A 3D Fracture Network Model for the Undisturbed Rock Mass at the Songta Dam Site Based on Small Samples

List of symbols w Width of the sampling window h Height of the sampling window ai Dip direction of the ith joint ar Strike of the sampling window hi Dip angle of the ith joint di Fracture diameter of the ith joint Wi Weight formula for the ith joint Rfi Corrected relative frequency of the ith joint n Number of joints in a fracture set ei The ith parameter of the supposed probability density function lj The jth trace length of the measured joint of a fracture set v Sample size or number of sectors S Statistic of the Kolmogorov–Smirnov test S Critical value of the Kolmogorov–Smirnov test p Approximate significance level lm Mean trace length rm Standard deviation of the measured trace length distribution ll True mean trace length rl Standard deviation of the true trace length distribution lD Mean joint diameter rD Standard deviation of the joint diameter distribution ðCOV)m Coefficient of variation of the measured trace length distribution EðDÞ The mth moment of the joint diameter, m = 1, 2, 3... EðlÞ The mth moment of the trace length, m = 1, 2, 3... k1i Normal line density of the ith fracture set kVi Fracture density in unit volume of the ith fracture set V Volume of simulated space region

[1]  Chung-In Lee,et al.  Estimation of joint length distribution using window sampling , 2001 .

[2]  P. L. Pointe,et al.  Advances in Discrete Fracture Network Modeling , 2004 .

[3]  M. Mauldon,et al.  Estimating Mean Fracture Trace Length and Density from Observations in Convex Windows , 1998 .

[4]  Peter A. Dowd,et al.  A Comparison of Methods for the Stochastic Simulation of Rock Fractures , 2007 .

[5]  Shengyuan Song,et al.  Identification of structural domain boundaries at the Songta dam site based on nonparametric tests , 2014 .

[6]  Hakan S. Sazak,et al.  Double-looped maximum likelihood estimation for the parameters of the generalized gamma distribution , 2014, Math. Comput. Simul..

[7]  Herbert H. Einstein,et al.  Mathematical algorithm development and parametric studies with the GEOFRAC three-dimensional stochastic model of natural rock fracture systems , 2014, Comput. Geosci..

[8]  R. Hammah,et al.  On Distance Measures for the Fuzzy K-means Algorithm for Joint Data , 1999 .

[9]  Wang Yizhuang EFFECTS OF MEASUREMENT RANGE ON ESTIMATION OF TRACE LENGTH OF DISCONTINUITIES , 2011 .

[10]  M. Vinches,et al.  Application of geostatistical characteristics of rock mass fracture systems in 3D model generation , 2008 .

[11]  Sheldon M. Ross Introduction to probability models , 1998 .

[12]  Anthony J. Jakeman,et al.  A NEW APPROACH TO MAXIMUM LIKELIHOOD ESTIMATION OF THE THREE‐PARAMETER GAMMA AND WEIBULL DISTRIBUTIONS , 1991 .

[13]  Sheldon M. Ross,et al.  Introduction to Probability Models (4th ed.). , 1990 .

[14]  G. K. Bhattacharyya,et al.  Statistics: Principles and Methods , 1994 .

[15]  J. Kemeny,et al.  Estimating three-dimensional rock discontinuity orientation from digital images of fracture traces , 2003 .

[16]  L. Xu,et al.  Fuzzy C-Means Cluster Analysis Based on Mutative Scale Chaos Optimization Algorithm for the Grouping of Discontinuity Sets , 2012, Rock Mechanics and Rock Engineering.

[17]  Richard A. Johnson,et al.  Statistics: Principles and Methods , 1985 .

[18]  Ki-Bok Min,et al.  Determining the equivalent permeability tensor for fractured rock masses using a stochastic REV approach: Method and application to the field data from Sellafield, UK , 2004 .

[19]  Kanti V. Mardia,et al.  A three-dimensional fracture network data set for a block of granite , 2009 .

[20]  Ying Zhang,et al.  Determination of Geometrical and Structural Representative Volume Elements at the Baihetan Dam Site , 2012, Rock Mechanics and Rock Engineering.

[21]  Jianping Chen,et al.  Size effect of RQD and generalized representative volume elements: A case study on an underground excavation in Baihetan dam, Southwest China , 2013 .

[22]  D. Marcotte,et al.  Automatic joint set clustering using a mixture of bivariate normal distributions , 2002 .

[23]  Lanru Jing,et al.  A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering , 2003 .

[24]  Chaoshui Xu,et al.  A new computer code for discrete fracture network modelling , 2010, Comput. Geosci..

[25]  Pinnaduwa H.S.W. Kulatilake,et al.  Comparison of rock discontinuity mean trace length and density estimation methods using discontinuity data from an outcrop in Wenchuan area, China , 2011 .

[26]  Lianyang Zhang,et al.  Estimating the Mean Trace Length of Rock Discontinuities , 1998 .

[27]  小田 匡寛,et al.  FABRIC TENSOR FOR DISCONTINUOUS GEOLOGICAL MATERIALS , 1982 .

[28]  Pinnaduwa Kulatilake,et al.  Estimation of mean trace length of discontinuities , 1984 .

[29]  Lianyang Zhang,et al.  Estimating the intensity of rock discontinuities , 2000 .

[30]  M. Mauldon,et al.  Circular scanlines and circular windows: new tools for characterizing the geometry of fracture traces , 2001 .

[31]  X. Zhuang,et al.  Estimation of fracture trace length distributions using probability weighted moments and L-moments , 2014 .

[32]  Reginald E. Hammah,et al.  Validity Measures for the Fuzzy Cluster Analysis of Orientations , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[33]  Jan Sijbers,et al.  A new non-local maximum likelihood estimation method for Rician noise reduction in magnetic resonance images using the Kolmogorov-Smirnov test , 2014, Signal Process..

[34]  Fulvio Tonon,et al.  Closed-form and numerical solutions for the probability distribution function of fracture diameters , 2007 .

[35]  R. Gorenflo,et al.  Abel Integral Equations: Analysis and Applications , 1991 .

[36]  Richard E. Goodman,et al.  Determination of principal joint frequencies , 1985 .

[37]  P. M. Warburton,et al.  A STEREOLOGICAL INTERPRETATION OF JOINT TRACE DATA , 1980 .

[38]  Deepa N. Wathugala,et al.  STOCHASTIC THREE DIMENSIONAL JOINT SIZE, INTENSITY AND SYSTEM MODELLING AND A VALIDATION TO AN AREA IN STRIPA MINE, SWEDEN , 1993 .

[39]  Michael S. Riley,et al.  Fracture trace length and number distributions from fracture mapping , 2005 .

[40]  Pinnaduwa Kulatilake,et al.  Sampling bias on orientation of discontinuities , 1984 .