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

Chapter 9 FOUNDATION ENGINEERING
The load-deflection and load-rotation relationships for a laterally-loaded pile are generally highly
non-linear. Three approaches have been proposed for predicting the behaviour of a single pile:
(a) The equivalent cantilever method,
(b) The subgrade reaction method, and
(c) The elastic continuum method.
Alternative methods include numerical methods such as the finite element and boundary element
methods as discussed in the subsequent sections of this chapter. However, these are seldom
justified for routine design problems.
A useful summary of the methods of determining the horizontal soil stiffness is given by
Jamiolkowski & Garassino (1977).
It should be noted that the currently available analytical methods for assessing deformation of
laterally-loaded piles do not consider the contribution of the side shear stiffness. Some allowance
may be made for barrettes loaded in the direction of the long side of the section with the use of
additional springs to model the shear stiffness and capacity in the subgrade reaction approach.
Where the allowable deformation is relatively large, the effects of non-linear bending behaviour of
the pile section due to progressive yielding and cracking, along with its effect on the deflection and
bending moment profile should be considered (Kramer & Heavey, 1988). The possible non-linear
structural behaviour of the section can be determined by measuring the response of an upstand
above the ground surface in a lateral loading test.
9.3.5.2 Equivalent Cantilever Method
This method represents a gross simplification of the problem and should only be used as an
approximate check on the other more rigorous methods unless the pile is subject to nominal lateral
load. In this method, the pile is represented by an equivalent cantilever and the deflection is
computed for either free-head or fixed-head conditions. Empirical expressions for the depths to the
point of virtual fixity in different ground conditions are summarised by Tomlinson (1994).
The principal shortcoming of this approach is that the relative pile-soil stiffness is not considered in a
rational framework in determining the point of fixity. Also, the method is not suited for evaluating
profiles of bending moments.
9.3.5.3 Subgrade Reaction Method
In this method, the soil is idealised as a series of discrete springs down the pile shaft. The continuum
nature of the soil is not taken into account in this formulation. The characteristic of the soil spring is
thus expressed as follows:
p = k h δ h (9.21)
P h = K h δ h (9.22)
= k h D δ h (for constant K h )
= n h z δ h (for the case of K h varying linearly with depth)
Where:
p = soil pressure
k h = coefficient of horizontal subgrade reaction
δ h = lateral deflection
March 2009 9-41