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The predicted fracture distribution provides a clear view of the fracture concentration and fracture development.
The fracture concentration parameter is defined as υ = N*a3, where N is the fractures number within single volume (fracture density).
One of the important consequences of this model is that E/Em parameter (which slightly depend on Poisson's ratio) is a measure of the fracture concentration.
The development of dissolution fingers is promoted by any initial pervious zone such as fracture concentration around a faulted zone and the characteristic time for instability development drops to 0.1 0.3 Ma.
Lattman and Parizek (1964) had studied the relationship between fracture traces and occurrence of groundwater in carbonate rocks and they had reported that fracture traces visible on aerial photographs are natural linear-drainage, soiltonal, and topographic alignments which are probably the surface manifestation of underlying zones of fracture concentration.
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They had used several bore-hole caliper surveys and these data support the concept that fracture traces reflect underlying fracture concentrations and are useful as a prospecting guide in locating zones of increased weathering, solutioning, and permeability.
The relative effective elastic modulus E/Em versus fractures concentration υ for isotropic and transversal-isotropic medium [20] are represented in Fig. 3a.
a Inter-relations between fractures concentration and relative velocity (V/Vm) for isotropic (1) and transversal isotropic (2) mediums; b Inter-relations between fractures summary volume (n%) and relative velocity (V/Vm).
The formation of an inter-connecting graphene network promoted easy fracture for concentration ⩾2 vol%.
Studies in USA had no clear evidence that consumption of water with fluoride level up to 8 mg/l had any association with dental and skeletal fluorosis, but the reports from India and China clearly present an evidence of dental fluorosis, osteosclerosis, and bone fracture at concentration of 6 mg/l (IPCS 2002).
The loaded rock is represented as a homogeneous isotropic or transversal-isotropic solid (or matrix) with elastic modulus Em (or velocity Vm) including the numerous statistically distributed isolated fractures whose concentration uniquely defines the effective elastic characters of the medium E or V.
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