{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T07:00:42Z","timestamp":1763535642490,"version":"3.41.2"},"reference-count":38,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2019,7,25]],"date-time":"2019-07-25T00:00:00Z","timestamp":1564012800000},"content-version":"vor","delay-in-days":205,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51878624","51878622"],"award-info":[{"award-number":["51878624","51878622"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006407","name":"Natural Science Foundation of Henan Province","doi-asserted-by":"publisher","award":["182300410116"],"award-info":[{"award-number":["182300410116"]}],"id":[{"id":"10.13039\/501100006407","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004773","name":"Henan University","doi-asserted-by":"publisher","award":["18IRTSTHN007"],"award-info":[{"award-number":["18IRTSTHN007"]}],"id":[{"id":"10.13039\/501100004773","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>The purpose of the present work is to develop a quasi\u20103D numerical method that can be used to study the diffusion mechanism of grout injection in a rock fracture based on the collocated structured grid of the finite volume method (FVM). Considering the characteristics of fracture in geometry that the aperture is much less than its length and width, the Hele\u2010Shaw model is introduced to deduce the <jats:italic>z-<\/jats:italic>derivatives of velocities <jats:italic>u<\/jats:italic> and <jats:italic>v<\/jats:italic> at walls, which is a function of the relevant average velocity and the fracture aperture. The traditional difference scheme for the diffusive term is partly substituted with the derived analytical expressions; hence a three\u2010dimensional problem of grout flow in the parallel fracture can be transformed into a two\u2010dimensional one that concerns fracture aperture. The new model is validated by the analytical solution and experimental data on three cases of grouting in the parallel\u2010plate fracture. Compared with the results from ANSYS\u2010Fluent software, the present model shows better agreement with the analytical solution for the distribution of pressure and velocity. Furthermore, the new model needs less grid unit, spends less time, but achieves greater accuracy. The complexity of the grout flow field in the rock fracture is reduced; thus the computational efficiency can be improved significantly.<\/jats:p>","DOI":"10.1155\/2019\/4139616","type":"journal-article","created":{"date-parts":[[2019,7,25]],"date-time":"2019-07-25T23:31:25Z","timestamp":1564097485000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Quasi\u20103D Numerical Model for Grout Injection in a Parallel Fracture Based on Finite Volume Method"],"prefix":"10.1155","volume":"2019","author":[{"given":"Xiaolong","family":"Li","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0481-9078","authenticated-orcid":false,"given":"Meimei","family":"Hao","sequence":"additional","affiliation":[]},{"given":"Yanhui","family":"Zhong","sequence":"additional","affiliation":[]},{"given":"Bei","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Fuming","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Lianbang","family":"Wang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2019,7,25]]},"reference":[{"key":"e_1_2_11_1_2","first-page":"62","article-title":"Stop criteria for cement grouting","volume":"25","author":"Gustafson G.","year":"2005","journal-title":"Zeitschrift f\u00fcr Geomechanik und Ingenieurgeologie im Bauwesen und Bergbau"},{"key":"e_1_2_11_2_2","first-page":"449","volume-title":"Rock Mechanics and Waterways Construction","author":"Wallner M.","year":"1976"},{"key":"e_1_2_11_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0257(81)80031-6"},{"volume-title":"Grouting of Rock\u2013Simulation and Classification","year":"1991","author":"H\u00e4ssler L.","key":"e_1_2_11_4_2"},{"key":"e_1_2_11_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/S1365-1609(00)00080-0"},{"key":"e_1_2_11_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00603-017-1237-8"},{"key":"e_1_2_11_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tust.2017.06.024"},{"key":"e_1_2_11_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/s13146-016-0332-3"},{"key":"e_1_2_11_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0886-7798(02)00024-X"},{"key":"e_1_2_11_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tust.2005.08.010"},{"key":"e_1_2_11_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tust.2006.12.004"},{"key":"e_1_2_11_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.minpro.2009.04.006"},{"key":"e_1_2_11_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tust.2014.04.010"},{"key":"e_1_2_11_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tust.2017.11.020"},{"key":"e_1_2_11_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tust.2014.08.003"},{"key":"e_1_2_11_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tust.2015.07.012"},{"key":"e_1_2_11_17_2","doi-asserted-by":"publisher","DOI":"10.12989\/gae.2017.12.5.771"},{"key":"e_1_2_11_18_2","first-page":"201","article-title":"Comparative experimental investigation of chemical grouting into a fracture with flowing and static water","volume":"21","author":"Gailing Z.","year":"2011","journal-title":"Mining Science and Technology"},{"key":"e_1_2_11_19_2","unstructured":"H\u00e4sslerL. 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