Symmetry–Asymmetry Framework for Rubberized Concrete: Logistic/Exponential Models for Fresh Properties and Corrected Predictions for Compressive Strength

In this study, the effects of rubber content, particle size (total surface area), and water–cement (W/C) ratio on the slump and air content of fresh concrete and the mechanical properties (compressive strength and Young's modulus) of hardened concrete were investigated for rubber-mixed concrete (RuC) using waste tire-derived rubber as a partial replacement for fine aggregates. An estimation formula was proposed, and the experimental results confirmed that the slump and air content were primarily governed by the total rubber surface area and exhibited an upper limit (saturation point). These properties can be approximated using simple symmetric mathematical models, such as logistic or exponential functions. Although the mechanical properties deteriorated with increasing rubber content, the degree of reduction was not constant and varied depending on the W/C ratio and rubber content. Based on these results, a symmetric mathematical model—the logistic function—was established to estimate the compressive strength under standard conditions (W/C = 0.56). Subsequently, a method was proposed to correct for these effects when W/C = 0.56. The verification demonstrated that the proposed two-tier model, consisting of a symmetric baseline equation and W/C-dependent correction, could estimate the compressive strength of RuC under any condition, including those with strong asymmetry. These findings provide a framework for the construction industry to design and implement rubberized concrete mixes, promoting this sustainable material in structural applications by enabling accurate predictions of mechanical performance under varied conditions.