This essential reference for graduate students and researchers provides a unified treatment of earthquakes and faulting as two aspects of brittle tectonics at different timescales. The intimate connection between the two is manifested in their scaling laws and populations, which evolve from fracture growth and interactions between fractures. The connection between faults and the seismicity generated is governed by the rate and state dependent friction laws - producing distinctive seismic styles of faulting and a gamut of earthquake phenomena including aftershocks, afterslip, earthquake triggering, and slow slip events. The third edition of this classic treatise presents a wealth of new topics and new observations. These include slow earthquake phenomena; friction of phyllosilicates, and at high sliding velocities; fault structures; relative roles of strong and seismogenic versus weak and creeping faults; dynamic triggering of earthquakes; oceanic earthquakes; megathrust earthquakes in subduction zones; deep earthquakes; and new observations of earthquake precursory phenomena.

The Mechanics of Earthquakes and Faulting

This paper reviews rock friction and the frictional properties of earthquake faults. The basis for rate- and state-dependent friction laws is reviewed. The friction state variable is discussed, including its interpretation as a measure of average asperity contact time and porosity within granular fault gouge. Data are summarized showing that friction evolves even during truly stationary contact, and the connection between modern friction laws and the concept of “static” friction is discussed. Measurements of frictional healing, as evidenced by increasing static friction during quasistationary contact, are reviewed, as are their implications for fault healing. Shear localization in fault gouge is discussed, and the relationship between microstructures and friction is reviewed. These data indicate differences in the behavior of bare rock surfaces as compared to shear within granular fault gouge that can be attributed to dilation within fault gouge. Physical models for the characteristic friction distance are discussed and related to the problem of scaling this parameter to seismic faults. Earthquake afterslip, its relation to laboratory friction data, and the inverse correlation between afterslip and shallow coseismic slip are discussed in the context of a model for afterslip. Recent observations of the absence of afterslip are predicted by the model.

/pdf/laboratory-derived-friction-laws-and-their-application-to-44s35v6won.pdf

Laboratory-derived friction laws and their application to seismic faulting

The concept of strength envelopes, developed in the 1970s, allowed quantitative predictions of the strength of the lithosphere based on experimentally determined constitutive equations. Initial strength envelopes used an empirical relation for frictional sliding to describe deformation along brittle faults in the upper portion of the lithosphere and power law creep equations to estimate the plastic flow strength of rocks in the deeper part of the lithosphere. In the intervening decades, substantial progress has been made both in understanding the physical mechanisms involved in lithospheric deformation and in refining constitutive equations that describe these processes. The importance of a regime of semibrittle behavior is now recognized. Based on data from rocks without added pore fluids, the transition from brittle deformation to semibrittle flow can be estimated as the point at which the brittle fracture strength equals the peak stress to cause sliding. The transition from semibrittle deformation to plastic flow can be approximated as the stress at which the pressure exceeds the plastic flow strength. Current estimates of these stresses are on the order of a few hundred megapascals for relatively dry rocks. Knowledge of the stability of sliding along faults and of the onset of localization during brittle fracture has improved considerably. If the depth to the bottom of the seismogenic zone is determined by the transition to the stable frictional sliding regime, then that depth will be considerably more shallow than the depth of the transition to the plastic flow regime. Major questions concerning the strength of rocks remain. In particular, the effect of water on strength is critical to accurate predictions. Constitutive equations which include the effects of water fugacity and pore fluid pressure as well as temperature and strain rate are needed for both the brittle sliding and semibrittle flow regimes. Although the constitutive equations for dislocation creep and diffusional creep in single-phase aggregates are more robust, few data exist for plastic deformation in two-phase aggregates. Despite the fact that localization is ubiquitous in rocks deforming both in brittle and plastic regimes, only a limited amount of accurate experimental data are available to constrain predictions of this behavior. Accordingly, flow strengths now predicted from laboratory data probably overestimate the actual rock strength, perhaps by a significant amount. Still, the predictions are robust enough that uncertainties in geometry, mineralogy, loading conditions and thermodynamic state are probably the limiting factors in our understanding. Thus, experimentally determined rheologies can be applied to understand a broad range of topical problems in regional and global tectonics both on the Earth and on other planetary bodies.

Strength of the lithosphere: Constraints imposed by laboratory experiments

https://cyberleninka.org/article/n/22310.pdf

Pore-scale imaging and modelling

https://www.whoi.edu/fileserver.do?id=180587&pt=2&p=59967

Water in the oceanic upper mantle: implications for rheology, melt extraction and the evolution of the lithosphere

Triaxial compression experiments were conducted to investigate the inelastic and failure behavior of six sandstones with porosities ranging from 15% to 35%. A broad range of effective pressures was used so that the transition in failure mode from brittle faulting to cataclastic flow could be observed. In the brittle faulting regime, shear-induced dilation initiates in the prepeak stage at a stress level C' which increases with effective mean stress. Under elevated effective pressures, a sample fails by cataclastic flow. Strain hardening and shear-enhanced compaction initiates at a stress level C* which decreases with increasing effective mean stress. The critical stresses C' and C* were marked by surges in acoustic emission. In the stress space, C* maps out an approximately elliptical yield envelope, in accordance with the critical state and cap models. Using plasticity theory, the flow rule associated with this yield envelope was used to predict porosity changes which are comparable to experimental data. In the brittle faulting regime the associated flow rule predicts dilatancy to increase with decreasing effective pressure in qualitative agreement with the experimental observations. The data were also compared with prediction of a nonassociative model on the onset of shear localization. Experimental data suggest that a quantitative measure of brittleness is provided by the grain crushing pressure (which decreases with increasing porosity and grain size). Geologic data on tectonic faulting in siliciclastic formations (of different porosity and grain size) are consistent with the laboratory observations.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/96JB03281

The transition from brittle faulting to cataclastic flow in porous sandstones: Mechanical deformation

Permeability exerts significant control over the development of pore pressure excess in the crust, and it is a physical quantity sensitively dependent on the pore structure and stress state. In many applications, the relation between permeability and effective mean stress is assumed to be exponential and that between permeability and porosity is assumed to be a power law, so that the pressure sensitivity of permeability is characterized by the coefficient γ and the porosity sensitivity by the exponent α. In this study, we investigate experimentally the dependence of permeability on pressure and porosity in five sandstones with porosities ranging from 14% to 35% and we review published experimental data on intact rocks, unconsolidated materials and rock fractures. The laboratory data show that the pressure and porosity sensitivities differ significantly for different compaction mechanisms, but for a given compaction mechanism, the data can often be approximated by the empirical relations. The permeabilities of tight rocks and rock joints show relatively high pressure sensitivity and low porosity sensitivity. A wide range of values for α and γ have been observed in relation to the mechanical compaction of porous rocks, sand and fault gouge, whereas the porosity sensitivity for chemical compaction processes is often observed to be given by α≈3. We show that since the ratio γ/α corresponds to the pore compressibility, the different dependences of permeability on porosity and pressure are related to the pore structure and its compressibility. Guided by the laboratory data, we conduct numerical simulations on the development of pore pressure in crustal tectonic settings according to the models ofWalder andNur (1984) andRice (1992). Laboratory data suggest that the pressure sensitivity of fault gouge is relatively low, and to maintain pore pressure at close to the lithostatic value in the Rice model, a relatively high influx of fluid from below the seismogenic layer is necessary. The fluid may be injected as vertically propagating pressure pulses into the seismogenic system, andRice's (1992) critical condition for the existence of solitary wave is shown to be equivalent to α>1, which is satisfied by most geologic materials in the laboratory. Laboratory data suggest that the porosity sensitivity is relatively high when the permeability is reduced by a coupled mechanical and chemical compaction process. This implies that in a crustal layer, pore pressure may be generated more efficiently than cases studied byWalder andNur (1984) who assumed a relatively low porosity sensitivity of α=2.

Laboratory measurement of compaction-induced permeability change in porous rocks: Implications for the generation and maintenance of pore pressure excess in the crust

The three-dimensional geometry and connectivity of pore space controls the hydraulic transport behavior of crustal rocks. We report on direct measurement of flow-relevant geometrical properties of the void space in a suite of four samples of Fontainebleau sandstone ranging from 7.5 to 22% porosity. The measurements are obtained from computer analysis of three-dimensional, synchrotron X-ray computed microtomographic images. We present measured distributions of coordination number, channel length, throat size, and pore volume and of correlations between throat size/pore volume and nearest-neighbor pore volume/pore volume determined for these samples. In order to deal with the ambiguity of where a nodal pore ends and a channel begins, we apportion the void space volume solely among nodal pores, with the channel throat surfaces providing the nodal pore delineations. Pore channels thus have length but no associated volume; channel length is defined by nodal pore center to nodal pore center distance. For a sample of given porosity our measurements show that the pore coordination number and throat area are exponentially distributed, whereas the channel length and nodal pore volume follow gamma and lognormal distributions, respectively. Our data indicate an overall increase in coordination number and shortening of pore channel length with increasing porosity. The average coordination number ranges from 3.4 to 3.8; the average channel length ranges from 200 to 130 μm. Average throat area increases from 1600 to 2200 μm 2 with increasing porosity, while average pore volume remains essentially unchanged at around 0.0004 mm 3 .

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000JB900208

Pore and throat size distributions measured from synchrotron X-ray tomographic images of Fontainebleau sandstones

The hydrostatic compaction behavior of a suite of porous sandstones was investigated at confining pressures up to 600 MPa and constant pore pressures ranging up to 50 MPa. These five sandstones (Boise, Kayenta, St. Peter, Berea, and Weber) were selected because of their wide range of porosity (5–35%) and grain size (60–460 μm). We tested the law of effective stress for the porosity change as a function of pressure. Except for Weber sandstone (which has the lowest porosity and smallest grain size), the hydrostat of each sandstone shows an inflection point corresponding to a critical effective pressure beyond which an accelerated, irrecoverable compaction occurs. Our microstructural observations show that brittle grain crushing initiates at this critical pressure. We also observed distributed cleavage cracking in calcite and intensive kinking in mica. The critical pressures for grain crushing in our sandstones range from 75 to 380 MPa. In general, a sandstone with higher porosity and larger grain size has a critical pressure which is lower than that of a sandstone with lower porosity and smaller grain size. We formulate a Hertzian fracture model to analyze the micromechanics of grain crushing. Assuming that the solid grains have preexisting microcracks with dimensions which scale with grain size, we derive an expression for the critical pressure which depends on the porosity, grain size, and fracture toughness of the solid matrix. The theoretical prediction is in reasonable agreement with our experimental data as well as other data from soil and rock mechanics studies for which the critical pressures range over 3 orders of magnitude.

Teng-fong Wong

Papers

The transition from brittle faulting to cataclastic flow in porous sandstones: Mechanical deformation

Laboratory measurement of compaction-induced permeability change in porous rocks: Implications for the generation and maintenance of pore pressure excess in the crust

Pore and throat size distributions measured from synchrotron X-ray tomographic images of Fontainebleau sandstones

Micromechanics of pressure-induced grain crushing in porous rocks

The brittle-ductile transition in porous rock: A review