Micromechanics of pressure‐induced grain crushing in porous rocks

Abstract

The hydrostatic compaction behavior of a suite of porous sandstones was investigated at confining pressures up to 600 MPa and constant pore pressures ranging up to 50 MPa. These five sandstones (Boise, Kayenta, St. Peter, Berea, and Weber) were selected because of their wide range of porosity (5–35%) and grain size (60–460 μm). We tested the law of effective stress for the porosity change as a function of pressure. Except for Weber sandstone (which has the lowest porosity and smallest grain size), the hydrostat of each sandstone shows an inflection point corresponding to a critical effective pressure beyond which an accelerated, irrecoverable compaction occurs. Our microstructural observations show that brittle grain crushing initiates at this critical pressure. We also observed distributed cleavage cracking in calcite and intensive kinking in mica. The critical pressures for grain crushing in our sandstones range from 75 to 380 MPa. In general, a sandstone with higher porosity and larger grain size has a critical pressure which is lower than that of a sandstone with lower porosity and smaller grain size. We formulate a Hertzian fracture model to analyze the micromechanics of grain crushing. Assuming that the solid grains have preexisting microcracks with dimensions which scale with grain size, we derive an expression for the critical pressure which depends on the porosity, grain size, and fracture toughness of the solid matrix. The theoretical prediction is in reasonable agreement with our experimental data as well as other data from soil and rock mechanics studies for which the critical pressures range over 3 orders of magnitude.

Failure behavior of single sand grains: Theory versus experiment

“…[5] However, the model derived by Wong and coworkers [Wong, 1990;Zhang et al, 1990] does not in itself lead to a strictly defined whole-grain failure criterion, as the porosity and grain size dependence of the critical effective pressure observed in compaction experiments is introduced to the model by relating the grain failure load to P cr on the basis of a random packing model and by assuming that the flaw dimension (at failure) scales linearly with grain size [see Zhang et al, 1990, equation 7]. In addition, this criterion does not directly offer an explanation for the grain size dependence of the grain failure load obtained from compaction experiments and single-grain crushing tests.…”

“…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].…”

“…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]. However, it should be noted that some of the above mentioned compaction experiments are performed at stress conditions below the critical crushing pressure.…”

“…At the same time, crushing tests conducted on single sand grains show an increase in the load at failure (F c = 30-350 N) with increasing grain size (d = 0.5-6.3 mm) [Gallagher, 1976;McDowell, 2002]. With regard to microscale failure mode, petrographic studies have revealed that the dominant grain failure mechanism leading to aggregate compaction and single-grain crushing is the development of tensile intra and transgranular cracks at grain contacts due to point loading [Bernabe and Brace, 1990;Chester et al, 2004;Chuhan et al, 2002;Gallagher et al, 1974;Gallagher, 1976Gallagher, , 1987Gill et al, 1990;Hangx et al, 2010;Karner et al, 2003;Myer et al, 1992;Wong, 1990;Zhang et al, 1990].…”

“…Previously, this approach was used to describe the hydrostatic compaction behavior of cemented porous rock, such as sandstone, by deriving an expression for the critical effective pressure for the onset of grain crushing (P cr ) as a function of porosity and flaw size [Wong, 1990;Zhang et al, 1990].…”