A micromechanical four-phase model to predict the compressive failure surface of cement concrete

In this work, a micromechanical model is used in order to predict the failure surface of cement concrete subject to multi-axial compression. In the adopted model, the concrete material is schematised as a composite with the following constituents: coarse aggregate (gravel), fine aggregate (sand) and cement paste. The cement paste contains some voids which grow during the loading process. In fact, the non-linear behavior of the concrete is attributed to the creation of cracks in the cement paste; the effect of the cracks is taken into account by introducing equivalent voids (inclusions with zero stiffness) in the cement paste. The three types of inclusions (namely gravel, sand and voids) have different scales, so that the overall behavior of the concrete is obtained by the composition of three different homogenizations; in the sense that the concrete is regarded as the homogenized material of the two-phase composite constituted of the gravel and the mortar; in turn, the mortar is the homogenized material of the two-phase composite constituted of the sand inclusions and a (porous) cement paste matrix; finally, the (porous) cement paste is the homogenized material of the two-phase composite constituted of voids and the pure paste. The pure paste represents the cement paste before the loading process, so that it does not contain voids or other defects due to the loading process. The abovementioned three homogenizations are realized with the predictive scheme of Mori-Tanaka in conjunction with the Eshelby method. The adopted model can be considered an attempt to find micromechanical tools able to capture peculiar aspects of the cement concrete in load cases of uni-axial and multi-axial compression. Attributing the non-linear behavior of concrete to the creation of equivalent voids in the cement paste provides correspondence with many phenomenological aspects of concrete behavior. Trying to improve this correspondence, the influence of the parameters of the evolution law of the equivalent voids in the cement paste is investigated, showing how the parameters affect the uni-axial stress-strain curve and the failure surfaces in bi-axial and tri-axial compression.