ABSTRACT:

Porosity strongly affects the overall ductile behavior of cohesive geomaterials undergoing plastic deformation. We propose in the present paper an original micromechanical approach for porous rocks. This model couples Drucker-Prager type plasticity of the solid matrix and evolving porosity under general triaxial loadings. The resulting model has the advantage to be physical relevant and based on a single macroscopic yield function which also plays the role of plastic potential. It is numerically implemented and validated by comparison with experimental data on a porous chalk.

1 INTRODUCTION

It is well-known that various features of rocks behavior cannot be satisfactorily understood and explained without reference to their porosity (see for instance (Li et al. 2009)). Homogenization theory constitutes a relevant way to incorporate the effects of such pores in the materials non linear mechanical behavior.As an example, Gurson model (Gurson 1977) allows to study voids growth process in engineering materials whose matrix obeys to a von Mises plasticity law. Despite its interest, the Gurson model fails to be applicable to geomaterials for which the solid matrix generally exhibits a plastic compressibility. The present study has two objectives: i) to evaluate the relevance of a recent macroscopic criterion of ductile porous materials having Drucker-Prager matrix; ii) to formulate, implement and validate the corresponding micromechanical model. The predictive capabilities of this constitutive model will be checked through numerical simulations of experiments performed on a porous chalk.

2 MACROSCOPIC CRITERION OF POROUS MEDIA HAVING COMPRESSIBLE MATRIX: DESCRIPTION AND EVALUATION

As mentioned before, in order to describe the mechanical behavior of geomaterials, it is desirable to develop a constitutive model of ductile porous material taking into account the plastic compressibility of the matrix. We present here a new Gurson-type model based on a recent macroscopic criterion, derived by (Guo et al. 2008).

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