrostatic compressional test. The compared results show that this incremental theory for acoustoelasticity in rocks can effectively describe the wave-induced wave velocity change in rocks with arbitrary constitutive relation, especially under the large predeformation, which will benefit the innovative technology of non-destructive rock stress measurement.
Acoustoelastic effect of rocks, which means the stress--induced wave-velocity change, has wide application in the fields of geoscience, petroleum exploration, and civil engineering (Nur & Simmons, 1969; Siegesmund & Kern, 1990; Simmons, 1964). Field observations in geophysics have shown that acoustoleastic constant of rocks is much greater than that of metal materials (Cheng, Niu, & Wang, 201 0; Nakata & Snieder, 2011; Niu, Silver, Daley, Cheng, & Majer, 2008; Sayers, 2010; Tosaya, 1982; Yamada, Mori, & Ohmi, 2010), which has also been verified in rock experiments (Sayers, 2010).
Based on the finite deformation theory of solids and the introduction of the third-order elastic constants in constitutive law, classic acoustoelastic theory for solids had been developed to macroscopically evaluate acoustoelasticity in metallic materials, which has been widely applied in the measurements of residual stresses, plastic damage, and plastic strain ratio of metallic materials (Hirao & Ogi, 2003; Pao, Sachse, & Fukuoka, 1984). This theory yields an explicit acoustoelastic relation, where the relevant parameters are independent of the stress states. Huang et al. (Huang, Burns, & Toksoz, 2001) applied the classic theory into the investigation of the rock acoustoelasticity.