X-section cast-in-place concrete (XCC) pile is a typical non-circular cross-sectional pile of which the mechanical characteristics are different from a traditional circular pile

namely the “geometrical effects”. So far

a rigorous theoretical method that considers the geometrical effects is still not given. To investigate the influence of geometrical effects of vertically loaded XCC single pile embedded into homogeneous soil on pile foundation settlement

the differential equations governing the displacements of the pile-soil system based on variational principles are obtained

which accounts for both vertical and horizontal soil displacements. The conformal mapping technique is applied to the governing differential equations in the physical plane with a complicated boundary. With the aid of Matlab software

a finite difference program is developed to solve the governing equations

yielding semi-analytical solutions of pile and soil displacement functions. The pile displacement function is selected to verify the convergence of the developed program. The pile displacement obtained from the present method is exactly the same as the existing theoretical solution. Compared with the finite element analysis

the solution for the XCC pile from our analysis is in reasonable agreement. Finally

parametric studies

which focus on the major effect factors of pile settlement

are conducted

and the geometrical effects of XCC pile are investigated by means of comparing the normalized head pile of stiffness with circular piles with the same area and the same perimeter. After that

a fitting equation for the percentage increase of the normalized pile head stiffness of the XCC pile relative to the circular pile with equal cross-section is given.