Supplement to the reliability index approach and its application to tunnel reliability problems

Abstract

With the growing demands on limit state design in engineering practices, the reliability index approach (RIA) has been widely used because it is simple and convenient. However, the RIA using a norm function cannot distinguish the negative reliability index, though it is based on the same concept with the HLRF method. Focusing on this issue, a finding from the HLRF concerning negative reliability indices is presented, and accordingly the sign of RIA is resolved. And then a supplement to the RIA is formed with a suggested formula of sensitivity factors for both positive and negative cases. Two nonlinear examples illustrating negative reliability problems are presented, which validates that the proposed supplement can ascertain negative cases whereas the conventional RIA could not. Additionally, results of sensitivity factors agree well with the proposed formula. Furthermore, the proposed supplement is applied to address tunnel reliability problems including assessment and design. Results reveal that the conventional RIA cannot get the real sign of reliability indices and could mislead search directions of the RBD, which would lead to dangerous decisions. Fortunately, the proposed supplement can help to make correct decisions and thus it can facilitate the application of RIA in the limit state design.