Static stress vs. strain response and stress dependent P- and S-wave velocities have been measured in isotropic and uniaxial compaction experiments with uncemented glass beads. Discrete particle modeling reproduces within experimental uncertainty the experimental behavior during hydrostatic loading and the axial stress vs. strain as well as axial P-wave velocity in uniaxial compaction. The numerical model underestimates the lateral stress response in uniaxial compaction, and as a consequence thereof, underestimates Swave velocities and P-wave velocity in the symmetry plane. Analytical modeling gives a good representation of the static stress vs. strain data in isotropic stress conditions, anticipating a coordination number . 6, but also underestimates lateral stress response. Wave velocities increase more with stress than expected from pure Hertz-Mindlin contact theory, as a result of increasing number of load bearing contacts and / or a gradual transition from slip to non-slip at grain contacts with increasing stress.
The use of discrete particle modeling as a practical tool in rock mechanics analysis is becoming more and more realistic due to improvements in computer technology and availability of 3D pore structure characterization. The work presented here is part of the development of a “numerical laboratory” for computation of constitutive rock mechanical behavior and stress dependent petrophysical properties. An important part of this development is a comparison between results of numerical simulations and controlled laboratory experiments. The model forming the basis of our numerical laboratory is PFC (Itasca 2005), in which the building blocks are spherical particles (disks in 2D) (Cundall & Strack 1979, Potyondy & Cundall 2004). Quantitative comparison between modeling and experiments can hence be obtained by performing experiments with unbonded spherical particles. Since spheres interact through the Hertzian contact law (Johnson 1987), contact stiffnesses are controlled by the elastic parameters of the particle forming material.