7.6 DESIGN CONSIDERATIONS IN SOIL-STRUCTURE INTERACTION
7.6.2 Load Distribution between Piles
A knowledge of the load distribution in a pile group is necessary in assessing the profile of movement and the forces in the pile cap. Linear elastic methods are usually used
for this purpose although the predictions tend to over-estimate the load differentials.
7.6.2.2 Piles subject to vertical loading
The distribution of vertical loads in a free-standing pile group with a rigid pile cap is predicted to be non-uniform by continuum analyses assuming a linear elastic soil (Poulos &
Davis, 1980). Piles near the centre of a group are expected to carry less loads than those at the edges. It is, however, incorrect to design for this load re-distribution by increasing the capacity of the outer piles in order to have the same factor of safety as for a pile loaded singly.
This is because the stiffness of the outer piles would then increase, thereby attracting more load.
The general predicted pattern of load distribution has been confirmed by measurements in model tests and field monitoring of prototype structures for piles founded in clayey soils. Typically, the measurements suggest that the outer piles could carry a load which is about three to four times that of the central piles at working load conditions in a large pile group (Whitaker, 1957; Sowers et al, 1961; Cooke, 1986).
For groups of displacement piles in granular soils, a different pattern was reported.
Measurements made by Vesic (1969) in model tests involving jacked piles indicate a different load distribution to that predicted by elastic theory, with the centre piles carrying between 20% and 50% more load than the average load per pile. The distribution of the shaft resistance component is however more compatible with elastic continuum predictions (i.e.
outer piles carrying the most load). The effects of residual stresses and proximity of the boundaries of the test chambers on the results of these model tests are uncertain (Kraft, 1991).
Beredugo (1966) and Kishida (1967) also studied the influence of the order of installing driven piles and found that, at working conditions, piles that have been installed earlier tend to carry less load than those installed subsequently.
At typical working loads, the load distribution for a pile group in granular soils is likely to be similar to that in clays, particularly for bored piles. This is supported qualitatively by results of model tests on instrumented strip footings bearing on sand reported by Delpak et al (1992). Their model test results indicate that at working load conditions the distribution of contact pressure is broadly consistent with elastic solutions, whereas at the condition approaching failure the central portion shows the highest contact pressure.
The non-uniform load distribution can be important where the mode of pile failure is brittle, e.g. for piles end-bearing in granular soils overlying a weaker layer where there is a risk of punching failure. The possibility of crushing or structural failure of the pile shaft should also be checked for piles, particularly for mini-piles.
7.6.2.3 Piles subject to lateral loading
For piles subject to lateral loading, centrifuge tests on model pile groups in sand showed that the leading piles carried a slightly higher proportion of the overall applied load than the trailing piles (Barton, 1982). The load split was of the order of 40% to 60% at
working conditions. Similar findings were reported by Selby & Poulos (1984) who concluded that elastic methods are not capable of reproducing the results observed in model tests.
Ochoa & O' Neill (1989) observed from full-scale tests in sand that 'shadowing' effects (i.e. geometric effects that influence the lateral response of individual piles), together with possible effects due to the induced overturning moment, can significantly affect the distribution of forces in the piles. Both the soil resistance and the stiffness of a pile in a trailing row are less than those for a pile in the front row because of the presence of the piles ahead of it. These effects are not modelled in conventional analytical methods, i.e. elastic continuum or subgrade reaction methods. Nevertheless, it was found that the elastic continuum method gave reasonable predictions of the overall group deflection, although not so good for predictions of load and moment distribution for structural design under working conditions. An empirically-based guideline is given by the New Zealand Ministry of Works and Development (1981) for the reduction in the modulus of horizontal subgrade reaction (Kh) for the trailing piles where the pile spacing is less than eight pile diameters along the loading direction.
Brown et al (1988) found from instrumented field tests that the applied load was distributed in greater proportion to the front row than to the trailing row by a factor of about two at maximum test load but the ratio is less at smaller loads. This resulted in larger bending moment in the leading piles at a given loading.
In contrast, results of model pile tests in clay indicate an essentially uniform sharing of the applied load between the piles (Fleming et al, 1992). Brown et al (1988) also found that the 'shadowing' effect is much less significant in the case of piles in clay than in sand.
The actual distribution of loads between piles at working condition is dependent on the pile group geometry and the relative stiffness between the cap, the piles and the soil. This is important in evaluating the deflection profile and structural forces in the cap and the superstructure.
For design purposes, the assumption that the applied working load is shared equally by the piles may be made for a uniform pile group. Where the pile group consists of piles of different dimensions, the applied lateral load should be distributed in proportion to the stiffness as follows :
Hxi = [7.3]
where Hxi = horizontal load on pile i in x-direction Hx = total horizontal load in x-direction
Iyi = moment of inertia of i-th pile about its y-axis np = number of piles in the pile group
In general, as long as the pile length is larger than the critical pile length under lateral loading for a given soil (Section 6.13.3.3), the group behaviour under lateral loading of a group of piles of differing lengths will not be different from a group of piles of equal lengths.
n Σp
i =1 Iyi
HxIyi