Calculation and analysis of acting forces on pile top of foundation with piles with different diameters

In an optimum design of pile foundation stiffness to reduce differential settlement, it is an effective approach to optimize pile foundation stiffness that different diameter piles are employed. No formula is presented in Technical Code for Building Pile Foundation (JGJ94-2008) and Code for Design of Building Foundation (GB50007-2002) for calculating acting forces on the tops of different diameter piles by a cap under loading of its upper building structure. General formulas are induced for calculating acting horizontal and vertical forces on tops of different diameter piles. If diameters of piles are the same, the general formulas are reduced to be the formulas in the two Codes of pile foundation design. It means that the general formulas are a general case of the formulas in the two Codes, which indicates that they are reasonable. A case is analyzed that a pile foundation with two types of pile diameters under a vertical axial force or a horizontal force. If the difference of pile diameters is ignored in the case, that is, the formulas of two design Codes are adopted, results of acting forces on the tops of thicker piles are less than those by the general formulas and results of the thinner piles are opposite. Errors of both thicker piles and thinner piles are more than 16% caused by ignoring the difference of pile diameters if the area ratio of the thicker pile to the thinner pile is 1.5. In an optimum design of pile foundation stiffness to reduce differential settlement, the errors will induce differential settlements of foundations underestimated, and cause unsafe design of pile foundations.