A constitutive law for low‐temperature creep of water‐saturated sandstones

An accurate predictive model for the long‐term strength of the continental lithosphere is important in a range of geophysical and geodynamic problems. While laboratory experiments are consistent with Mohr‐Coulomb brittle faulting in the cold, upper continental crust, there is increasing evidence that time‐dependent processes may also be important in these rocks, even at low temperature. However, there is some ambiguity as to the exact form of the constitutive law for describing time‐dependent behavior of upper crustal rocks. Here we present results of room temperature creep experiments on a suite of water‐saturated sandstones spanning a range of petrophysical and rheological properties and underlying deformation mechanisms. On physical and microstructural grounds our analysis suggests that a modified power law creep, of the form ε = A ′(σ d ‐ σ f ) n ′, where σ d is the differential stress and σ f is the long‐term failure (fundamental) strength, provides a more complete description of the experimental data. In particular, the parameters can be used to differentiate between sandstone types, with A ′, σ f and η′ varying systematically with cementation state, rock rheology, and confining pressure. The fundamental strength (σ f ) for time‐dependent deformation varies much more than the other parameters of the distribution, making it a potentially sensitive indicator of underlying creep mechanisms. Further tests would be needed to prove the constitutive law on a wider range of rock types and to prove that the three‐parameter model is statistically better in the general case.