As far as negative skin friction is concerned, group interaction effects are beneficial in that the dragload acting on individual piles will be reduced. The possible exception is for small pile groups (say less than five piles) in very soft soils undergoing substantial settlement such that slip occurs in all the piles, resulting in no reduction in dragload compared to that of a single pile. It should be noted that the distribution of dragload between piles will not be uniform, with the centre piles experiencing the least negative skin friction due to interaction effects.
dc
L e2
αL
Centroid
Legend :
e2 = eccentricity of applied load from centroid of pile group αL = angle of inclination of applied load
dc = thickness of clay stratum L = embedded length of pile
Note : These model test results form a consistent set of data on the relative effect of eccentricity and inclination of the applied load. The recommended group efficiency factors given in Section 7.3.2, 7.3.3 & 7.3.5 for concentric and vertical loading (i.e. e2 = 0 & αL = 0) should be scaled using the ratio deduced from this Figure to take into account the load eccentricity and inclination effects.
Figure 7.5 – Polar Efficiency Diagrams for Pile Groups under Eccentric and Inclined Loading (Meyerhof
& Purkayastha, 1985)
Clay
Sand Eccentricity Ratio, e2
L = 0 Eccentricity Ratio, e2
L = 0.8
∞
0.33 0.73
1.00
αL =0° 30°
45°
60°
0.33 ∞
0.73 0 1.00
0
αL = 0° 30°
45°
60°
Group Efficiency Factor for Horizontal Loading
0
1.0 0.8
0.6 0.4
0.2
0 0 0.2 0.4 0.6 0.8 1.0
0.2 0.4 0.6 0.8 1.0 1.1
0 0.2 0.4 0.6 0.8 1.0 1.1
Group Efficiency Factor for Vertical Loading
Thickness ratio, dc
L Thickness ratio, dc
L
Inclination of Load, αL
Group Efficiency Factor for Horizontal Loading
Group Efficiency Factor for Vertical Loading
90° 90°
Pai = P
np + My*xi
Ix + Mx*yi
Iy
Mx* =
Mx - MyIxy
Ix
1 - Ixy2
IxIy
and My* =
My - MxIxy
Iy
1 - Ixy2
IxIy
Legend :
Pai = axial load on an individual pile, i
P = total vertical load acting at the centroid of the pile group np = number of piles in the group
Mx, My = moment about centroid of pile group with respect to x and y axes respectively Ix, Iy = moment of inertia of pile group with respect to x and y axes respectively Ixy = product of inertia of pile group about the centroid
xi, yi = distance of pile i from y and x axes respectively
Mx*, My* = principal moment with respect to x and y axes respectively, taking into account the non-symmetry of the pile layout
Ix = Σnp
i=1 xi2
Iy = Σnp
i=1 yi2
Ixy = Σnp
i=1 xi yi
For a symmetrical pile group layout, Ixy = 0 and Mx*
= Mx and My*
= My
Notes : The assumptions made in this method are : (1) Pile cap is perfectly rigid,
(2) Pile heads are hinged to the pile cap and no bending moment is transmitted from the pile cap to the piles, and
(3) Piles are vertical and of same axial stiffness.
X Y
P
MX
My
xi
yi
Rigid cap
Pile
Figure 7.6 – Determination of Distribution of Load in an Eccentrically-loaded Pile Group Using the 'Rivet Group' Approach
For practical purposes, the limiting dragload may be taken as the lesser of : (a) the sum of negative skin friction around pile group
perimeter and effective weight of ground enclosed by the perimeter, and
(b) the sum of negative skin friction on individual piles (with a cautious allowance for interaction effects).
Wong (1981) reviewed the various analytical methods and put forward an approach based on the assumption that the settling soil is in a state of plastic failure as defined by the Mohr-Coulomb criterion. In this method, allowance can be made for group action, effect of pile spacing and arching on the vertical effective stress, together with the different stress condition for piles at different positions in a group.
For an internal pile (i.e. piles not along the perimeter of the group), the negative skin friction will be limited to the submerged weight of the soil column above the neutral plane (Section 6.8.2) as this is the driving force.
Kuwabara & Poulos (1989) carried out a parametric study on the magnitude and distribution of dragload using the boundary element method. It was shown that the method gave reasonable agreement with observed behaviour for a published field experiment in Japan.
The above methods are capable of predicting the distribution of negative skin friction in a large pile group and hence assess the average dragload on the group. For pile groups of five piles or more at a typical spacing of three to five pile diameters, interaction effects will result in a reduction in the average dragload. Analysis using the above methods together with available overseas instrumented full-scale data (e.g. Okabe, 1977; Inoue, 1979) indicates that the reduction can be in the range of 15% to 30%. Lee et al (2002) carried out numerical analyses to investigate the distribution of dragload in a pile group. The soil model allowed soil slip at the pile-soil interface. The analyses indicated that reduction in dragload varied from 19% to 79% for a 5 x 5 pile group with piles at a spacing of 2.5 times the pile diameter.
Piles at the centre carried less dragload as the soils arched between the piles.
In the absence of instrumented data in Hong Kong, it is recommended that a general reduction of 10% to 20% on the negative skin friction in a single pile within a group may be conservatively assumed for design purposes, for a pile group consisting of at least five piles at customary spacing. The appropriate value to be adopted will depend on the spacing and number of piles in a group.
Where the calculated reduction in negative skin friction due to group effects is in excess of that observed in field monitoring, consideration should be given to making a more cautious allowance or instrumenting the piles in order to verify the design assumptions.
The effect of negative skin friction may lead to reduction in the effective overburden pressure and hence the capacity of the bearing stratum. Davies & Chan (1981) developed an analysis put forward by Zeevaert (1959), which makes allowance for the reduction in effective overburden pressure acting on the bearing stratum as a result of arching between piles within a pile group.