Fractal relations for the diameter and trace length of disc‐shaped fractures

Piggott, Andrew R.

doi:10.1029/97jb01202

Cited by 60 publications

(30 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, the restriction that disks be parallel, as assumed by Warburton [1980a], is in fact unnecessary. An analogous result was also developed by Piggott [1997].…”

Section: G(c)= I½½m M C H(q))dq) Csupporting

confidence: 48%

“…Since the problem of quantifying chord distributions in a plane has already been treated by Warburton [1980a] and Piggott [1997], only a brief presentation will be provided here. First, consider a disk of a given diameter q); the intersection of this disk with a plane is a chord of length c. Since the disk population is isotropic and uniformly distributed in space, the distance r of the chord to the center of the disk is uniformly distributed.…”

Section: :1 Chord Distribution In a Planementioning

confidence: 99%

See 1 more Smart Citation

Stereological analysis of fracture network structure in geological formations

Berkowitz¹,

Adler²

1998

J. Geophys. Res.

View full text Add to dashboard Cite

Abstract. Relationships between three-dimensional fracture networks consisting of polydisperse disks and the corresponding two-dimensional trace maps are systematically analyzed. Bulk densities of disks and disk intersections are related to surface densities of traces and trace intersections; this results in a new relation for the average length of disk intersections. The probability densities of trace lengths and disk intersections are studied for several disk diameter distributions. The inverse problem of deriving the disk distribution from the trace distribution is then solved, assuming only that the disks have uniformly random locations and orientations. These results are applied to a variety of synthetically generated data, as well as to several sets of field data. Analysis of the field data suggests that fracture diameter distributions follow a power law, in agreement with previous conclusions based on trace length histograms, with exponents varying from 1.3 to 2.1.

show abstract

“…Moreover, the restriction that disks be parallel, as assumed by Warburton [1980a], is in fact unnecessary. An analogous result was also developed by Piggott [1997].…”

Section: G(c)= I½½m M C H(q))dq) Csupporting

confidence: 48%

Section: :1 Chord Distribution In a Planementioning

confidence: 99%

Stereological analysis of fracture network structure in geological formations

Berkowitz¹,

Adler²

1998

J. Geophys. Res.

View full text Add to dashboard Cite

show abstract

“…The number-size relation for the frequency of fractures is one of the ways to characterize a fracture system as a fractal (PIGGOTT, 1997;BONNET et al, 2001). The total fracture length (L) estimated at different scales inside the test map of size e ¼ A 1=2 , was related to the number (N) of observed fractures through the formula Ln N ¼ l Ln L þ const, that is N / L l .…”

Section: Fracture Length and Number Scaling Lawsmentioning

confidence: 99%

Spatial Distribution, Scaling and Self-similar Behavior of Fracture Arrays in the Los Planes Fault, Baja California Sur, Mexico

Nieto-Samaniego

Alaniz-Álvarez

Tolson

et al. 2005

Pure appl. geophys.

View full text Add to dashboard Cite

We present a case of detailed analysis of fracture arrays spanning four orders of magnitude in length; all of them measured at a single natural site by acquiring images at progressively larger scales. There is a high dispersion of cumulative-length exponents, box dimensions and fracture densities. However, the fractal analysis supports the fractal nature of fracture arrays. Our data indicate the existence of an upper limit for the density parameters, as similarly reported by other authors. We prove that box dimension is in inverse relation with fracture concentration and in direct relation with fracture density. These relations are also observed in our data and additionally there is an upper limit for the box dimensions. We interpret the dispersion in our results as more fundamental than methodological problems. It represents a truncation in the complete evolution of the fracture systems because in natural cases strain initiates overprinting of previous fracture arrays. Considering that larger fractures accommodate strain more efficiently than small fractures, the generation of small fractures is inhibited in the presence of preexisting larger fractures. Maximum values of fracture density prevent accommodating an excess of strain in a single or restricted range of scales; we claim this condition produces migration of fracturing to larger scales originating fracture scaling.

show abstract

“…One typical fractal application on Earth science is characterizing and modeling a fractured network (Piggott, 1997;Sahimi, 2011). Sun (2011) proposed the methodology to study fractal properties of fracture surfaces in two factors: qualitative analysis and quantitative analysis.…”

Section: Introductionmentioning

confidence: 99%