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<p>This study proposes a robust and efficient iterative algorithm (called iHLRF-BFGS algorithm) to find the design point of the copula-based first-order reliability method (FORM) for slope reliability analysis under incomplete probability information. First, a brief introduction to the copula theory for modeling the joint cumulative distribution function (CDF) of shear strength parameters is provided. Second, the copula-based FORM using the conventional HLRF algorithm is reviewed. Third, a novel iHLRF-BFGS algorithm for solving the copula-based FORM is derived. Finally, three cohesion-frictional slopes, namely an infinite slope, a two-dimensional (2-D) single-layered slope, and a three-dimensional (3-D) two-layered slope, are presented to illustrate and demonstrate the proposed iHLRF-BFGS algorithm. The results indicate that the iHLRF-BFGS algorithm not only demonstrates high accuracy for slope reliability problems involving explicit and implicit performance functions, but also it is more robust and efficient in finding the design point of the copula-based FORM than both first-order optimization algorithms and the HLRF-BFGS algorithm. In addition, the iHLRF-BFGS algorithm can comprehensively investigate the impact of the dependence structure of shear strength parameters on slope reliability. The prevalent use of the Gaussian copula can result in a hazardous slope design, which underscores the critical importance of proper copula selection in determining slope reliability.</p>

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Robust and efficient iterative algorithm for copula-based FORM and its application to slope reliability analysis

  • 期刊论文

  • 发表日期：

    2026年2月26日

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  • Xin Lin,
  • Xiao-Song Tang

摘要

This study proposes a robust and efficient iterative algorithm (called iHLRF-BFGS algorithm) to find the design point of the copula-based first-order reliability method (FORM) for slope reliability analysis under incomplete probability information. First, a brief introduction to the copula theory for modeling the joint cumulative distribution function (CDF) of shear strength parameters is provided. Second, the copula-based FORM using the conventional HLRF algorithm is reviewed. Third, a novel iHLRF-BFGS algorithm for solving the copula-based FORM is derived. Finally, three cohesion-frictional slopes, namely an infinite slope, a two-dimensional (2-D) single-layered slope, and a three-dimensional (3-D) two-layered slope, are presented to illustrate and demonstrate the proposed iHLRF-BFGS algorithm. The results indicate that the iHLRF-BFGS algorithm not only demonstrates high accuracy for slope reliability problems involving explicit and implicit performance functions, but also it is more robust and efficient in finding the design point of the copula-based FORM than both first-order optimization algorithms and the HLRF-BFGS algorithm. In addition, the iHLRF-BFGS algorithm can comprehensively investigate the impact of the dependence structure of shear strength parameters on slope reliability. The prevalent use of the Gaussian copula can result in a hazardous slope design, which underscores the critical importance of proper copula selection in determining slope reliability.