Joint Loading Configurations Inferred from Propagation Paths

Journal of Structural Geology 21 (1999) 1637±1652 www.elsevier.nl/locate/jstrugeo

Joint interaction with embedded concretions: joint loading con®gurations inferred from propagation paths

David T. McConaughy 1, Terry Engelder*

Department of Geosciences, The Pennsylvania State University, University Park, PA 16802, USA Received 16 December 1997; accepted 18 May 1999

Abstract

The interaction between propagating joints and embedded concretions in a Devonian black shale near Seneca Lake, NY, permits identi®cation of the loading con®gurations responsible for two joint sets of dierent ages striking at nearly the same orientation. The earlier set consists of systematic joints cut by later Alleghanian joints of the Appalachian Plateau. The later set consists of non-systematic curving cross joints that abut these same Alleghanian joints. Field evidence shows that concretions functioned as sti inclusions in a compliant black shale. As a consequence of this elastic contrast, local perturbations in the remote stress ®eld persisted around the concretions during burial, tectonic deformation, and exhumation. These stress perturbations in¯uenced joint propagation paths of both joint sets. Our conclusions about loading con®gurations are based on ®nite-element modeling of the eect of the local stress perturbation on concretion-modi®ed joint propagation. Modeling shows that the local stress perturbation from a thermoelastic loading was responsible for de¯ecting cross joints away from concretions in a curved propagation path near the concretion. This load con®guration also led to arrest of cross joints before they penetrated the shale±concretion interface. At greater distances from the concretion, the propagation path of cross joints was controlled by the contemporary tectonic stress ®eld. The interface between concretions and the surrounding shale was strongly bonded, as indicated by the crossing of the interface by some of the systematic ENE joints. Higher compressive stress levels within the concretions relative to the shale suppressed joint development in the concretion, causing the arrest of those joints once they had driven across the interface and a short distance into the concretion. Numerical modeling shows that interface penetration by the systematic ENE joints is consistent with a ¯uid load, the same loading con®guration postulated for the subsequent Alleghanian joints. The traces of the systematic ENE joints align on opposite sides of concretions, rather than curving toward the concretion as predicted by two-dimensional models of the ¯uid load. Co-planar traces are indicative of large, planar joints propagating in-plane around the concretion, making it energetically inecient for the crack front to curve as it enters the local stress perturbation near the concretion. A ¯uid load for the systematic ENE joints came from high pore pressure during the pre-Alleghanian stages of burial of the Devonian Catskill delta complex. # 1999 Elsevier Science Ltd. All rights reserved.

1. Introduction is aided by an analysis of joint surface morphology (e.g. Lacazette and Engelder, 1992). However, joints in Joints are driven in response to any of at least four shale are usually without any distinguishing surface loading con®gurations in the Earth: a joint-normal morphology and thus more dicult than joints in silt- load, a thermoelastic load, a ¯uid load, and an axial stone to diagnose for loading con®guration. This is the load (Engelder and Fischer, 1996). Identi®cation of the case for a systematic ENE joint set [i.e. the strike joint loading con®guration responsible for systematic joints set of Sheldon (1912), also called set III joints by Parker (1942)] best developed in Devonian black shales of the Finger Lakes District of the Appalachian Plateau, NY. * Corresponding author. E-mail address: [email protected] (T. Engelder) The discovery that the systematic ENE joints did 1 Now at Shell Oshore Inc., New Orleans, LA 70161, USA. not propagate completely through concretions gave us

Fig. 1. Outcrops containing siderite concretions at Squaw Point and Lodi Point, Finger Lakes district, NY. Stream channels along Seneca Lake cut down into the black shales of the Geneseo Formation, the basal unit in the Upper Devonian Genesee Group. The base of the Rhinestreet Formation (dashed line), marks the postulated location of a pre-Alleghanian pressure seal that contributed to the formation of the systematic ENE joints.

the idea that the joint±concretion interaction may hold whether or not the joints penetrated from the black information on the loading con®guration at the time shale into the concretion. of joint propagation. This idea was reinforced with the This study investigates two possible loading con- discovery of a second type of ENE-striking joint, one ®gurations for the formation of two distinct types of with curved joint propagation paths in the vicinity of ENE-striking joints in the Devonian black shales of concretions embedded in black shale. Our idea was the Appalachian Plateau. One con®guration is a ther- that the presence of the concretions created a local moelastic load, under which the rock mass is subject perturbation in the remote stress ®eld that in¯uenced to tensile stress and joints are driven by a mechanism the direction of joint propagation. In addition, the called elastic contraction (Engelder and Fischer, 1996). stress contrast between the shale and embedded con- The second loading con®guration requires the develop- cretion under various loading con®gurations controls ment of ¯uid pressure within a joint that exceeds the D.T. McConaughy, T. Engelder / Journal of Structural Geology 21 (1999) 1637±1652 1639 least horizontal stress. Under this latter con®guration, ENE set indicating that the ENE set is pre- natural hydraulic fractures propagate in response to a Alleghanian (Engelder et al., submitted). ¯uid load (e.g. natural gas, oil, water) on the inside of The black shales of the Geneseo Formation contain a ¯aw such as a large pore, crack, or small joint (i.e. approximately 1.5% total organic carbon (TOC) com- Engelder and Lacazette, 1990) as well as within matrix pared to an average of 0.5% TOC in the Devonian pore space (i.e. Miller, 1995). For natural hydraulic gray shales of the Catskill Delta complex (Engelder et fractures, ¯uid decompression is the driving mechan- al., submitted). The elevated organic content and redu- ism where the energy for formation of new joint sur- cing environment characteristic of black shales contrib- face area is released from the potential energy of the ute to the formation of siderite concretions that grow driving ¯uid as its pressure drops (Lacazette and relatively early in the diagenetic history of the shale Engelder, 1992; Engelder and Fischer, 1996). (Oertel and Curtis, 1972). Exposed within several Previously, the case for ¯uid decompression as a driv- stream beds of the area are rounded siderite concre- ing mechanism in the formation of systematic joints tions that have in¯uenced the local development of was based on incremental crack growth as displayed joints (Fig. 2). In the case of the two concretions on joint surface morphology in siltstones. Our analysis shown in Fig. 2, the more widely spaced Alleghanian of joint propagation in the vicinity of concretions in a joints do not intersect either of the concretions, Devonian black shale of the Appalachian Plateau pro- whereas the systematic ENE joints generally abut them vides additional evidence for joint growth driven by (Fig. 2). Close examination reveals that several sys- ¯uid loading despite lack of corroborating surface tematic ENE joints propagated without deviating from morphology. their plane a few centimeters into the larger concretion Finite-element techniques are used to model the before arresting. In rare cases systematic ENE joints propagation of joints under boundary conditions that curve toward the concretion to abut the normal to its approximate two joint-loading con®gurations: a ¯uid surface. If a concretion is small enough a systematic load and a thermoelastic load. The response of the ENE joint may cut o an edge (Fig. 2). modeled joints to local perturbations in the stress ®eld A number of shorter ENE-striking joints curve in caused by the concretions is used to infer the con- the immediate vicinity of the concretions. These ditions under which the two types of natural joints behave like cross joints, abutting earlier Alleghanian propagated within the Devonian black shales. This joints and terminating against concretions and are, paper was motivated by the desire to identify the load- thus, dierent from the systematic ENE joints. Cross ing con®guration leading to the systematic ENE joints joints are aligned sub-parallel to the systematic ENE in black shale of the Finger Lakes District, joints but curve away from the concretion as they Appalachian Plateau. approach it such that the joints become tangent to the perimeter of the concretions (Fig. 2). Both systematic ENE joints and cross joints are found interacting with other concretions in the study area including those at 2. Field observations Lodi Point. The Squaw Point outcrop oers an opportunity to Streams near Squaw Point on the western shore and examine in detail the eect of a spherical inclusion on Lodi Point on the eastern shore of Seneca Lake, NY, the propagation paths of two dierent types of joints. cut down into the black shales of the Geneseo As they approach the concretions, the joint traces of Formation (Fig. 1). The Geneseo Formation is the both the systematic ENE joints and the cross joints basal unit of the Upper Devonian Genesee Group, are diagnostic of joint propagation under dierent part of the Catskill Delta complex deposited during loading con®gurations (cf. Engelder and Fischer, the Acadian Orogeny (Ettensohn, 1985). The Geneseo 1996). The more widely spaced Alleghanian joints do Formation is a homogeneous black shale, about 30 m not interact with the concretions in this outcrop or at thick in the study area, that crops out in an E±W- Lodi Point and are not part of the analysis. trending band across the central Appalachian Plateau of New York. Systematic ENE and Alleghanian joint sets are well-developed within the Geneseo black 3. Modeling cross-joint propagation shales. The more closely spaced ENE set strikes 0758 at Squaw and Lodi Points. Alleghanian joints strike The curving propagation paths of the cross joints in approximately 3368 intersecting the systematic ENE the immediate vicinity of a concretion suggest that joints nearly at right angles (Engelder and Geiser, their development was aected by stress perturbations 1980). As is the case elsewhere on the Plateau, the two associated with the concretion. A series of models were sets mutually cross-cut one another with no sign of in- constructed to investigate joint propagation near a teraction. Slip on the Alleghanian joints osets the concretion using FRacture ANalysis Code (FRANC), 1640 D.T. McConaughy, T. Engelder / Journal of Structural Geology 21 (1999) 1637±1652

Fig. 2. (a) Field photograph showing the interaction between joints and two concretions embedded in the black shale of the Geneseo Formation. The larger concretion is approximately 40 cm in diameter (note compass for scale). (b) (On facing page.) Drawing of the ®eld photograph high- lighting the joint traces and cross-cutting relationships. The outcrop contains two systematic joint sets: an Alleghanian set oriented at 3368, and a nearly orthogonal set of 0758 joints. Also present are non-systematic cross joints that abut the systematic joints and curve in the vicinity of the concretions. a ®nite-element code developed at Cornell University ¯uid load producing an eective tensile stress (Wawrzynek and Ingraea, 1987) that is speci®cally (Engelder and Fischer, 1996). Near-surface thermoelas- designed to analyze two-dimensional crack propa- tic loading conditions are approximated by applying gation problems. FRANC has been successfully used uniform extensional strain to elastic, isotropic media, to apply the principles of linear elastic fracture mech- producing a tensile stress ®eld that is locally perturbed anics to a variety of geologic problems, including the near structures such as joints or inclusions. Conditions modeling of ¯uid-driven joints (Fischer et al., 1995). appropriate for the formation of joints at depth are Numerical modeling, using FRANC, follows Fischer produced by applying uniform biaxial contractional et al. (1995) in the application of boundary conditions strains, thereby generating a compressive stress ®eld to simulate environments in which joints propagate about joints. This stress ®eld represents the total stres- under either of two loading con®gurations: a joint-nor- ses that result from external loading and the poroelas- mal thermoelastic load producing a tensile stress, or a tic response of the rock to ¯uid pressure. Fluid-driven D.T. McConaughy, T. Engelder / Journal of Structural Geology 21 (1999) 1637±1652 1641

Fig. 3. Two-dimensional propagation of vertically oriented joints is modeled in a horizontal cross-section through the center of a spherical concretion. The model con®guration, ®nite-element mesh, and boundary conditions for two-dimensional modeling of crack propagation in the horizontal plane are as shown. The model contains two material domains, a carbonate concretion (radius=20 cm, E 25±50 GPa, n 0:16), and the surrounding shale (E 16 GPa, n 0:16). The concretion and the shale are bonded perfectly to one another. An imposed strain applied under plane strain conditions Fig. 2. (continued). produces a tensile stress ®eld.

joint indicate about the nature of the joint driving joints are simulated by applying uniform internal ¯uid mechanism? pressure, in excess of the total remote compressive stress, to the walls of a pre-existing fracture. Fischer 3.1. Model geometry and boundary conditions (1994) veri®ed the appropriateness of the two sets of boundary conditions for elastic models containing The natural system to be modeled consists of a joints by ®nding good agreement between ®nite- spherical concretion, 40 cm in diameter, surrounded by element solutions for one-dimensional variation in an homogeneous shale (Fig. 3). The propagation of joint normal stress with distance away from the wall vertical fractures in the shale is modeled in a horizon- of a joint and existing analytical solutions tal cross-section through the center of the concretion. (Lachenbruch, 1961; Pollard and Segall, 1987). These The geometry is speci®ed in Cartesian coordinates with boundary conditions are used to model local stress the origin (0, 0) located along a diameter at the perimeter of the concretion. The model contains two ma- perturbations around sti inclusions (e.g. concretions), terial domains for which elastic properties are and to model joint propagation within the stress sha- prescribed (Fig. 3). A comparison of representative dow of the concretions. A ®nite element approach is elastic moduli for shale vs carbonate indicates that the used to follow the evolving stress pattern as the frac- concretion should have a higher Young's modulus ture grows into the stress perturbation caused by the than the shale (Fischer, 1994). Slickenlines in shales concretion. surrounding similar concretions at Bear Valley Strip The goal of modeling the propagation of cross joints Mine, Shamokin, PA, suggest that shale was extruded was to answer the following questions: How is the around the concretions during folding. This provides stress ®eld modi®ed by the presence of a concretion? evidence for the role of the concretions as sti in- Could the resulting stress perturbation de¯ect cross clusions during deformation after both the concretion joints in a manner similar to that observed at the and surrounding shale have lithi®ed (Nickelsen, 1979). Squaw Point outcrop? What does the curved path of a Model runs were conducted using a Young's modulus 1642 D.T. McConaughy, T. Engelder / Journal of Structural Geology 21 (1999) 1637±1652

Fig. 5. Detail of the ®nite-element mesh showing placement of the initial joint. A 1-m-long joint is positioned with its nearer crack-tip r 2 m from the concretion (crack-tip coordinates [(3.0, 0.15), (2.0, Fig. 4. Contour map of the normalized (syy=syy) tensile stress ®eld produced by extensional loading prior to introduction of a joint. 0.15)]). Simulations were performed in which the crack position 4 Imposed strain (Ey) of 6.25 Â 10 produces a theoretical remote ten- along the y-axis was varied from y 0to20cm(y 15 cm shown). r sile stress (syy) of 10.26 MPa in the shale. The presence of the stier concretion generates stress shadows, regions of elevated stress along the y-direction. Similarly, regions of reduced tensile the y-axis and reduced tensile stress about the x-axis. The stress ®eld is symmetrical about the center of the concretion. Stress within the stress are distributed symmetrically along the x-axis concretion is uniform and approximately 40% higher than the immediately outside the perimeter of the concretion. remote stress. This ®gure is a magni®cation of the central portion of Because the nature of the initiation of the joints (in- Fig. 3. itial size, location, and orientation of the ¯aw) is unknown, the analysis places a 1-m-long joint oriented of 16 GPa for the shale, and values of 25±50 GPa for r perpendicular to the least principal stress (syy), with its the concretion. A Poisson's ratio of 0.16 was assigned tips positioned at the coordinates [(3.0, 0.15) (2.0, to the shale and values from 0.16 to 0.25 to the con- 0.15)], such that the nearer crack-tip was 2 m from the cretion. Fracture toughness (KIc) for the shale was concretion (Fig. 5). The joint driving stress (Ds )in considered to be 0.9 MPa m1/2. Fractures were not per- this loading con®guration is equal to the local tensile mitted to propagate into the concretion, making esti- stress acting normal to the crack walls (syy). Away mation of KIc for the concretion unnecessary. from the concretion syy is approximately equal to the r theoretical remote stress (syy 10:26 MPa). This crack- 3.2. Results: thermoelastic loading driving stress is on the same order of that reported for joint propagation elsewhere (e.g. Segall and Pollard, To approximate a thermoelastic load, the model was 1983). subjected to a uniform extensional strain (Ey,Fig.3)of FRANC automatically remeshes elements in the 6.25 Â 104. This produced a calculated tensile stress vicinity of the joint, increasing the model resolution of

(syy) at the boundaries of the model with a maximum the near-crack stress ®eld. Crack-tip singularities are dierence of 1.5% from the theoretical remote stress simulated using rosettes of eight quadratic, triangular, r (syy) of 10.26 MPa expected for a uniform material isoparametric quarter-point elements (after Barsoum, domain (E 16 GPa, n 0:16). The stress within the 1976). After solving for the initial displacements and concretion was uniform (within 1%), as expected for a associated stresses, the joint was then made to propa- circular inclusion (Eshelby, 1957). The contrast in gate toward the concretion in a series of discrete user- moduli (Eshale 16 GPa, Econcretion 50 GPa) caused syy controlled increments. Increment size was scaled to the within the concretion to be 40% higher than the characteristic size of the mesh in the region into which remote stress in the shale. the crack-tip was to move. For each increment of r A contour plot of normalized stress (syy=syy) around crack propagation, FRANC calculated the crack-tip the concretion, prior to introduction of a joint, shows stress ®eld, determined the crack growth direction the stress perturbation associated with the concretion using the calculated maximum circumferential stress, (Fig. 4). It is similar in geometry, but opposite in sign, and propagated the crack-tip by the speci®ed incre- to those associated with a circular hole in an elastic ment. medium. Regions of elevated tensile stress in the shale The thermoelastic loading conditions produced a are symmetrical about the center of the concretion in crack propagation path that remained perpendicular to D.T. McConaughy, T. Engelder / Journal of Structural Geology 21 (1999) 1637±1652 1643

A duplicate simulation was performed using the same mesh and boundary conditions, but with the material properties of the concretion set equal to those of the shale. The joint in the duplicate simulation was required to move through an identical series of crack- tip displacements, generating a second set of calculated

stress intensities (KInorm). To isolate the eect of the local stress perturbation associated with the concretion from possible edge eects or variations due to the changing size of the crack-tip elements, the stress intensity at each increment of growth was normalized

by dividing through by KInorm (Fig. 6). The normalized Mode I stress intensity decreases from unity as the joint tip passes through a region of reduced crack- driving stress. This is followed by a steep increase in

KI as the crack-tip de¯ects towards a region of elevated driving stress. Continued growth of the joint results in a propagation path that becomes tangent to the perimeter of the concretion. The crack propagation path proved insensitive to the magnitude of the extensional strain applied. Model 5 3 runs with strains (Ey) of 6.25 Â 10 and 6.25 Â 10 , producing remote stresses of 1.03 and 103 MPa, respectively, yielded crack paths and normalized stress intensity plots nearly identical to the initial case. Other Fig. 6. (a) Crack propagation path (solid line) and normalized Mode model runs showed that the amount of curvature of I stress intensity for a joint originating 2 m from the concretion and the propagating joint was directly related to the con- driven by remote tensile stress (sr 10:26 MPa) acting normal to yy trast in Young's modulus between the concretion and the crack walls. The propagation direction remains perpendicular to r the shale. A decrease in the contrast (i.e. lowering E syy until the crack-tip is about 10 cm from the concretion, beyond which point individual crack increments consistently kink upwards for the concretion from 50 to 25 GPa) resulted in (maximum kink angle=78). Further propagation follows a path that smaller stress perturbations and reduced tendency for becomes tangent to the perimeter of the concretion. Normalized the crack to de¯ect (Fig. 7). Maximum curvature, as Mode I stress intensity (KI/KI norm) decreases from unity as the indicated by kink angles for individual crack incre- crack-tip enters a region of reduced tensile stress centered on the x- axis. As the crack-tip curves away from the x-axis, the normalized ments, decreased from 7 to 2.68. Normalized Mode I stress intensity increases in response to an increase in crack-driving stress intensity remains close to unity (i.e. the value stress. (b) Detail of the crack propagation path showing re®nement expected for a crack propagating through a uniform of ®nite-element mesh. FRANC's automatic remeshing algorithm stress ®eld) until the crack-tip is very near to the con- reduces element size in the vicinity of the crack-tip as it nears a ma- cretion. Changes in Poisson's ratio for the concretion terial interface (the concretion). User-controlled crack increment size is re-scaled with element size, permitting the crack to respond had little eect on the propagation path of the crack. smoothly to local stress perturbations. Repositioning the initial joint along the y-axis in¯u- enced the crack propagation path. Joints positioned on the remote stress through nearly 2 m of crack growth the x-axis of the concretion (y 0) propagate perpen- dicularly to sr due to the symmetry of the stress per- (Fig. 6). From a point about 10 cm from the concre- yy turbation. When the initial position is shifted to a tion the crack-tip began to curve, approaching the con- point aligned with the perimeter of the concretion cretion tangentially. As the crack-tip approached a (y 20 cm), the crack shows a reduced tendency to material interface (i.e. the concretion), element size curve, re-establishing itself with respect to the remote was scaled with the distance to the interface, resulting stress as it moves beyond the in¯uence of the concre- in progressively ®ner mesh (Fig. 6). Mode I stress tion (Fig. 7). Maximum crack path curvature occurs intensity (KI) at the crack-tip re¯ects the magnitude of for initial joint positions between 5 and 15 cm above the crack-normal driving stress and the geometry of the x-axis. the crack. In these simulations, KI was calculated using the J-integral method, and was checked period- 3.3. Results: ¯uid loading ically for agreement with KI calculated by two other methods, displacement correlation and modi®ed crack Evidence points to a depth of about 3 km for the closure integral (e.g. Bittencourt et al., 1992). development of overpressure and the propagation of 1644 D.T. McConaughy, T. Engelder / Journal of Structural Geology 21 (1999) 1637±1652

¯uid loading conditions under which natural hydraulic fracture could occur. Contractional strains of Ey 3 3 3:0 Â 10 and Ex 4:0 Â 10 were applied, resulting in model values approximately equal to the theoretical remote stresses for the applied strain and rock r properties: 77.9 MPa parallel to the crack (sxx SH), r and a remote crack-normal stress (syy Sh)of 64.1 MPa. The resulting horizontal stress dierence of 13.8 MPa is within the limits given above. The model stresses are assumed to represent total stresses, the combined eects of external loading and the poroelastic response of the rock to ¯uid pressure. The presence of a sti concretion in this compressive environment generated stress perturbations of similar geometry to those produced in the extensional model. However, the region centered on the x-axis, outside the concretion, became a zone of reduced crack-normal compressive stress (Fig. 8b). Regions of reduced compressive stress are favored for local joint propagation when internal pore pressure acting against the walls of a joint exceeds the least compressive total stress (Pp > jShj). In this compressive model environment, the driving stress required for joint propagation is generated by ¯uid pressure (Secor, 1965):

Ds jPpjsyy: 1

The model assumes both the shale and the concretion Fig. 7. (a) Crack propagation path (solid line) and normalized stress to be porous and subject to uniform pore pressure. A intensity given a reduced stiness contrast (Econcretion 25 GPa, 1 m joint is introduced into this environment and an Eshale 16 GPa) under the same loading conditions as in Fig. 6 r internal crack pressure (Pp) of 75 MPa was applied to (syy 10:26 MPa). Maximum kink angle is reduced to less than 38, and overall de¯ection of the crack is lessened as the stiness contrast the joint walls (Fig. 8), generating a crack-driving is reduced. (b) Repositioning of the initial joint upwards along the y- stress, Ds, of approximately 10.9 MPa at distance from axis (y 20 cm) while using the same elastic properties as in Fig. 6 the concretion. The magnitude of the driving stress (Econcretion 50 GPa, Eshale 16 GPa) also results in a crack propa- varies with s , which varies with position around the gation path with reduced curvature (maximum kink angle=3.68). yy The joint reestablishes perpendicularity with respect to the remote concretion (Fig. 8). stress as it passes beyond the in¯uence of the concretion. Propagation of the crack under ¯uid loading conditions produced a joint trace that, like the thermoelas- natural hydraulic fractures on the Appalachian Plateau tic model, deviated only slightly from its initial plane (Engelder and Oertel, 1985; Engelder and Lacazette, over the ®rst meter of growth (Fig. 9). As the crack-tip 1990; Evans, 1994). The magnitude of the horizontal reaches a distance of about 1 m from the concretion, stress dierence (s S S ) for this analysis was the joint gradually de¯ected toward the zone of d H h reduced compressive stress near the x-axis of the con- constrained by two estimates. Analysis of free-face dis- cretion, attaining an orientation normal to the per- solution of crinoid columnals from Upper Devonian imeter as it approached to within a few centimeters of rocks of the Appalachian Plateau suggests a lower the concretion. The increase in normalized stress inten- limit of 6 MPa for s (Engelder, 1982). Data from the d sity re¯ects the increase in driving stress, Ds, that Wilkins well, South Canisteo, New York, which pene- occurred as the joint tip moved into the region of trates the Geneseo Formation, can be extrapolated to reduced compressive stress. A sharp drop in KI 3 km depth to obtain an upper estimate for sd of occurred as the crack-tip approached to within a few 30 MPa (Evans et al., 1989a). For vertical joints to millimeters of the concretion. As was the case for ther- propagate, the minimum principal stress must be in moelastic loading, the propagation path and normal- the horizontal plane (S ), whereas the maximum prin- h ized KI were insensitive to the magnitude of the cipal stress can be either horizontal (SH) or vertical applied loads. Also similar to the thermoelastic loading (Sv). results was the response of the model to the strength A second series of models were designed to simulate of the contrast in the modulus of the two materials. A D.T. McConaughy, T. Engelder / Journal of Structural Geology 21 (1999) 1637±1652 1645

Fig. 9. Crack propagation path (solid line) and normalized Mode I stress intensity for a joint originating 2 m from the concretion and driven by ¯uid loading. The stress perturbations associated with the concretion cause the crack to be de¯ected towards the x-axis. This is accompanied by an increase in normalized stress intensity as the crack-tip moves into a region of reduced compressive stress.

Normalized KI decreases sharply as the crack-tip approaches to within a few millimeters of the concretion, an eect caused by the presence of the interface.

¯uid-driven jointing, and away from the concretion for thermoelastic loading. The sense of curvature observed for cross joints located near the Squaw Point concretions (Fig. 2) was more accurately reproduced using thermoelastic loading of the model.

Fig. 8. (a) Loading con®guration for ¯uid-driven joints. The applied 4. Systematic ENE joints strain is contractional in both the x- and y-directions 3 3 (Ey 3:0 Â 10 ; Ex 4:0 Â 10 ), producing a theoretical remote r The planar and continuous nature of the systematic stress (sxx)of77.9 MPa parallel to the crack and a remote crack- r joints suggests that their origin may be relatively far normal stress (syy)of64.1 MPa. An internal crack pressure (Pp 75 MPa) is applied to the walls of the joint, producing a crack- from the concretion. Traces of the ENE joints are driving stress (Ds ) of 10.9 MPa. (b) Contour map of normalized aligned on opposite sides of the concretions, suggesting (s =sr ) compressive stress ®eld produced by contractional loading yy yy that the joints are larger-scale fractures that propa- prior to introduction of the joint. The stress shadows along the axes are reversed in nature compared to the extensional model, with gated through the surrounding shale and were locally regions of elevated compressive stress about the y-axis and regions arrested at or within a concretion (Fig. 2). There is no of reduced compressive stress, favorable for propagation of ¯uid-dri- observable de¯ection of these planar joints as they ven joints, along the x-axis. approach a concretion. There are two key questions prompted by the behavior of these joints: Why do the systematic joints fail to curve in response to stress per- reduced contrast produced a reduced tendency of the turbations near the concretion? Why is the propa- joint to curve. Increasing the horizontal stress dier- gation of the systematic joints suppressed as they enter ence also reduced the curvature of the crack path. An a concretion? increase from 13.8 to 30 MPa (sxx syy) resulted in a Both loading con®gurations produced joint propa- decrease in total y-displacement (initial y-position gation paths that curved, away from the concretion in ®nal y-position) of approximately 1 cm for 2 m of the case of thermoelastic loading, and towards the con- crack growth in the x-direction. Large horizontal stress cretion for ¯uid loading conditions. Neither model is ratios (sxx=syy > 1:5) caused instabilities in the model. consistent with the observed tendency of the systematic The two loading con®gurations, one with and one joints to remain in-plane. The explanation may lie in without pore pressure, produced crack trajectories with the use of a two-dimensional model in simulating opposite senses of curvature, toward the concretion for three-dimensional joint propagation. In the ®eld, sys- 1646 D.T. McConaughy, T. Engelder / Journal of Structural Geology 21 (1999) 1637±1652

Fig. 11. Photograph of two concretions taken from a direction or- Fig. 10. (a) Unbounded systematic joints commonly have vertical thogonal to Fig. 2. The plane of a systematic ENE joint is indicated dimensions that exceed the diameter of an embedded concretion. with a two-headed arrow. This joint can be seen emerging on the Such joints will tend to propagate in-plane where they interact with opposite side of the concretion. This joint penetrates a few centi- a concretion. The presence of the joint in-plane above and below the meters into a concretion, as does another into the concretion in the concretion requires an energetically inecient breakdown of the background (marked with arrows). The lack of oset of the joints crack front in order for curvature near the concretion to occur. (b) across the interface indicates either strong bonding or high normal Joints that are con®ned to mechanical layers whose vertical dimen- compressive stress. Alleghanian cross-fold joints (vertically oriented sion is small compared to that of the concretion are more able to in the photograph) cleanly cross-cut the systematic ENE joints. react to local variations in the stress ®eld and may curve as a result.

The removal of overburden reduces Sv and thereby reduces the normal compressive stress on horizontal shale parting planes, permitting them to function as mechanical bed boundaries. and above the concretion. This interpretation still leaves unanswered the question of why the ENE joints do not propagate through the concretion. tematic ENE joints in massive black shales are 4.1. Joint propagation through an interface unbounded in the vertical direction, having heights the same order of magnitude as their lengths. Thus a sys- Some systematic ENE joints propagated a few centi- tematic joint that encounters a concretion during meters into concretions before arresting (Fig. 11). This propagation will tend to be tall relative to the vertical phenomenon is observable elsewhere in the outcrop, dimension of the concretion. Above and below the but only when associated with long planar ENE joints. concretion, the joint can propagate in-plane, unaected Traces of these joints commonly align on opposite by the local stress ®eld surrounding the concretion sides of a concretion, indicating their continuity. The (Fig. 10). Kinking or curving of the leading edge of tendency of these to penetrate the interface between the joint, in response to the stress perturbations near the shale and a concretion may provide additional the concretion, would require an energetically demand- insight into the nature of the joint-driving mechanism. ing breakdown of the crack front. The joint will Factors that aect the propagation of the joints across instead tend to propagate in-plane, arresting as it inter- the interface include the strength of the interface, the acts with the concretion, producing a joint trace in geometry of the interface, the material properties of outcrop in which the joint aligns on opposite sides of the shale vs the concretion, and the loading conditions the concretion. The two-dimensional model is sensitive (Helgeson and Aydin, 1991). Assessing the interface to local stress perturbations associated with the concre- strength is problematic, but because ENE joints tion, whereas an unbounded (three-dimensional) joint crossed the interface without de¯ection or oset, it may be constrained by in-plane propagation below seems the interface was either strongly bonded or sub- D.T. McConaughy, T. Engelder / Journal of Structural Geology 21 (1999) 1637±1652 1647

Fig. 13. Normalized Mode I stress intensity for a joint propagating from a lower modulus material into a higher modulus material

(EConc=EShale 1:4) under extensional loading conditions. The decrease in stress intensity as the joint approaches the interface is consistent with the tendency of many joints to arrest as they approach a concretion. The rapid increase in stress intensity as the joint crosses into a stier material (i.e. the concretion) suggests that Fig. 12. Model geometry, ®nite-element mesh, and loading con®gur- a joint with sucient energy to reach the interface should propagate ation for modeling the propagation of a joint (initial length=1 m) into and through the higher modulus material. through a bonded interface separating two materials. This con®guration permits investigation of the factors controlling the propagation of a systematic joint into a concretion. In this series of models, the tation or arrest. This is not the case with the r theoretical joint normal stress (syy) is proportional to Young's mod- systematic ENE joints. 4 ulus for the two materials. An extensional strain (Ey) of 6.25 Â 10 A series of models was designed to investigate the produces a sr of 10.26 MPa in the shale (E 16 GPa) and yy Shale tendency of a joint to arrest or propagate as it crosses 14.11 MPa in the concretion (EConc 22 MPa). These moduli are chosen for the two materials to produce a joint-normal stress 40% an interface into a stier elastic material (e.g. a concre- higher in the material into which the joint will be driven, the same tion). The Mode I stress intensity at the crack-tip was stress ratio used in the previous concretion models (e.g. Fig. 4). used as an indicator of the likely behavior of the joint. If a propagating joint experienced an increase in stress intensity, it was expected to continue to propagate. Decreasing stress intensity signaled a tendency of the ject to high normal compressive stress. Since these joint to arrest. A series of joint propagation models joints vary in their angle of intersection with the inter- were constructed in which a planar joint was driven face, such that the magnitude of normal stress across through an interface between two materials of diering the interface would presumably vary, we favor bond- elastic properties. Prior to introduction of the joint, an ing of the interface as an explanation for the observed applied strain produces uniform tensile stress ®elds in lack of de¯ection. A sti concretion aects the propa- each of the two layers with magnitudes proportional gation to the moduli of the materials. Young's modulus was of a joint as it approaches the concretion from a more initially set at 16 and 22 GPa for the shale and concre- compliant shale. Linear elastic fracture theory predicts tion, respectively. The moduli were chosen to approxi- that for a perfectly bonded interface between ideal ma- mate the stress contrast produced in the earlier series terials, stress intensity decreases, and ultimately goes of models. Since Poisson's ratio had previously been to zero, as a joint subject to tension approaches an found to have minimal eect on the results, it was left interface across which Young's modulus increases as a constant (0.16 for both materials). (Hilton and Sih, 1971; Erdogan and Biricikoglu, 1973). To simulate a systematic ENE joint propagating Unless additional energy is added to the rock±joint into a concretion under thermoelastic loading con- 4 system to overcome the decrease in the release of ditions, an extensional strain (Ey) of 6.25 Â 10 was strain energy, the joint will arrest as it approaches an applied at the boundaries of the model, producing a interface. Under thermoelastic loading, once a joint uniform tensile stress (syy) of 10.26 MPa within the crosses the interface, the strain energy should increase shale (Fig. 12), and 14.1 MPa within the concretion. A in proportion to the ratio of the moduli, with the 1-m-long joint was placed in the more compliant ma- maximum increase coinciding with in-plane propa- terial (shale), and caused to propagate through the gation (Helgeson and Aydin, 1991). Thus we might interface. We assume a crack-driving stress equal in r expect a joint that had begun to fracture the concre- magnitude to syy is sucient to drive the joint. tion to continue to propagate through it without hesi- Propagation of the joint through an interface with 1648 D.T. McConaughy, T. Engelder / Journal of Structural Geology 21 (1999) 1637±1652

Fig. 14. Normalized stress intensity for a joint driven under ¯uid loading conditions. The crack-tip experiences a decrease in stress intensity, similar to that of a joint driven by extensional loading (Fig. 13), as the interface is approached. As the interface is crossed, an abrupt increase in stress intensity is followed by a rapid decline, suggesting that a joint driven by ¯uid loading should arrest after propagating a small distance into the stier material.

Fig. 15. The percent change in stress intensity as the crack-tip moves into the stier material is shown as a function of both stiness ratio FRANC was accomplished by using progressively and penetration depth relative to joint length. The results show smaller crack increments, and a correspondingly increases in KI for small penetration depths over a range of stiness reduced element size (Fig. 12). Mode I stress intensity ratios. Further penetration (i.e. 1% vs 0.5%) results in decreases in was normalized using the same procedure described KI for higher stiness ratios. previously (i.e. running a duplicate simulation with identical properties prescribed for the two materials to response to the increase in crack-normal stress (syy) generate a set of KI norm values). Fig. 13 shows nor- acting against the internal crack pressure. malized Mode I stress intensity vs position of the The results also show an abrupt positive spike in crack-tip relative to the interface for a crack driven stress intensity as the crack-tip moves into the stier through the interface under thermoelastic loading. material (Fig. 14). This spike appears to be a function Normalized stress intensity begins at 1.0 away from of two factors: the stiness ratio between the materials, the interface and decreases as the interface is and the depth of penetration into the stier material approached. This result is consistent with theoretical relative to the overall joint length. In a series of predictions for fractures in ideal elastic materials. The models the stiness ratio was varied from 1:1 to 3:1, model also indicates a sharp increase in stress intensity and the crack-tip stress intensity calculated for two once the joint crosses the interface and enters the stif- relative depths of penetration into the stier material fer material. (Fig. 15). Given a constant internal crack pressure, the To simulate natural hydraulic fractures propagating percent change in stress intensity from a crack-tip posi- through an interface into higher modulus material, a tioned in the interface to a second position within the 3 contractional strain (Ey)of4Â 10 is applied at the stier material changes with the ratio of Young's mod- boundary, producing a joint-normal compressive stress ulus for the two materials. For small relative pen- r etration depths, K increases as the joint moves into in the shale equal to the theoretical remote stress (syy) I of 65.5 MPa. In the stier material (i.e. the concre- the stier material for stiness ratios up to 2:1. A sti- r ness ratio of 3:1 results in a suciently high compres- tion), syy is 40% higher, 91.7 MPa. An internal crack pressure of 75 MPa, applied to the walls of a sive crack-normal stress to prevent the crack from one meter joint, produces a joint-normal driving stress opening in the stier material (KI 0). For a given of approximately 9.5 MPa within the shale. Compared material stiness ratio, KI decreases as the depth of to the result for thermoelastic loading, the decrease in penetration is increased (Fig. 15), thus we expect dee- normalized stress intensity is delayed until the crack- per penetration of the joint for more similar materials. tip is relatively close to the interface. It appears that The results demonstrate that joints driven under the less energy is required to drive the joint to the interface two loading con®gurations may behave very similarly under these conditions relative to the joint driven by as they approach an interface across which stiness extension (Figs. 13 and 14). As the crack is driven into increases. In both cases the decrease in stress intensity the stier material, the stress intensity falls rapidly in as the crack-tip approaches the interface may cause D.T. McConaughy, T. Engelder / Journal of Structural Geology 21 (1999) 1637±1652 1649 the joint to arrest. For joints with sucient energy to ture growth when normal stress across the interface is cross the interface, the modeling suggests that the low (e.g. in the near surface) (Teufel and Clark, 1984; behavior should dier depending on the loading con- Warpinski and Teufel, 1987). These parting planes ®guration. Under thermoelastic loading the joint appear to have served as bounding surfaces during the should propagate through the stier material due to a propagation of the vertical cross joints. rapid increase in stress intensity. Under ¯uid loading, In the outcrop, the sense of de¯ection observed for joints may propagate a small distance into the stier cross joints was away from the center of the concretion material, driven by the abrupt increase in KI as the (Fig. 2), consistent with a thermoelastic model. Where interface is crossed, but should subsequently arrest they are not strongly in¯uenced by stress perturbations within the concretion as the stress intensity decreases. such as those associated with the concretions or preex- Under the same conditions, longer joints, such as the isting joints, cross joints propagate in an orientation systematic ENE joints, would be more likely to pene- that is roughly parallel to the present day maximum trate into the sti concretions than the shorter cross compression direction (Zoback and Zoback, 1991; joints. Engelder and Gross, 1993). This evidence, coupled The stress intensities calculated from this simple with their tendency to abut systematic Alleghanian model most likely have very limited applicability for joints, suggests that cross joints propagate in the con- simulating the complex interactions at the crack-tip, temporary stress ®eld as late-stage joints. The driving particularly those very near the interface. The results mechanism for cross joints is thermoelastic contraction are primarily intended to demonstrate the inconsis- due to unloading during exhumation of the tency of the observed behavior of these joints with Appalachian Plateau in the Late Tertiary (Hancock loading due to thermoelastic contraction. and Engelder, 1989; Blackmer et al., 1994).

5.2. Interface penetration 5. Discussion A key characteristic of joint±concretion interaction 5.1. Loading con®gurations is that neither systematic ENE joints nor cross joints propagate through the central portion of the larger Our models con®rm that joint propagation is sensi- concretions. All cross joints arrest at the interface tive to two of the loading con®gurations proposed by between the shale and the concretion whereas some Engelder and Fischer (1996). Under both loading con- systematic ENE joints propagate a small distance into ®gurations, a concretion-generated stress perturbation the concretion. Arrest at or near the boundary clearly causes out-of-plane joint propagation in the vicinity of demonstrates that these joints did not originate within a concretion provided joint height is limited to the di- the concretions. Otherwise joints that initiate inside the ameter of the concretion. The direction of de¯ection is concretions would propagate through the relatively indicative of the type of loading con®guration. homogeneous stress ®eld generated within the concre- Thermoelastic loading produced joints that curved tion by either loading con®guration. Modeling suggests away from the center of the concretion (Fig. 6), that stress intensity falls as a joint approaches an in- whereas ¯uid loading of a joint in a compressive en- clusion of stier material for both the thermoelastic vironment caused the joint to curve towards the center and ¯uid loading conditions (Figs. 13 and 14). Thus, of the concretion as it propagated (Fig. 9). Although increased energy is required to drive the joint to the two-dimensional modeling of the systematic ENE interface in either case. Once the joint reaches the joints subject to ¯uid load predicted a tendency to interface, however, the energy requirements for further curve near the concretions, this characteristic is not propagation vary with loading con®guration. The observed in the outcrop. We interpret this as indicative increase in stress intensity experienced by a joint dri- of the unbounded nature of the systematic joints that ven by thermoelastic loading suggests that the joint remained in-plane as they propagated around the con- should propagate completely through the concretion. cretions. A ¯uid driven joint may experience an increase in A necessary condition for the formation of curvy stress intensity immediately upon entering the concre- cross joints near the concretion is that they propagate tion, but the model suggests that it should soon arrest, while con®ned to layers that are thin with respect to as KI decreases dramatically toward the central portion the vertical dimension of the concretion (Fig. 10). A of the concretion (Fig. 15). Researchers investigating decrease in vertical stress associated with removal of hydraulic fracture containment have documented this overburden may have permitted the development of tendency in experimentally induced hydraulic fractures layer-parallel parting planes within the black shale. and numerical models (Simonson et al., 1978; Weakly bonded interfaces such as parting planes have Warpinski et al., 1982; Teufel and Clark, 1984; been demonstrated to serve as eective barriers to frac- Warpinski and Teufel, 1987). They found that high 1650 D.T. McConaughy, T. Engelder / Journal of Structural Geology 21 (1999) 1637±1652 modulus layers may not consistently stop a propagat- postulate that high ¯uid pressure did exist at the time ing fracture at the interface, but tended to restrict its of joint propagation is supported by the presence of growth. The dominant factor in fracture containment undercompacted shales in the Devonian section, indi- was found to be stress contrast. Fracture growth was cated by shale density pro®les (Albrecht, 1992), com- con®ned eectively by regions of higher stress. The paction of ¯occulated clays estimated from preferred applied loading conditions in this study generate stress orientation of chlorite (Engelder and Oertel, 1985; contrasts by virtue of the dierences in modulus Evans et al., 1989a), and the anisotropy of magnetic between the concretion and the surrounding shale. At susceptibility (Hirt et al., 1995). Likewise, the distri- depths where the total stress is compressive, higher bution of volume loss strain by pressure solution, as joint-normal stresses in the concretion inhibit growth indicated by ®eld observations (Engelder, 1979, 1984) of the joint. and by modeling the chlorite fabric (Evans et al., 1989a), and the poroelastic relaxation of pore pressure 5.3. Fluid loading history inferred from the present in situ stress pro®le (Evans et al., 1989b), add further support to the high ¯uid The clastic rocks of the Appalachian Plateau contain pressure scenario. a complex network of cross-cutting and abutting joints (e.g. Parker, 1942; Helgeson and Aydin, 1991; Engelder and Gross, 1993; Younes and Engelder, 6. Conclusions 1999). The ®rst set to appear is the systematic ENE joints (Engelder et al., submitted). This set of joints is Concretions like those found at Squaw Point func- found in gray and black shales of the Catskill Delta tioned mechanically as stier inclusions in the more complex, but only in those located stratigraphically compliant matrix of black shale. Loading of the rock beneath the Rhinestreet Formation, a postulated press- produced local perturbations in the stress ®eld sur- ure seal (Albrecht, 1992). The restricted distribution of rounding the concretions that in¯uenced joint propa- these joints to rocks beneath a pressure seal suggests gation paths. The curved propagation paths of some that they formed at depth, in a compressive environ- cross joints near concretions are indicative of thermo- ment where ¯uid pressure is most likely required to elastic loading conditions during their formation. The generate eective tensile stresses. Our model for the general orientation of the cross joints is consistent with joint±concretion interaction indicates a loading con- the contemporary stress ®eld, suggesting that they ®guration that con®rms this earlier judgment. The developed as late-stage, unloading joints driven by ENE joints are parallel to nearby joints and veins in thermoelastic loading. the Lockport Formation that are interpreted as The planar nature and alignment of the systematic Acadian (Gross et al., 1992). If so, they propagated ENE joints on opposite sides of concretions indicates during burial of the black shale in the prograding that they formed in a regional stress ®eld. They propa- Catskill Delta Complex sometime during the gated in-plane above and below the concretion, mak- Devonian. The most likely mechanism for overpressur- ing it energetically inecient for the crack front to ing at this time would have been compaction disequili- curve as it interacted with the concretion. The interface brium. The systematic ENE joints are cross-cut by between concretions and the surrounding shale was Alleghanian joints suggesting that overpressure was strongly bonded, as evidenced by the crossing of the maintained from Devonian burial through Alleghanian interface by some fractures. Higher compressive stress compression. levels within the concretions relative to the shale sup- We know more about ¯uid loading during the pressed joint development, causing those joints that Alleghanian joint propagation. Perhaps the most con- were driven across an interface into a concretion to vincing evidence for high-pressure ¯uid loading during arrest. Our modeling suggests that the tendency for the fracture propagation is the near-lithostatic trapping ENE joints to propagate across the interface into a pressure of ¯uid inclusions in mineralized joints of the concretion before arresting is inconsistent with thermo- Appalachian Plateau (Lacazette, 1991; Evans, 1995). elastic loading conditions. A ¯uid-drive mechanism is Even in these structures, we only know that the miner- therefore proposed for the development of the ENE alized joint was once ®lled with high-pressure ¯uid, joints. Their formation is attributed to ¯uid pressure but the role of the ¯uid decompression in joint propa- during pre-Alleghanian stages of burial of the gation can only be inferred. Additional evidence con- Devonian Catskill delta complex. sistent with natural hydraulic fracturing by ¯uid decompression is the incremental growth of joints indicated by a fan-like pattern of plumose morphology on Acknowledgements Alleghanian joints in siltstone beds of the Catskill Delta complex (Lacazette and Engelder, 1992). The Discussions with Staci Loewy, Laura Silliphant, and D.T. McConaughy, T. Engelder / Journal of Structural Geology 21 (1999) 1637±1652 1651

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