# Fractures and Fracturing

copyright by Philip A. Candela, 1997.
Fractures in the elastic-brittle crust

Fractures in rocks are surfaces or narrow zones of structural discontinuity (loss of cohesion) that are the product of mechanical rupture. This mode of deformation is defined as brittle failure; at higher temperatures and higher pressures, ductile failure (permanent deformation due to flow, but without loss of cohesion) may occur before the point of brittle failure is reached (see the discussion of matter for a more in-depth discussion of the properties of materials). Fractures may be dilational, i.e., joints (mode I fractures), or may exhibit shearing with components parallel (mode II) or perpendicular (mode III) to the direction of propagation of the fracture front. Shear fractures are also known as faults. Many fractures can be envisaged as a loaf of pita bread (see figure 2.1 in Rock Fracture and Fluid Flow (National Research Council, 551pp., 1996); this book is one of the sources upon which this chapter is based).

Elementary fracture mechanics:
Changes in hydrostatic stress cause volume change, but the existence of non-hydrostatic stress (i.e. the deviatoric stress tensor with non-zero elements) is necessary for deformation. The application of a small differential stress produces an instantaneous, recoverable deformation in an elastic solid. However, if the brittle failure criterion is satisfied (again, see the "matter" page link, above), fracturing will result.

• EXTENSION FRACTURES (Mode I) form perpendicular to the minimum stress, and parallel to the maximum stress.
• TENSION FRACTURES are extensional, mode I fractures produced in response to a minimum stress that is tensile.
• SHEAR FRACTURES formed under triaxial compression, (the most common stress state in nature; see Twiss and Moores, 1992, page 172), may occur alone, or form a conjugate pair. Their planes form parallel to sigma 2, and form angles with sigma 1 that are less than 45 degrees. The planes of maximum shear stress lie at ± 45 degrees; however, at about ± 30 degrees, a balance is struck between a high shear stress, and a low normal stress, and failure usually occurs within a few degrees of a ± 30 degree angle with sigma 1.

• tensile fractures can form at depth in an environment of compressive stress if the pore fluid pressure is high enough.
• The age relationship of truncating joints is unambiguous; truncated joints belong to a later episode (Pollard and Aydin, 1988, page 1190).

JOINTS

Joint surfaces are characterized by plumose structures which record fracture propagation direction, whereas faults are polished and are marked by linear features known as grooves, striations or slickensides, which record slip directions. Multiple modes or directions of movement along a fracture produce mismatches between opposite sides of a fracture, and this mismatch provides porosity and permeability along the fracture.

According to Pollard and Aydin (GSA Bull., 1988), field observations indicate that joints initiate at flaws in the fractured rock units, and regional stress fields are generally insufficient to initiate fractures. These authors point out that fossils, grains, clasts, sole marks, pores and microcracks, which represent voids or materials of contrasting elastic properties relative to the host, can perturb the stress field such that local tensile stresses at the flaw exceed the tensile strength of the rock, resulting in MODE I fractures (joints). These tensions can result from an amplification of an otherwise insufficient remote tension, or the conversion of a remote compression into a local tension. Pore fluid pressures in slight excess of the least remote compressive stress can be an effective driving force for jointing.

Pollard and Aydin 1988 state: "Although a Mohr diagram is useful for representing a homogeneous stress or strain field, and for providing an empirical failure criterion, it does not represent the heterogeneous field associated with a joint". Hence, we see that heterogeneities of stress, such as those associated with heterogeneities in rocks and other solids, are critical in rock failure.

Further, the local stress directions can vary as a fracture propagates. If the principle stresses rotate about an axis within the plane of the fracture, some mode II shearing is induced, and the joint curves. Its surface may be decorated with conchoidal fracture ribs. However, rotation of the stress axes so as to produce mode III shearing along the newer parts of a fracture, result in a tilting of the plane of fracture. This manifests itself as a breakdown of the fracture front into en echelon segments, decorated by hackles (plumose structures) (Pollard and Aydin, 1988).

Pollard and Aydin also discuss the interesting cases of two parallel, but non-coplanar fractures propagating from opposite directions. The propagation of a joint is controlled by the stress field near its tip. From elastic theory, it can be shown (see refs in Pollard and Aydin, 1988) that the stress fields are heterogeneous, the region of stress intensification is small, and the stresses decrease according to an inverse square law (with distance; see also the discussion in Suppe's Structure Text of the Spanish Peaks fractures - near vs. far field). As two fractures propagate toward, (but laterally offset from) each other, the stress field from one fracture tip induces shear stresses in the other fracture, and their propagation directions interact mechanically. At first, the tension in one tip increases the tension in the other; however, as they near, they mutually induce a compression in the other, and if the orthogonal spacing between the fractures is small enough, they may "turn each other off", with the propagation of both fractures terminating. However, as the dike tips approach, the stress fields may be rotated (about the dike edge), causing the planes of the fractures to rotate. As they approach each other, they may, initially, bend away from each other; once the propagation positions have passed (like ships in the night), the fractures may converge, exhibiting hooks, rationalizing why joints commonly join tip to plane, rather than tip to tip. Along with T and + and X junctions, I would say these are elastic effects that, generally, increase in likelihood with decreasing temperature, and decreasing ductility.

FROM THE NRC book on Rock Fractures and fluid flow:

Faults - as a fault propagates, slip on it increases. Slip results in breccia and/or gouge. Breccia can have high permeability, and gouge tends to be impermeable. In low permeability rocks, the birth of a shear fracture is as follows: first en echelon dilational microcracks open perpendicular to sigma 3; as they grow and coalesce, the rock bridges between them rotate, and a shear fracture results.

Observations of joints in sedimentary rocks suggest that joints have lengths on the order of tens of meters. Similar lengths obtain for small faults, although fault zones can be much longer. Joints tend to be hairline in thickness, whereas faults are thicker.

Fracture sets comprise approximately parallel fractures. Joint spacing in a fracture set decreases with increasing total strain, increasing number of loading cycles, and decreasing strain rate. (This dependence upon strain rate is such that as strain rate increases, strain is accommodated in fewer fractures?). For intersecting joint sets, one joint set can cross an older joint set ONLY if the older joints were under compression, or were filled by minerals.

Adjacent fractures in a fracture set may link with a hook geometry. This interconnectivity, which can affect both aqueous and magmatic permeability, decreases with increasing differential stress. "For a large differential stress, the tendency for linkage is weak, so joint traces are straight and linear and overlap for long distances without being connected". Faults on the other hand, occur in en echelon geometry at a broad range of scales; the stepover zones along faults are broadly and pervasively fractured; extensional stepovers may form fluid conduits; the direction of permeability is probably sigma 2. Stepovers on strike slip faults can yield vertical permeability.

In a porous rock, faulting can cause a reduction in porosity and permeability, and may form "sealing faults", as they are known in the oil industry. The reduction in porosity can be many orders of magnitude. In low porosity rock such as granite, faulting can increase permeability by orders of magnitude.

Multiple modes of movement along a fracture juxtapose non-matching faces of a fracture, resulting in "asperity" bridges that hold open voids that are potential pathways for fluid flow. This geometry is modified by later mineralization, dissolution and other alteration that can change the permeability. Also, fluid pressure can keep a fracture open (zero effective normal stress), but the fracture will close later UNLESS it is held open by asperities or by mineralization. Apertures may reach several mm. Note that the amount of permeability NOW in a vein OR DIKE, may be unrelated to the permeability when under active fluid pressure. The voids of a fracture form an interconnected network through which fluid flows, and can be considered as a porous medium (continuum); because almost all connectivity is in the plane of the fracture, the fracture is a 2-D porous medium. However, the pores in the 2-D porous medium are elongate rather than spherical, and hence are more easily deformed. Permeability in this medium is quite stress- dependent.