This paper studies the optimum conceptual design of pile foundations at the initial design stage. A modular method is proposed, which divides the foundation into modules and each module is identified by its characteristics of pile length, diameter, number and layout. Modules with the same characteristics may be packed and represented by a design variable. A minimum-cost optimization model with multiple design constraints based on Chinese code and a cardinality constraint is built to achieve the concurrent optimization of pile size and layout. The model is solved by the improved automatic grouping genetic algorithms to obtain the design with optimal variables and optimal variable grouping. A practical example demonstrates the effectiveness of the proposed approach. 1. Introduction Pile foundations widely used in high-rise buildings often arrange identical piles on a regular grid pattern with constant spacing between them. Such design is very conservative and uneconomical. Several design strategies for pile foundations [1–3] are presented to achieve an economic design. Pile design optimization may be defined as minimum cost of the foundation, while maintaining satisfactory performance. Comparing with the wide study and application of optimization technique in structural engineering domain, the development of the optimization of pile foundations is relatively late for three main difficulties. Firstly, accurate performance prediction of pile foundation is almost impossible because of the uncertainty of soil parameters, the complexity of pile-soil-raft interaction, and the inaccurate constitutive law of layered soil. Even with many available studies based on the elastic-plastic theory [4–6], the nonlinear analysis needs various simplifications and assumptions which may not fit the real situation. As Poulos pointed out, “engineering theory should be based initially on the experience and extended or modified in the light of further experience” [7], the theoretical analysis results of pile foundations should be modified according to experience in practical design. Secondly, for the discrete nature of pile characteristics (number, diameter, and length), pile optimization is a discrete problem. In addition, the objective function and constraint conditions may be discontinuous, nondifferentiable or even difficultly expressed mathematically in terms of design variables [8]. As a result, pile optimization must be solved by an effective method. Thirdly, piles of a practical design must be grouped because designs with too many different piles will significantly
References
[1]
R. P. Cunha, H. G. Poulos, and J. C. Small, “Investigation of design alternatives for a pilled raft case history,” Journal of Geotechnical and Geoenvironmental Engineering, vol. 127, no. 8, pp. 635–641, 2001.
[2]
K. Horikoshi and M. F. Randolph, “A contribution to optimum design of piled rafts,” Geotechnique, vol. 48, no. 3, pp. 301–317, 1998.
[3]
O. Reul and M. F. Randolph, “Design strategies for piled rafts subjected to nonuniform vertical loading,” Journal of Geotechnical and Geoenvironmental Engineering, vol. 130, no. 1, pp. 1–13, 2004.
[4]
E. M. Comodromos, “Response evaluation of axially loaded fixed head pile groups using 3D nonlinear analysis,” Soils and Foundations, vol. 44, no. 2, pp. 31–39, 2004.
[5]
E. M. Comodromos and S. V. Bareka, “Response evaluation of axially loaded fixed-head pile groups in clayey soils,” International Journal for Numerical and Analytical Methods in Geomechanics, vol. 33, no. 17, pp. 1839–1865, 2009.
[6]
R. Katzenbach, U. Arslan, C. Moormann, and O. Reul, “Piled raft foundation-interaction between piles and raft,” Darmstadt Geotechnics, vol. 4, pp. 279–296, 1998.
[7]
H. G. Poulos and E. H. Davis, Pile Foundation Analysis and Design, Wiley, New York, NY, USA, 1980.
[8]
C. M. Chan, L. M. Zhang, and J. T. M. Ng, “Optimization of pile groups using hybrid genetic algorithms,” Journal of Geotechnical and Geoenvironmental Engineering, vol. 135, no. 4, pp. 497–505, 2009.
[9]
H. J. C. Barbosa and A. C. C. Lemonge, “A genetic algorithm encoding for a class of cardinality constraints,” in Proceedings of the genetic and evolutionary computation conference (GECCO '05), H. G. Beyer, Ed., pp. 1193–1120, ACM Press, New York, NY, USA, June 2005.
[10]
B. B. Budkowska, “Sensitivity analysis of short piles embedded in homogeneous soil. Part I (theoretical formulation),” Computers and Geotechnics, vol. 21, no. 2, pp. 87–101, 1997.
[11]
Y. K. Chow and V. Thevendran, “Optimisation of pile groups,” Computers and Geotechnics, vol. 4, no. 1, pp. 43–58, 1987.
[12]
A. J. Hurd and K. Z. Truman, “Optimization method of pile foundations,” in Advances in Engineering Structures, Mechanics and Construction, M. Pandey, W. C. Xie, and L. Xu, Eds., vol. 140, pp. 653–661, Springer, Amsterdam, The Netherlands, 2006.
[13]
K. N. Kim, S. H. Lee, K. S. Kim, C. K. Chung, M. M. Kim, and H. S. Lee, “Optimal pile arrangement for minimizing differential settlements in piled raft foundations,” Computers and Geotechnics, vol. 28, no. 4, pp. 235–253, 2001.
[14]
Y. F. Leung, A. Klar, and K. Soga, “Theoretical study on pile length optimization of pile groups and piled rafts,” Journal of Geotechnical and Geoenvironmental Engineering, vol. 136, no. 2, Article ID 003002QGT, pp. 319–330, 2010.
[15]
K. Z. Truman and A. S. Hoback, “Optimization of steel piles under rigid slab foundations using optimality criteria,” Structural Optimization, vol. 5, no. 1-2, pp. 30–36, 1992.
[16]
H. T. Kim, H. K. Yoo, and I. K. Kang, “Genetic algorithm-based optimum design of piled raft foundations with model tests,” Geotechnical Engineering, vol. 33, no. 1, pp. 1–11, 2002.
[17]
Ministry of Construction, Technical code for building pile foundations, Ministry of Construction, Beijing, China, 2008.
[18]
L. M. Penteado and J. de Brito, “Expert knowledge-based selection methodology for optimizing the construction of concrete piles,” Journal of Perfomance of Constructed Facilities, vol. 26, no. 1, pp. 95–103, 2012.
[19]
H. G. Poulos, “Piled raft foundations: design and applications,” Geotechnique, vol. 51, no. 2, pp. 95–113, 2001.
[20]
R. D. Mindlin, “Force at a point in the interior of a semi-infinite solid,” Journal of Applied Physics, vol. 7, no. 5, pp. 195–202, 1936.
[21]
H. G. Poulos, “Analysis of the settlement of pile groups,” Geotechnique, vol. 18, no. 4, pp. 449–471, 1968.
[22]
M. F. Randolph and C. P. Wroth, “analysis of the vertical deformation of pile groups,” Geotechnique, vol. 29, no. 4, pp. 423–439, 1979.
[23]
D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, New York, NY, USA, 1989.
[24]
J. P. B. Leite and B. H. V. Topping, “Improved genetic operators for structural engineering optimization,” Advances in Engineering Software, vol. 29, no. 7–9, pp. 529–562, 1998.
[25]
H. J. C. Barbosa, A. C. C. Lemonge, and C. C. H. Borges, “A genetic algorithm encoding for cardinality constraints and automatic variable linking in structural optimization,” Engineering Structures, vol. 30, no. 12, pp. 3708–3723, 2008.
[26]
A. C. C. Lemonge and H. J. C. Barbosa, “An adaptive penalty scheme for genetic algorithms in structural optimization,” International Journal for Numerical Methods in Engineering, vol. 59, no. 5, pp. 703–736, 2004.
[27]
S. Koziel and Z. Michalewicz, “Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization,” Evolutionary computation, vol. 7, no. 1, pp. 19–44, 1999.
[28]
X. F. Liu, G. D. Cheng, J. Yan, and L. Jiang, “Singular optimum topology of skeletal structures with frequency constraints by AGGA,” Structural and Multidisciplinary Optimization, vol. 45, no. 3, pp. 451–466, 2012.
