基于二维经验分布的不连续面产状 Monte Carlo模拟

doi:10.13722/j.cnki.jrme.2014.0982

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Abstract

There exist some probability distributions for describing rock discontinuity，e.g.，Fisher distribution， Bingham distribution，and bivariate normal distribution. But in reality they are not suitable to represent the statistical characteristics of rock discontinuity orientation data in most cases. In such cases one should use the bivariate empirical distributions obtained for the discontinuity orientations in representing the statistical distributions of discontinuity orientations. The paper introduces the empirical bivariate distribution into the Monte Carlo simulation(MSC) of rock discontinuity orientations and develops a corresponding computer code，named as EMCSDO. EMCSDO is a freeware designed for researchers and practicing engineers，and can be easily mastered by them with little computer knowledge. Two examples with satisfactory results are presented to show the validity of the code. The second example also show if a theoretical distribution can be found to fit discontinuity orientations well，we should prefer to use the theoretical distribution to simulate the orientations based on Monte Carlo technique.

Key words： rock mecharics rock mass joint network rock structure stereographic projection fitting chi- square test

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	Articles by authors
	Zheng Jun1
	2
	3
	KULATILAKE P H S W3
	Deng Jianhui 2
	WEI Jinbing2

Cite this article:

Zheng Jun1,2,3, et al. A MONTE CARLO SIMULATION FOR DISCONTINUITY ORIENTATIONS USING BIVARIATE EMPIRICAL DISTRIBUTION[J]. , 2015, 34(S2): 3922-3929.

URL:

https://rockmech.whrsm.ac.cn/EN/10.13722/j.cnki.jrme.2014.0982 OR https://rockmech.whrsm.ac.cn/EN/Y2015/V34/IS2/3922

[1] ZHANG L. Engineering properties of rocks[M]. Amsterdam，Netherlands：Elsevier Science，2005：304.

[2] ISRM. Suggested methods for the quantitative description of discontinuities in rock masses[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1978，15(6)：319–368.

[3] LIN CT，AMADEI B，JUNG J，et al. Extensions of discontinuous deformation analysis for jointed rock masses[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1996，33(7)：671–694.

[4] WU J，OHNISHI Y，NISHIYAMA S. Simulation of the mechanical behavior of inclined jointed rock masses during tunnel construction using discontinuous deformation analysis(DDA)[J]. International Journal of Rock Mechanics and Mining Sciences，2004，41(5)：731–743.

[5] KULATILAKE PHSW，HE W，UM J，et al. A physical model study of jointed rock mass strength under uniaxial compressive loading[J]. International Journal of Rock Mechanics and Mining Sciences，1997，34(3/4)：165.e1–165.e15.

[6] SINGH M，RAO SK. Empirical methods to estimate the strength of jointed rock masses[J]. Engineering Geology，2005，77(1/2)：127–137.

[7] BAGHBANAN A，JING L. Hydraulic properties of fractured rock masses with correlated fracture length and aperture[J]. International Journal of Rock Mechanics and Mining Sciences，2007，44(5)：704–719.

[8] LARSEN B，GRUNNALEITE I，GUDMUNDSSON A. How fracture systems affect permeability development in shallow-water carbonate rocks：an example from the Gargano Peninsula，Italy[J]. Journal of Structural Geology，2010，32(9)：1 212–1 230.

[9] TAI TW，HUANG TH. A constitutive model for the deformation of a rock mass containing sets of ubiquitous joints[J]. International Journal of Rock Mechanics and Mining Sciences，2009，46(3)：521–530.

[10] LIU DA，WANG SJ，LI LY. Investigation of fracture behavior during rock mass failure[J]. International Journal of Rock Mechanics and Mining Sciences，2000，37(3)：489–497.

[11] ZHENG J，KULATILAKE PHSW，SHU B，et al. Probabilistic block theory analysis for a rock slope at an open pit mine in USA[J]. Computers and Geotechnics，2014，61：254–265.

[12] PITEAU D R. Geological factors significant to the stability of slopes cut in rock[C]// Symposium on Planning Open Pit Mines. Johannesburg：South African Institute of Mining and Metallurgy，1970：33–53.

[13] PITEAU D R. Characterizing and extrapolating rock joint properties in engineering practice[J]. Rock Mechanics，1973，(Supp.2)：5–31.

[14] YE J，ZHANG Y，SUN J，et al. Correction of the probabilistic density function of discontinuities spacing considering the statistical error based on negative exponential distribution[J]. Journal of Structural Geology，2012，40：17–28.

[15] KULATILAKE P H S W. Fitting fisher distributions to discontinuity orientation data[J]. Journal of Geological Education，1985，33(5)：266–269.

[16] KULATILAKE P H S W，WU T H，WATHUGALA D N. Probabilistic modelling of joint orientation[J]. International Journal for Numerical and Analytical Methods in Geomechanics，1990，14(5)：325–350.

[17] PRIEST SD，HUDSON JA. Discontinuity spacings in rock[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1976，13(5)：135–148.

[18] HUDSON J A，PRIEST S D. Discontinuity frequency in rock masses[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1983，20(2)：73–89.

[19] PRIEST SD. Determination of discontinuity size distributions from scanline data[J]. Rock Mechanics and Rock Engineering，2004，37(5)：347–368.

[20] ZHANG L，EINSTEIN H H. Estimating the mean trace length of rock discontinuities[J]. Rock Mechanics Rock Engineering，1998，31(4)：217–235.

[21] FISHER SR. Dispersion on a sphere[J]. Proceedings of Royal Society A：Mathematical，Physical and Engineering Sciences，1953，217(1130)：295–305.

[22] PRIEST S D. Discontinuity analysis for rock engineering[M]. London：Chapman and Hall，1993：473.

[23] KEMENY J，POST R. Estimating three-dimensional rock discontinuity orientation from digital mages of fracture traces[J]. Computer Geosciences，2003，29(1)：65–77.

[24] 王双,，陈征宙，吴强，等. 基于节理产状不确定性的边坡稳定性及敏感度分析[J]. 岩土工程学报，2013，35(2)：348–354. (WANG Shuang，CHEN Zhengzhou，WU Qiang，et al. Stability and sensitivity analysis of slopes based on uncertainty of joint orientations[J]. Chinese Journal of Geotechnical Engineering，2013，35(2)：348–354.(in Chinese)).

[25] BINGHAM C. Distributions on the sphere and on the projective plane[Ph. D. Thesie][D]. New Haven，USA，：Yale University，1964.

[26] BINGHAM C. An antipodally symmetric distribution on the sphere[J]. The Annals of Statistics，1974，2(6)：1 201–1 225.

[27] KULATILAKE P H S W. Bivariate normal distribution fitting on discontinuity orientation clusters[J]. Mathematical Geology，1986，18(2)：181–195.

[28] WATHUGALA D N，KULATILAKE P H S W，WATHUGALA G W，et al. A general procedure to correct sampling bias on joint orientation using a vector approach[J]. Computers and Geotechnics，1990，10(1)：1–31.

[29] KULATILAKE P H S W，UM J，WANG M，et al. Stochastic fracture Geometry modeling in 3D including validations for a part of Arrowhead East Tunnel site，California，USA[J]. Engineering Geology，2003，70(1/2)：131–155.

[30] WU Q，KULATILAKE PHSW. REV and its properties on fracture system and mechanical properties，and an orthotropic constitutive model for a jointed rock mass in a dam site in China[J]. Computers and Geotechnics，2012，43：124–142.

[31] YU Q. Analyses for fluid flow and solute transport in discrete fracture network[Ph. D. Thesis][D]. Kyoto：Kyoto University，2000.

[32] 盛骤，谢式千，潘承毅. 概率论与数理统计[M]. 4版，北京：高等教育出版社，2008：198–205.(SHENG Zhou，XIE Shiqian，PAN Chenyi. Probability theory and mathematical statistics[M]. 4th ed. Beijing：Higher Education Press，2008：198–205.(in Chinese))

[33] GOODMAN R E，SHI G. Block theory and its application to rock engineering[M]. Englewood Cliffs：Prentice-Hall，1985：338.

[34] PRIEST S D. Hemispherical projection methods in rock mechanics[M]. London：Allen and Unwin，1985：128.

[35] ZHENG J，DENG J，YANG X，et al. An improved Monte Carlo simulation method for discontinuity orientations based on Fisher distribution and its program implementation[J]. Computers and Geotechnics，2014，61：266–276.

[36] 郑俊，邓建辉，魏进兵. 不连续面产状Fisher分布拟合度检验方法的改进[J]. 岩石力学与工程学报，2015，34(8)：1 561–1 568. (ZHENG Jun，DENG Jianhui，WEI Jinbing. An improved method of goodness- of-fit test for Fisher distribution to discontinuity orientations[J]. Chinese Journal of Rock Mechanics and Engineering，2015，34(8)：1 561–1 568.(in Chinese))