Westerly Granite Research Articles

Intermittent Criticality Multi‐Scale Processes Leading to Large Slip Events on Rough Laboratory Faults

AbstractWe discuss data of three laboratory stick‐slip experiments on Westerly Granite samples performed at elevated confining pressure and constant displacement rate on rough fracture surfaces. The experiments produced complex slip patterns including fast and slow ruptures with large and small fault slips, as well as failure events on the fault surface producing acoustic emission bursts without externally‐detectable stress drop. Preparatory processes leading to large slips were tracked with an ensemble of ten seismo‐mechanical and statistical parameters characterizing local and global damage and stress evolution, localization and clustering processes, as well as event interactions. We decompose complex spatio‐temporal trends in the lab‐quake characteristics and identify persistent effects of evolving fault roughness and damage at different length scales, and local stress evolution approaching large events. The observed trends highlight labquake localization processes on different spatial and temporal scales. The preparatory process of large slip events includes smaller events marked by confined bursts of acoustic emission activity that collectively prepare the fault surface for a system‐wide failure by conditioning the large‐scale stress field. Our results are consistent overall with an evolving process of intermittent criticality leading to large failure events, and may contribute to improved forecasting of large natural earthquakes.

Petrographic, Petrophysical, and Mechanical Characterisation of the Ultra- Tight Casa Cruz Sandstone, Moruga Formation, Southern Basin, Trinidad

Durability, compactness, and natural strength of sandstones are pivotal properties for its subsequent application as a building material. If a sandstone is tight and contains petroleum, then hydraulic fracturing is necessary to achieve commercial production. The Casa Cruz Sandstone Member, southern Trinidad, is currently being explored as a potential petroleum target and building material. This study investigates the petrographic, petrophysical, and mechanical characteristics of the Casa Cruz sandstone to understand the factors that control the quality of the sandstone and to determine the sandstone’s suitability as a natural resource. A thin-section analysis was performed to investigate the mineralogy, texture, and diagenesis of the sandstone. Permeability, porosity, density, P- and S-wave velocities, unconfined compressive strength (UCS) and confined compressive strength were measured. The elastic properties (Young’s modulus, shear modulus, bulk modulus, and Poisson’s ratio) were estimated from inversion of the P- and S-wave velocities. The results show that the Casa Cruz sandstone is one of the tightest sandstone types reported in the literature with porosity of 0.7% and permeability of 4.7 x 10-22 m2 (0.47 nD). Authigenic cementation and mechanical compaction are the main diagenetic processes that jointly controlled the quality of the sandstone. The sandstone was classified as a very strong (UCS of 128 MPa) quartz-arenite and is barren of petroleum and bioclasts. Brittle failure behaviour was exhibited, accompanied by axial splitting fractures and shear fractures under unconfined and confined conditions, respectively. The Casa Cruz sandstone is suggested to be an excellent building material as its petrophysical and mechanical properties are comparable to those of commercial industry grade of Westerly granite and Naparima Hill argillite.

Identifying the fracture characteristics that control deformation localization and catastrophic failure in fluid-saturated crystalline rocks in upper crustal conditions

Previous studies show that the total volume of fractures increases non-linearly during loading as rocks approach failure in triaxial compression at stress and temperature conditions representative of the upper crust. However, the factors that control the critical volume of fractures or the critical spatial organization of the fracture network that trigger macroscopic failure remain unclear. To identify the fracture characteristics that determine the timing of macroscopic failure and localization of the fracture networks, we analyze data from six X-ray tomography experiments on Westerly granite with varying confining stress, fluid pressure, and amounts of preexisting damage. We develop machine learning models to predict 1) the timing of failure, 2) the localization of the fracture networks as measured with the Gini coefficient of the fracture volume, and 3) the change in localization from one differential stress step to the next. When the models only have access to individual fracture characteristics, the fracture length produces the best predictions of the distance to failure. When the models have access to the fracture length and sets of other characteristics, the fracture volume, aperture, and distance between fractures produce the best predictions of the distance to failure. The characteristics that describe the time or loading in the experiment, the axial strain and differential stress, produce some of the best predictions of the Gini coefficient. The results are generally consistent among the different experiments, suggesting that the fracture characteristics that determine the timing of macroscopic failure, and the localization of the fracture network, are independent of the range of confining stress, fluid pressure, and amount of preexisting damage tested here. Our results are consistent with the idea that monitoring the spatial distribution of deformation and changes in the seismic wave properties indicative of fracture growth may improve forecasting efforts of failure in the crust.

Investigating Dynamic Weakening in Laboratory Faults Using Multi‐Scale Flash Heating Coupled With mm‐Scale Contact Evolution

AbstractFlash‐weakening models typically show good agreement with the total magnitude of weakening in high‐speed rock friction experiments, however deviations during the acceleration and deceleration phases, and at low and intermediate sliding velocities, remain unresolved. Here, we incorporate inhomogeneous mm‐scale normal stress evolution into a model for flash heating and weakening to resolve outstanding transient and hysteretic friction observed in laboratory experiments and to identify unique solutions to constitutive parameters. We conduced 37 rock friction experiments on Westerly granite using a high‐speed biaxial apparatus outfitted with a high‐speed infrared camera. We initiated velocity steps from quasi‐static rates of 1 mm/s to sliding velocities ranging from 300 to 900 mm/s and conducted both constant‐ and decreasing‐velocity tests following the velocity step. Two sliding surfaces geometries were used to control mm‐scale life‐times and rest‐times. Constant‐strength sliding is achieved within 2–3 mm of initiating the velocity step in all constant‐velocity experiments. Macroscopic surface temperature is inhomogeneous and increases with slip distance, velocity, and decreasing rest‐time. Weakening increases with sliding velocity and decreasing rest‐time. We combine thermal models with measured surface temperatures to constrain the evolution of local normal stress at the mm‐scale and incorporate this evolution into a flash‐weakening model that considers weakening at both the µm‐ and mm‐scale. The flash‐weakening model improves when the effects of mm‐scale wear processes are incorporated and multi‐scale weakening is considered, however some transient friction remains undescribed. Models will be advanced by further incorporating wear processes and by considering processes at the mm‐scale and above.

Time‐Dependent Weakening of Granite at Hydrothermal Conditions

AbstractThe evolution of a fault's frictional strength during the interseismic period is a critical component of the earthquake cycle, yet there have been relatively few studies that examine the time‐dependent evolution of strength at conditions representative of seismogenic depths. Using a simulated fault in Westerly granite, we examined how frictional strength evolves under hydrothermal conditions up to 250°C during slide‐hold‐slide experiments. At temperatures ≤100°C, frictional strength generally increases with hold duration but, at 200 and 250°C, an initial increase in strength transitions to rapid time‐dependent weakening for holds longer than 14 hr. Forward modeling of long hold periods at 250°C using the rate and state friction constitutive equations requires a second, strongly negative, state variable with a long evolution distance. This implies that significant hydrothermal alteration is occurring at 250°C, consistent with microstructural observations of dissolution and secondary mineral precipitation.

Stress‐Induced Anisotropic Poroelasticity in Westerly Granite

AbstractWe measured poroelastic properties of cracked granite under triaxial conditions, at elevated confining pressure and a range of differential stresses. Skempton's coefficients and undrained Young's modulus and Poisson's ratio were determined directly by recording in situ fluid pressure during rapid cycles of axial and radial stress. Drained properties were measured both statically and dynamically at ultrasonic frequencies. At a given confining pressure, increasing differential stress leads to the development of elastically transverse isotropy, with symmetry axis aligned with the compression axis. Skempton's coefficients are also anisotropic, with larger changes in pore pressure in response to radial stress (coefficient Bx) than to axial stress steps (Bz). The anisotropy in the Skempton coefficients increases with increasing differential stress, with Bz decreasing and Bx slightly increasing. The evolution of static moduli and the Skempton coefficients is well approximated by Gassmann's equation using dry moduli obtained from ultrasonic measurements. Simplified predictions of the Skempton coefficients based on crack density tensors inverted from dynamic data also shows acceptable agreement with direct observations. Perfect quantitative agreement is not reached, due to the imprecision of our dynamic measurements, model simplifications, and inherent differences between static moduli obtained using stress steps of several MPa stress and dynamic ultrasonic stress oscillations.

The Pressure‐ and Temperature‐Dependence of Thermal Pressurization in Localized Faults

AbstractThermal pressurization (TP) is predicted to be an important dynamic frictional weakening mechanism during earthquakes. The prevailing models, though, assume that the physical, thermal and hydraulic properties of the fluid‐saturated rock in the fault zone are constant during TP (the constant case) which inherently involves temperature and pressure changes. We solve the governing equations for TP in their general form with pressure‐ and temperature‐dependent physical, thermal and hydraulic parameters of a saturated fault zone with a one‐dimensional numerical model (the variable case). The model considers slip on a plane at a constant rate, and so does not account for dynamic frictional rupture scenario. We test a wide range of medium permeabilities of 10−22–10−16 m2 and porosities 0.5%–17%, based on experimental data for Frederick diabase, Westerly granite and the Hanaore Fault gouge. We find that the predicted shear stress drop and temperature rise is similar between the two cases for low permeability (<10−20 m2) and low porosity (<1%) fault rocks, owing to an increase in the fluid pressurization factor and hydraulic diffusivity. Differences between the two models are evident in more permeable and porous fault rocks. The increase in hydraulic diffusivity during TP results in a diffusional length which scales with time0.7 in the variable case. In addition, our calculations show that it is important to apply the constant case model with the ambient initial conditions for the modeled fault zone and not time‐averaged values that aim to represent the temperature and pressure changes that occur during TP.

Micromechanics of rock damage and its recovery in cyclic loading conditions

SUMMARY Under compressive stress, rock ‘damage’ in the form of tensile microcracks is coupled to internal slip on microscopic interfaces, such as pre-existing cracks and grain boundaries. In order to characterize the contribution of slip to the overall damage process, we conduct triaxial cyclic loading experiments on Westerly granite, and monitor volumetric strain and elastic wave velocity and anisotropy. Cyclic loading tests show large hysteresis in axial stress–strain behaviour that can be explained entirely by slip. Elastic wave velocity variations are observed only past a yield point, and show hysteresis with incomplete reversibility upon unloading. Irrecoverable volumetric strain and elastic wave velocity drop and anisotropy increase with increasing maximum stress, are amplified during hydrostatic decompression, and decrease logarithmically with time during hydrostatic hold periods after deformation cycles. The mechanical data and change in elastic properties are used to determine the proportion of mechanical work required to generate tensile cracks, which increases as the rock approaches failure but remains small, up to around 10 per cent of the net dissipated work per cycle. The pre-rupture deformation behaviour of rocks is qualitatively compatible with the mechanics of wing cracks. While tensile cracks are the source of large changes in rock physical properties, they are not systematically associated with significant energy dissipation and their aperture and growth is primarily controlled by friction, which exerts a dominant control on rock rheology in the brittle regime. Time-dependent friction along pre-existing shear interfaces explains how tensile cracks can close under static conditions and produce recovery of elastic wave velocities over time.

The evolving representative elementary volume size in crystalline and granular rocks under triaxial compression approaching macroscopic failure

SUMMARY Determining the size of the representative elementary volume (REV) for properties of fracture networks, such as porosity and permeability, is critical to robust upscaling of properties measured in the laboratory to crustal systems. Although fractured and damaged rock may have higher porosity and permeability than more intact rock, and thus exert a dominant influence on fluid flow, mechanical stability and seismic properties, many of the analyses that have constrained the REV size in geological materials have used intact rock. The REV size is expected to evolve as fracture networks propagate and coalesce, particularly when fracture development becomes correlated and the growth of one fracture influences the growth of another fracture. As fractures propagate and open with increasing differential stress, the REV size may increase to accommodate the larger fractures. The REV size may also increase as a consequence of the increasing heterogeneity of the fracture network, as many smaller fractures coalesce into fewer and longer fractures, and some smaller fractures stop growing. To quantify the evolving heterogeneity of fracture networks, we track the REV size of the porosity throughout eleven triaxial compression experiments under confining stresses of 5–35 MPa. Acquiring X-ray tomography scans after each increase of differential stress provides the evolving 3-D fracture network in four rock types: Carrara marble, Westerly granite, quartz monzonite and Fontainebleau sandstone. In contrast to expectations, the REV size does not systematically increase toward macroscopic failure in all of the experiments. Only one experiment on sandstone experiences a systematic increase in REV size because this rock contains significant porosity preceding loading, and it subsequently develops a localized fracture network that spans the core. The REV size may not systematically increase in most of the experiments because the highly heterogeneous porosity distributions cause the REV to become larger than the core. Consistent with this idea, when the rock does not have a REV, the fractures tend to be longer, thicker, more volumetric, and closer together than when the rock hosts a REV. Our estimates of the REV for the porosity of the sandstone are similar to previous work: about two to four times the mean grain diameter, or 0.5–1 mm. This agreement with previous work and the <15 per cent change in the REV size in two of the sandstone experiments suggests that when a system composed of sandstone does not host a localized, system-spanning fracture network, estimates of the REV derived from intact sandstone may be similar to estimates derived from damaged sandstone. Using the existing REV estimates derived from intact sandstone to simulations with more damaged crust, such as the damage zone adjacent to large crustal faults, will allow numerical models to robustly simulate increasingly complex crustal systems.

Comparative analysis of non-recursive three-dimensional (3D) modifications of Hoek-Brown failure criterion

A comparative analysis of three-dimensional (3D) modifications of Hoek & Brown (1988) rock failure criterion was carried out. The correlations between failure stress and the other principal stresses were first determined using polyaxial test data for five geomaterials including KTB amphibolites, Westerly granite, Dunham dolomite, Shirahama sandstone and Yuubari shale. The prediction accuracies of five non-recursive, three-dimensional modifications to Hoek-Brown failure criteria and the original two-dimensional Hoek-Brown criterion were later investigated using root mean square error and coefficient of determination as measures of misfit. The results reveal that the intermediate principal stress significantly affects strength in geomaterials like the Dunham dolomite. It also moderately affects the strength of geomaterials like the KTB amphibolites, the Westerly granite and the Yuubari shale. Moreover, the intermediate principal stress has mixed effects on strength in the Shirahama sandstone. In addition, the original Hoek-Brown failure criterion could still be used with reasonable accuracy for geomaterials whose strength shows low dependence on the intermediate principal stress. While a three-dimensional Hoek-Brown criterion must be used for geomaterials like the Dunham dolomite, whose strength shows a high dependence on the intermediate principal stress. The original Hoek-Brown failure criteria should be used with caution for geomaterials like the Shirahama sandstone, the KTB amphibolites, the Westerly granite, and the Yuubari shale, whose strength shows either mixed or intermediate dependence on the intermediate principal stress. Average prediction accuracies followed the order: simplified Priest (2012), Ma et al. (2020), and Jiang & Zhao (2015). Both original Hoek & Brown (1988) and Li et al. (2021) criteria were tied, while Liu et al. (2019) was the least.

Rotation of the Stress Tensor in a Westerly Granite Sample During the Triaxial Compression Test

We simulated the spatiotemporal modelling of 3D stress and strain distributions during the triaxial compression laboratory test on a westerly granite sample using finite-difference numerical modelling implemented with FLAC3D software. The modelling was performed using a ubiquitous joint constitutive law with strain softening. The applied procedure is capable of reproducing the macroscopic stress and strain evolution in the sample during triaxial deformation until a failure process occurs. In addition, we calculated focal mechanisms of acoustic emission (AE) events and resolved local stress field orientations. This detailed stress information was compared with that from numerical modelling. The comparison was made based on the 3D rotation angle between the cardinal axes of the two stress tensors. To infer the differences in rotation, we applied ANOVA. We identified the two time levels as the plastic deformation phase and the after-failure phase. Additionally, we introduced the bin factor, which describes the location of the rotation scores in the rock sample. The p values of the test statistics F for the bin and phase effects are statistically significant. However, the interaction between them is insignificant. We can, therefore, conclude that there was a significant difference in the time between the rotation means in the particular bins, and we ran post hoc tests to obtain more information where the differences between the groups lie. The largest rotation of the stress field provided by the focal mechanisms of AE events from the numerically calculated stress field is observed in the edge bins, which do not frame the damage zone of the sample.

A Micromechanical Anisotropic Damage Model for Brittle Rocks With Non-Associated Plastic Flow Rule Under True Triaxial Compressive Stresses

A micromechanical anisotropic damage model with a non-associated plastic flow rule is developed for describing the true triaxial behaviors of brittle rocks. We combine the Eshelby’s solution to the inclusion problem with the framework of irreversible thermodynamics. The main dissipative mechanisms of inelastic deformation due to the frictional sliding and damage by microcrack propagation are strongly coupled to each other. A Coulomb-type friction criterion is formulated in terms of the local stress applied onto the microcracks as the yielding function. The back-stress term contained in this local stress plays a critical role in describing the material’s hardening/softening behaviors. With a non-associated flow rule, a potential function is involved. Some analytical analysis of the non-associated micromechanical anisotropic damage model are conducted, which are useful for the model parameters calibration. The proposed model is used to simulate the laboratory tests on Westerly granite under true triaxial stresses. Comparing the numerical simulation results provided by the models with associated/non-associated plastic flow rule and experimental results, it is clear that the proposed non-associated model gives a better prediction than the previous associated model.

Inversion in the permeability evolution of deforming Westerly granite near the brittle\u2013ductile transition

Fluid flow through crustal rocks is controlled by permeability. Underground fluid flow is crucial in many geotechnical endeavors, such as CO2 sequestration, geothermal energy, and oil and gas recovery. Pervasive fluid flow and pore fluid pressure control the strength of a rock and affect seismicity in tectonic and geotechnical settings. Despite its relevance, the evolution of permeability with changing temperature and during deformation remains elusive. In this study, the permeability of Westerly granite at an effective pressure of 100 MPa was measured under conditions near its brittle–ductile transition, between 650 °C and 850 °C, with a strain rate on the order of 2·10–6 s−1. To capture the evolution of permeability with increasing axial strain, the samples were continuously deformed in a Paterson gas-medium triaxial apparatus. The microstructures of the rock were studied after testing. The experiments reveal an inversion in the permeability evolution: an initial decrease in permeability due to compaction and then an increase in permeability shortly before and immediately after failure. The increase in permeability after failure, also present at high temperatures, is attributed to the creation of interconnected fluid pathways along the induced fractures. This systematic increase demonstrates the subordinate role that temperature dilatancy plays in permeability control compared to stress and its related deformation. These new experimental results thus demonstrate that permeability enhancement under brittle–ductile conditions unveils the potential for EGS exploitation in high-temperature rocks.

COMPARISON OF PREDICTED FAILURE AREA AROUND THE BOREHOLES IN THE STRIKE-SLIP FAULTING STRESS REGIME WITH HOEK-BROWN AND FAIRHURST GENERALIZED CRITERIA

Breakout is a shear failure due to compression that forms around the borehole due to stress concentration. In this paper, the breakout theory model is investigated by combining the equilibrium elasticity equations of stress around the borehole with two Hoek-Brown and Fairhurst generalized fracture criteria, both of which are based on the Griffith criterion. This theory model provides an explicit equation for the breakout failure width, but the depth of failure is obtained by solving a quartic equation. According to the results and in general, in situ stresses and rock strength characteristics are effective in developing the breakout failure area, As the ratio of in-situ stresses increases, the breakout area becomes deeper and wider. Because in the shear zone, the failure envelope of the Fairhurst criterion is lower than the Hoek-Brown failure criterion, the Fairhurst criterion provides more depth for breakout than the Hoek-Brown criterion. However, due to the same compressive strength of the rock in these two criteria, the same failure width for breakout is obtained from these two criteria. Also, the results obtained for the depth of failure from the theoretical model based on the Fairhurst criterion are in good agreement with the laboratory results on Westerly granite.

Nonlinear elastodynamic behavior of intact and fractured rock under in-situ stress and saturation conditions

We probe mechanisms controlling the nonlinear elastodynamic response of intact and fractured rock under both fluid-saturated and dry conditions. We present the results of dynamic acoustoelastic testing (DAET) on Westerly granite in three states: dry-intact, dry-fractured and saturated-fractured to study the influence of in-situ stress, fracture and saturation state on nonlinear elastodynamic behavior. Each sample is tested at effective normal stresses from 10 to 20 MPa. Dynamic stresses of prescribed amplitudes (0.2 – 1.0 MPa) and frequencies (0.1, 1 and 10 Hz) are superimposed on the static stress field, while pulsed ultrasonic waves transit the sample and monitor stress-induced changes in wave velocity and spectral amplitude to infer sample's elastodynamic nonlinearity. Surprisingly, dry-intact rock exhibits higher nonlinearity than dry-fractured sample at all stress levels. We use numerical simulations to argue that the reduced nonlinearity is a result of the non-uniform strain field post fracture with highly strained regions on the fracture plane and weakly-strained regions in the surrounding host-rock, both leading to a nonlinearity reduction. In addition, we demonstrate that the saturated sample is less nonlinear than the dry intact except at 10 MPa normal stress, where the fracture is fairly open. The expected decrease in nonlinearity is due to increased fracture stiffness by the presence of fluid within the fracture interface. The reported in-situ measured nonlinear elastic properties along with their frequency dependencies will be of practical importance in predicting poromechanical properties of rock masses and will facilitate comparisons between the observations made in the laboratory and field scales.

Characterizing the Distribution of Temperature and Normal Stress on Flash Heated Granite Surfaces at Seismic Slip Rates

AbstractAt seismic slip rates, flash‐weakening can significantly reduce the coefficient of friction, and the magnitude of weakening increases with surface temperature. To quantify the distribution of flash temperature, high‐speed double‐direct shear experiments were conducted on Westerly granite blocks using velocity steps from 1 mm/s to 900 mm/s at 9 MPa normal stress. We employed a high‐speed infrared camera to measure surface temperatures on the moving block during sliding, and utilized a novel sliding‐surface geometry to control the mm‐scale contact history. Following the initial weakening upon the velocity step, the blocks slide at a constant coefficient of friction. Surface temperatures are inhomogeneously distributed across the sliding surface, and increase with displacement. To determine the local normal stress distribution at the mm‐scale, we combine a one‐dimensional thermal model with conventional flash‐weakening models that incorporate a surface temperature‐dependence informed by the controlled, mm‐scale contact history. Early contacts experience local normal stress exceeding 40 times the applied normal stress. As sliding progresses, the local normal stress at the hottest contacts decreases as contact area increases, leading to local normal stresses ranging from 2 to 6 times the applied normal stress on most contacts by 30 mm of slip. Increases in surface temperature, which would decrease the coefficient of friction, are buffered by wear processes that increase contact area and decrease the local normal stress. Treatments of flash heating are advanced by incorporating improved characterization of the state of the sliding surface at the mm and larger scales during sliding.

Fluid pressure heterogeneity during fluid flow in rocks: new laboratory measurement device and method

SUMMARY We present a new type of transducer capable of measuring local pore fluid pressure in jacketed rock samples under elevated confining pressure conditions. The transducers are passive (strain-gauge based), of small size (7 mm in diameter at the contact with the rock and around 10 mm in length), and have minimal dead volume (a few mm3). The transducers measure the differential pressure between the confining fluid and the internal pore pressure. The design is easily adaptable to tune the sensitivity and working pressure range up to several hundred megapascals. An array of four such transducers was tested during hydrostatic pressurization cycles on Darley Dale sandstone and Westerly granite. The prototypes show very good linearity up to 80 MPa with maximum deviations of the order of 0.25 MPa, regardless of the combination of pore and confining pressure. Multiple internal pore pressure measurements allow us to quantify the local decrease in permeability associated with faulting in Darley Dale sandstone, and also prove useful in tracking the development of pore pressure fronts during transient flow in low permeability Westerly granite.

Intrinsic Elastic Anisotropy of Westerly Granite Observed by Ultrasound Measurements, Microstructural Investigations, and Neutron Diffraction

AbstractWesterly granite (WG) has been generally accepted as an isotropic homogeneous rock. Here, we return to WG and observe significant elastic anisotropy using multidirectional ultrasonic sounding on spherical samples at pressures up to 400 MPa. Thermal treatment of WG leads to formation of microcracks that reduce elastic wave velocities and increase its elastic anisotropy. The 3D distribution of P‐wave velocities at low pressure is close to orthorhombic symmetry. Application of hydrostatic pressure closes most of thermally induced microcracks and decreases elastic anisotropy of WG, but at high pressure the anisotropy is practically reversed compared to low pressure: maximum P‐wave velocity direction at low pressures is near minimum velocity direction at high pressure and vice versa. To understand this effect, microstructures of the rock were investigated by optical and scanning electron microscopy. Preferred orientations of four major rock‐forming minerals—quartz, orthoclase, plagioclase, and biotite—were measured by time‐of‐flight neutron diffraction, which confirms significant crystal alignment. All these data were used to numerically model anisotropic elastic properties of WG. It is shown that WG possesses weak intrinsic elastic anisotropy related mainly to the preferred orientation of feldspars formed during igneous crystallization. Observed microcracks are mostly related to the cleavage planes of feldspars and biotite, and thus also demonstrate preferred orientation. Higher preheating temperatures produce larger quantity of longer microcracks. A numerical model shows that these microcracks act against the weak intrinsic elastic anisotropy of WG, and define the elastic anisotropy at low pressures.

Evidence for the Heterogeneity of the Pore Structure of Rocks from Comparing the Results of Various Techniques for Measuring Hydraulic Properties

We applied three oscillatory methods, the previously presented axial pore-pressure and pore-flow methods, and the laboratory application of the radial oscillatory pore-flow method, and performed steady-state flow-through experiments (Darcy tests), for comparison, in experiments on samples of Westerly granite and Wilkeson sandstone. The granite and the sandstone exhibit pore spaces dominated by micro-fractures and by the granular-medium character with a connected porosity of about 1 and 10 %, respectively. Permeability determined by the axial pore-pressure method shows the closest agreement with the results of the Darcy tests. Apparent porosity and drained modulus derived from specific storage capacity deviate from measured connected porosity and reference values, respectively. The observed deviations of the hydraulic properties between methods suggest that they bear information about the structure of the pore space. Only for the sandstone, anisotropy in hydraulic properties appears to contribute to differences between the results of the various methods. We argue that oscillatory testing provides three indicators for heterogeneity, period dependence, the relation between apparent and connected porosity, and the relation between amplitude ratio and apparent penetration depth, calculated from the simple scaling law for homogeneous materials. These indicators consistently classify the samples of Wilkeson sandstone as hydraulically homogeneous and those of Westerly granite as heterogeneous.

Acoustic Emission Events Interpreted in Terms of Source Directivity

During inversion for the source mechanisms of laboratory acoustic emission events, relatively high misfit values (expressed as the RMS of the inverted equations) were observed. Our experiment was performed on Westerly Granite. A processed set of data consisting of 2405 acoustic emission events was used and a semi-homogeneous velocity model was considered. A correction for sensor radiation patterns and individual sensor constants was taken into account, and an acausal attenuation model was assumed. Source mechanisms were inverted for the moment tensor. The application of a more sophisticated medium model improved inversion quality only for some events. Introducing the source directivity, a standard approach for earthquakes with magnitudes larger than approximately 4, increased the number of successfully inverted events. Directivity was introduced using a Haskell source model; optionally unilateral and bilateral versions of the source were considered. Lower values of RMS for the Haskell source model were considered to justify the directivity approach. This formalism enables us to select the preferable fault from the two nodal planes within the fault plane solution. The rupture directions were observed to tend to the dip direction of the preferred fault. They were found to be preferably subparallel to slip directions for acoustic emissions with a significant DC component. The source time functions retrieved from the seismograms are in agreement with finite source theory.