Keywords: pile foundations, layout optimisation, pile groups, concrete piles, lateral loads, nonlinear programming.

Two dimensional pile foundations occur in solutions for supporting retaining walls or long abutment walls for bridges. Due to usual symmetry of pile groups two- dimensional analysis is commonly used for other types of pile foundations as well. Once the choice of pile is made the layout of the group and possible batter of piles must be found so that bearing capacity, sectional strength, and allowable displacement of pile cap are not exceeded while maintaining the minimum distance between piles. This design may be time consuming because of possible multiple loading conditions which may include large horizontal forces and overturning moments coupled with small vertical loads since uplift resistance is much lower than bearing capacity of piles.

A procedure to help designers with preliminary design of two-dimensional pile foundations is presented. The optimised layout is obtained by solving a nonlinear programming problem. Proposed solution comprises one or more "plane of piles" that repeat themselves at certain spacing. Each plane of piles consists of given number of "pile families" which describe location and batter of each pile within the plane of piles. The design variables are: spacing of each plane of piles, the abscissa and batter angle of each family of piles in each plane of piles. The objective function is the foundation cost including cost of the pile cap and the cost of the piles themselves. Constraints enforce: minimum spacing between piles, maximum batter, concrete pile sectional strength and allowable displacement of the pile cap which can be subjected to multiple loading conditions.

For preliminary design purposes a simplified analysis procedure based on provisions of the Japanese bridge specifications [1] is used in the optimisation process to compute pile cap displacements as well as pile head forces. Simplified equations relate pile head stiffness matrix to SPT of the soil, type of pile and installation technique as well as mechanical properties of the pile cross-section. Pile head stiffness matrix is derived for caps on the ground surface or at some height above ground. Piles may be hinged or rigidly fixed at the pile cap

An example design problem is presented in order to demonstrate the potentials of the proposed procedure. It consists of a foundation for a long wall composed of a plane of piles with three families of precast spun concrete piles subjected to two loading conditions. In order to assess the quality of the obtained solution based on approximate code provisions a more refined analysis is made of the final design using nonlinear curves to model pile-soil interaction [2]. Pile-soil-pile interaction is modelled through -multipliers. The analysis is performed using software FB-Pier, version V 3.18 [3,4]. Reasonable agreement is found in pile head forces and therefore the obtained solution may be accepted for final design.

1

Japan Road Association, "Specifications for Highway Bridges - Part IV", JICA, Tokyo, Japan, 1984.

2

L.C. Reese, W.F. Van Impe, "Single Pile and Pile Groups Under Lateral Loading", Balkema, Rotterdam, Netherlands, 2001.

3

BSI, "FB-Pier Version 3 Help Manual", Florida Bridge Software Institute, University of Florida, Gainesville, USA, 2003.

4

M.I. Hoit, M.C. McVay, C.O. Hays, P.W. Andrade, "Nonlinear Pile Foundation Analysis Using Florida-Pier", Journal of Bridge Engineering, ASCE, USA, November, 1996. doi:10.1061/(ASCE)1084-0702(1996)1:4(135)

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