|
|
 |
|||||||||||||||||
|
|||||||||||||||||
 |
|||||||||||||||||
| JOURNAL HOME | HELP | CONTACT PUBLISHER | SUBSCRIBE | ARCHIVE | SEARCH | TABLE OF CONTENTS |
1 Department of Geosciences, The Pennsylvania State University, University Park, Pennsylvania 16827, USA
Correspondence: E-mail: engelder{at}geosc.psu.edu
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONBACKGROUNDDATA GATHERINGMICROCRACK ORIENTATION AND...DISCUSSIONCONCLUSIONSREFERENCES CITED |
|---|
2 and horizontal 3 so that the ratio of least compressive horizontal stress (Shmin) to vertical compressive stress (Sv) is >1 in much of the top 2 km of intracontinental crust. In theory, rocks exhumed from beneath 2 km should carry some record of this stress interchange, and this record is found in the orientation and density of healed, filled, and open micro-cracks in exhumed New England granitoids. Fluid inclusion planes (FIP) of older, healed microcracks are the best developed in a vertical orientation, and younger filled and open microcracks are best developed in the horizontal plane. Lateral unloading during initial isobaric cooling from the solidus of laterally constrained granite allows early microcrack growth once horizontal tension on the microscopic scale develops in response to vertical compression from the overburden load. During exhumation, further relaxation of lateral compressive stress takes place by a combination of decompression and cooling so that 
Shmin/Sv <1. Such behavior preserves a horizontal compression at depths <2 km where horizontal microcracks are found. Excess horizontal compressive stress, a remnant of incomplete relaxation, carries upward right to the bedrock surface where near-surface structures such as stress-relief buckles and topographically related sheet fractures are found. This excess compression is consistent with the abundance of thrust fault focal mechanisms found in the top 2 km of intracontinental crust east of the Rocky Mountain front and south of the U.S. border.
Key Words: granite • microcracks • exhumation • remnant stress • thermoelastic relaxation
|
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONBACKGROUNDDATA GATHERINGMICROCRACK ORIENTATION AND...DISCUSSIONCONCLUSIONSREFERENCES CITED |
|---|
In some instances, near-surface compressive stress is interpreted as residual arising from elastic stresses locked in the rock by forces balancing on either the microscopic (Friedman, 1972; Voight and St. Pierre, 1974) or macroscopic scale (Coates, 1964; Voight, 1974). The problem with any residual stress model is that tensile stress should be present to counterbalance compressive stress in near-surface bedrock, and it is not found in the near surface (Engelder, 1993). This missing tensile stress suggests that some inelastic "buffering" process acts to maintain horizontal compression (McGarr and Gay, 1978). Mechanisms for stress buffering include swelling accompanying water adsorption (Harper, et al., 1979) and crack growth driven by internal stresses that produces large compressive changes in macroscopic stress (Bruner, 1979, 1984). Rather than pursuing a residual stress model reflecting a local equilibrium volume (Varnes and Lee, 1972) or a buffer-related model (Bruner, 1984), this paper examines conditions under which near-surface compressive stress is a manifestation of deep-seated lithostatic stress that has partially but not completely relaxed during exhumation. In this context, near-surface compression is a remnant stress in the sense that it is a deep-seated stress with a tectonic component that has survived exhumation-related thermoelastic relaxation (Voight, 1966; Engelder, 1993).
Attempts to understand the effect of exhumation on state of stress have assumed a crust that can support thermoelastic stresses (e.g., Price, 1966; Narr and Currie, 1982; Turcotte and Schubert, 2002). Exhumation-related horizontal stress arises under uniaxial strain conditions and includes two components that Turcotte and Schubert (2002) call the "thermal effect" and the "elastic effect [as a consequence of erosion]". When acting independently, the former, here called isobaric cooling, leads to tension and is taken as the driving mechanism for joints during exhumation. Action of the latter during exhumation, here called isothermal decompression, may leave a component of horizontal compression in near-surface rocks depending on the pr-exhumation state of stress. Turcotte and Schubert (2002) state that these two effects "are comparable for typical values of the geothermal gradient." The purpose of this paper is to understand the origin of near-surface compressive stress by revisiting the question of whether Turcotte and Schubert's (2002) two effects are comparable. The answer to this question is found in the interpretation of two data sets, one new and one published. The new data set encompasses the orientation and density of three types of microcracks in New England granitoids, and these data serve as a record of the evolution of thermoelastic stress during exhumation. The published set is a compilation of in situ stress data in the upper crust, and these data serve as a control to constrain our interpretation of exhumation-related thermoelastic stress based on microcrack data from New England granitoids.
|
BACKGROUND |
|---|
|
TOPABSTRACTINTRODUCTIONBACKGROUNDDATA GATHERINGMICROCRACK ORIENTATION AND...DISCUSSIONCONCLUSIONSREFERENCES CITED |
|---|
3, is commonly horizontal in the middle portion of the brittle intracontinental crust but equally likely vertical in the upper kilometer or two (Fig. 1). This characteristic of the brittle crust is reflected in earthquake focal mechanism data from the eastern United States where strike-slip and normal fault mechanisms are indicative of horizontal 3 and thrust mechanisms indicate vertical 3. Using the 58 focal mechanisms in the World Stress Map database from the USA east of longitude 104°W, strike-slip faulting is the most prominent mechanism at depths greater than 8 km, whereas thrust faulting is the most prominent mechanism at depths less than 8 km (Fig. 1). In particular, thrust and thrust-strike-slip mechanisms constitute 90% of all data in the top 2 km east of the Rocky Mountain Front. These focal mechanism data come from a region of North America where the maximum horizontal compressive stress, SHmax, is uniformly ENE. This depth-related change in focal mechanisms is akin to an interchange of the orientation of principal stress axes, 3 and 2, in the shallow crust rather than a stress rotation.
|
3 and 2, in the shallow crust appears in global compilations of stress measurements. An upwardly increasing ratio, R, of least horizontal to vertical stress (R = Shmin/Sv with compressive stress positive) is found within the top 2 km of the crust (Brown and Hoek, 1978). R continues to increase upward and becomes extreme within the zone of thermally and topographically induced compressive stress in the top few meters of the crust (Sbar et al., 1984; Martel, 2006). An upwardly increasing R is characteristic of sedimentary basins including regions of normal faulting (Plumb, 1994) and in crystalline basement such as the Bohemian massif, Germany (Brudy et al., 1997), thus indicating that the causal mechanism for the interchange of the orientation of principal stresses (i.e., 2 and 3) is not an artifact of sedimentary rocks. Looking downward into the crust, the trend of R <1 continues into crystalline basement to depths of at least 8.6 km, the deepest in situ stress measurement to date (Brudy et al., 1997; Lund and Zoback, 1999). The same trend carries downward through a combination of sedimentary cover over crystalline basement as seen in the Great Lakes region of North America (Haimson and Doe, 1983). The stress profile showing an increase in R upward through the shallow crust is referred to as the Brown-Hoek stress profile (BHSP) in honor of its discoverers (Brown and Hoek, 1978). In this paper we make the case that the BHSP is a manifestation of an exhumation-related remnant stress.
Total stress in the crust reflects a superposition of components, some of which may be eliminated in searching for the mechanism responsible for the BHSP. First, vertical stress (Sv= g
obz), a function of integrated overburden density, ob, gravity, g, and depth, z, is nearly linear with depth in the upper crust except in the near surface in regions of topographic relief where horizontal compressive stress is high (e.g., Miller and Dunne, 1996; Martel, 2006). Because the upward increase in R starts below depths affected by topographic relief, the BHSP must reflect a mechanism that carries horizontal compressive stress, Shmin, into the top 2 km of the crust. The limits of horizontal stress in the upper crust are governed by frictional strength along fault zones (Byerlee, 1978). Such strength along normal and thrust faults provides lower and upper bounds for the BHSP in an actively deforming Earth (Zoback and Townend, 2001). However, frictional strength is overburden dependent so that friction-related stress is linear with depth and goes to zero in the near surface (Zoback, 2007). Friction does not offer a mechanism for the interchange of the orientation of 2 and 3 in the shallow crust (e.g., Brace and Kolstedt, 1980).
While stress measurements within some Plio-Pleistocene sedimentary basins come from rocks that are being buried for the first time and, hence, are still subject to consolidation (Karig and Hou, 1992), the majority of stress measurements come from either crystalline rocks (Herget, 1993) or sedimentary rocks where lithification terminates consolidation (Plumb, 1994). Many of these older rocks are partially unloaded as a consequence of exhumation as is the case for the western end of the Bohemian massif and the larger North America platform. Unloading takes place with the removal of overburden and its concomitant decrease in vertical stress (i.e., –Sv). Partial or complete exhumation causes a decrease in Shmin as well (i.e., –Shmin). For a shallow crust consistent with the BHSP, Shmin/Sv < 1, and this is also the condition necessary for an interchange of the orientation of 2 and 3 when 3 is horizontal in the deep crust. The guiding axiom of this paper is that such an interchange of 2 and 3 is the manifestation of thermoelastic relaxation as rocks are gradually exhumed (Price, 1966; Voight and St. Pierre, 1974; Haxby and Turcotte, 1976). In this context, thermoelastic relaxation is the response of the horizontal compressive stress (i.e., –Shmin) to a decrease in both vertical stress, –Sv, and temperature, where
|
|
Microcracks
In addition to those that may have propagated under a high-stress anisotropy usually through the superposition of a tectonic stress, micro-cracks are a product of thermoelastic relaxation (e.g., Nur and Simmons, 1970; Plumb et al., 1984; Fleischmann, 1990; Jang and Wang, 1991; Vollbrecht et al., 1991; Wise, 2005). In granite, quartz hosts both intragranular and transgranular microcracks (Kranz, 1983). These are of three general types: open, filled with a foreign mineral, and healed with crystallographically continuous quartz that leaves fluid inclusion "planes" (FIP). The thesis of this paper is that the differences in orientation and density among FIP, filled micro-cracks, and open microcracks in quartz grains reflect the evolution of earth stress accompanying thermoelastic relaxation during exhumation. It is an exhumation-related thermoelastic relaxation that leads to the BHSP, to a unique distribution of intracontinental focal mechanisms, and to the formation of near-surface structures such as sheet fractures, bornhardts, A-tents (or pop-ups), and displaced slabs.
Vertical microcracks commonly constitute a fabric in the upper crust as indicated by data from 200 granite and granite-gneiss quarries in New England (Dale, 1923). Two dominant strikes of vertical microcracks (i.e., NS and EW) are observed throughout much of New England (Wise, 1964). Other regions hosting a regional fabric of vertical and subvertical microcracks include the Piedmont of Virginia (Tuttle, 1949), the Massif Central of France (Lespinasse and Pecher, 1986; Pecher et al., 1985), the Oshima granite of Japan (Takemura et al., 2003), and the Beartooth uplift of Montana (Wise, 2005). Such a fabric is seen along core from wells drilled in Illinois (Kowallis et al., 1987), the Rhine Graben of France (Dezayes et al., 2000), and Japan (Takeshita and Yagi, 2001).
A particularly important, but commonly overlooked aspect to the regional microcrack fabric in granites is the pervasive occurrence of horizontal microcracks as indicated by the orientation of the rift plane (i.e., the quarry direction of easiest splitting) in granitoids of New England (Dale, 1923). The rift plane is horizontal in 96% of the granite quarries from Merrimack Synclinorium as reported by Dale (1923), while 21% of the granites west of the Bronson Hill anticlinorium in Vermont have a horizontal rift (Fig. 2). Farther to the northwest in the Canadian Shield, rift is predominantly horizontal in Precambrian granites (Osborne, 1935).
|
|
DATA GATHERING |
|---|
|
TOPABSTRACTINTRODUCTIONBACKGROUNDDATA GATHERINGMICROCRACK ORIENTATION AND...DISCUSSIONCONCLUSIONSREFERENCES CITED |
|---|
Except for the Chelmsford granite, samples from the quarries were oriented relative to the mutually perpendicular directions used to excavate the rock (Fig. 3). In the language of the quarryman, the rift is the plane of easiest splitting, and the hardway is the plane of greatest resistance to splitting with the grain falling between the extremes in terms of ease of splitting (Wise, 1964; Johnson, 1970; Engelder, 1993). In New England, the hardway is generally vertical, whereas the rift or grain may be horizontal depending on the region (Dale, 1923). Quarries in the Chelmsford, Concord, and Milford granites have a horizontal rift, whereas the quarries in the Barre granite have a vertical rift (Fig. 2).
|
, of quartz is more than three times larger than feldspar (Skinner, 1966), allowing thermal stresses to accumulation at a faster rate per T than feldspar when laterally confined. In each thin section, crack orientations, crack types, crack density, and grain size were recorded in ten or eleven of the largest quartz grains (
1 mm). We examined only the largest quartz grains on the presumption that microcracking was more likely to reflect larger scale stress fields rather than microscopic stress concentrations. However, the irregular shape of microcracking suggests that even in the larger grains, the regional stress field was modified by the irregular shape of the host grain (Fig. 4).
|
|
MICROCRACK ORIENTATION AND DENSITY |
|---|
|
TOPABSTRACTINTRODUCTIONBACKGROUNDDATA GATHERINGMICROCRACK ORIENTATION AND...DISCUSSIONCONCLUSIONSREFERENCES CITED |
|---|
Concord Granite
To depict microcrack development in New England granite, the fabric of the Neo-Acadian Concord granite serves as the standard against which the fabric of others is compared. The Concord was sampled in the Swenson quarry of the Swenson Granite Company, Concord, New Hampshire. During the early twentieth century, the Concord granite district consisted of six quarries, all with sheet fractures that are either subhorizontal or dipping gently but with dip directions that differed by as much as 180° (Dale, 1923). During early operations, grain walls were cut between N40°E and N90°E (Dale, 1923), whereas the modern Swenson quarry cuts its grain wall to the SE.
Quartz grains within the Concord granite contain the three types of microcracks mentioned above. The orientation fabric and relative density of each type is illustrated using a sample cube and an orthographic projection of the three faces of that sample cube (Fig. 5). Often the best view of a microcrack fabric is normal to the quarry hardway for the simple reason that microcracks of both the rift and grain planes are seen in cross section (Fig. 4). Looking normal to the hardway, the FIP are best developed vertically with a strike of ~330°, which is slightly off from the direction of the quarry's grain wall. A secondary set of FIP appears in the rift (horizontal) plane as seen in both vertical (i.e., hardway and grain) sections. The origin of the tilt of both the primary and secondary set of FIP to the NE, as seen normal to the hardway plane, does not correlate with the west-dipping sheet fractures of the Swenson quarry (Dale, 1923). Healed and open microcracks are best developed on the rift (horizontal) plane as seen in both vertical thin sections. The "horizontal" microcracks have a slight tilt in the same direction as the FIP normal to the quarry hardway. Because all the microcracks in each quartz grain were tabulated, it is readily apparent that the density of FIP far exceeds that of the open microcracks which, in turn, exceeds the density of filled microcracks. These observations apply to other granites where FIP are more common than open microcracks. Likewise, there is a preferred growth of open microcracks in the horizontal plane versus a preferred growth of FIP in the vertical orientation.
|
Microcracks in quartz grains of the Pennsylvanian Milford granite, sampled in the Mason quarry, constitute a fabric similar to that within the Concord granite (Fig. 6). In this case, the vertical FIP appear most prominently when looking normal to the rift (horizontal) plane, whereas the less common open microcracks are best developed in the horizontal plane as seen looking normal to the hardway. Filled microcracks only appeared in the vertical orientation and are thus combined with open microcracks. Horizontal FIP are less well developed than in the Concord granite but have about the same density as horizontal open microcracks. Vertical open cracks are less common yet, and scatter as is typical for a view normal to one preferred orientation of microcracks.
|
|
Bethlehem Granite
The one outcrop sample of this study is the Acadian Bethlehem granite, which displays a foliation of biotite dipping at 45° toward the SSE. Sheet fractures are poorly developed in this outcrop at the Grantham rest stop on Interstate 89, Vermont. The Bethlehem granite carries the same microcrack fabric as the three previous granites and thus shows a vertical FIP and horizontal open microcracks (Fig. 8). An additional set of vertical FIP have grown normal to the most prominent set. Filled and open microcracks in the vertical orientation show little tendency to cluster in a preferred orientation. Subhorizontal filled and open microcracks show a tendency to dip in the opposite direction from the foliation (Fig. 8). Based on the microcrack fabric, one might predict that a quarry in the Bethlehem granite would also be characterized by a horizontal rift.
|
|
|
Microcrack Density
A quantitative expression of fabric development is reflected in crack density data from these six samples of Paleozoic (i.e., #/mm) (Table 1). In terms of thin section orientation, the most densely developed microcracks are vertical FIP as seen in horizontal thin sections. Horizontal FIP are less dense. The most densely developed open microcracks are horizontal as seen in vertical thin sections. In vertical thin sections, it is seen that FIP are predominantly vertical cracks (Fig. 4). These numbers confirm the qualitative observations using sample cubes (Figs. 5–10).
|
|
DISCUSSION |
|---|
|
TOPABSTRACTINTRODUCTIONBACKGROUNDDATA GATHERINGMICROCRACK ORIENTATION AND...DISCUSSIONCONCLUSIONSREFERENCES CITED |
|---|
3 when the granite was deep and a vertical 3 after exhumation carried the granite to shallow levels of the crust. Such an interchange in orientation of 3 is consistent with an upper brittle crust characterized by the BHSP.
Other studies of microcracking in granite report the same paragenetic sequence starting with vertical FIP and ending with open, horizontal microcracks (e.g., Lespinasse and Pecher, 1986; Laubach, 1989). Within the Meso zoic granites of New England, FIP have been interpreted as propagating during "post-emplacement cooling," whereas open microcracks develop during "exhumation by recracking (vertical) healed fluid inclusion planes" (i.e., Fleischmann, 1990). Vertical FIP and open, horizontal microcracks are found in the Blanco Perla granite of Spain (Durucan et al., 2000). The same relative density of vertical FIP and horizontal microcracks is documented in the Oshima granite, Japan (Takemura et al., 2003). Even when the rift is vertical or not well developed, as is the case for other Japanese granites (and the Barre granite), the horizontal plane carries open microcracks (Chen et al., 1999). The granites of the western Bohemian massif, Germany, contain vertical FIP that are interpreted as consequence of "thermal cracking" at crustal levels >5 km, whereas open, horizontal microcracks form at <5 km where "tectonic and gravitational stresses" are key (Vollbrecht et al., 1991). We will make the case that while the driving stress for open, horizontal microcracks (SHmax) may have a tectonic component, it is the exhumation-related preservation of the horizontal stresses in the form of remnant stresses that leads to an interchange of 2 and 3 and gives rise to the BHSP.
There is a tendency for the growth of a modest number of horizontal FIP in each granite with the exception of Barre. Like the focal mechanisms from the eastern USA, which indicate some spatial variation in R between 8 and 3 km (Fig. 1), the FIP suggest a temporal variation in R. The simplest explanation is that exhumation carried the granite into the upper regime of R >1 before temperatures cooled to the point that microcrack healing ceased, the temperature for which may be as low as 85 °C (i.e., Laubach, 1989). Another explanation might involve the superposition of a component of tectonic shortening that would drive the interchange of stress principal at a deeper crustal level than seen in the BHSP.
The Stress that Drives Microcracks
Microcracks are a manifestation of absolute tension on the microscopic scale even when the host granite is subject to the large compression found several km below the Earth's surface. One candidate for driving microcracks is the tensile stress arising from mismatches between the thermoelastic properties of minerals within granite (Nur and Simmons, 1970; Savage, 1978; Bruner, 1984). Thermoelastic stresses are generated when grains lock together and act as lateral constraints on nearest neighbors during either a temperature change or a stress change or some combination of the two. Because the coefficient of thermal expansion of quartz exceeds that of feldspar, cooling of granite will lead to tensile stress in the quartz. Calculations involving an idealized granite show that a 300 °C temperature drop generates a change in stress, = –480 MPa in quartz, a stress sufficient to negate the effect of overburden compression and trigger crack propagation from all but the smallest of flaws in a quartz grain (Savage, 1978). An equally impressive suite of microcracks is produced by stress relief (i.e., decompression) upon removal of a core from depth, a consequence of the mismatch of elastic properties among locked grains (Carlson and Wang, 1986).
If thermoelastic mismatches on the microscopic scale operate without the superposition of body forces like gravity and other mechanisms for generating a stress anisotropy, micro-cracking in adjacent quartz grains of isotropic grain orientation are unlikely to assume a preferred orientation. A microcrack fabric is the product of the superposition of an overburden stress and/or tectonic stress upon thermoelastic stress (Jang and Wang, 1991). An axially symmetric anisotropy may be generated without the help of a tectonic stress, if thermoelastic relaxation takes place within a laterally constrained granite body (Narr and Currie, 1984). The FIP in New England granite develop a vertical fabric because of the presence of a post-solidus tectonic stress during cooling through the solidus. Here, tectonic stress arises through any process that causes a stress anisotropy in the horizontal plane (i.e., SHmax > Shmin) (Engelder, 1993). When granite is subject to a significant stress anisotropy, several mechanisms are likely responsible for the generation of microcracks including wedging grain boundaries, sliding along planes of weakness, elastic mismatches, and pore crushing (Wong, 1982; Hazzard et al., 2000). However, it may be a mistake to think that either the vertical FIP or horizontal microcracks within New England granites were "driven" by tectonic stress, per se.
Vertical Microcracks
Aside from the usual mechanisms for micro-crack generation under a stress anisotropy, another possibility for the generation of early, vertical microcracks is axial loading across vertical grain diameters (Fig. 11A). Compression in the form of a vertical load, Fv, across the vertical diameter can produce a horizontal tension within an unsupported short cylinder (Hondros, 1959). This suggests the possibility that, under the right conditions, quartz grains would develop vertical opening mode cracks, parallel to the gravitational body force. While it is a stretch to argue that the shape and interlocking of quartz in granite are natural examples of unsupported cylinders, the concept is worthy. In this model, thermoelastic relaxation of horizontal stress serves only to relieve the lateral constraint but not generate the tensile stress. As long as lateral stress is compressive, however small, problems such as buckling of a stack of grains do not arise (Fig. 11A).
|
h, at the central point on the vertical diameter of a cylinder laying on its side is
|
|
, is greater than a value, 2 >20° (Wang et al., 2004).
From Equation 2, the internal tension is proportional to the vertical load, but it is not immediately obvious that this internal tension will drive microcracks. The size of a "Griffith" flaw necessary for microcrack propagation within quartz grains is given by
|
|
The appeal of this model is that microscopic tensile stress within quartz grains are generated without the necessity of a net tension transmitted across the entire granite body. A net tension across the entire granite body would inevitably produce large vertical joints, something not seen in quarries such as the Mason (Fig. 3). The long-term uniaxial compressive strength of granite is greater than 100 MPa and much more when slightly confined (Eberhardt et al., 1999; Szczepanik et al., 2003). With its strength and a modest lateral confinement, granite will sustain the weight of overburden without collapsing under shear failure to depths approaching 8 km. However, at loads of about half their ultimate strength in laboratory tests, granite samples develop incipient microcracks (Brace et al., 1966). This accounts for growth of vertical microcracks in plutons cooling from the solidus. While tectonic stress generates a modest stress anisotropy in the horizontal plane, the responsible stress for crack propagation is vertical and comes from the large anisotropy developed between the vertical direction and horizontal plane.
Evolution of Stress in Granite
One of the most reliable rules for crack propagation is that cracks align normal to 3 during propagation and will curve during growth to find this preferred orientation (Pollard and Segall, 1987). From this rule, we know that early, deep microcrack propagation in granite took place where 3 was horizontal and late, shallow microcrack propagation took place where 3 was vertical. Aside from our argument involving microcrack paragenesis, a qualitative mechanical argument pointing to deeper propagation normal to a horizontal 3 comes from the spacing of FIPs. The traces of very closely spaced FIPs ("close" means the distance between the FIPs is small relative to their trace lengths) is diagnostic of the driving stress being small relative to the difference between the ambient principal stresses (Olson and Pollard, 1989). The ambient stress at the time the FIPs formed must have been highly anisotropic. A large stress anisotropy is characteristic of propagation at great depth where overburden stress (Sv) remains constant and high while horizontal stress is reduced by cooling.
A second general rule for crack propagation is that the driving stress comes from one of two general sources: absolute tension and internal fluid pressure (Pollard and Aydin, 1988; Bergbauer and Martel, 1999). Some have argued that super-hydrostatic fluid pressure is the primary driving stress for initial microcrack propagation in granite (Takeshita and Yagi, 2001). If this were so, fluid inclusions in quartz grains should have trapping pressures and temperatures at conditions found near the solidus of post-tectonic granites. Yet, the earliest fluid inclusions generally have trapping temperatures more than 100 °C below the solidus (i.e., Jang and Wang, 1991).
Small fluid-filled cavities trapped within quartz of granite undoubtedly serve as one flaw type capable of triggering initial microcrack propagation in subsolidus quartz. While fluids within the cavities could even lend a component to crack driving stress, they are not interconnected and have no mechanism for self-generating the higher fluid pressure required of hydraulic fracture. Rapid cooling relieves fluid pressure in inclusions and moves the host quartz grains away from a state favoring decrepitation of primordial fluid inclusions. For this reason, tension from gravitational loading (i.e., Equation 2), requires thermoelastic relaxation in a laterally constrained body before initiation of post-solidus microcracking, particularly the FIPs. Such relaxation occurs after a temperature drop of more than 100 °C below the solidus (Jang and Wang, 1991; Vollbrecht et al., 1991).
Lithostatic Stress
Because magma has relatively low shear strength under static conditions, tectonic stress rapidly dissipates and granites solidify from magmas under a stress state close to lithostatic stress, if not exactly lithostatic, SL, with
|
|
|
tShmin corresponding to a temperature change T is
|
|
= 0.15 (Birch, 1966), and the coefficient of thermal expansion is t = 8 x 10–6 °C–1 (Skinner, 1966). With these thermoelastic properties, the thermoelastic relaxation occurs at a rate between –15 MPa and –66 MPa per 100 °C decrease. Microcracking is expected where the thermal stress change overcomes the sum of the material tensile strength, t, (Nasseri et al., 2005) and the compressive lithostatic stress, SL, such that
|
|
Using the typical thermoelastic properties (i.e., E = 70 GPa) and Sv = SL = 159 MPa (assuming z 6 km with an overburden density of 2.65 g/cm3), a –T of 235 °C is required to completely negate the initial lithostatic stress after cooling through the solidus. This estimate of temperature drop is larger for granite with a lower E or higher . Of course, microcracking is possible long before the lithostatic stress is completely negated. Fluid inclusions in the healed microcracks suggest that crack healing began at temperatures of ~400 °C and that it was complete at ~200 °C assuming a relatively simple cooling history for Precambrian granite of the Illinois basin (Kowallis et al., 1987). In this case, healed microcracks are not found at higher temperatures because T >200 °C is required for microcrack initiation. This is consistent with a cap of ~400 °C for trapping temperature of fluid inclusions in post-tectonic granite of New England (Winslow et al., 1994). Finally, isobaric cooling sets up a state of stress consistent with the deep portion of the BHSP as horizontal stress decreases without a change in the vertical stress while generating a stress anisotropy favoring microcracking prior to the development of pluton-wide absolute tension. The fabric in FIP indicates the presence of a tectonic stress that is responsible for SHmax > Shmin.
Decompression and the BHSP
Isobaric cooling takes granite to a state of stress where Shmin < Sv, a state common in the brittle crust below a depth of 2 km (Brown and Hoek, 1978; Plumb, 1994). This is the starting point for exhumation driven thermoelastic relaxation, which reflects components of both decompression and cooling. Taken separately, isothermal decompression is the sum of the horizontal compressive stress change developed during the removal of laterally confined overburden
|
|
|
|
z is negative when a thickness of the crust removed by erosion, a is the radius of the Earth after erosion, c is the density of the crust, and m is the density of the mantle (Haxby and Turcotte, 1976). An early analysis pointed out that exhumation-related decompression could lead to a large excess horizontal compressive stress (Voight, 1966).
To achieve a stress state consistent with the interchange of the orientation of 2 and 3 and the BHSP, the following condition must be met: the rate of thermoelastic relaxation (i.e., Shmin/z), which also includes the effect of cooling along a geothermal gradient, must be a fraction of the overburden gradient so that
|
|
z is negative during exhumation. No tectonic term is present in Equation 9 so that Shmin = SHmax. Equation 9 means that Shmin/Sv <1 during exhumation.
Although we conclude that Shmin/Sv <1 for the development of the BHSP, we first need to define the range of Shmin/Sv (= R*) that allows a thermoelastic relaxation consistent with the BHSP starting at some initial stress representative of the BHSP, say R0 = (Shmin/Sv)0 = 0.73 at some reference depth z0 = 4 km. To do this, we calculate R = f(z) according to
|
|
Shmin = Shmin – Shmin0, Sv = Sv – Sv0 and z = depth (Fig. 13). If R* is a large fraction of the overburden gradient (e.g., 0.77 in Fig. 13A), tensile Shmin (indicated by a negative R) will develop during exhumation at a depth of ~200 m, and there will be no interchange of vertical 2 and horizontal 3, a situation inconsistent with the BHSP. R* <0.7 leads to an interchange of 2and 3 (curves bending right in Fig. 13A) and a stress profile consistent with the BHSP. The depth of the stress interchange is found where the curves of Figure 13 cross R = 1. For smaller values of R* starting at R0 = 0.73, a deeper onset of relaxation yields a larger R in the near surface and a deeper interchange of vertical 2 and horizontal 3 (Fig. 13B). When R* <0.6, Shmin in the upper km becomes large, however, topographic factors would come into play to limit the values of Shmin near the surface (Martel, 2006). In summary, values of R* in the range of 0.6–0.7 yield R-curves that best match the BHSP.
|
, , E, and the geothermal gradient T/z all affect R*
|
|
. The stiffest granite would enter the tensile field and fail by vertical jointing rather than follow BHSP into the uppermost crust. To generate the BHSP on a geothermal gradient near 20 °C/km, the granite body must have an E on the order of 40 GPa, = 0.000008 C°–1 and 0.1 < <0.15. These are representative properties for granite (Haas, 1989). For geothermal gradients >25 °C/km, relaxation must start at a much shallower depths to yield the BHSP.
|
The data compilation leading to the BHSP paradigm shows interchange of 2 and 3 at very shallow depths in some instances (Fig. 1). Likewise, our calculations show that the evolution of the BHSP is sensitive to rock properties and the geothermal gradient. Given these observations, it is not surprising that rift planes are sometimes vertical as is the case for the Barre granite, which may reflect an R* >0.7 (Fig. 13). The formation of vertical neotectonic joints also reflects a relatively large R* during the exhumation of sedimentary basins (e.g., Hancock and Engelder, 1989).
Near-Surface Structures and Earthquakes
Intracontinental crust carries a horizontal compression that persists to surface bedrock. Of course, the principal stresses are magnified and tilted by topography that is responsible for sheet fracturing (Miller and Dunne, 1996; Martel, 2006). Horizontal compression is responsible for other structures including bornhardts (Twidale and Bourne, 1998), A-tents (or pop-ups) (Ericson and Olvmo, 2004), and displaced slabs (Twidale and Bourne, 2000). It may also be a mechanism for effectively breaking bedrock apart and feeding it into the C-horizon of soil. Some data suggest that "microcracks commonly parallel sheets even where the sheets are steeply inclined" (Holzhausen, 1989). The data in the present paper suggest that while horizontal sheet fracturing is parallel to horizontal microcracks in the case of the Mason quarry (Fig. 3), such parallelism is not a universal rule as seen at the Kittredge quarry (Fig. 9).
The question about the timing of sheet fracturing relative to horizontal microcrack propagation persists. Horizontal to subhorizontal microcracking is pervasive and does not seem to follow topography in the same manner as sheet fracturing. Macroscopic tension is developed by topography and relieved by sheet fracturing. Microcracking is a manifestation of microscopic tension that may develop even in the presence of a small but vertical compressive stress. Although we invoke the "Brazil test mechanism" for microcrack growth amounting to a couple of grain diameters long, the length of the macroscopic joints suggests that they propagated in an environment of absolute tension by the type presented by topographic perturbations (Miller and Dunne, 1996; Martel, 2006). In this scenario, horizontal microcracking is a deeper phenomenon in the upper crust than sheet fracturing.
If the remnant stress mechanism operates globally, particularly in intracontinental settings as indicated by the BHSP, it might affect the distribution of earthquakes in the upper crust (<2 km). Certainly, in the World Stress Map database for the USA east of longitude 104°W, this is the case, with 90% of the mechanisms reflection thrust or thrust-strike slip earthquakes for events of 2 km or less (Fig. 1). The Canadian data set is not as a clear in this matter, although the two earthquakes <2 km are thrust mechanisms. This observation is, however, at odds with a California data set showing both P and T axes in the horizontal plane in the top 1.5 km of the crust (Bokelmann and Beroza, 2000).
|
CONCLUSIONS |
|---|
|
TOPABSTRACTINTRODUCTIONBACKGROUNDDATA GATHERINGMICROCRACK ORIENTATION AND...DISCUSSIONCONCLUSIONSREFERENCES CITED |
|---|
Shmin/Sv <1 so that the state of stress becomes SHmax > Shmin >> Sv in the near surface. The interchange of 2 and 3 leading to the BHSP takes place as long as the Young's modulus of the granite is on the order of 30–40 GPa. A stress state of SHmax > Shmin >> Sv is consistent with the growth of late-stage horizontal microcracks. Our analysis leads to the conclusion that tectonic stresses are not responsible for the interchange of 2 and 3 in the upper crust. If tectonic stress is present in the near surface as is suggested by SHmax > Shmin, it is a remnant stress carried to the surface during exhumation. Otherwise, tectonic stress would go to zero in the near surface as suggested by Zoback (2007). Thermoelastic relaxation leads to a remnant stress and the BHSP that is consistent with the depth distribution of earthquake focal mechanisms from the stable platform of the USA portion of North America. Finally, the BHSP is characteristic of the upper crust because the two components of exhumation-related horizontal stress that Turcotte and Schubert (2002) call the "thermal effect" and the "elastic effect [as a consequence of erosion]" are, in detail, not comparable.
|
ACKNOWLEDGMENTS |
|---|
|
REFERENCES CITED |
|---|
|
TOPABSTRACTINTRODUCTIONBACKGROUNDDATA GATHERINGMICROCRACK ORIENTATION AND...DISCUSSIONCONCLUSIONSREFERENCES CITED |
|---|
Adams, J. 1982, Stress-relief buckles in the McFarland quarry, Ottawa: Canadian Journal of Earth Sciences, v. 19, p. 1883– 1887.[GeoRef]
Adams, J. 1989, Postglacial faulting in Eastern Canada: Nature, origin and seismic hazard implications: Tectonophysics, v. 163, p. 323– 331, doi: 10.1016/0040-1951(89)90267-9.[CrossRef][Web of Science][GeoRef]
Bergbauer, S., and Martel, S.J. 1999, Formation of joints in cooling plutons: Journal of Structural Geology, v. 21, p. 821– 825, doi: 10.1016/S0191-8141(99)00082-6.[CrossRef][Web of Science][GeoRef]
Birch, F. 1966, Compressibility: Elastic constants, in Clark S.P. Jr. Handbook of physical constants: Geological Society of America Memoir 97, p. 97– 173.
Bokelmann, G.H.R., and Beroza, G.C. 2000, Depth-dependent earthquake focal mechanism orientation: Evidence for a weak zone in the lower crust: Journal of Geophysical Research, v. 105, p. 21,683– 21,695, doi: 10.1029/2000JB900205.[CrossRef]
Brace, W.F., and Kohlstedt, D.L. 1980, Limits on lithospheric stress imposed by laboratory experiments: Journal of Geophysical Research, v. 85, p. 6248– 6252, doi: 10.1029/JB085iB11p06248.[GeoRef]
Brace, W.F., Paulding, B., and Scholz, C.H. 1966, Dilatancy in the fracture of crystalline rocks: Journal of Geophysical Research, v. 71, p. 3939– 3954.[GeoRef]
Bradley, D.C., Tucker, R.D., Lux, D.R., Harris, A.G., and McGregor, D.C. 2000, Migration of the Acadian Orogen and Foreland Basin across the northern Appalachians of Maine and adjacent areas: U.S. Geological Survey Professional Paper 1624, 49 p.
Brown, E.T., and Hoek, E. 1978, Trends in relationships between measured in situ stresses and depth: International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, v. 15, p. 211– 215, doi: 10.1016/0148-9062(78)91227-5.[CrossRef]
Brudy, M., Zoback, M.D., Fuchs, K., Rummel, F., and Baumgartner, J. 1997, Estimation of the complete stress tensor to 8 km depth in the KTB scientific drill holes: Implications for crustal strength: Journal of Geophysical Research, v. 102, p. 18,453– 18,475, doi: 10.1029/96JB02942.[CrossRef]
Bruner, W.M. 1979, Crack growth and the thermoelastic behavior of rocks: Journal of Geophysical Research, v. 84, p. 5578– 5590, doi: 10.1029/JB084iB10p05578.[CrossRef][GeoRef]
Bruner, W.M. 1984, Crack growth during unroofing of crustal rocks: Effects on thermoelastic behavior and near-surface stresses: Journal of Geophysical Research, v. 89, p. 4167– 4184, doi: 10.1029/JB089iB06p04167.[GeoRef]
Byerlee, J. 1978, Friction in rocks: Pure and Applied Geophysics, v. 116, p. 615– 626, doi: 10.1007/BF00876528.[CrossRef][Web of Science][GeoRef]
Carlson, S.R., and Wang, H.F. 1986, Microcrack porosity and in situ stress in Illinois borehole UPH 3: Journal of Geophysical Research, v. 91, p. 10,421– 10,428, doi: 10.1029/JB091iB10p10421.[CrossRef]
Chen, Y., Nishiyama, T., Kusuda, H., Kita, H., and Sato, T. 1999, Correlation between microcrack distribution patterns and granitic rock splitting planes: International Journal of Rock Mechanics and Mining Sciences, v. 36, p. 535– 541, doi: 10.1016/S0148-9062(99)00014-5.[CrossRef][GeoRef]
Coates, D.F. 1964, Residual stress in rocks, in Judd W.R. ed., State of stress in the Earth's crust: Proceedings of the International Conference, 1–14 June 1963, Santa Monica, California: New York Elsevier p. 679– 688.
Dale, T.N. 1923, The commercial granites of New England: U.S. Geological Survey Bulletin 738, 488 p.
DeGraff, J.M., and Aydin, A. 1987, Surface morphology of columnar joints and its significance to mechanics and direction of joint growth: Geological Society of America Bulletin, v. 99, p. 605– 617, doi: 10.1130/0016-7606(1987)99<605:SMOCJA>2.0.CO;2.
Dezayes, C., Villemin, T., and Pêcher, A. 2000, Microfracture pattern compared to core-scale fractures in the borehole of soultz-sous-Forêts granite, Rhine graben, France: Journal of Structural Geology, v. 22, p. 723– 733, doi: 10.1016/S0191-8141(00)00003-1.[CrossRef][Web of Science][GeoRef]
Douglass, P.M., and Voight, B. 1969, Anisotropy of granites—A reflection of microscopic fabric: Geotechnique, v. 19, p. 376– 398.[Web of Science][GeoRef]
Durucan, S., Korre, A., and Diehl, M. 2000, Classification of micro-geoparametric parting planes in granites: International Journal of Surface Mining, Reclamation, and Environment, v. 14, p. 103– 119, doi: 10.1080/13895260008953307.[CrossRef]
Eberhardt, E., Stead, D., and Stimpson, B. 1999, Quantifying progressive pre-peak brittle fracture damage in rock during uniaxial compression: International Journal of Rock Mechanics and Mining Sciences, v. 36, p. 361– 380, doi: 10.1016/S0148-9062(99)00019-4.[CrossRef][GeoRef]
Engelder, T. 1984, The time-dependent strain relaxation of Algerie granite: International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, v. 21, p. 63– 73, doi: 10.1016/0148-9062(84)91174-4.
Engelder, T. 1993, Stress regimes in the lithosphere: Princeton, New Jersey Princeton Press 451 p.
Ericson, K., and Olvmo, M. 2004, A-tents in the central Sierra Nevada, California: A geomorphological indicator of tectonic stress: Physical Geography, v. 25, p. 291– 312, doi: 10.2747/0272-3646.25.4.291.[CrossRef][Web of Science][GeoRef]
Fleischmann, K.H. 1990, Rift and grain in two New Eng-land granites: Journal of Geophysical Research, v. 95, p. 21,463– 21,474, doi: 10.1029/JB095iB13p21463.[CrossRef]
Friedman, M. 1972, Residual elastic strain in rocks: Tectonophysics, v. 15, p. 297– 330, doi: 10.1016/0040-1951(72)90093-5.[CrossRef][Web of Science][GeoRef]
Friedman, M., and Bur, T.R. 1974, Investigation of the relations among residual strain, fabric, fracture and ultrasonic attenuation and velocity in rocks: International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, v. 11, p. 221– 234, doi: 10.1016/0148-9062(74)90129-6.[CrossRef]
Haas, C.J. 1989, Static stress-strain relationships, in Touloukian Y.S., Judd W.R., Roy R.F. eds., Physical properties of rocks and minerals: CINDAS Data Series on Material Properties, v. II-2, p. 123– 176.
Haimson, B.C., and Doe, T.W. 1983, State of stress, permeability, and fractures in the Precambrian granite of northern Illinois: Journal of Geophysical Research, v. 88, p. 7355– 7372, doi: 10.1029/JB088iB09p07355.[GeoRef]
Hancock, P.L., and Engelder, T. 1989, Neotectonic joints: Geological Society of America Bulletin, v. 101, p. 1197– 1208, doi: 10.1130/0016-7606(1989)101<1197:NJ>2.3.CO;2.
Harper, T.R., Appel, G., Pendleton, M.W., Szmanski, J.S., and Taylor, R.K. 1979, Swelling strain development in sedimentary rocks in northern New York: International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, v. 16, p. 271– 292, doi: 10.1016/0148-9062(79)90239-0.[CrossRef]
Haxby, W.F., and Turcotte, D.L. 1976, Stresses induced by the addition or removal of overburden and associated thermal effects: Geology, v. 4, p. 181– 184, doi: 10.1130/0091-7613(1976)4<181:SIBTAO>2.0.CO;2.
Hazzard, J.F., Young, R.P., and Maxwell, S.C. 2000, Micromechanical modeling of cracking and failure in brittle rocks: Journal of Geophysical Research, v. 105, p. 16,683– 16,697, doi: 10.1029/2000JB900085.[CrossRef]
Herget, G. 1993, Rock stresses and rock stress monitoring in Canada, in Hudson J.A. ed., Rock testing and site characterization: Comprehensive rock engineering: Oxford Pergamon Press p. 473– 496.
Holzhausen, G.R. 1989, Origin of sheet structures, 1, Morphology and boundary conditions: Engineering Geology, v. 27, p. 225– 278, doi: 10.1016/0013-7952(89)90035-5.[CrossRef][Web of Science][GeoRef]
Hondros, G. 1959, The evaluation of Poisson's ratio and the modulus of materials of low tensile resistance by the Brazilian (indirect tensile) test with particular reference to concrete: Australian Journal of Applied Science, v. 10, p. 243– 268.
Hooker, V.E., and Johnson, C.F. 1969, Near-surface horizontal stresses, including the effects of rock anisotropy: Washington, D.C., Report of Investigations 7224, U.S. Bureau of Mines, 29 p.
Jahns, R.H. 1943, Sheet structure in granites: Its origin and use as a measure of glacial erosion in New England: The Journal of Geology, v. 51, p. 71– 98.[Web of Science][GeoRef]
Jang, B.-A., and Wang, H.F. 1991, Micromechanical modeling of healed crack orientations as a paleostress indicator: Application to Precambrian granite from Illinois and Wisconsin: Journal of Geophysical Research, v. 96, p. 19,655– 19,664, doi: 10.1029/91JB01938.[CrossRef]
Johnson, A.M. 1970, Physical processes in geology: New York Freeman, Cooper and Company 577 p.
Karig, D.E., and Hou, G. 1992, High-stress consolidation experiments and their geological implications: Journal of Geophysical Research, v. 97, p. 289– 300, doi: 10.1029/91JB02247.[GeoRef]
Kowallis, B.J., Wang, H.F., and Jang, B.A. 1987, Healed microcrack orientations in granite from Illinois borehole UPH-3 and their relationship to the rocks stress history: Tectonophysics, v. 135, p. 297– 306, doi: 10.1016/0040-1951(87)90114-4.[CrossRef][Web of Science][GeoRef]
Kranz, R.L. 1983, Microcracks in review: Tectonophysics, v. 100, p. 449– 480, doi: 10.1016/0040-1951(83)90198-1.[CrossRef][Web of Science][GeoRef]
Laubach, S.E. 1989, Paleostress directions from the preferred orientation of closed microfractures (fluid-inclusion planes) in sandstone, East Texas basin, U.S.A: Journal of Structural Geology, v. 11, p. 603– 612, doi: 10.1016/0191-8141(89)90091-6.[CrossRef][Web of Science][GeoRef]
Lawn, B. 1993, Fracture of brittle solids: Second edition: Cambridge Cambridge University Press 378 p.
Lespinasse, M., and Pecher, A. 1986, Microfracturing and regional stress field: A study of the preferred orientations of fluid inclusion planes in a granite from the Massif Central, France: Journal of Structural Geology, v. 8, p. 169– 180, doi: 10.1016/0191-8141(86)90107-0.[CrossRef][Web of Science][GeoRef]
Lespinasse, M., Désindes, L., Fratczak, P., and Petrov, V. 2005, Microfissural mapping of natural cracks in rocks: Implications for fluid transfers quantification in the crust: Chemical Geology, v. 223, p. 170– 178, doi: 10.1016/j.chemgeo.2005.05.009.[CrossRef][Web of Science][GeoRef]
Lund, B., and Zoback, M.D. 1999, Orientation and magnitude of in situ stress to 6.5 km depth in the Baltic Shield: International Journal of Rock Mechanics and Mining Sciences, v. 36, p. 169– 190, doi: 10.1016/S0148-9062(98)00183-1.[CrossRef][GeoRef]
Martel, S.J. 2006, Effect of topographic curvature on near-surface stresses and application to sheeting joints: Geophysical Research Letters, v. 33, L01208, 5 p.
Martin, R.J. 1972, Time-dependent crack growth in quartz and its application to the creep of rocks: Journal of Geophysical Research, v. 77, p. 1406– 1419, doi: 10.1029/JB077i008p01406.[CrossRef][GeoRef]
McGarr, A., and Gay, N.C. 1978, State of stress in the Earth's crust: Annual Review of Earth and Planetary Sciences, v. 6, p. 405– 436, doi: 10.1146/annurev.ea.06.050178.002201.[CrossRef][Web of Science][GeoRef]
Miller, D.J., and Dunne, T. 1996, Topographic perturbations of regional stresses and consequent bedrock fracturing: Journal of Geophysical Research, v. 101, p. 25,523– 25,536, doi: 10.1029/96JB02531.[CrossRef]
Narr, W., and Currie, J.B. 1982, Origin of fracture porosity—Example from Altamont field, Utah: American Association of Petroleum Geologists Bulletin, v. 66, p. 1231– 1247.[Abstract]
Nasseri, M.H.B., Mohanty, B., and Robin, P.-Y.F. 2005, Characterization of microstructures and fracture toughness in five granitic rocks: International Journal of Rock Mechanics and Mining Sciences, v. 42, p. 450– 460, doi: 10.1016/j.ijrmms.2004.11.007.[CrossRef][GeoRef]
Nur, A., and Simmons, G. 1970, The origin of small cracks in igneous rocks: International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, v. 7, p. 307– 314, doi: 10.1016/0148-9062(70)90044-6.[CrossRef]
O'Connell, R.J., and Budiansky, B. 1974, Seismic velocities in dry and saturated cracked solids: Journal of Geophysical Research, v. 79, p. 5412– 5426, doi: 10.1029/JB079i035p05412.[GeoRef]
Olson, J.E., and Pollard, D.D. 1989, Inferring paleostress from natural fracture patterns: A new method: Geology, v. 17, p. 345– 348, doi: 10.1130/0091-7613(1989)017<0345:IPFNFP>2.3.CO;2.
Osborne, F.F. 1935, Rift, grain, and hardway in some Precambrian granites, Quebec: Economic Geology and the Bulletin of the Society of Economic Geologists, v. 30, p. 540– 551.
Pecher, A., Lespinasse, M., and Leroy, J. 1985, Relations between fluid inclusion trails and regional stress field: A tool for fluid chronology—An example of an intragranitic uranium ore deposit (northwest Massif Central, France): Lithos, v. 18, p. 229– 237, doi: 10.1016/0024-4937(85)90027-1.[CrossRef][Web of Science][GeoRef]
Plumb, R.A. 1994, Variations of the least horizontal stress magnitude in sedimentary rocks, in Nelson P.P., Laubach S.E. eds., Rock mechanics models and measurements: Challenges from industry: Rotterdam, Netherlands A.A. Balkema p. 71– 78.
Plumb, R.A., Engelder, T., and Yale, D. 1984, Near surface in situ stress, 3. Correlation with microcrack fabric within the New Hampshire granites: Journal of Geophysical Research, v. 89, p. 9350– 9364, doi: 10.1029/JB089iB11p09350.[CrossRef][GeoRef]
Pollard, D.D., and Aydin, A. 1988, Progress in understanding jointing over the past century: Geological Society of America Bulletin, v. 100, p. 1181– 1204, doi: 10.1130/0016-7606(1988)100<1181:PIUJOT>2.3.CO;2.
Pollard, D.D., and Segall, P. 1987, Theoretical displacements and stresses near fractures in rock: With applications to faults, joints, veins, dikes, and solution surfaces, in Atkinson B. ed., Fracture mechanics of rock: Orlando Academic Press p. 227– 350.
Price, N.J. 1966, Fault and joint development in brittle and semi-brittle rock: London Pergamon Press 176 p.
Price, N.J. 1979, Fracture patterns and stresses in granites: Geoscience Canada, v. 6, p. 209– 212.[Web of Science][GeoRef]
Ranalli, G., and Chandler, T.E. 1975, The stress field in the upper crust as determined from in situ measurements: Geologische Rundschau, v. 64, p. 653– 674, doi: 10.1007/BF01820688.[GeoRef]
Robinson, P., Tucker, R.D., Bradley, D., Berry, H.N.. IV, and Osberg, P.H. 1998, Paleozoic orogens in New England, USA: Geologiska Föreningens i Stockholm Förhandlingar (GFF), v. 120, p. 119– 148.
Savage, W.Z. 1978, The development of residual stress in cooling rock bodies: Geophysical Research Letters, v. 5, p. 633– 636, doi: 10.1029/GL005i008p00633.[CrossRef][Web of Science][GeoRef]
Sbar, M.L., Richardson, R.M., Flaccus, C., and Engelder, T. 1984, Near-surface in situ stress: 1. Strain relaxation measurements along the San Andreas fault in southern California: Journal of Geophysical Research, v. 89, p. 9323– 9332, doi: 10.1029/JB089iB11p09323.[CrossRef][GeoRef]
Skinner, B.J. 1966, Thermal expansion, in Clark S.P. Jr. Handbook of physical constants: Geological Society of America Memoir 97, p. 75– 96.
Smith, D. L., and Evans, B. 1984, Diffusional crack healing in quartz: Journal of Geophysical Research, p. 89, p. 4125– 4135.
Szczepanik, Z., Milne, D., Kostakis, K., and Eberhardt, E. 2003, Long term laboratory strength tests in hard rock, in Handley M., Stacey D. Technology roadmap for rock mechanics: Johannesburg, Tenth Congress of the International Society for Rock Mechanics, South African Institute of Mining and Metallurgy, p. 1179– 1184.
Takemura, T., Golshani, A., Oda, M., and Suzuki, K. 2003, Preferred orientations of open microcracks in granite and their relation with anisotropic elasticity: International Journal of Rock Mechanics and Mining Sciences, v. 40, p. 443– 454, doi: 10.1016/S1365-1609(03)00014-5.[CrossRef][GeoRef]
Takeshita, T., and Yagi, K. 2001, Paleostress orientation from 3-D orientation distribution of microcracks in quartz from the Cretaceous granodiorite core samples drilled through the Nojima Fault, south-west Japan: The Island Arc, v. 10, p. 495– 505, doi: 10.1046/j.1440-1738.2001.00348.x.[CrossRef][GeoRef]
Turcotte, D.L., and Schubert, G. 2002, Geodynamics—Second Edition: Cambridge Cambridge University Press 456 p.
Tuttle, O.F. 1949, Structural petrology of planes of liquid inclusions: The Journal of Geology, v. 57, p. 331– 356.[Web of Science][GeoRef]
Twidale, C.R., and Bourne, J.A. 1998, Origin and age of bornhardts, southwest Western Australia: Australian Journal of Earth Sciences, v. 45, p. 903– 914, doi: 10.1080/08120099808728444.[Web of Science][GeoRef]
Twidale, C.R., and Bourne, J.A. 2000, Rock bursts and associated neotectonic forms at Minnipa Hill, northwestern Eyre Peninsula, South Australia: Environmental and Engineering Geoscience, v. 6, p. 129– 140.
Varnes, D.J., and Lee, F.T. 1972, Hypothesis of mobilization of residual stress in rock: Geological Society of America Bulletin, v. 83, p. 2863– 2866, doi: 10.1130/0016-7606(1972)83[2863:HOMORS]2.0.CO;2.
Voight, B. 1966, Beziehung zwischen grossen horizontalen Spannungen im Begirge und der Tektonik und der Abtragung: Proceedings of the 1st Congress of International Society of Rock Mechanics, v. 2, p. 51– 56.
Voight, B. 1974, A mechanism for "locking-in" orogenic stress: American Journal of Science, v. 274, p. 662– 665.[Abstract]
Voight, B., and St. Pierre, B.H.P. 1974, Stress history and rock stress: Advances in rock mechanics: Proceedings Third Congress International Society of Rock Mechanics, v. 2, p. 580– 582.
Vollbrecht, A., Rust, S., and Weber, K. 1991, Development of microcracks in granites during cooling and uplift: Examples from the Variscan basement of NE Bavaria, Germany: Journal of Structural Geology, v. 13, p. 787– 799, doi: 10.1016/0191-8141(91)90004-3.[CrossRef][Web of Science][GeoRef]
Wang, Q.Z., Jia, X.M., Kou, S.Q., Zhang, Z.X., and Lindqvist, P.A. 2004, The flattened Brazilian disc specimen used for testing elastic modulus, tensile strength and fracture toughness of brittle rocks: Analytical and numerical results: International Journal of Rock Mechanics and Mining Sciences, v. 41, p. 245– 253, doi: 10.1016/S1365-1609(03)00093-5.[CrossRef][GeoRef]
Wilson, J.E., Chester, J.S., and Chester, F.M. 2003, Microfracture analysis of fault growth and wear process, Punchbowl Fault, San Andreas system, California: Journal of Structural Geology, v. 25, p. 1855– 1873, doi: 10.1016/S0191-8141(03)00036-1.[CrossRef][Web of Science][GeoRef]
Winslow, D.M., Bodnar, R.J., and Tracy, R.J. 1994, Fluid inclusion evidence for an anticlockwise metamorphic P-T path in central Massachusetts: Journal of Metamorphic Geology, v. 12, p. 361– 371, doi: 10.1111/j.1525-1314.1994.tb00029.x.[Web of Science][GeoRef]
Wise, D.U. 1964, Microjointing in basement, Middle Rocky Mountains of Montana and Wyoming: Geological Society of America Bulletin, v. 75, p. 287– 306, doi: 10.1130/0016-7606(1964)75[287:MIBMRM]2.0.CO;2.
Wise, D.U. 2005, Rift and grain in basement: Thermally triggered snapshots of stress fields during erosional unroofing of the Rocky Mountains of Montana and Wyoming: Rocky Mountain Geology, v. 40, p. 193– 209, doi: 10.2113/40.2.193.
Wong, T.F. 1982, Micromechanics of faulting in Westerly granite: International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, v. 19, p. 49– 64, doi: 10.1016/0148-9062(82)91631-X.
Zoback, M.D., and Townend, J. 2001, Implications of hydrostatic pore pressures and high crustal strength for the deformation of intraplate lithosphere: Tectonophysics, v. 336, p. 19– 30, doi: 10.1016/S0040-1951(01)00091-9.[CrossRef][Web of Science][GeoRef]
Zoback, M.D. 2007, Reservoir geomechanics: Cambridge Cambridge University Press 449 p.
RECEIVED FOR PUBLICATION February 14, 2007
REVISED MANUSCRIPT RECEIVED January 10, 2008
MANUSCRIPT ACCEPTED January 15, 2008
This article has been cited by other articles:
|
|
 |
|
  T. Engelder, G. G. Lash, and R. S. Uzcategui Joint sets that enhance production from Middle and Upper Devonian gas shales of the Appalachian Basin AAPG Bulletin, July 1, 2009; 93(7): 857 - 889. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| JOURNAL HOME | HELP | CONTACT PUBLISHER | SUBSCRIBE | ARCHIVE | SEARCH | TABLE OF CONTENTS |
