ABSTRACT An approximate method is proposed for the analysis of a pile under low or high-amplitude dynamic lateral loading applied at the pile head. The soil-pile system is modeled by the vibrations of a beam on elastic half- space. The uncoupled spring factor (k) and damping coefficient (c) of the foundation medium are defined. Appropriate dynamic soil properties are introduced to determine k and c considering both geometric and material damping. The governing equation of motion of the pile is a fourth order, non-linear, partial differential equation. Difference equation techniques with an iterative process were used in the solution of this equation for various boundary conditions. A computer program was developed for practical application of the proposed method. Comparison of computed results with those measured in instrumented, small-scale, pile tests in clay and sand is generally acceptable. INTRODUCTION Pile foundations in numerous applications are subjected to dynamic, lateral loading at the soil surface ranging from low to high-amplitude. Soil response to low-amplitude dynamic loading may be generally considered linear; therefore, the soil spring factor (k) and coefficient of damping (c) can be assumed constant. Under this soil condition, material damping effects are insignificant and consideration of only geometric damping in the soil to determine dynamic pile response may be justified. However, under high-amplitude dynamic loading, Boil behavior is non-linear. Thus, k and care strain-dependent and not constant. In this case, consideration of soil material damping in determining the behavior of the soil-pile system under dynamic loading is important and should not be disregarded. In an earlier publication (2), the authors introduced an approximate, yet rational approach for the analysis of a laterally-loaded pile subjected to low-amplitude, dynamic surface loading. The soil-pile system was represented by vibrations of a beam on an elastic half-space. The constant discrete, uncoupled spring factor and coefficient of damping were determined using the appropriate dynamic soil properties in accordance with the elastic half-space theory. Soil response was assumed linear and the computation was based only on consideration of geometric damping in the soil medium, while material damping was disregarded. The present paper extends the aforementioned analytical solution of the vibrating pile problem to the range of high-amplitude dynamic loading, which may be experienced in offshore situations. Soil behavior in this case is non-linear. Expressions for the soil k and c as functions of the shear modulus (G), Poisson's ratio, and density of the soil are developed taking into consideration geometric damping in the soil as well as its material damping characteristics. Values of k and c are strain-dependent and thus, variable, since G in this case is a function of the level of stress or strain. The governing equation of motion of a laterally vibrating pile embedded in an elastic half-space is shown in this case to be. a fourth order, partial differential equation with non-linear coefficients. As in previous work (2 & 4), Difference Equations techniques with iterative processes were adopted in the solution of the pile's equation of motion under several boundary conditions.