Influence of Limit State Function’s Form of Geotechnical Structures on Approximate Analytical Reliability Methods

Approximate analytical methods have been frequently used in geotechnical engineering to estimate the reliability of geotechnical structures due to their efficiency and simplicity. The main spirit of these methods is using the moments of the limit state function to estimate the reliability index. However, the moments are strongly dependent on the form of the limit state function, resulting in the fact that these methods are sensitive to the form of limit state functions. This study aims to systematically explore how various equivalent forms of limit state functions affect the performance of several commonly used approximate analytical methods, including the first-order second-moment method, the first-order reliability method, and the point estimation method. The applicable conditions of these methods are illustrated through five typical geotechnical examples. The results indicate that the estimated accuracy for the first-order second-moment method and the point estimation method is affected by the form of the limit state functions. Although the form of the limit state function does not affect the accuracy of the first-order reliability method, it affects computational efficiency. The limit state functions with an equivalent logarithmic form are almost always favorable for the investigated examples and are thus recommended in practice.