基于HBP本构模型的泥石流动力过程SPH数值模拟
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摘要
本构模型是描述泥石流流变特性的关键,也是决定其动力过程数值模拟准确性的核心问题之一。泥石流流体属多相混合物,现有的研究已证实其存在剪切增稠或剪切变稀的现象,传统基于Bingham及Cross线性本构关系的数值模型难以准确描述泥石流流变特性。文中探讨了Bingham模型在低剪应变率下的数值发散问题,在光滑粒子流体动力学(SPH)方法框架上建立了整合Herschel-Bulkley-Papanastasiou(HBP)本构关系的稀性泥石流动力过程三维数值模型。相比传统基于浅水波假设的二维数值模型,所述方法从三维尺度建立SPH形式下的泥石流浆体纳维-斯托克斯方程并进行数值求解,可获取泥石流速度场时空分布及堆积形态,同时采用HBP本构关系描述泥石流流变特性,能在确保数值收敛的前提下反映泥石流流体在塑性屈服过渡段及大变形状态下应力-应变的非线性变化。为验证提出方法的合理性,结合小型模型槽实验观测进行了对比,结果表明数值模拟与实测结果基本吻合。
A rational constitutive model is critical for numerical simulation of rheological behavior of debris-flow. It is also one of the key issues that determine the accuracy of numerical simulation of its dynamic process. The numerical models based on Bingham and Cross constitutive models has been observed failing to simulate the shearing thickening and thinning phenomenon of the rheological behavior of debris-flow that belongs to multi-phase mixture of fluid and debris. We discuss the numerical divergence problem of using the Bingham model with low shear strain rate. To simulate the dynamic flow process of diluted debris-flow, the 3 D numerical model is set up, applying an alternative solution of the Herschel-Bulkley-Papanastasiou(HBP) constitutive model with the smoothed particle hydrodynamic(SPH) method. Comparing to the traditional two-dimensional numerical model based on the hypothesis of shallow water wave, the proposed method in this paper solves Navier-Stokes equations describing the debris-flow with the SPH in three-dimension, thus the velocity field and deposition pattern of debris flow can be simulated. The proposed method incorporates the HBP constitutive model, ensuring the numerical convergence, can perform well to reveal the non-linear variation of stress-strain relationship of debris flow at transition phase of plastic yield and large shear rate. The proposed method is verified by a flume experiment. It indicates that the simulation results match well with the experimental measurements.
A rational constitutive model is critical for numerical simulation of rheological behavior of debris-flow. It is also one of the key issues that determine the accuracy of numerical simulation of its dynamic process. The numerical models based on Bingham and Cross constitutive models has been observed failing to simulate the shearing thickening and thinning phenomenon of the rheological behavior of debris-flow that belongs to multi-phase mixture of fluid and debris. We discuss the numerical divergence problem of using the Bingham model with low shear strain rate. To simulate the dynamic flow process of diluted debris-flow, the 3 D numerical model is set up, applying an alternative solution of the Herschel-Bulkley-Papanastasiou(HBP) constitutive model with the smoothed particle hydrodynamic(SPH) method. Comparing to the traditional two-dimensional numerical model based on the hypothesis of shallow water wave, the proposed method in this paper solves Navier-Stokes equations describing the debris-flow with the SPH in three-dimension, thus the velocity field and deposition pattern of debris flow can be simulated. The proposed method incorporates the HBP constitutive model, ensuring the numerical convergence, can perform well to reveal the non-linear variation of stress-strain relationship of debris flow at transition phase of plastic yield and large shear rate. The proposed method is verified by a flume experiment. It indicates that the simulation results match well with the experimental measurements.
引文
[1]徐林荣,韩征,苏志满,等.泥石流流速横向分布特征与防治工程结构优化[J].岩土力学, 2012, 33(12):3715-3728.XU Lin-rong, HAN Zheng, SU Zhi-man, et al. Research on lateral distribution features of debris flow velocity and structural optimization of prevention and control works[J]. Rock and Soil Mechanics, 2012, 33(12):3715-3728.
[2]胡卸文,刁仁辉,梁敬轩,等.基于CFX的江口沟泥石流危险区范围预测模拟[J].岩土力学, 2016, 37(6):1689-1696.HU Xie-wen, DIAO Ren-hui, LIANG Jing-xuan, et al.Prediction of the scope of Jiangkou gully debris flow hazard using CFX software[J]. Rock and Soil Mechanics, 2016, 37(6):1689-1696.
[3]乔成,欧国强,潘华利,等.泥石流数值模拟方法研究进展[J].地球科学与环境学报, 2016, 38(1):134-142.QIAO Cheng, OU Guo-qiang, PAN Hua-li, et al. Review on numerical modeling methods of debris flow[J].Journal of Earth Sciences and Environment, 2016,38(1):134-142.
[4]胡凯衡,崔鹏,田密,等.泥石流动力学模型和数值模拟研究综述[J].水利学报, 2012, 57(增刊2):79-84.HU Kai-Heng, CUI Peng, TIAN Mi, et al. A review of the debris flow dynamic models and numerical simulation[J].Journal of Hydraulic Engineering, 2012, 57(Suppl.2):79-84.
[5]缪吉伦,张文忠,周家俞.基于SPH方法的黏性泥石流堆积形态数值模拟[J].自然灾害学报, 2013, 22(6):125-130.MIAO Ji-lun, ZHANG Wen-zhong, ZHOU Jia-yu.Numerical simulation of the accumulation state of viscous debris flow by smooth particle hydrodynamics method[J].Journal of Natural Disasters, 2013, 22(6):125-130.
[6] GEORGE D L, IVERSON R M. A depth-averaged debris-flow model that includes the effects of evolving dilatancy.Ⅱ. Numerical predictions and experimental tests[J].ProceedingsoftheRoyalSociety A(Mathematical, Physical and Engineering Sciences),2014, 470:20130820.
[7] HAN Z, CHEN G Q, LI Y G, et al. Numerical simulation of debris-flow behavior incorporating a dynamic method for estimating the entrainment[J]. Engineering Geology,2015, 190:52-64.
[8] LIU G R, LIU M B.光滑粒子流体动力学——一种无网格粒子法[M].湖南:湖南大学出版社, 2005.LIU G R, LIU M B. Smoothed particle hydrodynamics:A meshfree particle method[M]. Hunan:Hunan University Press, 2005.
[9] CUNDALL P A, STARCK O D L. A discrete numerical model for granular assemblies[J]. Geotechnique, 1979,29(1):47-65.
[10] HAN Z, CHEN G, LI Y, et al. A numerical simulation of volumetric enlargement for seismic debris flow using integrated DDA and KANAKO 2D[C]//Frontiers of Discontinuous Numerical Methods and Practical Simulations in Engineering and Disaster Prevention.USA:CRC Press, 2013:281-287.
[11] WANG W, CHEN G, HAN Z, et al. 3D numerical simulation of debris-flow motion using SPH method incorporating non-Newtonian fluid behavior[J]. Natural Hazards, 2016, 81(3):1981-1998.
[12] HUANG Y, ZHANG W, XU Q, et al. Run-out analysis of flow-like landslides triggered by the Ms8.0 2008Wenchuanearthquakeusingsmoothedparticle hydrodynamics[J]. Landslides, 2012, 9(2):275-283.
[13]罗明,廖维,郭双,等.低丘缓坡地区小型崩塌的DDA方法模拟[J].地质灾害与环境保护, 2016, 27(2):84-88.LUO Ming, LIAO Wei, GUO Shuang, et al. Simulation of small collapse in low-slope hilly land by DDA method[J].Journal of Geological Hazards and Environment Preservation, 2016, 27(2):84-88.
[14]殷坤龙,姜清辉,汪洋.新滩滑坡运动全过程的非连续变形分析与仿真模拟[J].岩石力学与工程学报, 2002,22(7):959-962.YIN Kun-long, JIANG Qing-hui, WANG Yang.Discontinuous deformation analysis and simulation of the whole process of the landslide in the Xintan beach[J].Chinese Journal of Rock Mechanics and Engineering,2002, 22(7):959-962.
[15]胡嫚,谢谟文,王立伟.基于弹塑性土体本构模型的滑坡运动过程SPH模拟[J].岩土工程学报, 2016, 38(1):58-67.HU Man, XIE Mo-wen, WANG Li-wei. SPH simulations of post-failure flow of landslides using elastic-plastic soil constitutive model[J]. Chinese Journal of Geotechnical Engineering, 2016, 38(1):58-67.
[16] MCDOUGALL S, HUNGR O. Dynamic modelling of entrainmentinrapidlandslides[J].Canadian Geotechnical Journal, 2005, 42(5):1437-1448.
[17] PASTOR M, BLANC T, HADDAD B, et al. Application of a SPH depth-integrated model to landslide run-out analysis[J]. Landslides, 2014, 11(5):793-812.
[18]许波,谢谟文,胡嫚.基于GIS空间数据的滑坡SPH粒子模型研究[J].岩土力学, 2016, 37(9):2696-2705.XU Bo, XIE Mo-wen, HU Man. SPH landslide model based on GIS spatial data[J]. Rock and Soil Mechanics,2016, 37(9):2696-2705.
[19]张锋.计算土力学[M].北京:人民交通出版社, 2007.ZHANG Feng. Computational soil mechanics[M].Beijing:People’s Communications Press, 2007.
[20] JEFFREY D P, KELIN X W, ALESSANDRO S.Experimental study of the grain-flow, fluid-mud transition in debris flows[J]. The Journal of Geology, 2001, 109:427-447.
[21] JON J M, THOMAS C P. Debris flow rheology:experimental analysis of fine-grained slurries[J]. Water Resources Research, 1992, 28(3):841-857.
[22] PAPANASTASIOU T C. Flows of materials with yield[J].Journal of Rheology, 1987, 31(5):385-404.
[23] FRIGAARD I A, NOUAR C. On the usage of viscosity regularisation methods for visco-plastic fluid flow computation[J]. Journal of Non-Newtonian Fluid Mechanics, 2005, 127:1-26.
[24]乔成,潘华利,欧国强.两相光滑粒子流体动力学方法在动床溃坝问题中的应用[J].中国科学院大学学报,2017, 34(5):625-632.QIAO Cheng, PAN Hua-li, OU Guo-qiang. Application of two-phase smoothed particle hydrodynamics method to dam break over movable bed[J]. Journal of University of Chinese Academy of Sciences, 2017, 34(5):625-632.
[25] ULRICH C, LEONARDI M, RUNG T. Multi-physics SPH simulation of complex marine-engineering hydrodynamic problems[J]. Ocean Engineering, 2013,64:109-121.
[26] MONAGHAN J J. Simulating free surface flows with SPH[J]. Journal of Computational Physics, 1994,110(2):399-406.
[27] UZUOKA R, YASHIMA A, KAWAKAMI T, et al. Fluid dynamics based prediction of liquefaction induced lateral spreading[J]. Computers&Geotechnics, 1998, 22(3-4):243-282.
[28] KOMATINA D, JOVANOVIC M. Experimental study of steady and unsteady free surface flows with water-clay mixtures[J]. Journal of Hydraulic Research, 1997,35(5):579-590.
[2]胡卸文,刁仁辉,梁敬轩,等.基于CFX的江口沟泥石流危险区范围预测模拟[J].岩土力学, 2016, 37(6):1689-1696.HU Xie-wen, DIAO Ren-hui, LIANG Jing-xuan, et al.Prediction of the scope of Jiangkou gully debris flow hazard using CFX software[J]. Rock and Soil Mechanics, 2016, 37(6):1689-1696.
[3]乔成,欧国强,潘华利,等.泥石流数值模拟方法研究进展[J].地球科学与环境学报, 2016, 38(1):134-142.QIAO Cheng, OU Guo-qiang, PAN Hua-li, et al. Review on numerical modeling methods of debris flow[J].Journal of Earth Sciences and Environment, 2016,38(1):134-142.
[4]胡凯衡,崔鹏,田密,等.泥石流动力学模型和数值模拟研究综述[J].水利学报, 2012, 57(增刊2):79-84.HU Kai-Heng, CUI Peng, TIAN Mi, et al. A review of the debris flow dynamic models and numerical simulation[J].Journal of Hydraulic Engineering, 2012, 57(Suppl.2):79-84.
[5]缪吉伦,张文忠,周家俞.基于SPH方法的黏性泥石流堆积形态数值模拟[J].自然灾害学报, 2013, 22(6):125-130.MIAO Ji-lun, ZHANG Wen-zhong, ZHOU Jia-yu.Numerical simulation of the accumulation state of viscous debris flow by smooth particle hydrodynamics method[J].Journal of Natural Disasters, 2013, 22(6):125-130.
[6] GEORGE D L, IVERSON R M. A depth-averaged debris-flow model that includes the effects of evolving dilatancy.Ⅱ. Numerical predictions and experimental tests[J].ProceedingsoftheRoyalSociety A(Mathematical, Physical and Engineering Sciences),2014, 470:20130820.
[7] HAN Z, CHEN G Q, LI Y G, et al. Numerical simulation of debris-flow behavior incorporating a dynamic method for estimating the entrainment[J]. Engineering Geology,2015, 190:52-64.
[8] LIU G R, LIU M B.光滑粒子流体动力学——一种无网格粒子法[M].湖南:湖南大学出版社, 2005.LIU G R, LIU M B. Smoothed particle hydrodynamics:A meshfree particle method[M]. Hunan:Hunan University Press, 2005.
[9] CUNDALL P A, STARCK O D L. A discrete numerical model for granular assemblies[J]. Geotechnique, 1979,29(1):47-65.
[10] HAN Z, CHEN G, LI Y, et al. A numerical simulation of volumetric enlargement for seismic debris flow using integrated DDA and KANAKO 2D[C]//Frontiers of Discontinuous Numerical Methods and Practical Simulations in Engineering and Disaster Prevention.USA:CRC Press, 2013:281-287.
[11] WANG W, CHEN G, HAN Z, et al. 3D numerical simulation of debris-flow motion using SPH method incorporating non-Newtonian fluid behavior[J]. Natural Hazards, 2016, 81(3):1981-1998.
[12] HUANG Y, ZHANG W, XU Q, et al. Run-out analysis of flow-like landslides triggered by the Ms8.0 2008Wenchuanearthquakeusingsmoothedparticle hydrodynamics[J]. Landslides, 2012, 9(2):275-283.
[13]罗明,廖维,郭双,等.低丘缓坡地区小型崩塌的DDA方法模拟[J].地质灾害与环境保护, 2016, 27(2):84-88.LUO Ming, LIAO Wei, GUO Shuang, et al. Simulation of small collapse in low-slope hilly land by DDA method[J].Journal of Geological Hazards and Environment Preservation, 2016, 27(2):84-88.
[14]殷坤龙,姜清辉,汪洋.新滩滑坡运动全过程的非连续变形分析与仿真模拟[J].岩石力学与工程学报, 2002,22(7):959-962.YIN Kun-long, JIANG Qing-hui, WANG Yang.Discontinuous deformation analysis and simulation of the whole process of the landslide in the Xintan beach[J].Chinese Journal of Rock Mechanics and Engineering,2002, 22(7):959-962.
[15]胡嫚,谢谟文,王立伟.基于弹塑性土体本构模型的滑坡运动过程SPH模拟[J].岩土工程学报, 2016, 38(1):58-67.HU Man, XIE Mo-wen, WANG Li-wei. SPH simulations of post-failure flow of landslides using elastic-plastic soil constitutive model[J]. Chinese Journal of Geotechnical Engineering, 2016, 38(1):58-67.
[16] MCDOUGALL S, HUNGR O. Dynamic modelling of entrainmentinrapidlandslides[J].Canadian Geotechnical Journal, 2005, 42(5):1437-1448.
[17] PASTOR M, BLANC T, HADDAD B, et al. Application of a SPH depth-integrated model to landslide run-out analysis[J]. Landslides, 2014, 11(5):793-812.
[18]许波,谢谟文,胡嫚.基于GIS空间数据的滑坡SPH粒子模型研究[J].岩土力学, 2016, 37(9):2696-2705.XU Bo, XIE Mo-wen, HU Man. SPH landslide model based on GIS spatial data[J]. Rock and Soil Mechanics,2016, 37(9):2696-2705.
[19]张锋.计算土力学[M].北京:人民交通出版社, 2007.ZHANG Feng. Computational soil mechanics[M].Beijing:People’s Communications Press, 2007.
[20] JEFFREY D P, KELIN X W, ALESSANDRO S.Experimental study of the grain-flow, fluid-mud transition in debris flows[J]. The Journal of Geology, 2001, 109:427-447.
[21] JON J M, THOMAS C P. Debris flow rheology:experimental analysis of fine-grained slurries[J]. Water Resources Research, 1992, 28(3):841-857.
[22] PAPANASTASIOU T C. Flows of materials with yield[J].Journal of Rheology, 1987, 31(5):385-404.
[23] FRIGAARD I A, NOUAR C. On the usage of viscosity regularisation methods for visco-plastic fluid flow computation[J]. Journal of Non-Newtonian Fluid Mechanics, 2005, 127:1-26.
[24]乔成,潘华利,欧国强.两相光滑粒子流体动力学方法在动床溃坝问题中的应用[J].中国科学院大学学报,2017, 34(5):625-632.QIAO Cheng, PAN Hua-li, OU Guo-qiang. Application of two-phase smoothed particle hydrodynamics method to dam break over movable bed[J]. Journal of University of Chinese Academy of Sciences, 2017, 34(5):625-632.
[25] ULRICH C, LEONARDI M, RUNG T. Multi-physics SPH simulation of complex marine-engineering hydrodynamic problems[J]. Ocean Engineering, 2013,64:109-121.
[26] MONAGHAN J J. Simulating free surface flows with SPH[J]. Journal of Computational Physics, 1994,110(2):399-406.
[27] UZUOKA R, YASHIMA A, KAWAKAMI T, et al. Fluid dynamics based prediction of liquefaction induced lateral spreading[J]. Computers&Geotechnics, 1998, 22(3-4):243-282.
[28] KOMATINA D, JOVANOVIC M. Experimental study of steady and unsteady free surface flows with water-clay mixtures[J]. Journal of Hydraulic Research, 1997,35(5):579-590.
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