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Generating Stochastic Structural Planes Using Statistical Models and Generative Deep Learning Models: A Comparative Investigation

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  • Han Meng

    (School of Engineering and Technology, China University of Geosciences (Beijing), Beijing 100083, China)

  • Nengxiong Xu

    (School of Engineering and Technology, China University of Geosciences (Beijing), Beijing 100083, China)

  • Yunfu Zhu

    (Geological Environment Monitoring Institute of Jiangxi Geological Survey and Exploration Institute, Nanchang 330006, China)

  • Gang Mei

    (School of Engineering and Technology, China University of Geosciences (Beijing), Beijing 100083, China)

Abstract

Structural planes are one of the key factors controlling the stability of rock masses. A comprehensive understanding of the spatial distribution characteristics of structural planes is essential for accurately identifying key blocks, analyzing rock mass stability, and addressing various rock engineering challenges. This study compares the effectiveness of four stochastic structural plane generation methods—the Monte Carlo method, the Copula-based method, generative adversarial networks (GAN), and denoised diffusion models (DDPM)—in generating stochastic structural planes and capturing potential correlations between structural plane parameters. The Monte Carlo method employs the mean and variance of three parameters of the measured factual structural planes to generate data that follow the same distributions. The other three methods take the entire set of measured factual structural planes as the overall input to generate structural planes that exhibit the same probability distributions. Five sets of structural planes on four rock slopes in Norway are examined as an example. The validation and analysis were performed using histogram comparison, data feature comparison, scatter plot comparison, and linear regression analysis. The results show that the Monte Carlo method fails to capture the potential correlation between the dip direction and dip angle despite the best fit to the measured factual structural planes. The Copula-based method performs better with smaller datasets, and GAN and DDPM are better at capturing the correlation of measured factual structural planes in the case of large datasets. Therefore, in the case of a limited number of measured structural planes, it is advisable to employ the Copula-based method. In scenarios where the dataset is extensive, the deep generative model is recommended due to its ability to capture complex data structures. The results of this study can be utilized as a valuable point of reference for the accurate generation of stochastic structural planes within rock masses.

Suggested Citation

  • Han Meng & Nengxiong Xu & Yunfu Zhu & Gang Mei, 2024. "Generating Stochastic Structural Planes Using Statistical Models and Generative Deep Learning Models: A Comparative Investigation," Mathematics, MDPI, vol. 12(16), pages 1-37, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2545-:d:1458427
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    References listed on IDEAS

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    4. Jonathan Frazer & Pascal Notin & Mafalda Dias & Aidan Gomez & Joseph K. Min & Kelly Brock & Yarin Gal & Debora S. Marks, 2021. "Disease variant prediction with deep generative models of evolutionary data," Nature, Nature, vol. 599(7883), pages 91-95, November.
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