A Temperature- and Pressure-Sensitive Visco-Plasticity Theory based on Interface Mechanisms for Sedimentary Rocks

Mustafa Sari, Sotiris Alevizos, Thomas Poulet, Jack Lin, Emmanouil Veveakis

Constitutive modelling in geotechnical engineering and applied earth sciences is facing the challenge of assessing the long-term potential of both man-made and natural geohazards. This involves designing engineering operations for length scales and timescales well beyond those observable in the laboratory. In order to bridge the gap between scales, study rock behaviours well beyond their yield point and provide predictive capabilities to long term problems, constitutive models need to be equipped with multi-physical information that can be measured at laboratory time-scales and extrapolated beyond them. Enriching constitutive models with a sufficient level of details from the physical mechanisms taking place at the microstructure could provide such functionalities.

In this work, a physics-based constitutive theory for sedimentary rocks is proposed combining the results of laboratory tests, theoretical analysis and numerical validation. The viscosity of the material is assumed to be a function of the temperature, pore-pressure and energy required to alter the inter-granular interfaces. The resulting flow law and corresponding stress equilibrium are coupled to the energy and mass conservation laws, constituting a closed system of equations. To solve this system, the theoretical framework is implemented using the Finite Element \redback{} simulator and its qualitative behaviour is analysed in monotonous and cyclic isotropic compression, as well as in direct shear for different loading rates.

A series of numerical calibration tests is then performed against different types of rocks (sandstone, mudstone), saturating conditions (dry, wet), stress paths (triaxial, isotropic) and temperatures (from room temperature to over 800K). It concludes that the mechanical response of sedimentary porous rocks at strains usually achieved in laboratory testing is determined by the strength of the cementitious material bonding the grains. This strength is shown to be stress path dependent under the hypotheses made in this work and the interfaces are shown to obey a Kelvin-like interface law at the microscopic level.