A micromechanical‐based elasto‐viscoplastic model for the Callovo‐Oxfordian argillite: Algorithms, validations, and applications

Abstract

SummaryFor a potential geological barrier of high‐level radioactive waste repositories in France, the long‐term mechanical behavior of the Callovo‐Oxfordian (COx) argillite is the most concern for engineers. In this paper, a micromechanical‐based elasto‐viscoplastic model is proposed, and its numerical realization is our main object. The COx argillite is considered as a three‐phase composite consists of porous clay, quartz, and calcite. By assigning appropriate constitutive laws to those constituents, the macroscopic elasto‐viscoplastic behavior of the COx argillite is determined with an extended Hill's incremental approach. The numerical aspects includes (a) a new formulation is proposed for the plastic multiplier when adopting the overstress (Perzyna) model to define the viscoplastic strain. Meanwhile, a new formulation is also proposed to solve it within the framework of an implicit returning mapping scheme. (b) The corresponding consistent tangent moduli are strictly derived by extending the method proposed for solving plastic problems; (c) the efficiency of the proposed integration algorithms for the local constitutive equations and the homogenization procedure are validated, receptively, by a built‐in porous plasticity model of a commercial finite element (FE) program ABAQUS and by FE computations of a two‐phase unit cell; and (d) the proposed micromechanical model is finally applied to simulate experiment data in short‐term triaxial compression tests and long‐term triaxial creep tests. And the numerical results show that it is able to reflect the variation of the mechanical behavior with respect to the varied mineralogical compositions.

Automatically adaptive stabilized finite elements and continuation analysis for compaction banding in geomaterials

“…with j the mass rate of fluid produced by the chemical reaction (A2) and v (1) z and v (2) z the velocities of phases 1 and 2, respectively. Combining (A4) with Darcy's law for the filter velocity 𝜙…”

“…For completeness, this section briefly recapitulates the formulation of the physical model behind (2), presented more in detail in Reference 34. We consider a one-dimensional representative elementary volume (REV) of porous material under compression in the z direction.…”

“…The lack of a robust numerical solution for this equation is related to the complexity of this class of nonlinear problems. We seek to overcome this issue by developing a consistent numerical solution for (2). Therefore, we extend a new adaptive stabilized finite element method based on residual minimization to tackle nonlinear problems.…”

“…Among all localized geological features, spatially periodic patterns are increasingly gaining popularity due to their impact in a wide range of applications, such as mining, 1 particularly now when larger‐scale and deeper mines are pursued. Localization features are particularly relevant when they affect permeability, which plays a critical role in various fields, including radioactive waste deposition, 2 mineral prospection, 3,4 as well as unconventional resources exploration and exploitation 5 …”