⚡ electrical engineering

A Physics-Informed Machine Learning Approach for Predicting Punching Shear Strength of Reinforced Concrete Flat Slabs

This study proposes an interpretable, physics-informed machine learning framework that combines XGBoost regression with a logarithmic transformation to derive a highly accurate and transparent power-law equation for predicting the punching shear strength of reinforced concrete flat slabs, significantly outperforming conventional ACI 318-19 provisions while maintaining practical usability for structural engineers.

Original authors: Aaqib Ali, Aslam Faqeer Mohammad

Published 2026-08-31

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CC BY 4.0

Original authors: Aaqib Ali, Aslam Faqeer Mohammad

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of modern construction, flat concrete floors are a common choice for everything from apartment buildings to parking garages. They offer a clean, open look and allow for flexible interior layouts, but they come with a hidden structural challenge. When a heavy load presses down on a floor, the force must travel from the wide slab into the narrow column supporting it. At this junction, the concrete is subjected to intense, localized stress that can cause it to fail suddenly and without warning. This type of failure, known as punching shear, happens when the concrete around the column cracks and breaks away, much like a cookie cutter punching through dough. If this occurs, the floor can collapse onto the one below, potentially triggering a chain reaction that brings down an entire building.

For decades, engineers have relied on standard rules of thumb to prevent this disaster. These rules, found in building codes, use simplified math to estimate how much weight a slab can hold before it punches through. While these formulas are easy to use, they are based on old data and make broad assumptions that often miss the complex reality of how concrete and steel interact. They can be overly cautious, leading to wasted materials, or dangerously optimistic in specific situations. To solve this, researchers have begun turning to machine learning, a type of computer intelligence that can find patterns in vast amounts of data. However, these computer models are often seen as "black boxes," meaning they give an answer without explaining how they got there, which makes engineers hesitant to trust them for life-safety calculations.

A team of researchers at NED University of Engineering and Technology in Pakistan has developed a new approach that bridges this gap. They wanted to create a prediction tool that is as accurate as the smartest computer models but as clear and usable as the traditional rules engineers already know. To do this, they gathered a massive collection of real-world test results from laboratories around the world. Their database included 408 different concrete slab specimens, each tested until it failed. These tests varied widely in their properties, using concrete with strengths ranging from 16.5 to 119 megapascals and slabs with effective depths between 70 and 456 millimeters. The researchers also looked at the size of the supporting columns and the amount of steel reinforcement inside the concrete.

The team first fed this data into a powerful machine learning algorithm called XGBoost. This system acted like a highly skilled detective, analyzing thousands of combinations of concrete strength, steel ratios, and dimensions to learn exactly how they influenced the failure point. The computer model learned that the most critical factors were the depth of the slab, the size of the column, and the amount of steel reinforcement, along with a calculated measure of the perimeter around the column where the failure would occur. The machine learning model proved to be remarkably accurate, correctly predicting the failure load for 95.95 percent of the variations in the data. In contrast, the standard building code formula only captured about 81.85 percent of the variations.

More importantly, the researchers did not stop at a computer prediction. They took the complex patterns the machine had learned and translated them into a single, simple mathematical equation that any engineer could use with a basic calculator. This new formula looks and feels like the traditional rules found in building codes, but it is built on the deeper understanding provided by the machine learning. When tested against the same data, this new equation reduced the average error in prediction by nearly 60 percent compared to the standard code. While the old code often underestimated the strength of heavily reinforced slabs or overestimated the safety of thin ones, the new formula adjusted for these nuances, providing a much more reliable estimate of when a slab would fail.

The study confirms that the new method is not just a statistical trick but is grounded in the actual physics of how concrete behaves. The researchers found that the computer correctly identified the same physical principles that human experts have long understood: that a deeper slab and a larger perimeter around the column provide more resistance to failure. By combining the pattern-recognition power of machine learning with the transparency of a simple formula, the team has created a tool that is both highly accurate and easy to trust. This work suggests that the future of structural design does not require choosing between complex computer models and simple rules; instead, it is possible to use the former to refine the latter, ensuring that buildings are safer and more efficient without requiring engineers to become data scientists.

Technical Summary: A Physics-Informed Machine Learning Approach for Predicting Punching Shear Strength of Reinforced Concrete Flat Slabs

Problem Statement
Accurately predicting the punching shear capacity ( $V_u$ ) of reinforced concrete (RC) flat slabs is a persistent challenge in structural engineering due to the complex, non-linear interactions between material properties, reinforcement characteristics, and geometric parameters. Conventional design provisions, such as ACI 318-19, rely on simplified empirical formulations. While easy to implement, these equations often exhibit significant prediction uncertainty because they assume linear relationships and neglect key variables, such as the direct mechanical contribution of the flexural reinforcement ratio ( $\rho$ ). This can lead to overly conservative designs in highly reinforced regions or unsafe, liberal estimations in thin slabs with low reinforcement. Conversely, while advanced Machine Learning (ML) models like eXtreme Gradient Boosting (XGBoost) offer superior predictive accuracy, their "black-box" nature—relying on hundreds of discontinuous decision splits—limits their adoption in practical structural design, where transparent, closed-form equations are required for rapid calculation and code compliance.

Methodology
The study proposes a data-driven, code-oriented framework that bridges the gap between high-fidelity ML accuracy and practical engineering utility. The research utilized a comprehensive experimental database comprising 408 interior RC flat slab–column connection specimens from various historical studies. The methodology proceeded through four systematic phases:

Data Compilation and Preprocessing: A structural matrix was compiled, cleaning null values and transforming the reinforcement ratio ( $\rho$ ) from a percentage to a decimal scale to ensure statistical integrity.
Physics-Informed Feature Engineering: To enforce mechanical transparency, the input vector was augmented with physics-informed features derived from structural mechanics. Specifically, the critical shear perimeter ( $b_0 = 4(c+d)$ ) and the concrete tensile metric ( $\sqrt{f'_c}$ ) were computed. The final input vector included concrete compressive strength ( $f'_c$ ), steel yield strength ( $f_y$ ), effective depth ( $d$ ), column width ( $c$ ), reinforcement ratio ( $\rho$ ), $b_0$ , and $\sqrt{f'_c}$ .
Model Training and Benchmarking: An XGBoost regressor was trained on 80% of the data (326 specimens) and validated on a held-out 20% test set (82 specimens). The model's performance was benchmarked against the standard ACI 318-19 empirical equation.
Logarithmic Transformation Multiplicative Engine: To address the "black-box" limitation, the authors developed a specialized engine. The dataset was mapped to log-space to linearize the relationships, allowing for the optimization of power-law exponents via least-squares regression. These optimized parameters were then transformed back into a compact, closed-form multiplicative power-law equation.

Key Contributions

Development of an Interpretable Design Equation: The primary contribution is the derivation of a standalone, single-line power-law equation ( $V_u = \alpha \cdot (f'_c)^a \cdot (f_y)^b \cdot (d)^c \cdot (c)^e \cdot (\rho)^g$ ) that retains the predictive accuracy of a complex ML model while adhering to the format of conventional design codes.
Integration of Physics-Informed Features: The study demonstrates that incorporating domain-specific physical parameters (critical shear perimeter and concrete tensile strength) into the ML feature space enhances the model's ability to capture physically meaningful relationships.
Quantitative Superiority over Empirical Codes: The framework provides a rigorous statistical comparison showing that the ML-derived approach significantly outperforms the ACI 318-19 code provisions in terms of variance explanation and error minimization.

Results
The performance of the proposed frameworks was evaluated using the Coefficient of Determination ( $R^2$ ), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE) on the independent test set:

XGBoost Model: Achieved an $R^2$ of 0.9595, with an MAE of 26.21 kN and an RMSE of 43.79 kN.
Derived Multiplicative Formula: Achieved an $R^2$ of 0.9542, with an MAE of 35.5 kN and an RMSE of 56.22 kN.
ACI 318-19 Benchmark: Achieved an $R^2$ of 0.8185, with an MAE of 64.42 kN and an RMSE of 92.74 kN.

The XGBoost model demonstrated a 17.23% increase in variance explanation compared to the ACI 318-19 baseline. Furthermore, the ML approach reduced the MAE by 59.31% and the RMSE by 52.78%, indicating a substantial reduction in prediction scatter and the elimination of high-magnitude outlier errors. Feature importance analysis confirmed that the model prioritized geometric scales (effective depth $d$ and critical perimeter $b_0$ ) and material properties ( $\rho$ and $\sqrt{f'_c}$ ) in a manner consistent with classical concrete fracture mechanics.

Significance and Claims
The paper claims that this approach successfully bridges the gap between the accuracy of high-fidelity machine learning and the practical requirements of structural design. By translating complex algorithmic patterns into a transparent, multiplicative power-law equation, the study provides engineers with a tool that is both highly accurate and immediately usable in the field without requiring complex computational tools, internet connectivity, or software runtime environments. The derived equation offers a reliable alternative for predicting punching shear capacity, potentially reducing the risk of brittle failure through more precise capacity estimations than current empirical codes allow. The authors note that while the current model is optimized for interior slab-column connections without shear reinforcement, the framework establishes a pathway for future extensions to include shear reinforcement, eccentric loading, and complex geometries.

Technical Summary: A Physics-Informed Machine Learning Approach for Predicting Punching Shear Strength of Reinforced Concrete Flat Slabs

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