A weak-unsupervised learning approach for assessing approximate solutions in combined piled-raft foundation analysis

The combined piled-raft foundation (CPRF) is a cost-effective system for tall buildings, but its design remains computationally demanding. Although several closed-form approximate methods have been proposed, their reliability—especially for pre-design—has not been fully established. This study develops an analytical equation to delineate the validity ranges of common approximate CPRF methods by integrating three-dimensional finite element simulations (Abaqus) with principal component analysis (PCA) and weakly unsupervised learning to reduce the high-dimensional input space to a three-dimensional principal component domain. A total of 700 CPRF models were examined for each method—including the Poulos–David–Randolph (PDR) method, equivalent pier (EP) method, equivalent raft (ER) method, and full 3D FEM—covering 20 geometric variables such as pile length, diameter, spacing, and raft dimensions. The comparative results enable a quantitative evaluation of the accuracy of each approximate solution and support the formulation of a practical CPRF assessment tool. The primary contribution of this study is the development of a PCA-based validity-domain framework that quantitatively identifies the reliable application ranges of commonly used approximate methods for combined piled raft foundations. Rather than proposing a new predictive model, the proposed framework provides a practical pre-design assessment tool that enables engineers to evaluate whether simplified analytical or data-driven approaches can be trusted for a given foundation configuration.