A Note on the Stress-Dilatancy Relation for Simulated Fault Gouge

-Theoretical constraints on the stress-dilation relation for a deforming Coulomb material require v -< 0 if C = 0 and v -< sin-l(Tm/e,n) always, where v is the dilation angle, 0 is the friction angle, C is cohesion, z,, is the maximum shear stress, and a,~ is the mean effective stress. Recent laboratory measurements of friction and dilatancy of simulated fault gouge show that small amplitude shear-toad cycling causes compaction and consolidation. Comparison of the data with theory indicates that such load cycling produces: (1) increased coefficient of friction (or friction angle), (2) increased cohesion, and (3) increased dilatancy rate (or dilation angle). Under certain conditions of load cycling without significant plastic shear strain accumulation (7 p < 0.005) we find that v exceeds both 0 and, in contrast to theory, sinl(v,~ /%). This result is interpreted in terms of enhanced cohesion and overeonsolidation, which lead to residual stresses within the gouge. An analogy is drawn between these special loading conditions and those extant on natural faults. In particular, our results imply that jostling and minor stress variations associated with microearthquakes may produce strengthening of fault gouge and changes in the fault zone's stress-dilatancy relation. Hence, compaction associated with microseismicity may lead to subsequent dilation of fault gouge, even for faults with large displacement rates and large net offsets (e.g., San Andreas). In regions where such dilation persists over sufficient displacements (on the order of the critical slip distance for seismic faulting) it may tend to inhibit unstable slip.