ABSTRACT
After selecting materials for the pile foundation to make sure of durability, the designer begins with the components of loading on the single pile or the group. With the axial load, lateral load, and overturning moment, the engineer must ensure that the single pile, or the critical pile in the group, is safe against collapse and does not exceed movements set by serviceability. If the loading is purely axial, the design of a pile can frequently be accomplished by solving the equations of static equilibrium. The design of a single pile or a group of piles under lateral loading, on the other hand, requires the solution of a nonlinear differential equation. Linear solutions of the differential equation for single piles are available and imple-
mented in some codes of practice, but are of limited value. Another simplification is to assume that raked piles in a group do not deflect laterally; the equations that result can be solved readily, but such solutions are usually seriously in error. The following sections show that treating the soil, and sometimes the material in the pile, as nonlinear complicates the mathematics for the single pile and pile group, but solutions can be made by numerical methods that are both rational and in close to reasonable agreement with results from full-scale experiments. The traditional technique of limit analysis, so useful in finding the ultimate capacity
of many foundations, has only a marginal application to assessing the behavior of a laterally loaded pile. As will be demonstrated, acceptable solutions are only possible if explicit, nonlinear relationships are employed that give soil stiffness and resistance as a function of pile deflection, point by point, along the length of a pile. The solutions of the resulting equations can then be made to satisfy the required conditions of equilibrium and compatibility. The problem involves the interaction of the soil and the pile, is one of the class of
soil-structure-interaction problems, and is classified as Geotechnical Category 3 by the Eurocode 7 (Reference). The resistance of the soil, in force per unit length at points along the pile, depends on the deflection of the pile, and the soil resistance must be at hand in order to solve the relevant equations. Therefore, iteration is necessary to find a solution. In this model, the pile is taken as a free body and the soil is simulated by a series of Winkler-type mechanisms, which we discuss further in a later chapter. The equations to be solved for the pile response come directly from ordinary mechanics. A presentation of the methods of design is made initially for isolated or single piles.
A later chapter will deal with the design of pile groups. Two classes of pile-group
problems can be identified: (1) the distribution of loading to the heads of the various piles in the group; and (2) the efficiency of each of the piles in the group, a problem in pile-soil-pile interaction. Both problems are addressed herein; the first is solved satisfactorily by numerical procedures; and the second is discussed fully with respect to available, empirical information.
