A FORM‐based approach for probabilistic analysis in geotechnics: Application to a reinforced concrete drainage culvert

Abstract

Summary As numerical models are increasingly used as a design tool in geotechnical engineering, it is highly desirable if geotechnical reliability analysis can be conducted based on numeral models. Currently, the practical use of geotechnical reliability analysis‐based numerical models is still quite limited. In this study, an easy to access method is derived to conduct geotechnical reliability analysis based on numerical models. To facilitate its application, a procedure is outlined to implement the suggested method such that geotechnical reliability analysis can be automated using existing geotechnical numerical packages. The procedure is illustrated in detail with an example, and the source codes provided can be easily adapted to analyze other similar problems. The method described in this paper is used to study the reliability of a deteriorating reinforced concrete drainage culvert in Shanghai, China. The suggested method provides a convenient means for reliability analysis of complex geotechnical problems.

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

“…FORM is another commonly used approximate analytical method in the geotechnical engineering field [7,15,[36][37][38][39]. Low et al [36] applied and compared three constrained optimization FORM procedures in the context of a rock slope and an embankment on soft ground.…”

“…A large number of geotechnical reliability analysis methods have been developed in the past decades to effectively calculate the reliability index (β) of geotechnical structures. These analysis methods are generally classified into two types: simulation-based methods [10][11][12][13][14] and approximate analytical methods [7,8,[15][16][17][18]. The former can generally obtain more accurate reliability analysis results with sufficiently large evaluation times of the limit state function (LSF) of geotechnical structures.…”

Robust reliability‐based design approach by inverse FORM with adaptive conjugate search algorithm

“…From a geometric perspective, the FORM applies gradient and curvature information to construct a local approximation of the LSF, and searches for the design point which is also referred to as minimum performance target point (MPTP) $${{{\bf u}}}^*$$ according to the LSF. The reliability index β is obtained by the formula $$\beta \ = \|{{{\bf u}}}^*\|$$, and the probability of structural failure is estimated as $${P}_f = \ {{\Phi}}( { - \beta } )$$ 10,11 . A method proposed by Hasofer and Lind 12 for calculating reliability index, later extended by Rackwitz and Fiessler 13 to include information on the distribution of random variables, is one of the typical FORM algorithms and now widely known as the HLRF recursive algorithm.…”

“…The reliability index 𝛽 is obtained by the formula 𝛽 = ‖𝐮 * ‖, and the probability of structural failure is estimated as 𝑃 𝑓 = Φ(−𝛽). 10,11 A method proposed by Hasofer and Lind 12 for calculating reliability index, later extended by Rackwitz and Fiessler 13 to include information on the distribution of random variables, is one of the typical FORM algorithms and now widely known as the HLRF recursive algorithm. In the past 40 years, since the pioneering work of Hasofer and Lind, various FORM algorithms have been proposed for the solution of reliability index.…”

Independent cover isogeometric Reissner‐Mindlin shell model for the simulation of the fabricated lining

“…By virtue of the strong adaptability to surrounding rock, little impact on environment, mechanized operation, high construction speed and low labor intensity, the fabricated lining is widely used in the underground rail transit, the water conveyance system and the river‐crossing tunnel, for instance, the circular subway tunnel in Figure 1 and the rectangular underground passage in Figure 2 1–5 . With the rapid development of the urban infrastructure construction, the burial depth, diameter and load of the fabricated lining all present an increasing trend, which brings enormous challenges to the design 6–8 .…”