This paper, describes a procedure for estimating the uncertainties in the computed deflections and bending moments in a pile subjected to lateral loads. In this procedure, the uncertainties in the soil properties and soil response are first estimated; then, employing the finite difference equations governing the pile behavior, estimates are made of the uncertainties in the computed curves which describe the lateral behavior of the pile.
Several example studies are presented in which a thirty-inch diameter pile embedded in clay is analyzed to obtain the uncertainties in the computed pile behavior as a function of the uncertainties in the input parameters. The results show that the accuracy of the solutions to the problem of a laterally loaded deep foundation obtained using the finite difference technique is very much dependent upon the accuracy of the predicted average soil properties and soil response.
Of all the sources of uncertainties studied in this paper, the uncertainties in the undrained strength of the clay and in the ultimate resistance coefficient, which together define the ultimate lateral soil resistance, contribute most significantly to the uncertainties in the computed pile deflections and bending moments.
The design of a laterally loaded pile involves the estimation of the pile deflections and bending moments corresponding to some design load (5). Insofar as uncertainties exist in the analysis procedure and in the input parameters, the computed pile behavior will also be inexact. Therefore, the actual behavior of the pile may not necessarily be the same as that predicted by the analysis. To account for the possible variation in pile behavior and to safeguard against failure of the pile, the common practice is to use conservative estimates of the input data and then to adopt a factor of safety in the design, thus "ensuring" that in the future the pile deflections and bending moments will be within design specifications. Often, such a practice is overconservative and results in unnecessarily expensive designs.
An alternate approach to the design of a laterally loaded pile is to first estimate the "expected" behavior of the pile, based on the average values of the input data, and then to obtain estimates of the uncertainties in the computed results. This approach enables the design engineer to assess the risk of failure for different design alternatives. The "best" design will then correspond to that which satisfies both economic considerations and a particular level of acceptable risk of failure (10).
The purpose of this paper is to present a procedure for estimating the uncertainties in the computed deflections and bending moments of a pile subjected to lateral loads and to study the reliability of the analysis for laterally loaded piles using the procedure developed. This procedure is based upon a probabilistic model which employs the uncertainties in the soil properties and soil response together with the finite difference equations for the solution of the pile problem. In the present paper, only piles in clays are considered.
