1 Structural Geology Brittle Deformation 1 Lecture 12 – Spring 2016

2 Faults and Fault Zones When used in the strict sense, a fault is the actual fracture surface along which displacement occurs Fault zone includes a band of rock on either side of the displacement, or a band which includes many small faults

Shear Zone A shear zone is a band or rock in which the shear stress is concentrated. Movement can occur in several ways:  Cataclasis - Crushing and frictional sliding of grains of rock or rock fragments  Crystal plastic deformation - Dislocation glide or climb  Diffusion - Migration of ions, usually towards regions of lower stress 3

4 Fracture Termination Fractures may terminate within a rock, or extend to the surface of the rock body A line extending from the fracture that extends to the rock body surface produces the fracture trace The point where the fracture trace terminates along the surface is called the fracture tip Figure 6.2a in text

5 Fracture Front The line separating the fractured rock from the nonfractured region is the fracture front Figure 6.2b in text

6 Atomic Scale On an atomic scale, fracture depends on the stretching and breaking of bonds Atoms in equilibrium position Figure 6.3a in text

7 Stretched Bonds Individual bonds very in strength and the ability to stretch, but all bonds have a limit beyond which they will rupture Stretched bonds require less energy to break than unstretched bonds Figure 6.3b in text

8 Broken Bonds Brittle deformation is nonrecoverable, meaning the bonds are permanently stretched, usually with atomic displacement, or are broken Patterns of breakage in brittle deformation vary, and can be classified into four categories Figure 6.3c in text

9 Joint and Shear Fracture Formation Figure 6.4a-c in text b represents joint formation by tensile cracking c represents shear fracture by shear rupture

10 Sliding on Joint Left, Figure 6.4a in text Right, Figure 6.4d-e in text d represents frictional sliding on a joint reactivated by a change in stress field orientation e represents cataclastic sliding on a former joint

11 Sliding on Shear Fracture Left, Figure 6.4a in text Right, Figure 6.4f-g in text f represents sliding on a shear fracture g represents cataclastic flow in a cataclastic shear zone

12 Tensile Cracking Tensile cracking might be thought to originate when all the bonds across a plane of atoms break simultaneously Figure 6.5 in text

13 Internal Flaws If there are flaws in the material, the stress is concentrated at the edges of the flaws For circular flaws, the concentration factor is about three Figure 6.6a in text

14 Elliptical Flaws For elliptical holes, the concentration depends on the ratio of the major (a) and minor (b) axis, in the ratio (2a + 1)/b For elongated ellipses, the concentration can be significant If a is 10 and b is 1, the concentration is 21 If a = 50, b =1, the concentration is 101 Figure 6.6b in text

15 Inhibited Propagation They do not propagate because the crack tips are blunted in the process zone, where the material deforms plastically

16 Paper Tears This hypothesis suggests that if all other factors are equal, long cracks will propagate before a shorter crack Figure 6.7 in text

17 Cracking in Ice Observations of cracks forming in ice-covered lakes show the initial crack propagates outwards at a finite velocity Thus the chemical bonds are breaking in sequence, rather than all at once

18 Crack Development At some point, the concentrated stress exceeds the theoretical strength and the crack grows Note that the crack develops perpendicular to the tensile stress Figure 6.8a in text

19 Failure When the crack reaches the edge of the sample, it fails Figure 6.8b in text

20 Longitudinal Splitting Under conditions of uniaxial compression, cracks parallel to σ 1 can open, while those perpendicular to σ 1 will close Figure 6.9 in text

21 Hydraulic Fracturing Rock experiments using a triaxial load rig can also illustrate the tensile cracking process The pore pressure exerted by a fluid can create a local tensile stress at the tips of cracks, concentrating stress, and allowing cracks to propagate Figure 6.10 in text

22 Use in Petroleum Production Artificial use of hydraulic pulsing has occurred in the petroleum industry, where hydraulic fracturing of source rock is used to increase the flow of petroleum to wells

23 Crack-Surface Displacements Three modes of crack-surface displacements are recognized  Mode I – tensile cracking  Mode II – sliding mode  Mode III – tearing mode

24 Mode 1 Displacements Form in direction perpendicular to the σ 3 direction Can grow in their plane with no orientation change Upper left – Figure 6.11a in text Lower left – Figure 6.4b in text Right – fm1/crackstress/crackstress_help.html

25 Mode II Displacement Sliding of one block past another so that movement is parallel to the fracture surface, but perpendicular to the fracture front Upper left – Figure 6.11b in text Lower left - ress/crackstress_help.html

26 Mode III Displacement Sliding is parallel to the fracture front, in a direction parallel to the fracture front Upper left – Figure 6.11b in text Lower left - rackstress/crackstress_help.html

27 Shear-mode Cracks Both Modes II and III are shear-mode cracks, and do not grow in their plane They either curve, becoming Mode I cracks, or they form tensile cracks called wing cracks Note that shear-mode is not the same as shear fracture Figure 6.12 in text

28 Fibrous Calcite Stepped calcite fibers on a fault surface Pencil shows scale and indicates displacement direction

29 Cataclasis Cataclasis refers to movement on a fault surface by a combination of processes  Microcracking  Frictional sliding of fragments past one another  Rotation and transport of grains

30 Shear Fracturing The second type of brittle deformation is the shear fracture, a.k.a. shear rupture Fracturing occurs when the shear parallel to the fracture surface is large enough In rock cylinder experiments, shear fractures initiate at an acute angle to σ 1, if we expose the cylinder to confined compression (σ 1 > σ 2 = σ 3 )

31 Confined Compression Experiment The sample is jacketed, with the jacket being squeezed by a fluid under pressure This generates σ 3 ( = σ 2 ) Pistons on the ends of the rock squeeze it, generating σ 1 Figure 6.14c in text

32 σ d versus e a In this experiment we measure σ d, the dilation Δ, and the change in cylinder length, which is the axial strain, e a Plot of σ d versus e a shows four distinct stages Figure 6.14a in text

33 Stages I and II In Stage I, both σ d and e a increase, producing a concave upward curve As the experiment enters Stage II, the curve becomes a straight line with positive slope

34 Stage III In Stage III, the slope of the line decreases and the line begins to curve, so that it is convex upward The point at which the experiment enters stage III is called the yield strength

35 Dilatancy During stage I and most of stage II, dilation is negative During the end of stage II and stage III dilation becomes slightly positive, a phenomenon known simply as dilatancy Figure 6.14b in text

36 Stage IV At this point, microcracks are developing and beginning to grow When σ d = σ f, a shear rupture surface develops at an angle of about 30 º to the long axis of the cylinder

37 Failure Strength The value of σ d at the time of the stress drop (σ f ) is the failure strength for shear rupture Further deformation depends only on the resistance of the ruptured surfaces to sliding (in other words, friction)

38 Initiation of Experiment Griffith Cracks are randomly oriented As compression begins, cracks flatten and close Figure 6.14 c-d

39 Crack Closure During stage I, preexisting cracks are closing This accounts for the small negative dilation The sample begins to shorten elastically

40 Poisson Effect During stage II, the sample shortened elastically parallel to σ 1 and expanded perpendicular to the cylinder axis due to the Poisson effect Figure 6.14e in text

41 Microcrack Growth At the start of stage III, tensile microcracks are beginning to grow throughout the sample, accounting for the positive dilation Wing-cracks grow at the tips of shear-mode cracks

42 Tensile Microcrack Development Tensile cracking increases along the band at 30º to the axial compression

43 Cracks Coalesce Once these cracks coalesce into a continuous surface, failure (Stage IV) occurs

44 Conjugate Fractures In some experiments, two fractures, each about 30º to the cylinder axis, will develop The angle between the conjugate fractures is thus 60º, and their acute bisectrix is parallel to σ 1 Both fractures cannot continue to develop, so in most cases only one fracture elongates through the entire sample, causing failure

45 Slipping Without Deformation Brittle faulting occurs when measurable slipping occurs with little or no plastic deformation Brittle faulting is the result of differential stress, with slipping occurring in response to shear stress parallel to the fault plane