Soil Behavior from Analysis of Tests of Uninstrumented Piles under Lateral Loading

Abstract

The most up-to-date method for the design of laterally loaded piles is to solve numerically the differential equation describing pile behavior. Iterative solutions are necessary since there is a nonlinear relationship between soil resistance and pile deflection. Curves giving soil resistance as a function of pile deflection, called p-y curves, have been the subject of research for a number of years. The development of p-y curves normally requires that a test be performed on an instrumented laterally loaded pile. A curve showing bending moment in the pile needs to be obtained for each of the applied loads. This curve can be differentiated twice to obtain soil resistance, and it can be integrated twice to obtain pile deflection. Cross plots of these values can be made at desired depths to obtain the p-y curves. This paper shows that nondimensional curves, developed from the numerical solutions of the differential equation, can be used to estimate p-y curves if only the following easily obtainable information is reported; pile properties, magnitude of the individual lateral loads, point of load application, deflection of the top of the pile, slope of the top of the pile, and condition of restraint (if any) at the top of the pile. Thus, there needs to be no instrumentation of the pile except above ground. The procedure is illustrated by applying it to a test reported in the literature.

Analysis of laterally loaded piles with rectangular cross sections embedded in layered soil

“…The total potential energy of the pile-soil system, including both the internal and external potential energies, is given by (1) where w is the lateral pile deflection; pq and pq are the stress and strain tensors ( Figure 2) in the soil, respectively (summation is implied by repetition of the indices p and q); and represents the soil domain surrounding the pile. extends from −∞ to +∞ in the x and y directions and from 0 to +∞ in the z direction, but excludes the volume L p × 2a × 2b occupied by the pile.…”

“…Piles subjected to lateral forces and moments at the head are mostly analysed using the p-y method [1][2][3][4][5]. According to this method, the pile is discretized into small segments and the soil mass surrounding the pile is represented by a series of discrete springs (connected to the pile segments) that represent the local resistance offered by the soil to lateral movement of the pile.…”

A continuum-based model for analysis of laterally loaded piles in layered soils

“…Piles subjected to lateral forces and moments at the head are analysed in practice with the p-y method (Reese & Cox, 1969;Matlock, 1970;Reese et al, 1974Reese et al, , 1975Reese & Van Impe, 2001). In the p-y method the pile is assumed to behave as an Euler-Bernoulli beam with the soil modelled as a series of discretely spaced springs, each connected to one of the pile segments into which the pile is discretised.…”

Analysis of Laterally Loaded Piles in Multilayered Soil Deposits

“…Similar empirical approach is adopted to develop the p-y curves as well (Reese and Cox 1969, Matlock 1970, Reese et al 1974, 1975.…”

“…For nonlinear springs, the spring constant k (per unit pile or beam length) depends on the pile (beam) deflection w (in general, the value of k decreases with increasing w). Hence, the soil reaction per unit length p = kw does not increase linearly with w. The nonlinear modification of the one-parameter model culminated in the development of the p-y method (Reese and Cox 1969, Matlock 1970, Reese et al 1974, 1975, Reese and Van Impe 2001. In the p-y method, k is no longer given as input (as a function of w); the nonlinear relationship of k (or p) with w are given as inputs to the analysis in the form of p-w curves, which are widely known in the literature as "p-y" curves.…”