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

A. Caporale,R. Luciano

doi:10.3221/igf-esis.29.03

Abstract

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.

Highlights

Micromechanical methods [1,2,3] have been widely used to homogenize fiber reinforced composites such as FRP, frequently employed to strengthen existing structures made of concrete [4,5,6,7,8]
In [17], a four-phase micromechanical model has been proposed in order to simulate the nonlinear instantaneous pre-peak response of cement concrete subjected to monotonically increasing loads of uni-axial compression
The three types of inclusions 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 cement paste matrix; the 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

Summary

INTRODUCTION

Micromechanical methods [1,2,3] have been widely used to homogenize fiber reinforced composites such as FRP, frequently employed to strengthen existing structures made of concrete [4,5,6,7,8]. It is noted that the iterative procedure begins with the first iteration ( i 1 ), where the void volume fraction fv,i 1 fv,0 is required: fv,0 may represent a measure of the defects in the paste before the loading process If this information is already contained in the constant elasticity C pp of the pure paste fv,0 can be assumed equal to zero. In [17], the proposed micromechanical model has been used in order to capture peculiar aspects of the stressstrain curve in the load case of uni-axial compression: in most concrete materials, a higher compressive strength is associated with a higher initial tangent Young’s modulus E0 ; the formation and evolution of voids in the cement paste cause a reduction of the tangent line to the stress-strain curve;.

45 GPa 65 GPa

CONCLUSIONS