Visitors from around the world trek to Arches National Park in southeastern Utah (USA) to marvel at its graceful natural arches. These arches appear to have been carved through high, but relatively thin, free-standing sandstone walls. From the air, you can see that the park contains a multitude of such walls, making its landscape resemble a sliced-up loaf of bread (Figure 4.1a). The surfaces of rock walls in Arches Park initiated as joints, which are natural fractures in rock across which there has been no shear displacement. Erosive processes through the ages have preferentially attacked the walls of the joints, so that today you can walk in the space between the walls. Though joints are not always as dramatic as those in Arches National Park, nearly all outcrops contain joints. At first glance, joints may seem to be simple and featureless geologic structures, but in fact they are well worth studying, not only because of their importance in controlling landscape morphology, but also because they profoundly affect rock strength, influence hydrologic properties (such as permeability), and because they can provide a detailed, though subtle history of stress and strain in a region.

Although the basic definition of the term joint is non-genetic, contemporary geologists recognize that they form during Mode I loading (see Chapter 3); that is, that they are tensile fractures that form perpendicular to the σ3 trajectory and parallel to the principal plane of stress that contains the σ1 and σ2 directions. Not all geologists share this viewpoint, and some researchers use the term “joint” when referring to shear fractures as well. This second usage is discouraged, however, because structures that are technically faults would be confused with joints, so we do not use the term “joint” in reference to a shear fracture.

FIGURE 4.1. Examples of joints and veins on different scales. (a) Oblique aerial view of regional joints in sandstone near Arches National Park, Utah (USA). Note the Colorado River for scale (upper left). GE: 38°35'58.89" N 109°31'17.97" W. (b) Veining in limestone exposed in a road cut near Catskill (New York State, USA). [7.1]

In this chapter, we begin by describing the morphology of individual joints and the geometric characteristics of groups of joints. Then, we discuss how to study joints in the field, and how to interpret them. We conclude by describing veins, which are fractures filled with minerals that precipitated from a fluid (Figure 4.1b). But before we begin, we offer a note of caution. The interpretation of joints and veins remains quite controversial, and it is common for field trips that focus on these structures to end in heated debate. As you read this chapter, you’ll discover why.

SURFACE FEATURES OF JOINTS

If you look at an exposed joint surface, you’ll discover that the surface is not perfectly smooth. Rather, joint surfaces display a subtle roughness that often resembles the imprint of a feather. This pattern is called a plumose structure (Figure 4.2).


FIGURE 4.2. Photographs of plumose structure on joint surfaces (New York State, USA). (a) Wavy plumose structure on a joint in siltstone. (b) Plumose structure in thin bedded siltstone; pencil points to the point of origin. [7.2]

Plumose Structure

Plumose structures form at a range of scales, depending on the grain size of the host rock. In very finegrained coal, for example, components of plumose structure tend to be much smaller than in relatively coarser siltstone. Some of the best examples of plumose structure form in fine-grained rocks like shale, siltstone, and basalt, but you might not see obvious plumose structure on joints in very coarse-grained rocks like granite. Let’s look at plumose structure a little more closely (Figure 4.3a).

FIGURE 4.3 (a) Block diagram showing the various components of an ideal plumose structure on a joint. The face of joint 1 is exposed; joint 2 is within the rock. (b) Simple cross-sectional sketch showing the dimple of a joint origin, controlled by an inclusion. [7.3]

A plumose structure spreads outward from the joint origin, which, as the name suggests, represents the point at which the joint started to grow. Joint origins typically look like small dimples in the fracture plane (Figure 4.3b). Several distinct morphologies surround the joint origin. In the mirror zone, which lies closest to the origin, the joint surface is very smooth. Further from the origin, the mirror zone merges with the mist zone, in which the joint surface slightly roughens. Mirror and mist zones, while they are well developed in joints formed in glassy rocks, are difficult to recognize in coarser rocks. Continuing outward, the mist zone merges with the hackle zone, in which the joint surface is even rougher. It is the hackle zone that forms most of the plumose structure. Roughness in the hackle zone defines vague lineations, or barbs, that curve away from a plume axis, which together comprise the feather-like plume. The acute angle between the barbs and the axis points back toward the joint origin, so the plume defines the local direction of joint propagation. The median line may be fairly straight and distinct, or it may be wavy and diffuse. On some joint surfaces, concentric ridges known as arrest lines (Figure 4.3) form on the joint surface at a distance from the origin. These ridges represent, as the name indicates, breaks in the growth of the joint.

Why Does Plumose Structure Form?

Mode I loading of an isotropic and homogeneous material should yield a perfectly smooth, planar fracture that is oriented perpendicular to the remote σ3. Real joints are not perfectly smooth for two reasons. First, real rocks are not perfectly isotropic and homogeneous, meaning that the material properties of a rock change from point to point in the rock. Inhomogeneities exist because not all grains in a rock have the same composition and because not all grains are in perfect contact with one another. The presence of such inhomogeneities distorts the local stress field at the tip of a growing joint, so that the principal stresses at the tip are not necessarily parallel to the remote σ3. As a consequence, the joint-propagation path slightly twists and tilts as the joint grows.

Second, the stress field at the tip of a crack changes as the crack tip propagates. Recall from Chapter 3 that the stress intensity at the crack tip is proportional to the length of elongate cracks, and that the magnitude of the local tensile stress at the tip of the crack is, in turn, proportional to the stress intensity factor. Thus, as the crack grows, the stress intensity at the crack tip grows, up to a limiting value. Experimental work demonstrates that the velocity of crack-tip propagation is also proportional to the stress intensity. Stress magnitude and tip propagation velocity are relatively small near the joint origin, because the crack is very short, and increase with distance from the origin, eventually reaching a maximum (called terminal velocity). If the stress magnitude at the tip exceeds a critical value, the energy available for cracking rock exceeds the energy needed to create a single surface. The excess energy goes into breaking bonds off the plane of the main joint surface, resulting in the formation of microscopic cracks that splay off the main joint. If the energy becomes very large, the crack may actually split into two separate, parallel surfaces.

With these two conditions in mind, we can now explain why plumose structure has distinct morphological features. The dimple at the origin forms because the flaw at which the joint nucleated either was not perpendicular to the remote σ3, or caused a local change in the orientation of stress trajectories. Flaws at which joints initiate include open pores, preexisting microcracks, irregularities on a bedding plane, inclusions (like a pebble, fossil, amygdule, or concretion), or primary sedimentary structures (a sole mark or ripple). The portion of the joint that formed in the immediate vicinity of the origin was, therefore, not perpendicular to the remote σ3. As soon as the crack propagated away from the flaw, it curved into parallelism with the σ1-σ2 principal plane (Figure 4.3). In the mirror zone, the joint is still short, so the stress intensity, tensile stress magnitude, and tip-propagation velocity are all relatively small. As a consequence of the low stress, only bonds in the plane exactly perpendicular to the local σ3 can break, so the joint surface that forms is very smooth. In the mist zone, however, the joint moves faster, stress is higher, and stress at the joint tip is sufficiently large to break off-plane bonds, thereby forming microscopic off-plane cracks that make the surface rougher than in the mirror zone. In the hackle zone, the joint tip is moving at its terminal velocity and stresses at the crack tip are so large that larger off-plane cracks propagate and the crack locally bifurcates at its tip to form microscopic splays that penetrate the joint walls. The roughness of the hackle zone also reflects the formation of tiny splays and warps of the joint surface where the joint tip twists or tilts as it passes an inclusion and breaks into microscopic steps.

Arrest lines on a joint surface represent places where the fracture tip pauses between successive increments of propagation. The visible ridge of the arrest line, in part, represents the contrast between the rough surface of the hackle and the relatively smooth surface of the mirror/mist zone formed as the fracture begins to propagate, and in part may be analogous to the dimple formed at a crack origin. Thus, plumose structures form because of the twisting, tilting, and splitting occurring at the tip due to variations in local stress magnitude and orientation. Features such as bedding planes and preexisting fractures locally modify the orientation of principal stresses because they approximate free surfaces. A “free surface” is a surface across which there is no cohesion, so it cannot transmit shear stresses. By definition, a free surface is, therefore, a principal plane of stress. Remote stress trajectories will change orientation so that they become either parallel or perpendicular to the free surface. If a growing joint enters a region where it no longer parallels a principal plane of stress (for example, as occurs when the crack tip of a joint in a sedimentary bed approaches the bedding plane), the crack tip pivots to a new orientation. As a consequence, the joint splits into a series of small en echelon joints, because a joint surface cannot twist and still remain a single continuous surface. The resulting array of fractures is called twist hackle, and the edge of the fracture plane where twist hackle occurs is called the hackle fringe (Figure 7.3a). Note that if the hackle fringe intersects an outcrop face, the trace of a large planar joint within the outcrop may look like a series of small joints in an en echelon arrangement.

JOINT ARRAYS

Joints that comprise a family in which they are parallel or subparallel to one another are called systematic joints, and typically maintain roughly the same average spacing over the region of observation (Figure 4.4).

FIGURE 4.4. (a) Three sets of systematic joints controlling erosion in Cambrian sandstone (Kangaroo Island, Australia). (b) Block diagram showing occurrence of both systematic and nonsystematic joints in a body of rock. [7.5]

Systematic joints may cut through many layers of strata, or be confined to a single layer. Nonsystematic joints have an irregular spatial distribution, they do not parallel neighboring joints, and they tend to be nonplanar (Figure 4.4b). Nonsystematic joints may terminate at other joints. You will often find both systematic and nonsystematic joints in the same outcrop.

Joint Sets and Joint Systems

Describing groups of joints efficiently requires a fair bit of jargon. Matters are made even worse because not all authors use joint terminology in the same way, so it’s good practice to define your terminology in context. We’ll describe joint patterns here and give the explanations of why these various different groups of joints form later in the chapter.

FIGURE 4.5. (a) Traces of various types of joint arrays on a bedding surface. (b) Idealized arrangement of joint arrays with respect to fold symmetry axes. The “hk0” label for joints that cut diagonally across the fold-hinge is based on the Miller indices from mineralogy; they refer to the intersections of the joints with the symmetry axes of the fold. [7.6]

A joint set is a group of systematic joints. Two or more joint sets that intersect at fairly constant angles comprise a joint system, and the angle between two joint sets in a joint system is the dihedral angle. If the two sets in a system are mutually perpendicular (i.e., the dihedral angle is ∼90°), we call the pair an orthogonal system (Figure 4.5a), and if the two sets intersect with a dihedral angle significantly less than 90° (e.g., a dihedral angle of 30° to 60°), we call the pair a conjugate system (Figure 4.5a). Many geologists use the terms “orthogonal” or “conjugate” to imply that the pair of joint sets formed at the same time. However, as you will see later in this chapter, nonparallel joint sets typically form at different times. So, we use the terms merely to denote a geometry, not a mode or timing of origin.

As shown in Figure 4.5, many different configurations of joint systems occur, which are distinguished from one another by the nature of the intersections between sets and by the relative lengths of the joints in the different sets. In joint systems where one set consists of relatively long joints that cut across the outcrop whereas the other set consists of relatively short joints that terminate at the long joints, the throughgoing joints are master joints, and the short joints that occur between the continuous joints are cross joints (see definitions in Chapter Supplements).

In the flat-lying sedimentary rocks that occur in continental interior basins and platforms (e.g., the Midwest region of the United States), joint sets are perpendicular to the ground surface (and, therefore, to bedding) and orthogonal systems are common. In gently folded sedimentary rocks, such as along the foreland margin of a mountain range (e.g., the western side of the Appalachians), strata contain both vertical joint sets that cut across the folded layers, and joints that are at a high angle to bedding and fan around the folds (Figure 4.5b). Both orthogonal and conjugate systems occur in such gently folded strata. The joint sets of an orthogonal system in folded sedimentary rocks commonly have a spatial relationship to folds of the region, so we can distinguish between strikeparallel joints, which parallel the general strike of bedding (roughly parallel to regional fold hinges), and cross-strike joints, which trend at high angles (∼60° to 90°) to the regional bedding strike (Figure 4.5b). Conjugate systems in gently folded rocks consist of two cross-strike sets with their acute bisector at a high angle to the fold hinge. Because both sets of joint systems need not form at the same time, a conjugate geometry of a system of joints does not require that they are conjugate shear ruptures.

In the internal portions of mountain belts, where rocks have been intensely deformed and metamorphosed, outcrops may contain so many joints that joint systems may be difficult to recognize or simply do not exist. In such regions, joints formed prior to deformation and metamorphism have been partly erased. New joints then form at different times during deformation, during subsequent uplift, or even in response to recent stress fields. Rocks in such regions are so heterogeneous that the stress field varies locally, and thus joints occur in a wide range of orientations. Nevertheless, in some cases, younger joints, meaning those formed during uplift or due to recent stress fields, may stand out as distinct sets.

Cross-Cutting Relations between Joints

The way in which nonparallel joints intersect one another provides information concerning their relative ages. For example, if joint A terminates at its intersection with joint B, then joint A is younger, because a propagating fracture cannot cross a free surface, and an open preexisting joint behaves like a free surface. Note that joints that are filled (veins; see below) or joint faces tightly held together by stress, can transmit some shear stress, and thus do not behave like perfect free surfaces.

A younger joint’s orientation also may change where it approaches an older joint that behaves like a free surface. Why? Remember that at, or near, a free surface, a Mode I fracture must be either parallel, or perpendicular, to the surface so as to maintain perpendicularity to σ3. Thus, near a free surface, the local stress field differs from the remote stress field if the free surface does not parallel a principal plane of the remote stress field. If an older joint (joint B) acts as a free surface, then the younger joint (A) curves in the vicinity of joint B to become parallel to the local principal plane of stress adjacent to B, unless it already happens to parallel a principal plane of stress. The way in which the younger joint curves depends on the stress field. If the local σ3 adjacent to the older joint is parallel to the walls of the older joint, then the younger joint curves so that it is orthogonal to the first joint at their point of intersection, a relationship called hooking; such a structure is called a J junction (Figure 7.6a). However, if the local σ3 is perpendicular to the walls of the older joint, then the younger joint curves into parallelism with joints of the first set, and has a sigmoidal appearance (Figure 4.5a).

In some joint systems, two nonparallel joints appear to cross one another without any apparent interaction; in other words, they are mutually cross cutting. Such intersections are sometimes referred to as “+” intersections, if the joints are orthogonal, or “×” intersections if they are not orthogonal (Figure 4.5a). These relationships may represent situations where (1) the earlier joint did not act as a free surface, (2) the intersection of two younger joints at the same point on an older joint is simply coincidental, or (3) the cross-cutting relationship is an illusion—within the body of the outcrop, the older joint terminated, and the younger joint simply grew around it.

Joint Spacing

When looking at jointing in a sequence of stratified sedimentary rock, you will notice that within a bed, joints are often evenly spaced. Where this occurs, we define joint spacing as the average distance between adjacent members of a joint set, measured perpendicular to the surface of the joint. Informally, geologists refer to joints as being “closely spaced” or “widely spaced” in a relative sense, but to be precise, you should describe joint spacing in units of length (for example, 5 cm).

FIGURE 4.6. A model of the sequence of development of joints. Time 1 refers to the time before the first joint forms, and time 7 is the present day. This scenario indicates that joints form in random sequence, but with regular spacing (dm). [7.8]

In order to understand why joints are evenly spaced, we look at how an array of joints develops in a bed. Consider a bed of sandstone that contains five joints (Figure 4.6). Experimental work suggests that joints form in sequence; that is, first joint 1, then joint 2, then joint 3, and so on. When a new joint forms, it is at some distance greater than a minimum distance (dm) from a preexisting joint. Formation of a joint relieves tensile stress for a critical distance, dm (Figure 4.7). The zone on either side of a joint in which there has been a decrease in tensile stress is called the joint stress shadow. Stresses sufficient to create the next joint are only achieved outside of this shadow, and are created by traction between the bed and beds above and below it, as well as by stress transmitted within the bed beyond the fracture front of the preexisting joint.

FIGURE 4.7. The concept of stress shadows around joints. The heavy vertical lines are joints; dm refers to the average spacing between joints. (a) Block diagram illustrating stress shadow (shaded area) around each joint. Note how stress is transmitted across regions that are unfractured in the third dimension. Stresses are also exerted by tractions at bedding contacts. (b) Thin bedded sequence, containing joints with narrow stress shadows, so that the joints are closely spaced. (c) Thick bedded sequence, containing joints with wide stress shadows, so that the joints are widely spaced. [7.9]

The spacing between joints is determined by the width of the joint stress shadow; so, because the shadow is about the same width for all joints in the bed, the spacing ends up being fairly constant. Joint spacing depends on four parameters: bed thickness, stiffness, tensile strength, and strain. We’ll examine each of these parameters in turn.

Joint spacing and Bed thickness

All other parameters being equal, joints are more closely spaced in thinner beds, and are more widely spaced in thicker beds. The relationship is a reflection of joint-stress shadow width, because the greater the length of the joint (i.e., length of the joint trace in a plane perpendicular to bedding and joint), the wider the stress shadow (Figure 4.7b and c). To picture why this is so, imagine a net composed of springs (Figure 4.8a). If you reach into the net and cut one spring, only a few of the neighboring springs relax (Figure 4.8b); however, if you cut many of the springs in a row, a much wider zone of neighboring springs relaxes (Figure 4.8c). In thicker beds, joint stress shadows are wider, so joints tend to be more widely spaced.

FIGURE 4.8. Why joint stress shadows exist. (a) A grid of springs. (b) Cutting one spring causes only a few springs to relax around the cut, so only a relatively small area is affected, as indicated. (c) Cutting many springs in a row causes a wider band of springs to relax; thus, a larger area is affected. [7.10]

Joint spacing and Lithology

Recall that the stiffness (i.e., the elastic value E, Young’s Modulus) of a rock layer depends on lithology; Hooke’s law states that σ = E ⋅ e (see Chapter 3). Imagine a block of rock composed of sandstone and dolomite (Figure 4.9). Dolomite is stiffer (E ≈ 80 GPa) than sandstone (E ≈ 20 GPa). We stretch the block under brittle conditions by a uniform amount so that all layers undergo exactly the same elongation (e). The stress that develops in each bed is defined by Hooke’s law; however, since the elongation is the same for each bed, the magnitude of σ depends on E. Thus, beds composed of rock with a larger E develop a greater stress and fracture first. In the model of Figure 4.9, the stiffer dolomite bed probably fractured a few times before the sandstone bed fractured for the first time, so more joints develop in the dolomite bed than in the sandstone bed. In sum, for a given strain, stress is larger in stiffer beds, so other factors being equal, stiffer beds have smaller joint spacing.

FIGURE 4.9. Cross-sectional sketch illustrating a multilayer that is composed of rocks with different values of Young’s modulus. The stiffer layers (dolomite) develop more closely spaced joints. [7.11]

Joint spacing and Tensile strength

Predicting fracture spacing cannot be done by considering E alone, because, in some circumstances, a rock with a smaller E may actually have a lower tensile strength than a rock with a larger E. Thus, it will crack at a lower strain than a rock with a larger E, if the rock with the larger E also has a larger tensile strength. Other factors being equal, rocks with smaller tensile strength develop more closely spaced joints.

Joint spacing and Strain

A bed that has been stretched more contains more joints than a bed that has been stretched less, as you might expect.

Overall, the spacing of well-developed joints is about equal to bed thickness. If you ever have the chance to hike down the Grand Canyon, don’t forget to look at the jointing in different units as you descend. Bedding planes tend to be weak and do not transmit shear stress efficiently, so joints typically terminate at bedding planes. Because joint spacing depends on bed thickness and lithology, joint spacing varies from bed to bed. Weak, thinly bedded shales contain such closely spaced joints that they break into tiny fragments, and, as a consequence, they tend to form slopes. In contrast, thick sandstone beds develop only widely spaced fractures, so thick sandstone beds typically protrude and hold up high cliffs.

ORIGIN AND INTERPRETATION OF JOINTS

Why do joints form? In Chapter 3, we learned that joints develop when stress exceeds the tensile fracture strength of a rock, and Griffith cracks begin to propagate. But under what conditions in the Earth’s brittle crust are stresses sufficient to crack rocks? In this section, we describe several possible settings to explain how stress states leading to joint formation develop in a rock body. But before you read further, a note of caution. When using these ideas as a basis for field interpretation of jointing, keep in mind that different joints in the same outcrop may have formed at different times and for different reasons. Once formed, a joint doesn’t heal and disappear unless the rock gets metamorphosed or becomes pervasively deformed. Further, local variations in the stress field, which are a natural feature of inhomogeneous rock, may cause joints that formed at the same time to have different orientations at different locations. Because of these factors, joint interpretation continues to challenge geologists, and will do so for years to come.

Related to Uplift and Unroofing

Lithostatic pressure due to the weight of overlying rock compresses rock at depth. Also, because of the Earth’s geothermal gradient, rock at depth is warmer than rock closer to the surface. Subsequent regional uplift leads to erosion of the overburden and the unroofing of buried rock (Figure 4.10). This unroofing causes a change in the stress state for three reasons: cooling, the Poisson effect, and the membrane effect.

FIGURE 4.10. Joint formation during unroofing. As the block of rock approaches the ground surface, subsequent to the erosional removal of overburden, it expands in the vertical direction and contracts in the horizontal direction. It also cools (vertical axis shows approximate isotherms). [7.14]

As the burial depth of rocks decreases, they cool and contract. The rock can shrink in a vertical direction without difficulty, because the Earth’s surface is a free surface. But, because the rock is embedded in the earth, it is not free to shrink elastically in the horizontal direction as much as if it were unconfined, so horizontal tensile stress develops in the rock. Furthermore, as the overburden diminishes, rock expands (very slightly) in the vertical direction. Therefore, because of the Poisson effect (see Chapter 3), it contracts in the horizontal direction. Again, because the rock is embedded in the earth, it cannot shorten in the horizontal direction as much as it would if it were unconfined, so a horizontal tensional stress develops. Uplift and unroofing effectively cause rock layers to move away from the center of Earth. The layer stretches like a membrane as its radius of curvature increases, thereby creating tensile stress in the layer, called the membrane effect.

If the horizontal tensional stress created by any or all of these factors overcomes the compressive stresses due to burial and exceeds the rock’s tensile strength, it will cause the rock to crack and to form joints. Joints formed by the processes just described tend to be vertical because they generate a horizontal σ3. Recall that the Earth’s surface is a free surface, so it must be a principal plane of stress. Therefore, the other two principal planes of stress must be vertical. Uplift and unroofing are particularly important causes of joint formation in sedimentary basins of continental interiors, which are subjected to epeirogenic movements, and in orogens that are uplifted long after collisional or convergent tectonism has ceased.

Sheeting (or Exfoliation) Joints

Intrusive and metamorphic rocks without a strong schistosity (such as granite, migmatitic gneiss) commonly contain a set of joints that roughly parallels ground surface topography, and whose spacing decreases progressively toward the surface. Such joints are called sheeting joints or exfoliation joints (Figure 4.11). If the ground surface is not horizontal, as is the case on the sloping side of a mountain, sheeting joints curve and follow the face of the mountain, thus giving the mountain the appearance of a partially peeled onion. Rock sheets detach off the mountain along these joints, thereby creating smooth dome-shaped structures known as exfoliation domes. Half Dome, a challenge that draws mountain climbers to Yosemite National Park in the Sierra Nevada Mountains of California, is an exfoliation dome, one half of which was cut away by glacial erosion.

FIGURE 4.11. Sheeting joints (or exfoliation) in granite of the Sierra Nevada (Yosemite Park, CA).

Uplift and exhumation of rocks may lead to the development of sheeting joints within a few hundred meters of the Earth’s surface. As we mentioned earlier, sheeting joints are commonly subparallel to topographic surfaces, and are most prominent in rocks that do not contain bedding or schistosity, particularly granitic rocks.

The origin of sheeting joints is a bit problematic. At first glance, you might not expect joints to form parallel to the ground surface, because they are tensile fractures, and near the ground surface there is a compressive load perpendicular to the ground surface due to the weight of the overlying rock, and the lack of high fluid pressure. It appears that sheeting joints form where horizontal stress is significantly greater than the vertical load, allowing joints to propagate parallel to the ground surface. In this regard, formation of sheeting joints resembles cracks formed by longitudinal splitting in laboratory specimens.

FIGURE 4.12. Formation of sheeting joints. (a) Consider a situation where a pluton cools and contracts more than country rock, so σt (tensile stress) is oriented perpendicular to the intrusive contact. (b) Later, when the pluton is exhumed, joints form parallel to the intrusive contact and create an exfoliation dome. [7.15]

The stresses causing sheeting joints may, in part, be tectonic in origin, but they may also be residual stresses. A residual stress remains in a rock even if it is no longer loaded externally (e.g., in an unconfined block of rock sitting on a table). Residual stresses develop in a number of ways. Imagine a layer of dry sand that gets deeply buried. Because of the weight of the overburden, the sand grains squeeze together and strain elastically. If, at a later time, groundwater fills the pores between the strained grains, unstrained cement may precipitate and lock the grains together. As a consequence, the elastic strain in the grains gets locked into the resulting sandstone. When unroofing later exposes the sandstone, the grains and the cement expand by different amounts, and as a consequence stress develops in the sandstone. In the case of pluton, residual stresses develop because its thermal properties (e.g., coefficient of thermal expansion) differ from those of the surrounding wall rock, and because, during cooling, the pluton cools by a greater amount than the wall rock. The pluton and the wall rock tend to undergo different elastic strains as a result of thermal changes during cooling and later unroofing (Figure 4.12a and b). Because the pluton is welded to the surrounding country rock, the differential strain creates an elastic stress in the rock. For example, if the pluton shrinks more than the wall rock, tensile stresses develop perpendicular to the wall. At depth, compressive stress due to the overburden counters these tensile stresses, but near the surface, residual tensile stress perpendicular to the walls of the pluton may exceed the weight of the overburden and produce sheeting joints parallel to the wall of the pluton.

We earlier noted that sheeting joints tend to parallel topography. This relationship either reflects topographic control of the geometry of joints (because the vertical load is perpendicular to the ground surface), or joint control of the shape of the land surface (because rocks spall off the mountainside at the joint surface).

Hydraulic Fracturing

As we saw in Chapter 3, the three principal stresses at depth in most of the continental lithosphere are compressive. Yet joints form in these regions, and these joints may be decorated with plumose structure indicating that they were driven by tensile stress. How can joints form if all three principal stresses are compressive? As we described late in Chapter 3, the solution to this paradox comes from considering the effect of pore pressure on fracturing. In simple terms, the increase in pore pressure in a preexisting crack pushes outward and causes a tensile stress to develop at the crack tip that eventually exceeds the magnitude of the least principal compressive stress. If the pore pressure is sufficiently large, a tensile stress that exceeds the magnitude of σ3 develops at the tip the crack, even if the remote principal stresses are all compressive (Figure 4.13a), and the crack propagates, a process called hydraulic fracturing. Oil well engineers commonly use hydraulic fracturing to create fractures and enhance permeability in the rock surrounding an oil well (also called "fracking"). They create hydraulic fractures by increasing the fluid pressure in a sealed segment of the well until the wall rock breaks. Likewise the injection of societal waste water underground may activate fractures. But hydraulic fracturing also occurs in nature, due to the fluid pressure of water, oil, and gas in rock, and it is this natural hydraulic fracturing that causes some joints to form.

FIGURE 4.13. (a) Block diagram showing the stresses in the vicinity of a crack in which there is fluid pressure that exceeds the magnitude of σ3. As a result, there is a tensile stress, σt, along the crack. (b) Enlargement of the crack tip, illustrating the poroelastic effect. The opening stress (σo) due to fluid pressure in the crack exceeds the closing stress (σc), which is the sum of σcp, the closing stress where a pore is in contact with the crack, and σcg, the closing stress where a grain is in contact with the crack. [7.16]

If you think hard about the explanation of hydraulic fracturing that we just provided, you may wonder whether the process implies that the pore pressure in the crack becomes greater than pore pressure in the pores of the surrounding rock. It doesn’t! Pore pressure in the crack can be the same as in the pores of the surrounding rock during natural hydraulic fracturing. Thus, we need to look a little more closely at the problem to understand why pore pressure can cause joint propagation.

Imagine that a cemented sandstone contains fluid-filled pores and fluid-filled cracks (Figure 4.13b). Let’s focus our attention on the crack and its walls. Because the pores and the crack are connected, the fluid pressure in the pores and the crack are the same. Fluid pressure within the crack is pushing outwards, creating an opening stress, but at the same time, the fluid pressure in the pores, as well as the stress in the rock, is pushing inwards, creating a closing stress. As long as the closing stress exceeds the opening stress, the crack does not propagate. If the fluid pressure increases, the opening stress increases at the same rate as the increase in fluid pressure, but the closing stress increases at a slower rate. Eventually, the opening stress exceeds the closing stress so that the crack propagates; effectively, the outward push of the fluid in the crack creates a tensile stress at the crack tip. Why does the closing stress increase at a slower rate than the fluid pressure and the opening stress? The reason is that grains in the rock are cemented to one another, so that the grains cannot move freely in response to the increase in fluid pressure in the pores. The elasticity of the grains themselves, therefore, takes up some of the push caused by the fluid pressure. Thus, the closing stress acting on the fluid in the crack where it is in contact with a grain is less than where the fluid in the crack is in contact with a pore, but the outward push of the fluid in the crack is the same everywhere (also known as the poroelastic effect). As a result, the net outward push exceeds the net inward push, and tensile stress locally develops.

Once the crack propagates, the volume of open space between the walls of the crack increases, so the fluid pressure in the crack decreases. As a consequence, the crack stops growing until an increase in fluid pressure once again allows the stress intensity at the crack tip to drive the tip into unfractured rock. Thus, the surfaces of joints formed by natural hydraulic fracturing tend to have many arrest lines.

Figure 4.14. Large joint face in Entrada sandstone near Moab (Utah, USA). Note how the cliff face is a large joint surface. The thin bedded shale unit below the sandstone has more closely spaced joints. GE: 38°37'46.48" N 109°36'11.85" W [USGS] [7.20]

JOINT TERMINATIONS

Having discussed various ways in which joints initiate, we also need to address the issue of why joints stop growing. Recall from Chapter 6 that the stress intensity at the tip of a crack depends on the length of the crack. Thus, the stress intensity increases as the crack grows, and as long as the stress driving joint growth remains unchanged, the joint will keep growing. For this reason, joints that grow in large bodies of homogeneous rock can become huge surfaces, as seen in the massive beds of sandstone in southern Utah shown in Figure 4.14. But joints clearly do not propagate from one side of a continent to the other. They stop growing for one or more of the following reasons.

The joint tip may intersect a (nearly) free surface. Joints obviously stop growing when they reach Earth’s surface. They stop growing in the subsurface where they intersect a preexisting open fracture (joint or fault) or a weak bedding plane, or where they pass downward into ductile rock. Two joints that are growing towards each other, but are not coplanar, stop growing when they enter each other’s stress shadow (Figure 4.15a). In some cases, the interaction of joint tips causes curvature where the two joints link (Figure 4.15b). If, however, the preexisting joint is squeezed together so tightly that friction allows shear stress to be transmitted across it, or if it has been sealed by vein material, then a younger joint can cut across it.

FIGURE 4.15 Joint terminations. (a) Joints terminating without curving when they approach one another. (b) Joints curving into each other and linking. (c) Map view sketch illustrating how joint spacing is fairly constant because joints that grow too close together cannot pass each other. [7.21]

Formation of the joint itself may cause a local drop in fluid pressure, because creation of the joint creates space for fluid. This increase in space temporarily causes a drop in fluid pressure, so that the stress intensity at the joint tip becomes insufficient to propagate into unfractured rock. When fluid flow into the joint increases the fluid pressure to a large enough value, the joint growth resumes. Thus, as mentioned earlier, it is characteristic of joints being driven by high fluid pressures to grow in a start-stop manner, so their surfaces show many arrest lines.

Finally, if the joint grows into a region where energy at the crack tip can be dissipated by plastic yielding, the joint stops growing. Similarly, propagation of a joint into a rock with a different stiffness or tensile strength may cause it to stop growing. Also, if the joint tip enters a region where the stress intensity at the crack tip becomes too small to drive the cracking process, then the joint stops growing. The decrease in stress intensity may be due to a decrease in the tensile stress magnitude in the rock, or due to an increase in compressive stress that holds the joint together.

VEINS AND VEIN ARRAYS

In the vast desert ranges of western Arizona, there are few permanent residents, save for the snakes and scorpions, but almost every square meter of the rugged terrain has been trod upon by a dusty prospector in search of valuable deposits of gold, silver, or copper. Modern geologists mapping in the region frequently come upon traces of prospectors from years past. When you poke into many of these excavations, you find that the focus of their efforts, the days and days of agonizing labor with pick and shovel, is nothing more than a vein of milky white quartz. What are veins? Simply speaking, a vein is a fracture filled with mineral crystals that precipitated from a watery solution. Quartz or calcite form the most common vein fill, but other minerals do occur in veins, including numerous ore minerals, zeolites, and chlorite. Some veins initiated as joints, whereas others initiated as faults or as cracks adjacent to faults. Veins come in all dimensions; some are narrower and shorter than a strand of hair, while others comprise massive tabular accumulations that are meters across and tens of meters long. Groups of veins are called vein arrays and these have a variety of forms.

Formation of Vein Arrays

FIGURE 4.16. Vein arrays. (a) Planar array of veins. (b) Stockwork array of veins. Vein fill is dark. [7.22]

Planar systematic arrays (Figure 4.16a) represent mineralization of a preexisting systematic joint set or mineralization during formation of a systematic joint set. Stockwork vein arrays (Figure 4.16b) form where rock has been shattered, either by the existence of locally very high fluid pressure, or as a result of pervasive fracturing in association with folding and faulting.

FIGURE 4.17. (a) En echelon veins in the Lachlan Orogen (southeastern Australia). (b) Formation of a simple en echelon array. (c) Formation of sigmoidal en echelon veins, due to rotation of the older, central part of the veins, and the growth of new vein material at ∼45° to the shear surface. [7.23]

En echelon vein arrays form in a couple of different ways. They may form by filling en echelon joints in the twist hackle fringe of a larger joint. As we saw earlier in this chapter, the twist hackle fringe represents the breakup of a joint into short segments when it enters a region of the rock with a different stress field. En echelon vein arrays also develop as a consequence of shear within a rock body that is associated with displacement across a fault zone (Figure 4.17). The fractures comprising an en echelon array initiate parallel to σ1, typically at an angle of about 45° to the borders of the shear. Fractures open as displacement across the shear zone develops, and fill with vein material (Figure 4.17b). Once formed, the veins are material objects within the rock, so continued shear will rotate the veins and the angle increases. If, however, a new increment of vein growth occurs at the tip, these new increments initiate at 45° to the shear surfaces. Therefore, the veins become sigmoidal in shape (Figure 4.17c). Locally, a second generation of veins may initiate at the center of the original veins; this second set cuts obliquely across the first generation of veins. Because of the geometric relationship between en echelon veins and displacement, the orientation of shear related en echelon veins can be used to determine shear sense.

Blocky and Fibrous Vein Fill

Vein fill, the mineral crystals within a vein, is either blocky (also called sparry) or fibrous. In blocky veins, the crystals of vein fill are roughly equant, and may exhibit crystal faces (Figure 4.18a). The occurrence of blocky veins means that the vein was an open cavity when the mineral precipitated (this is possible only in veins formed near the surface, where rock strength is sufficient to permit a cavity to stay open or fluid pressure is great enough to hold the fracture open), that previously formed vein fill later recrystallized to form blocky crystals, or that there were few nucleation sites for crystals to grow from during vein formation.

FIGURE 4.18. Vein fill types. (a) Blocky vein fill. (b) Fibrous vein fill. [7.24]

In fibrous veins, the crystals are long relative to their width, so that the vein has the appearance of being spanned by a bunch of hairs (Figure 4.18b). Geologists don’t fully agree on the origin of fibrous veins, but many fibrous veins may form by a crack-seal process. The starting condition for this process is an intact rock containing pore fluid that in turn contains dissolved minerals. If the fluid pressure becomes great enough, the vein cracks and a very slight opening (only microns wide) develops. This crack immediately fills with fluid; but, since the fluid pressure within the open crack is less than in the pores of the surrounding rock, the solubility of the dissolved material decreases and mineral precipitates, thereby sealing the crack. The process repeats tens to hundreds of times, and each time the vein width grows slightly (Figure 4.19). During each increment of growth, existing grains in the vein act as nuclei on which the new vein material grows, and thus continuous crystals grow. Figure 4.19 shows microscopic evidence for this crack-seal process in the formation of a fibrous vein. Alternatively, formation of some fibrous veins may occur by a diffusion process, whereby ions migrate through fluid films on grain boundaries and precipitate at the tips of fibers while the vein walls gradually move apart. During this process, an open crack never actually develops along the vein walls or in the vein.

FIGURE 4.19. Photomicrograph of fibrous calcite filling in tensile fractures. Width of view is ~3 cm. [7.25]

Interpretation of Fibrous Veins

Fibrous veins, in particular those consisting of calcite and quartz, are informative because they can record useful information about the deformation history in an outcrop. There are two end-member types of fibrous veins, syntaxial and antitaxial veins (Figure 4.20).

FIGURE 4.20. Cross-sectional sketches, at the scale of individual grains, contrasting the stages of crack-seal deformation in antitaxial veins and syntaxial veins. (a) Antitaxial veins. The increments of cracking form along margins of the vein, and the vein composition differs from wall rock (i.e., fibers are not in optical continuity with grains of the wall). During increments of cracking, tiny slices of wall rock spall off. The slices bound the growth increments in a fiber. (b) Syntaxial veins. During each increment, cracking is in the center of the vein. The composition of fibers is the same as that of grains in the wall rock (that is, the fibers are in optical continuity with grains of the wall rock). Optical continuity between fiber and grain means that the grain’s crystal lattice has the same orientation as the crystal of the fiber. Optically continuous fibers and grains go extinct at the same time, when viewed with a petrographic microscope. [7.26]

Syntaxial veins typically form in rocks where the vein fill is the same composition as the wall rock; for example, quartz veins in a quartz sandstone. The vein fibers nucleate on the surface of grains in the wall rock and grow inwards to meet at a median line. Each successive increment of cracking occurs at the median line, because at this locality separate fibers meet, whereas at the walls of the vein, vein fibers and grains of the wall rock form single continuous crystals that make stronger connections. Each growth increment of a fiber is bounded by a trail of fluid inclusion.

Antitaxial veins form in rocks where the vein fill is different from the composition of the wall rock; for example, a calcite vein in a quartz sandstone. In antitaxial veins, the increments of cracking occur at the boundaries between the fibers and the vein wall, because that is where the bonds are weakest. Thus, antitaxial veins grow outward from the center. Increments of growth are sometimes bounded by trails of small dislodged flakes of the wall rock.

FIGURE 4.21. Schematic sketches showing that the long axis of fibers in a vein tracks the direction of extension, and that a change in extension direction leads to the formation of sigmoidal fibers. (a) If extension direction is perpendicular to the vein wall then the fibers are perpendicular to the grain. (b) If extension is oblique to the vein wall, then the fibers are oblique to the wall. If the extension direction is effectively parallel to the vein surface (i.e., the vein is a fault surface), then the fibers are almost parallel to the wall, and on exposed surfaces would form slip lineations.

(c, d) A change in extension direction forms sigmoidal fibers. Here, opening is first perpendicular to the vein wall, and then is oblique. Because of the locus of vein fiber precipitation, (c) antitaxial veins and (d) syntaxial veins have different shapes. [7.27]

In many cases, the long axis of a fiber in a fibrous vein tracks the direction of maximum extension (stretching) at the time of growth (i.e., it parallels the long axis of the incremental strain ellipsoid; see Chapter 6). When fibers are perpendicular to the walls of the vein, the vein progressively opened in a direction roughly perpendicular to its walls (Figure 4.21a). However, vein fibers oblique to the vein walls indicate that the vein opened obliquely and that there was a component of shear displacement during vein formation (Figure 4.21b). When vein fibers are sigmoidal in shape, the extension direction rotated relative to the vein-wall orientation. Note that for identical-looking fibers, the order of the movement stages depends on whether the vein is antitaxial or syntaxial (Figure 4.21c-d). For example, if the fibers in a syntaxial vein are perpendicular to the walls in the center and oblique to the walls along the margins, it means that in the early stage of vein formation the vein had an oblique opening component, while at a later stage it did not (remember that the fibers grow toward the center). However, fibers with exactly the same shape in an antitaxial vein would indicate the opposite strain history, because in antitaxial veins the fibers grow toward the walls. The presence and nature of a median line helps you in recognizing this important kinematic difference, but uncertainty about the interpretation can remain.

LINEAMENTS

FIGURE 4.22. Aerial image (Landsat 5) of diamond mine district around Lac de Gras (Northwest Territories, Canada) showing lineaments and structural control of topography at.

GE: 64°35'13.66" N 110°27'58.20" W

[USGS]

Lastly, we mention the general term lineament, which is a linear feature that is recognized on aerial photos, satellite imagery, or topographic maps. Lineaments generally are defined only at the regional scale; that is, they are not mesoscopic or microscopic features. Structural lineaments, meaning ones that are a consequence of the localization of known geologic features, are defined by structurally controlled alignments of topographic features like ridges, depressions, or escarpments (Figure 4.22). They may also be manifested by changes in vegetation, which is, in turn, structurally controlled. Most lineaments are the geomorphologic manifestation of joint arrays, faults, folds, dikes, or contacts, but some remain a mystery and do not appear to be associated with obvious structures. You should maintain a healthy skepticism when reading articles about lineaments that do not confirm imagery interpretations with ground truth. Some “lineaments” that have been described in the literature turn out to be artifacts of sunlight interaction with the ground surface, and thus do not have geologic significance. Others are human-made ((or extraterrestrial?). While variously unevenly defined, study of true structural lineaments often provides insight into the distribution of regional structural features, mining deposits, impacts, seismicity and other phenomena associated with deformation in the frictional regime.

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