Effects of porosity and crack density on the compressive strength of rocks

• New UCS data on 11 porous sandstones are presented.
• A compilation of new and published data is analyzed using the pore-emanated crack and the sliding wing crack models.
• An analytical simplification of the Ashby and Sammis' model for uniaxial compression is presented.
• The normalized fracture toughness inferred for failure is always significantly larger than that for wing crack initiation.
• Analytic estimates of the Coulomb failure parameters are derived.

We analyzed a compilation of previously published and new data on the uniaxial compressive strength (UCS) of various rock types using the pore-emanated crack and the wing crack models. While previous empirical studies have highlighted the strong control of porosity over the strength, the comparison with the pore-emanated crack model demonstrates that the pore size can be another microstructural parameter that exerts strong influence on the UCS of a rock that contains significant equant pores. We proposed an analytical simplification of the Ashby and Sammis wing crack model for uniaxial compression. Our model explicitly shows the relation between the UCS and the initial level of damage and/or the crack density in a rock. Our analysis also reveals that the normalized fracture toughness for ultimate failure is always significantly larger than the normalized fracture toughness for wing crack initiation. It is therefore more appropriate to consider two different parameters for the toughness in the micromechanical analysis. To gain insights into the physics of the Coulomb criterion, we derived analytic approximations for the empirical failure parameters with reference to the sliding wing crack model. The internal friction coefficient can be approximated as related linearly to the friction coefficient of the sliding crack, and the difference between the two coefficients has a logarithmic dependence on the square root of the crack density.