A Strut and Tie Neural Network Surrogate for Failure-Load Prediction of Concrete D-Regions Designed by the Compatible Stress Field Method

Abstract

The Compatible Stress Field Method (CSFM) designs the discontinuity regions (D-regions) of structural concrete by combining a lower-bound stress field with kinematic compatibility and realistic constitutive behaviour. Its nonlinear solution procedure is, however, too slow for the repeated evaluations demanded by design-space exploration, reinforcement optimisation and reliability analysis. This study presents a neural-network surrogate that predicts the failure load factor of a D-region directly from its design parameters. A multilayer perceptron maps a normalised description of a design directly to the failure load factor and the strut and tie (STM) member forces at the failure state, so the surrogate returns an interpretable force state, not the strength alone. Training data come from sweeping an existing CSFM solver over a Latin Hypercube design of experiments across four D-region archetypes: deep beam, hammerhead pier, multi-column bent and pile cap. Trained per archetype, the surrogate predicts the failure load factor with a coefficient of determination of 0.95–0.99 and a mean absolute percentage error of 3–5 %, far more accurately than a gradient-boosted-tree baseline and at roughly three orders of magnitude lower cost than the reference solver. The reference solver is itself checked against an experimental pier-cap benchmark, completing a two-tier validation, though that tier rests on a single five-specimen series. A bagged deep ensemble with split-conformal calibration equips each prediction with an interval that has a finite-sample coverage guarantee. The surrogate makes the design-space exploration, reinforcement optimisation and reliability analysis of D-regions tractable.