Development of lateral load resistance-deflection curves for piles in cohesionless soils under earthquake excitation

Abstract

Pile foundations must be designed safely to withstand the lateral loads such as wave loads and seismic loads in offshore/onshore structures, seismic loads in bridges, buildings, port structures etc. The most common analysis method for the design is the Winkler spring approach. Researchers have suggested nonlinear formulations for the lateral load resistance-deflection (p-y) curves, but the contribution of the degree of soil nonlinearity was not studied thoroughly. The main drawback of the current approach is the use of a single stiffness in considering the soil nonlinearity. This study investigates the laterally loaded pile problem using the pressure-dependent hardening soil model with small-strain stiffness (HS-Small Model), where the degree of soil nonlinearity is better integrated. The numerical model was created, and parametric analyses were carried out on the verified model for various pile and soil properties. A modified hyperbolic model was proposed for static p-y relation, including the initial stiffness, ultimate soil resistance, and degree of nonlinearity parameters based on the numerical analysis results. The validity of the model was shown by simulating the field and centrifuge tests from the literature. The proposed model agrees with the test results in the variation of bending moment along the pile. Besides, a significant enhancement was provided in the estimation of pile deflections. Therefore, the proposed model with four parameters can more precisely consider the soil nonlinearity from very small to large displacements. The proposed p-y curves can be utilized in the design of piles subject to static lateral loading. The analysis of dynamic soil-pile interaction problems requires the relation of soil resistance to lateral loading that is represented by nonlinear p-y curves in the beam on the nonlinear Winkler foundation (BNWF) approach. Current methods for p-y curves are either based on static load tests or cannot accurately consider the dynamic soil nonlinearity. This study investigates the dynamic soil-pile interaction in cohesionless soils by numerical analyses to better characterize the p-y curves considering the nonlinear soil behavior under dynamic loading. A numerical pile-soil-structure model was created in FLAC3D and verified by two centrifuge tests published in the literature. The parametric analyses were performed to obtain the p-y curves for various pile diameters, soil relative densities, and degrees of nonlinearities. Based on the parametric analyses, a mathematical model was proposed for the dynamic p-y curves for cohesionless soils. The proposed model characterizes the backbone of dynamic p-y curves based on the three leading parameters (initial stiffness Kpy, ultimate resistance pu, and degree of nonlinearity n). The numerical analyses showed that the p-y curve nonlinearity mainly depends on the employed modulus reduction curves of soils. In the model, the degree of nonlinearity parameter (n) was directly related to the soil parameter "reference strain" (r), which solely represents the modulus reduction curve of soils. In this regard, the dependence on various dynamic soil parameters was diminished by correlating the dynamic p-y curves to the reference strain. The validation analyses performed in structural analysis software demonstrated that the proposed dynamic p-y model could accurately estimate the pile and structure response under earthquake loading by incorporating the hysteretic nonlinear soil behavior. Superstructure accelerations and bending moments along the single pile obtained using the proposed model under different earthquake records were closer to the 3-dimensional numerical analysis results when compared with the results calculated by API. Finally, the proposed static and dynamic p-y models will contribute to the design of piles by improving the initial stiffness, ultimate resistance and nonlinearity of the static load-displacement behavior and by integrating the dynamic soil nonlinearity and hysteretic behavior under directly applied seismic loads.