Inference of crack statistics from observations on an outcropping
It is difficult to examine the cracks in a three-dimensional body; one is usually limited to observations on an outcropping, a cut, or a plane obtained by sectioning a sample. This paper considers two problems. The direct problem is to find the distribution of line segments in a plane section when the three-dimensional distribution of cracks is homogeneous, isotropic, and exponential. This distribution can be expressed in closed form by means of Hankel functions. It is shown that the distribution in a plane section is qualitatively different from the three-dimensional distribution in having a peak for a finite value of segment length, i.e., there is a most probable (non-zero) segment length. It is also concluded that the mean segment size in the plane is ..pi../2 times the mean crack diameter in three dimensions. This result is consistent with the well-known observation that small cracks have a lower probability of being intercepted by a plane than larger cracks. The number density of line segments is finally expressed in terms of the Hankel function of order zero. The indirect problem is to infer the three-dimensional distribution of cracks from the distribution on a section, which could be, for example, an outcropping. This problem is solved by deriving an integral equation relating the three-dimensional distribution of cracks and the distribution of line segments in a plane, and showing that it can be solved for an arbitrary distribution of segments on the out-cropping. The special case of the Hankel distribution leads to the exponential distribution in three dimensions; thus, thesolution method is verified. 3 figures.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 6162994
- Report Number(s):
- LA-UR-79-522; CONF-790606-5
- Resource Relation:
- Conference: 20. US symposium on rock mechanics, Austin, TX, USA, 3 Jun 1979
- Country of Publication:
- United States
- Language:
- English
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