Simulation of seismic velocity changes in brittle rocks subjected to triaxial stresses using 3-D microstructural models

Abstract

SUMMARY Numerical simulation of non-linear elastic wave propagation in rocks is indispensable for understanding stress/damage dependence of wave velocity changes and the associated micromechanisms. A numerical microstructural model is presented here to investigate seismic velocity changes due to stress and damage. By introducing pre-existing cracks and considering the valid microstructures in the bonded particle model, the proposed method successfully reproduces velocity changes of experiments on dry Lac du Bonnet granite and dry Darley Dale sandstone in both loading and unloading processes. Velocity increasing results from the closure of pre-existing cracks during loading stages, while the reopen of cracks during the unloading process causes velocity decreasing. Particle velocity vectors are used to illustrate wave propagation in a micromechanical way. P wave wave fronts are observed from the source to travel through the model, and wave intersections are clearly shown in the medium when the tensile wave front meets the compressive wave. The microstructure of the model shows a significant effect on rock mechanical behaviour and velocities and lends credibility to the velocity simulation. The valid microstructure produces realistic mechanical behaviour and velocity changes. Also, it replicates the initial hardening in the axial stress versus the axial strain curve, while invalid microstructures (e.g. cement overlap) underestimate the elastic modulus. The simulations also show that the wave velocities scale with the square root of the corresponding component of the coordination number, which can be used to quantify the mechanisms behind the velocity changes. Direct relations were established between velocity changes and opened crack density, which displays a similar tendency compared with predictions of the effective elastic theory. The microstructural model provides the ability to simulate the macro behaviour of rock under loadings in a more realistic manner and to directly examine the microprocesses underlying velocity changes.