First Order Reliability Method

Abstract

First/second-order reliability method (FORM/SORM) is considered to be one of the most reliable computational methods for structural reliability. A relative advantage of such analytical methods is that they provide physical interpretations and do not require much computation time. Designs based on FORM/SORM are usually performed using commercial software packages in which the underlying concept of the Reliability method is hidden. Also, the available literature is not easy to read and the basic concept is buried in complex mathematical equations. This document aims to give a comprehensive understanding of First Order Reliability Methods. In this document, practical application of FORM is demonstrated with a retaining wall and slope stability problem, both analysed using a spreadsheet model developed by Low (2003). Both applications presented are existing examples by Low (2003, 2005). These are briefly explained, and later modified to understand the efficiency of the model, and to investigate the effect of geometrical uncertainties in a slope’s stability. Additional Graduation Thesis - The efficiency of spreadsheet model is investigated by considering uncertainty of geometrical parameters. Taking advantage of FORM’s ability to reflect sensitivity of the parameters, a sensitivity interpretation of the parameters involved in the slope stability problem is made. The influence of uncertainty of soil layering on the stability of the slope is analysed. Additional investigation on the effect of one dimensional spatial variation on the outcome of slope reliability is made. The spreadsheet model uses intuitive First Order Reliability approach and MS Excels’s inbuilt solver with constrained optimisation to compute Reliability index and probability of failure. It was found to be relatively less user friendly when compared to the existing commercial software packages but it serves as a very efficient tool to understand the concepts of FORM better. The major disadvantage of Monte Carlo regarding its high computational cost has triggered the need to find better alternatives. In most applications, FORM only needs a small number of iterations for convergence, making it more computationally efficient than MCS. This is particularly so when the failure probabilities are low. With the limited research here, it is safe to say that FORM could serve as a first step in Reliability based design to study the relative importance of parameters.