Simple Baselines Outperform Machine Learning When the Bearing-Capacity Generator Is Affine: A Controlled Synthetic Benchmark

Models using machine learning (ML) algorithms have been increasingly adopted for predicting bearing capacity of shallow foundations, but rarely, their superiority to ordinary regression is evaluated using a controlled benchmark. This paper presents a controlled synthetic benchmark where linear, quadratic, and third-order polynomial regression, random forest (RF) model, and artificial neural network (ANN) are compared with the noise-free Meyerhof–Vesić analytical formula for the prediction of a shear-based allowable bearing pressure. Since the Meyerhof–Vesić formula with constant soil properties is an affine function of foundation depth D and width B in each USCS category, there is no curvature in the base generator. Two scenarios are created: (i) smooth scenario with 4% multiplicative Gaussian noise and (ii) complex scenario with fourth-order interaction. All models are analyzed under both soil-specific and pooled training approaches with equal stratified partitions; per-soil R2, RMSE, MAE, and bias are presented with 95% bootstrap confidence intervals, and a blocked holdout with D ∈ [1.00, 2.50] tests extrapolation ability. There is no universally best model. Linear per-soil baseline gives the largest average per-soil R2 under both approaches (0.9686 smooth; 0.9340 complex), equaling or surpassing analytical formula (0.9675; 0.9302), poly33 (0.9650; 0.9308) and ANN (0.9661; 0.9294). In a noiseless setting, all four baselines (analytical, linear, quadratic, cubic) perfectly reconstruct the target (R2 = 1.0000), while RF gets only 0.8901 (pooled) and 0.5902 (per-soil), which proves that there is no point using a cubic polynomial over a linear one. ANN-pooled is the best model for the most nonlinear soil (CH in the complex scenario; R2 = 0.9166 vs. 0.8734 for poly33), indicating that the ML approach brings benefits only when there is some curvature in the data. RF is consistently the worst model (R2 = 0.8789 smooth; 0.8465 complex) and totally fails on a blocked holdout (R2 = −0.059), proving inability to extrapolate. Globally pooled R2 obscures soil-specific problems. Such observations apply to the specific synthetic generator studied; further empirical validation in the field using data from SPT/CPT and a load test is essential before making any suggestions.