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.