Axial load–settlement (P–S) curves govern pile serviceability checks and support performance-based foundation decisions, yet full static load tests to high load levels remain expensive and are often unavailable. This paper presents PILE-Stack, a physics-guided, monotone stacked ensemble that predicts the complete P–S response of single piles from routine site investigation inputs, including SPT–\(\sigma '\) depth profiles and pile geometry. The method combines mechanics-aware feature design with diverse level-0 experts and a monotone-constrained meta-learner, then applies a pile-wise isotonic projection that guarantees non-decreasing settlement with increasing load. The framework also quantifies uncertainty using quantile models that are calibrated with split-conformal prediction to obtain distribution-free prediction intervals. Evaluation follows a leakage-safe protocol using GroupKFold by PileID and a disjoint 20% PileID-wise holdout. On the external test set, PILE-Stack achieves \(R^2=0.931\), RMSE \(=8.62\) mm, and MAE \(=4.93\) mm. Service-range accuracy remains stable (SMAPE\(_{\text {service}}=50.2\%\), WAPE\(_{\text {service}}=30.5\%\)), while curve-level agreement is strong (mean normalized AUC error \(=0.0886\); mean DTW \(=5.60\) mm). The monotonicity audit reports zero predicted violations. Conformalized intervals deliver near-nominal pile-wise coverage, stay tight at working loads, and widen logically as nonlinearity increases. Ablation results show that including a lightweight mechanistic base and expert diversity reduces RMSE by \(\sim\)12% and MAE by \(\sim\)17% relative to a no-physics variant. The proposed approach produces accurate, mechanically admissible, and uncertainty-aware settlement curves from widely available SPT–\(\sigma '\) data, enabling direct serviceability screening when load tests are limited.
