Monotonicity-constrained machine learning for CPT-based liquefaction triggering assessment

Various machine learning methods have been applied to the prediction of seismic liquefaction triggering of sands with promising success. However, most of the machine learning methods employed are purely data-driven and the intrinsic physical relationships between the liquefaction potential and various physical quantities are rarely examined. In this study, the monotonic relationships between the cyclic stress ratio and cone tip resistance from the cone penetration test with the liquefaction potential are statistically and quantitatively explored. Three widely used machine learning methods, namely Random Forest (RF), Gradient Boosted Decision Trees (GBT), and Support Vector Machine (SVM) are then used to investigate the effects of monotonicity constraints (MCs) on the resulting machine learning models for liquefaction prediction. It is found that for RF and GBT, enforcing MCs also enhances the model performance in terms of AUC (Area Under the Receiver Operating Characteristic curve) by pruning physically implausible splits. For SVM, a simple gradient-penalty method is proposed that penalizes monotonicity violations during model selection, and a derivative-constrained quadratic programming formulation is developed that jointly optimizes the margin and monotonicity, though pointwise constraints cannot guarantee global monotonicity for the RBF kernel. Both SVM methods reduce violations at a modest cost to prediction performance. Enforcing MCs helps align models with physical reality, making them more reliable for geotechnical practice.