Elastoplastic solutions for single piles under combined vertical and lateral loads

In order to improve the reliability of the design and calculation of single piles under the combined vertical and lateral loads,the solutions were presented based on the subgrade reaction method,in which the ultimate soil resistance was considered and the coefficient of subgrade reaction was assumed to be a constant.The corresponding computational program was developed using FORTRAN language.A comparison between the obtained solutions and the model test results was made to show the validity of the obtained solutions.The calculation results indicate that both the maximum lateral displacement and bending moment increase with the increase of the vertical and lateral loads and the pile length above ground,while decrease as the pile stiffness,the coefficient of subgrade reaction and the yielding displacement of soil increase.It is also shown that the pile head condition controls the pile responses and the vertical load may cause the instability problem to the pile.In general,the proposed method can be employed to calculate the pile responses independent of the magnitude of the pile deflection.