Estimating Macroscopic Mechanical Properties Via Grain-Scale Simulations

Holtzman, Ran¹, Dmitriy, B. Silin², Tadeusz W. Patzek¹ (1) University of California, Berkeley, Berkeley, CA (2) University of California, Berkeley, berkeley, CA

We have developed a technique for estimating the changes in macroscopic mechanical properties of a granular medium. These changes are caused by processes which are not captured by a macroscopic model. Such processes are extensive compaction, rock damage propagation, and gas hydrate dissociation in hydrate-bearing sediments.

In this study, we estimate the macroscopic elastic moduli of a heterogeneous grain pack by modeling mechanical interactions among the grains. This is done in a sequence of computer-simulated experiments. Each grain is considered elastic, and the contact interactions between the grains are modeled using Hertz and Mindlin theories. The deformation is simulated as a sequence of static equilibrium configurations. Our model is elastic, so that the solution is sought by minimization of the potential energy of the pack. An algorithm based on the conjugate gradient method has been proven to be robust and efficient.

Starting with an initial loose or pre-stressed grain pack, we simulate a number of loading and unloading cycles. For loose configurations, we observe that by grain rearrangement only, our algorithm produces a tighter pack than other methods. The resulting elastic moduli estimates match experimental values reported in literature. The computed rock stiffness increases with the density of the pack. Throughout the numerical experiment, we analyze the principle mechanisms of compaction by comparing the relative contributions of rearrangement and deformation of the grains. We were able to capture and analyze hysteretic events, such as different loading and unloading responses or abrupt changes due to breakage of grain clusters.