Broad bandwidth study of the topography of natural rock surfaces

Brown, Stephen R.; Scholz, Christopher H.

doi:10.1029/jb090ib14p12575

Cited by 814 publications

(454 citation statements)

References 23 publications

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“…The relation between the two surfaces is the one suggested by several recent studies [Brown et al, 1986;Plourabou• et al, 1994;Brown, 1995]' they are well mated on the larger scales and unmated on the smaller, local scales. The transition length between mated and unmated behavior is -1/X/-N of the lattice size, so that the complete surface contains a large number of No mechanical model of deformation is assumed; wherever the surfaces "interpenetrate," a contact (i.e., aperture zero) is shown [Brown, 1987].…”

Section: Three Dimensions: Importance Of Contacts and Non-lcl Regionsmentioning

confidence: 83%

Flow in rock fractures: The local cubic law assumption reexamined

Oron¹,

Berkowitz²

1998

Water Resources Research

318

187

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Abstract. We investigate the validity of applying the "local cubic law" (LCL) to flow in a fracture bounded by impermeable rock surfaces. A two-dimensional order-of-magnitude analysis of the Navier-Stokes equations yields three conditions for the applicability of LCL flow, as a leading-order approximation in a local fracture segment with parallel or nonparallel walls. These conditions demonstrate that the "cubic law" aperture should not be measured on a point-by-point basis but rather as an average over a certain length. Extending to the third dimension, in addition to defining apertures over segment lengths, we find that the geometry of the contact regions influences flow paths more significantly than might be expected from consideration of only the nominal area fraction of these contacts. Moreover, this latter effect is enhanced by the presence of non-LCL regions around these contacts. While contact ratios of 0.1-0.2 are usually assumed to have a negligible effect, our calculations suggest that contact ratios as low as 0.03-0.05 can be significant. Analysis of computer-generated fractures with self-affine walls demonstrates a nonlinear increase in contact area and a faster-than-cubic decrease in the overall hydraulic conductivity, with decreasing fracture aperture; these results are in accordance with existing experimental data on flow in fractures. Finally, our analysis of fractures with selfaffine walls indicates that the aperture distribution is not lognormal or gamma as is frequently assumed but rather truncated-normal initially and increasingly skewed with fracture closure.

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Section: Three Dimensions: Importance Of Contacts and Non-lcl Regionsmentioning

confidence: 83%

Flow in rock fractures: The local cubic law assumption reexamined

Oron¹,

Berkowitz²

1998

Water Resources Research

318

187

View full text Add to dashboard Cite

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“…The original profilometer, designed and built by S. Brown and T. Koczynski, is described by Brown and Scholz [1985]. and has since been automated.…”

Section: Methodsmentioning

confidence: 99%

Utility of elastic models in predicting fault displacement fields

Gupta¹,

Scholz²

1998

J. Geophys. Res.

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Abstract. Although elastic models have long been used to model earthquake deformation, their application to fault problems is questionable, as accumulated fault strain is higher and the relevant timescales are longer. We test the utility of using elastic models to predict fault displacement fields by independently measuring the three-dimensional slip (offset) distribution and displacement field of small normal faults. The displacement field is constrained from the topography of the deformed bedding planes; the slip distribution is constrained from stratal offsets in multiple sections of fault-normal saw-cuts. Using the observed slip distribution, we calculate both one-and three-dimensional elastic displacement fields. We find that the large strain associated with fault growth can be accommodated with linear elastic models. Much of the remaining misfit between the data and the model may result from elastic interaction with other nearby faults, the inelastic zone around surrounding fault tips, and prefaulting irregularities in the measured bedding plane surface.

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“…Anderson [1951] recognized that natural fault surfaces are not planar but irregular at all scales. Early measurements by Brown and Scholz [1985], Power and Tullis [1988, 1991, 1995, and Lee and Bruhn [1996] concluded that natural fault surfaces are self-similar fractals, in the sense that root-mean-square (RMS) height fluctuations are proportional to profile length.…”

Section: Field and Laboratory Measurements Of Fault Roughnessmentioning

confidence: 99%

Additional shear resistance from fault roughness and stress levels on geometrically complex faults

2013

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[1] The majority of crustal faults host earthquakes when the ratio of average background shear stress b to effective normal stress eff is b / eff 0.6. In contrast, mature plate-boundary faults like the San Andreas Fault (SAF) operate at b / eff 0.2. Dynamic weakening, the dramatic reduction in frictional resistance at coseismic slip velocities that is commonly observed in laboratory experiments, provides a leading explanation for low stress levels on mature faults. Strongly velocity-weakening friction laws permit rupture propagation on flat faults above a critical stress level pulse / eff 0.25. Provided that dynamic weakening is not restricted to mature faults, the higher stress levels on most faults are puzzling. In this work, we present a self-consistent explanation for the relatively high stress levels on immature faults that is compatible with low coseismic frictional resistance, from dynamic weakening, for all faults. We appeal to differences in structural complexity with the premise that geometric irregularities introduce resistance to slip in addition to frictional resistance. This general idea is quantified for the special case of self-similar fractal roughness of the fault surface. Natural faults have roughness characterized by amplitude-to-wavelength ratios˛between 10 -3 and 10 -2 . Through a second-order boundary perturbation analysis of quasi-static frictionless sliding across a band-limited self-similar interface in an ideally elastic solid, we demonstrate that roughness induces an additional shear resistance to slip, or roughness drag, given by drag = 8 3˛2 G * / min , for G * = G/(1 -) with shear modulus G and Poisson's ratio , slip , and minimum roughness wavelength min . The influence of roughness drag on fault mechanics is verified through an extensive set of dynamic rupture simulations of earthquakes on strongly rate-weakening fractal faults with elastic-plastic off-fault response. The simulations suggest that fault rupture, in the form of self-healing slip pulses, becomes probable above a background stress level b pulse + drag . For the smoothest faults (˛ 10 -3 ), drag is negligible compared to frictional resistance, so that b pulse 0.25 eff . However, on rougher faults (˛ 10 -2 ), roughness drag can exceed frictional resistance. We expect that drag ultimately departs from the predicted scaling when roughness-induced stress perturbations activate pervasive off-fault inelastic deformation, such that background stress saturates at a limit ( b 0.6 eff ) determined by the finite strength of the off-fault material. We speculate that this strength, and not the much smaller dynamically weakened frictional strength, determines the stress levels at which the majority of faults operate.Citation: Fang, Z., and E. M. Dunham (2013), Additional shear resistance from fault roughness and stress levels on geometrically complex faults,

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Broad bandwidth study of the topography of natural rock surfaces

Cited by 814 publications

References 23 publications

Flow in rock fractures: The local cubic law assumption reexamined

Flow in rock fractures: The local cubic law assumption reexamined

Utility of elastic models in predicting fault displacement fields

Additional shear resistance from fault roughness and stress levels on geometrically complex faults

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