Joint pattern development: Effects of subcritical crack growth and mechanical crack interaction

Abstract

Fracture networks are examined in the light of subcritical crack growth theory. Examples of equilibrium crack geometries are generated using a fracture mechanics model that explicitly tracks the propagation of multiple fractures. It is determined that propagation velocity as modeled using a subcritical fracture growth law exerts a controlling influence on fracture length distributions and spacing. Velocity is modeled as proportional to the n‐th power of the mode I stress intensity. Numerous, closely spaced, similar length fractures result for n=1, with many en echelon arrays forming due to fracture interaction. Increasing the value of n results in the growth of fewer fractures that are more widely spaced. Fractures tend to cluster in narrow zones, with limited fracture growth in the intervening areas. The spacing between zones is controlled by the stress shielding effects of longer fractures on shorter ones. The amount of time required for fracture pattern development is also influenced by the subcritical velocity exponent, n. At low n, patterns take seconds to minutes to develop, while patterns generated at higher n can require hundreds of years or more.

Calculation of dike trajectories from volcanic centers

“…Various studies have considered how the presence of one or more neighboring cracks influences the stress field near another and hence the propagation path [e.g., Pollard et al, 1982;Sempere and Macdonald, 1986;Olson and Pollard, 1989;Cruikshank et al, 1991;Olson, 1993;Thomas and Pollard, 1993]. These analyses largely focus on crack curvature as a crack-crack interaction effect caused by the approach and overlap of echelon segments.…”

“…Several straight cracks can be dealt with by reflection techniques [Pollard et al, 1982] and small deflections from a straight path can be dealt using the analysis of Cotterell and Rice [1980] [Cruikshank et al, 1991]. However, previous calculations of propagation along more general curving trajectories [e.g., Olson and Pollard, 1989;Olson, 1993;Thomas and Pollard, 1993] have largely been based on the boundary element method of Crouch and Starfield [1983]. This method employs a simple discretization in which the dike shape is approximated by elements consisting of straight-line segments and the wall displacement on each element is taken to be constant.…”

Advanced Technology for Predicting the Fluid Flow Attributes of Naturally Fractured Reservoirs From Quantitative Geologic Data and Modeling

“…Two dimensional, plane-strain, static analysis demonstrates how the stress relief around a pre-existing crack can create a propagation "exclusion" zone (Pollard and Segall, 1987). Olson (1993) showed how this stress shielding can develop in an areal sense as multiple fractures grow in length and their stress shadows overlap, diminishing the stress available for additional parallel fractures to grow. Recent work (Bai and Pollard, 2000b) has shown that in wellbonded, layered materials under crack-normal, extensional loading, the crack-normal stress between closely spaced, parallel fractures (spacing ≤ layer thickness) actually becomes compressive ( Figure 5.1).…”

“…This treatment of lateral propagation is crucial to understanding fracturing in mechanically layered materials, as the shortest dimension of fractures in layered material will be their vertical (or layer-perpendicular) extent or height (Olson, 1993). Consequently, most of the fracture propagation in bedded rock involves increasing the lateral dimension of the fracture (length as measured along the layer).…”

Ultrasonic constraint of the microfracture anisotropy of flysch rocks from the Podhale Synclinorium (Poland)

“…Olson 1993), based on the experimental works of Griffith (1921) as well as field evidence that joints propagated from microfractures located at fossils or sedimentary structures (e.g. Helgeson and Aydin 1991;Savalli and Engelder 2005).…”