IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0270400.html
   My bibliography  Save this article

An investigation of integrating the finite element method (FEM) with grey system theory for geotechnical problems

Author

Listed:
  • Yao Li
  • Guowei Zhu
  • Qingchao Zhang

Abstract

Numerical simulation is very important to solve geotechnical problems. However, it is difficult to obtain required comprehensive and accurate information such as parameters, boundary conditions, and etc. In this paper, a grey distributed parameter model, which integrates the finite element method (FEM) with the grey system theory, was proposed to address the issue. The analysis of grey properties on rock and soil system was performed. The equilibrium equations, geometric equations, physics equations and related differential equations were obtained, each of the equations contains grey parameters and variables. And the discretization and solution methods of the FEM with the grey variables were discussed. An example of deep-buried circular mining tunnel was applied to test the proposed model. The calculation results were compared with those of the exact solution (analytical solution) and the classical FEM, respectively, through which the rationality of the proposed model was demonstrated. For the first time, grey variables and grey parameters are defined in geotechnical numerical simulation. The expressions of basic equations with grey variables are given respectively. A grey distributed parameter model which integrates the FEM with the grey system theory is proposed to solve geotechnical problems, and the optimal solution to the proposed model is determined through calculation and comparison of an application example. The proposed numerical model with grey variables not only has the advantage of grey system theory, but also greatly improves the adaptability and application effect of the model, which contributes to the prediction and evaluation problems in geological engineering, geotechnical engineering, water conservancy engineering and civil engineering with complex structures.

Suggested Citation

  • Yao Li & Guowei Zhu & Qingchao Zhang, 2022. "An investigation of integrating the finite element method (FEM) with grey system theory for geotechnical problems," PLOS ONE, Public Library of Science, vol. 17(6), pages 1-24, June.
  • Handle: RePEc:plo:pone00:0270400
    DOI: 10.1371/journal.pone.0270400
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0270400
    Download Restriction: no

    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0270400&type=printable
    Download Restriction: no

    File URL: https://libkey.io/10.1371/journal.pone.0270400?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. P. Lu & M. Rosenbaum, 2003. "Artificial Neural Networks and Grey Systems for the Prediction of Slope Stability," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 30(3), pages 383-398, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Arunava Ray & Vikash Kumar & Amit Kumar & Rajesh Rai & Manoj Khandelwal & T. N. Singh, 2020. "Stability prediction of Himalayan residual soil slope using artificial neural network," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 103(3), pages 3523-3540, September.
    2. Xiuzhen Li & Jiming Kong & Zhenyu Wang, 2012. "Landslide displacement prediction based on combining method with optimal weight," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 61(2), pages 635-646, March.
    3. Min-Yuan Cheng & Nhat-Duc Hoang, 2015. "Typhoon-induced slope collapse assessment using a novel bee colony optimized support vector classifier," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 78(3), pages 1961-1978, September.
    4. Liulei Bao & Guangcheng Zhang & Xinli Hu & Shuangshuang Wu & Xiangdong Liu, 2021. "Stage Division of Landslide Deformation and Prediction of Critical Sliding Based on Inverse Logistic Function," Energies, MDPI, vol. 14(4), pages 1-24, February.
    5. Leilei Liu & Guoyan Zhao & Weizhang Liang, 2023. "Slope Stability Prediction Using k -NN-Based Optimum-Path Forest Approach," Mathematics, MDPI, vol. 11(14), pages 1-31, July.
    6. He Jia & Sherong Zhang & Chao Wang & Xiaohua Wang & Zhonggang Ma & Yaosheng Tan, 2023. "MSC-1DCNN-based homogeneous slope stability state prediction method integrated with empirical data," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 118(1), pages 729-753, August.
    7. Jamil Amanollahi & Shahram Kaboodvandpour & Hiva Majidi, 2017. "Evaluating the accuracy of ANN and LR models to estimate the water quality in Zarivar International Wetland, Iran," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 85(3), pages 1511-1527, February.
    8. Shakti Suman & S. Z. Khan & S. K. Das & S. K. Chand, 2016. "Slope stability analysis using artificial intelligence techniques," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 84(2), pages 727-748, November.
    9. Daxing Lei & Yaoping Zhang & Zhigang Lu & Hang Lin & Zheyuan Jiang, 2024. "Predicting Factor of Safety of Slope Using an Improved Support Vector Machine Regression Model," Mathematics, MDPI, vol. 12(20), pages 1-17, October.
    10. Yukun Yang & Wei Zhou & Izhar Mithal Jiskani & Xiang Lu & Zhiming Wang & Boyu Luan, 2023. "Slope Stability Prediction Method Based on Intelligent Optimization and Machine Learning Algorithms," Sustainability, MDPI, vol. 15(2), pages 1-18, January.
    11. Abiodun Ismail Lawal & Shahab Hosseini & Minju Kim & Nafiu Olanrewaju Ogunsola & Sangki Kwon, 2024. "Prediction of factor of safety of slopes using stochastically modified ANN and classical methods: a rigorous statistical model selection approach," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 120(2), pages 2035-2056, January.
    12. Paraskevas Tsangaratos & Andreas Benardos, 2014. "Estimating landslide susceptibility through a artificial neural network classifier," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 74(3), pages 1489-1516, December.
    13. Chong Xu & Xiwei Xu & Fuchu Dai & Zhide Wu & Honglin He & Feng Shi & Xiyan Wu & Suning Xu, 2013. "Application of an incomplete landslide inventory, logistic regression model and its validation for landslide susceptibility mapping related to the May 12, 2008 Wenchuan earthquake of China," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 68(2), pages 883-900, September.
    14. Chonghao Zhu & Jianjing Zhang & Yang Liu & Donghua Ma & Mengfang Li & Bo Xiang, 2020. "Comparison of GA-BP and PSO-BP neural network models with initial BP model for rainfall-induced landslides risk assessment in regional scale: a case study in Sichuan, China," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 100(1), pages 173-204, January.
    15. Zaiwu Gong & Caiqin Chen & Xinming Ge, 2014. "Risk prediction of low temperature in Nanjing city based on grey weighted Markov model," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 71(2), pages 1159-1180, March.
    16. Wei-ping Lou & Hai-yan Chen & Xin-fa Qiu & Qi-yi Tang & Feng Zheng, 2012. "Assessment of economic losses from tropical cyclone disasters based on PCA-BP," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 60(3), pages 819-829, February.
    17. Sina Shaffiee Haghshenas & Sami Shaffiee Haghshenas & Zong Woo Geem & Tae-Hyung Kim & Reza Mikaeil & Luigi Pugliese & Antonello Troncone, 2021. "Application of Harmony Search Algorithm to Slope Stability Analysis," Land, MDPI, vol. 10(11), pages 1-12, November.
    18. Arsalan Mahmoodzadeh & Mokhtar Mohammadi & Hunar Farid Hama Ali & Hawkar Hashim Ibrahim & Sazan Nariman Abdulhamid & Hamid Reza Nejati, 2022. "Prediction of safety factors for slope stability: comparison of machine learning techniques," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 111(2), pages 1771-1799, March.
    19. Arsalan Mahmoodzadeh & Abed Alanazi & Adil Hussein Mohammed & Ahmed Babeker Elhag & Abdullah Alqahtani & Shtwai Alsubai, 2024. "An optimized model based on the gene expression programming method to estimate safety factor of rock slopes," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 120(2), pages 1665-1688, January.
    20. Shahram Kaboodvandpour & Jamil Amanollahi & Samira Qhavami & Bakhtiyar Mohammadi, 2015. "Assessing the accuracy of multiple regressions, ANFIS, and ANN models in predicting dust storm occurrences in Sanandaj, Iran," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 78(2), pages 879-893, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0270400. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.