Non-elastic pore deformations and crack propagations are the principal causes of dynamic damage in rocks and soils. In the case of downhole blasting from wellbores, these two mechanisms compete with each other. Therefore, to carry out a mechanical analysis of rock blasting, a sufficiently complete model that takes these various mechanisms into account has to be developed. To address this issue, this paper proposes the use of an elastic–plastic model, which includes a yield condition with a non-associated plastic flow rule, the effects of pore fluid saturation, and a brittle failure criterion under extension. The results presented in this paper describe underground explosions with spherical motion (cavity growth under the internal pressure of detonated gases without leakage into the formation), typical for oil or water reservoirs. The governing equations are written in a Cartesian system of coordinates for the case of spatial dynamic medium deformation. For this case, Cartesian coordinates are more convenient than spherical coordinates because they avoid numerical difficulties connected with the non-divergent terms of the non-linear form of the Biot–Frenkel equations. The numerical method uses the Wilkins approach, which has been generalized for the model described in this paper. The dilatancy of the material during plastic deformation is neglected for simplicity. The numerical results show that, when using typical parameters for relatively “soft” porous skeleton, the plastic flow overcomes the brittle failure. An extension zone only appears near the cavity. The results also show the presence of the two Biot P-waves. The second Biot wave, however, is only seen in the case of an extremely high permeability rock. Furthermore, in the case of the first Biot wave, the saturating liquid and the solid skeleton particles are moving with different velocities in a 100 darcy rock and with the same velocity in a 0.01 darcy rock. Calculated radial particle velocities as a function of the scaled radius are close to measured velocities in rigid dense media but are larger than measured ones in clays. It is suggested that the difference is due to different levels of water saturation, assumed full saturation in the calculation, partial saturation in the experiments.
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Nikolaevskiy, V.N., Kapustyanskiy, S.M., Thiercelin, M. et al. Explosion Dynamics in Saturated Rocks and Solids. Transp Porous Med 65, 485–504 (2006). https://doi.org/10.1007/s11242-006-6752-0