Volume 6 – Geotechnical Manual, Site Investigation and Engineering ...

Chapter 9 FOUNDATION ENGINEERING
of computer models similar to those described by Bowles (1992), which can be used to take into
account variation of deformation characteristics with depth. In this approach, the pile is represented
by a number of segments each supported by a spring, and the spring stiffness can be related to the
deformation parameters by empirical correlations (e.g. SPT N values). Due allowance can and should
be made for the strength of the upper, and often weaker, soils whose strength may be fully
mobilised even at working load condition.
Alternatively, the load-transfer curves can be determined based on instrumented pile loading tests, in
which a series of 'p-y' curves are derived for various types of soils. Nip & Ng (2005) presented a
simple method to back-analyse results of laterally loaded piles for deriving the 'p-y' curves for
superficial deposits. Reese & Van Impe (2001) discussed factors that should be considered when
formulating the 'p-y' curves. These include pile types and flexural stiffness, duration of loading, pile
geometry and layout, effect of pile installation and ground conditions.
Despite the complexities in developing the 'p-y' curves, the analytical method is simple once the nonlinear
behaviours of the soils are modelled by the 'p-y' curves. This method is particularly suitable for
layered soils.
9.3.5.4 Elastic Continuum Method
Solutions for deflection and rotation based on elastic continuum assumptions are summarised by
Poulos & Davis (1980). Design charts are given for different slenderness ratios (L/D) and the
dimensionless pile stiffness factors under lateral loading (K r ) for both friction and end-bearing piles.
The concept of critical length is however not considered in this formulation as pointed out by Elson
(1984).
A comparison of these simplified elastic continuum solutions with those of the rigorous boundary
element analyses have been carried out by Elson (1984). The comparison suggests that the solutions
by Poulos & Davis (1980) generally give higher deflections and rotations at ground surface,
particularly for piles in a soil with increasing stiffness with depth.
The elastic analysis has been extended by Poulos & Davis (1980) to account for plastic yielding of
soil near ground surface. In this approximate method, the limiting ultimate stress criteria as
proposed by Broms (1915) have been adopted to determine factors for correction of the basic
solution.
An alternative approach is proposed by Randolph (1981b) who fitted empirical algebraic expressions
to the results of finite element analyses for homogeneous and non-homogeneous linear elastic soils.
In this formulation, the critical pile length, L c (beyond which the pile plays no part in the behaviour of
the upper part) is defined as follows:
2⁄
L c = 2r o E 7
pe
G c
(9.25)
Where:
G * = G(1+0.75v s )
G c = mean value of G * over the critical length, L c , in a flexible pile
G = shear modulus of soil
r o = radius of an equivalent circular pile
v s = Poisson’s ration of soil
E p I p = bending stiffness of actual pile
March 2009 9-43