Proceedings of the International workshop on the Nojima Fault core and borehole data analysis
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Geology topics
D.A. Lockner
Publications and source records attributed to D.A. Lockner.
A generalized law for brittle deformation of Westerly granite
A semiempirical constitutive law is presented for the brittle deformation of intact Westerly granite. The law can be extended to larger displacements, dominated by localized deformation, by including a displacement-weakening break-down region terminating in a frictional sliding regime often described by a rate- and state-dependent constitutive law. The intact deformation law, based on an Arrhenius type rate equation, relates inelastic strain rate to confining pressure P c , differential stress σ Δ , inelastic strain ε i and temperature T . The basic form of the law for deformation prior to fault nucleation is where σ o and ε o are normalization constants (dependent on confining pressure), a is rate sensitivity of stress, and α is a shape parameter. At room temperature, eight experimentally determined coefficients are needed to fully describe the stress-strain-strain rate response for Westerly granite from initial loading to failure. Temperature dependence requires apparent activation energy ( E * ∼ 90 kJ/mol) and one additional experimentally determined coefficient. The similarity between the prefailure constitutive law for intact rock and the rate- and state-dependent friction laws for frictional sliding on fracture surfaces suggests a close connection between these brittle phenomena.
Journal of Geophysical Research B: Solid Earth↗
A test of the double-shearing model of flow for granular materials
The double-shearing model of flow attributes plastic deformation in granular materials to cooperative slip on conjugate Coulomb shears (surfaces upon which the Coulomb yield condition is satisfied). The strict formulation of the double-shearing model then requires that the slip lines in the material coincide with the Coulomb shears. Three different experiments that approximate simple shear deformation in granular media appear to be inconsistent with this strict formulation. For example, the orientation of the principal stress axes in a layer of sand driven in steady, simple shear was measured subject to the assumption that the Coulomb failure criterion was satisfied on some surfaces (orientation unspecified) within the sand layer. The orientation of the inferred principal compressive axis was then compared with the orientations predicted by the double-shearing model. The strict formulation of the model [ Spencer , 1982] predicts that the principal stress axes should rotate in a sense opposite to that inferred from the experiments. A less restrictive formulation of the double-shearing model by de Josselin de Jong [1971] does not completely specify the solution but does prescribe limits on the possible orientations of the principal stress axes. The orientations of the principal compression axis inferred from the experiments are probably within those limits. An elastoplastic formulation of the double-shearing model [ de Josselin de Jong , 1988] is reasonably consistent with the experiments, although quantitative agreement was not attained. Thus we conclude that the double-shearing model may be a viable law to describe deformation of granular materials, but the macroscopic slip surfaces will not in general coincide with the Coulomb shears.
Journal of Geophysical Research B: Solid Earth↗
Permeability and porosity of the Illinois UPH 3 drillhole granite and a comparison with other deep drillhole rocks
Permeability, porosity, and volumetric strain measurements were conducted on granite cores obtained at depths of 0.7 to 1.6 km from the Illinois UPH 3 drillhole at effective confining pressures from 5 to 100 MPa. Initial permeabilities were in the range of 10-17 to 10-19 m2 and dropped rapidly with applied pressure to values between 10-20 and 10-24 m2 at 100 MPa, typical of other deep granite core samples. These values are several decades lower than equivalent weathered surface granites at comparable effective confining pressures, where weathering products in cracks and pores inhibit crack closure with applied pressure. Permeabilities of the Illinois cores were inversely related to sample depth, suggesting that stress relief and thermal microfractures induced during core retrieval dominated the fluid flow. Thus these samples provide an upper bound on in situ matrix permeability values. A comparison of core permeability from UPH 3 and other deep drillholes shows that stress relief damage can often dominate laboratory permeability measurements. We conclude that it may be difficult to make meaningful estimates of in situ permeability based on either borehole samples (possible damage during retrieval) or surface-derived analogs (altered by weathering). Volumetric strain determined from porosity measurements was compared with differential strain analysis (DSA) data reported by other investigators on samples from the same depths in the drillhole. Our strain measurements (0.002 to 0.005 at 100 MPa) were nearly twice as large as the DSA values, probably because of the crack-enhancing effects of fluids present in our samples that are absent in the dry DSA cores, as well as other time-dependent deformation effects. This difference in observed strain magnitudes between the two measurement methods may be an important consideration if strain and/or porosity data from deep core samples are used in models of stress, fluid circulation, and excess fluid pressure generation in the midcrust.
Journal of Geophysical Research B: Solid Earth↗
Physical modeling of the formation and evolution of seismically active fault zones
Acoustic emission (AE) in rocks is studied as a model of natural seismicity. A special technique for rock loading has been used to help study the processes that control the development of AE during brittle deformation. This technique allows us to extend to hours fault growth which would normally occur very rapidly. In this way, the period of most intense interaction of acoustic events can be studied in detail. Characteristics of the acoustic regime (AR) include the Gutenberg-Richter b -value, spatial distribution of hypocenters with characteristic fractal (correlation) dimension d , Hurst exponent H , and crack concentration parameter P c . The fractal structure of AR changes with the onset of the drop in differential stress during sample deformation. The change results from the active interaction of microcracks. This transition of the spatial distribution of AE hypocenters is accompanied by a corresponding change in the temporal correlation of events and in the distribution of event amplitudes as signified by a decrease of b -value. The characteristic structure that develops in the low-energy background AE is similar to the sequence of the strongest microfracture events. When the AR fractal structure develops, the variations of d and b are synchronous and d = 3 b . This relation which occurs once the fractal structure is formed only holds for average values of d and b . Time variations of d and b are anticorrelated. The degree of temporal correlation of AR has time variations that are similar to d and b variations. The observed variations in laboratory AE experiments are compared with natural seismicity parameters. The close correspondence between laboratory-scale observations and naturally occurring seismicity suggests a possible new approach for understanding the evolution of complex seismicity patterns in nature.
Tectonophysics↗
Failure in laboratory fault models in triaxial tests
A model of a fault in the Earth is a sand-filled saw cut in a granite cylinder subjected to a triaxial test. The saw cut is inclined at an angle α to the cylinder axis, and the sand filling is intended to represent gouge. The triaxial test subjects the granite cylinder to a constant confining pressure and increasing axial stress to maintain a constant rate of shortening of the cylinder. The required axial stress increases at a decreasing rate to a maximum, beyond which a roughly constant axial stress is sufficient to maintain the constant rate of shortening. Such triaxial tests were run for saw cuts inclined at angles α of 20°, 25°, 30°, 35°, 40°, 45°, and 50° to the cylinder axis, and the apparent coefficient of friction μ a (ratio of the shear stress to the normal stress, both stresses resolved onto the saw cut) at failure was determined. Subject to the assumption that the observed failure involves slip on Coulomb shears (orientation unspecified), the orientation of the principal compression axis within the gouge can be calculated as a function of μ a for a given value of the coefficient of internal friction μ i . The rotation of the principal stress axes within the gouge in a triaxial test can then be followed as the shear strain across the gouge layer increases. For μ i ∼ 0.8, an appropriate value for highly sheared sand, the observed values μ a imply that the principal axis of compression within the gouge rotates so as to approach being parallel to the cylinder axis for all saw cut angles (20° < α < 50°). In the limiting state (principal compression axis parallel to cylinder axis) the stress state in the gouge layer would be the same as that in the granite cylinder, and the failure criterion would be independent of the saw cut angle.
Journal of Geophysical Research B: Solid Earth↗
Strength of chrysotile-serpentinite gouge under hydrothermal conditions: Can it explain a weak San Andreas fault?
Chrysotile-bearing serpentinite is a constituent of the San Andreas fault zone in central and northern California. At room temperature, chrysotile gouge has a very low coefficient of friction (μ ≈ 0.2), raising the possibility that under hydrothermal conditions μ might be reduced sufficiently (to ≤0.1) to explain the apparent weakness of the fault. To test this hypothesis, we measured the frictional strength of a pure chrysotile gouge at temperatures to 290 °C and axial-shortening velocities as low as 0.001 μm/s. As temperature increases to ≈ 100 °C, the strength of the chrysotile gouge decreases slightly at low velocities, but at temperatures ≥200 °C, it is substantially stronger and essentially independent of velocity at the lowest velocities tested. We estimate that pure chrysotile gouge at hydrostatic fluid pressure and appropriate temperatures would have shear strength averaged over a depth of 14 km of 50 MPa. Thus, on the sole basis of its strength, chrysotile cannot be the cause of a weak San Andreas fault. However, chrysotile may also contribute to low fault strength by forming mineral seals that promote the development of high fluid pressures.
Geology↗
Sample characterizations and strength measurements of serpentinite gouges
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An earthquake instability model based on faults containing high fluid-pressure compartments
It has been proposed that large strike-slip faults such as the San Andreas contain water in seal-bounded compartments. Arguments based on heat flow and stress orientation suggest that in most of the compartments, the water pressure is so high that the average shear strength of the fault is less than 20 MPa. We propose a variation of this basic model in which most of the shear stress on the fault is supported by a small number of compartments where the pore pressure is relatively low. As a result, the fault gouge in these compartments is compacted and lithified and has a high undisturbed strength. When one of these locked regions fails, the system made up of the neighboring high and low pressure compartments can become unstable. Material in the high fluid pressure compartments is initially underconsolidated since the low effective confining pressure has retarded compaction. As these compartments are deformed, fluid pressure remains nearly unchanged so that they offer little resistance to shear. The low pore pressure compartments, however, are overconsolidated and dilate as they are sheared. Decompression of the pore fluid in these compartments lowers fluid pressure, increasing effective normal stress and shear strength. While this effect tends to stabilize the fault, it can be shown that this dilatancy hardening can be more than offset by displacement weakening of the fault (i.e., the drop from peak to residual strength). If the surrounding rock mass is sufficiently compliant to produce an instability, slip will propagate along the fault until the shear fracture runs into a low-stress region. Frictional heating and the accompanying increase in fluid pressure that are suggested to occur during shearing of the fault zone will act as additional destabilizers. However, significant heating occurs only after a finite amount of slip and therefore is more likely to contribute to the energetics of rupture propagation than to the initiation of the instability. We present results of a one-dimensional dynamic Burridge-Knopoff-type model to demonstrate various aspects of the fluid-assisted fault instability described above. In the numerical model, the fault is represented by a series of blocks and springs, with fault rheology expressed by static and dynamic friction. In addition, the fault surface of each block has associated with it pore pressure, porosity and permeability. All of these variables are allowed to evolve with time, resulting in a wide range of phenomena related to fluid diffusion, dilatancy, compaction and heating. These phenomena include creep events, diffusion-controlled precursors, triggered earthquakes, foreshocks, aftershocks, and multiple earthquakes. While the simulations have limitations inherent to 1-D fault models, they demonstrate that the fluid compartment model can, in principle, provide the rich assortment of phenomena that have been associated with earthquakes. ?? 1995 Birkha??user Verlag.
Pure and Applied Geophysics PAGEOPH↗
High-temperature permeability studies; 1, Permeability of granite and novaculite at 300 degrees to 500 degrees C
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Triaxial testing of Lopez Fault gouge at 150 MPa mean effective stress
Triaxial compression experiments were performed on samples of natural granular fault gouge from the Lopez Fault in Southern California. This material consists primarily of quartz and has a self-similar grain size distribution thought to result from natural cataclasis. The experiments were performed at a constant mean effective stress of 150 MPa, to expose the volumetric strains associated with shear failure. The failure strength is parameterized by the coefficient of internal friction ??, based on the Mohr-Coulomb failure criterion. Samples of remoulded Lopez gouge have internal friction ??=0.6??0.02. In experiments where the ends of the sample are constrained to remain axially aligned, suppressing strain localisation, the sample compacts before failure and dilates persistently after failure. In experiments where one end of the sample is free to move laterally, the strain localises to a single oblique fault at around the point of failure; some dilation occurs but does not persist. A comparison of these experiments suggests that dilation is confined to the region of shear localisation in a sample. Overconsolidated samples have slightly larger failure strengths than normally consolidated samples, and smaller axial strains are required to cause failure. A large amount of dilation occurs after failure in heavily overconsolidated samples, suggesting that dilation is occurring throughout the sample. Undisturbed samples of Lopez gouge, cored from the outcrop, have internal friction in the range ??=0.4-0.6; the upper end of this range corresponds to the value established for remoulded Lopez gouge. Some kind of natural heterogeneity within the undisturbed samples is probably responsible for their low, variable strength. In samples of simulated gouge, with a more uniform grain size, active cataclasis during axial loading leads to large amounts of compaction. Larger axial strains are required to cause failure in simulated gouge, but the failure strength is similar to that of natural Lopez gouge. Use of the Mohr-Coulomb failure criterion to interpret the results from this study, and other recent studies on intact rock and granular gouge, leads to values of ?? that depend on the loading configuration and the intact or granular state of the sample. Conceptual models are advanced to account for these descrepancies. The consequences for strain-weakening of natural faults are also discussed. ?? 1994 Birkha??user Verlag.
Pure and Applied Geophysics PAGEOPH↗
Reduction of permeability in granite at elevated temperatures
The addition of hydrothermal fluids to heated, intact granite leads to permeability reductions in the temperature range of 300° to 500°C, with the rate of change generally increasing with increasing temperature. The addition of gouge enhances the rate of permeability reduction because of the greater reactivity of the fine material. Flow rate is initially high in a throughgoing fracture but eventually drops to the level of intact granite. These results support the fault-valve model for the development of mesothermal ore deposits, in which seals are formed at the base of the seismogenic zone of high-angle thrust faults. The lower temperature results yield varying estimates of mineral-sealing rates at shallower depths in fault zones, although they generally support the hypothesis that such seals develop in less time than the recurrence interval for moderate to large earthquakes on the San Andreas fault.
California↗
How geometrical constraints contribute to the weakness of mature faults
Increasing evidence that the San Andreas fault has low shear strength 1 has fuelled considerable discussion regarding the role of fluid pressure in controlling fault strength. Byerlee 2,3 and Rice 4 have shown how fluid pressure gradients within a fault zone can produce a fault with low strength while avoiding hydraulic fracture of the surrounding rock due to excessive fluid pressure. It may not be widely realised, however, that the same analysis 2–4 shows that even in the absence of fluids, the presence of a relatively soft 'gouge' layer surrounded by harder country rock can also reduce the effective shear strength of the fault. As shown most recently by Byerlee and Savage 5 , as the shear stress across a fault increases, the stress state within the fault zone evolves to a limiting condition in which the maximum shear stress within the fault zone is parallel to the fault, which then slips with a lower apparent coefficient of friction than the same material unconstrained by the fault. Here we confirm the importance of fault geometry in determining the apparent weakness of fault zones, by showing that the apparent friction on a sawcut granite surface can be predicted from the friction measured in intact rock, given only the geometrical constraints introduced by the fault surfaces. This link between the sliding friction of faults and the internal friction of intact rock suggests a new approach to understanding the microphysical processes that underlie friction in brittle materials.
Nature↗
An earthquake mechanism based on rapid sealing of faults
Recent seismological, heat flow and stress measurements in active fault zones such as the San Andreas have led to the suggestion 1,2 that such zones can be relatively weak. One explanation for this may be the presence of overpressured fluids along the fault 3–5 , which would reduce the shear stress required for sliding by partially 'floating' the rock. Although several mechanisms have been proposed for overpressurizing fault fluids 3,4,6,7 , we recall that 'pressure seals' are known to form in both sedimentary 8 and igneous 9 rocks by the redistribution of materials in solution; the formation of such a seal along the boundaries of a fault will prevent the communication of fluids between the porous, deforming fault zone and the surrounding country rock. Compaction of fault gouge, under hydrostatic loading and/or during shear, elevates pore pressure in the sealed fault and allows sliding at low shear stress. We report the results of laboratory sliding experiments on granite, which demonstrate that the sliding resistance of faults can be significantly decreased by sealing and compaction. The weakening that results from shear-induced compaction can be rapid, and may provide an instability mechanism for earthquakes.
Nature↗
Quasi-static fault growth and shear fracture energy in granite
The failure process in a brittle granite sample can be stabilized by controlling axial stress to maintain a constant rate of acoustic emission. As a result, the post-failure stress curve can be followed quasistatically, extending to hours the fault growth process which normally would occur violently in a fraction of a second. Using a procedure originally developed to locate earthquakes, acoustic emission arrival-time data are inverted to obtain three-dimensional locations of microseisms. These locations provide a detailed view of fracture nucleation and growth.
Nature↗
Stick slip, charge separation and decay
Measurements of charge separation in rock during stable and unstable deformation give unexpectedly large decay times of 50 sec. Time-domain induced polarization experiments on wet and dry rocks give similar decay times and suggest that the same decay mechanisms operate in the induced polarization response as in the relaxation of charge generated by mechanical deformation. These large decay times are attributed to electrochemical processes in the rocks, and they require low-frequency relative permittivity to be very large, in excess of 105. One consequence of large permittivity, and therefore long decay times, is that a significant portion of any electrical charge generated during an earthquake can persist for tens or hundreds of seconds. As a result, electrical disturbances associated with earthquakes should be observable for these lengths of time rather than for the milliseconds previously suggested. ?? 1986 Birka??user Verlag.
Pure and Applied Geophysics PAGEOPH↗
Changes in complex resistivity during creep in granite
A sample of Westerly granite was deformed under constant stress conditions: a pore pressure of 5 MPa, a confining pressure of 10 MPa, and an axial load of 170 MPa. Pore volume changes were determined by measuring the volume of pore fluid (0.01 M KClaq) injected into the sample. After 6 days of creep, characterized by accelerating volumetric stain, the sample failed along a macroscopic fault. Measurements of complex resistivity over the frequency range 0.001-300 Hz, taken at various times during creep, showed a gradual increase in both conductivity and permittivity. When analysed in terms of standard induced polarization (IP) techniques, the changing complex resistivity resulted in systematic changes in such parameters as percent frequency effect and chargeability. These results suggest that it may be possible to monitor the development of dilatancy in the source region of an impending earthquake through standard IP techniques. ?? 1986 Birka??user Verlag.
Pure and Applied Geophysics PAGEOPH↗
Laboratory measurements of velocity-dependent frictional strength
Water levels, location, depths, and aquifers tapped are given for 113 observation wells in Michigan. Tabulated data include extremes of water levels for 1985 and for the period of record, pumpage of most major groundwater users in the state, and water quality data from selected wells. (USGS)
Open-File Report↗