Andreas K. Kronenberg

Fracture surface energy of the Punchbowl fault, San Andreas system.

Fracture energy is a form of latent heat required to create an earthquake rupture surface and is related to parameters governing rupture propagation and processes of slip weakening. Fracture energy has been estimated from seismological and experimental rock deformation data, yet its magnitude, mechanisms of rupture surface formation and processes leading to slip weakening are not well defined. Here we quantify structural observations of the Punchbowl fault, a large-displacement exhumed fault in the San Andreas fault system, and show that the energy required to create the fracture surface area in the fault is about 300 times greater than seismological estimates would predict for a single large earthquake. If fracture energy is attributed entirely to the production of fracture surfaces, then all of the fracture surface area in the Punchbowl fault could have been produced by earthquake displacements totalling <1 km. But this would only account for a small fraction of the total energy budget, and therefore additional processes probably contributed to slip weakening during earthquake rupture.

Strength and anisotropy of foliated rocks with varied mica contents

We have shortened 15 schists and gneisses with varying compositions (15–75% mica by volume) at angles (β) of 45° and 90° to foliation (S) to investigate the influence of micas on the strength and anisotropy of foliated rocks. At the conditions tested (T = 25°C, Pc = 200 MPa ande = 10−5s−1), compressive strengths vary by a factor > 4 in the β = 45° and β = 90° orientations, and individual rock types exhibit directional responses ranging from isotropic to strongly anisotropic. Trends of decreasing strength, decreasing anisotropy and increasing ductility are observed with increasing mica content. Strains in all samples were localized within inclined shear zones, accommodated by dislocation slip and grain-scale microkinking in micas and microcracking in all other silicates. Stress-strain response and grain-scale deformation microstructures both indicate that mechanical behavior is strongly influenced by the concentration and spatial arrangement of micas. Shear zone formation is associated either with discrete brittle fracture, transitional strain softening or steady-strength ductile shear. In both brittle and transitional samples, extensive microcracking of strong quartzo-feldspathic bridges occurs, and stress drop magnitudes decrease with decreasing spacing and increasing overlap of adjacent, critically-oriented micas. Steady-strength ductile shear zones develop in samples containing domains of interconnected micas, and isotropic mechanical response is observed in those in which micas are contiguous in nearly all directions.

Experimental deformation of muscovite

Abstract The strength and mechanical anisotropy of muscovite have been investigated by shortening single crystals at 45°, 0° and 90° to the basal plane (001) at temperatures T from 20 to 400°C, confining pressures Pc from 10 to 400 MPa, and strain rates e from 2.5 × 10−7 to 2.3 × 10−4 s−1. Samples deformed as 45° to (001) exhibit smooth undulatory extinction in thin section associated with dislocation glide, with few well developed low-angle kink boundaries. Basal shear strengths depend on confining pressure at Pc e = A exp (aσ) exp (-Q/ RT) , results from temperature- and strain rate-stepping experiments performed at Pc = 200 MPa yield an activation energy Q of 47 ± 19 kJ mol−1 and an exponential constant a of 0.5 ± 0.2 MPa−1. Samples loaded parallel to the basal plane shorten by the development of sharply defined kink bands. Strengths associated with kink band formation are higher than those associated with glide in samples compressed at 45° to (001) and exhibit significant pressure dependence ( μ ≊ 0.8 ) up to confining pressures of 200 MPa. Kink bands are generated at the ends of samples where contact is made with the pistons. Samples loaded at 90° to (001) are much stronger than samples of all other orientations and deformation is accomplished by fracture. Fracture strengths exhibit a strong dependence on confining pressure ( μ ≊ 0.9 ), similar in magnitude to other silicates that are brittle at the same conditions. By comparison with biotite, muscovite is weaker in shear on (001) at the experimental conditions tested with an activation energy for glide, Q, that is significantly smaller than that for glide in biotite.

Permeability of Wilcox shale and its effective pressure law

The permeability of illite-rich shale from the Wilcox formation has been measured as a function of effective pressure for bedding-parallel flow of 1 M NaCl pore fluid. Permeability k decreases from ∼300×10−21 m2 to 3×10−21 m2 as effective pressure Pe is increased from 3 to 12 MPa; these values confirm that shales form effective barriers to fluid transport in sedimentary strata over extended geologic times. The variation of k with Pe for Wilcox shale is given by k = k0 [1 − (Pe/P1)m]3, where P1 = 19.3 (±1.6) MPa and m = 0.159 (±0.007). The value of k0 for Wilcox shale is of the order of 10−17 m2 and may vary among samples by as much as 70%. Effective pressure is given in terms of the external confining pressure Pc and internal pore pressure Pp by Pe = Pc − χPp, where χ = 0.99 (±0.06). While our measurements yield χ = ∼1 for shale with a clay content of ∼45%, others have reported χ values for clay-bearing sandstones that rise from ∼0.75 to 7.1 with increasing clay content (from 0 to 20%). The trends between χ and clay content revealed by these comparisons imply that the value of χ depends upon the relative distributions of compliant clay minerals and other stiffer minerals. These values of χ also suggest that effective pressures within interbedded sandstones and shales may differ, even at the same equilibrium Pc and Pp conditions.

Permeability of illite-bearing shale: 1. Anisotropy and effects of clay content and loading

direction relative to bedding, clay content (40–65%), and effective pressure Pe (2– 12 MPa). Permeability k is anisotropic at low Pe; measured k values for flow parallel to bedding at Pe = 3 MPa exceed those for flow perpendicular to bedding by a factor of 10, both for low clay content (LC) and high clay content (HC) samples. With increasing Pe, k becomes increasingly isotropic, showing little directional dependence at 10–12 MPa. Permeability depends on clay content; k measured for LC samples exceed those of HC samples by a factor of 5. Permeability decreases irreversibly with the application of Pe, following a cubic law of the form k = k0 [1 � (Pe/P1) m ] 3 , where k0 varies over 3 orders of magnitude, depending on orientation and clay content, m is dependent only on orientation (equal to 0.166 for bedding-parallel flow and 0.52 for flow across bedding), and P1 (18–27 MPa) appears to be similar for all orientations and clay contents. Anisotropy and reductions in permeability with Pe are attributed to the presence of crack-like voids parallel to bedding and their closure upon loading, respectively. INDEX TERMS: 5114 Physical Properties of Rocks: Permeability and porosity; 5139 Physical Properties of Rocks: Transport properties; 5112 Physical Properties of Rocks: Microstructure; 1832 Hydrology: Groundwater transport; KEYWORDS: permeability, shale, connected pore space

Rheology and deformation mechanisms of an isotropic mica schist

We have investigated the transitional, semibrittle deformation of a mica schist (∼75 % biotite) by shortening cylinders cored at 0°, 45°, and 90° to foliation to varying strains, at confining pressures Pc to 500 MPa, constant strain rates e from 1.5 × 10−7 to 1.6 × 10−4 s−1 and temperatures T from 25° to 400°C. Deformation is concentrated within one or more throughgoing, millimeter-wide shear zones at all conditions; these localize at low strains (e < 2%) through the nucleation and coalescence of dense sets of intragranular microkink bands (MKBs). Despite distinct differences in the relative number of mica grains oriented favorably for slip and kinking in different loading directions, the differential stresses required for shear zone development vary little with fabric orientation. Biotite schist undergoes a transition from strain-softening to steady strength mechanical response at confining pressures in the range 75 to 150 MPa. The pressure sensitivity of strength (characterized by the slope μ of the Mohr envelope) decreases from μ ∼0.5 (at Pc <100 MPa) to μ < 0.1 at pressures greater than 200 MPa, reflecting the increasing contribution of glide and kinking in biotite at higher pressures. However, dilatancy associated with microcracking and void formation along MKB boundaries persists to at least 500 MPa. Within the pressure-insensitive regime (200 ≤ Pc ≤ 500 MPa), temperature and strain rate dependencies of strength determined in stepping tests reveal a strong history dependence to flow that cannot strictly be described by a steady state constitutive law. Samples deformed in steps from low to high temperatures or fast to slow strain rates consistently exhibit stronger temperature and strain rate sensitivities than those deformed along T decreasing or e increasing paths. Path-dependent effects may reflect differences in the degree to which inherited dislocation substructures are utilized or overprinted during later deformation increments. By assuming an exponential relationship between differential stress σd and strain rate e of the form e = C exp(ασd) exp (−Q/RT), we fit the data with two end-member flow laws with a single activation energy Q = 89 kJ/mol, and exponential constants αss = 0.15 ± 0.01 MPa−1 and αws=0.55 ± 0.04 MPa−1 that account for the different responses observed along stepping paths that are strongly sensitive or weakly sensitive to T and e, respectively. Application of the results to crustal deformation suggests that mica-rich aggregates are weaker than other common rock types throughout a broad midcrustal depth range, supporting the inference that retrograde reaction to phyllosilicates may be important in localizing crustal deformations within large faults and shear zones.

Fourier transform infrared spectroscopy determinations of intragranular water content in quartz-bearing rocks: implications for hydrolytic weakening in the laboratory and within the earth

Abstract Fourier transform infrared (FTIR) spectroscopy has been used to measure intragranular water contents of quartz (and feldspar) within fine-grained quartzites, granite, and naturally-deformed mylonites. Calibrations and tests of methods developed for this application using natural and synthetic quartz standards indicate that hydrogen concentrations down to 30 ppm are detectable (within apertured regions 100–200 μm in diam.) and concentrations of ≥ 400 ppm measurable to an accuracy of 30%. Quartzite and novaculite starting materials, used in previous studies of mechanical properties, contain substantial intragranular water contents (2400–3900 ppm), much larger than water concentrations commonly found in large clear natural crystals and more comparable to those of wet synthetic crystals. However, unlike molecular water within rapidly-grown synthetic quartz, most of this water is freezable, resembling fluid inclusion water of natural milky quartz crystals. Likewise, quartz and feldspar grains within granite and mylonites deformed at greenschist to upper amphibolite facies conditions contain large amounts of water (from 500 to 8000 ppm) as fine (often submicron size) fluid inclusions and IR spectra are dominated by a freezable O-H absorption band. Comparisons between dry natural and wet synthetic quartz crystals have formed the basis for our understanding of hydrolytic weakening. However, mechanisms by which water-related defects access dislocation cores within quartzites deformed in the laboratory and mylonites deformed within natural shear zones may differ from those within idealized natural and synthetic single crystals, and their mechanical properties may not be directly comparable.

Laboratory deformation of granular quartz sand: Implications for the burial of clastic rocks

We explore the influence of mechanical deformation in natural sands through experiments on water-saturated samples of quartz sand. Stresses, volumetric strain, and microseismicity (or acoustic emission, AE) rates were monitored throughout each test. Deformation of quartz sand at low stresses is accommodated by granular flow without significant grain breakage, whereas at high stresses, granulation and cataclastic flow are dominant. Sands deformed under isotropic conditions show compactive strains with an inverse power-law dependence of macroscopic crushing strength on mean grain size. Triaxial compression at high effective pressures produces compactive strain and a high AE rate associated with considerable particle-size reduction. Triaxial compression at low effective pressure produces dilatant granular flow accommodated by grain boundary frictional sliding and particle rotation. On the basis of experiment results, we predict the evolution of porosity and macroscopic yield strength as a function of depth for extensional and contractional basins. Sand strength increases linearly with depth for shallow burial, whereas for deep burial, strength decreases nonlinearly with depth. At subyield stresses, porosity evolves as a function of applied mean stress and is independent of distortional stress. Our predictions are in qualitative agreement with observations of microfracture density obtained from laboratory creep-compaction experiments and with natural sandstones of the Gulf of Mexico basin. Mechanical deformation contributes as much as a 30% increase to fluid pressure evolution, which has particular application to sedimentary systems that display zones of fluid overpressure. Furthermore, deformational strains cannot be fully recovered during uplift, erosion, and unloading of a sedimentary basin.

Stationary and mobile hydrogen defects in potassium feldspar

Hydrogen defects in adularia from Kristallina, Switzerland (Or90.2 Ab8.7 An0.0 Cs1.1) have been investigated by examining their vibrational modes in the infrared and near-infrared, and by measuring rates of hydrogen loss and hydrogen gain at elevated temperatures. Principal absorption bands exhibited by adularia at wavenumbers of 362 and 345.5 mm^(−1) (corresponding to O-H stretching modes) are strongly dichroic, with maximum and minimum absorptivities measured for vibrations α (E at 5° to a) and β (E at 5° to c^∗), respectively, whereas bands at 328 and 309 mm^(−1) are more nearly isotropic. Similarly, near-infrared bands at 525 and 513 mm^(−1) (associated with combination H-OH bend, O-H stretch modes) exhibit maximum peak heights for α while a lesser band at 475 mm^(−1) appears to be nearly isotropic. Comparison of fundamental and combination band intensities reveal that molecular water is the predominant hydrogen-bearing species, consistent with previous results for microcline and orthoclase crystals in which H_2O substitutes for K. However, differences in magnitude of fundamental and combination band polarizations suggest multiple defect sites or potentially a secondary population of hydroxyl defects. Rates at which these defects can be eliminated from samples annealed in air at temperatures T from 500° to 900°C are much faster than those predicted by oxygen mobilities, yielding diffusivities of D[/_s]=6.2x10^(-4)exp ( -l72 ± 15[^(kJ)/mol))/RT indistinguishable from those reported for proton interstitials in quartz. Dissociation of stationary molecular water defects to mobile proton interstitials which leave crystal interiors requires that oxygen defects are left behind. Hydrogen defects can be added to adularia crystals annealed at elevated water pressures (corresponding to H_2O fugacities of 412 and 1710 MPa and H_2 fugacities up to 174 MPa), again at rates that exceed oxygen mobilities. In addition, significant redistribution amongst sites is suggested by changes in band character and polarization. Neither Fe nor other multivalent impurities are sufficiently abundant to accommodate local charge balance upon the loss or gain of protons and other mechanisms of internal adjustment are required.

Experimental deformation of shale: Mechanical properties and microstructural indicators of mechanisms

Abstract The mechanical properties and deformation mechanisms of an illite-rich shale have been investigated in triaxial compression experiments at varying confining pressures (Pc), temperatures (T), and strain rates (ϵ). Shale deforms by brittle processes at low Pc and deforms by semi-brittle processes at high Pc leading to the development of macroscopic fractures, semi-brittle shear zones, and kink bands. Differential stresses (σ1-σ3) depend on Pc as well as T and ϵ at high Pc. The effects of Pc are non-linear and those of T and ϵ at a selected Pc may be described by an exponential dislocation glide law. The strength of shale depends on water content as well; loss of 2.1 weight % water from clay interlayers increases shale strength by 30%.