Fracture Notes

What are cracks and fractures? What are hydraulic fractures?


For this post, I have prepared a bunch of figures that explain cracks (fractures) and crack propagation from a Geologist's perspective. It will not be an exhaustive treatment of the subject by any means, but it will cover natural fluid-driven tensile fractures in sediments and rocks (i.e., clastic dikes). My goal is to review the pertinent parts of Fracture Mechanics using a set of new illustrations, brief discussions, and a few equations. I'll add content as I make it. Things will be kind of messy for a while.


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Stuff to do...

Principal stresses...........

Blades, wings, and apertures...........

Crack tip theory........

K, Kt, KIc........

Fracture patterns in plan view and cross section.........

Irregular fracture fronts in outcrop........

PKN, KGD, penny, t-shaped.......

Polygonal patterns in 2D and 3D.........

Reactivation in successive layers.........

Cyclic deformation and fatigue........

DFIT test curve........

Skin factor and silt skins.....

Nearfield and farfield hydrofracture.......

Propped fractures both induced and natural.......

Hall plots and sheeted dike structure....


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Fractures. When we talk about fractures, we're talking about stresses, materials, and the response of different types of materials to different magnitudes and orientations of stresses.

Materials have flaws. No material is perfect. All materials - metal, wood, rock, polymers, ceramics - contain flaws (cracks, notches, holes, etc.). Small flaws can grow into larger fractures. For our purposes, flaws are microscopic cracks (i.e., the scale of grain boundaries in a sandstone or granite) and fractures are things you can see with your eye. Most flaws go undetected, don't grow significantly over time, and don't threaten the integrity of the material. Fractures, if large enough, can lead to material failure.



Positive and negative pressure along a crack. Here's a different way to visualize stress along a crack. Instead of using arrows to show principal stress orientations of the material, I put arrows on the crack. So, stress from the crack's perspective. I'm trying to illustrate the competition between stress inside the crack (positive, arrows pointing up) with that of the material, which is trying to close it (negative, arrows pointing down). The closure pressure, or the material's resistance to opening, is equal to the minimum principal stress (O3) because a tension crack will open against O3 in the O1-O2 plane. In an open crack Pf > O3. Figure A shows how it is possible for different parts of the same crack to feel positive and negative pressure. Figure B takes the concept a bit further. The solid line represents a visible crack or flaw (positive pressure). The dashed lines represent incipient cracks, or microfractured region lying just beyond the crack tip (negative pressure). Figure C shows an open crack and incipient cracks beyond the crack tip. The open crack has positive pressure because it is pushing outward against the material that surrounds it (against O3). Incipient cracks are not technically part of the crack; the crack tip marks the boundary between crack and the microcrack region. Incipient cracks must be closed due to negative pressure. Important to note the terms "stress" and "pressure" are sometimes used interchangeably, but that's not entirely correct. We use "stress" (units = MPa) for dry materials and "pressure" where pore fluids are involved (i.e, wet, porous material and hydraulic fracture, units = psi). Fracturing in geologic materials - as opposed to engineered foundations or steel structures - is almost always is hydraulic fracturing.



Stress and strain. A stressed object will bend before it breaks. Rocks, wood, steel, plastics, and ceramics all behave in this manner. If the amount of applied stress remains below the material's elastic limit (linear part of curve), only bending will occur and the object will resume its original shape once the stress is removed. If the stress exceeds the material's elastic limit (its yield strength), permanent deformation (strain) occurs from which the material cannot fully recover. Its shape is permanently changed (non-linear region). Wherever along the curve fracture occurs (failure occurs), drop a line straight down to the x-axis to find the corresponding strain, or amount of deformation expressed as a percent.



Brittle and ductile fracture. If a stressed material breaks at point B, it is a brittle material that has undergone brittle fracture (failure) at a relatively low strain amount corresponding to point C on the x-axis. An example of a brittle material is blackboard chalk. If a material breaks at point B', it stretched a bit before breaking. It is a ductile material with a failure point at B' corresponding to relatively high strain at point C'. An example of a ductile material would be steel rod.


Another look at a stress strain curve for a ductile material. The curve may wander a bit. Young's modulus (E, or stiffness) is the slope of the line that approximates the linear portion of the curve.





Strain energy, resilience, toughness. The area under the curve is energy. If the strain remains elastic, energy is absorbed (bending not breaking, returns to shape). If permanent deformation occurs (stressed beyond yield strength), energy has been expended on the material during deformation and dissipated.




Failure. What do we mean by failure? A fracture is a break in some material, which is certainly a permanent type of deformation, but a fracture may not equate to failure. The term "failure" is something humans define, typically for a structure built to do a specific job. While a material in one part of a structure may be said to have failed along a fracture, the entire structure, composed of several parts, may remain standing and acceptably functional - even safe. Looking at it another way, an unfractured material can be said to have failed even if no fracturing occurs. A chair made entirely of soft rubber will fail to serve its structural purpose (supporting you), but snap back into shape after it dumps you on the floor. Another example might be small cracks around rivets in an aluminum airplane wing. The cracks will grow very slowly over the working life of the aircraft, but by design never reach a critical length that would cause the wing structure fail. The cracks will never threaten passenger safety under normal use. Fully functional structures may contain flaws, cracks, and fractures yet do their job just fine (not fail).

Photo credit: peteradamsphoto.com



Shapes of fractures in 2D and 3D. Its easy to draw fractures in 2D, but its important to understand fracture geometry in 3D because fractures propagate along curved fronts. In the 2D drawing, the fracture tip - the forwardmost part of propagation - can be drawn as a point. In the 3D view, however, we see the fracture front is not a point at all, but a curved line. The fracture front is an arris formed by the intersection of two planes or two slightly curved surfaces. For this reason, the "fracture front" is sometimes called the "tip-line".


Fracture opening modes. Mode I: Horizontal tension creates a vertical fracture. Mode II: Sliding in the vertical plane. Mode III: Out-of-plane shear (tearing). We will focus mostly on Mode I, tensile opening.



Rapid loading and hydrofracture. Fluid pressure inside a crack increases in response to rapid deposition of a thick slug of sediment or by a deep flood. The key ingredient is the seal. If the substrate is a low permeability material, it can create the seal. In unconsolidated sediment (high porosity, high permeability) the seal must form during loading event. As pressurized fluid enters the fracture, some of it will leak out through the crack wall into the surrounding sediment. The exiting fluid drags fine particles with it toward the wall where they accumulate as a low-permeability skin (filter cake) sealing the fracture.




Parts of a fluid-driven fracture (hydraulic fracture). Fluid-driven fractures are common in geological materials. By dissecting a crack, we see how its various parts relate to the process of crack propagation and filling (i.e., hydrofracture and clastic dike formation). Modified from Phillips et al. (2013).





Sharp cracks and blunt cracks. Stress at a the tip of a blunt crack is distributed over more surface area than a sharp crack. Consider an oval-shaped crack. We can depict the sharpness of its tip with a circle. We're zoomed in to a coarse microscopic scale - near the limit of what the human eye can resolve. Small radius circle = sharp crack. Large radius circle = less sharp. So that's crack sharpness. The next idea involves what happens at the tip of a crack as it begins to propagate. Crack propagation means the tip advances forward through the material. Because the region just beyond the tip experiences ductile deformation (think: Poisson's ratio and the shape a squashed/stretched material assumes), an initially sharp crack will begin to blunt a bit. A blunt-tipped crack can be depicted with two points, now spaced slightly apart. The two points describe a larger radius of curvature at the crack tip.


Maximum stress at crack tip. Whether sharp or blunt, stress is concentrated at the crack tip. The material is in tension. Maximum principal stress (O1) is oriented vertically. Minimum principal stress is horizontal (O3, arrows).



Stress increases near hole. Stresses will rise considerably as you approach a hole in a plate under stress (stress field = Sinf). Stress is 3 times greater within 1 radius distance from the edge of the hole than the stress field in general. But at a distance of 2 radii, stress is indistinguishable from the background. This non-linear stress-distance idea is similar to what goes on at a crack tip.



Hydraulic fractures in wellbores. Fracking is done to stimulate tight gas reservoir rocks. Fractures greatly increase the effective surface area of the wellbore, making gas/oil more available for pumping. A wellbore with a very large circumference would accomplish the same thing, but wide bores are not technically feasible or desirable for safety reasons. It works like this: A well is drilled and cased (pipe, cement). The case is perforated through one or more target zones. A targeted portion of the wellbore is shut in, fluids are pumped in, and the pressure inside the shut-in portion jacked way up using pumps. The point at which fluid pressure reaches the minimum confining pressure (O3) of the rock, fractures will begin to propagate. Fractures initiate from the perforations and advance outward into the formation. Fractures rapidly fill with the fracking fluid (water + sand + chemicals) and be propped open by the sand. Propped fractures will flow gas and oil back to the wellbore when pumping begins. in the figure above, horizontal fractures extend from the vertical wellbore. Vertical fractures extend from the horizontal wellbore. But fracture orientation and wellbore engineering is far more complicated than this.



Irregular fracture fronts. Let's examine the shape of a fracture front (tip-line) as it advances. Each "contour" in the figure above represents the position of the fracture front at a moment in time. Modified from Beilin and Carey (1997). A few observations:


a.) The fracture front in this example is irregular, with two distinct lobes (A and B).


b.) Rate of advance through the material is not constant for all parts of the fracture front. The rate of advance for lobe A shows a decelerating pattern through time, while the advance of lobe B remains fairly constant.


c.) The front becomes more irregular with distance and time.


d.) The 3D shape of an irregular fracture front will look different when intersected by a plane orthogonal to it (plane = face of outcrop). We'll come back to this later.




Fracture propagation in steps. End view and profile views of an advancing fracture tip-line. Context here is an induced fracture propagating from a vertical well bore, but the concept applies to natural fractures. The fracture aperture increases slightly over time (widening).



irregular fracture front. Time steps show a growing fracture, the advance of its tip-line, and how its final geometry expresses as projections on faces of a cube. Cube faces represent vertical and horizontal faces of outcrops. What we see in outcrop may only tell part of the story about the fracture's 3D geometry.




Cross sections through an irregularly-shaped fracture. Cross sections (A-A', B-B', C-C') through a wedge-shaped fracture with an irregular front will appear quite different from one another depending on where the intersecting plane (outcrop) it is located. 2D shapes may lead you to conclude taper direction (infill direction) is one way, when in reality it might be just the opposite. Outcrops, for the most part, are random slices (planes) through the geology. Make sure to do a little digging in order to determine true taper direction of filled fractures if you suspect curved or irregular fronts (which you should).



En echelon and straight. Fractures that appear separated can merge in the third dimension. Consider a fracture in the shape of a slightly inflated disc. Plane A intersects one part, Plane B intersects another. The expressions of the fractures are very different. The planes represent the outcrop.



Nearfield and farfield deformation. Formation of sheeted clastic dikes in the Touchet Beds of WA-OR-ID appears to have involved two different scales of stress and strain. Vertical dikes form in thick, laterally extensive bodies of sediment; they almost are never near the edge of the material. One one hand, free face edge effects in such thick layers are not significant in dike injection (i.e., toppling of bluffs, lateral spreading), but edges may be important in other ways (pressure shadows and fracture toughness in thin vs. thick materials). More on that later. Dike formation in the Touchet Beds was driven by internal phenomena (i.e., elevated pore fluid pressures, partially-sealed cracks, fluid-driven fracture), not free face toppling. The hydraulic fracture model best fits the observed geometries, crosscutting relationship, and internal structures. More on this later...



Far field hydrofracture. A single curve is typically used to represent a fracture's opening, propagation, filling, closure, and leak-off. But there may be two different scales of fracture at play, near field and fa field. A single curve does not capture this.



Hydrofracture at two scales explains sheeted clastic dike formation in the Touchet Beds. I think sheeted clastic dikes in megaflood deposits form by hydrfracture where the pressure fluctuates during the propagation phase. As one fracture opens, propagates, fills, and closes another one adjacent to it repeats the cycle. The far field pressure (the flood load applied to the sediment) is constant and sustained through fracture period, but the near field pressure fluctuates above and below the O3 line (fracture closure threshold). Each time the blue curve dips below the O3 line, one crack closes. Each time pressure rises above it, another opens. Volume-pressure relationship of a growing and filling fracture behaves in much the same way.



Fracture will not propagate unless the minimal principal stress (minimum confining pressure, O3) is exceeded by the pore fluid pressure (Pf) inside the crack (flaw in material). the red curve describes a crack that does not grow (Pf > O3).




Formation of sheeted dike fills. Sheeting forms in response to near field fluid pressure fluctuations (pressure pulses) during fracture propagation. A single flood event can produces packages of sheets. Multiple flood-load events produce composite clastic dikes.



Silt skins and slurry wall filter cake. In heavy construction, foundations are sometimes build below ground. We're talking foundations for big buildings. A deep trench is excavated, a cage of rebar is lowered into it, and the trench is filled to the top with a concrete slurry. Water diffuses out of the slurry into the soil walls, leaving behind a filter cake. In a fracture, this diffusion is called "leak off" and the slurry wall/filter cake is called a "silt skin".




Relative permeability of reservoir rocks and everyday materials. Fracking is used where the rate of fluid flow through a rock formation is too slow for natural gas and oil to be produced economically (i.e., tight gas shales). These are sometimes called unconventional reservoirs. Conventional reservoirs, on the other hand, contain higher permeability rocks which will generally flow under pumping along, requiring less stimulation in order to produce gas and oil economically (i.e., uncomplicated sandstones and limestones). Fractures reach beyond the wellbore itself, greatly increasing its effective size (i.e., amount of surface area of reservoir rock connected to the wellbore). Propped fractures make them flow faster. Hydraulic fractures propagated from the wellbore serve as fast conduits for moving hydrocarbons out of the rock and to the surface through pumping.



Dike-sill-dike geometry. Grainsize and the orientation of principal stresses controls fracture propagation in sediment and the form of clastic dikes in the Columbia Basin, WA-OR-ID. This stair-stepping dike has an overall wedge shape (tapers downward) at the scale of the outcrop near Lewiston, ID (see figure below). This dike propagated from left to right and terminates in a high-porosity boulder gravel (Bonneville flood) that underlies Touchet Beds (Missoula floods). Zooming in, we see its width thins through the horizontal sill segment though the number of fill bands remains the same. That cannot happen without significantly elevated pore fluid pressures. Pore fluid pressure in the dike segment opens against the least principle stress (O3, horizontal). Fluid pressure in the sill segment opens against the maximum principal stress, therefore must equal or exceed the vertical weight of the sediment above plus weight of the pore water and the column of floodwater (O1, vertical). But since its the same fracture whether dike or sill, the same fluid pressure applies to both (though pressure reduces along its length, shown as R --> r). We can explain the width difference can be explained with an efficiency factor (R, r) corresponding with coarse grained layer (higher porous, permeability) followed by the sill segment. Fluid pressure that opened this dike, and most others in megaflood sediments, just barely exceeded confining pressures. See photo and figure below.


Lewiston dike. Dike in figure above. Lewiston, ID.


Lewiston dike. Dike in photo and figure above. Lewiston, ID.



Sand injectites. About 20 years ago, oil companies began discovering huge sand-filled fracture networks formed by hydraulic injection in deep marine basins around the world. Sand injectites, formed in turbidite fan-lobe complexes at the base of the continental slope, are large enough to be seen in modern seismic images. They are porous sand bodies surrounded by impermeable mudstone - near perfect reservoirs commonly targeted for drilling in places like the North Sea. The sand originates from the continental shelf (where we expect sand to be). The surrounding mud lies on the abyssal plain (where it should be). Narrow submarine canyons rapidly deliver the shelf sand to the seafloor, forming fans and intrusive bodies (where we don't expect). Voluminous sand bodies residing on the seafloor is not something predicted by sequence stratigraphy, but the secret is out now. Geologists noted anomalous sand dike-sill complexes 100 years ago in outcrops (i.e., Panoche Hills, CA), but didn't fully recognize them for what they were. Researchers like Andrew Hurst at University of Aberdeen (UK) have greatly improved our understanding of sand injectites in recent years. Modified from Cobain et al. (2016).



Spurs define fluid pressure gradient. Downward and horizontal injection in a clastic dike at Latah Creek, WA mimic the geometry of injectites in petroleum basins. The two spurs pioneer new routes through the host sediment, but follow paths identical to the larger, stair-stepping dike above, from which they branch. Photo is 50cm across.



Early work on sand injectites. Early mentions of large-scale sand dike-sill networks now recognized as injectite complexes were made by Muchison (1827), Gottis (1953), Rutten and Schonberger (1957), Truswell (1972), and Hiscott (1979). Seismic surveys have imaged the precise 3D architecture of injectite networks (Timbrell, 1993; MacLeod et al., 1999; Lonergan et al., 2000; Molyneux et al., 2002; Huuse and Mickelson, 2004; Huuse et al., 2004, 2007; De Boer et al., 2007; Jackson, 2007, 2011; Szarawarska et al., 2010; Cobain et al., 2016). In a few truly remarkable locations, injectite networks are revealed in outcrop (Surlyk and Noe-Nygaard, 2001; Fries and Parize, 2003; Hubbard et al., 2007; Vetel and Cartwright, 2009; Kane, 2010; Monnier et al., 2015). Downward and lateral propagation of sand injectites has been discussed by several authors (Gottis, 1953; Rutten and Schonberger, 1957; Beaudoin and Fries, 1982; Beaudoin et al., 1985a,b; Parize, 1988; Huang, 1988; Parize and Fries, 2003; Parize et al., 2007a,b; Scholz, 2009, 2010). Propagation in all directions is also recognized (Philips and Alsop, 2000; Surlyk, 2001, 2007; Rowe et al., 2002; Ribeiro et Terrinha, 2007). In most known injectite complexes, however, fractures propagate primarily upward and laterally from sources located at deeper levels (Smyers and Peterson, 1971; Truswell, 1972; Hiscott, 1979; Hillier and Cosgrove, 2002; Huuse et al., 2004; Hubbard et al., 2007; Cartwright et al., 2008; Monnier et al., 2014).



Grippa. A beautifully drawn example of sand injectite fracture network geometry from Grippa et al. (2019). Note the 2D vs. 3D geometries. Does this figure change your concept of what fracture networks look like and how fractures intersect?


Monnier. A stylized rendering of sand injectite fracture network geometries in the Vocantian Basin from Monnier et al. (2015). Fracture wings extend from the same source, turbidite channel (narrow, voluminous sand bodies). How are the principal stresses oriented for each fracture network (LePuy, LeCouvent, La Beaume, Vieux-Bevons, Les Houlettes)?



Reinjection of fractures. Repeated deposition of sediment by large floods, repeated fracture widening, and development of sheeted fills. Each new crack and fill episode begins with a slightly new stress condition. Modified from LeHeron and Etienne (2005).

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