Simulations of S waves from the piezoelectric source to the receiver to assist in laboratory measurements of rock properties

Abstract

An accurate determination of the emitted S-wave arrival time at the piezoelectric receiver of laboratory triaxial cells is challenging due to the complex preceding P- and S-wave patterns. To analyze this pattern and decipher the true arrival time of the emitted S wave, we simulate wave propagation from the actuator to the receiver. The piezoelectric response is accounted for, and the electromechanical coupling is solved, using the spectral finite-element method or approximated using a linear spatial variation of the electric potential over the actuator to capture the same field over the receiver. The fully coupled algorithms are validated with 1D simulations and compared with an exact solution constructed with the method of characteristics. Simulations for a 2D simplified experimental system indicate the validity of the linear simplification. The comparison of the simulated results through a section of the triaxial cell with laboratory calibration data for a steel specimen validates our choice of damping material proxy within the actuator. A final series of simulations for two orthotropic shales with different anisotropy axis orientations with respect to the cell, and two Fontainebleau sandstones with very different [Formula: see text]/[Formula: see text] ratios, is presented. These differences in physical properties have little impact on the wave pattern at and just after the arrival of the main S wave. The pattern is influenced more by the experimental setup geometry and the actuator’s internal structure than by the nature of the specimen.