The "p-y + M-θ" model for cyclic laterally-loaded rigid piles in sand

Within 40-meter water depths, large-diameter monopiles have become the preferred foundation type for offshore wind turbines due to their high efficiency and low cost. Our research team has previously established a "p-y + M-θ" model for large-diameter monopiles under cyclic horizontal loading in clay, which has been successfully applied in numerous engineering analyses. However, the analytical model for horizontally loaded monopiles in sand remains under investigation, with no unified standards yet established. This study develops a "p-y + M-θ" model for predicting the response of horizontally loaded piles in sand under static loading, which is then extended to cyclic loading to analyze displacement ratcheting and shakedown behavior. At the ISFOG-2025, this team participated in a blind prediction competition for static and cyclic horizontal responses of monopiles using this model. The results demonstrated top-ranking accuracy in cyclic loading prediction and, notably, this model was the only one to accurately replicate cyclic shakedown behavior in sandy soils. The "p-y + M-θ" model proposed in this paper offers advantages such as few parameters and high precision, making it a valuable tool for the design and analysis of monopile foundations in sand for offshore wind turbines.