Keywords: single vertical pile, planar frame element, p-y curves, finite element scheme, lateral deflection.

This paper presents a scheme for analyzing the distribution of deflection; bending moment, shear force, and soil reaction along a single vertical pile which may subject to large lateral deflection. The pile is treated as a planar frame element with six degree of freedom represented by a combination of the so-called conventional stiffness matrix in elastic domain [1] and the so-called geometrical stiffness matrix for large deformation [2]. The strain energy of this element in elastic domain is composed of contributions due to bending of equivalent beam element as well as axial compression of equivalent bar element [1]. In dealing with the behavior of soils surrounding the pile, curves are employed. Procedures described in [3] for establishing curves for cohesionless soils and soft to firm clays are adopted in this analysis in order to meet the needs of current application. A computer program using finite element scheme has been prepared to do all required calculations. A Newton-Raphson iterative procedure is used to obtain the solution of nonlinear finite element problem.

A comparison of the presented results with a series of field load test data shows similar variation of lateral deflection with the depth. The calculated lateral deflection can be well agreed with the test data if the constant of horizontal subgrade reaction were appropriately determined. The results also appear that the constant of horizontal subgrade reaction of silty sand decreases from about 3460T/m at lateral load 48.7T to about 553.6T/m at lateral load 130T indicating the loss of lateral soil resistance during the increase of lateral load. The variation of moment with the depth as well as the amount of lateral load indicates that the location of the maximum moment shifts closer to the ground surface with the increase of lateral load. It occurs at a depth varying from about 5.5m for the lateral load of 48.7T to about 3.5m below the ground surface for the lateral load of 130T for this particular study. Also, the moment diminishes at a depth about 20m below the ground surface. In Figure 59.1 the variation of the maximum moment of the pile with the lateral load and the constant of horizontal subgrade reaction is shown. The results indicate that the amount of moment linearly increasing with the increase of the lateral load. The maximum moment increases with the decrease of the constant of horizontal subgrade reaction of the soils indicating the merit of dense silty sand soils.

This study has shown that the proposed scheme is capable of analyzing a single vertical pile subject to large lateral deflection.

1

Astley, R.J., "Finite Elements in Solid and Structures", Chapman & Hall, Chapter 9, 225-260, 1992.

2

Przemieniecki, J.S., "Theory of Matrix Structural Analysis", McGraw-Hill Book Company, Chapter 15, 383-407, 1968.

3

Prakash, S. and Sharma, H.D., "Pile Foundations in Engineering Practice", John Wiley & Sons, Inc., Chapter 6, 322-474, 1990.

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