A Nonlinear Viscoelastic Model for Wave Propagation in Porous Sandstones Under Uniaxial Loads

Wave propagation is widely used in geologic mining and geotechnical engineering to acquire the structure information of rock masses. As rocks, by their nature, are filled with cracks and pores, wave propagation in rocks shows its clear dependence on stress. To describe the stress dependence of wave propagation, a nonlinear viscoelastic model consisting of a modified Hooke Model and Kelvin Model was proposed based on experimental observations on sandstones under uniaxial loads. With this model, the nonlinear behavior of rocks at the early stage of compression is attributed to the deformation of voids with a variable tangent modulus. Thus, wave velocity and wave attenuation can be altered, which change with the closure of voids and act as a function of stress. The proposed model was validated by comparison with experimental measurements from ultrasonic transmission at varying uniaxial stresses. It is shown that the effects of applied stress on the stress–strain relationship, wave velocity and wave attenuation for P-waves are well describe by the developed viscoelastic model. Changes in wave attenuation are also analyzed in terms of viscosity-like parameter defined by this model, which is found to be negatively proportional to the uniaxial stress. Highlights The wave propagation in porous sandstones under uniaxial loads was investigated in experimental and analytical ways. A viscoelastic model was proposed to incorporate the nonlinear mechanical and acoustic behaviors observed at the early stage of compression. Both the nonlinear stress-strain relationship and the stress dependence of wave velocity and wave attenuation can be well described by the proposed model.