Implementation and Verification of Enhanced Munson-Dawson Creep Model for Rock Salt
Authors: Cheng Z. 
Published: August 2024

ABSTRACT:
The Munson-Dawson (MD) constitutive model has played a significant role in the simulation of subsurface rock salt behaviors on nuclear storage caverns, mines, and waste repositories since its inception in the 1980s. To effectively capture the unique creep behavior exhibited by salt under conditions of low equivalent stress, an enhanced version of the MD model has been developed which incorporates additional transient and steady-state rate terms, thereby extending its capability to accurately represent complex material behavior. In the enhanced MD model, a more flexible Hosford stress measure has been adopted, enabling the accommodation of both Tresca and von-Mises stress states as specific instances, contingent upon the assignment of a material parameter. The primary objective of this study is the implementation of this enhanced MD model into FLAC3D, a widely used three-dimensional geotechnical software framework. During the numerical implementation, an iterative algorithm is applied for time integration, and a series of verification procedures are executed to validate the robustness and accuracy of the implementation. The efficiency of iteration algorithm and automatic time step scheme for this model are discussed. Furthermore, the application of the model is illustrated through a multi-zone boundary-value problem, demonstrating its practical utility and robustness.

1. INTRODUCTION
Munson and Dawson (1979, 1982) and Munson et al (1989) developed the now called Munson-Dawson (MD) model for the creep behavior for rock salts in nuclear storage caverns, subsurface mines, and waste repositories. Both steady-state and transit strain rates are treated in this model. The steady-state strain rate of the MD model consists of three components: dislocation climb, an undefined mechanism, and dislocation glide. The transit strain rate captures recovery effect where the rate of strain hardening is stress dependent. Reedlunn (2016) revealed some drawbacks of the original MD model including less accurate creep behavior at low equivalent stresses less than 8 MPa, lack of the flexibility to capture true triaxial creep measurements, and frequently instable numerical performance of implementation. In order to overcome the shortcomings, Reedkunn (2018) reported an enhanced version of MD model by using a more flexible Hosford stress measure and improved numerical implementation with implicit solution scheme mainly for finite element software. However, this enhanced version has not yet been implemented into FLAC3D, a widely used three-dimensional geotechnical software which is mainly based on explicit solution scheme in a finite volume numerical framework. This paper focuses on the implementation of the enhanced MD model in FLAC3D by applying an iterative algorithm for time integration and conducting a series of verification tests to ensure the implementation's robustness and precision. The discussion includes the effectiveness of the iterative algorithm and the recommendation of time step scheme with verification and application examples.