A multi-axial bounding surface p-y model with application in analyzing pile responses under multi-directional lateral cycling

Multi-directional cyclic loads, as often experienced by piles supporting offshore wind turbines (OWTs), could reduce global soil-pile stiffness, and jeopardize the serviceability of OWTs. Most of the existing p-y models focus on uni-directional soil-pile interaction, with a few multi-directional models developed at the cost of additional parameters that require unusual tests for multi-directional cycling. This study presents a multi-directional bounding-surface based cyclic model for lateral soil-pile interaction in both sand and clay. It can model multi-directional cyclic hysteresis and shakedown using only six parameters, without requiring extra parameters and tests for multi-directional cycling. This is achieved by introducing several uni-directionally loaded springs around the pile at each depth. The cyclic p-y relation for multi-directional loading is derived from that for uni-directional loading, by solving equations on equality of work required for the two models under a given displacement increment. The proposed model is validated against experimental results on piles under uni-and multi-directional cycling with various load-and displacement-controlled paths. It is found that following change of loading direction, the pile displacement accumulation is not only limited to the new loading direction, but includes transverse cycling towards the direction of least soil stiffness softened by the recent loading directions. The transverse cycling causes an additional reduction in the global soil-pile stiffness, facilitating the accumu-lation of lateral pile displacement.