Abstract
A flow erosion model of water inrush was developed that couples the Darcy, Forchheimer, and Navier–Stokes fields under the theory of continuum mechanics. Water flow and fluidized particles were regarded as single-phase mixed fluids based on the fundamentals of flow transition (aquifer laminar flow to turbulent flow) being the main cause of mine water inrush; the effects of rock disintegration and the coupled effects of flow and erosion were incorporated. The water source of the aquifer, water-inrush channel of the fracture network, and flow path of the slope roadway export were organically connected in a unified flow field. The weak integral forms of the Darcy, Forchheimer, and Navier–Stokes equations were constructed according to the principle of virtual displacement. The convective terms were discretized by the finite volume method and the other terms were discretized by the finite element method; the calculation source program was developed based on the finite element language and its compiler (FELAC). The source program system was used to numerically simulate water inrush in a fractured zone in the Jiangjiawan Mine. It reproduced the entire dynamic process of a water inrush and revealed the distribution and variation characteristics of the pressure field, velocity field, porosity, and concentration, as well as the mechanisms underlying the sudden change in water flow.
Zusammenfassung
Es wurde ein Fließerosionsmodell des Wassereinbruchs entwickelt, das die Darcy-, Forchheimer- und Navier–Stokes-Felder gestützt auf die Theorie der Kontinuumsmechanik miteinander verbindet. Wasserströmung und fluidisierte Partikel wurden als einphasige Mischfluide betrachtet, basierend auf den Grundlagen des Strömungsübergangs (Aquifer-Laminarströmung zu turbulenter Strömung), der die Hauptursache für Wassereinbruch in Bergwerken ist. Die Auswirkungen des Gesteinszerfalls und die gekoppelten Effekte von Strömung und Erosion wurden einbezogen. Die Wasserquelle des Aquifers, der Wassereinbruchskanal des Bruchnetzes und der Fließweg des Hangstreckenaustrags waren in einem einheitlichen Strömungsfeld auf natürliche Weise miteinander verbunden. Die schwachen Integralformen der Darcy-, Forchheimer- und Navier–Stokes-Gleichungen wurden nach dem Prinzip der virtuellen Verschiebung konstruiert. Die konvektiven Terme wurden mit der Finite-Volumen-Methode und die anderen Terme mit der Finite-Elemente-Methode diskretisiert; das Quellprogramm zur Berechnung wurde auf der Grundlage der Finite-Elemente-Programmiersprache und deren Compiler (FELAC) entwickelt. Das Quellprogrammsystem wurde verwendet, um den Wassereinbruch in einer Bruchzone in der Jiangjiawan-Mine numerisch zu simulieren. Es reproduzierte den gesamten dynamischen Prozess eines Wassereinbruchs und enthüllte die Verteilungs- und Schwankungscharakteristika des Druckfeldes, des Geschwindigkeitsfeldes, der Porosität und der Konzentration sowie die Mechanismen, die der plötzlichen Änderung des Wasserflusses zugrunde liegen.
Resumen
Se desarrolló un modelo de erosión del flujo de entrada de agua que acopla los campos de Darcy, Forchheimer y Navier–Stokes bajo la teoría de la mecánica del continuo. El flujo de agua y las partículas fluidizadas se consideraron como fluidos mixtos monofásicos basándose en los fundamentos de la transición de flujo (flujo laminar a flujo turbulento) como la principal causa de irrupción de agua en la mina; se incorporaron los efectos de la desintegración de la roca y los efectos acoplados del flujo y la erosión. La fuente de agua del acuífero, el canal de irrupción de agua de la red de fracturas y la ruta de flujo de la exportación del talud se conectaron orgánicamente en un campo de flujo unificado. Las formas integrales débiles de las ecuaciones de Darcy, Forchheimer y Navier–Stokes fueron construidas de acuerdo con el principio de desplazamiento virtual. Los términos convectivos se discretizaron por el método de volúmenes finitos y los demás términos se discretizaron por el método de elementos finitos; el programa fuente de cálculo se desarrolló basándose en el lenguaje de elementos finitos y su compilador (FELAC). El sistema del programa fuente se utilizó para simular numéricamente la entrada de agua en una zona fracturada en la mina de Jiangjiawan. Se reprodujo todo el proceso dinámico de una irrupción de agua y se revelaron las características de distribución y variación del campo de presión, el campo de velocidad, la porosidad y la concentración, así como los mecanismos subyacentes al cambio repentino del flujo de agua.
概要
基于连续介质力学理论, 建立了耦合Darcy, Forchheimer和Navier–Stokes场的突水水流侵蚀模型。依据流态转换(含水层的层流转变为紊流)是矿井突水主要原因的基础认识, 视水流与液化颗粒为单相混合流, 综合考虑岩石破裂和水流与侵蚀耦合的作用。含水层水源, 裂隙网络突水通道和斜巷出口水流路径在均匀流场中有机相连。根据虚位移原理, 构造了达西, Forchheimer和Navier–Stokes方程的弱积分形式。有限体积法离散对流项, 有限元法离散其它项, 计算源程序基于有限元语言及编译器(FELAC)开发。利用源程序系统数值模拟了江家湾矿裂隙带突水; 再现了突水的完整动力学过程, 揭示了压力场, 速度场, 孔隙度和浓度的分布与变化, 揭示了水流突变的机理。
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References
Cao T, Chen X, Qiu ZF (2016) Experimental research on the disintegration of sandstone and mudstone particle. China Science 11(01):17–20 (in Chinese)
Dontsov EV, Peirce AP (2017) Modeling planar hydraulic fractures driven by laminar-to-turbulent fluid flow. Int J Solids Struct 128:73–84
Fei XJ (1982) Viscous coefficient (stiffness coefficient) of high concentration muddy water. Shuili Xuebao 03:59–65 (in Chinese)
Javadi M, Sharifzadeh M, Shahriar K (2014) Critical Reynolds number for nonlinear flow through rough-walled fractures: the role of shear processes. Water Resour Res 50(2):1789–1804
Klimczak C, Schultz RA, Parashar R, Reeves DM (2010) Cubic law with aperture-length correlation: implications for network scale fluid flow. Hydrogeol J 18(04):851–862
Li ZH (2015) “4.19” major water disaster accident in Jiangjiawan coal mine of Tongmei group. Shanxi coal Geology Bureau, Taiyuan (in Chinese)
Lin P (2019) Hydro-mechanical coupling models for water and mud inrush induced by suffusion of filling material and failure of surrounding rock. PhD Thesis, Shandong Univ, Shandong (in Chinese)
Liu R, Jiang Y, Li B (2016) Effects of intersection and dead-end of fractures on nonlinear flow and particle transport in rock fracture networks. Geosci J 20:415–426
Paranamana P, Aulisa E, Ibragimov A, Toda M (2019) Fracture model reduction and optimization for Forchheimer flows in reservoir. J Math Phys 60(5):1–32
Shi WH (2018) A non-Darcy flow model for water inrush through broken rock mass and its engineering application. PhD Thesis, Northeastern Univ, Shenyang (in Chinese)
Shi LQ, Xin HQ, Zhai PH, Li SC, Wei WX (2012) Calculating the height of water flowing fracture zone in deep mining. J Chin Univ Min Technol 41(1):37–41 (in Chinese)
Shi WH, Yang TH, Liu HL, Yang B (2018) Numerical modeling of non-Darcy flow behavior of groundwater outburst through fault using the Forchheimer equation. J Hydrol Eng 23(2):1–9
Stavropoulou M, Papanastasiou P, Vardoulakis I (2015) Coupled wellbore erosion and stability analysis. Int J Numer Anal Methods Geomech 22(09):749–769
Su BY, Zhan ML, Guo XE (1997) Experimental study on cross-fracture water flow. Shuili Xuebao 05:2–7 (in Chinese)
Wang JX, Jiang AN, Song ZP (2014) Study of the coupling model of rock elastoplastic stress-seepage-damage (I): modelling and its numerical solution procedure. Rock Soil Mech 35(S2):626–637 (in Chinese)
Wilson CR, Withspoon PA (1976) Flow interference effects at fracture intersections. Water Resour Res 12(01):102–104
Xia XG, Huang QX (2014) Study on the dynamic height of caved zone based on porosity. J Min Saf Eng 31(1):102–107 (in Chinese)
Xie HP, Gao F, Ju Y (2015) Research and development of rock mechanics in deep ground engineering. Chin J Rock Mech Eng 34(11):2161–2178 (in Chinese)
Xiong X, Li B, Jiang Y (2011) Experimental and numerical study of the geometrical and hydraulic characteristics of a single rock fracture during shear. Int J Rock Mech Min Sci 48(8):1292–1302
Yang B (2019) Experimental and modeling study on non-linear seepage characteristics of filling fracture networks. PhD Thesis, Northeastern Univ, Shenyang (in Chinese)
Yang TH, Tham LG, Tang CA, Liang ZZ, Tsui Y (2004) Influence of heterogeneity of mechanical properties on hydraulic fracturing in permeable rocks. Rock Mech Rock Eng 37(4):251–275
Yang TH, Shi WH, Li SC, Yang X, Yang B (2016) State of the art and trends of water-inrush mechanism of nonlinear flow in fractured rock mass. J Chin Coal Soc 41(07):1598–1609 (in Chinese)
Yang B, Yang TH, Xu ZH (2018) Numerical simulation of the free surface and water inflow of a slope, considering the nonlinear flow properties of gravel layers: a case study. R Soc Open Sci 5:172109. https://doi.org/10.1098/rsos.172109
Yang B, Yang TH, Xu ZH, Liu HL, Yang X, Shi WH (2019) Impact of particle-size distribution on flow properties of a packed column. J Hydrol Eng 24(3):1–11
Yao BH, Wang LC, Wei JP, Li ZH, Liu XJ (2018) A deformation-seepage-erosion coupling model for water outburst of Karst collapse pillar and its application. J Chin Coal Soc 43(7):2007–2013 (in Chinese)
Zhang Z, Nemcik J (2013) Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures. J Hydrol 477(1):139–151
Zhao Y, Cao P, Wang Y, Liu Y (2008) Coupling model of seepage-damage-fracture in fractured rock masses and its application. Chin J Rock Mech Eng 27(8):1634–1643 (in Chinese)
Zhao Y, Wang CL, Wan W (2016) Seepage flow during crack propagation process and stress coupled model under compression-shear stress conditions. Rock Soil Mech 37(8):2180–2186 (in Chinese)
Zhu HG, Yi C, Jiang YD (2015) Effect of fractures cross connection on fluid flow characteristics cross connection. J Chin Univ Min Technol 44(01):24–28 (in Chinese)
Zimmerman RW, Al-yaarubi A, Pain CC (2004) Non-linear regimes of fluid flow in rock fractures. Int J Rock Mech Min Sci 41(3):163–169
Xia XG, Huang QX (2012) Study on the dynamic height of caved zone based on porosity. J Mining Safety Eng 31(01):102–107 (in Chinese)
Acknowledgements
The current thesis was supported by the State Key Program of National Natural Science of China (U1710253) and the National Natural Science Foundation of China (51574059, 51274053).
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10230_2021_762_MOESM1_ESM.eps
Supplementary file1. Supplemental Figure S-1 Space-time evolution process of the pressure (Unit: Pa): a t = 1 s; b t = 25 s; c t = 50 s; d t = 100 s; e t = 150 s; f t = 200 s. (EPS 26293 KB)
10230_2021_762_MOESM8_ESM.eps
Supplementary file8. Supplemental Figure S-2 Space-time evolution process of the velocity (Unit: m/s): a t = 1 s; b t = 25 s; c t = 50 s; d t = 100 s; e t = 200 s; f t = 1000 s. (EPS 26060 KB)
10230_2021_762_MOESM15_ESM.eps
Supplementary file15. Supplemental Figure S-3 Space-time porosity evolution: a t = 1 s; b t = 25 s; c t = 50 s; d t = 100 s; e t = 200 s; f t = 1000 s. (EPS 23807 KB)
10230_2021_762_MOESM22_ESM.eps
Supplementary file22. Supplemental Figure S-4 Space-time evolution of the concentration: a t = 1 s; b t = 25 s; c t = 50 s; d t = 100 s; e t = 200 s; f t = 1000 s. (EPS 26286 KB)
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Yang, B., Yang, T. & Hu, J. Numerical Simulation of Non-Darcy Flow Caused by Cross-Fracture Water Inrush, Considering Particle Loss. Mine Water Environ 40, 466–478 (2021). https://doi.org/10.1007/s10230-021-00762-6
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DOI: https://doi.org/10.1007/s10230-021-00762-6