Predicting critical shear stress using multivariate adaptive regression splines and genetic expression programming for cohesive soils on the Island of Oahu, Hawaii

Abstract 31 undisturbed cohesive silts with plasticity indices ranging from 3 to 55% were tested in an erosion function apparatus to obtain their erodibility curves. The critical shear stress ( τ cr) τ cr ) was estimated by fitting a hyperbolic function to the erodibility curves. Tests were also conducted to obtain the index properties of each sample. Existing regression-based approaches cannot capture the complex and highly nonlinear relationship between τ cr τ cr and other common parameters of cohesive soils with great accuracy. Hence, two robust approaches, namely multivariate adaptive regression splines (MARS) and genetic expression programming (GEP) are utilized to estimate the τ cr τ cr from easily measurable index soil properties. These soil properties are selected based on a literature review and correlation analysis between the τ cr τ cr and other parameters [e.g., water content, plastic limit, liquid limit, plasticity index, liquidity index, activity, median grain size, percent fines (particles smaller than 0.075 mm), percent clay (particles smaller than 2 μm), undrained shear strength, compression and recompression indices, soil unit weight, consolidation pressure, pre-consolidation pressure and void ratio]. Three statistical metrics namely coefficient of determination ( R 2 ), mean absolute error ( MAE ), and root mean square error ( RMSE ) were used to evaluate the performance of the models. Results indicate that the MARS approach outperformed GEP based on: (1) estimates from MARS ( R 2 = 0.992, MAE = 0.483 N/m 2 , and RMSE = 0.641 N/m 2 ) were better than those from GEP ( R 2 = 0.906, MAE = 1.445 N/m 2 and RMSE = 1.686 N/m 2 ); and (2) the MARS approach was able to detect the change in rate of variations of τ cr τ cr (i.e., points where the trend showed a change in slope) when samples from different locations were compared. Also, a sensitivity analysis was performed to investigate the importance of each selected model parameter on τ cr τ cr .