Semi-analytical solutions for vertically and laterally loaded piles in multilayered soil deposits

In geotechnical practice, it is of considerable importance to assess the behavior of vertical–lateral coupled loading piles in multilayered soil deposits. This study deals with a semi-analytical formulation for the performance of a pile suffering from combined vertical and lateral loads. The emphasis is on quantifying the mobilization of the subgrade reaction provided by the layered soil stratums. In the proposed method, subgrade reactions, correlated with both the accumulative axial load transfer and side resistances depending upon the pile–soil interaction, are abstracted as a series of nonlinear springs in both vertical and lateral directions. On account of this, an alternative transfer matrix method is applied to characterize the pile reaction along the depth under the identified boundary conditions atop the pile; meanwhile, the condition of static equilibrium, between two specific pile segments located at the border of soil layers, is also essential. On this basis, validation of the solution is conducted by comparing with observations from experiments and predictions obtained from other existing methods. In addition, the influence of properties in shallow soil layer and the vertical load on the lateral response of the pile is also discussed. The results indicate a reduction in the lateral displacement and the maximum bending moment within the pile with the increase in the shallow soil stiffness, but a growth with the increase in vertical load due to the “P-Δ effect.”