Reply to Discussion on “Analysis of Bingham fluid radial flow in smooth fractures” |
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Authors: | Liangchao Zou Ulf Håkansson Vladimir Cvetkovic |
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Affiliation: | 1. Division of Resources, Energy and Infrastructure, Department of Sustainable Development, Environmental Science and Engineering, Royal Institute of Technology, Stockholm, 10044, Sweden;2. Division of Soil and Rock Mechanics, Department of Civil and Architectural Engineering, Royal Institute of Technology, Stockholm, 10044, Sweden;3. Skanska AB, Stockholm, 11274, Sweden |
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Abstract: | Recently, Hoang et al. (2021) discussed our paper Zou et al. (2020). In our paper, we made a statement that Dai and Bird (1981)'s solution for two-dimensional (2D) radial Bingham fluid flow between parallel plates violates mass balance. Hoang et al. pointed out that Dai and Bird (1981)'s solution does not violate the mass balance because Dai and Bird (1981)'s solution and our analysis are based on different assumptions, i.e. with consideration of the vertical velocity component in the continuity equation or not, which leads to two different approximation models. In this sense, the mass balance of Dai and Bird (1981)'s solution should not be checked using our solution as a reference. In this reply, we add remarks on the two approximation models and their implication for rock grouting analysis. The discussion by Hoang et al. and this reply are helpful to thoroughly eliminate the existing confusion regarding the two solutions in the rock grouting research community. |
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Keywords: | Rock grouting Radial flow Bingham fluid Approximation solution |
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