A missing piece in the design of bridge substructure is that the equation given in structural mechanics that assesses the axial forces in the piles of a deep foundation does not take into account the effect of lateral forces acting on the pile cap. In practice, pile forces are determined using a FEA software. This method, however, can not be easily incorporated into an automated program that performs local and global optimizations of a structure. One of the reasons is that this method is particularly demanding on the computational resources. Since a bridge can have a number of deep foundations, which must be verified for various combinations of actions, which need to be optimized, recalculated in various scenarios and then the entire process reiterated for all structural solutions, computational cost can become prohibitive. Another reason is that due to the lack of a relation between all the parameters and dimensions that influence the behaviour of a deep foundation, their optimization is difficult.
For this purpose, a parametric study has been carried out to investigate what parameters influence the relation between the lateral forces applied to the foundation and the axial forces that develop in the piles, and ultimately propose an equation that takes into account the lateral forces. The study is carried out using experimental data obtained on models using the finite element analysis method using SAP 2000 (v.15) software.