A constitutive model for compressible materials: application to the study of interaction between supports and rock mass

Abstract : Characterization and modeling of the mechanical behavior for compressible materials are well-known issues, and have been studied for a long time in the field of : (a) soil mechanics, including the foundations on soft ground or stability of embankments, structures on compressible soils etc.; (b) rock mechanics for highly porous geomaterials; (c) metallurgy for the behavior of metal foam containing voids (one of the first ductile damage model has been proposed by Gurson (1977), and widely used in the literature for geomaterials) or for compaction of metal and pharmaceutical powders, snow or crushed salt compaction (for instance) or in the ceramic industry. The common thread for these materials is that when they are subjected to loadings, significant modifications of their microstructure (compaction, stiffening, increase of their cohesion, etc.) are experimentally observed. Indeed, several models of mechanical behavior for highly porous materials (chalk for the oil industry, metal powders or PVC in metallurgy or pharmaceutical industry, ceramics, etc.) can be found in the literature (Baud et al. 2006, Azami & Khoei 2006, Wu et al. 2005). In this paper, we propose a macroscopic phenomenological model for the mechanical behavior of the compressible materials for use at the interface between support elements and the host rock at the Meuse/Haute-Marne underground research laboratory (URL). Such materials are intended to absorb the strain energy of the host rock in the near field due to its creep and therefore to minimize the transmission of forces in the support elements during the transient phase following their emplacement. A specific compressible material has been designed and uniaxial, triaxial and oedometric tests have been carried out with the aim to characterize the short-term behavior of this material, but also to specify the main strain and failure mechanisms. According to the composition of the compressible material, two types of shear behavior have been observed: (a) a strain-hardening after a small elastic phase or (b) an elastic behavior up to the peak followed by brittle failure and a strain hardening. Based on this characterization, a constitutive model was proposed. Fig. 1 summarizes the proposed modeling of each mechanism which is characterized by (a) an elastic limit with or without a brittle failure based on the Drucker-Prager's criterion. The advantage of this criterion compared to Mohr-Coulomb or Hoek-Brown ones is the dependency on the intermediate principal stress s2; (b) a strain hardening modelled by an exponential function with respect to the internal plastic variable (plastic distortion), (c) a cut-off in tension. For the pore collapse mechanism (volumetric cap yield), the yield function is based on the Gurson (1977) criterion, that is to say, an incorporated elliptical yield surface for both pore collapse and compaction. The main advantage of this micromechanics-based criterion is that the yield function depends explicitly on the porosity of the medium. The hardening due to pore collapse is governed by a local hardening variable which depends on the macroscopic plastic deformation with respect to the pore collapse mechanism (e.g. volumetric plastic strain due to the hydrostatic failure). Finally, the densification mechanism occurs after the pores collapse results in a medium becoming more and more cohesive during its compaction. These two phenomena are determined by the principle of equivalence plastic energy and approached on the basis of the ductile damage model of Tvergaard and Needleman (1984). The model parameters have been identified despite of the small number of the available tests. The proposed multi-mechanism model has been implemented in the 3D computation code, FLAC3D. As a verification of the proposed model and its numerical implementation, two laboratory tests (triaxial compression and oedometric tests) carried out on this compressible material were simulated. The experimental curves have been satisfactorily reproduced by the numerical simulations as illustrated in Fig.2 for oedometric test. The contribution of this mechanical model for compressible materials compared to a classical elastoplastic model was evaluated under simplified conditions (2D) for a GVA2 gallery of the Meuse / Haute-Marne underground research laboratory (URL). This is a gallery of large diameter (f = 6.37 m) oriented in the direction of the minor horizontal stress was simulated in 2D following the convergenceconfinement method. A first support consisted of projected concrete with an average thickness of 0.185 m was set up after the complete passage of the face front. A rigid liner of outer and inner radii of 2.85 and 2.42 m respectively, was also set up and a soft packing material (compressible material) is used to fill the gap between the two different supports (Fig. 3). The thickness of the compressible material is about 0.15 m. Both supports elements have an elastic and perfectly plastic behavior based on the Mohr- Coulomb criterion. Otherwise, in the framework of a scientific collaboration between Andra and INERIS, a macroscopic isotropic visco-elastoplastic model, which accounts for the impact of induced damage (modeled through a plastic hardening function) on the viscoplastic strain rates, has been developed (Souley et al. 2017) and used in several design and predicting studies of the mechanical and hydromechanical behaviors around the Meuse/Haute-Marne URL structures. It is also this model that has been used in this study for the viscoplastic behavior of Callovo-Oxfordian claystone (COx). Finally, for the short-term mechanical behavior of the compressible material, two models of behavior were used: one corresponding to the proposed model and the other perfectly elastoplastic type. In particular, we evaluated the discrepancies between the use of the proposed model and the hypothesis of an elastic or elastoplastic behavior for the compressible material on the distribution and magnitude of stresses in the rigid liner as well as the liner bending. Compared to the use of classical compressible material, the proposed model reproduces a reduction of 30 to 50% of the stresses in the rigid liner, for a duration of the simulation about 100 years. This constitutes a considerable gain for a more accurate design of different URL structures as well as in terms of realization costs.
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Submitted on : Friday, August 3, 2018 - 2:02:17 PM
Last modification on : Saturday, August 4, 2018 - 1:01:07 AM

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Mountaka Souley, J. Zghondi, M. Vu, Gilles Armand. A constitutive model for compressible materials: application to the study of interaction between supports and rock mass. 7. International Conference "Clays in natural and engineered barriers for radioactive waste Confinement", Sep 2017, Davos, Switzerland. pp.456-457. ⟨ineris-01853536⟩

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