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Assessment of rigorous solutions for pseudo-dynamic slope stability: Finite-element limit-analysis modelling

地震边坡稳定性有限元塑性极限分析拟动力法研究

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Abstract

This study developed a finite-element lower-bound procedure to investigate seismic slope stability in homogeneous and non-homogeneous soils. In order to account for dynamic earthquake inputs, horizontal and vertical accelerations are expressed by the pseudo-dynamic approach, in the form of sinusoidal functions. Within the framework of lower-bound theory, the seismic slope stability analysis is transformed to a linear programming problem subjected to: stress equilibrium, stress discontinuity, stress boundary and yield conditions. An interior-point algorithm implemented into MATLAB was adopted to seek optimal lower-bound solutions of slope bearing capacity and safety factor. The proposed procedure for lower-bound analysis of seismic slope stability was validated by comparing the slope safety factor obtained from different approaches including limit equilibrium and Abaqus. A nonuniform soil slope with linearly varied and layered soil strength parameters and non-associated flow rule are considered, and the corresponding effects on seismic slope stability are discussed. The true solution of safety factor to seismic slope stability is well assessed by rigorous lower and upper bounds with the discrepancy no greater than 4.5%.

摘要

地震诱发边坡失稳是地震灾害的主要类型之一, 开展地震作用下边坡稳定性研究具有重要意义。常规拟静力法无法准确模拟地震波在边坡土体中传播的时间和空间效应, 难以真实反映地震荷载。本文采用拟动力法模拟地震动荷载输入, 基于塑性极限分析下限定理, 结合有限元离散技术, 建立了满足静力平衡条件、屈服条件、应力边界条件和间断条件的地震边坡稳定性有限元极限分析下限法数学规划模型, 基于内点算法寻求边坡超载系数和安全系数的下限解。通过对典型边坡算例分析, 验证了本文方法的正确性。进一步分析了均质土边坡、抗剪强度参数随深度线性增加的非均质土边坡以及双层土边坡的地震稳定性, 讨论了关联和非关联流动准则对地震边坡稳定性的影响。结果表明: 拟静力法和非关联流动法则会低估地震边坡稳定性; 边坡安全系数有限元极限分析下限解与上限解之间的差异小于4.5%, 本文方法计算结果接近地震边坡稳定性真解。

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Authors and Affiliations

  1. College of Civil Engineering, Huaqiao University, Xiamen, 361021, China

    Jian-feng Zhou  (周建烽), Zi-yu Zheng  (郑子玉) & Bing-xiong Tu  (涂兵雄)

  2. School of Civil Engineering, Chongqing University, Chongqing, 400045, China

    Ting Bao  (鲍挺) & Chang-bing Qin  (覃长兵)

  3. School of Civil Engineering, Tongji University, Shanghai, 200092, China

    Jian Yu  (俞剑)

  4. Chongqing Field Scientific Observation Station for Landslide Hazards in Three Gorges Reservoir Area, Chongqing, 400045, China

    Chang-bing Qin  (覃长兵)

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  1. Jian-feng Zhou  (周建烽)
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  2. Zi-yu Zheng  (郑子玉)
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  3. Ting Bao  (鲍挺)
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  4. Bing-xiong Tu  (涂兵雄)
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  6. Chang-bing Qin  (覃长兵)
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Contributions

ZHOU Jian-feng provided the concept and the methodology, performed numerical calculations and the proofing work. ZHENG Zi-yu conducted the literature review and validated the proposed method. BAO Ting edited the manuscript and provided suggestions. TU Bing-xiong edited the manuscript. YU Jian offered some valuable suggestions for the content of the manuscript. QIN Chang-bing provided the concept, wrote and revised the manuscript. All authors replied to reviewers’ comments.

Corresponding author

Correspondence to Chang-bing Qin  (覃长兵).

Ethics declarations

ZHOU Jian-feng, ZHENG Zi-yu, BAO Ting, TU Bing-xiong, YU Jian, and QIN Chang-bing declare that they have no conflict of interest.

Additional information

Foundation item: Projects(52009046, 52108302) supported by the National Natural Science Foundation of China; Project(ZQN-914) supported by the Fundamental Research Funds for the Central Universities, China; Project (3502ZCQXT2022002) supported by the Collaborative Innovation Platform of Fuzhou-Xiamen-Quanzhou National Self-Innovation Zone, China; Project(23ZR1468500) supported by the Natural Science Foundation of Shanghai, China

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Zhou, Jf., Zheng, Zy., Bao, T. et al. Assessment of rigorous solutions for pseudo-dynamic slope stability: Finite-element limit-analysis modelling. J. Cent. South Univ. 30, 2374–2391 (2023). https://doi.org/10.1007/s11771-023-5370-0

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  • DOI: https://doi.org/10.1007/s11771-023-5370-0

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