Analysis of Bingham fluid radial flow in smooth fractures
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 pl...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-10-01
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| Series: | Journal of Rock Mechanics and Geotechnical Engineering |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1674775520300950 |
| _version_ | 1828966164763508736 |
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| author | Liangchao Zou Ulf Håkansson Vladimir Cvetkovic |
| author_facet | Liangchao Zou Ulf Håkansson Vladimir Cvetkovic |
| author_sort | Liangchao Zou |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-14T11:26:32Z |
| format | Article |
| id | doaj.art-17ed074d686c4b0c98a03fb26eb0db2a |
| institution | Directory Open Access Journal |
| issn | 1674-7755 |
| language | English |
| last_indexed | 2024-12-14T11:26:32Z |
| publishDate | 2020-10-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of Rock Mechanics and Geotechnical Engineering |
| spelling | doaj.art-17ed074d686c4b0c98a03fb26eb0db2a2022-12-21T23:03:30ZengElsevierJournal of Rock Mechanics and Geotechnical Engineering1674-77552020-10-0112511121118Analysis of Bingham fluid radial flow in smooth fracturesLiangchao Zou0Ulf Håkansson1Vladimir Cvetkovic2Division of Resources, Energy and Infrastructure, Department of Sustainable Development, Environmental Science and Engineering, Royal Institute of Technology, Stockholm, 10044, Sweden; Corresponding author.Division of Soil and Rock Mechanics, Department of Civil and Architectural Engineering, Royal Institute of Technology, Stockholm, 10044, Sweden; Skanska Sweden AB, Stockholm, 11274, SwedenDivision of Resources, Energy and Infrastructure, Department of Sustainable Development, Environmental Science and Engineering, Royal Institute of Technology, Stockholm, 10044, SwedenSolutions 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.http://www.sciencedirect.com/science/article/pii/S1674775520300950Rock groutingRadial flow of Bingham fluidsPlug flow regionForce balanceEnergy dissipationAnalytical solution |
| spellingShingle | Liangchao Zou Ulf Håkansson Vladimir Cvetkovic Analysis of Bingham fluid radial flow in smooth fractures Journal of Rock Mechanics and Geotechnical Engineering Rock grouting Radial flow of Bingham fluids Plug flow region Force balance Energy dissipation Analytical solution |
| title | Analysis of Bingham fluid radial flow in smooth fractures |
| title_full | Analysis of Bingham fluid radial flow in smooth fractures |
| title_fullStr | Analysis of Bingham fluid radial flow in smooth fractures |
| title_full_unstemmed | Analysis of Bingham fluid radial flow in smooth fractures |
| title_short | Analysis of Bingham fluid radial flow in smooth fractures |
| title_sort | analysis of bingham fluid radial flow in smooth fractures |
| topic | Rock grouting Radial flow of Bingham fluids Plug flow region Force balance Energy dissipation Analytical solution |
| url | http://www.sciencedirect.com/science/article/pii/S1674775520300950 |
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