Physics-guided monotone stacking for reliable prediction of pile load–settlement curves using SPT–σ ' profiles and geometry

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– \(σ '\) 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 \(service=50.2%\) , WAPE \(service=30.5%\) ), 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 \(~\) 12% and MAE by \(~\) 17% relative to a no-physics variant. The proposed approach produces accurate, mechanically admissible, and uncertainty-aware settlement curves from widely available SPT– \(σ '\) data, enabling direct serviceability screening when load tests are limited.