Transfer matrix solutions for responses of laterally loaded piles in multilayered soil deposits

Currently, there are few references available on the researches on the internal force and deflection of laterally loaded piles in multilayered soil deposits. Based on the assumptions of postulating that layered soils are homogeneous elastic media and the pile is a vertically embedded foundation beam, as well as the interaction between pile and soil is simulated by three-parametric subgrade reaction model, the governing differential equations for the pile responses in different soil layers are established, and the transfer matrix coefficients at arbitrary depth are obtained using the Laplace transform. Subsequently, the transfer matrix solutions for pile deflection, slope, bending moment and shear force under lateral loading are obtained. Compared with the conventional finite difference method and power series approach, the transfer matrix method is more convenient to solve pile responses in layered soils. Some comparisons are made between the results of references and the calculated ones by the proposed approach, and reasonable agreement is obtained. Finally, parametric studies on influence factors are also performed. The results indicate that the boundary conditions at pile head have a significant impact on the distribution of pile internal force and deflection along pile shaft. Besides that, z₀ and n of reaction model have a remarkable influence on the maximum pile deflection and bending moment.