Relaxation of Viscoelastic Properties of Sandstones: Hysteresis and Anisotropy

Elastic nonlinearity in sandstones is given by the combination of slow and fast effects, leading to hysteresis and relaxation of the viscoelastic properties after the sample is perturbed (conditioning). While a lot of experimental evidences of slow dynamics are available, quantification of nonclassical nonlinearity is still difficult: nonlinear indicators must be introduced which are independent of both experimental configuration and on conditioning strain amplitude, which is often difficult to quantify in an accurate way. In this contribution, we introduce and analyze some possible quantities describing nonlinear viscoelasticity in sandstones, derived from a non-equilibrium strain model. We will show that they identify real material properties, in the sense that they are not dependent on experimental details (such as experiment duration, conditioning protocol, frequency, ...) and can be measured easily with good repeatability.We quantify the temporal relaxation of viscoelastic properties of sandstones;We introduce measurable indicators allowing to quantify hysteresis, anisotropy, and relaxation in sandstones;We propose a non-equilibrium strain model to describe observed hysteresis and anisotropy in nonlinear hysteretic viscoelastic properties;We show a linear correlation exists between modulus and damping evolution during relaxation in sandstones.