Error‐controlled implicit time integration of elasto‐visco‐plastic constitutive models for rock salt

Abstract

The mechanical behavior of rock salt is rate-dependent at different time scales. Using caverns in rock salt formations for renewable energy storage implies that the underground structures are subjected to both short-term and long-term loads, increasing robustness and flexibility requirements for numerical simulators used to assess the safety of such structures. So far, explicit time integration with model-specific heuristics for time-step size determination dominate in application studies. In this paper, the suitability of error-controlled adaptive time-integration schemes of the diagonally implicit Runge-Kutta type is investigated in comparison with the Backward Euler and Crank-Nicolson schemes when applied to the integration of typical elasto-visco-plastic constitutive models of rock salt. The comparison is made both for monotonic and for cyclic loads as well as taking account of thermo-mechanical coupling. Analyses of the time-integration errors and the time step-size evolution show the suitability of the integration scheme for these material models. The automatic adjustment of the time-step size was found to be robust across all material models and boundary conditions as well as for non-isothermal situations for a single algorithmic parameter set. KEYWORDS error control, implicit Runge-Kutta, rock salt, time adaptivity, viscoplasticity INTRODUCTIONA wide range of time-integration schemes, both implicit and explicit, have been implemented into software packages for the numerical simulation quasi-static and dynamic problems in geotechnics. 1,2 Because a balance has to be sought between using shorter step sizes to increase accuracy and decreasing simulation times by using larger step sizes, 3,4 researchers have paid much attention to the numerical stability and accuracy of different integration schemes depending on the chosen step size. 5-8 The choice of a suitable time-integration scheme depends to a certain degree on the problem modelled. This article is concerned with the integration of complex inelastic constitutive models for rock salt.The mechanical behavior of rock salt is rate-dependent, causing time-dependent stress and strain fields associated with primary, secondary, or tertiary creep or stress-relaxation processes developing at different time scales. 9 These processes are furthermore dependent on the current state of the material, eg, the acting stress, the presence of damage, or the current This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Micromechanical modeling for rate‐dependent behavior of salt rock under cyclic loading

“…_ γ c can be thought of as a viscoplastic strain rate _ ϵ vp , similar to the viscoplastic strain rate used in other models. [39][40][41] For example, Duvaut and Lions suggested that _ ϵ vp should be a function of local stress, local stiffness, and the relaxation time. 42 In Perzyna's model, _ ϵ vp is proportional to the derivative of yield surface with respect to local stress.…”

Extensive overview of soil constitutive relations and applications for geotechnical engineering problems

“…An elastic-viscoplastic model was proposed by Yin and Graham [ 215 ] in terms of the flow surface and the modified Cam-clay model. Recently, new visco-plastic constitutive models have been used for creep analysis in soft rocks or soils that some of them mentioned in the following [ [216] , [217] , [218] ].…”

A nonlinear constitutive model for whole stress–strain behaviors of compressed rocks incorporating crack closure effect

“…On the other hand, implementing the models into the finite element method (FEM) commercial software is significant for applying in the practical engineering. Diverse algorithms for integration of complex and highly nonlinear constitutive models have been developed, which can be generally divided into the following three categories, implicit algorithms, [31][32][33] explicit algorithms, [34][35][36] and semi-implicit algorithms. 37,38 The implicit integrations update the unknown values of the variables at current loading step through an iterative process.…”