Incorporating Intergranular Pressure Solution Into Models of Fault Zone Deformation

Constraints on the mechanisms and kinetics of pressure solution and its role in interseismic compaction and other fault-zone processes are typically derived from: 1) numerical simulations for which all macro- and micro- scale variables and parameters are prescribed, 2) laboratory experiments under hydrothermal conditions where macro-scale physical conditions (e.g., temperature, stress) are controlled but not the micro-scale internal state variables (e.g., area of contact, number of contacts per unit volume, local contact stresses), and 3) field observations in which large-scale structural relationships, deformation microstructures and geochemical mass-balances can be obtained but for which macro-scale physical conditions are poorly known. Our goal is to use results from numerical simulations to interpret hydrothermal laboratory experiments and then extend these results to the larger spatial and temporal scales appropriate to fault zone processes in the Earth. Previous work shows that even in well-controlled experiments specifically designed to study the mechanisms and kinetics of pressure solution, constitutive relations can deviate significantly from the stress exponent of 1 and apparent activation energy between 35 and 75 kJ/mol often assumed for intergranular pressure solution. Deviations from this simple model may arise due to a complex or evolving grain packing, competing creep mechanisms, or changes in rate-limiting step during pressure-solution creep. Even when considering deformation at single contacts, numerical simulations by Bernabe and Evans (2007) (BE) show that activation energy can evolve over time through the interplay between the dissolution rate at the asperity and the diffusion rate along the contact area. Lehner and Leroy (2004)(LL) propose a model similar to that of BE but less computer intensive, allowing for longer simulations. To better understand factors controlling the evolution of rate parameters during compaction under hydrothermal conditions, we extended the Bayesian inference scheme developed by Fitzenz et al. (2007) to analyze numerical simulations based on the BE and the LL models run on several time scales ranging from months to 1,000 years. We studied increasing complex cases with one asperity, with two coupled asperities, and with an initial contact followed by the creation of a new one. Particular attention was paid to the robustness of the analysis technique and to the time-evolution of the inferred creep parameters. We show that for short time scales, the rate is mostly controlled by dissolution, whereas at long time-scales it is controlled by diffusion with an apparent activation energy close to 36 kJ/mol and a stress exponent close to 1 (one asperity case). Regime-change analyses show that the evolution between the two end-members is continuous with time. We also show that a broad initial grain-size distribution and the early-time decay of the initial elastic stress concentrations both contribute to stress exponents greater than 1, but that this effect is not large enough to explain exponents larger than 3 as sometimes observed in the laboratory. In addition, we find that stress transfer from the most stressed asperities to the least stressed has the effect of slowing down creep compaction by pressure-solution. Our ultimate aim is to provide predictive creep laws in the temperature and pressure range of interest to fault modelers, first based on the single contact simulations, and then in the more realistic cases involving multiple asperities, rough fractures or heterogeneous granular materials.