Deformation analysis of pile under combined axial and lateral loads by using the energy method

An analysis of deformation and inner force of pile under combined axial and lateral loads is one of the most important aspects for pile foundation. Under the action of lateral load, the single pile will produce certain lateral displacement and bending moment, at this time, the axial load will make the pile appear certain buckling and additional bending moment. The deformation of a single pile under the action of combined axial and lateral loads is different from that under the action of the lateral load or axial load. By using the energy method, this study firstly deduces the energy equations for the pile under combined axial and lateral loads and the surrounding soils, respectively. Combining with deformation compatibility and certain interaction for the pile-soil, the governing differential equation of pile deformation is obtained based on the principle of the minimum potential energy. A power series method is employed to solve the equation, and the power series solutions for the deformation and inner force of pile under the axial and lateral loads is finally obtained. To validate the presented solutions in this study, the results from current solutions are compared with the test results, numerical results, and the calculation results from the code method, showing a good agreement with the existed methods. The influence parameters are discussed. The results indicate that the ratio of length to pile diameter, the ratio of elastic modulus of pile to soil and the coefficient of modulus of soil around pile all have certain influence on the lateral displacement and the maximum bending moment of pile under the axial and lateral loads. It is found that the coefficient of modulus of soil around pile should be no less than 0.6.