Reliability-Based Determination of the Water–Cement Ratio for Concrete Mix Design — Data and Code

A fundamental KPI in RC structural design is the concrete characteristic compressive strength fck, defined as the 5% lower fractile of the strength distribution and constituting a probabilistic material parameter within structural reliability frameworks. However, conventional mix design procedures used to achieve a prescribed fck remain largely deterministic and rely on empirical safety margins rather than explicit uncertainty propagation.Unlike data-driven approaches focused on predictive accuracy, the methodology proposed here is explicitly design-oriented and reliability-based. It provides a transparent link between production variability, statistical confidence, and material efficiency, enabling a rational transition from empirical to performance-based mix design.This study reformulates concrete mix design as a one-dimensional reliability problem driven by bounded physical uncertainty. The primary source of aleatory variability is identified as aggregate moisture content, modeled as a bounded random variable. The effective water/cement ratio is expressed as an affine transformation of aggregate moisture, and compressive strength is derived analytically through the exponential form of Abrams’ law.Calibration of the Abrams parameters is performed using publicly available experimental datasets, confirming that deterministic strength models explain only part of the observed variability. Assuming a Beta distribution for aggregate moisture, a closed-form expression for the characteristicstrength is obtained without resorting to Monte Carlo simulation.The formulation defines an explicit reliability-based design operator mapping structural strength requirements into the controllable production variable the added water content. Sensitivity analyses quantify the influence of process control quality and model parameters, while the framework is shown to be equivalent to an exact one-dimensional First-Order Reliability Method (FORM) solution.The proposed approach establishes a transparent bridge between production variability, material reliability, structural safety calibration, and sustainability-oriented optimization.