Analytical model for uncertainty characterization of fracture intensity measurement in rock masses

Yu Chen Lu, Yong Ming Tien, Charng Hsein Juang, Himatul Farichah, Che Jui Hsu, Van Binh Bui

Research output: Contribution to journalArticlepeer-review


This paper presents an analytical model for quantifying the uncertainty of three-dimensional fracture intensity measurements (P32), which measure fracture area per sampling volume, and for determining the geometrical representative elementary volume (REV) of fractured rock. The analytical model for estimating the variance of P32 is derived from the probability of a given number of fractures in a sample of rock. This model is validated through numerical simulations of fractured rock masses based on the discrete fracture network method. A series of parametric studies are conducted considering the dip angle, dip direction, Fisher constant, size and shape of the rock mass space, specimen volume, fracture diameter, and P32. Based on the results of the analytical model and the parametric studies, a simple model to quantify the coefficient of variation (COV) of P32 is established, which requires only the data of specimen volume, fracture diameter, and P32. Four engineering applications of the proposed analytical model are presented, including two case studies of estimating the geometrical REV at a given COV, one of assessing the variation of mechanical properties, and another of determining the variation of permeability.

Original languageEnglish
Article number45
JournalBulletin of Engineering Geology and the Environment
Issue number1
StatePublished - Jan 2022


  • Analytical model
  • Fractured rock mass
  • Intensité de fracture tridimensionnelle
  • Masse rocheuse fracturée
  • Modèle analytique
  • Numerical simulation
  • Representative elementary volume
  • Simulation numérique
  • Three-dimensional fracture intensity
  • Volume élémentaire représentatif


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