Anthony J. Hurd and Kevin Z. Truman

Department of Civil Engineering, Washington University in St. Louis,
St. Louis, Missouri 63130, USA


A computer-automated design and optimization process for pile foundations with rigid concrete slabs is presented. Optimality Criteria methodology is used to provide optimal pile designs. A three­dimensional optimization computer program has been developed that designs a foundation system with an optimal number of piles, geometric layout, pile orientation, batter, and size for a given structure subjected to multiple load cases. The optimization procedure controls displacements while reducing the overall weight of the pile foundation design. A new method for optimizing weightless variables, such as batter, was also created. Thus, the challenges of optimizing variables that indirectly affect the weight of the pile foundation can still be designed to create weight savings. In one example, the total volume of the steel piles is reduced from 61,920 in3 to 49,570 in3 by optimizing only the pile sizes. Furthermore, the weight is reduced again by simultaneously optimizing each pile group’s size coupled with the weightless variable, batter.

1. Introduction

The purpose of this research is to create a computer-automated optimization process for large pile foundations. The U. S. Army Corps of Engineers (USACE) designs large-scale locks and dams that can easily contain thousands of piles, costing millions of dollars. The USACE currently uses pile analysis computer programs but none with optimal design. Therefore, the process for reducing the number and size of the piles is very time-consuming and uncertain, involving the tedious process of manual design, computer analysis, and redesign. This can easily take months and still result in a non­optimal final design. An automated computer optimization process would find an optimal design and take only minutes rather than months. The designer only enters an initial design, load cases, soil conditions, and constraints while the program alters the many design variables to create an optimal foundation design.

Work in pile foundation optimization was originally developed for the USACE by Hill in 1981, using a trial and error approach (Hill, 1981). His method involved first optimizing the batter and then finding an optimal pile spacing. The process finished by iteratively deleting the most and/or least stressed piles. However, this method is not numerically based, and it does not simultaneously optimize all the pile variables, so a true optimum solution is never found. Hoback and Truman used a numerical method to optimize pile designs of both rigid-slab foundations (Hoback et al., 1991) and flexible-slab foundations (Hoback et al., 1993). Their method utilized an Optimality Criteria method employed earlier by Cheng and Truman for structural frames (Cheng et al., 1983).

Optimality Criteria was chosen for this optimization for the following reasons: first, the Optimality Criteria method converges quickly with most examples converging in less than ten iterations. Second, Hoback and Truman were able to simultaneously optimize pile size, layout, batter, orientation, and number while still controlling all stress, strain, or displacement constraints.

The Optimality Criteria method works very well when optimizing a variable that directly affects the
objective function, whether the objective function to minimize is weight, volume of steel, or cost. For


M. Pandey et al. (eds), Advances in Engineering Structures, Mechanics & Construction, 653-661.

© 2006 Springer. Printed in the Netherlands.

example, pile size directly affects the weight of a design. However, some variables such as batter or geometric layout do not have direct effects on the weight of a design, but altering these weightless variables can clearly create large reductions in weight. Thus, a novel approach to optimizing these weightless variables was developed. Using a weightless scaling factor that acts as a pseudo-weight gradient, the Optimality Criteria method can still optimize these weightless variables. The challenges in choosing an appropriate weightless scaling factor were overcome by creating a unique way of gradually decreasing the scaling factor from iteration to iteration, approaching a more optimal design.