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Characterization of discontinuity surface morphology based on 3D fractal dimension by integrating laser scanning with ArcGIS

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Abstract

The fractal geometry method has been employed to quantitatively characterize the roughness of a rock discontinuity, which is one of the key factors affecting its shear strength and the seepage characteristics of a rock mass. However, the current fractal methods involving the three-dimensional discontinuity morphology suffer from one or more problems, such as a complicated calculation procedure, an inaccurate calculation result and an inability to characterize the undulation and anisotropy of a discontinuity. To cope with these problems, the discontinuities in artificial granite samples with irregular and undulating surfaces were taken as examples, and a quantitative study on the discontinuity morphology was conducted based on the method of three-dimensional laser scanning in combination with ArcGIS data processing, geographical research, theoretical calculations and regression analysis. After performing systematic research, we proposed an extensive 3D fractal dimension including three discontinuity morphological parameters, i.e. the fractal dimension of discontinuity morphology, the ratio between the maximal undulating amplitude and the discontinuity length, and the average value of all the apparent dip angles of the discontinuity surfaces dipping opposite the shear direction. The extensive 3D fractal dimension can comprehensively characterize the roughness, undulation and anisotropy of the discontinuity morphology. A set of theoretical calculation methods were then developed to determine the three discontinuity morphological parameters of the extensive 3D fractal dimension based on ArcGIS. We finally established a mathematical expression of the extensive 3D fractal dimension. Compared with the current fractal methods, the extensive 3D fractal dimension can effectively compensate for the inability to characterize the undulation and anisotropy of the discontinuity morphology. Its calculation methods have the advantages of simplification, low-time consumption and high precision.

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Acknowledgements

This research was supported by the Second Tibetan Plateau Scientific Expedition and Research Program (STEP) under Grant No. 2019QZKK0904, Key Deployment Program of the Chinese Academy of Sciences under Grant No. KFZD-SW-422, National Natural Science Foundation of China under Grants Nos. 41825018, 41941018, 41672307, 41902289, 41807273 and 41702345, the National Key Research and Development Plan of China under Grant No. 2019YFC1509701, China Postdoctoral Science Foundation under Grant No. 2017M620903. Thanks for the help of Drs. Mingdong Zang, Xianglong Yao, Xiaokun Hou and Jiao Wang.

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Authors and Affiliations

  1. Key Laboratory of Shale Gas and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, No.19, Beitucheng Western Road, Chaoyang District, Beijing, 100029, People’s Republic of China

    Bowen Zheng, Shengwen Qi, Guangming Luo, Fangcui Liu, Xiaolin Huang & Songfeng Guo

  2. Innovation Academy for Earth Science, Chinese Academy of Sciences, No.19, Beitucheng Western Road, Chaoyang District, Beijing, 100029, People’s Republic of China

    Bowen Zheng, Shengwen Qi, Guangming Luo, Fangcui Liu, Xiaolin Huang & Songfeng Guo

  3. College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, No.19(A), Yuquan Road, Shijingshan District, Beijing, 100049, People’s Republic of China

    Bowen Zheng, Shengwen Qi, Guangming Luo, Fangcui Liu, Xiaolin Huang & Songfeng Guo

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  1. Bowen Zheng
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  2. Shengwen Qi
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  3. Guangming Luo
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  4. Fangcui Liu
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  5. Xiaolin Huang
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  6. Songfeng Guo
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Correspondence to Shengwen Qi.

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Highlights

• An extensive 3D fractal dimension was proposed to comprehensively characterize the roughness, undulation and anisotropy of the discontinuity morphology.

• A set of theoretical calculation methods were developed for the extensive 3D fractal dimension based on ArcGIS.

• A mathematical expression was established for the extensive 3D fractal dimension.

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Zheng, B., Qi, S., Luo, G. et al. Characterization of discontinuity surface morphology based on 3D fractal dimension by integrating laser scanning with ArcGIS. Bull Eng Geol Environ 80, 2261–2281 (2021). https://doi.org/10.1007/s10064-020-02011-6

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  • DOI: https://doi.org/10.1007/s10064-020-02011-6

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