The Strength of Hydrate-Bearing Sediments: A Grain-Scale Approach

We seek to develop an efficient technique of estimating the macroscopic mechanical properties of hydrate- bearing sediments. These properties change due to deformation and damage caused by hydrate dissociation, and are calculated from simulations that account for mechanical interactions among the grains. For the solid phase, it is assumed that all dynamic processes involved occur on a timescale such that the deformation process can be modeled as a sequence of static equilibrium configurations. The contact interactions between the grains are modeled using the theories developed by Hertz and Mindlin. The contact forces under consideration are elastic and, therefore, potential. Hence, each equilibrium problem is formulated in a variational setting and the solution is sought by minimizing the total potential energy of the entire pack. A descent algorithm based on the conjugate gradient method, has been proven to be robust and efficient. Here we present results of computer simulations of deforming a heterogeneous pack of spherical grains, neglecting slip and adhesion. Given a loose pack, e.g., generated by other codes, as input, our code first produces a tight compact pack by grain rearrangement only. Then, additional compaction is applied, and the resulting macroscopic stress is calculated in several loading/unloading cycles. The results are analyzed in order to estimate the principle mechanism of compaction, i.e. the amount of rearrangement vs. the amount of elastic deformations of inter-granular contacts. Results generally agree with linear elasticity for relatively short loading intervals on a pre-stressed pack, as the calculated stiffness falls within the range of values reported in literature. On larger intervals, the calculated stiffness increases with the density of the pack, and the process is, in general, nonlinear. Sequential loading and unloading produce different stress-strain curves. Such hysteretic effects can be explained by the irreversible rearrangements of grains. Tracking displacements and deformations of individual grains confirms this explanation. A comprehensive set of simulations for different scenarios will provide valuable insights into the mechanisms of deformation and damage propagation in hydrate-bearing sediments.