Compatibility-based reliability optimization of concrete mix design under strength and workability constraints

Concrete mix design entails balancing two antagonistic requirements: compressive strength reliability, which demands a low water–cement ratio, and workability, which demands a high one. Deterministic methods address these constraints sequentially through empirical safety margins, while numerical multi-objective algorithms handle the antagonism explicitly but without exposing the underlying feasibility structure or enabling closed-form interpretability. This paper develops a unified reliability-based optimization framework that integrates both requirements into a single analytically tractable problem. Compressive strength is modeled through the exponential form of Abrams’ law, calibrated by log-linear regression on the UCI Concrete Compressive Strength dataset. Moisture-induced variability, the dominant aleatory uncertainty in industrial production, is rep-resented by a Beta-distributed aggregate moisture coefficient whose bounded support makes the reliability constraint analytically exact without Monte Carlo simulation. Workability is expressed through a monotonic exponential function of the water–cement ratio, shown in the Appendix to follow from Bingham rheology and calibrated from ACI 211.1 water–slump data. Exploiting the antagonistic monotonic structure of both constraints, the formulation reduces analytically to a one-dimensional optimization problem. The central result is a closed-form expression for the minimum cement content, governed by a compatibility parameter Δ that quantifies the gap between the strength-imposed admissible water–cement ratio and the workability-imposed lower bound. This parameter governs both the existence of feasible designs (Δ > 0) and the asymptotic di-vergence of cement demand as the compatibility boundary is approached (C* ∝ 1/Δ). Chemical admixtures such as superplasticizers are accommodated analytically as an additive shift of the effective water–cement ratio, enlarging the feasible and sustainable design domain. An environmental constraint on cement consumption introduces a parallel shift of the compatibility boundary without altering its slope, enabling integrated sustainability assessment. Predicted optimal cement contents are validated against ACI 211.1 specifications and de Larrard data, confirming agreement within typical industrial ranges for compatible specifications. The framework provides engineers with explicit feasibility conditions, a transparent compatibility map, and closed-form sensitivity estimates of cement demand with respect to strength class, slump, reliability level, and process control quality.