Keywords: optimization, genetic algorithms, pile groups, foundations, non-linear analysis, load combination.

Foundations are crucial to the safety and serviceability of support structures such as bridges and buildings. Any potentially unsafe foundation designs could spell disaster for human lives and economic losses. Unlike many structures of which the behaviour is well known, foundation designs involve much uncertainty in the soil properties and the behaviour of soil-pile interaction. Due to limited design time and budget, engineers generally tend to provide unnecessary conservative designs.

Much progress in numerical optimization has been made in recent years and such optimization approaches have been widely used in many civil engineering applications such as transportation and the structural design of trusses, frames and bridges. Very few attempts, however, have been made in developing an effective optimization methodology for foundation design.

Most relevant previous research studies on numerical foundation design optimization were based on traditional gradient methods, which are restricted to design problems that must be mathematically formulated and differentiable. As a result, the traditional design techniques are limited to problems with continuous design variables and are not applicable to realistic design problems with discrete design variables. In addition, due to the complexity of practical foundation design, many previous studies on foundation optimization were carried out with over-simplified assumptions such as the use of linear elastic soil and approximate analysis techniques.

In this paper, an automated optimal design method using genetic algorithms (GAs) is presented for pile group foundation design. GAs are particularly suitable for pile group foundation optimization, in which the design variables are often discrete in nature and the relationships between the objective function and design constraints cannot be easily expressed mathematically in term of design variables.

The design process is a sizing and topology optimization for pile group foundations. In the problem formulation, the objective function is the material volume of the foundation. Design constraints that the optimal design must satisfy are the bearing capacity of the soil, the structural capacity of the pile and the pile cap, the lateral displacement as well as the differential and total settlements of the pile group. Design variables are the configuration, number and cross sectional dimensions of the piles as well as the thickness of the pile cap. Without introducing any simplification into the analysis of the pile group foundation, a nonlinear finite element analysis program, FB-Pier, is used to perform rigorous analyses on the pile groups.

The proposed optimization algorithm has been applied to the design of a number of pile group foundations founded on rock. An example is presented to illustrate the capability of the algorithm in searching for the optimal foundation design in terms of its total volume, by varying the location, number and diameter of the piles, as well as the pile cap thickness. Two loading cases have been studied: gravity loading alone and a combination of gravity and wind induced loads.

Optimization of the pile group under a uniform gravity loading alone has resulted in a slight asymmetric distribution of piles. Due to their stochastic nature, GAs cannot always achieve the ideal optimal symmetric solution unless piles are intentionally grouped to result in a symmetric pattern.

Under the condition of combined gravity and wind induced loads, piles with larger diameter are placed to their most favourable locations where the loads are larger. Such a result matches with our expectation as the pile cap is relatively more expensive in term of material volume as compared to the piles. By allocating piles to their most favourable locations, the need for load redistribution through the pile cap can then be lessened.

The optimization algorithm developed is capable of optimizing the topological arrangement and element sizes of pile group foundations under a variety of different loading conditions. The proposed algorithm has great potential to be applied to real life practical foundation design problems.

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