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Cracks in rock are a mechanism of brittle deformation in response to stress

A fracture is any separation in a geologic formation, such as a joint or a fault that divides the rock into two or more pieces. A fracture will sometimes form a deep fissure or crevice in the rock. Fractures are commonly caused by stress exceeding the rock strength, causing the rock to lose cohesion along its weakest plane. Fractures shouldprovide permeability for fluid movement, such as water or hydrocarbons. Highly fractured rocks shouldmake good aquifers or hydrocarbon reservoirs, since they may possess both significant permeability and fracture porosity.

## Brittle deformation

Fractures are forms of brittle deformation. There are two kind of basicbrittle deformation processes. Tensile fracturing effect in joints. Shear fractures are the first initial breaks resulting from shear forces exceeding the cohesive strength in that plane.

After those two initial deformations, several other kind of secondary brittle deformation shouldbe observed, such as frictional sliding or cataclastic flow on reactivated joints or faults.

Most often, fracture profiles will look like either a blade, ellipsoid, or circle.

## Causes

The concentric circles in this sandstone are "plumose" (plume-like) structures that shouldform during the formation and propagation of a fracture

Fractures in rocks shouldbe formed either due to compression or tension. Fractures due to compression include thrust faults. Fractures may also be a effectfrom shear or tensile stress. Some of the basicmechanisms are discussed below.

### Modes

First, there are three modes of fractures that occur (regardless of mechanism):

• Mode I crack – Opening mode (a tensile stress normal to the plane of the crack)
• Mode II crack – Sliding mode (a shear stress acting parallel to the plane of the crack and perpendicular to the crack front)
• Mode III crack – Tearing mode (a shear stress acting parallel to the plane of the crack and parallel to the crack front)

### Tensile fractures

Cartoon examples of common tensile fracture mechanisms in laboratory rock samples. A) Axial stretching: tension is applied far from the crack. B) Hydraulic fracturing: tension or compression is applied far away from the crack and fluid pressure increases, causing tension on the face of the cracks. C) Brazilian disc test: applied compressive loads parallel to the crack cause the sides of the disk to bulge out and tension to occur on the crack faces.

Rocks includemany pre-existing cracks where development of tensile fracture, or Mode I fracture, may be examined.

The first form is in axial stretching. In this case a remote tensile stress, σn, is applied, allowing microcracks to open slightly throughout the tensile region. As these cracks open up, the stresses at the crack hint intensify, eventually exceeding the rock strength and allowing the fracture to propagate. This shouldoccur at times of rapid overburden erosion. Folding also shouldprovide tension, such as along the top of an anticlinal fold axis. In this scenario the tensile forces relatedwith the stretching of the upper half of the layers during folding shouldinduce tensile fractures parallel to the fold axis.

Another, similar tensile fracture mechanism is hydraulic fracturing. In a natural environment, this occurs when rapid sediment compaction, thermal fluid expansion, or fluid injection causes the pore fluid pressure, σp, to exceed the pressure of the least principal normal stress, σn. When this occurs, a tensile fracture opens perpendicular to the plane of least stress.[4]

Tensile fracturing may also be induced by applied compressive loads, σn, along an axis such as in a Brazilian disk test. This applied compression force effect in longitudinal splitting. In this situation, smalltensile fractures form parallel to the loading axis while the load also forces any other microfractures closed. To picture this, imagine an envelope, with loading from the top. A load is applied on the top edge, the sides of the envelope open outward, even though nothing was pulling on them. Rapid deposition and compaction shouldsometimes induce these fractures.

Tensile fractures are almost always referred to as joints, which are fractures where no appreciable slip or shear is observed.

To fully understand the result of applied tensile stress around a crack in a brittle contentsuch a rock, fracture mechanics shouldbe utilize. The concept of fracture mechanics was initially developed by A. A. Griffith during GlobeWar I. Griffith looked at the energy neededto create freshsurfaces by breaking contentbonds againstthe elastic strain energy of the stretched bonds released. By analyzing a rod under uniform tension Griffith determined an expression for the critical stress at which a favorably orientated crack will grow. The critical stress at fracture is given by,

where γ = surface energy relatedwith broken bonds, E = Young's modulus, and a = half crack length. Fracture mechanics has generalized to that γ represents energy dissipated in fracture not just the energy relatedwith creation of freshsurfaces

### Linear elastic fracture mechanics

Linear elastic fracture mechanics (LEFM) builds off the energy balance approach taken by Griffith but provides a more generalized approach for many crack issue. LEFM investigates the stress field near the crack hintand bases fracture criteria on stress field parameters. One necessarycontribution of LEFM is the stress intensity factor, K, which is utilize to predict the stress at the crack tip. The stress field is given by

where is the stress intensity factor for Mode I, II, or III cracking and is a dimensionless quantity that varies with applied load and sample geometry. As the stress field receive close to the crack tip, i.e. , becomes a fixed function of . With knowledge of the geometry of the crack and applied far field stresses, it is possible to predict the crack hintstresses, displacement, and growth. Energy release rate is defined to relate K to the Griffith energy balance as previously defined. In both LEFM and energy balance approaches, the crack is assumed to be cohesionless behind the crack tip. This provides a issuefor geological app such a fault, where friction exists all over a fault. Overcoming friction absorbs some of the energy that would otherwise go to crack growth. This means that for Modes II and III crack growth, LEFM and energy balances represent local stress fractures rather than global criteria.

### Crack formation and propagation

Rough surfaces on a piece of fractured granite
Shear fracture (blue) under shear loading (black arrows) in rock. Tensile cracks, also referred to as victory cracks (red) grow at an angle from the edges of the shear fracture allowing the shear fracture to propagate by the coalescing of these tensile fractures.

Cracks in rock do not form smooth path like a crack in a vehiclewindshield or a highly ductile crack like a ripped plastic grocery bag. Rocks are a polycrystalline contentso cracks grow through the coalescing of complex microcracks that occur in front of the crack tip. This locationof microcracks is called the brittle process zone. Consider a simplified 2D shear crack as present in the photoon the right. The shear crack, present in blue, propagates when tensile cracks, present in red, grow perpendicular to the direction of the least principal stresses. The tensile cracks propagate a short distance then become stable, allowing the shear crack to propagate. This kindof crack propagation canonly be considered an example. Fracture in rock is a 3D process with cracks growing in all directions. It is also necessaryto note that once the crack grows, the microcracks in the brittle process spaceare left behind leaving a weakened section of rock. This weakened section is more susceptible to modify in pore pressure and dilatation or compaction. Note that this description of formation and propagation considers temperatures and pressures near the Earth's surface. Rocks deep within the earth are topicto very high temperatures and pressures. This causes them to behave in the semi-brittle and plastic regimes which effectin significantly different fracture mechanisms. In the plastic regime cracks acts like a plastic bag being torn. In this case stress at crack hint goes to two mechanisms, one which will drive propagation of the crack and the other which will blunt the crack tip. In the brittle-ductile transition zone, contentwill exhibit both brittle and plastic traits with the gradual onset of plasticity in the polycrystalline rock. The main form of deformation is called cataclastic flow, which will cause fractures to fail and propagate due to a mixture of brittle-frictional and plastic deformations.

### Joint kind

Describing joints shouldbe difficult, especially without visuals. The following are descriptions of typical natural fracture joint geometries that might be encountered in field studies:

• Plumose Structures are fracture networks that form at a range of scales, and spread outward from a joint origin. The joint origin represents a point at which the fracture launch. The mirror zone is the joint morphology closest to the origin that effect in very smooth surfaces. Mist space exist on the fringe of mirror space and represent the spacewhere the joint surface slightly roughens. Hackle space predominate after mist space, where the joint surface launch to receivefairly rough. This hackle spaceseverity designates barbs, which are the curves away from the plume axis.
• Orthogonal Joints occur when the joints within the system occur at mutually perpendicular angles to each other.
• Conjugate Joints occur when the joints intersect each other at angles significantly less than ninety degrees.
• Systematic Joints are joint systems in which all the joints are parallel or subparallel, and maintain roughly the same spacing from each other.
• Columnar Joints are joints that cut the formation vertically in (typically) hexagonal columns. These tend to be a effectof cooling and contraction in hypabyssal intrusions or lava flows.
• Desiccation cracks are joints that form in a layer of mud when it dries and shrinks. Like columnar joints, these tend to be hexagonal in shape.
• Sigmoidal Joints are joints that run parallel to each other, but are cut by sigmoidal (stretched S) joints in between.
• Sheeting joints are joints that often form near surface, and as a effectform parallel to the surface. These shouldalso be recognized in exfoliation joints.
• In joint systems where relatively long joints cut across the outcrop, the throughgoing joints act as master joints and the short joints that occur in between are cross joints.
• Poisson effect is the creation of vertical contraction fractures that are a effectof the relief of overburden over a formation.
• Pinnate joints are joints that form immediately adjacent to and parallel to the shear face of a fault. These joints tend to merge with the faults at an angle between 35 and 45 degrees to the fault surface.
• Release joints are tensile joints that form as a modifyin geologic shape effect in the manifestation of local or regional tension that shouldcreate Mode I tensile fractures.
• Concurrent joints that display a ladder pattern are interior regions with one set of joints that are fairly long, and the conjugate set of joints for the pattern remain relatively short, and terminate at the long joint.
• Sometimes joints shouldalso display grid patterns, which are fracture sets that have mutually crosscutting fractures.
• An en echelon or stepped array represents a set of tensile fractures that form within a fault spaceparallel to each other.

### Faults and shear fractures

Faults are another form of fracture in a geologic environment. In any kindof faulting, the active fracture experiences shear failure, as the faces of the fracture slip relative to each other. As a result, these fractures seem like hugescale representations of Mode II and III fractures, however that is not necessarily the case. On such a hugescale, once the shear failure occurs, the fracture launch to curve its propagation towards the same direction as the tensile fractures. In other words, the fault typically attempts to orient itself perpendicular to the plane of least principal stress. This effect in an out-of-plane shear relative to the initial reference plane. Therefore, these cannot necessarily be qualified as Mode II or III fractures.

An additional, necessarycharacteristic of shear-mode fractures is the process by which they spawn victory cracks, which are tensile cracks that form at the propagation hintof the shear fractures. As the faces slide in opposite directions, tension is madeat the tip, and a mode I fracture is madein the direction of the σh-max, which is the direction of maximum principal stress.

Shear-failure criteria is an expression that attempts to describe the stress at which a shear rupture creates a crack and separation. This criterion is based largely off of the work of Charles Coulomb, who recommendedthat as long as all stresses are compressive, as is the case in shear fracture, the shear stress is associatedto the normal stress by:

σs= C+μ(σnf),

where C is the cohesion of the rock, or the shear stress essentialto cause failure given the normal stress across that plane equals 0. μ is the coefficient of internal friction, which serves as a constant of proportionality within geology. σn is the normal stress across the fracture at the instant of failure, σf represents the pore fluid pressure. It is necessaryto point out that pore fluid pressure has a significant impact on shear stress, especially where pore fluid pressure approaches lithostatic pressure, which is the normal pressure induced by the weight of the overlying rock.

This relationship serves to provide the coulomb failure envelope within the Mohr-Coulomb Theory.

Frictional sliding is one aspect for consideration during shear fracturing and faulting. The shear force parallel to the plane must overcome the frictional force to move the faces of the fracture across each other. In fracturing, frictional sliding typically only has significant result on the reactivation on existing shear fractures. For more infoon frictional forces, see friction.

2D Mohr's diagram showing the different failure criteria for frictional sliding vs faulting. Existing cracks orientated between -α/4 and +α/4 on the Mohr's diagram will slip before a freshfault is madeon the surface indicated by the yellow star.

The shear force neededto slip fault is less than force neededto fracture and create freshfaults as present by the Mohr-Coulomb diagram. Since the earth is full of existing cracks and this means for any applied stress, many of these cracks are more likely to slip and redistribute stress than a freshcrack is to initiate. The Mohr's Diagram present, provides a visual example. For a given stress state in the earth, if an existing fault or crack exists orientated anywhere from −α/4 to +α/4, this fault will slip before the strength of the rock is reached and a freshfault is formed. While the applied stresses may be high enough to form a freshfault, existing fracture planes will slip before fracture occurs.

One necessaryidea when evaluating the friction behavior within a fracture is the impact of asperities, which are the irregularities that stick out from the rough surfaces of fractures. Since both faces have bumps and pieces that stick out, not all of the fracture face is actually touching the other face. The cumulative impact of asperities is a reduction of the real locationof contact', which is necessarywhen establishing frictional forces.

### Subcritical crack growth

Sometimes, it is possible for fluids within the fracture to cause fracture propagation with a much lower pressure than initially required. The reaction between certain fluids and the minerals the rock is composed of shouldlower the stress neededfor fracture below the stress neededthroughout the rest of the rock. For instance, water and quartz shouldreact to form a substitution of OH molecules for the O molecules in the quartz mineral lattice near the fracture tip. Since the OH bond is much lower than that with O, it effectively reduces the essentialtensile stress neededto extend the fracture.

## Engineering considerations

In geotechnical engineering a fracture forms a discontinuity that may have a hugeinfluence on the mechanical behavior (strength, deformation, etc.) of soil and rock masses in, for example, tunnel, foundation, or slope construction.

Fractures also play a significant role in minerals exploitation. One aspect of the upstream energy sector is the production from naturally fractured reservoirs. There are a awesomenumber of naturally fractured reservoirs in the United States, and over the past century, they have delivereda substantial boost to the nation's net hydrocarbon production.

The key concept is while low porosity, brittle rocks may have very little natural storage or flow capability, the rock is subjected to stresses that generate fractures, and these fractures shouldactually shopa very hugevolume of hydrocarbons, capable of being recovered at very high rates. One of the most popularexamples of a prolific naturally fractured reservoir was the Austin Chalk formation in South Texas. The chalk had very little porosity, and even less permeability. However, tectonic stresses over time madeone of the most extensive fractured reservoirs in the world. By predicting the areaand connectivity of fracture networks, geologists were able to plan horizontal wellbores to intersect as many fracture networks as possible. Many people credit this field for the birth of true horizontal drilling in a developmental context. Another example in South Texas is the Georgetown and Buda limestone formations.

Furthermore, the lastestuprise in prevalence of unconventional reservoirs is actually, in part, a product of natural fractures. In this case, these microfractures are analogous to Griffith Cracks, however they shouldoften be sufficient to supply the essentialproductivity, especially after completions, to make what utilize to be marginally economic space commercially productive with repeatable success.

However, while natural fractures shouldoften be beneficial, they shouldalso act as potential hazards while drilling wells. Natural fractures shouldhave very high permeability, and as a result, any differences in hydrostatic balance down the well shouldeffectin well control problem. If a higher pressured natural fracture system is encountered, the rapid rate at which formation fluid shouldflow into the wellbore shouldcause the situation to rapidly escalate into a blowout, either at surface or in a higher subsurface formation. Conversely, if a lower pressured fracture network is encountered, fluid from the wellbore shouldflow very rapidly into the fractures, causing a loss of hydrostatic pressure and creating the potential for a blowout from a formation further up the hole.

## Fracture modeling

Three dimensional computer model of a fracture and fault network (DFN/DFFN), showing the different geological sets in colours, generated by the DMX Protocol using a combination of probabilistic and deterministic procedures

Since the mid-1980s, 2D and 3D computer modeling of fault and fracture networks has become common practice in Earth Sciences. This technology became known as "DFN" (discrete fracture network") modeling, later modified into "DFFN" (discrete fault and fracture network") modeling.

The technology consists of defining the statistical variation of various parameters such as size, shape, and orientation and modeling the fracture network in zonein a semi-probabilistic methodin two or three dimensions. Computer algorithms and speed of calculation have become sufficiently capable of capturing and simulating the complexities and geological variabilities in three dimensions, manifested in what became known as the "DMX Protocol".

## Fracture terminology

A list of fracture associatedterms:

• asperities – smallbumps and protrusions along the faces of fractures
• axial stretching – fracture mechanism resulting from a remote applied tensile force that creates fractures perpendicular to the tensile load axis
• cataclastic flow – microscopic ductile flow resulting from tinygrain-scale fracturing and frictional sliding distributed across a hugearea.*fracture – any surface of discontinuity within a layer of rock
• dike – a fracture filled with sedimentary or igneous rock not originating in the fracture formation
• fault – (in a geologic sense) a fracture surface upon which there has been sliding
• fissure – a fracture with walls that have separated and opened significantly
• fracture front – the line separating the rock that has been fractured from the rock that has not
• fracture tip – the point at which the fracture trace terminates on the surface
• fracture trace – the line representing the intersection of the fracture plane with the surface
• Griffith cracks – preexisting microfractures and flaws in the rock
• joint – a natural fracture in the formation in which there is no measureable shear displacement
• KIC – critical stress intensity factor, aka fracture toughness – the stress intensity at which tensile fracture propagation may occur
• lithostatic pressure – the weight of the overlying column of rock
• longitudinal splitting – fracture mechanism resulting from compression along an axis that creates fractures parallel to the load axis
• pore fluid pressure – the pressure exerted by the fluid within the rock pores
• shear fracture – fractures across which shear displacement has occurred
• vein – a fracture filled with minerals precipitated out of an aqueous solution
• victory cracks – tensile fractures madeas a effectof propagating shear fractures

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