考虑分界面的黏性泥石流下游演进数学模型研究
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摘要
基于分界面理论,以泥石流屈服深度对应的面为分界面,将黏性泥石流分为理想流体和Bingham流体,建立了模拟黏性泥石流演进过程的数学模型和相应计算方法。该模型基于泥石流的运动特征,注重不同层间泥石流流速的差异,并可合理反映泥石流运动速度对其演进形态的影响机制;同时,全面考虑了黏性泥石流在演进过程中所呈现的"舌状体"和"龙头"由上向下翻落现象,因此可更准确描述黏性泥石流在演进过程中的运动状态。采用3组模型试验结果对建立的数学模型与计算方法进行了验证,结果表明:模型计算得出的泥石流泛滥范围和最大堆积厚度与模型试验结果误差在±5%以内,验证了模型的合理性。
Based on the interface theory, taking the corresponding surface of the yielding depth of debris flows as the interface,the viscous debris flow can be divided into ideal fluid and Bingham fluid. Thus, a numerical model and the relative algorithm are developed to simulate the evolution of debris flows. The model is based on the motion feature of the debris and cosiders the velocity differences of debris flows in different layers, thereby, it can reasonably describe the evolution mechanism and the influences on the morphology of debris flows due to the flow velocity. Meanwhile, the model fully considers the phenomena of"tongue-like" and "debris flow head" of actual debris flows, thus, the motion state of the debris flows during the evolution can be depicted accurately. A series of model tests are adopted to verify the proposed numerical model and the algorithm. The comparison between the measured and calculated results indicates that the relative errors of the inundation areas and the maximum accumulation thicknesses are within ±5%, and the rationality of the proposed model is validated.
Based on the interface theory, taking the corresponding surface of the yielding depth of debris flows as the interface,the viscous debris flow can be divided into ideal fluid and Bingham fluid. Thus, a numerical model and the relative algorithm are developed to simulate the evolution of debris flows. The model is based on the motion feature of the debris and cosiders the velocity differences of debris flows in different layers, thereby, it can reasonably describe the evolution mechanism and the influences on the morphology of debris flows due to the flow velocity. Meanwhile, the model fully considers the phenomena of"tongue-like" and "debris flow head" of actual debris flows, thus, the motion state of the debris flows during the evolution can be depicted accurately. A series of model tests are adopted to verify the proposed numerical model and the algorithm. The comparison between the measured and calculated results indicates that the relative errors of the inundation areas and the maximum accumulation thicknesses are within ±5%, and the rationality of the proposed model is validated.
引文
[1]赵学宏,陈志,沈发兴.泥石流灾害国内外研究动态评述[J].自然科学,2015,3(4):225-231.(ZHAO Xue-hong,CHEN Zhi,SHEN Fa-xing.Review on international research dynamic of debris flows disaster[J].Open Journal of Nature Science,2015,3(4):225-231.(in Chinese))
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[3]杜榕桓,李鸿琏,唐邦兴,等.三十年来的中国泥石流研究[J].自然灾害学报,1995,4(1):64-73.(DU Rong-huan,LIHong-lian,TANG Bang-xing,et al.Research on debris flows for thirty years in China[J].Journal of Natural Disasters,1995,4(1):64-73.(in Chinese))
[4]费祥俊,舒安平.泥石流运动机理与灾害防治[M].北京:清华大学出版社,2004.(FEI Xiang-jun,SHU An-ping.Debris flows movement mechanism and disaster prevention[M].Beijing:Tsinghua University Press,2004.(in Chinese)
[5]康志成,李焯芬,马蔼乃,等.中国泥石流研究[M].北京:科学出版社,2004.(KANG Zhi-cheng,LI Chuo-fen,MAAi-nai,et al.Research on debris flow in China[M].Beijing:Science Press,2004.(in Chinese))
[6]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.(in Chinese))
[7]吴积善,康志成,田连权.云南蒋家沟泥石流观测研究[M].北京:科学出版社,1990.(WU Ji-shan,KANG Zhi-cheng,TIAN Lian-quan.Observation and study of debris flow in Jiangjiagou,Yunnan[M].Beijing:Science Press,1990.(in Chinese))
[8]陈春光,姚令侃,杨庆华.入汇主河的泥石流龙头运动机理研究[J].水利学报,2004(1):11-16.(CHEN Chun-guang,YAO Ling-kan,YANG Qing-hua.Movement of debris flow head in main channel at the confluence[J].Journal of Hydraulic Engineering,2004(1):11-16.(in Chinese))
[9]柳金峰,欧国强,游勇,等.沟道约束条件下泥石流扇状堆积试验研究[J].人民黄河,2009(9):72-73.(LIUJin-feng,OU Guo-qiang,YOU Yong,et al.Test and study on fan-like accumulation of mud-rock flow under the conditions of gulley constraint[J].Yellow River,2009(9):72-73.(in Chinese))
[10]王洋,崔鹏,王兆印,等.泥石流龙头的形成及特征研究[J].水利学报,2017(4):473-479.(WANG Yang,CUIPeng,WANG Zhao-yin,et al.Study on the formation and characteristics of height of debris flow head[J].Journal of Hydraulic Engineering,2017(4):473-479.(in Chinese))
[11]JOHNSON A M,RAHN P H.Mobilization of debris flows[J].Zeitschrift Fur Geomorphologie,1970,9(S0):168-186.
[12]弗莱施曼C M.泥石流[M].北京:科学出版社,1986.(FLEISHMAN C M.Debris flow[M].Beijing:Science Press,1986:218-231.(in Chinese))
[13]康志成.泥石流产生的力学分析[J].山地研究,1987(4):225-230.(KANG Zhi-cheng.The mechanical analyses of the generation of debris flow[J].Mountain Research,1987(4):225-230.(in Chinese))
[14]熊刚,费祥俊.泥石流浆体屈服应力的计算方法[J].泥沙研究,1996(1):56-66.(XIONG Gang,FEI Xiang-jun.Calculation of yield stress of debris flow slurry[J].Journal of Sediment Research,1996(1):56-66.(in Chinese))
[15]SCHAMBER D R,MACARTHUR R C.One-dimensional model for mud flows[J].Nasa Sti/recon Technical Report N,1985,86:1334-1339.
[16]王纯祥,白世伟,江崎哲郎,等.泥石流的二维数学模型[J].岩土力学,2007(6):1237-1241.(WANG Chun-xiang,BAI Shi-wei,ESAKI Tetsuro,et al.Two-dimensional mathematical model of debris flow[J].Rock and Soil Mechanics,2007(6):1237-1241.(in Chinese))
[17]MARTINEZ C,MIRALLES W F,GARCIA M R.Verification of a 2D finite element debris flow model using Bingham and cross rheological formulations[J].WITTransactions on Engineering Sciences,2008,60:61-69.
[18]OUYANG C J,HE S,TANG C.Numerical analysis of dynamics of debris flow over erodible beds in Wenchuan earthquake-induced area[J].Engineering Geology,2015,194(SI):62-72.
[19]ILSTAD T,ELVERHOI A,ISSLER D,et al.Subaqueous debris flow behaviour and its dependence on the sand/clay ratio:a laboratory study using particle tracking[J].Marine Geology,2004,213(1/2/3/4):415-438.
[20]乐茂华,韩其为,方春明.基于固液两相流模型的泥石流流速垂向分布研究[J].水利学报,2017(2):168-174.(LEMao-hua,HAN Qi-wei,FANG Chun-ming.Study of vertical velocity distribution in debris flow based on solid-liquid two-phase flow model[J].Journal of Hydraulic Engineering,2017(2):168-174.(in Chinese))
[21]MEI C C,YUHI M.Slow dow of a Bingham fluid in a shallow channel of finite width[J].Journal of Fluid Mechanics,2001,431:135-159.
[22]PELLEGRINO A M,SANTOLO A S D,SCHIPPA L.An integrated procedure to evaluate rheological parameters to model debris flows[J].Engineering Geology,2015,196:88-98.
[23]贺治国,WU W M.考虑水沙相互作用的河堤溃决二维数值模型[J].水动力学研究与进展(A辑),2010,25(2):147-154.(HE Zhi-guo,WU Wei-ming.Two-dimensional levee breaching model considering flow and sediment interaction[J].Chinese Journal of Hydrodynamics,2010,25(2):147-154.(in Chinese))
[24]DOUGLAS J,RUSSELL T F.Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures[J].Siam Journal on Numerical Analysis,1982,19(5):871-885.
[25]刘希林,唐林,张松林,等.泥石流堆积扇地貌特征及其模型试验研究[J].中国地质灾害与防治学报,1992(4):34-42.(LIU Xi-lin,TANG Lin,ZHANG Song-lin,et al.The geomorphological characteristics of debris fans and their model experiments[J].The Chinese Journal of Geological Hazards and Control,1992(4):34-42.(in Chinese))
[2]吴积善,田连权,康志成.泥石流及其综合治理[M].北京:科学出版社,1993.(WU Ji-shan,TIAN Lian-quan,KANGZhi-cheng.Debris flows and comprehensive measures[M].Beijing:Science Press,1993.(in Chinese))
[3]杜榕桓,李鸿琏,唐邦兴,等.三十年来的中国泥石流研究[J].自然灾害学报,1995,4(1):64-73.(DU Rong-huan,LIHong-lian,TANG Bang-xing,et al.Research on debris flows for thirty years in China[J].Journal of Natural Disasters,1995,4(1):64-73.(in Chinese))
[4]费祥俊,舒安平.泥石流运动机理与灾害防治[M].北京:清华大学出版社,2004.(FEI Xiang-jun,SHU An-ping.Debris flows movement mechanism and disaster prevention[M].Beijing:Tsinghua University Press,2004.(in Chinese)
[5]康志成,李焯芬,马蔼乃,等.中国泥石流研究[M].北京:科学出版社,2004.(KANG Zhi-cheng,LI Chuo-fen,MAAi-nai,et al.Research on debris flow in China[M].Beijing:Science Press,2004.(in Chinese))
[6]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.(in Chinese))
[7]吴积善,康志成,田连权.云南蒋家沟泥石流观测研究[M].北京:科学出版社,1990.(WU Ji-shan,KANG Zhi-cheng,TIAN Lian-quan.Observation and study of debris flow in Jiangjiagou,Yunnan[M].Beijing:Science Press,1990.(in Chinese))
[8]陈春光,姚令侃,杨庆华.入汇主河的泥石流龙头运动机理研究[J].水利学报,2004(1):11-16.(CHEN Chun-guang,YAO Ling-kan,YANG Qing-hua.Movement of debris flow head in main channel at the confluence[J].Journal of Hydraulic Engineering,2004(1):11-16.(in Chinese))
[9]柳金峰,欧国强,游勇,等.沟道约束条件下泥石流扇状堆积试验研究[J].人民黄河,2009(9):72-73.(LIUJin-feng,OU Guo-qiang,YOU Yong,et al.Test and study on fan-like accumulation of mud-rock flow under the conditions of gulley constraint[J].Yellow River,2009(9):72-73.(in Chinese))
[10]王洋,崔鹏,王兆印,等.泥石流龙头的形成及特征研究[J].水利学报,2017(4):473-479.(WANG Yang,CUIPeng,WANG Zhao-yin,et al.Study on the formation and characteristics of height of debris flow head[J].Journal of Hydraulic Engineering,2017(4):473-479.(in Chinese))
[11]JOHNSON A M,RAHN P H.Mobilization of debris flows[J].Zeitschrift Fur Geomorphologie,1970,9(S0):168-186.
[12]弗莱施曼C M.泥石流[M].北京:科学出版社,1986.(FLEISHMAN C M.Debris flow[M].Beijing:Science Press,1986:218-231.(in Chinese))
[13]康志成.泥石流产生的力学分析[J].山地研究,1987(4):225-230.(KANG Zhi-cheng.The mechanical analyses of the generation of debris flow[J].Mountain Research,1987(4):225-230.(in Chinese))
[14]熊刚,费祥俊.泥石流浆体屈服应力的计算方法[J].泥沙研究,1996(1):56-66.(XIONG Gang,FEI Xiang-jun.Calculation of yield stress of debris flow slurry[J].Journal of Sediment Research,1996(1):56-66.(in Chinese))
[15]SCHAMBER D R,MACARTHUR R C.One-dimensional model for mud flows[J].Nasa Sti/recon Technical Report N,1985,86:1334-1339.
[16]王纯祥,白世伟,江崎哲郎,等.泥石流的二维数学模型[J].岩土力学,2007(6):1237-1241.(WANG Chun-xiang,BAI Shi-wei,ESAKI Tetsuro,et al.Two-dimensional mathematical model of debris flow[J].Rock and Soil Mechanics,2007(6):1237-1241.(in Chinese))
[17]MARTINEZ C,MIRALLES W F,GARCIA M R.Verification of a 2D finite element debris flow model using Bingham and cross rheological formulations[J].WITTransactions on Engineering Sciences,2008,60:61-69.
[18]OUYANG C J,HE S,TANG C.Numerical analysis of dynamics of debris flow over erodible beds in Wenchuan earthquake-induced area[J].Engineering Geology,2015,194(SI):62-72.
[19]ILSTAD T,ELVERHOI A,ISSLER D,et al.Subaqueous debris flow behaviour and its dependence on the sand/clay ratio:a laboratory study using particle tracking[J].Marine Geology,2004,213(1/2/3/4):415-438.
[20]乐茂华,韩其为,方春明.基于固液两相流模型的泥石流流速垂向分布研究[J].水利学报,2017(2):168-174.(LEMao-hua,HAN Qi-wei,FANG Chun-ming.Study of vertical velocity distribution in debris flow based on solid-liquid two-phase flow model[J].Journal of Hydraulic Engineering,2017(2):168-174.(in Chinese))
[21]MEI C C,YUHI M.Slow dow of a Bingham fluid in a shallow channel of finite width[J].Journal of Fluid Mechanics,2001,431:135-159.
[22]PELLEGRINO A M,SANTOLO A S D,SCHIPPA L.An integrated procedure to evaluate rheological parameters to model debris flows[J].Engineering Geology,2015,196:88-98.
[23]贺治国,WU W M.考虑水沙相互作用的河堤溃决二维数值模型[J].水动力学研究与进展(A辑),2010,25(2):147-154.(HE Zhi-guo,WU Wei-ming.Two-dimensional levee breaching model considering flow and sediment interaction[J].Chinese Journal of Hydrodynamics,2010,25(2):147-154.(in Chinese))
[24]DOUGLAS J,RUSSELL T F.Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures[J].Siam Journal on Numerical Analysis,1982,19(5):871-885.
[25]刘希林,唐林,张松林,等.泥石流堆积扇地貌特征及其模型试验研究[J].中国地质灾害与防治学报,1992(4):34-42.(LIU Xi-lin,TANG Lin,ZHANG Song-lin,et al.The geomorphological characteristics of debris fans and their model experiments[J].The Chinese Journal of Geological Hazards and Control,1992(4):34-42.(in Chinese))