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Treatment for a fracture is based on the type of break, the bone affected, and the patient's age.
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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
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Interaction between a fracture network and a cubic cavity.

D Sangaré1, V V Mourzenko, J-F Thovert

  • 1UPMC Sisyphe, Boîte 105, 4 place Jussieu, 75252 Paris Cedex 05, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 16, 2013
PubMed
Summary
This summary is machine-generated.

This study numerically investigates fracture network and cubic cavity intersections. Probabilities of cluster intersection depend on domain size, fracture density, and relative sizes, with findings extrapolated to infinite domains.

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Area of Science:

  • Geosciences
  • Computational Modeling
  • Network Analysis

Background:

  • Understanding fluid flow and transport in fractured rock masses is crucial for subsurface engineering applications.
  • Polygonal fracture networks and cubic cavities represent common geological structures and underground excavations.
  • Quantifying the interaction between these features is essential for risk assessment and resource management.

Purpose of the Study:

  • To numerically investigate the intersection probabilities between a polygonal fracture network and a cubic cavity.
  • To analyze the influence of domain size, fracture density, and relative feature sizes on intersection behavior.
  • To develop and validate analytical approximations for these probabilities.

Main Methods:

  • Numerical simulation of polygonal fracture networks intersecting a cubic cavity.
  • Definition and calculation of various intersection probabilities.
  • Extrapolation of probabilities to infinite domain sizes.
  • Development of analytical approximations and comparison with numerical data.

Main Results:

  • Intersection probabilities are dependent on domain size, fracture density, and the relative dimensions of fractures and the cavity.
  • Extrapolation to infinite domains provides asymptotic probability values.
  • Analytical approximations show good agreement with numerical results for high fracture densities.
  • The study quantifies the likelihood of a percolating fracture cluster intersecting the cavity.

Conclusions:

  • The numerical study provides valuable insights into the geometric intersection of fracture networks and cavities.
  • Analytical approximations offer a simplified yet accurate method for estimating intersection probabilities under certain conditions.
  • Findings have implications for modeling fluid flow, contaminant transport, and rock mass stability in fractured geological formations.