A New Constitutive Model for Rock Salt Viscoplasticity: Formulation, Implementation, and Demonstrations

Abstract

ABSTRACT: This paper presents the formulation, implementation, and demonstration of a new, largely phenomenological, model for the damage-free (micro-crack-free) thermomechanical behavior of rock salt. Unlike most salt constitutive models, the new model includes both drag stress (isotropic) and back stress (kinematic) hardening. The implementation utilizes a semi-implicit scheme and a fall-back fully-implicit scheme to numerically integrate the model’s differential equations. Particular attention was paid to the initial guesses for the fully-implicit scheme. Of the four guesses investigated, an initial guess that interpolated between the previous converged state and the fully saturated hardening state had the best performance. The numerical implementation was then used in simulations that highlighted the difference between drag stress hardening versus combined drag and back stress hardening. Simulations of multi-stage constant stress tests showed that only combined hardening could qualitatively represent reverse (inverse transient) creep, as well as the large transient strains experimentally observed upon switching from axisymmetric compression to axisymmetric extension. Simulations of a gas storage cavern subjected to high and low gas pressure cycles showed that combined hardening led to substantially greater volume loss over time than drag stress hardening alone. 1 INTRODUCTION Rock salt constitutive models are used to simulate the evolution of mines, boreholes, storage caverns for gases and liquids, and nuclear waste repositories in rock salt formations. A wide variety of models have been proposed for rock salt, yet even the damage-free (micro-crack-free) thermo-viscoplastic behavior remains difficult to capture. The Munson-Dawson model, for example, was recently extended in Reedlunn et al. (2022), but it still cannot capture monotonic hardening behavior over the full range of strain rates typically utilized in laboratory tests (10−12 to 10−4 1/s), or transient non-monotonic hardening behaviors, such as the Bauschinger effect and reverse (inverse transient) creep (Reedlunn, 2020, Section 1).