Elastoplastic analytical computation of long piles under combined lateral loads

Based on the linear elastic subgrade reaction method and simplified elastoplastic constitutive relations of soil around the piles, the fundamental solutions of the governing equation for the semi-infinite long piles under lateral loading are given in the case of the coefficient of subgrade reaction increasing linearly with depth. The dimensionless analytical expressions of the load-maximum deflection, load-maximum rotation and load-maximum moment relationships under combined lateral loads are deduced. The maximum deflection of the high piles as a special case is also derived. The results show that the three relationships are nonlinear and asymmetrical, so using the linear superposition method for the combined loads will be on the unsafe side. Simultaneously, the complex analytical solutions are simplified for easier application to engineering calculation, and the results of the fitted formulas which can be calculated using a calculator show high accuracy. Comparisons between the results and published data indicate that the present method is capable of analyzing piles under lateral loads.