An efficient quasi-Newton approximation-based SORM to estimate the reliability of geotechnical problems |
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| Institution: | 1. State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (Chengdu University of Technology), Chengdu, China;2. Department of Ground Engineering, Technical University of Madrid, Madrid, Spain;1. Department of Urban and Environmental Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Republic of Korea;2. School of Civil and Environmental Engineering, Urban Design and Studies, Chung-Ang University, Seoul 06974, Republic of Korea;1. Earthquake Engineering Research and Test Center, Guangzhou University, China;2. Institute of Structural Engineering, Swiss Federal Institute of Technology in Zürich, Switzerland;3. Department of Civil and Environmental Engineering, Seoul National University, South Korea;1. Center for Research on Leading Technology of Special Equipment, School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, China;2. School of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha 410114, China;1. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China;2. Zhejiang Highway and Water Transportation Engineering Consulting Limited Liability Company, Hangzhou, Zhejiang 310006, China;3. Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing 210098, China;1. School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China;2. Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China |
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| Abstract: | The first order reliability method (FORM) is efficient, but it has limited accuracy; the second order reliability method (SORM) provides greater accuracy, but with additional computational effort. In this study, a new method which integrates two quasi-Newton approximation algorithms is proposed to efficiently estimate the second order reliability of geotechnical problems with reasonable accuracy. In particular, the Hasofer–Lind–Rackwitz–Fiessler–Broyden–Fletcher–Goldfarb–Shanno (HLRF–BFGS) algorithm is applied to identify the design point on the limit state function (LSF), and consequently to compute the first order reliability index; whereas the Symmetric Rank-one (SR1) algorithm is nested within the HLRF–BFGS algorithm to compute good approximations, yet with a reduced computational effort, of the Hessian matrix required to compute second order reliabilities. Three typical geotechnical problems are employed to demonstrate the ability of the suggested procedure, and advantages of the proposed approach with respect to conventional alternatives are discussed. Results show that the proposed method is able to achieve the accuracy of conventional SORM, but with a reduced computational cost that is equal to the computational cost of HLRF–BFGS-based FORM. |
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| Keywords: | Second order reliability method BFGS SR1 Rectangular foundation Shallow footing Layered soil slope |
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