Spatially cross-validated machine learning for predicting the Ménard Pressuremeter modulus of the Kanjancham Earth Dam foundation

Accurate determination of deformation parameters in heterogeneous alluvial foundations is critical for the safety and structural integrity of earth dams. The Ménard Pressuremeter Test (PMT) provides a reliable direct measurement of soil stiffness via the pressuremeter modulus ( \(\:{E}ₚ\) ); however, PMT operations are time-consuming, equipment-intensive, and financially demanding. This study develops a spatially cross-validated machine learning (ML) framework to predict \(\:{E}ₚ\) from routinely measured geotechnical index and strength parameters using field exploration data ( \(\:N=48\) test points across 16 boreholes) from the Kanjancham Earth Dam foundation site in Iran. Five distinct algorithms—Linear Regression (LR), an \(\:{L}₂\) -regularized Artificial Neural Network (ANN), Extreme Gradient Boosting (XGBoost), Extra Trees Regressor (ETR), and Random Forest (RF)—were trained and evaluated. To prevent spatial data leakage inherent to contiguous geotechnical sampling, a borehole-grouped 4-fold cross-validation scheme (GroupKFold) was implemented, assessing model predictive capacity on spatially held-out borehole clusters. The empirical findings demonstrate that ensemble tree-based models and regularized neural networks substantially outperform traditional linear approaches. The RF model exhibited the highest predictive accuracy, achieving a pooled out-of-fold coefficient of determination ( \(\:{R}²\) ) of 0.95, a Root Mean Squared Error (RMSE) of 2.82 MPa, and a Mean Absolute Error (MAE) of 2.33 MPa. The \(\:{L}₂\) -regularized ANN ranked second ( \(\:{R}²=0.91\) , RMSE = 3.51 MPa), followed by ETR ( \(\:{R}²=0.82\) , RMSE = 4.61 MPa), XGBoost ( \(\:{R}²=0.78\) , RMSE = 5.04 MPa), and the baseline LR model ( \(\:{R}²=0.52\) , RMSE = 7.48 MPa). Permutation feature importance analysis identified effective cohesion ( \(\:c{\:}\) ), natural moisture content ( \(\:{w}ₙ\) ), and testing depth ( \(\:z\) ) as the primary governing variables controlling soil stiffness predictions, reflecting underlying geomechanical stress states and moisture conditions. Sequential feature-inclusion analysis further revealed that a parsimonious four-parameter subset—comprising \(\:c{\:}\) , \(\:{w}ₙ\) , \(\:z\) , and dry unit weight ( \(\:{γ\:}d\) )—retained robust predictive performance ( \(\:{R}²=0.912\) , RMSE = 2.66 MPa). While the proposed spatially validated models serve as robust decision-support tools for preliminary site characterization and spatial interpolation, they are intended to supplement rather than replace direct field PMT soundings for final detailed engineering designs.