65 The problem of loaded elastic beams resting on an elastic medium (Hetenyi 1946; Vesic 1961) was the original concept used in the solution of laterally loaded deep foundation elements. The classical problem of the elastic beam can be rotated to consider the case of a deep foundation.
In this case, the pile/shaft reaction
p is considered as the distributed load of the beam. Applying the
concept of subgrade reaction,
p =
k y, in which
k is a
subgrade reaction modulus and y is the deflection, solutions can be found for various boundary and load conditions for the elastic problem (Terzaghi 1955). Solutions of the elastic problem are overly simplified and unreliable
to be used in practice, but the concept provides the framework on which many analytical methods are based. There area number of available methods for analyzing laterally loaded deep foundation elements. The most widely accepted methods are the p-y method, which is a computer based
solution based on p-y behavior, and the strain wedge model (SWM), which is another computer based solution based on a limit- equilibrium approach and the Broms method for short piles. As discussed in this chapter, the p-y method is recommended for analysis. All loads used in analysis
should be factored loads, with applicable load factors for the Strength, Service, and Extreme Limit States (refer to Chapter 4).
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