Skip to main content
SpringerLink
Log in

A Practical Method for Estimating the Volumetric Intensity of Non-persistent Discontinuities on Rock Exposures

  • Original Paper
  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Abstract

The volumetric discontinuity intensity (\(P_{32}\)) is defined as the total discontinuity area by rock mass volume. \(P_{32}\) has been considered the most suitable parameter to quantify discontinuities within rock masses because it takes into account density and size and does not depend on orientation. Currently, determining the \(P_{32}\) from discontinuity mapping of rock exposures requires a series of discrete fracture network (DFN) simulations. This method is time-consuming and requires advanced software; thus, it is generally not used in practical rock engineering applications. This paper proposes a new method to obtain the \(P_{32}\) of rock masses from 2D rock exposures, based on well-known weighted joint density (\({\text{wJd}}\)) and mean trace length (\(\mu_{\text{l}}\)) estimates. The method was developed and validated using DFN modeling and compared with \(P_{32}\) estimates obtained by computational simulations in a real case study (Monte Seco tunnel). Finally, the synthetic rock mass (SRM) modeling technique was used to investigate the effects of \(P_{32}\) on the mechanical behavior of a hypothetical rock mass, highlighting the individual contributions of \({\text{wJd}}\) and \(\mu_{\text{l}}\). The results demonstrate that the proposed method is reliable and can estimate the \(P_{32}\) of rock masses without requiring computation simulations. Moreover, the SRM analysis showed that discontinuity density and size have a similar impact on the mechanical behavior of rock masses with non-persistent discontinuity sets.

Highlights

  • A new method for obtaining the volumetric intensity of rock masses from discontinuity mapping of 2D rock exposures.

  • The method was developed and validated using parametric discrete fracture network analysis and applied in a tunneling case study.

  • A synthetic rock mass case demonstrated the volumetric intensity and discontinuity size's contributions to the mechanical behavior of rock masses.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Abbreviations

\(P_{32}\) :

Volumetric discontinuity intensity (m−1)

\(P_{32}^{{{\text{max}}}}\) :

Maximum volumetric discontinuity intensity (m−1)

\(P_{20}\) :

Areal discontinuity density (m−2)

\(P_{10}\) :

Linear discontinuity intensity (m−1)

\({\text{wJd}}\) :

Weighted joint density (m−1)

\({\text{wJd}}^{{\text{u}}}\) :

Unbiased weighted joint density (m−1)

\(\delta_{\text{i}}\) :

Acute angle between the discontinuity dip and the mean rock face (°)

\(A\) :

Area of the square-shape sampling window (m2)

\(L\) :

Length of the square-shape sampling window’s edge (m)

\(r\) :

Radius of the circular window (m)

\(m\) :

Number of trace endpoints in the window

\(n\) :

Number of trace endpoints cut by the window boundary

\(f_{\text{i}}\) :

Correction factors for \(\delta_{\text{i}}\)

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

Unbiased mean trace length (m)

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

Unbiased standard deviation of trace lengths (m)

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

Mean discontinuity diameter (m)

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

Standard deviation of discontinuity diameter (m)

\({\text{CoV}}\) :

Coefficient of variation of discontinuity diameters

\(C_{31}\) :

Constant factors for \(P_{10}\)

\(C_{32}\) :

Constant factors for \(P_{20}\) (m)

\(S_{{\text{f}}}\) :

Biased size factor

\(S_{{\text{f}}}^{{\text{u}}}\) :

Unbiased size factor

\(V_{{\text{f}}}\) :

Size variation factor

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

Uniaxial compressive strength of the intact rock (MPa)

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

Uniaxial compressive strength of the synthetic rock mass (MPa)

References

Download references

Acknowledgements

The authors would like to thank the Brazilian National Council for Scientific and Technological Development (CNPq) logistical and financial support.

Author information

Authors and Affiliations

  1. Department of Civil, Geological and Mining Engineering, Polytechnique Montréal, 2900 Boulevard Edouard-Montpetit, Montréal, QC, H3T 1J4, Canada

    Pedro Pazzoto Cacciari

  2. Civil Engineering Graduate Program, School of Engineering, University of São Paulo. Cidade Universitária, Butantã, São Paulo, SP, Brasil

    Marcos Massao Futai

Authors
  1. Pedro Pazzoto Cacciari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marcos Massao Futai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pedro Pazzoto Cacciari.

Ethics declarations

Conflict of Interest

The authors declare that they have no conflicts of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cacciari, P.P., Futai, M.M. A Practical Method for Estimating the Volumetric Intensity of Non-persistent Discontinuities on Rock Exposures. Rock Mech Rock Eng 55, 6063–6078 (2022). https://doi.org/10.1007/s00603-022-02966-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-022-02966-w

Keywords

Search

Navigation