Elastic instabilities in dry, mesoporous minerals and their relevance to geological applications

The collapse of minerals and mineral assemblies under external stress is modelled using a master curve where the stress failure is related to the relative, effective elastic moduli which are in turn related to the porosity of the sample. While a universal description is known not to be possible, we argue that for most porous materials such as shales, silica, cement phases, hydroxyapatite, zircon and also carbonates in corals and agglomerates we can estimate the critical porosity phi(c) at which small stresses will lead to the collapse of the sample. For several samples we Find phi(c) similar to 0.5 with an almost linear decay of the bulk moduli with porosity at phi(c) <0.5. The second scenario involves the persistence of elasticity for porosities until almost 1 whereby the bulk modulus decreases following a power law kappa similar to (1-phi(m), m>2, between phi = 0.5 and phi = 1.