Alternative methods for designing laterally loaded piles have been proposed in the literature. These alternative approaches can generally be classified as follows:

- Limit state methods
- Elasticity methods
- Finite element methods
- Numerical methods

Simplest of all the methods are the limit state methods (e.g. Broms, 1964), considering only the ultimate soil resistance. The assumption for short piles is that the ultimate lateral resistance is governed by the passive earth pressure of the surrounding soil. The ultimate lateral resistance for piles with larger penetration depths is governed by the ultimate or yield resistance of the pile (Fig. 1). Broms (1964) provides a simple hand calculation or spreadsheet solution to analyze groundline deflection and moment demand in a single pile. Effects of axial load are neglected and this method requires the subsurface profile to be idealized as homogeneous soils, either sand or clay. Despite these limitations, Broms methods provides a useful tool for establishing the required depth of single foundations (e.g. foundations for signs, high mast lighting, single-pole electrical transmission structures). Moreover, the calculation of the serviceability limit state is possible, but not very accurate, since the pile-soil reaction is assumed to be linearly elastic and the validation showed large differences between calculation and measurement.

Fig.1 Failure Modes for Free-Headed Piles: (a) Long Pile; (b) Short Pile (Broms 1964)

The step-by-step procedure for Broms’ Method for laterally loaded piles is included in FHWA-HI-97-013.

The elasticity methods (e.g. Banerjee and Davis, 1978, Poulos, 1971, and Poulos and Davis, 1980) include the soil continuity. Elastic solutions treat the soil as an elastic, homogeneous, isotropic half-space with a Young’s modulus and Poisson’s ratio. The pile is idealized as a thin beam with representative elastic properties. However, the response is assumed to be elastic. As soil is more likely to behave elasto-plastically, this elasticity method is not to be preferred unless only small strains are considered. Hence, the method is only valid for small strains and thereby not valid for calculating the ultimate lateral resistance. In addition to Poulos’s chart solutions, there are a number of computer programs available including: PIGLET, DEFPIG, and PILGPI (Poulos 1989).

Another way to deal with the soil continuity and the non-linear behaviour is to apply a 2D or 3D finite element model (e.g. Abdel-Rahman and Achmus, 2005). When applying a finite element model both deformations and the ultimate lateral resistance can be calculated. Pile displacements and stresses are evaluated by solving the classic beam bending equation (Winkler’s method) and using one of the standard numerical methods such as Galerkin (Iyer and Sam 1991) or Rayleigh-Ritz (Kishida and Nakai 1977). The soil or rock can be modelled as a nonlinear elasto-plastic solid, complex loading (e.g. dynamic loads or any combinations of axial, torsion, and lateral loads) and soil-structure interactions can be modelled. However, due to the complexity of a 3D model, significant computational power is needed and calculations are often very time consuming. Hence, a finite element approach is a useful method but the accuracy of the results is highly dependent on the applied constitutive soil models as well as the calibration of these models.

Numerical methods (finite element and finite difference) for analyzing laterally-loaded piles are implemented in the following software packages:

- Abaqus (Dassault Systemes 1978)
- GPILE-3D (Kimura et al. 1995)
- Florida Pier (Bridge Software Institute, University of Florida 1997)
- FLAC (Itasca 1998)
- PLAXIS (Brinkgreve et al. 2004)
- OpenSees (PEER University of California, Berkeley 2004)