Analytical solution for vertical additional stress under circular uniformly distributed loads based on pile diameter

The calculation of vertical additional stress on the foundation under uniformly distributed circular loads is fundamental for settlement calculation. The Code for Design of Builiding Foundation continues to use the Geddes stress solution to calculate additional stresses, considering pile end resistance and pile side resistance are concentrated forces acting on the pile axis, yet neglecting the pile diameter’s influence. Therefore, there is a certain degree of error. The Technical Code for Building Pile Foundations considers the size of pile diameter when calculating the effect of end resistance, and an analytical expression for the additional stress along the axis of the pile has been obtained, but no analytical expression was provided for the additional stress outside the pile axis, as well as ignoring the size of the pile diameter. Addressing the shortcomings of the above methods, based on the uniformly distributed load of the circular area, considering the size of pile diameter, the Mindlin analytical formula for the vertical additional stress at any point outside the pile axis and under the side resistance was derived by integral operation. By using these analytical formulas to develop calculation programs, it is convenient to calculate vertical additional stress at any point in an elastic body in a semi-infinite space. Comparative calculations show that the method proposed has reliable accuracy. The method can be applied to practical engineering and has certain reference significance for further research on the calculation of additional stress under uniformly distributed circular loads.