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A three dimensional probabilistic approach to analyzing laterally loaded piles is presented. Two typical subsurface models are used in the analyses: the first one consists of layered linear elastic soil where each layer has a random modulus of elasticity; while the second model takes the form of linear elastic soil with a random modulus of elasticity that increases with depth. Efficient step by step procedures for the reliability computation involving pile displacements are proposed. The solution is based on three-dimensional modeling by the finite element method. A series of results has been obtained for various values of elastic parameters of the soil. Next by a non-linear regression procedure a response surface is obtained. To get the final response surface allowing for a reliability analysis, an iterative algorithm based on the so-called design point concept is applied. The failure criterion is defined as the pile head displacement exceeding displacement threshold. The two cases of piles subjected to lateral load are computed. The paper illustrates the influence of the two distinct types of subsurface variability on the probabilistic analysis. A pronounced effect of the random variability of both the lateral force and the elastic modulus of the upper layer on reliability indices has been shown in results of numerical examples.

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The paper presents an application of High Dimensional Model Representation (HDMR) to reliability assessment of a single pile subjected to lateral load. The purpose is to compare HDMR with some classical method based on response surface technique. First 3D numerical model of the problem for finite elements computations in the ABAQUS STANDARD program has been presented. The soil model is assumed to be linear elastic. However, contacts between the sidewall and the foundation of the pile and the soil are modelled as Coulomb one with friction and cohesion.Next the Response Surface Method is briefly reviewed in conjunction with reliability approach. Then the High Dimensional Model Representation approach is presented. In our approach the HDMR algorithm is based on polynomial of the second degree. Finally the numerical studies have been carried out. The first series of computations demonstrate the efficiency of HDMR in comparison to neural network approach. The second series allows comparison of reliability indices resulting from three different approaches, namely neural network response surface, first-order HDMR and second-order HDMR. It has been observed that for increasing values of the length of the pile reliability indices reach similar values regardless of the method response surface applied.

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