A method to model the effect of pre-existing cracks on P-wave velocity in rocks
Crack closure is one of the reasons inducing changes of P-wave velocity of rocks under compression. In this context, a method is proposed to investigate the relationships among P-wave velocity, pre-existing cracks, and confining pressure based on the discrete element method (DEM). Pre-existing open cracks inside the rocks are generated by the initial gap of the flat-joint model. The validity of the method is evaluated by comparing the P-wave velocity tested on a sandstone specimen with numerical result. As the crack size is determined by the diameter of particles, the effects of three factors, i.e. number, aspect ratio, and orientation of cracks on the P-wave velocity are discussed. The results show that P-wave velocity is controlled by the (i.e. number) of open micro-cracks, while the closure pressure is determined by the aspect ratio of crack. The reason accounting for the anisotropy of P-wave velocity is the difference in crack number in measurement paths. Both of the number and aspect ratio of cracks can affect the responses of P-wave velocity to the applied confining pressure. Under confining pressure, the number of open cracks inside rocks will dominate the lowest P-wave velocity, and the P-wave velocity of the rock containing narrower cracks is more sensitive to the confining pressure. In this sense, crack density is difficult to be back-calculated merely by P-wave velocity. The proposed method offers a means to analyze the effect of pre-existing cracks on P-wave velocity.
Keywords: Pre-existing cracks, P-wave velocity, Discrete element method (DEM), Anisotropic rock