1. Analysis of Bingham fluid radial flow in smooth fractures
- Author
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Vladimir Cvetkovic, Ulf Håkansson, and Liangchao Zou
- Subjects
0211 other engineering and technologies ,02 engineering and technology ,engineering.material ,010502 geochemistry & geophysics ,01 natural sciences ,Rock grouting ,Radial flow of Bingham fluids ,Physics::Fluid Dynamics ,lcsh:Engineering geology. Rock mechanics. Soil mechanics. Underground construction ,Shear stress ,Force balance ,021101 geological & geomatics engineering ,0105 earth and related environmental sciences ,Plug flow ,Analytical solution ,Grout ,Energy dissipation ,Mechanics ,Penetration (firestop) ,Geotechnical Engineering and Engineering Geology ,Volumetric flow rate ,Open-channel flow ,Plug flow region ,lcsh:TA703-712 ,engineering ,Radial flow ,Bingham plastic ,Geology - Abstract
Solutions for radial flow of a Bingham fluid are analyzed in this paper. It aims to eliminate confusions in the literature concerning the plug flow region in different solutions for analysis and design of grouting in rock fractures. The analyses based on the force balance equation reveal that the plug flow region in Bingham radial flow is independent of the fracture radius, and is not a growth function adapted from the solution of one-dimensional (1D) slit flow according to ‘similarity’. Based on the shear stress distribution, we analytically proposed that a non-uniform plug flow region cannot exist. The Bingham fluid (grout) penetration and flowrate evolution as functions of grouting time are given using the correct expression for the plug flow region. The radius-independent plug flow region and the presented flowrate evolution equation are also verified numerically. For radial flow, the relative penetration length is equal to the relative width of plug flow region, which is the same as that for 1D channel flow. Discrepancies in analytical solutions for grout penetration and flowrate evolution were also illustrated. The clarification of the plug flow region and evaluation of discrepancies in analytical solutions presented in this work could simplify modeling and design of grouting in rock engineering applications.
- Published
- 2020