Micromechanics of pressure-induced grain crushing in porous rocks

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.