A modified p-y curve method considering rotation of soil resistance

The combined load of moments and horizontal forces which are not coplanar at pile top generally cause a complex pile deformation. Under this circumstance, analysis is often performed by using the three-dimensional finite element method, which is not convenient and practical. To simplify the procedure, a modified p-y curve method is proposed in 3D space under the assumption that soil resistance springs can be rotated on the horizontal plane. A corresponding mathematical programming (optimization) model is established for solving this method. Based on the principle of the minimum potential energy, the generalized potential energy equation is selected as the objective function in which the soil spring acting work is represented by the integrated p-y curve functions, and the pile deformation compatibility conditions are selected as constraints, forming a nonlinear programming model. This model assumes five DOFs (degrees of freedom) per node, and the p- effect is considered. The mathematical programming model is validated through three examples. The results show that the assumptions in the proposed method are reasonable, and the model is feasible. Analysis of the soil resistance rotation on the horizontal plane is carried out under bi-directional unevenness bending, and the coordination of displacement and force is presented effectively in the proposed model.