A mathematical formulation to find effective bulk and shear moduli of recycled aggregate concrete

A mathematical formulation incorporating a compatible 6-phase model is proposed and implemented to find the homogenized linear elastic properties of recycled aggregate concrete (RAC) in terms of its effective bulk and shear moduli. The model comprises of five concentric spherical shells to represent new matrix, new Interfacial Transition Zone (ITZ), old matrix, old ITZ and the core raw aggregate embedded in equivalent homogenous medium by following generalized self-consistent scheme. The model is built on the primary assumption that RAC is made of only recycled aggregates, which are described by spherical inclusions of constant volume fraction and constant radii ratios of the constituent phases. Cauchy equilibrium equations and compatibility conditions are made use of to frame the relation between the variables at the constituents' interface, while Eshelby's energy equivalence is applied for solution. Validation is done by following an indirect approach, according to which the characteristic constituents of RAC - the old ITZ and old matrix - are forced to take relatively negligible values and by comparing the predicted values with those of experiments corresponding to normal aggregate concrete. Further, a parametric study is carried out for quantification of the effect of attached mortar (includes old matrix and old ITZ) and new ITZ on the elastic properties of RAC. This first attempt on analytical prediction of the effective elastic properties of RAC yields enough information to make judicious decision on the means - either remove attached mortar or improve new ITZ - to arrive at a design mix of RAC.