Analytical solutions for laterally loaded step-tapered piles by state space method

To analyze the response of laterally loaded step-tapered piles, a four-spring model is proposed based on the Timoshenko beam theory considering the effects of pile diameter, shear deformation and nonlinear pile material behavior. The analytical solutions for the internal forces and deformations with arbitrary slenderness ratio can be derived by the state space method considering the nonlinear pile–soil interaction. The solutions are validated through the available field test results in the literatures. Furthermore, the influences of pile parameters, such as the variation position of the diameter, diameter ratio and Young's modulus ratio, on the pile loading responses are proposed. The results show that: (1) The sensitivity of these parameters follows the descending order: pile diameter ratio > variation position of pile diameter > Young's modulus ratio. (2) After trade-off between the pile lateral bearing capacity and the cost, it is suggested that the optimal variation position of the diameter, the pile diameter ratio and Young's modulus ratio should be set as 0.6.