Interpretable Ensemble Learning with Effective Binder Formalism, Hyperbolic Hydration Kinetics, and Fickian Service-Life Projection for Grey Relational Pareto Optimization of Quaternary SCBA–GGBS–Zeolite–Nano-Silica Cementitious Systems

The construction industry’s dependence on ordinary Portland cement (OPC) makes low-carbon binder systems an urgent priority; yet, the nonlinear interactions among multiple supplementary cementitious materials (SCMs) and nanomaterials complicate rational mix design. This study fuses explainable artificial intelligence (XAI) with a hierarchy of closed-form mathematical formalisms and an experimental durability programme for a quaternary sustainable concrete in which OPC is partially replaced by sugarcane bagasse ash (SCBA, 40 kg/m3), ground granulated blast furnace slag (GGBS, 60 kg/m3), natural zeolite (20 or 40 kg/m3) and nano-silica (0–20 kg/m3) at a constant water–binder ratio of 0.45. Thirteen mixes were tested for compressive and flexural strength, rapid chloride penetration (RCPT) and sulfuric acid resistance at 7, 28 and 56 days. The optimum blend (12 kg/m3 nano-silica) reached 45.0 MPa at 28 days, 49.5% above the control, while reducing chloride charge by 70% and acid mass loss by 65%. Information theoretic discrimination among three competing hydration kinetics laws selects the hyperbolic rate model with an Akaike weight of 1.000 (ΔAICc > 32), showing the blend raises the ultimate strength ceiling by 46% while delaying half-strength by only two days. Within this mix series, effective binder (k-value) analysis indicates that, at low dosage, one kilogram of nano-silica contributes 28-day strength broadly comparable to that of several tens of kilograms of OPC (a dataset-specific, dose-dependent estimate rather than a general mass equivalence), and three independent estimators—the experimental peak, the response surface stationary point (12.8 kg/m3) and the marginal efficiency zero (13.2 kg/m3)—converge on an optimum nano-silica dosage of 3.0–3.3% of binder. Principal component analysis compresses the six-dimensional strength–durability response into a single latent statistical axis (interpreted as an indicator of pore connectivity) carrying 91.5% of the variance, and a Fickian error function solution seeded by Berke–Hicks conversion of RCPT charge projects a 3.4-fold extension of the chloride-initiation service life (36.7 versus 10.8 years at 50 mm cover). Six machine learning models were benchmarked; extremely randomized trees performed best (R2 = 0.9905, RMSE = 0.920 MPa; leave-one-out R2 = 0.986; bootstrap 95% CI on R2 [0.981, 0.996]), and SHAP force plot attributions were triangulated with Sobol global sensitivity indices (curing age 75.4%, nano-silica 23.1% of output variance) and response surface significance tests. The optimized mixes cut embodied CO2 by 26–32% and improve eco-strength efficiency 2.1-fold; grey relational analysis over six strength, durability and carbon criteria ranks the 12 kg/m3 nano-silica mixes first. The framework demonstrates how interpretable machine learning, information theoretic model selection, diffusion theoretic service-life projection and experimental durability evidence can be unified into a transparent, physically validated basis for sustainable concrete mix design.