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

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Abbreviations

\(w\) :

Width of the sampling window

\(h\) :

Height of the sampling window

\(\alpha_{i}\) :

Dip direction of the ith joint

\(\alpha_{r}\) :

Strike of the sampling window

\(\theta_{i}\) :

Dip angle of the ith joint

\(d_{i}\) :

Fracture diameter of the ith joint

\(W_{i}\) :

Weight formula for the ith joint

\({\text{Rf}}_{i}\) :

Corrected relative frequency of the ith joint

\(n\) :

Number of joints in a fracture set

\(\varepsilon_{i}\) :

The ith parameter of the supposed probability density function

\(l_{j}\) :

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

\(\mu_{m}\) :

Mean trace length

\(\sigma_{m}\) :

Standard deviation of the measured trace length distribution

\(\mu_{l}\) :

True mean trace length

\(\sigma_{l}\) :

Standard deviation of the true trace length distribution

\(\mu_{D}\) :

Mean joint diameter

\(\sigma_{D}\) :

Standard deviation of the joint diameter distribution

\(( {\text{COV)}}_{m}\) :

Coefficient of variation of the measured trace length distribution

\(E(D^{m} )\) :

The mth moment of the joint diameter, m = 1, 2, 3…

\(E(l^{m} )\) :

The mth moment of the trace length, m = 1, 2, 3…

\(\lambda_{i}^{1}\) :

Normal line density of the ith fracture set

\(\lambda_{i}^{V}\) :

Fracture density in unit volume of the ith fracture set

\(V\) :

Volume of simulated space region

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Acknowledgments

This work was supported by the State Key Program of the National Natural Science Fund of China (Grant No. 41330636), the National Natural Science Fund of China (Grant Nos. 41402242, 41402243, and 41202197), and Graduate Innovation Fund of Jilin University (Grant No. 2014062). We thank Dr. Giovanni Barla and an anonymous reviewer for the excellent reviews that helped to improve the manuscript.

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Authors and Affiliations

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

    Xudong Han, Jianping Chen, Qing Wang, Yanyan Li, Wen Zhang & Tianwen Yu

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  1. Xudong Han
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Correspondence to Jianping Chen.

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Han, X., Chen, J., Wang, Q. et al. A 3D Fracture Network Model for the Undisturbed Rock Mass at the Songta Dam Site Based on Small Samples. Rock Mech Rock Eng 49, 611–619 (2016). https://doi.org/10.1007/s00603-015-0747-5

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