Westerly Granite Research Articles

Stress and time‐dependent failure of brittle rocks under compression: A theoretical prediction

A micromechanics‐based continuum theory called interaction field theory (IFT) can reproduce localization phenomena such as shear faulting and axial splitting of rock under compression. The validity of IFT is examined by comparing its predictions of short‐term strength and creep behavior of hard rock with reported experimental data. The theory is formulated through an averaging scheme for an elastic solid containing many microcracks. The growth of the microcracks is assumed to occur through two mechanisms: stress‐induced crack growth and stress corrosion. Failure of rock under compression is known to be governed by the interactive behavior of microcracks. Yet in many earlier analyses the information on interaction is lost through conventional averaging schemes. IFT introduces a new field quantity which represents the interaction effect and the associated governing integral equation. IFT reproduces not only inelastic deformation of rock but also eventual macroscopic failure due to localization of microcracking. In the numerical analysis of short‐term behavior, macroscopic failure is reproduced as a bifurcation from a homogeneous state of deformation into a localized one. The strengths are obtained as a result of numerical analysis with material constants of an intact matrix and the quantities related to initial defects. The strengths of Westerly granite obtained as a function of the confining pressure are compared with published experimental data. For time‐dependent behavior of hard rock, creep tests of granite are analyzed. Comparisons are made between experimental failure times and numerical results for different confining pressures and environmental conditions.

Hydrodynamic erosion: A potential mechanism of sand production in weak sandstones

We conducted laboratory simulation tests of borehole breakouts and investigated their potential use as an indicator of in situ stress magnitudes in Westerly granite and Berea sandstone. We also carried out simple triaxial tests and used the results to derive several strength criteria for these rocks. Using the assumption that the state of stress at the breakout boundary on the borehole wall is in a state of limit equilibrium with the rock strength, we attempted to determine the appropriate strength criterion for each of the two rocks. We concluded that the well known Mohr-Coulomb criterion is not compatible with the condition of stress at breakout failure. On the other hand, truly triaxial (polyaxial) strength criteria, which incorporate the effect of the intermediate principal stress on failure, are much more in agreement with the stress at the breakout boundary. One such criterion due to Nadai and another due to Mogi, appear suitable for determining breakout failure in the sandstone and the granite, respectively. Thin-section analysis suggests that breakout failure mechanism may play an important role in determining the appropriate strength criterion for a given rock type. Utilizing the appropriate strength criterion for the corresponding rock type, and having knowledge of the breakout span at the borehole wall and the minimum horizontal and vertical principal stresses, we were able to estimate the maximum far-field principal stress within an average of 14% error.

Polyaxial strength criteria and their use in estimating in situ stress magnitudes from borehole breakout dimensions

Abstract We conducted laboratory simulation tests of borehole breakouts and investigated their potential use as an indicator of in situ stress magnitudes in Westerly granite and Berea sandstone. We also carried out simple triaxial tests and used the results to derive several strength criteria for these rocks. Using the assumption that the state of stress at the breakout boundary on the borehole wall is in a state of limit equilibrium with the rock strength, we attempted to determine the appropriate strength criterion for each of the two rocks. We concluded that the well known Mohr-Coulomb criterion is not compatible with the condition of stress at breakout failure. On the other hand, truly triaxial (polyaxial) strength criteria, which incorporate the effect of the intermediate principal stress on failure, are much more in agreement with the stress at the breakout boundary. One such criterion due to Nadai and another due to Mogi, appear suitable for determining breakout failure in the sandstone and the granite, respectively. Thin-section analysis suggests that breakout failure mechanism may play an important role in determining the appropriate strength criterion for a given rock type. Utilizing the appropriate strength criterion for the corresponding rock type, and having knowledge of the breakout span at the borehole wall and the minimum horizontal and vertical principal stresses, we were able to estimate the maximum far-field principal stress within an average of 14% error.

The observations of faulting in westerly granite under triaxial compression by X-ray CT scan

The observations of faulting in westerly granite under triaxial compression by X-ray CT scan

The observations of faulting in westerly granite under triaxial compression by X-ray CT scan

Abstract Observations of the spatial development of cracks in granite undergoing triaxial compression provide new insights into the proces of fault formation. Dry intact Westerly granite samples were loaded under confining pressure of 100 MPa, and the progress of fault formation was controlled by maintaining the increment of circumferential displacement at a constant rate. The samples were unloaded when they experienced stress drops and were successfully recovered without severe crushing. A stereo microscope was used to observe the spatial pattern of cracks on the sample surfaces, and an X-ray CT scanning system was used to non-destructively image the sample interiors. Microscope observations show that several fault-like linear cracks developed on the surfaces of all the samples and have an angle of about 30 degrees to the maximum compression axis. This suggests that fault nucleation began just after peak stress. The X-ray CT images show that a fault-like linear crack grew inward toward the sample interior as axial stress decreased. It is concluded that the fault nucleated locally on the sample surface just after peak stress, and developed into an apparent fault by the plateau stage of the complete stress-strain relationship.

Toward an Iconography of American Labor: Work, Workers, and the Work Ethic in American Art, 1930-1945

In America, a certain reverence for work together with an abiding faith in the work ethic have played a significant role in shaping self and civic identity from the Republican era of the early nineteenth century to the present day. Indeed, it is a commonplace assumption that what we do as Americans is often the most outstanding indicator of who we are. Moreover, the meaning of work as a crucial, moral link between individuals and public life is so strong that it might almost be considered a calling that ties individual Americans to the larger, national, community that is the United States. It is ironic, then, that the history of American art reveals a paucity of both public memorials and private objects focused on and laborers. Even during periods when issues of labor and capital, work and wages were central to the nation's political and social life, such as in the late nineteenth century, art which focused on work and workers was relatively sparse.' An exception is found in the 1930s, when American artists ranging in stylistic diversity from regionalist painter Thomas Hart Benton to social realist cartoonist William Gropper, responded to the crisis of the Great Depression with an extensive iconography celebrating work and workers. In both their private paintings and their public commissions, these modern artists generally depicted American wage laborers as heroic figures of action and autonomy, and thus as exemplars of the work ethic. In such New Deal agencies as the Works Progress Administration/Federal Art Project, and the Treasury Section of Painting and Sculpture, an iconography of was courted by American arts administrators, who recognized the powerful social and political import of upbeat images of rugged, dynamic workers during the severe unemployment and cultural malaise of the Great Depression. Leo Raiken's 1938-1939 Rock Quarry, for example, a mural study that was originally painted in a section competition for a U.S. Post Office in Westerly, Rhode Island, is a perfect example (figure 1).2 Emphasizing the strength, individuality, determination, and utility of the workingmen of Westerly's granite industry, from bluecollar drillers and stonecutters to professional-class engineers and architects, Raiken's sketch extolled work as a symbol of community, collectivity, and shared experience. Twelve sturdy figures were Robert N. Bellah et al, Habits of the Heart, Individualism and Commitment in American Life (Berkeley: University of California Press, 1985), 66; and Herbert G. Gutman et al, Who BuiltAmerica (New York: Pantheon, 1989), 561. 2. See Karal Ann Marling, Wall-to-Wall America: A Cultural History of Post Office Murals in the Great Depression (Minneapolis: University of Minnesota Press, 1982), 161-70, for a full analysis of the Westerly post office mural compe-

On Constitutive Equations and Effective Stress Principles for Deformable, Double‐Porosity Media

Tuncay and Corapcioglu [1995] used volume averaging methods to derive an effective stress principle for the bulk volumetric strain in a deformable double‐porosity medium. The coefficients of the matrix pore pressure and fracture pore pressure in their equation for the effective stress are shown to be identical to those which can be obtained from the constitutive equation approach of Berryman and Wang [1995]. Representative values for a fractured Berea sandstone show that a change in pore pressure within matrix blocks produces about 10% of the volume change resulting from an equal but opposite change in confining pressure, whereas the same change in pore pressure within fractures is about 90% as effective. A similar result is true for Westerly granite.

Temperature and the Seismic/Aseismic Transition: Observations from the 1992 Landers Earthquake

An important constraint on the size and destructive potential of earthquakes is the depth extent of rupture. Laboratory studies of the transition from unstable to stable sliding, along with observed relationships between surface heat flow and the thickness of the seismogenic crust, provide strong evidence for the significance of temperature in determining the maximum nucleation depth of large earthquakes. The June 28, 1992, Mw 7.3 Landers earthquake ruptured fault segments within 20 km of 11 pre‐existing heat flow measurements, and shallowing of the base of aftershock seismicity along strike correlates with an increase in heat flow. Crustal geotherms estimated from these measurements place the base of seismicity along the 250°C isotherm. This temperature is consistent with predictions from laboratory studies of the frictional stability of Westerly granite, but estimated temperatures for the seismic‐aseismic transition along other faults within the San Andreas fault system are in the range of 350 to 400°C. Variations in country rock and fault gouge composition, together with higher slip rates, may account for this difference, although part of the Landers seismogenic crust might remain unruptured.

Frictional behavior of large displacement experimental faults

The coefficient of friction and velocity dependence of friction of initially bare surfaces and 1‐mm‐thick simulated fault gouges (<90 μm) of Westerly granite were determined as a function of displacement to >400 mm at 25°C and 25 MPa normal stress. Steady state negative friction velocity dependence and a steady state fault zone microstructure are achieved after ∼18 mm displacement, and an approximately constant strength is reached after a few tens of millimeters of sliding on initially bare surfaces. Simulated fault gouges show a large but systematic variation of friction, velocity dependence of friction, dilatancy, and degree of localization with displacement. At short displacement (<10 mm), simulated gouge is strong, velocity strengthening and changes in sliding velocity are accompanied by relatively large changes in dilatancy rate. With continued displacement, simulated gouges become progressively weaker and less velocity strengthening, the velocity dependence of dilatancy rate decreases, and deformation becomes localized into a narrow basal shear which at its most localized is observed to be velocity weakening. With subsequent displacement, the fault restrengthens, returns to velocity strengthening, or to velocity neutral, the velocity dependence of dilatancy rate becomes larger, and deformation becomes distributed. Correlation of friction, velocity dependence of friction and of dilatancy rate, and degree of localization at all displacements in simulated gouge suggest that all quantities are interrelated. The observations do not distinguish the independent variables but suggest that the degree of localization is controlled by the fault strength, not by the friction velocity dependence. The friction velocity dependence and velocity dependence of dilatancy rate can be used as qualitative measures of the degree of localization in simulated gouge, in agreement with previous studies. Theory equating the friction velocity dependence of simulated gouge to the sum of the friction velocity dependence of bare surfaces and the velocity dependence of dilatancy rate of simulated gouge fails to quantitatively account for the experimental observations.

A New Pressure Decay Technique Measurement Of Live Heavy Oil Mobility In Unconsolidated Oil Sands Cores

Abstract The pressure decay test is an efficient and fast method for determining the mobility of fluid in porous media. Previous test procedures by other investigators require the use of upstream and downstream reservoirs. To facilitate data analysis, some conditions are imposed on the upstream or downstream reservoirs. This paper presents an alternative method to conduct pressure decay tests without using the upstream and downstream reservoirs. Mobility is calculated from the pressure decay in the sample using the finite difference method. The proposed testing method eliminates restrictions imposed on the reservoirs, shortens the testing period, and has the capability to analyse poorly controlled upstream and downstream pressures. It is validated by comparing the mobilities measured by the new pressure decay method with that measured under the steady state condition. Introduction The usual method of measuring mobility in the laboratory is to establish steady state flow through the sample. The mobility is calculated from the measured flow rate and pore pressure gradient. If the mobility is low, steady state takes a long time to establish. Therefore, the steady-state-flow method is generally impractical for the measurements of very low mobility. Brace et al,(l) introduced a transient flow method to measure the low permeability of Westerly Granite. Their experimental set up consists of a cylindrical rock sample that is connected to two fluid reservoirs. At the start of the experiment, the fluid pressure in the upstream reservoir is suddenly increased. As this pressure decays, fluid flows from the upstream reservoir, across the sample, to the downstream reservoir. They found that the mobility can be estimated from a semi-log plot of the observed pressure difference across the sample versus time when the compressive storage of the rock sample is negligible(2,3). Taking the compressive storage of the sample into consideration, Lin(4) interpreted the mobility from the pressure decay using a numerical method. Lin's analysis, however, assumed that the specific storage was known. To determine the specific storage, other independent tests are required, as Hsieh et al.(5) commented. Hsieh et al.(5,6) presented an analytical solution using the pore pressure gradients at both ends of the sample as boundary conditions. The pressure responses at the upstream and the downstream ends can be expressed as a series. A graphical method, utilizing type curves, was developed to calculate both the mobility and the specific storage of the rock sample. Bourbie and Walls(7) developed another analytical solution for the pulse decay test. The constant upstream pressure was used as one of the boundary conditions in their solution. The downstream pressure can be expressed as an explicit function of mobility. However, the mobility cannot be solved explicitly, so a computer program was written to find the mobility from the pulse decay. To maintain a constant upstream pressure the upstream reservoir volume must be much larger than the total volume of the sample pore and the downstream reservoir. Chen and Stagg(8) presented an analytical solution using the boundary conditions similar to those in Bourbie and Walls' solution.

Pseudotachylyte controversy: Fact or friction?

High-speed slip experiments performed on Westerly granite using friction welding apparatus reveal that comminution is an essential precursor to melting by friction. Observations of slip surfaces via analytical scanning electron microscopy (SEM) document the following sequence of events occurring in 2 s with increasing velocity (up to 2 m/s): fracture; progressive comminution; surface melting of mineral fragments; fragment-to-fragment adhesion; and, finally, production of a fragment-laden, melt-supported suspension. Explosive dehydration and melting of the epidote-group mineral allanite indicates that temperatures of at least 1000 °C were realized at the interface. This is corroborated by calculation of the temperature rise for the known operating conditions. Contrary to earlier proposals, these results show that comminution and frictional melting are complementary and not mutually exclusive processes. Depending on the velocity–shear stress–displacement relations prevailing during frictional slip, rocks produced in seismogenic zones can be predominantly comminuted wall rock or fragment-melt mixes (pseudotachylytes).

Squirt flow in fully saturated rocks

We estimate velocity/frequency dispersion and attenuation in fully saturated rocks by employing the squirt‐flow mechanism of solid/fluid interaction. In this model, pore fluid is squeezed from thin soft cracks into the surrounding large pores. Information about the compliance of these soft cracks at low confining pressures is extracted from high‐pressure velocity data. The frequency dependence of squirt‐induced pressure in the soft cracks is linked with the porosity and permeability of the soft pore space, and the characteristic squirt‐flow length. These unknown parameters are combined into one expression that is assumed to be a fundamental rock property that does not depend on frequency. The appropriate value of this expression for a given rock can be found by matching our theoretical predictions with the experimental measurements of attenuation or velocity. The low‐frequency velocity limits, as given by our model, are identical to those predicted by Gassmann’s formula. The high‐frequency limits may significantly exceed those given by the Biot theory: the high‐frequency frame bulk modulus is close to that measured at high confining pressure. We have applied our model to D’Euville Limestone, Navajo Sandstone, and Westerly Granite. The model realistically predicts the observed velocity/frequency dispersion, and attenuation.

A shear failure strength law of rock in the brittle‐plastic transition regime

As a first step to establish the law governing shear failure of typical crustal materials in the brittle‐plastic transition regime under lithospheric conditions, and thereby to properly estimate a depth profile of lithospheric strength in quantitative terms, the effects of the normal stress σn across the fault surfaces and ambient temperature T on the shear failure strength of dry Westerly granite in the brittle to brittle‐plastic transition regimes are evaluated quantitatively, using experimental data published by earlier authors. The empirical law proposed can predict the shear failure strength at strain rates of 10−4‐10−5/S under any (σn, T) conditions in the brittle to brittle‐plastic transition regimes.

The role of microcracking in shear-fracture propagation in granite

Microcracking related to the formation of a laboratory shear fracture in a cylinder of Westerly granite has been investigated using image-analysis computer techniques. Well away from the fracture (farfield), the deformed granite has about twice the crack density (crack length per unit area) of undeformed granite. The microcrack density increases dramatically in a process zone that surrounds the fracture tip, and the fracture tip itself has more than an order of magnitude increase in crack density over the undeformed rock. Microcrack densities are consistently higher on the dilational side of the shear than on the compressional side. Microcracks in the undeformed rock and in the far-field areas of the laboratory sample are concentrated within and along the margins of quartz crystals, but near the shear fracture they are somewhat more abundant within K-feldspar crystals. The energy release rate, g II , for mode II fracture progagation is estimated from the microcrack density data to be ≥ 1.7–8.6 kJ m −2. The microcracks that formed during the experiment are principally tensile cracks whose orientations reflect the local stress field: those formed prior to the nucleation of the fault are roughly parallel to the cylinder axis (loading direction), whereas those generated in the process zone make angles averaging 30 ° to the overall fault strike (and 20 ° to the cylinder axis). The preferred orientation and uneven distribution of microcracks in the process zone tends to pull the propagating fracture tip towards the dilational side, even though the trend is away from the overall fault strike. As a result, the propagating shear follows the microcrack trend for some distance and then changes direction in order to maintain an overall in-plane propagation path. This recurring process produces a zig-zag or sawtooth segmentation pattern similar to the sawtooth geometries of faults such as the San Andreas fault.

Conductive heat flow and thermally induced fluid flow around a well bore in a poroelastic medium

Transient analytical solutions for temperature and pore pressure changes near a circular borehole under instantaneous temperature and fluid pressure changes inside the borehole are presented. The solutions couple conductive heat transfer with Darcy fluid flow, and a borehole under a nonhydrostatic far‐field stress state is simulated. The heat conduction equation is decoupled from the coupled system of isothermal governing equations, and the complete solution is obtained by superimposing this decoupled solution on the isothermal one. The solution is therefore applicable to low‐permeability media, where heat transfer is dominated by conduction only. Both cold and warm injection processes are studied, and the applications to hydraulic fracture initiation and thermally induced fluid flow are discussed. Taking Westerly granite as an example, it is concluded that the maximum thermally induced pore pressure inside the rock formation can be 30% higher than the isothermal pore pressure, with a borehole temperature and fluid pressure change ratio (ΔT/Δp) = 1°C/MPa. It is emphasized that the thermally induced pore pressure change can be significant inside a low‐permeability porous medium, and a coupled solution must be obtained to address the mechanical, hydraulic, and thermal responses appropriately.

Nucleation and growth of faults in brittle rocks

We present a model for the nucleation and growth of faults in intact brittle rocks. The model is based on recent experiments that utilize acoustic emission events to monitor faulting processes in Westerly granite. In these experiments a fault initiated at one site without significant preceding damage. The fault propagated in its own plane with a leading zone of intense microcracking. We propose here that faults in granites nucleate and propagate by the interaction of tensile microcracks in the following style. During early loading, tensile microcracking occurs randomly, with no significant crack interaction and with no relation to the location or inclination of the future fault. As the load reaches the ultimate strength, nucleation initiates when a few tensile microcracks interact and enhance the dilation of one another. They create a process zone that is a region with closely spaced microcracks. In highly loaded rock, the stress field associated with microcrack dilation forces crack interaction to spread in an unstable manner and recursive geometry. Thus the process zone propagates unstably into the intact rock. As the process zone lengthens, its central part yields by shear and a fault nucleus forms. The fault nucleus grows in the wake of the propagating process zone. The stress fields associated with shear along the fault further enhance the microcrack dilation in the process zone. The analysis shows that faults should propagate in their own plane, making an angle of 20°–30° with the maximum compression axis. This model provides a physical basis for “internal friction,” the empirical parameter of the Coulomb criterion.

Self‐propping and fluid flow in slightly offset joints at high effective pressures

We have made laboratory measurements of joint closure and permeability of both well‐ and poorly mated, laboratory‐produced joints in Westerly granite under joint normal stresses to 160 MPa, appropriate to midcrustal depths. We have also made detailed topographic measurements of the joint surfaces, both before and after pressure testing. The purpose of the study was to characterize and understand the hydraulic behavior of joints under conditions where fluid migration under natural settings is known to occur but where physical conditions, namely high lithostatic load, suggest that the presence of open, fluid‐conducting joints might be improbable. Normal stress was applied by hydrostatic confinement of cylindrical samples, each containing a single axial tensile fracture. Experiments were performed at room temperature under conditions designed to minimize chemical effects of dissolution or precipitation. We found that while a mated joint can be completely closed by the application of high normal stresses, the same joint laterally offset by 0.53 mm remains open and many orders of magnitude more hydraulically conductive than the mated joint even at highest stresses. Detailed topographic observations are consistent with self‐propping of the offset joint. Permanent damage to the surfaces of the offset joint is not widespread but occurs at isolated locales covering about 10% of the surface. Damage is confined to regions of negative (convex upward) curvature, such as summits and the edges of plateaus. Approximately 20% of the joint surface is in wall‐to‐wall contact at 160 MPa, and the flow tortuosity thus induced is probably the cause of the breakdown of the parallel plate approximation for fluid flow in the offset joint.

Micromechanics of the velocity and normal stress dependence of rock friction

Among the second-order effects on friction the most important are those of variable normal stress and of slip velocity. Velocity weakening, which is usually considered the source of the stick-slip instability in rock friction, has been observed in velocity stepping experiments with Westerly granite. The friction change, Δμ, was −0.01 to −0.008 for a tenfold velocity increase. Using normal closure measurements, we observed dilation upon each increase in sliding rate. We also observed, for the first time, time-dependent closure between surfaces during static loading. The dilation that occurred during the velocity stepping experiment was found to be that expected from the static time-dependent closure phenomenon. This change in closure was used to predict friction change with an elastic contact model. The calculated friction change which results from a change in contact area and asperity interlocking, is in good agreement with the observed velocity dependence of steady-state friction. Variable normal stress during sliding has two effects, first in creating new partial slip contacts and locking some existing fully sliding contacts and second in increasing interlocking, for instance when normal load is suddenly increased. As a result, a transient change in friction occurs upon a sudden change in normal load.

A thermo-plastic constitutive law for brittle-plastic behavior of rocks at high temperatures

Mechanical properties of rocks change under the influence of, temperature. Stress at the onset of yielding, ultimate strength, dilatancy, strain hardening and softening, and the confining pressure at brittle-ductile transition are all reduced by the increasing temperature. This study presents a framework of constitutive modeling of thermo-brittle-plastic behavior of rocks which encompasses these changes. The constitutive law is based on a thermo-plasticity theory first proposed for metals byPrager (1958). Two phenomenological mechanisms have been identified as central for the modeling: temperature dependence of the yield locus (thermal softening), and temperature dependence of the strain-hardening function (thermally enhanced ductility). Material parameters for two rocks, Carrara marble and Westerly granite, were determined on the basis of additional hypotheses. These parameters are used in numerical simulations of triaxial tests at different temperatures. The obtained stress-strain curves compare well to the experimental results. The changes with temperature in the stress at the onset of yielding are more accurately reproduced that the evolution of hardening or softening. Suggestions for possible improvements and future research directions are indicated.

Complexities of rock fracture and rock friction from deformation of Westerly granite : Chen, G; Spetzler, H Pure Appl GeophysV140, N1, 1993, P95–121

Complexities of rock fracture and rock friction from deformation of Westerly granite : Chen, G; Spetzler, H Pure Appl GeophysV140, N1, 1993, P95–121