# Optimization of a 2-D Pile Foundation, Optimizing Only Pile Size

The problem consists of a rigid slab foundation with 5-piles, arranged into 4 groups, as seen in figure

4.1. Group 1 initially has no batter but is only allowed to batter to the left while groups 2, 3, and 4 are battered to the right, initially at a value of 5. The loading, constraints, and site conditions are listed in figure 4.1.

Figure 4.1. Example problem, showing constraints, initial design, and constant site and design conditions.

From analysis of the initial design and the prescribed loading, the displacements are already rather close to the maximum displacements. The lateral displacement is 0.46”, and the rotational displacement is 0.0015 rad., both just under the constraints of 0.5” and 0.002 rad., respectively. The weight of the initial volume of steel in the five HP14x117 piles is 61,920 in3. With the displacements this close to their maximums, it is difficult to find a significantly lighter design by hand.

For this first optimization, only the pile sizes are optimized, keeping all other variables constant. After only four iterations, the design converged, and the total volume of the piles reduced to 49,570 in3. Even though the total weight of the piles decreased, the displacements remained under their constraints. The lateral displacement is now 0.49” and the rotational displacement is 0.0020 rad. The volume decrease is shown in Figure 4.2, and the original and optimized pile foundation design is compared in Table 4.1.

 Figure 4.2. Convergence of optimization iterations.

 Original Design Optimized Design Pile Size: Group 1 HP14x117 HP14x117 Group 2 HP14x117 HP14x73 Group 3 HP14x117 HP14x89 Group 4 HP14x117 HP14x73 Lateral Displacement 0.46” 0.49” Rotational Displacement 0.0015 rad. 0.0020 rad. Total Volume of Piles 61,920 in3 49,570 in3
 Table 4.1. Original and Optimized Foundation Design