Design Charts and Equations for Laterally Loaded Piles

Dipanjan Basu

In the proceedings of: GeoRegina 2014: 67th Canadian Geotechnical Conference

Session: Earth Walls and Foundations

ABSTRACT: Laterally loaded flexible and rigid piles embedded in elastic soil with constant and linearly varying modulus are analyzed using the finite element method. The pile responses were found to be functions of the relative stiffness of pile and soil, and of the pile slenderness ratio. Based on the analysis, plots describing pile head deflection, rotation, and maximum bending moment as functions of pile-soil stiffness ratio and pile slenderness ratio are produced and equations describing these quantities are proposed. These equations and plots can be used in design. RÉSUMÉ Pieux flexibles et rigides chargés latéralement incorporés dans le sol élastique avec un module constant et variant linéairement sont analysés en utilisant la méthode des éléments finis. Les réponses de pieux ont été trouvés à être des fonctions de la rigidité relative de la pile et le sol, et du rapport tas d'élancement. Basé sur l'analyse, les parcelles décrivant tête du pieu déviation, rotation, et le moment de flexion maximale en fonction du pile-sol ratio de rigidité et pile élancement sont produites et équations décrivant ces quantités sont proposées. Ces équations et les parcelles peuvent être utilisés dans la conception. 1 INTRODUCTION Pile foundations supporting high rise buildings, bridge abutments, quays, harbors and earth-retaining structures are often subjected to lateral loads of large magnitude arising from wind, traffic and seismic activities. Proper analysis and design of piles subjected to lateral forces and moments is very important to ensure the stability and serviceability of various structures. Methods of analysis of laterally loaded piles can be broadly categorized into two types ¾ the p-y method and the continuum-based methods. In the p-y method, the lateral resistance of soil against pile movement is represented by discrete soil springs characterized by nonlinear p-y relationships (p is the pressure at the pile-soil interface due to lateral pile deflection y) which are given as inputs to the discretized pile nodes at different depths, and the differential equation governing the lateral pile displacement is solved numerically following an iterative algorithm (Matlock 1970, Reese et al. 1974, 1975). The available p-y relationships are developed by giving them as inputs to the numerical simulations of some field pile-load tests and adjusting the curves until the results of the numerical simulations match the field results. Consequently, there is no rigorous theoretical basis for the p-y curves, which makes them site specific and often not sufficiently accurate. The continuum approach, in which the pile is assumed to be embedded in a continuum, is conceptually superior to the spring approach of the p-y method. Poulos (1971) applied Mindlin's solution for horizontal force in an elastic continuum to calculate displacements at the nodes of discretized piles by the integral equation method of analysis. Similar boundary element algorithm was also adopted by Banerjee and Davies (1978). Sun (1994) and Basu et al. (2009) used variational principles to obtain analytical solutions for lateral pile displacements in elastic media. Apart from these analytical approaches, numerical analyses using the three-dimensional finite element, finite difference and boundary element methods have also been carried out to analyze laterally loaded piles (Hsiung and Chen 1997, Klar and Frydman 2002, Budhu and Davies 1988). The computationally-efficient Fourier series-coupled finite element method has been employed as well (Randolph 1981, Carter and Kulhawy 1992, Higgins et al. 2013). This paper presents a parametric study on laterally loaded single piles of circular cross section with different lengths, diameters, flexibilities and boundary conditions embedded in elastic soils. The analysis was performed using the finite element method coupled with Fourier techniques. Single-layer subsurface profiles with constant and linearly varying shear modulus and with constant Poisson's ratio were considered. Based on the study, design equations are proposed and charts are produced using which pile deflection, slope and bending moment can be calculated if the correct elastic soil constants are available. 2 MODIFIED SOIL SHEAR MODULUS The equivalent shear modulus Gs* of the elastic soil is defined in this study as ()*10.75sssGGu=+ [1] where Gs is the actual shear modulus and us is the Poisson's ratio of soil. Gs* is used to represent the elastic

RÉSUMÉ: n Charts and Equations for Laterally Loaded Piles

Access this article:
Canadian Geotechnical Society members can access to this article, along with all other Canadian Geotechnical Conference proceedings, in the Member Area. Conference proceedings are also available in many libraries.

Cite this article:
Dipanjan Basu (2014) Design Charts and Equations for Laterally Loaded Piles in GEO2014. Ottawa, Ontario: Canadian Geotechnical Society.

@article{GeoRegina14Paper310,author = Dipanjan Basu,title = Design Charts and Equations for Laterally Loaded Piles,year = 2014}