Physics-Informed Gaussian Process Regression for the Constitutive Modeling of Concrete: A Data-Driven Improvement to Phenomenological Models

Abstract

Understanding and modeling the constitutive behavior of concrete is crucial for civil and defense applications, yet widely used phenomenological models such as Karagozian \& Case concrete (KCC) model depend on empirically calibrated failure surfaces that lack flexibility in model form and associated uncertainty quantification. This work develops a physics-informed framework that retains the modular elastoplastic structure of KCC model while replacing its empirical failure surface with a constrained Gaussian Process Regression (GPR) surrogate that can be learned directly from experimentally accessible observables. Triaxial compression data under varying confinement levels are used for training, and the surrogate is then evaluated at confinement levels not included in the training set to assess its generalization capability. Results show that an unconstrained GPR interpolates well near training conditions but deteriorates and violates essential physical constraints under extrapolation, even when augmented with simulated data. In contrast, a physics-informed GPR that incorporates derivative-based constraints aligned with known material behavior yields markedly better accuracy and reliability, including at higher confinement levels beyond the training range. Probabilistic enforcement of these constraints also reduces predictive variance, producing tighter confidence intervals in data-scarce regimes. Overall, the proposed approach delivers a robust, uncertainty-aware surrogate that improves generalization and streamlines calibration without sacrificing the interpretability and numerical efficiency of the KCC model, offering a practical path toward an improved constitutive models for concrete.

Figures (13)

• Figure 1: Schematic illustration of the Karagozian & Case (KCC) model.
• Figure 2: Unconstrained GPR constitutive model trained using four experimental datasets showing $\Gamma$–$\varepsilon_s$ relations at representative confinement levels in between 5 to 39MPa. Experimental training data are highlighted in orange.
• Figure 3: Illustration of when the $\Gamma$-hardening constraint $\mathcal{C}_1$ is violated in the unconstrained GPR constitutive model across the $\varepsilon_s$–$\varepsilon_v$ space: (a) mean derivative prediction; (b) 95% probability violation map considering predictive variance. Blue color shows regions where the constraint is satisfied. Red regions show where the constraint is not satisfied by (a) the mean function and (b) with 95% confidence.
• Figure 4: Unconstrained GPR constitutive model trained using four experimental and four simulation datasets showing $\Gamma$–$\varepsilon_s$ relations at representative confinement levels in between 5 to 39MPa. Experimental training data are highlighted in orange and simulated training datasets are highlighted in yellow.
• Figure 5: Unconstrained GPR constitutive model trained using four experimental and eight simulation datasets showing $\Gamma$–$\varepsilon_s$ relations at representative confinement levels in between 5 to 39MPa. Experimental training data are highlighted in orange and simulated training datasets are highlighted in yellow.