Continuum Mechanics of Lateral Soil–Pile Interaction

A rigorous mathematical formulation is presented for a flexible tubular pile of finite length embedded in a semi-infinite soil medium under lateral loading. In the framework of three-dimensional elastostatics and classical beam theory, the complicated structure–medium interaction problem is shown to be reducible to three coupled Fredholm integral equations. Through an analysis of the associated Cauchy singular kernels, the intrinsic singular characteristics of the radial, angular, and vertical interfacial load transfers are rendered explicit and incorporated into a rigorous numerical procedure. Detailed results on the three-dimensional load–transfer process, as well as their resultant one-dimensional analogs, are also provided for benchmark comparison and practical applications.