clasification of structural discontinuities

7/31/2019 Clasification of Structural Discontinuities

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2 FRACTURES AND BANDS IN ROCK: FIELD GUIDE AND MECHANICS

1.1.1 Representative Terms from the Literature

Discontinuity

In rock engineering, a discontinuity is a general term meant to

include a wide range of mechanical defects, aws, orplanes of weak-

ness, in a rock mass without regard to consideration of their origins

(e.g., Fookes and Parrish, 1969; Attewell and Woodman, 1971; Priestand Hudson, 1976, Goodman, 1976, 1989; International Society for

Rock Mechanics, 1978; Bieniawski, 1989; see Fig. 1.1). This term

includes bedding planes, cracks, faults, schistosity, and other planar

surfaces that are characterized by small shear strength, small tensile

strength, reduced stiffness, strain softening, and large uid conductiv-

ity relative to the surrounding rock mass (Brady and Brown, 1993,

pp. 5253; Priest, 1993, p. 1; Bell, 1993, p. 37; Hudson and Harrison,

1997, p. 20). By implication, cataclastic deformation bands and so-

lidied igneous dikes or veins in sedimentary host rock, for example,

that are stronger and/or stiffer than their surroundings would not beconsidered as a discontinuity by a rock engineer.

Pollard and Segall (1987) dened a discontinuity as two opposing

surfaces that are bounded in extent, approximately planar compared

to the longest dimension, and having a displacement of originally

adjacent points on the opposing walls that is both discontinuous and

small relative to the longest dimension. According to this deni-

tion, cracks, faults, veins, igneous dikes, stylolites, pressure solution

surfaces, and anticracks would be considered by them as discontinui-

ties.

Fig. 1.1. Examples ofdiscontinuities in a rock mass as seen through the eyes of

a rock engineer. Several joint planes are visible, including vertical ones exhibiting

plumose structure that dene the vertical face of the exposure, another vertical set

perpendicular to the plane of the exposure that is restricted to certain of the horizontal

sandstone layers, and subhorizontal joints that mark separation along the bedding

planes. A few inclined cracks in the uppermost massive bed suggest bedding-planeslip of that layer (top to the right) along the subjacent interface. The section shown

is part of the Permian Elephant Canyon Formation exposed in southern Devils Lane

graben, Canyonlands National Park, Utah.


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CLASSIFICATION OF STRUCTURAL DISCONTINUITIES 3

Fracture

The term fracture is commonly used in structural geology and

related elds. According to Jaeger (1969, p. 73) and others, a fracture

is the pair of distinct surfaces of separation (either opening or shear) in

a material. Griggs and Handin (1960) considered joints and faultsin

experiments and also in the eldas two types of fracture, with joints

accommodating dilation without shear and faults accommodatingshear displacement, as did Reid et al. (1913) and Lahee (1961) from

the perspective of eld geology.

The study prepared by the U.S. National Academy of Sciences

(1996), and Aydin (2000), dene a fracture as a structure dened

by two surfaces or a zone across which a displacement discontinuity

occurs. They include in this denition: (a) dilatant-mode fractures,

such as joints, veins, dikes; (b) contraction/compaction-mode frac-

tures, such as pressure solution seams and compaction bands; and

(c) shear-mode fractures, such as faults. A fracture using this broader

basis refers to a structural heterogeneity whose opposing surfaces aredisplaced relative to one another, regardless of its mode of displace-

ment or mechanics of formation. Others, such as van der Pluijm and

Marshak (2004), pp. 115116, use fracture as a general and scale-

invariant term for a surface in a material across which there has been

loss of continuity (i.e., a discontinuity in displacement) and strength.

They consider joints, veins, dikes, and faults as types of fractures.

By loss of strength a reduction in stiffness and strain softening,

analogous to their use in dening discontinuities, is commonly applied

to the denition of fractures. For example, Neuendorf et al. (2005)

dene a fracture as any surface across which there is no cohesion,

and include both cracks and faults under the term. In contrast, Price

and Cosgrove (1990) restrict the term fracture to dilatant or mixed-

mode (obliquely opening) cracks. Pollard and Aydin (1988) suggest

that the term fracture be reserved for those ambiguous cases in

which the sense of displacement (e.g., opening, closing, or shear) is

not denitively determined.

Joint

A joint has been dened as a fracture on which there has been no

visible shear displacement (Billings, 1972, p. 140; Hobbs et al., 1976,

p. 289; Neuendorf et al., 2005), or even, no visible displacement at all(Hodgson, 1961; Price, 1966; Ramsay and Huber, 1987). Based on

their comprehensive review and evaluation of the literature, Pollard

and Aydin (1988) recommended that joints be dened as fractures

having eld evidence for predominantly opening displacements be-

tween their opposing walls (Fig. 1.2). Additionally, the opening or

separation of the joint walls implies that a joint also be dened by a

discontinuous (opening) displacement across it (e.g., Pollard and Hol-

zhausen, 1979; van der Pluijm and Marshak, 2004, p. 140). Although

joints are mechanically equivalent to cracks, as dened by their inner

boundary conditions in materials science and engineering (e.g., Kan-ninen and Popelar, 1985, pp. 138147), Pollard and Fletcher (2005,

p. 335) recommend that the term joint be restricted to cracks that

Fig. 1.2. Several thin, parallel joints

from a granitic pluton near Ward Lake,

California are visible to the naked eye.

Closer examination reveals that these

joints are lled with epidote and other

hydrothermal minerals that were pres-

ent in the uid that circulated within

the joints as they dilated and propa-

gated at mid-crustal depths.


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occur in geologic contexts (i.e., in the eld) rather than in laboratory

experiments.

Anticrack

An anticrack is dened as a planar or tabular zone that accom-

modates localized contractional strain (e.g., Fletcher and Pollard,

1981; Mollema and Antonellini, 1996; Pollard and Fletcher, 2005,pp. 1619). A tabular zone is one having a measurable width at the

particular scale of interest. Contraction can result from volume loss,

such as porosity reduction associated with grain reorganization and

crushing in sandstones (e.g., Mollema and Antonellini, 1996; Sternlof

et al., 2005), mineralogical phase changes in deep mantle rocks (e.g.,

Green et al., 1990), or water-enhanced chemical dissolution that can

produce disjunctive (spaced) pressure-solution cleavage and stylolites

(e.g., Engelder and Marshak, 1985). Many workers including Tapp and

Cook (1988), Wojtal (1989), Fueten and Robin (1992), Raynaud and

Carrio-Schaffhauser (1992), Ohlmacher and Aydin (1995), NationalAcademy of Sciences (1996), Aydin (2000), Karcz and Scholz (2003),

and Neuendorf et al. (2005) envision pressure-solution cleavage and

stylolites accommodating the localized contractional strain kinemati-

cally as a system of anticracks.

Fault

Faults can be dened as planar or zonal structures across which

appreciable shear displacement discontinuities occur (e.g., Billings,

1972, p. 174; Aydin, 2000; van der Pluijm and Marshak, 2004, p.

166; Crider and Peacock, 2004; Johnson, 1995; Neuendorf et al.,

2005; see Fig. 1.3). Price (1966) and Hobbs et al. (1976) restrict the

term fault to a single plane, which has then been called a shear

fracture (see Pollard and Aydin, 1988). In detail, the slip plane is

associated with a comparatively thin zone of intensely crushed or

smeared rock. For small faults this zone can be less than 1 mm thick,

while for larger faults it is commonly found to be several centimeters

or decimeters thick. This zone is now commonly referred to as the

fault core (Caine et al., 1996). The fault core is generally considered

to be part of the fault because most of the fault displacement is taken

up within it (Chambon et al., 2006). Surrounding the fault is thefault

damage zone, which is the volume of brittle deformation around andrelated to a fault (e.g. Peacock et al., 2000).

In some contexts, the term fault includes not only discrete slip

surfaces, fault rock or fault core composed of the products of friction

and wear, but also the surrounding damage zone (e.g., Childs et al.,

1997; Aydin, 2000; Du Bernard et al., 2002; Davatzes et al., 2005).

Mandl (2000, p. 101) states explicitly that faults should be consid-

ered to vary in width from single planes (called slip surfaces) to

wide zones of pervasive shearing, regardless of any changes or loss

of cohesion in the sheared material. Davatzes et al. (2005) dene a

fault as a complex and continuously evolving zone of localized shearthat is composed of smaller, fundamental structures, reinforcing

Johnsons (1995) tenant that a fault is the end product of a sequence

Fig. 1.3. Normal faults exposed on this

dip slope of Upper Cretaceous carbon-

ate rock (Garumnian Formation, Col-

lado de Fumany) from the Spanish

Pyrenees demonstrate a consistentspacing and clear fault terminations.

The shadowed indentations are dino-

saur footprints that predate the faults.


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of deformational events. Faults in nature may contain more elements

than are created in controlled laboratory experiments on sand, clay,

or cylindrical samples, implying a wider range of physical processes

operating in the eld than in the laboratory. This led Jaeger and Cook

(1979) and Pollard and Fletcher (2005) to advocate restricting the

term fault to natural examples of localized shear deformation that

occur in the Earths crust.

Fault Zone

According to Hobbs et al. (1976, p. 300), Davis and Reynolds,

1996, p. 269, van der Pluijm and Marshak (2004), p. 166, Johnson

(1995), and Neuendorf et al. (2005), a fault zone is a tabular region

that contains many parallel or anastomosing fault surfaces. The term

is often used when a fault is taken to be a single plane or slip surface,

in which case a fault zone is a set of subparallel slip planes (see Fig.

1.4). Childs et al. (1996) pointed out that many faults with more than

decimeters of offset are bounded by paired slip surfaces envelopingmore or less complex zones of deformation. They regard the sheared

volume between the two bounding slip surfaces as the fault zone. In

many cases, this volume is equivalent to the fault core, although this

would depend on both the strain between the bounding faults and the

scale of observation.

Deformation Band

These common and intriguing structures (Fig. 1.5) were previ-

ously called Lders bands (Friedman and Logan, 1973) and braided

shear fractures (Engelder, 1974). Later, Aydin (1978) and Aydin

Fig. 1.4. A prominent normal fault cuts through the precursory zone of deformation

bands in this view of Aydins Wall that formed in Entrada Sandstone east of the

San Rafael Swell in eastern Utah. The bright, sun-lit high-angle planes are large slipsurfaces whose corrugations are inherited from the architecture of the deformation

band network. A second normal fault at the upper right denes this area as a fault

zone having two major subparallel strands.

Fig. 1.5. Deformation bands are an im-

portant deformation mechanism in po-

rous rocks such as sandstone, and theydene intricate and informative arrays

as in this fine example from Utah.

Photograph by Peter Hudleston.


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and Johnson (1978) applied the term deformation band to describe

thin tabular zones of shear strain that occur within porous rocks, and

with some exceptions this term is now routinely used to label these

structures (e.g., Davis and Reynolds, 1996, p. 317; Borja and Aydin,

2004; Johnson, 1995; Neuendorf et al., 2005; Aydin et al., 2006; Fig.

1.5). Analogous structures in soil, sand, and clay are referred to as

shear bands (e.g., Palmer and Rice, 1973; Mandl, 2000, pp. 365375;Davis and Selvadurai, 2002, pp. 4243; Wolf et al., 2003).

Shear Zone

Shear zones have been dened as relatively narrow structures

that accommodate predominantly large ductile shear strains (i.e.,

nonlocalized, spatially distributed ow) that may also include faults

(Hobbs et al., 1976, p. 266). van der Pluijm and Marshak (2004), p.

167, dene a shear zone as a zone of denable width in which the rock

deforms ductilely (i.e., without localization of shearing onto discrete

planes; see also Crider and Peacock, 2004), by cataclasis (fracturing,crushing, and frictional sliding of grains or rock fragments), crystal

plasticity, or a combination of both. Johnson (1995) denes a shear

zone by its continuous yet localized shearing within a tabular zone

of given width, that may also exhibit volumetric change (dilation or

contraction) across the zone. Davis and Reynolds (1996), pp. 503

508, and Mandl (2000), p. 103, classify shear zones by deformation

mechanism into brittle, semi-brittle, brittle-ductile, and ductile shear

zones. Neuendorf et al. (2005) dene a shear zone as a tabular zone

of rock that has been brecciated by many parallel fractures, sigmoidal

mineral-lled veins, cleavage or foliation planes, grain size reduc-

tion, or mylonitization, paralleling the generic usage of this term in

the minerals industry.

Damage Zone

Originating from engineering design in brittle materials (e.g.,

Broek, 1986; Lawn, 1993), a damage zone is a dense population of

small defects such as cracks that are subequal in size; the defects

serve as precursors to the localization of a large defect, which either

grows more rapidly than the others or differs sufciently from them

to be considered as a separate element (Kanninen and Popelar, 1985,

p. 90). Thus, cracks and faults can be thought of as propagating outof their precursory damage zones to become the dominant structural

discontinuity in their part of the rock mass (e.g., McGrath and Da-

vison, 1995; Fossen and Hesthammer, 2000; Pollard and Fletcher,

2005, p. 355; Schultz and Siddharthan, 2005). However, damage can

also occur in the wallrocks of an already established fault, resulting

in widening of the damage zone (e.g., Shipton and Cowie, 2001).

The term is sometimes limited to the fracturing around a fault that is

produced as a by-product of displacement accumulation on the fault

itself (e.g., Neuendorf et al., 2005). Peacock et al. (2000) suggested

a general denition of a fault damage zone as the area of fracturingaround and related to a fault. Kim et al. (2004) dene a damage zone

as the volume of deformed wall rocks around a fault surface that


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results from the initiation, propagation, interaction, and build-up of

slip along faults, thereby including both pre- and syn-faulting dam-

age.

1.1.2 Discussion and Synthesis of the TerminologySeveral common themes emerge from the literature review sum-

marized above. First is the desire for a term that encompasses all the

types of structures that may be encountered. Second is the need to

dene these structures in such a way that scale-dependent deni-

tions are avoided (see, for example, Wojtal, 1989, Mandl, 2000, van

der Pluijm and Marshak, 2004, and Price and Cosgrove, 2000, for

representative and thoughtful discussions of scale-dependent termi-

nology). Third is the need to respect differences in the characteristics

or properties of the structures that have led to certain classical, and

therefore potentially widespread, denitions. Fourth is the need to

balance simplicity of terminology with generality of application. The

resulting set of denitions is listed in Table 1.1 (after Schultz andFossen, 2008).

One issue that required clarication is the common practice of

considering cracks, joints, or faults as a single surface. Field exami-

nation shows instead that these structures are dened by a pair of

surfaces, or fracture walls, that have been displaced (by opening or by

shearing) from their original positions (Fig. 1.6). For example, a crack

or joint is open between its two walls; these walls join smoothly at a

crack or joint tip, dening the maximum horizontal or vertical extent

of this structure in the rock. Similarly, a fault must be considered to

be a pair of planes that are in frictional contact; a single fault planebegs the question of what was sliding against it. These paired fault

walls or planes may be separated by gouge or other deformed mate-

rial, and like cracks, join at a tip where the displacement magnitude

Fig. 1.6. A pair of echelon igneous dikes is shown in granitic rock of the central

Sierra Nevada near Donner Lake, California. Each dike segment beyond the overlap

region, where the dikes are linked, exhibits a separation of host rock by ~10 cm,

with the intervening void within the dike being lled by a sequence of hydrothermal

(light-toned) and igneous (dark-toned) uids that have since crystallized, preserv-ing the extensional strain in the pluton. The later crack in the left-hand part of the

image (that cuts the dike) also demonstrates that a fracture must be dened by a

pair of subparallel walls or surfaces, rather than a single plane.


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decreases to zero. In the case of deformation bands, the walls can beidentied by a comparatively rapid change in displacement gradient

or porosity, although they can be more indistinct than the clean sharp

breaks typical of joints and fault planes (e.g., Aydin, 1978).

A brittle fracture implies creation of these surfaces under condi-

tions of relatively small strain and with a decreasing resistance to

continued deformation (i.e., a strain-softening response in the post-

peak part of the stress-strain curve for the rock; Jaeger, 1969; see

also Hudson and Harrison, 1997; Chapter 8). Brittle deformation

additionally implies localization of strain into a discrete planar ele-

ment, whereas ductile deformation implies nonlocalized, spatiallydistributed deformation (e.g., Pollard and Fletcher, 2005, p. 334).

The term fracture thus implies a local reduction in strength and/

Table 1.1. Denitions for structural discontinuities.

Discontinuity Mechanical defect, aw, or plane of weakness in a rock mass without

regard to its origin or kinematics

Structural Discontinuity A localized curviplanar change in strength or stiffness caused by

deformation of a rock that is characterized by two opposing surfaces that

are bounded in extent, approximately planar compared to the longest

dimension, and having a displacement of originally adjacent points on

the opposing walls that is small relative to the longest dimension

Sharp Discontinuity A structural discontinuity having a discontinuous change in strength or

stiffness that occurs between a pair of discrete planar surfaces

Tabular Discontinuity A structural discontinuity having a continuous change in strength or

stiffness that occurs across a relatively thin band

Fracture A sharp structural discontinuity having a local reduction in strength and/or stiffness and an associated increase in uid conductivity between the

opposing pair of surfaces

Joint A sharp structural discontinuity having eld evidence for predominantly

opening displacements between the opposing walls

Anticrack A sharp structural discontinuity having eld evidence for predominantly

closing displacements between the opposing walls

Deformation Band A tabular structural discontinuity having a continuous change in strength

or stiffness across a relatively narrow zone in porous rocksFault A sharp structural discontinuity dened by slip planes (surfaces of

discontinuous displacement) and related structures including fault

core and damage zones that formed at any stage in the evolution of the

structure

Fault Zone A set of relatively closely spaced faults having similar strikes


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or stiffness and an associated increase in uid conductivity between

the pair of surfaces. Cracks, joints, and faults are, as a consequence,

various types of brittle fractures. A solidied igneous dike that cuts a

weaker and/or less stiff sedimentary sequence, however, would not be

considered to be a fracture according to this denition, although the

contact between the igneous rock and the country rock may qualify

if it is weaker, or less stiff, than the igneous or country rock.Fractures are seen to be a pair of surfaces that separate their

displaced surroundings from what is between them (e.g., Johnson,

1995). In the case of a joint that daylights into a rock slope in an

outcrop at the Earths surface, the joint is lled by air or other ma-

terial, such as water, snow, or ice. Joints in the subsurface are lled

by a variety of liquids including groundwater (e.g., Engelder, 1985;

National Academy of Sciences, 1996), natural gas (Lacazette and

Engelder, 1992), and petroleum (Dholakia et al., 1998). Joints lled

by solidied hydrothermal or magmatic minerals are called veins and

igneous dikes (Fig. 1.7), respectively. Rubin (1995b) calls igneousdikes magma-lled cracks to emphasize the mechanical basis for

dike dilation and propagation. In all of these examples, it becomes

important to determine whether the lling material was there initially,

inside the joint, as it dilated and propagated, or whether the lling

material came afterwards and simply occupied the volume within the

joint.

Fault walls may be separated by gouge (e.g., Chambon et al.,

2006); those of a stylolite, by insoluble residue such as clays (e.g.,

Fletcher and Pollard, 1981; Engelder and Marshak, 1985; Pollard

and Fletcher, 2005, p. 17). Deformation bands typically have either

increased or decreased porosity within them (e.g., Aydin et al., 2006);

grain size reduction may also characterize the interior of a deforma-

tion band (e.g., Aydin, 1978; Davis, 1999; Fossen et al., 2007). As

a result, cracks, joints, faults, stylolites, and deformation bands all

Fig. 1.7. The detailed shape of the dike tip is clearly revealed by this view of the

stepover between a pair of closely spaced igneous dikes. The dike segment width,

normal to its trace, is ~10 cm (camera lens cap for scale). Dike shapes such as these

can be predicted very well by representing the dikes as dilatant cracks propagating

through a continuous elastic medium.


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contain various materials between their walls that differ signicantly

from the host rock that surrounds them.

The term discontinuity has two distinct meanings when applied

to localized structures. First, joining of the paired crack or fault walls

at the fracture tips denes the dimensions of the fracture, such as its

length, width, or height. Fractures that have discrete lengths are called

discontinuous (e.g., Pollard and Segall, 1987) and this is the basis forthe eld of engineering fracture mechanics (because discontinuous

fractures end at the fracture tips). The second, and more recent, use

of discontinuity refers to the rate of change ofdisplacementacross

the structure (e.g., Johnson, 1995; Borja, 2002). Fractures having a

discrete step-wise change in displacement across them, such as cracks

and faults (or slip surfaces), are said to have, or be, a displacement

discontinuity. In contrast, shear zones and deformation bands exhibit

a continuous displacement across them. The boundary element model-

ing approach developed by Crouch and Stareld (1983, pp. 208210)

and used by many researchers in geologic fracture mechanics clearlyillustrates how these (strong and weak) discontinuities can both be

easily represented in a fracture model by specifying the properties

of the lling material along with the strengths of the enclosing walls.

This computational approach parallels the geologic work summarized

in this section that motivates the integration of terminology espoused

in this book.

The scale of the structure relative to its surroundings is also im-

portant to consider. For example, the rock cut by a structure is com-

monly taken as an effective continuum (e.g., Pollard and Segall,

1987, and references therein). A geologic unit is considered to be

continuous when its properties at the scale of the structure are statisti-

cally constant, leading to homogeneous values and behavior (Priest

and Hudson, 1981; see Chapter 3). Rock units with spatially variable

properties, such as joint sets, at a given scale are called discontinuous.

In mechanics, a continuous material is said to be simply-connected,

whereas a discontinuous one is multiply-connected (e.g., Nehari,

1952).

An outcrop of columnar-jointed basaltic lava ows (e.g., Fig. 1.8)

provides an informative example of relative scale (Schultz, 1996).

For a scale of observation of mm to cm, the rock within a column

is intact basaltic rock, and it can be idealized by those properties.At signicantly smaller scales, grain size and microcracks become

important enough that the assumption of a continuous material may

not apply. For a scale of a few meters, however, the rock unit can be

described as intact basalt partly separated into irregular blocks by

numerous discontinuous fractures (i.e., the columnar joints). Because

this scale of observation is comparable to the scale of the fracturing

(or equivalently, the block size), the ow must be considered as a dis-

continuum within which the properties of the rock and fractures both

must be considered to understand and represent the behavior of the

ow, as in the example shown in Fig. 1.8. An approach called blocktheory (Goodman and Shi, 1985; Priest, 1993, pp. 246250) would

be the method of choice here. At dimensions for which the scale of

Discontinuity I:

Finite Dimensions

Discontinuity II:

Displacement Gradient

Fig. 1.8. View of columnar joints inbasalt near Donner Lake, California,

looking down the column axes; rock

hammer for scale.


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observation greatly exceeds (e.g., by a factor of 510) the block size

or fracture spacing, such as would be found on an aerial or satel-

lite image, the lava ow can be described as an effective continuum

(Priest, 1993) and a rock mass (see also Bieniawski, 1989; Schultz,

1993, 1995, 1996; Fig. 1.1).

To summarize, a 10-cm core of the basaltic rock within a basalt

column, and a 10-m outcrop of jointed basalt, are both effectivelycontinuous at their respective scales, although the values for strength,

deformability, and hydrologic properties will differ in detail for each

scale. The ow is discontinuous at scales of observation comparable

to the grain or block size. Rock engineers have coined the acronyms

CHILE (continuous, homogeneous, linearly elastic) and DIANE (dis-

continuous, inhomogeneous, anisotropic, non-elastic) to describe the

characteristics of a rock units at the particular scale of interest (see

Hudson and Harrison, 1997, pp. 164165). Continuum methods such

as fracture mechanics work well with CHILE materials, but processes

at the block or grain scale, such as grain reorganization and forcechain stability (e.g., Cates et al., 1998; Mandl, 2000, pp. 100101;

Mair et al., 2002; Peters et al., 2005) within a deformation band, re-

quire methods such as distinct element or particle ow codes instead

to explicitly represent these DIANE materials (e.g., Antonellini and

Pollard, 1995; Morgan and Boettcher, 1999). In this book we adopt

terminology and analysis techniques for structures consistent with

CHILE behavior of their surroundings.

1.1.3 Suggested DenitionsOn the basis of the preceding discussion, the term structural

discontinuity is adopted in this book to encompass the various types

of geologic structures.

tA structural discontinuity is a localized curviplanar change

in strength or stiffness caused by deformation of a rock that is

characterized by two opposing surfaces that are bounded in ex-

tent, approximately planar compared to the longest dimension,

and having a displacement of originally adjacent points on the

opposing walls that is small relative to the longest dimension.

Quantication of small displacements of rock on either side of astructural discontinuity can be done by means of a displacement-

length diagram (Fig. 1.9), which is a standard tool in geologic frac-

ture mechanics and structural geology (e.g., Cowie and Scholz,

1992a; Dawers et al., 1993; Clark and Cox, 1996; Schlische et al.,

1996; Marrett, 1996; Fossen and Hesthammer, 1997; Schultz, 1999;

Cowie and Roberts, 2001; Scholz, 2002, pp. 115117; Olson, 2003;

Schultz et al., 2008; see Chapter 10). As can be seen on Fig. 1.9, lon-

ger faults are associated with systematically larger displacements,

or shear offsets (Dmax

on the diagram), so that faults accommodate

offsets between 0.1 and 10% of their lengths, with smaller varia-tions found for faults in a particular area. Other types of geologic

structural discontinuities, such as joints and deformation bands, also


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small fraction of the discontinuitys length or height. With these

kept in mind, the term structural discontinuity can easily be used

to encompass those having either abrupt or continuous changes in

displacement across them.

A fracture is a subtype of structural discontinuity. It is dened as

follows (Table 1.1):

tA fracture is a sharp structural discontinuity having a lo-

cal reduction in strength and/or stiffness and an associatedincrease in uid conductivity between the opposing pair of

surfaces; the displacement is discontinuous across the fracture.

Cracks, joints, and faults are different types of fractures.

Most geologic fractures are brittle structures, in the sense (Rutter,

1986; Knipe, 1989) that they break or shear the rock using pressure-

dependent deformation mechanisms (e.g., grain cracking, Pollard

and Aydin, 1988; frictional sliding, Byerlee, 1978; Scholz, 2002, pp.

53100). This strain-softening behavior explains why cracks and

faults can both be considered to be types of fractures. However, cracks

that propagate by temperature-dependent deformation mechanisms,

such as void growth ahead of the crack tip, are also known from

high-temperature settings; these are referred to as ductile fractures

(e.g., Eichhubl, 2004).

The denitions of structural discontinuity and fracture given above

require that the rock surrounding the discontinuity be an effective

continuum. For example, grain-scale diffusion or cracking implies

a different scale than ow in gouge, which is different in scale from

fault population statistics. In other words, you have to get far enough

out of, for example, the fault gouge to see the fault itself, and then

to see that the fault has a width and a length, with fault tips withinthe host rock. This is a less restrictive requirement than the CHILE

(continuous, homogeneous, linearly elastic) or DIANE (discontinu-

Table 1.2. Classication of structural discontinuities according to the rate of change of displacement

across them (sharp planes with discontinuous displacement vs. tabular zones with continuous

displacement) and by kinematics (displacement sense across the structure).

Sharp TabularDiscontinuity Discontinuity

Opening Crack (Joint, Dike, Sill, Dilation bandHydrofracture) Dilational shear band

Shearing Fault (Slip patch) Shear band; also Shear zone

Compactional shear bandClosing Stylolite Compaction band

DISPLACEMENT CONTINUITY

DISPLACEMENT

SENSE


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ous, inhomogeneous, anisotropic, non-elastic) assumptions that may

come into play with more detailed investigations however. Specify-

ing statistically homogeneous and continuous properties outside the

discontinuity (an effective continuum) clearly denes the appropriate

scale of observation at which these denitions are meant to apply.

Structural discontinuities that do not rupture the entire rock mass

are characteristically discontinuous in length in one or more directions

(e.g., Davison, 1994). That is, discontinuities end, or terminate, where

the displacements across them go to zero (the discontinuity tips, or

tipline; Fig. 1.11b). However, many discontinuities open or intersect at

surfaces such as the ground, excavation faces, or other discontinuities;

here, the discontinuity does not have a sharp termination as it wouldif it ended inside the rock. Discontinuities that completely rupture a

rock, causing it to fall apart, have no physical terminations.

Discontinuities with lengths less than the dimensions of the rock

in which they occur have clearly dened terminations: these are called

boundeddiscontinuities. Sometimes the discontinuity intersects an-

other planar element such as the Earths surface or another disconti-

nuity. In this case the discontinuity is considered to be unbounded at

the intersection yet is bounded by the rock elsewhere; this is called a

semi-boundeddiscontinuity. Faults that intersect the ground surface,

for example, are semi-bounded discontinuities. This distinction ofbounded vs. unbounded discontinuities can be important in applying

engineering principles, such as those embodied by the Coulomb fric-

tion and Mohr circles, as well as stress intensity factors, to naturally

and articially occurring structural discontinuities in the Earth (e.g.,

Palmer and Rice, 1973; Rudnicki, 1980). This is because discontinu-

ity propagation occurs at its tips, along with most of the close-range

mechanical (stress) interaction that governs whether closely spaced

discontinuities will link.

Adisplacement-based classication of structural discontinui-

ties is constructed by evaluating the sense, and continuity, of displace-

ment relative to the plane of the structure (e.g., Griggs and Handin,

1960; Pollard and Aydin, 1988; Jamison, 1989; Wojtal, 1989; Johnson,

1995; Aydin, 2000; Aydin et al., 2006). In the eld, you would ex-

Fig. 1.11. Denition of dimensional terms for a structural discontinuity (after Schultz and Fossen, 2002). (a) Discontinu-

ity plane dipping in a layer of given thickness has a horizontal length L, a down-dip height (measured in the plane of the

discontinuity)H, and a thickness or width W; all three measurements are orthogonal and relative to the structure. (b) View

normal to the discontinuity showing the tipline (elliptical in shape for this example).

Down-dipHeight

Horizontal Length L

Dmax

tiplineb

Layerthickness

LH

eight

aW


16/25


amine and demonstrate the two key parameters: displacement sense

and displacement continuity, as shown in Table 1.2. Assessing the

displacement sense is straightforwardthe methods of crosscut-

ting and shear-sense criteria are available in any structural geology

text. Assessing the continuity of displacement across the structure

reduces in most cases to determining the width of the structure and

then examining if the opening, shearing, or closing displacement issmoothly varying across the zone (i.e., a continuous displacement)

or if it changes abruptly (i.e., a discontinuous displacement). More

often than not, there is a correlation between width of the structure

and the displacement continuity (i.e., continuous shearing across a

tabular structure 1 mm thick), especially in the early development of

a structure.

The issue of whether a fault should be considered to be a single,

solitary structure or a zone can now be considered. As emphasized

by many including Johnson (1995) and Crider and Peacock (2004),

a fault is an end-product of shearing in a rock, and there is more toa fault than just the slip surface (e.g., Rice, 1992; Caine et al., 1996;

Aydin, 2000; Mandl, 2000; Shipton and Cowie, 2001; Scholz, 2002).

Certainly, the fault plane that is recognized by geologists by its

smooth, polished, and grooved or corrugated surface accommodates

a large fraction of the offset, but other elements that formed before

and after the fault plane nucleated are also important to recognize

and include as parts of the structure. The denition of a fault as a

single plane, or as a pair of planes, that accommodates the offset is

necessary, but not sufcient, to encompass the major characteristics

of this important structure.

tA fault is a sharp structural discontinuity, dened by its fault

planes (surfaces of discontinuous displacement) and related

structures including fault core and damage zones (e.g., cracks,

deformation bands, slip surfaces, and other structural disconti-

nuities) that formed at any stage in the evolution of the structure.

Commonly associated ductile deformation structures known

as drag or faulted fault-propagation folds, are associated ele-

ments not included in the term fault, although clay smearing

or other early forms of strain localization may be included.

tA fault zone is a set of relatively closely spaced faults having

similar strikes.

tAshear zone is a tabular structural discontinuity having a continu-

ous change in strength or stiffness across a relatively narrow zone

of shearing; shear and volumetric strains are continuous across

the zone and large or continuous (linked) slip surfaces are rare or

absent.

In order of maturity, or degree of strain localization, a shear zoneprecedes a fault, which precedes a fault zone.


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1.1.4 The Role of Lithology and Rock PropertiesThe physical properties of a rock affect its strength, deformability

(see Bell, 1993, pp. 165179, and Evans and Kohlstedt, 1995, for

concise syntheses) and the types of structural discontinuities that

form within it (see also Crider and Peacock, 2004). In particular, the

porosity of a rock or soil exerts a primary inuence on the type of

structural discontinuities that form (see reviews and discussions byWong et al., 1992, 2004; Brgmann et al., 1994; Aydin, 2000, Pol-

lard and Fletcher, 2005, p. 382; Aydin et al., 2006; and Fossen et al.,

2007).

There is a good correlation between the amount of porosity in a

rock or soil and the volumetric changes it undergoes during deforma-

tion (e.g., Evans and Kohlstedt, 1995; Davis and Selvadurai, 2002;

Wong et al., 1992, 2004). For example, a compact rock (Paterson

and Wong, 2005) with negligible porosity, such as a granite or basalt,

or a low-porosity soil (called overconsolidated), typically expands

in volume during shearing, leading to dilatant behavior and localizedzones of concentrated shear. In contrast, a rock with high porosity

(e.g., n > 1020%), or a high-porosity soil (called normally consoli-

dated), generally contracts in volume during shearing, leading to

porosity reduction and distributed deformation. In the rock mechanics

literature, brittle deformation is associated with localized dilatancy

and strain localization, whereas ductile deformation is associated with

non-localized macroscopic ow (e.g., Evans and Kohlstedt, 1995).

A good correlation also exists between the porosity of a rock and

the type of structural discontinuitysharp or tabularthat forms in it

(e.g., Aydin et al., 2006). Tabular structural discontinuities (deforma-

tion bands) form most easily in high-porosity rocks, like sandstone,

chalks, some pyroclastic tuffs, and many limestones, whereas sharp

structural discontinuities (cracks and faults) form in rocks of any value

of porosity. Although other variables such as stress state, mineralogy,

and pore-water conditions appear to inuence the type ofstructural

discontinuities that form in a rock (e.g., Davatzes et al., 2005), tabular

structural discontinuities are clearly restricted to formation in rocks

having non-negligible values of porosity.

This dichotomy in structure type (sharp vs. tabular structural

discontinuities) is illustrated in Fig. 1.12 after Schultz and Fossen

(2008). Here, the kinematics of the structural discontinuities also mustbe specied before the structural discontinuities can be named. By

specifying the kinematics, a broad class such as deformation bands

(see also Table 1.2) can be divided into its ve kinematic classes (i.e.,

dilation bands, dilational shear bands, shear bands, compactional shear

bands, and compaction bands), depending on the relative amounts

of volumetric change (dilation or compaction) and shear strain ac-

commodated across the structural discontinuity. Similarly, cracks

and faults can be distinguished by the amounts of opening or shear

displacements across them. These diagrams indicate the initial types

of geologic structural discontinuities (e.g., sharp or tabular) that canoccur in a rock, depending on its porosity.


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1.2 DISPLACEMENT MODES

The approach developed in this book for structural discontinui-

ties is based on the deformation of rock or other material in a local

coordinate system that is dened by the plane of the structural

discontinuity (Irwin, 1957; Sih et al., 1962; Paris and Sih, 1965; Sih

and Liebowitz, 1968; Pollard and Segall, 1987; see Kies et al., 1975,

for an historical overview). Analysis of the stresses and displace-

ments associated with structural discontinuities (sharp or tabular) of

any displacement mode lays the foundation for the eld ofgeologic

fracture mechanics (Chapters 9 and 10) that therefore includes all

types of geologic structural discontinuities, including fractures and

bands.

Suppose we observe a vertical joint that cuts a thin sedimentary

layer (as in Fig. 1.13). In order to investigate this joint using the

concept of displacement modes and the techniques of fracture me-

chanics, we can orient this structural discontinuity most convenientlywith its plane parallel to thex-axis and centered at the origin of this

localxy coordinate system, as shown in Fig. 1.14 (see also Crouch

Fig. 1.13. Geologists examine a joint

exposed in a thin horizontal sedimen-

tary layer in New York State.

Fig. 1.12. A more precise classication of structural discontinuities is possible when the porosity of the host rock is consid-

ered (after Schultz and Fossen, 2008). The lower-left diagram assumes a porous host rock, such as sandstone, chalk, and

many limestones and shales. Tabular discontinuities (deformation bands) form most easily in porous rocks, with the type

of band depending on the relative amounts of shear strain and volume change they accommodate. The upper-right diagram

assumes a low-porosity rock, such as a granite, gneiss, or basalt. Sharp discontinuities (fractures) characteristically form

in these rocks. In particular cases, anticracks (stylolites) may form given appropriate conditions of pressure, temperature,and host-rock composition. Although sharp discontinuities can also form in porous rocks, tabular discontinuities rarely if

ever occur in the low porosity rocks.

Fault(Slip Surface)

Sharp Discontinuity(Plane)Crack

Dila

tional

Shear B

and

ShearStrain

Dilation Compaction

Volumetric Change

Compactional

ShearBand

Shear Band

Tabular Discontinuity(Band)DilationBand

CompactionBand

Anticrack


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and Stareld, 1983, p. 91; Lawn, 1993, p. 3). In this case the hori-zontal layer containing the discontinuity (as in Fig. 1.13) denes in

thexy-plane, and is represented for clarity in Fig. 1.12 as being thin

in the vertical, z-direction. Stresses acting in the xy-plane, such as

layer-parallel shear, compression, or tension, are called in-plane

stresses and those acting perpendicular to this plane (having a z

component) are called out-of-plane or antiplane stresses (e.g.,

Pollard and Segall, 1987, pp. 316317). Thexy-plane can be thought

of as the Earths surface, with a vertically or steeply dipping structural

discontinuity in map view cutting down into the layer (Figs. 1.13 and

1.14). Although the layer itself is shown as thin in this example, the

denition of displacement mode applies regardless of layer thick-

ness. This means we can start with the joints that cut a large granitic

pluton, such as those shown in Fig. 1.2, or the rotated normal faults

as shown in Fig. 1.3, and dene our coordinate systems using these

structural discontinuities and these layers (i.e., the Earths surface in

Fig. 1.2 and the inclined bedding in Fig. 1.3). In-plane stresses can

produce rock rotations about vertical axes, as in strike-slip tectonics,

whereas antiplane stresses can induce rock rotations about horizontal

axes, as in normal or thrust faulting.

The three displacement modes are dened in the upper set of

diagrams in Fig. 1.15; these are oriented as is typical in engineeringtreatises (e.g., Paris and Sih, 1965; Sih and Liebowitz, 1968; Kanninen

and Popelar, 1985, p. 139; Broek, 1986, p. 8; Atkinson, 1987; Lawn,

Fig. 1.14. Dening the reference plane of interest, such as the horizontal plane shown here, is needed to determine whether

the stresses that load a structural discontinuity are (a) in-plane (layer-parallel) or (b) out-of-plane. The structural discontinuity

is shown as an ellipse on the surface of the layer. The two-dimensional stress states associated with in-plane loading (top

view) and out-of-plane loading (cross-strike view and along-strike view) are shown along with the axis of rotation

implied by the shear stresses for each planar view. Note thattxy

=tyx

,txz

=tzx

, andtyz

=tzy

(see Chapter 3).

zy

x

yy

zz

zz

xz

y

xx

yz yy

yz

zz

xyyx

xzzx

yy

xx

xy

z

a. In-plane Stresses (xy-plane)

b. Out-of-plane Stresses(xz-plane or yz-plane)

x

x

zyyz

Top view(horizontal plane)

Cross-strike view(vertical section)

Along-strike view(vertical section)

xx


20/25


1993, p. 24; Anderson, 1995, p. 53; Tada et al., 2000, p. 2; see also

Dmowska and Rice, 1986; Pollard and Fletcher, 2005, p. 372). They

were dened originally in the engineeringcontext for design of ships,

bridges, railroads, and buildings (e.g., Kanninen and Popelar, 1985;

Broek, 1986; Lawn, 1993; Anderson, 1995). Structural discontinuities

that accommodate more than one principal (or pure) displacement

mode are called mixed-mode. For example, a crack (mode-I) that

opens obliquely is called a mixed-mode crack (mode I-II or I-III

depending on the sense of shearing along the crack walls; see Chap-

ter 2). The shearing modes (II and III) are commonly introduced in

engineering fracture mechanics treatises to explain crack propagation

paths (mixed-mode I-II cracks) or breakdown of the crack tip during

propagation (mixed-mode I-III) (e.g., Erdogan and Sih, 1963; Sih,

1974; Ingraffea, 1987; Lawn, 1993, p. 23).

The displacement modes have also been applied to the analysis

and interpretation ofgeologic structural discontinuities (e.g., see

Brace and Bombolakis, 1963; Segall and Pollard, 1980; Engelder,

1987; Pollard et al., 1982, 1993; Aydin, 1985; Pollard and Segall,

1987; Pollard and Aydin, 1988; Cowie and Scholz, 1992b; Engelderet al., 1993; Schultz and Balasko, 2003; Pollard and Fletcher, 2005;

see also Chapters 2, 4, 5, 7, 9, and 10). For example, a deformation

Fig. 1.15. The three displacement modes of a structural discontinuity are identied relative to the reference plane (here, the

unshadedxy-plane) and the edge, or tipline, of the discontinuity. The upper diagrams are oriented following standard engi-

neering practice, with mode-II shearing dened as being normal to the leading edge and mode-III shearing being parallel to

the leading edge (Tada et al., 2000). The lower diagrams are rotated so that the reference (xy-) plane is horizontal, as is the

case for many geologic situations (e.g., Fig. 1.13); modes II and III are dened relative to the tipline.

x

y

z

x

y

z

+

Mode-II

+

x

y

z

Mode-IIIMode-I

x

y

z x

y

z

+

+

x

y

z

Tipline

LeadingEdge

LeadingEdge

Tip

line

Tiplin

e


21/25


band that accommodates both shearing and volumetric dilation (i.e.,

a dilational shear band; see Table 1.2 and Chapter 5) would be a

mixed-mode tabular structural discontinuity, with the order of the

mode numerals indicating the relative amounts of each component

(greater magnitude listed rst; i.e., mode II-I or III-I for the case of

shear displacement exceeding the dilational displacement).

The displacement mode diagrams can be made more intuitivelyapplicable to geologic situations by rotating them so that the reference

xy-plane becomes the horizontal plane; this is shown by the lower

set of diagrams in Fig. 1.15. The displacement mode of a geologic

structural discontinuity (e.g., the joint shown in Fig. 1.13) is now eas-

ily established in relation to the edge (tipline) of the discontinuity

(Fig. 1.15). The tipline is the intersection between the plane of the

structural discontinuity and the reference plane (e.g., the xy-plane

as in Figs. 1.13 and 1.14). The displacement sense on the tipline, in

relation to the reference plane, determines the displacement mode.

If the tipline opens (or dilates) in the in-plane direction, the struc-tural discontinuity is called mode-I (mode one, not mode eye),

analogous to a joint, vein, or dike (e.g., Pollard et al., 1982; Pollard

and Segall, 1983a, b; Pollard and Aydin, 1984, 1988; Kulander and

Dean, 1985; Delaney et al., 1986; Pollard, 1987; Rubin, 1993a). If

the tipline accommodates shearing in the xy-plane (with the shear

or displacement sense normal to the faults vertical edge, as in Fig.

1.15, upper center diagram), the structural discontinuity is mode-II,

analogous to a strike-slip fault in map view (e.g., Chinnery, 1961,

1963, 1965; Rodgers, 1980; Segall and Pollard, 1980; Rispoli, 1981;

Aydin and Page, 1984; Pollard and Segall, 1987; Petit and Barquins,

1988; Davison, 1994). Out-of-plane (i.e., subvertical) shearing along

the tipline (with the shear or displacement sense parallel to the faults

vertical edge, as in Fig. 1.15, upper right diagram) corresponds to

mode-III, analogous to a normal or thrust fault seen in map view

(e.g., King and Yielding, 1984; Aydin, 1985; Pollard and Segall, 1987;

Davison, 1994; Willemse et al., 1996; Crider and Pollard, 1998; Gupta

and Scholz, 2000a). Mode-I structural discontinuities are discussed

in detail in Chapter 2; mode-II and mode-III structural discontinuities

are considered in Chapter 4.

A sharp or tabular structural discontinuity can thus be categorized

as:

tMode-I: opening along a structural discontinuity (called opening

mode).

tMode-II: in-plane shear along a structural discontinuity (called

shearing mode).

tMode-III: out-of-plane shear along a structural discontinuity

(called tearing mode).

The mode-I case with a horizontal reference plane (Fig. 1.15, lower-

left diagram) was used by DeGraff and Aydin (1987) and Pollard andAydin (1988) to illustrate crack propagation paths for a vertically dip-

ping joint. Segall and Pollard (1980) and Pollard and Segall (1987,


22/25


their gure 8.18) note that a strike-slip fault corresponds to a mode-II

structural discontinuity in map view and a mode-III structural discon-

tinuity in cross-sectional view. The reoriented mode-II diagram in Fig.

1.15 (lower center) follows those of Marone (1998b, his gure 15) and

Pollard and Segall (1987, their gure 8.16a). Similarly, a normal or

thrust fault corresponds to a dipping mode-III structural discontinuity

in map view and a mode-II structural discontinuity in cross-sectionalview (e.g., Aydin, 1985). Determination of the displacement mode in

relation to the shear sense is also important in the study of deformation

bands (e.g., Aydin, 1978; Aydin and Johnson, 1978, 1983; Schultz and

Balasko, 2003; Okubo and Schultz, 2006).

Denition of the displacement mode for a dilatant crack is straight-

forward, as shown in Fig. 1.16a; mixed mode (I-II and I-III) cracks

are discussed in Chapter 2. In contrast, the displacement mode along

a shearing elliptical structural discontinuity surface, such as a fault

or shear deformation band, depends on where you are along it. The

dependence of displacement mode on the discontinuitys tipline andshear-offset vector are shown in detail in Fig. 1.17. For example, a

strike-slip fault is a mode-II structural discontinuity in map (horizon-

tal) view but in a vertical section the shear sense is mode-III (e.g.,

Segall and Pollard, 1980; Pollard and Segall, 1987; Martel and Boger,

1998; Figs. 1.16b, 1.17a). A dip-slip (normal or thrust) fault is a mode-

III structural discontinuity in map (horizontal) view but in a vertical

section the shear sense is mode-II (Figs. 1.16c, d, 1.17b). The same

relationships hold for tabular discontinuities such as deformation

bands (Aydin, 2000; Schultz and Balasko, 2003; Aydin et al., 2006;

Okubo and Schultz, 2006).

Fig. 1.16. Modes of predominant displacement sense for (a) mode-I, including

joints, veins, dikes, and dilation bands; (b) mode-II, strike-slip (faults and defor-

mation bands) in map view; (c) mode-III, normal (faults and deformation bands)in map view; and (d) mode-III, thrust (faults and deformation bands) in map view.

The mode for faults and shear deformation bands depends on the orientation of the

slice, or reference plane, in relation to the slip vector.

OPENING

VECTOR

SHEAR

OFFSET

VECTOR

Mode-II

Mode-III

Mode-II

Mode-III

SHEAR

OFFSET

VECTOR

SHEAR OF

FSETVECT

OR

Mode-II

Mode-III

a. Dilation b. Strike-slip offset

c. Normal offset d. Thrust offset


23/25


24/25


Sternlof et al., 2005; Rudnicki, 2007; Tembe et al., 2008), resulting

in closing (or interpenetrating) discontinuity walls. Mollema and An-

tonellini, (1996) suggested using anti-mode-I for their anticracks,

as did Green et al. (1990); the term mode I (minus one) has also

been used informally to describe these structures (Scholz, 2002, p.

331). Introducing a negative sign before mode-I elegantly conveys

the kinematic signicance of anticracks but it may also blur the im-portant physical distinctions between cracks and the several varieties

of anticracks (e.g., Fletcher and Pollard, 1981; Knipe, 1989) such as

pressure-solution seams (stylolites) and compaction bands. As shown

in Table 1.2, anticracks can be either sharp or tabular, permitting both

stylolites and compaction bands to be investigated kinematically and,

to a degree, mechanically, as anticrack structural discontinuities.

1.3 USING GEOLOGIC FRACTURE MECHANICS

IN RESEARCH AND PRACTICE

Throughout this book and your study of fracture mechanics ap-

plied to geologic fractures and deformation bands, you will repeatedly

encounter a number of major concepts, such as stress concentration or

displacement-length scaling. Sometimes these concepts or principles

that are based on mechanics are readily apparent, as for example

when working out the growth history of a set of tectonic joints or in

reconstructing the sequence of fault segment linkage by measuring

the displacement proles along the faults. In other situations, how-

ever, you might not think that fracture mechanics would apply. For

example, the lateral margins of regional-scale detachment structuresin Tertiary-age extensional terranes, of thrust sheets in a Paleozoic

contractional orogen, and of landslides that scallop out a mountainside,

all likely nucleated, and continued to function, as particular types of

fault arrays. Many problems in nite strain started as small, inni-

tesimal strains and developed from there (for example, see the nice

papers by Chinnery (1961), Aydin and Nur (1982), Aydin and Page

(1984), ten Brink et al. (1996), and Kattenhorn and Marshall (2006)

on strike-slip tectonics; Cowie and Scholz (1992b) and Schultz et al.

(2006) on fault displacement-length scaling; Willemse (1997) and

Soliva et al. (2008) on fault growth and linkage; Nio et al. (1998)

and Cooke and Kameda (2002) on fold-and-thrust belts; and Martel

(2004) on landslide nucleation). These phenomena obey the laws of

fracture mechanics even though the strains involve may ultimately

become large, nite values (such as several tens of percent or more).

Once you learn how fractures operate, you will be able to work out the

sequence of deformation regardless of how complicated a structural

suite has eventually become.

The material in this book will also give you a number of new

tools and techniques that should become part of your arsenal in the

eld. For example, you will learn to decipher what the shape of the

termination of a dike or fault means mechanically, and what thatsays about how the fracture grew. Youll learn several reliable rules

of thumb for relating the amount of offset or opening displacement

Acquire new tools

Mechanics is to structural

geology as thermodynamics is

to petrology


25/25

clasification of structural discontinuities

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