Analytical solution for the dynamic response of a pile with a variable-section interface in low-strain integrity testing

Considering the displacement and stress continuity conditions at the pile-soil interface, ring-soil pile theory (RSPT) and an amended impedance function transfer method (AIFTM) are proposed as models of rigid pile-soil interaction that consider the interaction at the variable-section interface of a pile with the surrounding soil. The interactions between adjacent three-dimensional soil layers are simplified as uniformly distributed Voigt models to derive the impedance function at the pile top. An inverse Fourier transform is applied to derive the velocity response at the top of the pile under transient excitation. An engineering example is described to confirm the rationality of the proposed solution. The solution simplifies into other previously proposed solutions for specific geometric parameters of the pile shaft. The proposed solution is compared with one that neglects the interaction at the variable-section interface of the pile with the surrounding soil; additionally, the coupled effects of the related pile-soil parameters and the interaction at the variable-section interface with the surrounding soil are analyzed.