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.

Nonlinear analysis of pile groups subjected to combined lateral and torsional loading

An empirical approach has been developed to analyze the nonlinear response of a pile group with arbitrarily distributed piles subjected to combined lateral and torsional loading.In this approach,the concept of instantaneous twist center is applied to analyze the displacement relationship of pile heads and establish the static equilibrium equations of the pile cap.The horizontal interaction among the individual piles is considered through the generalized p-multiplier.The coupling effect of lateral resistance on the torsional resistance of each pile is quantified using an empirical factorβ;the lateral and torsional nonlinear responses of individual piles are modeled by p-y andτ-θcurves,respectively.The proposed approach not only captures the most significant aspect of the group effect and coupling effect in a pile group subjected to combined lateral and torsional loading,but also automatically updates p-multipliers of individual piles based on pile cap displacements.The proposed approach was verified using results of model tests on pile groups subjected to lateral loading,torsional loading,and combined lateral and torsional loading,separately.In general,the pile cap response and the transfer of applied loads in the pile groups agree well with the test results.