A bidirectional m-method for allocating spatial effects of special pile groups

The load distribution from a pile group to a single pile is the key issue in calculation of pile foundations. Aiming at the limitation that the one-way m-method in the Chinese specifications and codes is only applicable to plane action, the formulas are derived from three levels: stiffness of a single pile, stiffness of pile groups and equation for force balance, and the stiffness matrix for a deformation-coordinated pile group and the equation for spatial force balance are established, forming a bidirectional m-method suitable for spatial loads. Based on the examples of symmetric straight piles with equal length, bidirectional inclined piles and asymmetric piles, the calculated results by the one-way m-method and the bidirectional m-method are compared and analyzed. The results show that when using the one-way m-method to calculate the symmetric straight piles with equal length, the results are accurate. When calculating the bidirectional inclined piles, the bending moment and shear force of a single pile fluctuate greatly, with the maximum value being about 20% smaller. When calculating the asymmetric piles, the sum of external forces of a single pile is not closed to the total external force, and the reliability is low. The theoretical solutions for the bidirectional m-method can cover these pile foundation types, and the results are closer to the finite element numerical solutions. The research results provide a fast and simple method for special pile foundations, expanding the scope of application of the Chinese design specifications and codes for pile foundations of highway and railway bridges.