Three-dimensional strut-and-tie models for reinforced concrete pile caps subjected to concentric and eccentric column loads

This study proposes two types of three-dimensional strut-and-tie models for the rational and effective design of square four-pile reinforced concrete pile caps subjected to concentric and eccentric column loads. To enhance the practical applicability of the proposed models, effective strength values for strut and nodal zones were determined through iterative numerical analyses across various combinations of key design parameters, and effective strength equations for the strut and nodal zones were formulated by integrating linear regression analysis, a machine learning technique, with grid search methods. The primary design variables of strength equations included the shear span-to-depth ratio for concentric loads and both the shear span-to-depth ratio and eccentricity ratio for eccentric loads. To validate the proposed models and equations, the ultimate strength of 190 experimental pile cap specimens and 35 numerical pile cap models was predicted. For pile caps under concentric loads, the ratio of experimental to predicted strength (with coefficient of variation) was 1.04 (17.5%), showing improved accuracy and consistency compared to existing design codes (mean strength ratio of 1.45–2.15, coefficient of variation of 47.4%–60.5%). For eccentric loads, the ratio was 1.07 (12.6%), indicating significantly enhanced predictive performance compared to existing design codes (mean strength ratio of 2.17–4.62, coefficient of variation of 32.6%–66.8%). These results confirm that the proposed three-dimensional strut-and-tie models and effective strength equations effectively capture the complex three-dimensional stress flow and reinforcement effects in pile caps, enabling more accurate and reliable evaluation of ultimate strength under both concentric and eccentric loads compared to current design codes.