Figure 7-7: Example plots of load versus pile head deflection pile and bending moment versus pile

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7.4.2
Combined Lateral and Axial Loads from Frame Action
Design of groups of deep foundation elements requires analysis of the group behavior to determine the distribution of forces to the individual foundation elements from the combined axial, lateral, and overturning loads applied to the group. An efficient group will distribute loads to the foundation elements such that all of them are effectively utilized for providing appropriate load resistance. Calculation of load distribution maybe done using one of the following approaches (Brown et al. 2010):
7. Simple static equilibrium – This approach maybe used for very simple group arrangements. The following conditions and assumptions apply:
a. Applicable if the group is very simple and can be modeled as a determinate simple frame.
b. Loads are calculated using the equations of static equilibrium.
c. A weighted average p-multiplier is assumed to apply. The weighted average p-multiplier approach is discussed in Section d. Rotational restraint provided by the pile/shaft head to the rotation of the cap is ignored.
e. The moment applied to the cap is assumed to be resisted solely by pile/shaft axial forces.
f. Axial stiffness of all piles/shafts are all assumed to be the same.
g. Applies to vertical foundation elements only. Elastic Solution – Individual deep foundation elements are modeled as springs and the cap is considered to be rigid. The following conditions and assumptions apply:
a. The axial, transverse, and rotational stiffness of each foundation element are modeled as simple elastic springs.
b. Foundation elements can be modeled as having different stiffness, or can be assumed to have the same stiffness if a weighted average p-multiplier is used (as discussed in Section c. The cap is assumed to deform as a rigid body.
d. The rotational restraint of the foundation element head to rotation of the cap can be included in the model.
e. Applies to vertical foundation elements only. Nonlinear Solution – Requires a nonlinear computer code for group analysis of deep foundations.
If the simple static solution or simple elastic solution is used to determine the loads applied to each individual foundation element in the group, the foundation element is analyzed for these loads using the average p-multiplier in a p-y analysis, as described in Section 7.4.1. The simple static solution and simple elastic solution are described in detail, including equations for the simple elastic solution and a calculation example of each, in Brown et al. (2010).

111 The more widely used approach is to use the nonlinear solution, which requires use of specialty computer software analyses. In preliminary structural analysis of superstructures supported by deep foundations it is commonly assumed that the foundation cap is rigid. However, the cap rotates around two orthogonal horizontal axes and one vertical axis, and displaces along two orthogonal horizontal axes and vertically. This trend causes the load to be redistributed non-uniformly among individual deep foundation elements within the group. As the pile cap rotates, those foundation elements in the group located off the group center induce additional vertical displacement that affect the overall response of those piles/shafts. These effects are collectively termed pile cap effects The effects of pile cap displacement and rotation are not commonly calculated manually instead, these are more efficiently estimated using computer programs that account for the cap.

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