Investigation of compressive and tensile behaviors for porous sandstone by a microstructure-based constitutive model.

For the design and stability analysis of rock structures in underground engineering, a micromechanics-based constitutive model is established in this work to describe the macroscopic mechanical behavior of Fontainebleau quartz sandstone. At the microscopic scale, the Drucker–Prager criterion is adopted to describe the plastic behavior of the solid matrix. The pores are assumed to be spherical and randomly distributed. The influences of porosity and dilatation of the solid phase are fully considered in the elastic behavior with a dilute homogenization scheme and plastic behavior through a macroscopic yield criterion. With the effect of porosity, one finds that the macroscopic tensile and compressive yield strengths of the porous material reduce quickly. By introducing a plastic hardening rule, a macroscopic plastic potential for non-associated flow rule and considering the evolution of porosity, a complete micro–macro constitutive model is constructed and implemented. In addition to the conventional triaxial compression (CTC) test for the study of compressive strength, the tensile strength under the triaxial direct tension (TDT) test is also taken into account by the proposed micro–macro model. The tensile behavior of the studied porous material is quite different from the compressive one. The loading path has a great influence on the porosity evolution. Compared with the experimental data carried out in CTC and TDT tests under different confining pressures, the proposed micromechanics-based model is able to capture the main features of the studied quartz sandstone. [ABSTRACT FROM AUTHOR]