A reliability-based optimisation framework for pervious concrete gradation: Balancing strength and permeability under uncertainty

Abstract

The design of pervious concrete is primarily influenced by a crucial balance between permeability and mechanical strength, which is highly dependent on aggregate gradation. Conventional methods do not account for material and model uncertainties, resulting in designs with uncertain reliability. This study develops an uncertainty-aware Reliability-Based Design Optimisation framework for the gradation of pervious concrete. A new hybrid surrogate model, combining a Scheffé polynomial with a Gaussian Process (Kriging) residual model, was created to thoroughly quantify and propagate uncertainty. Comparison with deterministic optimisation shows that mixtures optimal in terms of mean predictions can exhibit high failure risk, with tensile-strength failure probabilities reaching 40%. The proposed framework enforces explicit reliability constraints, using a serviceability-level target failure probability of 5%, and identifies mixtures that satisfy hydraulic and mechanical requirements under uncertainty. The optimal mixtures achieved mean permeability of 3.5–4.5 mm/s, compressive strength of 15–17 MPa, and tensile strength of 2.1–2.4 MPa, with verified failure probabilities below the threshold and, in several cases, below 0.01%. A coarse-dominated gradation between approximately 85–89% consistently satisfied reliability constraints across all optimisations, whereas deterministic optima required trade-offs that resulted in unacceptable reliability. The results show that incorporating uncertainty shifts the optimal mixture locations and prevents selecting designs that are optimal only in expectation. The proposed framework provides a statistically grounded method for reliability-informed pervious concrete mixture design within the validated experimental domain. © 2026 The Authors.