Reliability Analysis and Design of Vertically Loaded Piles in Spatially Variable Soils

Abstract

At present, the reliability analysis and design method of vertically loaded piles embedded in spatially variable soils is difficult to be applied in practical engineering due to the huge computation effort required. To improve computational efficiency, this paper proposes a new method called the FORM–KL–LTM, which integrates the advantages of the first-order reliability method (FORM), the Karhunen–Loève (KL) expansion method, and the load transfer method (LTM). The main framework of the FORM–KL–LTM is the FORM, which is used to perform reliability analysis for the pile. The KL expansion method is adopted to carry out random discretization to generate the discrete soil parameters required by each iterative computation of the reliability index using the FORM, and the LTM is employed to evaluate the nonlinear load–settlement behavior of the pile head and to compute the values of limit state functions required by the FORM. The proposed method is computationally efficient because the number of random variables is controlled by the limit number of KL expansion terms. Based on the FORM–KL–LTM, a reliability sensitivity analysis method is proposed, which can compute the sensitivity index for measuring the relative sensitivity of the reliability index with respect to soil properties. Furthermore, a procedure for the reliability-based design (RBD) of piles embedded in spatially variable soils is established for the design of pile geometry, and a design ratio is defined to select the controlling limit state in the RBD of pile for both the ultimate limit state and the serviceable limit state. The procedure, accuracy, and efficiency of the proposed methods are demonstrated by providing an example of the reliability analysis and design of a vertically load pile in spatially variable soils. The spatial variability of soil has been recognized as an important source of uncertainty of the bearing performance of the pile, and therefore, it should be considered in the reliability analysis and design of a pile foundation. However, the methods used in the current literature, such as the discretization of a random field, the calculation of load–displacement curves, and the reliability analysis of a pile foundation, require a huge computation effort. Low computational efficiency is highly disadvantageous to designers, which makes the reliability analysis and design method by considering a soil’s spatial variability difficult to be widely applied to practical engineering. Therefore, this study proposes a new method called the FORM–KL–LTM to perform the reliability analysis and design of vertically loaded piles in spatially variable soils. This method greatly reduces the number of random variables and simulations of the performance function, thus improving the computational efficiency. Based on the FORM–KL–LTM, a reliability sensitivity analysis method is proposed to carry out a sensitivity analysis of soil parameters on the reliability of a pile foundation. Moreover, this paper defines the design ratios for discussing which limit state mainly controls the failure state of the pile foundation under different soil properties and pile geometry.