{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T17:37:25Z","timestamp":1787852245021,"version":"build-2784847793"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,5,31]],"date-time":"2021-05-31T00:00:00Z","timestamp":1622419200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,5,31]],"date-time":"2021-05-31T00:00:00Z","timestamp":1622419200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Study on the Mechanism of Water-Gas Coupling Fracture Expansion and Ultrasonic Characteristics of Coal Rock Mass in Drilling Holes","award":["51774234"],"award-info":[{"award-number":["51774234"]}]},{"name":"Fracture Evolution and Water-Gas Coupled Permeability Mechanism of Coal Body Around Extraction Borehole","award":["2021JM-390"],"award-info":[{"award-number":["2021JM-390"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The initiation process of the mine water inrush accident, the essence of this process is the sudden change of the seepage state of the broken coal medium under pressure and the instability of the skeleton. In order to study the re-crushing mechanism and seepage characteristics of the broken coal medium under load, a set of three-axis seepage system was designed independently. Using the steady-state infiltration method, multiple flow factors under different particle size combinations and different stress conditions of the broken coal medium were obtained. The results of the study indicate: in one hand, the reduction of the porosity of the broken coal medium will cause the flow channel to be rebuilt, and the sudden change of flow rate will directly lead to the non-Darcian flow behavior. The early stage of compaction mainly affects the permeability <jats:italic>k<\/jats:italic> value, and the later stage of compaction mainly affects the non-Darcian <jats:italic>\u03b2<\/jats:italic> value; On the other hand, the seepage throat in the broken coal medium may have a sharp increase in its flow rate, leading to a sudden change in the flow pattern. The critical Reynolds number is also used to determine whether non-Darcian flow is formed, and its value in the water inrush system is about 40\u2013133; at the same time, the non-Darcian flow in the broken coal medium conforms to the Forchheimer-type flow law. By analyzing the dependence relationship between factors, a seepage factor representation algebraic relationship suitable for Forchheimer type non-Darcian flow of broken coal medium is given, which can be used as a calculation basis in the prevention and treatment of mine water inrush accidents.<\/jats:p>","DOI":"10.1038\/s41598-021-90449-3","type":"journal-article","created":{"date-parts":[[2021,5,31]],"date-time":"2021-05-31T10:05:58Z","timestamp":1622455558000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Re-crushing process and non-Darcian seepage characteristics of broken coal medium in coal mine water inrush"],"prefix":"10.1038","volume":"11","author":[{"given":"Mingkun","family":"Pang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tianjun","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi","family":"Guo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lei","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,5,31]]},"reference":[{"issue":"4","key":"90449_CR1","doi-asserted-by":"publisher","first-page":"735","DOI":"10.1007\/s12665-010-0562-y","volume":"62","author":"W Sui","year":"2011","unstructured":"Sui, W. et al. Hydrogeological analysis and salvage of a deep coalmine after a groundwater inrush. Environ. Earth Sci. 62(4), 735\u2013749 (2011).","journal-title":"Environ. Earth Sci."},{"key":"90449_CR2","doi-asserted-by":"crossref","unstructured":"Galhardi, J. A. & Bonotto, D. M. Hydrogeochemical features of surface water and groundwater contaminated with acid mine drainage (AMD) in coal mining areas: a case study in southern Brazil. Environ. Sci. Pollut. Res. Int. 23(18), 18911\u201327\n (2016).","DOI":"10.1007\/s11356-016-7077-3"},{"issue":"2","key":"90449_CR3","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1023\/A:1016018020180","volume":"49","author":"Y Wu","year":"2002","unstructured":"Wu, Y. Numerical simulation of single-phase and multiphase non-Darcy flow in porous and fractured reservoirs. Transp. Porous Media 49(2), 209\u2013240 (2002).","journal-title":"Transp. Porous Media"},{"issue":"2","key":"90449_CR4","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1007\/s11242-011-9735-8","volume":"88","author":"Y Wu","year":"2011","unstructured":"Wu, Y., Lai, B. & Miskimins, J. Analysis of multiphase non-Darcy flow in porous and fractured media. Transp. Porous Media 88(2), 205\u2013223 (2011).","journal-title":"Transp. Porous Media"},{"key":"90449_CR5","doi-asserted-by":"crossref","unstructured":"Aarnoudse, E.,\u00a0 Qu, W., Bluemling, B. & Herzfeld, T. Groundwater quota versus tiered groundwater pricing: Two cases of groundwater management in north-west China. EconStor Open Access Articles (2017).","DOI":"10.1080\/07900627.2016.1240069"},{"issue":"3","key":"90449_CR6","doi-asserted-by":"publisher","first-page":"1732","DOI":"10.1016\/j.jngse.2015.10.039","volume":"27","author":"Y Yao","year":"2015","unstructured":"Yao, Y., Li, G. & Qin, P. Seepage features of high-velocity non-Darcy flow in highly productive reservoirs. J. Nat. Gas Sci. Eng. 27(3), 1732\u20131738 (2015).","journal-title":"J. Nat. Gas Sci. Eng."},{"issue":"19","key":"90449_CR7","doi-asserted-by":"publisher","first-page":"19719","DOI":"10.1007\/s11356-019-05311-x","volume":"26","author":"D Ma","year":"2019","unstructured":"Ma, D., Wang, J. & Li, Z. Effect of particle erosion on mining-induced water inrush hazard of karst collapse pillar. Environ. Sci. Pollut. Res. 26(19), 19719\u201319728 (2019).","journal-title":"Environ. Sci. Pollut. Res."},{"issue":"6","key":"90449_CR8","first-page":"771","volume":"34","author":"T Yang","year":"2009","unstructured":"Yang, T. et al. Numerical model of nonlinear flow-diffusion for gas mitigation in goaf and atmosphere. J. China Coal Soc. 34(6), 771\u2013777 (2009).","journal-title":"J. China Coal Soc."},{"key":"90449_CR9","doi-asserted-by":"crossref","unstructured":"Celik, E. & Hoang, L. Maximum estimates for generalized Forchheimer flows in heterogeneous porous media. Int. J. Differ. Equ. 29(3), 5\u20136 (2016).","DOI":"10.1088\/0951-7715\/29\/3\/1124"},{"issue":"9","key":"90449_CR10","first-page":"756.1","volume":"75","author":"Y Wang","year":"2016","unstructured":"Wang, Y. et al. Experimental study on the non-Darcy flow characteristics of soil-rock mixture. Environ. Earth Sci. 75(9), 756.1-756.18 (2016).","journal-title":"Environ. Earth Sci."},{"issue":"1","key":"90449_CR11","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/s00603-006-0081-z","volume":"40","author":"G Cammarata","year":"2007","unstructured":"Cammarata, G. et al. The hydro-mechanically coupled response of rock fractures. Rock Mech. Rock Eng. 40(1), 41\u201361 (2007).","journal-title":"Rock Mech. Rock Eng."},{"issue":"5","key":"90449_CR12","doi-asserted-by":"publisher","first-page":"1125","DOI":"10.1007\/s00603-012-0328-9","volume":"46","author":"Z Zhang","year":"2013","unstructured":"Zhang, Z. & Nemcik, J. Friction factor of water flow through rough rock fractures. Rock Mech. Rock Eng. 46(5), 1125\u20131134 (2013).","journal-title":"Rock Mech. Rock Eng."},{"issue":"3","key":"90449_CR13","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1007\/s11242-014-0385-5","volume":"105","author":"D Ma","year":"2014","unstructured":"Ma, D. et al. An experimental investigation of permeability measurement of water flow in crushed rocks. Transp. Porous Media 105(3), 571\u2013595 (2014).","journal-title":"Transp. Porous Media"},{"issue":"4","key":"90449_CR14","doi-asserted-by":"publisher","first-page":"527","DOI":"10.3390\/en10040527","volume":"10","author":"M Dan","year":"2017","unstructured":"Dan, M. et al. Experimental investigation of stress rate and grain size on gas seepage characteristics of granular coal. Energies 10(4), 527 (2017).","journal-title":"Energies"},{"issue":"8","key":"90449_CR15","first-page":"1","volume":"2020","author":"T Zhang","year":"2020","unstructured":"Zhang, T., Pang, M., Zhang, X. & Pan, H. Determining the seepage stability of fractured coal rock in the Karst Collapse Pillar. Adv. Civil Eng. 2020(8), 1\u201311 (2020).","journal-title":"Adv. Civil Eng."},{"issue":"5","key":"90449_CR16","doi-asserted-by":"publisher","first-page":"612","DOI":"10.3390\/en10050612","volume":"10","author":"W Jiangyu","year":"2017","unstructured":"Jiangyu, W., Qiang, L. & Haibo, B. Grain size distribution effect on the hydraulic properties of disintegrated coal mixtures. Energies 10(5), 612 (2017).","journal-title":"Energies"},{"key":"90449_CR17","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/j.enggeo.2016.12.006","volume":"217","author":"D Ma","year":"2017","unstructured":"Ma, D. et al. Variations of hydraulic properties of granular sandstones during water inrush: Effect of small particle migration. Eng. Geol. 217, 61\u201370 (2017).","journal-title":"Eng. Geol."},{"issue":"6","key":"90449_CR18","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1007\/BF00192153","volume":"2","author":"A Barak","year":"1987","unstructured":"Barak, A. Comments on high velocity flow in porous media by Hassanizadeh and Gray. Transp. Porous Media 2(6), 533\u2013535 (1987).","journal-title":"Transp. Porous Media"},{"issue":"3","key":"90449_CR19","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/BF01063962","volume":"7","author":"D Ruth","year":"1992","unstructured":"Ruth, D. & Ma, H. On the derivation of the Forchheimer equation by means of the average theorem. Transp. Porous Media 7(3), 255\u2013264 (1992).","journal-title":"Transp. Porous Media"},{"issue":"2","key":"90449_CR20","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1007\/s10596-018-9779-8","volume":"23","author":"M Koeppel","year":"2019","unstructured":"Koeppel, M., Martin, V., Jaffre, J. & Roberts, J. E. A Lagrange multiplier method for a discrete fracture model for flow in porous media. Comput. Geosci. 23(2), 239\u2013253 (2019).","journal-title":"Comput. Geosci."},{"key":"90449_CR21","unstructured":"Ren, S. L.,\u00a0 Han, F. P.,\u00a0 Xie, B.,          et al.     Numerical simulation of flow fields in porous media based on the 3D CFD-DEM. Appl. Math. Mech. 38(10), 1093\u20131102 (2017)."},{"key":"90449_CR22","volume-title":"Convection in Porous Media","author":"D Nield","year":"2006","unstructured":"Nield, D. & Bejan, A. Convection in Porous Media 3rd edn. (Springer, 2006).","edition":"3"},{"issue":"2","key":"90449_CR23","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1007\/s11242-014-0398-0","volume":"106","author":"D Lyubimov","year":"2015","unstructured":"Lyubimov, D., Kolchanova, E. & Lyubimova, T. Vibration effect on the nonlinear regimes of thermal convection in a two-layer system of fluid and saturated porous medium. Transp. Porous Media 106(2), 237\u2013257 (2015).","journal-title":"Transp. Porous Media"},{"issue":"8","key":"90449_CR24","doi-asserted-by":"publisher","first-page":"913","DOI":"10.1021\/ie50260a016","volume":"23","author":"T Chilton","year":"1931","unstructured":"Chilton, T. & Colburn, A. Pressure drop in packed tubes. Ind. Engng. Chem 23(8), 913\u2013919 (1931).","journal-title":"Ind. Engng. Chem"},{"key":"90449_CR25","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1016\/j.amc.2019.01.042","volume":"353","author":"W Liu","year":"2019","unstructured":"Liu, W., Cui, J. & Wang, Z. Numerical analysis and modeling of multiscale Forchheimer-Forchheimer coupled model for compressible fluid flow in fractured media aquifer system. Appl. Math. Comput. 353, 7\u201328 (2019).","journal-title":"Appl. Math. Comput."},{"key":"90449_CR26","unstructured":"Shchelkachev V. N. & Lapouk, B. B. Underground Hydraulics. Moscow-Leningrad (1949)."},{"key":"90449_CR27","unstructured":"Mironenko, V. A. & Shestakov, V. M. Fundamentals of Geohydromechanics, Moscow (1974)."},{"key":"90449_CR28","doi-asserted-by":"publisher","first-page":"1109","DOI":"10.1016\/j.ijheatmasstransfer.2017.08.067","volume":"115","author":"Y Takatsu","year":"2017","unstructured":"Takatsu, Y. Modification of the fundamental theorem for transport phenomena in porous media. Int. J. Heat Mass Transf. 115, 1109\u20131120 (2017).","journal-title":"Int. J. Heat Mass Transf."},{"key":"90449_CR29","doi-asserted-by":"crossref","unstructured":"Lasseux, D., Vald\u00e9s-Parada, Francisco, J. & Bellet, F. Macroscopic model for unsteady flow in porous media. J. Fluid Mech. 862, 283\u2013311 (2019).","DOI":"10.1017\/jfm.2018.878"},{"key":"90449_CR30","doi-asserted-by":"publisher","first-page":"106640","DOI":"10.1016\/j.engfracmech.2019.106640","volume":"220","author":"D Ma","year":"2019","unstructured":"Ma, D. et al. Effects of height\/diameter ratio on failure and damage properties of granite under coupled bending and splitting deformation. Eng. Fract. Mech. 220, 106640 (2019).","journal-title":"Eng. Fract. Mech."},{"key":"90449_CR31","doi-asserted-by":"crossref","unstructured":"Wang, S., Elsworth, D. & Ji, B. Permeability evolution in fractured coal: The roles of fracture geometry and water-content. Int. J. Coal Geol. 87(1), 13\u201325 (2011).","DOI":"10.1016\/j.coal.2011.04.009"},{"key":"90449_CR32","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1016\/j.coal.2009.11.001","volume":"81","author":"F Han","year":"2010","unstructured":"Han, F. et al. Experimental study of gas and water transport processes in the inter-cleat (matrix) system of coal: Anthracite from Qinshui Basin, China. Int. J. Coal Geol. 81, 128\u2013138 (2010).","journal-title":"Int. J. Coal Geol."},{"key":"90449_CR33","first-page":"1","volume":"2018","author":"L Wang","year":"2018","unstructured":"Wang, L. & Kong, H. Variation characteristics of mass-loss rate in dynamic seepage system of the broken rocks. Geofluids 2018, 1\u201317 (2018).","journal-title":"Geofluids"},{"key":"90449_CR34","doi-asserted-by":"crossref","unstructured":"Yu, B.,\u00a0 Chen, Z.,\u00a0 Ding, Q., et al. Non-Darcy flow seepage characteristics of saturated broken rocks under compression with lateral constraint. J. Min. Sci. Tech. 26(6), 1145\u20131151 (2016).","DOI":"10.1016\/j.ijmst.2016.09.025"},{"key":"90449_CR35","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1007\/s12182-011-0115-3","volume":"1","author":"Y Yao","year":"2011","unstructured":"Yao, Y. & Ge, J. Characteristics of non-Darcy flow in low-permeability reservoirs. Pet. Sci. 1, 55\u201362 (2011).","journal-title":"Pet. Sci."}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-90449-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-90449-3","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-90449-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,3]],"date-time":"2022-12-03T09:02:15Z","timestamp":1670058135000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-90449-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,31]]},"references-count":35,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["90449"],"URL":"https:\/\/doi.org\/10.1038\/s41598-021-90449-3","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,31]]},"assertion":[{"value":"7 January 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 May 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 May 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"11380"}}