Philip George Meredith

Temporal variations in seismicity during quasi-static and dynamic rock failure

Abstract A comprehensive model is presented which can explain temporal fluctuations in seismic b-values in the period leading to mechanical failure in terms of the underlying physical processes of time-varying applied stress and stress corrosion-enhanced crack growth under conditions of constant strain rate. The form of the b-value anomaly in the period leading to failure depends on the form of the stress/time relationship. For the case where dynamic failure occurs at peak stress after a period of strain hardening, the model predicts a single cusp-like b-value anomaly, reaching a critically low value of 0.5 at failure. For the physically most realistic case where dynamic failure is preceded by a period of precursory strain energy release during strain softening, the model predicts two minima in the b-value. separated by a temporary maximum or inflection point. These fluctuations in the b-value are consistent with reported “intermediate-term” and “short-term” earthquake precursors separated by a period of seismic quiescence. For the case of quasi-static cataclastic flow, the b-value mirrors the stress and never falls to the critical value because there is no critical rupture. New results from a series of controlled laboratory experiments are presented in which microseismic event rates and b-value were monitored contemporaneously with stress/time data for all variants of the stress/time relationship. Recent field observations of temporal changes in seismicity rates and b-value preceding major earthquakes are also reported. Both data sets exhibit b-value anomalies which are consistent with the model predictions.

Fracture toughness and subcritical crack growth during high-temperature tensile deformation of Westerly granite and Black gabbro

Abstract The double torsion testing method has been used to determine catastrophic and subcritical crack propagation parameters for pre-cracked specimens of Westerly granite and Black gabbro under a number of environmental conditions. The critical stress intensity factor for catastrophic crack propagation (fracture toughness) of granite and gabbro has been measured at temperatures from 20 to 400°C, in a vacuum. At 20°C, the fracture toughness of Westerly granite was 1.79 ± 0.02 MPa · m 1 2 , and for two blocks of Black gabbro it was 3.03 ± 0.08 MPa · m 1 2 and 2.71 ± 0.15 MPa · m 1 2 , respectively. These values are very close to those reported by other investigators for tests conducted in air of ambient humidity at room temperature. For both rocks, fracture toughness at first increased slightly, and then decreased steadily on raising the temperature above ambient conditions. This behaviour is explained in terms of the density and distribution of thermally induced microcracks, as determined by quantitative optical microscopy. Subcritical crack growth behaviour has been studied at temperatures up to 300°C, and under water vapour at pressures of 0.6 to 15 kPa. Both the load relaxation and incremental constant displacement rate forms of the double torsion testing method were utilised to generate stress intensity factor/crack velocity diagrams. Crack growth was measured over the velocity range 5 × 10−3 to 10−7 m · s−1. Increasing both temperature and water vapour pressure resulted in substantially higher crack growth rates. The overall effect of raising the temperature over the range studied here (20–300°C) was to increase the crack growth rate in granite and gabbro by ∼5 and 7 orders of magnitude, respectively, at constant stress intensity factor and vapour pressure of water. For both rocks, the slopes of stress intensity factor/crack velocity curves were sensitive to changes in both temperature and water vapour pressure at low values of the latter parameter. Slopes fell substantially on raising the water vapour pressure, but were relatively insensitive to changes in temperature at these higher pressures. No subcritical crack growth limit was encountered. Estimates of the uncertainty in our experimental data are given. From the results of multiple load relaxation experiments on Westerly granite specimens, we estimate the uncertainty in position of stress intensity factor/crack velocity curves along the stress intensity axis to be c. 10% of the fracture toughness, and the uncertainty in slope of such curves to be c. 12%. Problems associated with the extrapolation of our experimental data to regions of higher effective confining pressure in the Earths crust are discussed.

MICROCRACK FORMATION AND MATERIAL SOFTENING IN ROCK MEASURED BY MONITORING ACOUSTIC EMISSIONS

Abstract Brittle deformation in rocks is accompanied by the formation of microcracks which emit elastic energy partly as acoustic emissions. Acoustic emission parameters such as amplitude may be related to geometric parameters such as crack size. We have analyzed catalogues of acoustic emission events recorded during compression tests in rock in terms of the information they give about the accumulated state of damage in a material. We combine this measured damage state with a model for the softening behaviour of cracked solids, and show that reasonable predictions of the mechanical behaviour are possible. Several strategies have to be used to allow for incomplete recording of the acoustic emissions. An independent calibration of the scaling relation between the acoustic emission parameters and the microcrack geometry remains outstanding, although the results here suggest constraints on the scaling relation. We show, however, that this quantitative approach is markedly superior to the more traditional methods of acoustic emission analysis in correlating the acoustic activity with the weakening of the material.

Seismogenic lavas and explosive eruption forecasting

Volcanic dome-building episodes commonly exhibit acceleration in both effusive discharge rate and seismicity before explosive eruptions. This should enable the application of material failure forecasting methods to eruption forecasting. To date, such methods have been based exclusively on the seismicity of the country rock. It is clear, however, that the rheology and deformation rate of the lava ultimately dictate eruption style. The highly crystalline lavas involved in these eruptions are pseudoplastic fluids that exhibit a strong component of shear thinning as their deformation accelerates across the ductile to brittle transition. Thus, understanding the nature of the ductile–brittle transition in dome lavas may well hold the key to an accurate description of dome growth and stability. Here we present the results of rheological experiments with continuous microseismic monitoring, which reveal that dome lavas are seismogenic and that the character of the seismicity changes markedly across the ductile–brittle transition until complete brittle failure occurs at high strain rates. We conclude that magma seismicity, combined with failure forecasting methods, could potentially be applied successfully to dome-building eruptions for volcanic forecasting.

Laboratory simulation of volcano seismicity

The physical processes generating seismicity within volcanic edifices are highly complex and not fully understood. We report results from a laboratory experiment in which basalt from Mount Etna volcano (Italy) was deformed and fractured. The experiment was monitored with an array of transducers around the sample to permit full-waveform capture, location, and analysis of microseismic events. Rapid post-failure decompression of the water-filled pore volume and damage zone triggered many low-frequency events, analogous to volcanic long-period seismicity. The low frequencies were associated with pore fluid decompression and were located in the damage zone in the fractured sample; these events exhibited a weak component of shear (double-couple) slip, consistent with fluid-driven events occurring beneath active volcanoes.

Experimental and theoretical fracture mechanics applied to Antarctic ice fracture and surface crevassing

Recent disintegration of ice shelves on the Antarctic Peninsula has highlighted the need for a better understanding of ice shelf fracture processes generally. In this paper we present a fracture criterion, incorporating new experimental fracture data, coupled with an ice shelf flow model to predict the spatial distribution of surface crevassing on the Filchner-Ronne Ice Shelf. We have developed experiments that have enabled us to quantify, for the first time, quasi-stable crack growth in Antarctic ice core specimens using a fracture initiation toughness, Kinit, for which crack growth commences. The tests cover a full range of near-surface densities, ρ = 560–871 kg m−3 (10.9–75.7 m depth). Results indicate an apparently linear dependence of fracture toughness on porosity such that Kinit = 0.257 ρ-80.7, predicting a zero-porosity toughness of Ko = 155 kPa m1/2. We have used this data to test the applicability to crevassing of a two-dimensional fracture mechanics criterion for the propagation of a small sharp crack in a biaxial stress field. The growth of an initial flaw into a larger crevasse, which involves a purely tensile crack opening, depends on the size of the flaw, the magnitude of Kinit and the nature of the applied stress field. By incorporating the criterion into a stress map of the Filchner-Ronne Ice Shelf derived from a depth-integrated finite element model of the strain-rate field, we have been able to predict regions of potential crevassing. These agree well with satellite imagery provided an initial flaw size is assumed in the range 5–50 cm.

Microcracking during triaxial deformation of porous rocks monitored by changes in rock physical properties, I. Elastic-wave propagation measurements on dry rocks

We present results from two series of triaxial deformation experiments performed on “dry” samples of two sandstones (Darley Dale and Gosford) carried out at confining pressures from 25 MPa to 200 MPa. Over this pressure range the mode of failure in both these sandstones passes from localized brittle failure with a clear through-going fault to distributed cataclastic flow. During these experiments, stress, strain, compressional-wave velocity (VP) and shear-wave velocity (VS) measurements were made simultaneously in the direction of the maximum principal compressive loading axis. Initial application of the hydrostatic confining pressure causes both VP and VS to increase, and upon raising the axial stress above the confining pressure both velocities increase further at first (generally by only a few percent), but then decrease as dilatant crack growth commences. During dilatancy, VS decreases proportionately more than VP, and this decrease is generally of the order of 10–15%. These velocity measurements allow changes in rock physical properties to be calculated along with the axial and transverse crack volume density parameters, ϵX and ϵZ. The results from two selected tests are analysed in detail. These tests were chosen because they exhibit; (a) typical brittle shear failure, and (b) typical ductile cataclastic flow, respectively. The full interrogating elastic waveforms were also recorded during testing, and these have been used to calculate the seismic quality factors QP and QS. To our knowledge, this is the first time this has been reported for rock samples undergoing triaxial deformation. The changes in Q values generally exhibit similar trends to those observed in the velocity measurements, but the percentage changes in Q are an order of magnitude greater, suggesting that this parameter is a more sensitive measure of dilatant crack damage. The measurements on dry rock samples reported here provide the basis for comparison with measurments of changes in complementary physical properties made on water-saturated rock samples under the same experimental conditions, and reported in a companion paper in this issue (Read et al., 1995).

Stress corrosion cracking of quartz: A note on the influence of chemical environment

Abstract Tensile (mode I) stress corrosion growth of cracks on the a-plane of quartz in a direction normal to z has been studied in de-ionized water, in 2N HCl and in 2N NaOH solutions at 20° C. The double torsion testing method was used to obtain crack velocity (v) stress intensity factor (KI) curves. The stress corrosion index, n (where v = αKIn) was 19.3 for 2N HCl, 12.8 for deionized water, and 9.5 for 2N NaOH. The degree of influence of reagent chemistry on crack velocity was most marked at low KI values (at 0.5 KIc 3 orders of magnitude increase in crack velocity results from substituting 2N NaOH for 2N HCl as the corrosive medium), but decreased monotonically on raising KI so that close to KIc there was no clearly discernible influence on crack growth rates (ca. 10−3 m s−1). These observations are explained in terms of a model of crack propagation in which at low KI values the chemistry of the bulk fluid environment controls the corrosion reaction. The rate of crack growth is enhanced by increasing environmental OH− concentration. At high KI (or velocity), however, the chemical composition of the quartz surface may control crack propagation rates through its influence on the chemistry of the crack tip fluid. As the pH of natural pore fluids is likely to vary widely in different geological environments these results should be noted when invoking stress corrosion to explain geophysical phenomena.

Damage accumulation during triaxial creep of darley dale sandstone from pore volumometry and acoustic emission

Abstract We performed triaxial creep tests on water-saturated samples of Darley Dale sandstone to investigate the effect of pressure on the process of time-dependent brittle deformation under all-round compression. Axial strain, acoustic emission (AE) output and pore volume change were monitored continuously during each test. We observed the three classical creep regimes (primary, steady-state and tertiary). The level of applied differential stress has a crucial effect on the creep rate and on the time-to-failure; from 30 minutes at 90% of the short-term strength to almost one day at 80%. For the experiments performed at the lower levels of stress, the duration of the primary creep phase increases, while the acoustic emission level during the steady-state phase decreases dramatically. The variations of axial strain and differential pore-fluid volume are more regular when the tests are conducted at stresses closer to the strength of the material. AE measurements suggest that the final stage of the deformation occurs for similar levels of cumulative events and cumulative AE energy, regardless of stress level. The same comment can be made for the pore-fluid volumometry results. This suggests that the final stage that leads to failure occurs for almost the same level of damage in all samples.

Fracture toughness measurements on igneous rocks using a high-pressure, high-temperature rock fracture mechanics cell

Abstract A sound knowledge of mechanical properties of rocks at high temperatures and pressures is essential for modelling volcanological problems such as fracture of lava flows and dike emplacement. In particular, fracture toughness is a scale-invariant material property of a rock that describes its resistance to tensile failure. A new fracture mechanics apparatus has been constructed enabling fracture toughness measurements on large (60 mm diameter) rock core samples at temperatures up to 750°C and pressures up to 50 MPa. We present a full description of this apparatus and, by plotting fracture resistance as a function of crack length, show that the size of the samples is sufficient for reliable fracture toughness measurements. A series of tests on Icelandic, Vesuvian and Etnean basalts at temperatures from 30 to 600°C and confining pressures up to 30 MPa gave fracture toughness values between 1.4 and 3.8 MPa m1/2. The Icelandic basalt is the strongest material and the Etnean material sampled from the surface crust of a lava flow the weakest. Increasing temperature does not greatly affect the fracture toughness of the Etnean or Vesuvian material but the Icelandic samples showed a marked increase in toughness at around 150°C, followed by a return to ambient toughness levels. This material also became tougher under moderate confining pressure but the other two materials showed little change in toughness. We describe in terms of fracture mechanics probable causes for the changes in fracture toughness and compare our experimental results with values obtained from dike propagation modelling found in the literature.