Thermomechanics for Geological, Civil Engineering and Geodynamic Applications: Rate-Dependent Critical State Line Models

Equilibrium thermodynamics has been of fundamental importance to many branches of engineering including cyclical mechanical applications. However, in geomechanics and geological applications it has not yet reached a consensus in the community. Reason for the failure of establishing thermodynamic laws as a ground principle is the far from equilibrium nature of geomechanical problems which prevent the local equilibrium assumption. Problems including rate-dependence and poromechanical complexity, where deformation often occurs in a highly localized manner, were therefore thought to be not amenable to a thermodynamic approach. Here we show that the theory of thermomechanics, originally proposed for quasi-static hyperplastic deformation problems can be extended to include rate-dependent critical state-line models for porous rocks. The development therefore makes thermodynamic-consistent modeling available for civil engineering, geological and even geodynamic problems. In this two-part contribution, we present extensions of the thermomechanics theory to account for the poromechanics of path- and rate-dependent critical state line models and we cover the relevance of this thermodynamic-consistent model for civil engineering, geological and geodynamic applications. In this first part, we review the concepts behind the thermomechanics theory and present a thermodynamic extension of generic critical state line models for visco-plasticity and damage mechanics and analyze the model prediction for strain localization.