Porosity dependence and mechanism of brittle fracture in sandstones

Abstract

Brittle fracture tests of 105 fine‐grained quartz arenites were conducted at 25°C, 1.0‐kb confining pressure, a constant strain rate of 6.5 × 10−5/sec, and pore pressure ranging from 0 to 750 bars. Orientation of planar anisotropy (bedding or cross‐bedding) with respect to principal stresses has little influence on the fracture strength. The Donath orientation effect depends on rock type. Strong dependence of fracture strength on porosity is of the form y = axb (where y equals stress difference at failure, x equals porosity, and a > 0 > b; in our samples, values for a ranged between 16 and 25 kb, and b between −0.8 and −1.0). Through‐going shear fractures result from coalescence of grain boundary cracks, extension fractures within grains, and void space. Rocks with low porosity develop through‐going shears only after many grains are extension fractured. The functional relationship between porosity and fracture strength derives from the lower energy required for propagating cracks to use void space rather than forming extension fractures.

Relationships between Strengths and Physical Properties of Samples Recovered during Legs 137, 140, and 148 from Hole 504B

“…For example, Dunn et al (1973) suggested that a roughly inverse linear relationship between porosity and strength is caused by the fact that the higher the porosity, the fewer the number of new cracks that would have to be created prior to sample failure. More recently, Jizba (1991) proposed a simple relationship between porosity and strength in clean sandstones based on the idea that any applied stress must be borne by that fraction of the material that is load bearing (that is, the grains), and thus that porosity reduces strength by reducing the cross-sectional area available to carry the load.…”

“…Typically, static Young's modulus and compressive strength have been found to be well correlated (Jaeger and Cook, 1979;Bauer and Handin, 1985), as are porosity and strength (Dunn et al, 1973;Jizba, 1991). Turk and Dearman (1983) demonstrate for a variety of rocks that there is a power-law relationship between the ratio of Young's modulus to Poisson's ratio and the uniaxial compressive strength.…”

Sequential growth of deformation bands in the laboratory

“…Microcracks are commonly observed in the laboratory associated with macroscopic shear during brittle deformation (e.g. Dunn et al, 1973;Engelder, 1974). There is some debate over whether the axial cracks form a`process zone' prior to shear fracture (Dunn et al, 1973), or à wake' of damage after shear fracture (Friedman and Logan, 1970).…”

“…Dunn et al (1973), Logan (1973), Engelder (1974). They have oered good explanations to certain stages of the faulting process, in particular the formation of a single deformation band.…”

Failure behavior of single sand grains: Theory versus experiment

“…Experimental studies on time-independent compaction of porous sandstones and sands at room temperature have shown irrecoverable porosity reduction during loading, which increases significantly beyond a specific critical effective pressure (P cr ) [Borg et al, 1960;Chuhan et al, 2003;Dunn et al, 1973;Karner et al, 2003Karner et al, , 2005Lambe and Whitman, 1969;Lee and Farhoomand, 1967;McDowell and Humphreys, 2002;Nakata et al, 2001;Vesíc and Clough, 1968;Wissler and Simmons, 1985;Wong and Baud, 1999;Zhang et al, 1990;Zoback and Byerlee, 1976]. Experiments on sand aggregates and sandstones have shown that the amount of compaction obtained at a given effective pressure generally increases with increasing porosity (8) and increasing grain size (d) [Borg et al, 1960;Chuhan et al, 2002Chuhan et al, , 2003Dunn et al, 1973;Hangx et al, 2010;Karner et al, 2005;Lambe and Whitman, 1969;Lee and Farhoomand, 1967;McDowell and Humphreys, 2002;Nakata et al, 1999;Vesíc and Clough, 1968;Zhang et al, 1990]. This is in accordance with the observation that with increasing porosity and grain size, the critical pressure for grain crushing P cr decreases, i.e., the rock becomes weaker [Karner et al, 2005;Wong and Baud, 1999;Zhang et al, 1990].…”