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Modeling a Shallow Rock Tunnel Using Terrestrial Laser Scanning and Discrete Fracture Networks

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Abstract

Discontinuity mapping and analysis are extremely important for modeling shallow tunnels constructed in fractured rock masses. However, the limited exposure and variability of rock face orientation in tunnels must be taken into account. In this paper, an automatic method is proposed to generate discrete fracture networks (DFNs) using terrestrial laser scanner (TLS) geological mapping and to continuously calculate the volumetric intensities (P 32) along a tunnel. The number of fractures intersecting rectangular sampling planes with different orientations, fitted in tunnel sections of finite lengths, is used as the program termination criteria to create multiple DFNs and to calculate the mean P 32. All traces and orientations from three discontinuity sets of the Monte Seco tunnel (Vitória Minas Railway) were mapped and the present method applied to obtain the continuous variation in P 32 along the tunnel. A practical approach to creating single and continuous DFNs (for each discontinuity set), considering the P 32 variations, is also presented, and the results are validated by comparing the trace intensities (P 21) from the TLS mapping and DFNs generated. Three examples of 3DEC block models generated from different sections of the tunnel are shown, including the ground surface and the bedrock topographies. The results indicate that the proposed method is a practical and powerful tool for modeling fractured rock masses of uncovered tunnels. It is also promising for application during tunnel construction when TLS mapping is a daily task (for as-built tunnel controls), and the complete geological mapping (traces and orientations) is available.

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Abbreviations

\(P_{32}\) :

Volumetric intensity

\(P_{32}^{i}\) :

Volumetric intensity of the ith tunnel position

\(P_{32}^{t}\) :

Volumetric intensity of a finite section of the tunnel

\(Er(i)\) :

Volumetric intensity error

\(P_{21}\) :

Trace intensity

\(C_{21}\) :

Constant of proportionality between P 32 and P 21

\(P_{10}\) :

Linear intensity

\(k\) :

Fisher dispersion factor

\(T_{\text{cc}}\) :

Trace with both ends contained

\(T_{\text{tc}}\) :

Trace with one end contained and the other end censored

\(T_{\text{tt}}\) :

Trace with both ends censored

\(l_{\text{m}}\) :

Measured mean trace length

\(l_{\text{sd}}\) :

Standard deviation of measured trace lengths

\(\mu\) :

Unbiased mean trace length

\(\sigma\) :

Standard deviation of unbiased trace lengths

\(\mu_{\text{D}}\) :

Mean discontinuity diameter

\(\sigma_{\text{D}}\) :

Standard deviation of discontinuity diameters

\(f\left( l \right)\) :

Probability density function of measured trace lengths

\(g\left( l \right)\) :

Probability density function of unbiased trace lengths

\(g\left( D \right)\) :

Probability density function of discontinuity diameters

\(N\) :

Number of discontinuities intersecting a sampling window

\(N_{\hbox{min} }\) :

Minimum number of discontinuities intersecting a sampling window

\(N_{\text{l}}\) :

Number of foliation planes cutting the scanline

\(L_{\text{T}}\) :

Total scanline length

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Acknowledgements

The authors would like to thank the company VALE SA, the Brazilian National Council for Scientific and Technological Development (CNPq) and the São Paulo Research Foundation (FAPESP) for logistical and financial support.

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  1. Graduate Program of Civil Engineering, Structural and Geotechnical Engineering Department, Engineering School, University of São Paulo, Av. Prof. Luciano Gualberto, travessa 3 nº 380, São Paulo, SP, CEP 05508-010, Brazil

    Pedro Pazzoto Cacciari & Marcos Massao Futai

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  1. Pedro Pazzoto Cacciari
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  2. Marcos Massao Futai
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Correspondence to Pedro Pazzoto Cacciari.

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Cacciari, P.P., Futai, M.M. Modeling a Shallow Rock Tunnel Using Terrestrial Laser Scanning and Discrete Fracture Networks. Rock Mech Rock Eng 50, 1217–1242 (2017). https://doi.org/10.1007/s00603-017-1166-6

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