Second-order reliability analysis of an energy pile with CPT data

Abstract

As pile foundations and ground source heat producers, energy piles are becoming more and more popular. Even after much research, engineers find their design to be challenging. An effective way for using the Second-Order Reliability method (SORM) in foundation engineering scenarios including explicit limit state functions is shown in this article. The suggested SORM process is simple to implement in a spreadsheet and is based on an approximate paraboloid fitted to the limit state surface close to the design point. Using well-established closed-form SORM formulae, the failure probability is automatically determined using the primary curvatures of the limit state surface and the reliability index. An energy pile foundation engineering design examples are analyzed using the proposed method and discussed. Comparison with FORM, SORM and Genetic Programming (GP)-based FORM and SORM are made. In the case of determination of group capacity of pile and thermal load the input random variables are qc0, qc1, qc2, fs and E. The reliability index and probability of failure value are found to be 9.34 for FORM, 9.55 for SORM, 9.24 for GP-based FORM, and 9.45 for GP-based SORM. The probability of failure value for FORM 4.60E-21, SORM 3.24E-21, GP-based FORM 1.20E-20, and GP-based SORM is 8.50E-21. The relative percentage error for the average second-order approximation corresponding to FORM is also calculated, and found that Pf2 is 29.48 % in the case of simple SORM and 29.15 % in the case of GP-based SORM. The Breitung provides the most accurate estimation, and the Cai_Elishakoff provides the least accurate estimate.