A general procedure to correct sampling bias on joint orientation using a vector approach

https://doi.org/10.1016/0266-352X(90)90006-HGet rights and content

Abstract

Observed relative frequencies of joints should be corrected for sampling bias before inferring statistical distributions for orientations. The procedure available for sampling bias correction when finite size joints intersect finite size sampling domains is directly applicable only for vertical sampling planes [1–3]. Thus, a general procedure applicable for sampling domains of any orientation is developed in the present study. The corrected frequency of a joint is obtained by assigning a weight to each joint through a weighting function which is inversely propotional to the probability of intersection between the joint and the sampling plane. This probability of intersection is determined from a hypothesis indicating “the probability of intersection is proportional to the volume in which the center of the sampling domain should lie in order to intersect the joint”. A vector approach to find this volume is described herein, followed by applications of this method to study the influence of the sampling bias correction on orientation frequency and to find statistical distributions for orientation data.

References (19)

  • P.M. Warburton

    Vector stability analysis of an arbitrary polyhedral rock block with any number of free faces

    Int. J. Rock Mechanics and Min. Sci. and Geomechanics Abstr.

    (1981)
  • M. Oda

    Fabric tensor for discontinuous geological materials

    Soils and Foundations

    (1982)
  • P.H.S.W. Kulatilake et al.

    Sampling Bias on orientation of discontinuities

    Rock Mechanics and Rock Engineering

    (1984)
  • P.H.S.W. Kulatilake

    A correction for sampling bias on joint orientation for finite size joints intersecting finite size exposures

  • P.H.S.W. Kulatilake et al.

    Probabilistic modelling of joint orientation

    Int. J. for Numerical and Analytical Methods in Geomechanics

    (1990)
  • P.H.S.W. Kulatilake

    State-of-the-art in joint geometry modelling

  • W.S. Dershowitz et al.

    Characterizing rock joint geometry with joint system models

    Rock Mechanics and Rock Engineering

    (1988)
  • P.H.S.W. Kulatilake et al.

    Three dimensional stochastic joint geometry modelling including a verification: a case study

  • Kulatilake, P.H.S.W., Wathugala, D.N., Poulton, M. and Stephansson, O., Analysis of structural homogeneity of rock...
There are more references available in the full text version of this article.

Cited by (0)

Also, a Visiting Research Professor, Luleå University of Technology, Luleå, Sweden.

View full text