A multidirectional p–y model for lateral sand–pile interactions

The lateral loads applied to pile foundations, as induced by winds or earthquakes, are usually multidirectional. Experimental studies have indicated that the lateral resistance of the pile under multidirectional paths is generally lower than that under a unidirectional path and the degree of reduction depends on the characteristics of the loading paths. On the other hand, most currently used p–y models can take the soil–pile interaction under unidirectional lateral loading into account, but it cannot be applied directly to analyze the response of piles under multidirectional lateral loading. A multidirectional p–y model is proposed in this study, which is formulated within the framework of the bounding-surface elastoplastic theory and consists of two loading mechanisms: the parallel loading and the orthogonal loading. The model has five parameters, which are readily available or calibrated. To demonstrate its ability to model soil–pile interactions under both unidirectional and multidirectional lateral loadings, the proposed model is incorporated into a finite-element program to analyze laterally loaded piles. The responses of piles with different embedment lengths subject to various loading paths are investigated. The non-coaxial relationship between the force increment and the displacement increment vectors at the pile head under the multidirectional loading, and the impact of the multidirectional loading on the lateral resistance are well captured in the analyses.