Modified p–y Curve by Cone Penetration Test for Predicting Lateral Load–Displacement Behavior of Helical Steel Piles

In order to investigate the lateral load–displacement behavior of helical steel piles in sand, by considering the nonlinear pile-soil interaction, three p-y curves (p denoted soil reaction per unit length, and y denoted lateral displacement of the pile shaft) were selected to predict and compare lateral bearing behaviors. First, the existing classical sand p-y curve and two CPT-based p-y curves (power function and hyperbola) were analyzed, and their shortcomings were identified. Second, a linearly varying correction factor was introduced within the helical plate influence zone to modify three p-y curves, thereby incorporating the lateral bearing action of the helical plates. Third, the finite-difference method was employed to solve the bending differential equation of the laterally loaded helical steel pile, with pile shaft displacements obtained through iterative solution. Finally, by using the field tests of lateral bearing capacity for helical steel piles conducted in the literature, the prediction results of the three modified p-y curves were subjected to error and statistical analysis against the actual field measurements. The results show that the hyperbola-modified p-y curve produces load–displacement predictions closest to the measurements, with an average predicted-to-measured ratio of 1.04 and a goodness of fit of 98.5%. Among the three methods, the hyperbola approach yields the mean absolute percentage error of 11.63%, compared to 36.32% for the power function method and 24.25% for the classical p-y curve method. Its 95% confidence interval for mean prediction error spans from −6.0% to 11.9%, and the average error of 90% confidence interval spans from −4.6% to 10.5%, which verifies the reliability of the method. These findings provide a robust reference for accurately predicting the lateral load–displacement behavior of helical steel piles.