V3I11P4

Hybrid Physics–Machine Learning Model for CPT-Based Settlement Prediction of Shallow Foundations

Clifford S. Njah^1*, T. K. S. Abam², S. Cliff-Teme³, G. W. T. Jaja⁴

Abstract

Classical settlement methods for shallow foundations were calibrated largely on temperate sedimentary soils and may perform poorly in lateritic and other tropical residual soils, whose behavior is governed by cementation and uneven weathering. Machine learning (ML) can capture such nonlinear behavior, but most ML models are opaque, which limits their adoption in design practice. This study developed the Hybrid Physics-Informed Settlement Model (HPISM), which predicts shallow-foundation settlement from eight cone penetration test (CPT)-derived parameters: embedment depth, corrected cone resistance, soil behavior type index, unit weight, overconsolidation ratio, foundation width, foundation length, and applied pressure. A database of 8,934 CPT records was compiled from four public repositories. Because these repositories contain no measured footing settlements, a reference settlement was computed for each record with the Schmertmann strain-influence method, and the data were split 70:30 into training and testing sets. Twelve supervised algorithms were trained and compared, and the four best were tuned. The tuned Extra Trees ensemble reproduced the reference settlements most accurately (test coefficient of determination 0.995, root-mean-square error 6.13 mm). SHapley Additive exPlanations (SHAP) ranked foundation width and applied pressure as the most influential predictors. Symbolic regression distilled the tuned ensemble into an explicit equation (test coefficient of determination 0.913), and a gradient boosting residual correction raised this to 0.990 (root-mean-square error 8.65 mm); a fully closed polynomial form suitable for hand or spreadsheet calculation retained a value of 0.973. Three worked examples compare the proposed models with the Terzaghi, Janbu, Meyerhof, and Schmertmann methods. The HPISM offers an inspectable, spreadsheet-ready alternative to a black-box model, although its use for lateritic ground requires verification against measured footing settlements.

Keywords:

Shallow foundation settlement; Lateritic soils; Cone penetration test; Machine learning; Extra Trees; Explainable artificial intelligence; SHAP; Symbolic regression; Hybrid physics–machine learning model