Fracturing in the Solid Earth

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概要

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• In the Solid Earth, fracturing is a pervasive phenomenon : weathering, explosion, impact, faulting, earthquake and so forth. Several empirical studies on fractures have demonstrated a power-law dependence of the cumulative number N(r) of fragments of which sizes are larger than size r, N(r)〜r^<-D>. This is taken as evidence that the fracturing is a scale-invariant process concerning the size distribution. Therefore, fractures can be described from the viewpoint of fractal. This description derives mathematically Gaudin-Schuhmann relation and Charles' relation and is sufficiently in incorporation of the three theories on size reduction : Rittinger's, Kick's and Bond's theories. The fractal dimension (D) provides a measure of the relative importance of large versus small objects and is related to both energy density for fracturing and Weibull's coefficient of uniformity (w) when the "size effect" of tensile strength is taken into consideration. Fracture surface is also a typical example of fractals. The specific surface area S of each fragment is plotted as functions of the mean fragment size r^^^-. Then the surface fractal dimension D′ can be defined by S〜r^^^-^<D′-3>. The D′-value for fractures increases as the energy of fracturing increased. This indicates that the surface fractal dimension D′ can be a measure of fracture intensity. By analyzing the self-affinity of fracture trace curve, however, the fracture trace actually seems to be self-affine but not self-similar. Similarly, the growth pattern of various fractures, such as faults, pull-apart basins, landslides, crater morphologies and stream patterns, over a wide range of size scales is not necessarily isometric (self-similar). Therefore, the scaling law should be represented as C_Y=C^β_X, where C_Y and C_X are scale ratios on Y and X between fractures in scale. Moreover, this relation can also be extended to the relation between individual and system of the fracture and the relationship between the displacement and thickness of the ductile shear zone.FracturefractalSelf-affinityScaling lawSolid Earth

• 東北大学の論文
• 1991-02-25

著者

• Nagahama Hiroyuki

  Institute Of Geology And Paleontology Graduate School Of Science Tohoku University

• Nagahama Hiroyuki

  Institute Of Geosciences School Of Science Shizuoka University

関連論文

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• Fracturing in the Solid Earth
• Curie Symmetry Principle in Nonlinear Functional Systems
• Curie Symmetry Principle:Does It Constrain the Analysis of Structural Geology?
• Symmetropy and Self-Organized Criticality
• Symmetry Properties of Spatial Distribution of Microfracturing in Rock

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