Evolution of the Gouge Particle Size Distribution: A Markov Model

The hydrologic and mechanical properties of faults are determined by their internal structures and zoning due to fracturing, grain breakage and diagenesis. The proposed model in this study is a first step in the development of a more complete model of fault internal structure. It describes the evolution of the gouge particle size distribution (PSD) with shear induced grain breakage within a small, assumed uniform volume element. A Markov formalism is applied for binary breakage within each time step over the many time steps constituting the evolution. The particle size, strain- and stress-dependent breaking probability is constructed based on physical arguments and data on natural and simulated gouge PSDs. The model is calibrated by using the results of on Ottawa sand PSD experiments. A perfect fit is obtained between experimental and numerically simulated PSDs for a range of normal effective stress (NES). Results of the numerical simulations capture the bimodal form of gouge PSD and also clearly define two different breakage mechanisms. The gouge development behavior makes a dramatic transition as the normal effective stress exceeds the grain crushing stress of the gouge mineral.For a more complete intrafault structure analysis, the interplay of diagenesis and the mechanics of grain breakage can be integrated into a single mechano-chemical model of the type presented here. The model proposed here has great potential for predicting the complex roles of faults as seals or fluid conduits.