求解岩体裂隙产状三维概率分布的数值方法

赵萌; 唐辉明; 詹红兵; 张俊荣

doi:10.3799/dqkx.2021.056

Volume 47 Issue 4

Apr. 2022

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Zhao Meng, Tang Huiming, Zhan Hongbing, Zhang Junrong, 2022. A Numerical Method for Solving Three-Dimensional Probability Distribution of Rockmass Fracture Orientations. Earth Science, 47(4): 1470-1482. doi: 10.3799/dqkx.2021.056

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Zhao Meng, Tang Huiming, Zhan Hongbing, Zhang Junrong, 2022. A Numerical Method for Solving Three-Dimensional Probability Distribution of Rockmass Fracture Orientations. Earth Science, 47(4): 1470-1482. doi: 10.3799/dqkx.2021.056

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A Numerical Method for Solving Three-Dimensional Probability Distribution of Rockmass Fracture Orientations

doi: 10.3799/dqkx.2021.056

Zhao Meng^{1
,
,},
Tang Huiming^{1, 2
,
,
,},
Zhan Hongbing³,
Zhang Junrong¹

1.
Faculty of Engineering, China University of Geosciences, Wuhan 430074, China
2.
Three Gorges Research Center for Geo-Hazard, Ministry of Education, China University of Geosciences, Wuhan 430074, China
3.
Department of Geology & Geophysics, Texas A & M University, Texas 77843-3115, USA

Received Date: 2020-11-04
Available Online: 2022-04-29
Publish Date: 2022-04-25

Abstract

Abstract

The scanline mapping is a widely-used 1D field technique for fracture geometry observation. However, the 1D orientation observations from this technique poorly represent the 3D probability distribution. In this work, a numerical method for solving the 3D probability distribution of orientations is presented. It makes the assumption of observed dip direction-angle independence and adopts a mathematical relationship between the 1D observations and the 3D distribution. This method follows a two-step procedure that first using the relationship to solve the 3D cumulative, and then estimating the distribution type and parameters over the probabilities by employing the Kolmogorov-Smirnov approximation. Two cases of fractures (bedding planes and joints) illustrate that the presented method provides a smaller-error solution in comparison with the Fouché method. The minimum solution error of the presented method can be attained when the sample size is closely 150; if the sample size exceeds this value, the solution error will not decrease significantly as sample size increases. Moreover, the effectiveness of the presented method is investigated. The results show that the presented method performs effectively when applied to non-parallel fracture individuals, e.g. joints, whereas with low effectiveness when applied to sub-parallel fracture individuals, e.g. bedding planes.
- 3D probability distribution of orientation,
- Fouché method,
- sample size,
- fracture geometry,
- scanline mapping,
- engineering geology.

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References(26)

References

Alghalandis, Y.F., 2017. ADFNE: Open Source Software for Discrete Fracture Network Engineering, Two and Three Dimensional Applications. Computers & Geosciences, 102: 1-11. https://doi.org/10.1016/j.cageo.2017.02.002

Berrone, S., Canuto, C., Pieraccini, S., et al., 2015. Uncertainty Quantification in Discrete Fracture Network Models: Stochastic Fracture Transmissivity. Computers & Mathematics with Applications, 70(4): 603-623. https://doi.org/10.1016/j.camwa.2015.05.013

Bisdom, K., Bertotti, G., Bezerra, F.H., 2017. Inter-Well Scale Natural Fracture Geometry and Permeability Variations in Low-Deformation Carbonate Rocks. Journal of Structural Geology, 97: 23-36. https://doi.org/10.1016/j.jsg.2017.02.011

Brereton, R.G., 2015. The Chi Squared and Multinormal Distributions. Journal of Chemometrics, 29(1): 9-12. https://doi.org/10.1002/cem.2680

Carvalho, L., 2015. An Improved Evaluation of Kolmogorov's Distribution. Journal of Statistical Software, 65(3): 1-7. https://doi.org/10.18637/jss.v065.c03

Follin, S., Hartley, L., Rhén, I., et al., 2014. A Methodology to Constrain the Parameters of a Hydrogeological Discrete Fracture Network Model for Sparsely Fractured Crystalline Rock, Exemplified by Data from the Proposed High-Level Nuclear Waste Repository Site at Forsmark, Sweden. Hydrogeology Journal, 22(2): 313-331. https://doi.org/10.1007/s10040-013-1080-2

Fouché, O., Diebolt, J., 2004. Describing the Geometry of 3D Fracture Systems by Correcting for Linear Sampling Bias. Mathematical Geology, 36(1): 33-63. https://doi.org/10.1023/B:MATG.0000016229.37309.fd

Kang, J.T., Wu, Q., Tang, H.M., et al., 2019. Strength Degradation Mechanism of Soft and Hard Interbedded Rock Masses of Badong Formation Caused by Rock/Discontinuity Degradation. Earth Science, 44(11): 3950-3960(in Chinese with English abstract).

Kolmogorov, A.N., 1933. Foundations of Probability. American Mathematical Society Chelsea Publishing Company, Houston, Texas.

Manda, A.K., Mabee, S.B., 2010. Comparison of Three Fracture Sampling Methods for Layered Rocks. International Journal of Rock Mechanics and Mining Sciences, 47(2): 218-226. https://doi.org/10.1016/j.ijrmms.2009.12.004

Mauldon, M., Mauldon, J.G., 1997. Fracture Sampling on a Cylinder: From Scanlines to Boreholes and Tunnels. Rock Mechanics and Rock Engineering, 30(3): 129-144. https://doi.org/10.1007/BF01047389

Peacock, D.C.P., Harris, S.D., Mauldon, M., 2003. Use of Curved Scanlines and Boreholes to Predict Fracture Frequencies. Journal of Structural Geology, 25(1): 109-119. https://doi.org/10.1016/S0191-8141(02)00016-0

Pearson, K.X., 1900. On the Criterion That a Given System of Deviations from the Probable in the Case of a Correlated System of Variables is Such That It can be Reasonably Supposed to have Arisen from Random Sampling. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 50 (302): 157-175. doi: 10.1080/14786440009463897

Roy, P., du Frane, W.L., Kanarska, Y., et al., 2016. Numerical and Experimental Studies of Particle Settling in Real Fracture Geometries. Rock Mechanics and Rock Engineering, 49(11): 4557-4569. https://doi.org/10.1007/s00603-016-1100-3

Ruan, Y.K., Chen, J.P., Li, Y.Y., et al., 2016. Identification of Homogeneous Structural Domains of Jointed Rock Masses Based on Joint Occurrence and Trace Length. Rock and Soil Mechanics, 37(7): 2028-2032(in Chinese with English abstract).

Smirnov, N., 1948. Table for Estimating the Goodness of Fit of Empirical Distributions. The Annals of Mathematical Statistics, 19(2): 279-281. doi: 10.1214/aoms/1177730256

Tang, H.M., Huang, L., Bobet, A., et al., 2016. Identification and Mitigation of Error in the Terzaghi Bias Correction for Inhomogeneous Material Discontinuities. Strength of Materials, 48(6): 825-833. https://doi.org/10.1007/s11223-017-9829-9

Tang, H.M., Huang, L., Juang, C.H., et al., 2017. Optimizing the Terzaghi Estimator of the 3D Distribution of Rock Fracture Orientations. Rock Mechanics and Rock Engineering, 50(8): 2085-2099. https://doi.org/10.1007/s00603-017-1254-7

Tang, H.M., Zhang, J.R., Huang, L., et al., 2018. Correction of Line-Sampling Bias of Rock Discontinuity Orientations Using a Modified Terzaghi Method. Advances in Civil Engineering, 2018: 1-9. https://doi.org/10.1155/2018/1629039

Terzaghi, R.D., 1965. Sources of Error in Joint Surveys. Géotechnique, 15(3): 287-304. https://doi.org/10.1680/geot.1965.15.3.287

Williams-Stroud, S., Ozgen, C., Billingsley, R.L., 2013. Microseismicity-Constrained Discrete Fracture Network Models for Stimulated Reservoir Simulation. Geophysics, 78(1): B37-B47. https://doi.org/10.1190/geo2011-0061.1

Xia, D., Ge, Y.F., Tang, H.M., et al., 2020. Segmentation of Region of Interest and Identification of Rock Discontinuities in Digital Borehole Images. Earth Science, 45(11): 4207-4217(in Chinese with English abstract).

Zaree, V., Riahi, M.A., Khoshbakht, F., et al., 2016. Estimating Fracture Intensity in Hydrocarbon Reservoir: An Approach Using DSI Data Analysis. Carbonates and Evaporites, 31(1): 101-107. https://doi.org/10.1007/s13146-015-0246-5

亢金涛, 吴琼, 唐辉明, 等, 2019. 岩石/结构面劣化导致巴东组软硬互层岩体强度劣化的作用机制. 地球科学, 44(11): 3950-3960. doi: 10.3799/dqkx.2019.110

阮云凯, 陈剑平, 李严严, 等, 2016. 基于裂隙产状和迹长划分岩体统计均质区研究. 岩土力学, 37(7): 2028-2032. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201607025.htm

夏丁, 葛云峰, 唐辉明, 等, 2020. 数字钻孔图像兴趣区域分割与岩体结构面特征识别. 地球科学, 45(11): 4207-4217. doi: 10.3799/dqkx.2020.003

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