Long-term creep tests and viscoelastic constitutive modeling of lower Paleozoic shales from the Baltic Basin, N Poland

We ran a series of creep tests on samples from Baltic Basin in Northern Poland and analyzed theoretically the viscoelastic properties. Both elastic and creep data are reported. Elasticity data acquired during loading and unloading show that the tested shales exhibit a significant VTI (vertical transverse isotropy) symmetry, with elastic parameters in the following ranges: E-h from 37.4 to 60.0 GPa, E-nu from 21.4 to 26.9 GPa, nu(hv), from 0.29 to 0.39, nu(vh) from 0.19 to 0.23, and nu(hh) from 0.18 to 0.21, and E-h/E-v anisotropy ratio from 1.4 to 2, where subscripts v and h indicate the symmetry axis and the perpendicular directions, respectively. The creep data show significant time-dependent deformations even in the time-scale of engineering operations, and strain at constant load may achieve more than a half of the observed instantaneous elastic strain in only two weeks. The creep data have been analyzed using fractional Maxwell model, with a novel fitting approach which takes into account the finite loading time. Such fitting strategy allowed to fit precisely the entire dataset, both the initial and long-term creep regimes. The obtained creep parameters n(alpha), which may be referred to as quasi-viscosity are in the range 2.63.10(2) to 1.40.10(4) GPa.s(alpha), with alpha ranging from 0.10 to 0.36 for the tested shales. Lateral strain data showed that during axial differential stress loading after initial extension, strain reversal may occur, which suggests a complex deformational behavior leading to volumetric compaction. To quantify this phenomenon, time-dependent Poisson's ratio has been introduced. However, because of data limitations (number of samples and duration of experiments), only qualitative description of the time-dependent Poisson's ratio has been provided.