The shear failure of ultra-high performance concrete (UHPC) beams is governed by the complex interaction among fibre bridging, aggregate interlock, dowel action, and size-dependent fracture mechanics. However, the effect of these interactions on the shear capacity is not well understood, and current design-code provisions do not account for them adequately, leading to large prediction scatter and uncertain safety margins. This study introduces Phys-MAIN, a physics-informed and interpretable Monotone Additive Interaction Network for design-oriented shear capacity prediction and resistance factor calibration of UHPC beams, developed on an experimental database of 510 specimens across four reinforcement configurations. Each configuration-specific submodel operates on a mechanism-motivated feature subset with monotone piecewise-linear shape functions that enforce physically consistent relationships, complemented by bivariate interaction surfaces. Distribution-free conformal prediction intervals provide finite-sample coverage without residual-distribution assumptions. Configuration-specific resistance factors are calibrated under the ACI 318 LRFD framework at a target reliability index of $\beta_T = 3.5$. Phys-MAIN achieves a cross-validated $R^2 = 0.933$ with zero physical monotonicity violations, and reveals that reinforcement type strongly governs the required safety margin (calibrated $\phi$ ranges from 0.485 for fibre-only beams to 0.625 for fibre + prestress beams).
Phys-MAIN combines four configuration-specific submodels within an adaptive neuro-fuzzy inference system (ANFIS), equipped with physics-informed constraints and distribution-free uncertainty quantification.
Configuration-specific submodels — Four mechanism-motivated submodels (fibre only, fibre + stirrups, fibre + prestress, no fibre) operate on physically relevant feature subsets within an ANFIS architecture, avoiding the mechanism-mixing that plagues global ML surrogates.
Monotone shape functions — Piecewise-linear univariate shape functions with pool-adjacent-violator projection enforce sign-correct sensitivities, achieving a 0% violation rate across all monotonicity-constrained features.
Bivariate interaction surfaces — Tensor-product monotone grids capture the nonlinear interactions established by fracture mechanics theory (size effect, fibre–matrix synergy, prestress–concrete bond).
Distribution-free conformal intervals — Split-conformal calibration on held-out residuals delivers finite-sample coverage guarantees, yielding a rigorous lower-bound design resistance $V_d = V_u / \gamma_{CRC}$ without residual-distribution assumptions.
Configuration-specific LRFD calibration — Resistance factors are calibrated across four reinforcement configurations and five shear-mechanism sub-populations under ACI 318 LRFD at $\beta_T = 3.5$.
Out-of-fold predictions on 510 UHPC beam specimens, calibrated resistance factors per reinforcement configuration, and physics-violation rates versus baseline machine-learning models.
OOF predictions coloured by reinforcement configuration; dashed line is the 1:1 reference. Phys-MAIN achieves $R^2 = 0.933$.
ACI 318/LRFD resistance factors $\phi^{\ast}$ calibrated at $\beta_T = 3.5$.
Physics-violation rate per monotonicity-constrained feature (% of specimens where a +10% perturbation decreases predicted capacity). Phys-MAIN shows zero violations across all features.
Configure the beam and inspect the predicted shear capacity with distribution-free conformal prediction intervals.
Configuration
Beam inputs
@article{wakjira2026physmain,
title = {Phys-MAIN: Physics-Informed Monotone Additive Interaction Network for Design-Oriented Shear Capacity Prediction and Resistance Factor Calibration of UHPC Beams},
author = {Wakjira, Tadesse G. and Goshu, Hana L.},
journal = {Under Review},
year = {2026},
note = {Under Review}
}