The acoustoelasticity method has been developed to estimate the in-situ rock stresses by the measurement of velocity anisotropy around a borehole. The velocity anisotropy around a borehole can be induced by intrinsic anisotropy or the applied stresses of rocks. The practical rocks exhibit the anisotropy inevitably. Therefore, In order to advance the acoustoelasticity method for the measurement of in-situ rock stresses, the influence of intrinsic anisotropy of rocks on the stress-induced velocity anisotropy around a borehole is investigated in this paper. First, the acoustoelasticity theory of finite-deformation solids is introduced briefly. Secondly, The stress and displacement fields around the anisotropic borehole subjected to the far-field stress fields are given by Stroh formalism. Thirdly, the assumption of the body waves propagation along the direction of the borehole axes yields the quantitative borehole acoustoelasticity. Lastly, we discuss the intrinsic anisotropy of the borehole on the stress-induced velocity anisotropy around the borehole in detail.
It has been shown in many experiments that the stress induced wave velocity variations in rocks are about 10−2∼10−3/MPa, which are much more than that of metallic materials (Hirao & Ogi 2003, Johnson & Rasolofosaon 1996, Nur & Simmons 1969, Pao et al 1984, Thurston & Brugger 1964, Toupin & Bernstein 1961,Vega 2003). Mao et al. are the first authors to my knowledge to estimate in situ stresses by measuring stress-induced body-wave velocity anisotropy around a borehole of 10.2 cm diameter on a 35.6 cm cube of Nugget sandstone under biaxial compressional loadings in 1984 (Mao et al 1984). They measured the shearwave velocities of polarization either parallel or perpendicular to the principal stress directions in the borehole. They introduced a simple form of the stress-induced velocity variations around the borehole and used the biaxial velocity data to back-calculate the applied stresses.