A physics-constrained neural network with guided local search for rapid code-compliant design of reinforced concrete box culverts

Abstract

Reinforced concrete box culverts must satisfy hydraulic, structural and geotechnical requirements simultaneously, and the conventional design workflow of successive trial sizing and code checking is slow and tends to produce conservative sections. This study develops a physics-constrained neural network (PCNN) that maps site conditions directly to a complete culvert design – clear span, clear rise, member thickness and flexural reinforcement – and couples it with a network-guided local search (GLS) that restores strict code compliance. The engineering model is written entirely in terms of design-code relationships: headwater is computed from the FHWA HDS-5 inlet-control and outlet-control equations; internal actions are obtained from a direct-stiffness analysis of the closed box frame under AASHTO LRFD Strength-I and Service-I load combinations, including earth pressure, design-truck live load with dynamic allowance and lateral surcharge; and the sections are verified for ACI 318-19 flexure, one-way shear, minimum reinforcement and crack control, together with foundation bearing capacity. Six normalised constraint residuals are included in the training loss, and their gradients with respect to the design variables are propagated back through the network weights. A reference database of 5,191 least-cost code-compliant designs was generated by an exhaustive search of 32,513 candidate geometries per scenario, with the reinforcement obtained in closed form. Across 10 random initialisations, the PCNN satisfies all 6 code checks in 92.5 ± 1.0% of unseen scenarios, compared with 25.6 ± 1.5% for an identically sized purely data-driven network. Adding the guided local search raises compliance to 100.0% while remaining 1.73 ± 0.99% above the exhaustive optimum, evaluating only 3.5% of the candidate designs and running 30 times faster than the exhaustive search on identical hardware. Compared with a rule-based design procedure representative of routine practice, the proposed workflow reduces concrete volume by 31.9% and material cost by 30.8%. The framework is deliberately positioned as a preliminary sizing tool. Direct network inference remains unreliable outside the training domain – feasibility falls to 0.0% on an extended-domain sample – and it is the deterministic local search, not the network, that provides the compliance guarantee.