Lemaitre's viscoplastic model is widely used to model the long-term behavior of rocks, especially argillaceous rocks that are being considered as host rocks for radioactive waste repositories. However, this model has marked disadvantages, such as pressure independency and no volumetric viscoplastic strain, which greatly limit its ability to reproduce the complex phenomena in underground structures. In view of these, based on thermodynamic principles, Lemaitre's phenomenological viscoplastic model is extended in this paper. Two equivalent surfaces are introduced in the p-q stress plane in order to consider the contribution of hydrostatic stress on the viscoplastic strain and damage respectively. The inherent concept is that the stress points located on the same equivalent surface share the same intensity for both viscoplastic strain and damage. Moreover, in this model, the non-associated flow rule is assumed and a hyperbolic viscoplastic potential is used to reproduce volumetric viscoplastic deformation. The time dependent damage evolution law is also modified to rely on inelastic strain. In order to verify the constitutive model and to study the newly added parameters, several numerical procedures were performed corresponding to quasi-static tests, creep tests and relaxation tests. Finally, a detailed discussion about the influences of these parameters on both compression and tension cases is presented.

1 Introduction

Lemaitre's viscoplastic model is widely used to characterize the long-term behavior of argillite (Souley et al. 2011) as well as to model the time dependent evolution of the Excavation Damage Zone (EDZ) around underground openings (Pellet et al. 2009). However this constitutive model assumes that the hydrostatic stress has no influence on the viscoplastic behavior and it imposes no volumetric viscoplastic strain. These are obvious drawbacks in its ability to model geomaterial behavior.

In this paper, an extension of Lemaitre's model that will overcome these drawbacks is presented. Based on thermodynamic principles, two equivalent surfaces are introduced to take into account the influence of hydrostatic stress on both the evolution of viscoplastic strain and damage. In addition, the volumetric viscoplastic strain is introduced by using a hyperbolic viscoplastic potential. The time dependent damage evolution law is also modified to be dependent on inelastic strain. This model is implemented into the finite element software ABAQUS 6.10, and detailed studies of the new parameters are performed by modeling quasi-static tests, creep tests and relaxation tests.

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