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

2026-01-06

arXiv.org

AI Summary

This work addresses the limitations of traditional concrete constitutive models—such as the Karagozian–Case Concrete (KCC) model—which rely on empirical failure surfaces and lack both functional flexibility and uncertainty quantification. Building upon the KCC elastoplastic framework, the study introduces, for the first time, derivative-based physical constraints into Gaussian process regression (GPR) to directly learn the failure surface from triaxial compression experimental data. This approach seamlessly integrates physical consistency with probabilistic modeling, significantly enhancing extrapolation accuracy and reliability under unseen confining pressures. Compared to unconstrained GPR, the proposed method yields lower predictive variance and tighter confidence intervals while preserving the interpretability and computational efficiency inherent to the KCC model.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

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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.

Problem

• constitutive modeling
• concrete
• failure surface
• uncertainty quantification
• generalization

Innovation

• Physics-Informed Gaussian Process
• Constitutive Modeling
• Concrete Failure Surface
• Uncertainty Quantification
• Extrapolation Constraints