To better predict the response of laterally loaded caissons and the displacement distribution around the foundations, three different beam theories [Timoshenko beam theory with vertical (z) displacement in soil, Timoshenko beam theory without z displacement, and rigid beam theory with z displacement] were compared in the energy-based variationally method, and two caissons from real projects under the initial loading state were studied. The results from the three methods are compared with measured data from field tests and three-dimensional differential analysis. From the study, the method of the Timoshenko beam theory that considers z displacement in the soil domain produces the most accurate results. The rigid beam theory produced the worst prediction when estimating caisson displacement, rotation, and bending moment. Therefore, for the structure–soil interaction of a laterally loaded caisson, the suggested structure is a Timoshenko beam, and the vertical soil movement around the beam should be considered.

This paper establishes an approximate circular cone strain wedge model and proposes an analytical method that can effectively connect practice with theory for the behavior of laterally loaded flexible piles with both free-head and fixed-head conditions in various types of soil based on the real shape of the strain wedge. The analytical method of the curved strain wedge model, in which the Duncan-Chang model is used to describe the stress-strain relationship of the soil and the relationship between the shear strain $\gamma$ and the horizontal strain $\epsilon$ is improved on the basis of the Mohr circle of strain, is applicable to clay and sand as well as $c\text{-}\phi$ soil. A method of calculating the shear stress along the pile is proposed for circular piles according to the friction direction between the pile and the surrounding soil. The modulus of the soil foundation reaction is calculated along the whole pile length based on the finite-difference method, without calculating the height of the strain wedge, which can truly reflect the nonlinear deformation characteristics of the pile foundation under lateral loading. The proposed method is verified by six case studies, including five field measurement experiments for various types of soil and one finite-element analysis. Comparisons show that the agreement between the results from the curved strain wedge method and those from the field tests and the finite element analysis is generally satisfactory.