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F
Fialko, YA, Rubin AM.  1997.  Numerical simulation of high-pressure rock tensile fracture experiments: Evidence of an increase in fracture energy with pressure? Journal of Geophysical Research-Solid Earth. 102:5231-5242.   10.1029/96jb03859   AbstractWebsite

High confining pressure fracture tests of Indiana limestone [Abou-Sayed, 1977] and Iidate granite [Hashida et al., 1993] were simulated using boundary element techniques and a Dugdale-Barenblatt (tension-softening) model of the fracture process zone. Our results suggest a substantial (more than a factor of 2) increase in the fracture energy of Indiana limestone when the confining pressure was increased from zero to only 6-7 MPa. While Hashida es al. [1993] concluded that there was no change in the fracture energy of Iidate granite at confining pressures up to 26.5 MPa, we find that data from one series of experiments (''compact-tension'' tests in their terminology) are also consistent with a significant (more than a factor of 2) increase in fracture energy. Data from another set of their experiments (thick-walled cylinder tests) seem to indicate a decrease in the fracture energy of Iidate granite at confining pressures,of 6-8 MPa, but these may be biased due to the very small specimen size. To our knowledge these results are the first reliable indication from laboratory experiments that rock tensile fracture energy varies with confining pressure. Based on these results, some possible mechanisms of pressure sensitive fracture are discussed. We suggest that the inferred increase in fracture energy results from more extensive inelastic deformation near the crack tip that increases the effective critical crack opening displacement. Such deformation might have occurred due to the large deviatoric stress in the vicinity of the crack tip in the Abou-Sayed experiments, and due to the enlarged region of significant tensile stress near the crack tip in the Hashida et al. compact tension tests. These results also highlight the fact that at confining pressures that exceed the tensile strength of the material, tensile fracture energy will in general depend upon the crack size and the distribution of loads within it, as well as the ambient stress.

H
Hamiel, Y, Katz O, Lyakhovsky V, Reches Z, Fialko Y.  2006.  Stable and unstable damage evolution in rocks with implications to fracturing of granite. Geophysical Journal International. 167:1005-1016.   10.1111/j.1365-246X.2006.03126.x   AbstractWebsite

We address the relation between the rock rigidity and crack density by comparing predictions of a viscoelastic damage rheology model to laboratory data that include direct microscopic mapping of cracks. The damage rheology provides a generalization of Hookean elasticity to a non-linear continuum mechanics framework incorporating degradation and recovery of the effective elastic properties, transition from stable to unstable fracturing, and gradual accumulation of irreversible deformation. This approach is based on the assumption that the density of microcracks is uniform over a length scale much larger than the length of a typical crack, yet much smaller than the size of the entire deforming domain. For a system with a sufficiently large number of cracks, one can define a representative volume in which the crack density is uniform and introduce an intensive damage variable for this volume. We tested our viscoelastic damage rheology against sets of laboratory experiments done on Mount Scott granite. Based on fitting the entire stress-strain records the damage variable is constrained, and found to be a linear function of the crack density. An advantage of these sets experiments is that they were preformed with different loading paths and explicitly demonstrated the existence of stable and unstable fracturing regimes. We demonstrate that the viscoelastic damage rheology provides an adequate quantitative description of the brittle rock deformation and simulates both the stable and unstable damage evolution under various loading conditions. Comparison between the presented data analysis of experiments with Mount Scott granite and previous results with Westerly granite and Berea sandstone indicates that granular or porous rocks have lower seismic coupling. This implies that the portion of elastic strain released during a seismic cycle as brittle deformation depends on the lithology of the region. Hence, upper crustal regions with thick sedimentary cover, or fault zones with high degree of damage are expected to undergo a more significant inelastic deformation in the interseismic period compared to 'intact' crystalline rocks.

T
Trugman, DT, Shearer PM, Borsa AA, Fialko Y.  2016.  A comparison of long-term changes in seismicity at The Geysers, Salton Sea, and Coso geothermal fields. Journal of Geophysical Research-Solid Earth. 121:225-247.   10.1002/2015jb012510   AbstractWebsite

Geothermal energy is an important source of renewable energy, yet its production is known to induce seismicity. Here we analyze seismicity at the three largest geothermal fields in California: The Geysers, Salton Sea, and Coso. We focus on resolving the temporal evolution of seismicity rates, which provides important observational constraints on how geothermal fields respond to natural and anthropogenic loading. We develop an iterative, regularized inversion procedure to partition the observed seismicity rate into two components: (1) the interaction rate due to earthquake-earthquake triggering and (2) the smoothly varying background rate controlled by other time-dependent stresses, including anthropogenic forcing. We apply our methodology to compare long-term changes in seismicity to monthly records of fluid injection and withdrawal. At The Geysers, we find that the background seismicity rate is highly correlated with fluid injection, with the mean rate increasing by approximately 50% and exhibiting strong seasonal fluctuations following construction of the Santa Rosa pipeline in 2003. In contrast, at both Salton Sea and Coso, the background seismicity rate has remained relatively stable since 1990, though both experience short-term rate fluctuations that are not obviously modulated by geothermal plant operation. We also observe significant temporal variations in Gutenberg-Richter b value, earthquake magnitude distribution, and earthquake depth distribution, providing further evidence for the dynamic evolution of stresses within these fields. The differing field-wide responses to fluid injection and withdrawal may reflect differences in in situ reservoir conditions and local tectonics, suggesting that a complex interplay of natural and anthropogenic stressing controls seismicity within California's geothermal fields.