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Determination of Geometrical and Structural Representative Volume Elements at the Baihetan Dam Site

Rock Mechanics and Rock Engineering volume 45, pages 409–419 (2012)Cite this article

Abstract

A case study at the Baihetan dam site was undertaken to obtain a representative volume element (RVE) size. Two-dimensional fracture information in an exploration tunnel was used to generate a large three-dimensional fracture network. By dividing the entire modeled rock mass into cubes, the volumetric fracture density (P32) value of each cube was determined. The size effect can be determined by changing the cube size. The RVE was determined using P32 calculation and statistical tests, including Kolmogorov-Smirnov (KS) and Wilcoxon rank-sum tests. The P32 value depends on the geometrical parameters of fracture density and size; in this study, this value is called the geometrical RVE. P32 is dependent on fracture density and size, and cannot appropriately reflect certain data such as fracture dip or dip angle. Therefore, we propose a structural RVE (SRVE) considering fracture dip direction, dip angle, density, and size, which together constitute the available information about the fracture network. Therefore, the SRVE is more applicable for use in solving geological problems than the RVE. In this analysis, the KS and Wilcoxon rank-sum tests were used to determine the SRVE size.

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Abbreviations

K :

Fisher constant

KS:

Kolmogorov–Smirnov test

P21 :

Total length of fracture traces per unit area (m/m2)

P32 :

Fracture area per rock volume (m2/m3)

RVE:

Representative volume element

SRVE:

Structural representative volume element

V :

Cube volume (m3)

θ :

Acute angle between the scanline and the line normal to the mean orientation of the joint set (°)

N :

Cube number

L :

Length of the overall rock mass (m)

W :

Width of the overall rock mass (m)

H :

Height of the overall rock mass (m)

l :

Serial number of the cube in the x direction

m :

Serial number of the cube in the y direction

n :

Serial number of the cube in the z direction

x 0 :

X-coordinate of a fracture disc center (m)

y 0 :

Y-coordinate of a fracture disc center (m)

z 0 :

Z-coordinate of a fracture disc center (m)

α :

Dip angle (°)

β :

Dip direction (°)

(A, B, C):

Normal vector of a fracture plane

D :

Fracture disc diameter (m)

D-stat :

Statistic of Kolmogorov–Smirnov test

S i (x i ):

Value of sample 1 at x i

R i (x i ):

Value of sample 2 at x i

N :

Number of data points in sample 1

M :

Number of data points in sample 2

D*:

Critical value of Kolmogorov-Smirnov test

p value:

Probability value (%)

Q KS (λ):

Probability distribution of D-stat with parameter λ

N e :

Effective number of data points

H 0 :

Null hypothesis

α :

Significant level (%)

R 1 :

The sum of ranks attached to the observations in sample 1

K 1 :

Statistic parameter of Wilcoxon rank-sum test

U s :

Statistic of Wilcoxon rank-sum test

U :

Critical value of Wilcoxon rank-sum test

References

  • Baecher GB, Lanney NA, Einstein HH (1977) Statistical description of rock properties and sampling. In: Proceedings of the 18th US Symposium on Rock Mechanics, Colorado School of Mines, Golden: American Institute of Mining Engineers, NewYork, pp 1–8

  • Chen JP (2001) 3-D network numerical modeling technique for random discontinuities of rock mass. Chin J Geotech Eng 23:397–402

    Google Scholar 

  • Chen JP, Xiao SF, Wang Q (1995) Three dimensional network modeling of stochastic fractures. Jilin, China

    Google Scholar 

  • Chen JP, Shi BF, Wang Q (2005) Study on the dominant orientations of random fractures of fractured rock masses. Chin J Rock Mech Eng 24:241–245

    Google Scholar 

  • Dershowitz WS, Einstein HH (1988) Characterizing rock joint geometry with joint system models. Rock Mech Rock Eng 21:21–51

    Article  Google Scholar 

  • Drew JH, Glen AG, Leemis LM (2000) Computing the cumulative distribution function of the Kolmogorov-Smirnov statistic. Comput Stat Data An 34:1–15

    Article  Google Scholar 

  • Esmaieli K, Hadjigeorgiou J, Grenon M (2010) Estimating geometrical and mechanical REV based on synthetic rock mass models at Brunswick Mine. Int J Rock Mech Min 47:915–926

    Article  Google Scholar 

  • Fisher RA (1953) Dispersion on a sphere. Proc R Soc A 217:295–305

    Article  Google Scholar 

  • Hill R (1963) Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids 11:357–372

    Article  Google Scholar 

  • Hou ZS, Han WF, Li X (2004) Numerical analysis on spatial effect of mechanical parameter of surrounding rocks in Jinchuan deposit. Chin J of Rock Mech Eng 23:64–68

    Article  Google Scholar 

  • Karzulovic A, Goodman RE (1985) Determination of principal joint frequencies. Int J Rock Mech Min Sci Geomech Abstr 22:471–473

    Article  Google Scholar 

  • Kulatilake PHSW (1985) Estimating elastic constants and strength of discontinuous rock. J Geotech Engrg, ASCE 111:847–864

    Article  Google Scholar 

  • Kulatilake PHSW, Wu TH (1984a) Estimation of mean trace length of discontinuities. Rock Mech Rock Eng 17:215–232

    Article  Google Scholar 

  • Kulatilake PHSW, Wu TH (1984b) Sampling bias on orientation of discontinuities. Rock Mech Rock Eng 17:243–253

    Article  Google Scholar 

  • Kulatilake PHSW, Wu TH (1986) Relation between discontinuity size and trace length. Proc of the 27th US Symp on Rock Mech, pp 130–133

  • Lama RD, Vutukuri VS (1978) Handbook on properti of rocks. Borntraeger, Berlin

    Google Scholar 

  • Lu B, Ge XR, Zhu DL, Chen JP (2005) Fractal study on the representative element volume of jointed rock masses. Chin J Rock Mech Eng 24:1355–1361

    Google Scholar 

  • Min KB, Jing L (2003) Numerical determination of the equivalent elastic compliance tensor for fractured rock masses using the distinct element method. Int J Rock Mech Min 40:795–816

    Article  Google Scholar 

  • Oda M (1982) Fabric tensor for discontinous geological materials. Soil Found 22:96–108

    Article  Google Scholar 

  • Pang ZH (1998) A numerical method to evaluate the representative elemental volume (REV) of rock mass based on the probability model of jointed network and the element free Galerkin method (EFGM). Dissertation, Chinese Academy of Sciences, Wuhan

  • Pariseau WG, Puri S, Schmelter SC (2008) A new model for effects of impersistent joint set on rock slope stability. Int J Rock Mech Min 45:122–131

    Article  Google Scholar 

  • Peng LM, Shi CH, Wu B, Liu BC (2004) Study on spatial action between high building foundation and underground shelter cave. Chin J Rock Mech Eng 23:1496–1501

    Google Scholar 

  • Petrich W, Staib A, Otto M, Somorjai RL (2002) Correlation between the state of health of blood donors and the corresponding mid-infrared spectra of the serum. Vib Spectrosc 28:117–129

    Article  Google Scholar 

  • Pierce M, MasIvars D, Cundall PA, Potyondy D (2007) A synthetic rock mass model for jointed rock. In: Proceedings of the first CA–US rock mechanics symposium, Vancouver, BC, 2007, pp 341–349

  • Pinto A, Da CH (1993) Scale effects in rock mechanics. A.A.Balkema Publishers, Rotterdam

    Google Scholar 

  • Priest SD (1993) Discontinuity analysis for rock engineering. Chapman & Hall, London

    Book  Google Scholar 

  • Priest SD, Hudson JA (1981) Estimation of discontinuity spacing and trace length using scanline surveys. Int J Rock Mech Min Sci Geomech Abstr 18:183–197

    Article  Google Scholar 

  • Wang SJ, Chen JB (2008) Nonlinear analysis for dimensional effects of temperature field of highway embankment in permafrost regions on Qinghai–Tibet plateau. Chin J Geotech Eng 30:1544–1549

    Google Scholar 

  • Wang M, Kulatilakea PHSW, Uma J, Narvaiz J (2002) Estimation of REV size and three-dimensional hydraulic conductivity tensor for a fractured rock mass through a single well packer test and discrete fracture fluid flow modeling. Int J Rock Mech Min 39:887–904

    Article  Google Scholar 

  • Wang SL, Chen JP, Shi BF (2004) Verification of random 3-D fractures network models of rock mass. J Eng Geol 12:177–181

    Google Scholar 

  • Zhang GK, Xu WY (2008) Analysis of joint network simulation method and REV scale. Rock Soil Mech 29:1675–1680

    Google Scholar 

  • Zhou CB, Yu SD (1999) Representative elementary volume REV—a fundamental problem for selecting the mechanical parameters of jointed rock mass. J Eng Geol 7:332–336

    Google Scholar 

  • Zhu DL (2003) Estimation of REV and deformation and strength of jointed rock masses. Dissertation, Chinese Academy of Sciences, Wuhan

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Acknowledgments

This work was supported by the Natural Science Foundations of China (grant nos.: 40872170 and 40902077), Doctoral Program Foundation of Higher Education of China (grant no.: 20090061110054), Jilin University’s 985 project (grant no.: 450070021107), Interdisciplinary Research Plan Project of Jilin University (grant no.: 2011J014) and Basic Research (grant no.: 200903202).

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Authors and Affiliations

  1. College of Construction Engineering, Jilin University, Changchun, 130026, China

    Wen Zhang, Jian-ping Chen, Rui Huang, Ming Li & Ying Zhang

  2. Jilin Institute of Architecture and Civil Engineering, Changchun, 130000, China

    Chang Liu

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  1. Wen Zhang
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  2. Jian-ping Chen
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  3. Chang Liu
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  4. Rui Huang
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  5. Ming Li
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Correspondence to Jian-ping Chen.

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Zhang, W., Chen, Jp., Liu, C. et al. Determination of Geometrical and Structural Representative Volume Elements at the Baihetan Dam Site. Rock Mech Rock Eng 45, 409–419 (2012). https://doi.org/10.1007/s00603-011-0191-0

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Keywords

  • Representative volume element
  • Size effect
  • Statistical test
  • Three-dimensional fracture network