Ronald L. Biegel

Internal structure and weakening mechanisms of the San Andreas Fault

New observations of the internal structure of the San Gabriel fault (SGF) are combined with previous characterizations of the Punchbowl fault (PF) to evaluate possible explanations for the low frictional strength and seismic characteristics of the San Andreas fault (SAF). The SGF and PF are ancient, large-displacement faults of the SAF system exhumed to depths of 2 to 5 km. These fault zones are internally zoned; the majority of slip was confined to the cores of principal faults, which typically consist of a narrow layer (less than tens of centimeters) of ultracataclasite within a zone of foliated cataclasite several meters thick. Each fault core is bounded by a zone of damaged host rock of the order of 100 m thick. Orientations of subsidiary faults and other fabric elements imply that (1) the maximum principal stress was oriented at large angles to principal fault planes, (2) strain was partitioned between simple shear in the fault cores and nearly fault-normal contraction in the damaged zones and surrounding host rock, and (3) the principal faults were weak. Microstructures and particle size distributions in the damaged zone of the SGF imply deformation was almost entirely cataclastic and can be modeled as constrained comminution. In contrast, cataclastic and fluid-assisted processes were significant in the cores of the faults as shown by pervasive syntectonic alteration of the host rock minerals to zeolites and clays and by folded, sheared, and attenuated cross-cutting veins of laumontite, albite, quartz, and calcite. Total volume of veins and neocrystallized material reaches 50% in the fault core, and vein structure implies episodic fracture and sealing with time-varying and anisotropic permeability in the fault zone. The structure of the ultracataclasite layer reflects extreme slip localization and probably repeated reworking by particulate flow at low effective stresses. The extreme slip localization reflects a mature internal fault structure resulting from a positive feedback between comminution and transformation weakening. The structural, mechanical, and hydrologic characteristics of the Punchbowl and San Gabriel faults support the model for a weak San Andreas based on inhomogeneous stress and elevated pore fluid pressures contained within the core of a seismogenic fault. Elevated fluid pressures could be repeatedly generated in the core of the fault by a combination of processes including coseismic dilatancy and creation of fracture permeability, fault-valve behavior to recharge the fault with fluid, post-seismic self-sealing of fracture networks to reduce permeability and trap fluids, and time-dependent compaction of the core to generate high pore pressure. The localized slip and fluid-saturated conditions are wholly compatible with additional dynamic weakening by thermal pressurization of fluids during large seismic slip events, which can help explain both the low average strength of the San Andreas and seismogenic characteristics such as large stress relief. In addition, such a dynamic weakening mechanism is expected only in mature fault zones and thus could help explain the apparent difference in strength of large-displacement faults from smaller-displacement, subsidiary seismogenic faults.

The kinematics of gouge deformation

The methods and first results of a new approach to examining fault gouge are described. Samples of undisturbed fault gouge from the exhumed Lopez fault zone in the San Gabriel Mountains, California were impregnated with low viscosity epoxy resin and sectioned to produce microscope slides. The slides were photographed using optical and electron microscopy with magnifications ranging in factors of 2 from 12.5 to 1600. At all scales, the particles appeared angular with planar faces, suggesting tensile failure. No shear zones were discernable. The particle size distribution was studied. At each magnification the particles were sorted by diameter into four classes, differing in mean diameter by factors of 2. The numbers in each class were then scaled by the characteristic class dimension. The process revealed a remarkable degree of self-similarity. Over the range examined, the fractal dimension was within 5% of 2.60.On the basis of the observations, a new model for the mechanical processes that generate gouge is offered. It is argued that self-similarity results from repeated tensile splitting of grains. Unlike earlier models that consider splitting probability to be either independent of particle size or due to the preexisting distribution of defects, we propose that failure probability depends largely on the relative size of nearest neighbors. If nearest neighbors of the same size are preferentially broken, any initial distribution of particles will tend toward a self-similar distribution having a fractal dimension of 2.58.The model allows us to outline a procedure whereby the observed comminution in a fault zone can be related to the shear strain that the zone has accommodated and propose a theoretical frequency magnitude relation for the seismic energy emitted by the fracture process.

The frictional properties of a simulated gouge having a fractal particle distribution

The frictional properties of a layer of simulated Westerly granite fault gouge sandwiched between sliding blocks of Westerly granite have been measured in a high-speed servo-controlled double-direct shear apparatus. Most gouge layers were prepared to have a self-similar particle distribution with a fractal dimension of 2.6. The upper fractal limit was varied between 45 and 710 μm. Some gouges were prepared with all particles in the range between 360 and 710 μm. In each experiment the sliding velocity was cyclically alternated between 1 and 10 μms−1 and the coefficient of friction μm and its transient parameters a, b and Dc were measured as functions of displacement. In addition to the particle size distribution, the following experimental variables were also investigated: the layer thickness (1 and 3 mm), the roughness of the sliding surfaces (Nos 60 and 600 grit) and the normal stress (10 and 25 MPa). Some of the sample assemblies were epoxy impregnated following a run so the gouge structure could be microscopically examined in thin section. We observed that gouges which were initially non-fractal evolved to a fractal distribution with dimension 2.6. Gouges which had an initial fractal distribution remained fractal. When the sliding blocks had smooth surfaces, the coefficient of friction was relatively low and was independent of the particle distribution. In these cases, strong velocity weakening was observed throughout the experiment and the transient parameters a, b and Dc, remained almost constant. When the sliding blocks had rough surfaces, the coefficient of friction was larger and more dependent on the particle distribution. Velocity strengthening was observed initially but evolved to velocity weakening with increased sliding displacement. All three transient parameters changed with increasing displacement. The a and b values were about three times as large for rough surfaces as for smooth. The characteristic displacement Dc was not sensitive to surface roughness but was the only transient parameter which was sensitive to the normal stress. For the case of rough surfaces, the coefficient of friction of the 1 mm thick gouge was significantly larger than that for the 3 mm thick layers. Many of these observations can be explained by a micromechanical model in which the stress in the gouge layer is heterogeneous. The applied normal and shear stresses are supported by ‘grain bridges’ which span the layer and which are continually forming and failing. In this model, the frictional properties of the gouge are largely determined by the dominant failure mode of the bridging structures.

Fractals, fault-gouge, and friction

The particle-size distribution of a natural fault-gauge has been determined over the range from 5 μm to 40 cm. The gouge is self-similar over the range from 5 μm to 1 cm having a fractal dimension of 2.60 ± 0.11. The lower and upper fractal limits were also determined. The lower fractal limit occurs at a dimension of about 1–10 μm where mineral cleavage and intergranular porosity dominate the cataclasis. The upper fractal limit occurs at particle sizes on the order of 1 cm where the scaled particle density decreases abruptly by a factor of about three. By analogy to soil-mechanics shear box tests and laboratory rock friction experiments, it is argued that the upper fractal limit of the gouge determines the characteristic displacement parameter in stick-slip friction models. A characteristic displacement on the order of 1 cm is consistent with estimates based on numerical simulations of faulting.

The effect of asymmetric damage on dynamic shear rupture propagation II: With mismatch in bulk elasticity

We investigate asymmetric rupture propagation on an interface that combines a bulk elastic mismatch with a contrast in off-fault damage. Mode II ruptures propagating on the interface between thermally shocked (damaged) Homalite and polycarbonate plates were studied using high-speed photographs of the photoelastic fringes. The anelastic asymmetry introduced by damage is defined by ‘T’ and ‘C’ directions depending on whether the tensile or compressive lobe of the rupture tip stress concentration lies on the damaged side of the fault. The elastic asymmetry is commonly defined by ‘+’ and ‘-’ directions where ‘+’ is the direction of slip of the more compliant material. Since damaged Homalite is stiffer than polycarbonate, the propagation directions in our experiments were ‘T+’ and ‘C-’. Theoretical and numerical studies predict that a shear rupture on an elastic bimaterial interfaces propagates in the ‘+’ direction at the generalized Rayleigh wave speed or in some numerical cases at the P-wave speed of the stiffer material, Pfast. We present the first experimental evidence for propagation at Pfast in the ‘+’ direction for the bimaterial system undamaged Homalite in contact with polycarbonate. In the ‘-’ direction, both theory and experiments find ruptures in elastic bimaterials propagate either at sub-shear speed or at the P-wave speed of the softer material, Pslow, depending on the loading conditions. We observe that the off-fault damage effect dominates the elastic bimaterial effect in dynamic rupture propagation. In the ‘C-’ direction the rupture propagates at sub-shear to supershear speeds, as in undamaged bimaterial systems, reaching a maximum speed of Pslow. In the ‘T+’ direction however the rupture propagates at sub-shear speeds or comes to a complete stop due to increased damaged activation (slip and opening along micro-cracks) which results in a reduction in stored elastic potential energy and energy dissipation. Biegel et al. [2008a] found similar results for propagation on the interface between Homalite and damaged Homalite where rupture speeds were slowed or even stopped in the ‘T-’ direction but were almost unaffected in the ‘C+’ direction.

An experimental study of the effect of off-fault damage on the velocity of a slip pulse

The effect of off-fault damage on the speed of ruptures propagating on faults in photoelastic Homalite plates was measured using high-speed digital photography. The off-fault damage was composed of a network of fractures introduced by thermally shocking the Homalite in liquid nitrogen. The mode II rupture speed measured in damaged Homalite was significantly lower than the limiting Rayleigh speed of v_r = 0.92 v_s, even after the shear wave speed v_s was reduced to a value appropriate for the fracture-damaged Homalite. The additional slowing is most likely caused by frictional sliding on preexisting cracks, especially since we did not observe the generation of new fractures. The spatial extent of the interaction between the rupture and the off-fault damage was measured using samples in which the damage was limited to a band of width 2w centered on the fault and also using damaged samples containing a band of undamaged Homalite centered on the fault. By measuring the rupture velocity as a function of w, the interaction between the rupture and off-fault damage was observed to be limited to a distance of about 1 cm from the fault plane. This agrees with the spatial extent of Coulomb failure near the tip of a dynamic slip pulse predicted by the analytic model developed by Rice et al. (2005).