基于变渗透系数的地下水开采-地面沉降三维模拟研究
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摘要
在地面沉降过程中伴随着土体孔隙率和渗透系数的变化,但在模拟计算中为了降低计算量而忽略其变化,因而在一定程度上造成模拟结果与实际偏离。为了研究地面沉降数值模拟过程中孔隙率和渗透系数变化对模拟结果的具体影响,在Biot固结理论的基础上,耦合了Kozeny-Carman方程,建立了考虑固结过程中渗透系数变化的三维固结模型。以北京平原区的典型含水层结构为模拟对象,分别在考虑和忽略渗透系数变化的情况下进行抽水模拟,发现在考虑渗透系数变化的情况下,抽水后地层的渗透率体现了不均匀变化,在抽水井井壁附近渗透系数有所降低;考虑渗透系数变化下的地表最终形变量大于忽略渗透系数变化的情况;忽略渗透系数变化导致的模拟误差在沉降初期较小且具有继续发展的趋势,中后期较大并逐渐趋于平稳,且这一误差与抽水量正相关,与承压含水层压缩模量和渗透系数负相关,且随着承压含水层厚度的增加呈现先增大后减小的趋势。
Porosity and permeability of soil keep on changing during the process of land subsidence. However,these are often ignored in order to reduce the computation in the simulation,thus the simulation results may deviate from the actual situation. In order to examine the influence of variable porosity and permeability on the simulation results of subsidence,a 3D consolidation model considering the variation in permeability during consolidation is established based on the coupling of the Biot consolidation theory and Kozeny-Carman equation. Pumping simulations are carried out under the condition of considering and neglecting the variation of permeability in the typical aquifer structure in the Beijing plain. It is found that the change in the layer permeability after pumping is uneven,and the permeability is reduced near the well wall. Considering the change in permeability,the final deformation of the surface is larger than that of ignoring the variation in permeability. The simulation error caused by neglecting the variation in permeability is smaller and has atendency to develop in the early stage of settlement,and it is larger and more stable in the middle and later stages. This error is positively correlated with the pumping volume and is negatively correlated with the compression modulus and permeability of confined aquifer. With the increasing thickness of the confined aquifer,the error first increases and then decreases.
Porosity and permeability of soil keep on changing during the process of land subsidence. However,these are often ignored in order to reduce the computation in the simulation,thus the simulation results may deviate from the actual situation. In order to examine the influence of variable porosity and permeability on the simulation results of subsidence,a 3D consolidation model considering the variation in permeability during consolidation is established based on the coupling of the Biot consolidation theory and Kozeny-Carman equation. Pumping simulations are carried out under the condition of considering and neglecting the variation of permeability in the typical aquifer structure in the Beijing plain. It is found that the change in the layer permeability after pumping is uneven,and the permeability is reduced near the well wall. Considering the change in permeability,the final deformation of the surface is larger than that of ignoring the variation in permeability. The simulation error caused by neglecting the variation in permeability is smaller and has atendency to develop in the early stage of settlement,and it is larger and more stable in the middle and later stages. This error is positively correlated with the pumping volume and is negatively correlated with the compression modulus and permeability of confined aquifer. With the increasing thickness of the confined aquifer,the error first increases and then decreases.
引文
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[14]陈武,裴万胜,李双洋,等.饱和多孔介质流-固耦合的数值模型及工程应用[J].岩石力学与工程学报,2013,32(增刊2):3346-3354.[CHEN W,PEI W S,LI S Y,et al.Numerical simulation and engineering application of solid-fluid coupled model for saturated porous media[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(Sup2):3346-3354.(in Chinese)]
[15]金玮泽,骆祖江,陈兴贤,等.地下水渗流与地面沉降耦合模拟[J].地球科学-中国地质大学学报,2014,39(5):611-619.[JIN W Z,LUO Z J,CHEN X X,et al.Coupling simulation of groundwater seepage and land subsidence[J].Earth Science Journal of China University of Geosciences,2014,39(5):611-619.(in Chinese)]
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[17]Terzaghi K.Principle of soil mechanics IV:settlement and consolidation of Clay[J].Engineering News Record,1925,5(8):874-878.
[18]Biot M A.General theory of three-dimensional consolidation[J].Journal of Applied Physics,1941,38(12):155-164.
[19]Seelheim F.Methoden zur bestimmung der durchlssigkeit des bodens[J].Zeitschrift für Analytische Chemie,1880,19(1):387-402.
[20]Carman P C.Fluid flow through granular beds[J].Transactions-Institution of Chemical Engineeres,1937,15:150-166.
[21]刘波,张功,江永华,等.基于变渗透系数的深基坑单井抽水沉降研究[J].工程地质学报,2014,22(6):1123-1127.[LIU B,ZHANG G,JIANG Y H,et al.Settlement research on single pumping well of foundation pit using changeable permeability coefficient model[J].Journal of Engineering Geology,2014,22(6):1123-1127.(in Chinese)]
[22]刘江涛,廖东良,葛新民.基于Kozeny-Carman方程的水相相对渗透率计算方法[J].科学技术与工程,2012,12(29):7500-7504.[LIU J T,LIAO D L,GE X M.Water Phase Relative Permeability Calculation Based on Kozeny-Carman Equation[J].Science Technology and Engineering,2012,12(29):7500-7504.(in Chinese)]
[23]徐鹏,邱淑霞,姜舟婷,等.各向同性多孔介质中Kozeny-Carman常数的分形分析[J].重庆大学学报,2011,34(4):78-82.[XU P,QIU S X,JIANG Z T,et al.Fractal analysis of Kozeny-Carman constant in the homogenous porous media[J].Journal of Chongqing University,2011,34(4):78-82.(in Chinese)]
[24]郑斌,李菊花.基于Kozeny-Carman方程的渗透率分形模型[J].天然气地球科学,2015,26(1):193-198.[ZHENG B,LI J H.A New fractal permeability model for porous media based on KozenyCarman equation[J].Natural Gas Geoscience,2015,26(1):193-198.(in Chinese)]
[25]Dvorkin J,Gvirtzman H,Nur A.Kozeny-Carman Relation for a Medium with Tapered Cracks[J].Geophysical Research Letters,1991,18(5):877-880.
[26]Zhu L,Gong H,Li X,et al.Land subsidence due to groundwater withdrawal in the northern Beijing plain,China[J].Engineering Geology,2015,193:243-255.
[27]王非,缪林昌,黎春林.抽水地面沉降中含水层渗流变形耦合模型研究[J].铁道工程学报,2011(7):1-5.[WANG F,MIAO L C,LI C L.Study on coupled model for aquifer seepage deformation during pumped ground subsidence[J].Journal of Railway Engineering Society,2011(7):1-5.(in Chinese)]
[28]熊小锋,施小清,吴剑锋,等.弹塑性变形条件下抽水引起的地面沉降三维数值模拟[J].水文地质工程地质,2017,44(2):151-159.[XIONG X F,SHI X Q,WU J F,et al.3D numerical simulation of elas to-plastic land subsidence induced by groundwater pumping[J].Hydrogeology&Engineering Geology,2017,44(2):151-159.(in Chinese)]
[29]苏晨,崔亚莉,邵景力,等.基于理论法的地面沉降数值模型进展[J].水文地质工程地质,2014,41(6):147-152.[SU C,CUI Y L,SHAO J L,et al.Advances in numerical models of land subsidence based on comprehensive theories[J].Hydrogeology&Engineering Geology,2014,41(6):147-152.(in Chinese)]
[2]杨建民,纪森林.抽水导致区域性地面沉降中的slnr线性关系[J].岩土工程学报,2016,38(9):1606-1614.[YANG J M,JI S L.Linear s-lnr relation of regional land subsidence induced by groundwater withdrawal[J].Chinese Journal of Geotechnical Engineering,2016,38(9):1606-1614.(in Chinese)]
[3]王祎萍.北京市超量开采地下水引起的地面沉降研究[J].勘察科学技术,2004(5):46-49.[WANG Y P.Study on land subsidence caused by overexploiting groundwater in Beijing[J].Site Investigation Science and Technology,2004(5):46-49.(in Chinese)]
[4]杨勇,郑凡东,刘立才,等.北京平原区地下水水位与地面沉降关系研究[J].工程勘察,2013,41(8):44-48.[YANG Y,ZHENG F D,LIU L C,et al.Study on the correlation between groundwater level and ground subsidence in Beijing plain areas[J].Geotechnical Investigation&Surveying,2013,41(8):44-48.(in Chinese)]
[5]周毅,罗郧,郭高轩,等.冲洪积平原地面沉降特征及主控因素——以北京平原为例[J].地质通报,2016,35(12):2100-2110.[ZHOU Y,LUO Y,GUO G X,et al.A study of the characteristics of land subsidence and the main control factors in the alluvial plain:a case study of Beijing plain[J].Geological Bulletin of China,2016,35(12):2100-2110.(in Chinese)]
[6]吴意谦,朱彦鹏.考虑侧向变形下抽降潜水引起地面沉降的计算[J].华中科技大学学报(自然科学版),2016,44(4):116-120.[WU Y Q,ZHU Y P.Calculation of settlement considering lateral deformation due to pumping of phreatic aquifer[J].J Huazhong Univ of Sci&Tech(Natural Science Edition),2016,44(4):116-120.(in Chinese)]
[7]吴意谦,朱彦鹏.考虑疏干带非饱和土影响下基坑降水引起地面沉降的计算[J].工程力学,2016,33(3):179-187.[WU Y Q,ZHU Y P.Calculation of settlement considering unsaturated soil influence on the dewatering of foundation pits[J].Engineering Mechanics,2016,33(3):179-187.(in Chinese)]
[8]田芳,郭萌,罗勇,等.北京地面沉降区土体变形特征[J].中国地质,2012,39(1):236-242.[TIAN F,GUO M,LUO Y,et al.The deformation behavior of soil mass in the subsidence area of Beijing[J].Geology in China,2012,39(1):236-242.(in Chinese)]
[9]张雯,宫辉力,陈蓓蓓,等.北京典型区地面沉降演化特征与成因分析[J].地球信息科学学报,2015,17(8):909-916.[ZHANG W,GONG H L,CHEN B B,et al.Evolution and genetic analysis of land subsidence in Beijing typical area[J].Geo Information Science,2015,17(8):909-916.(in Chinese)]
[10]姜洪涛.苏锡常地区地面沉降及其若干问题探讨[J].第四纪研究,2005,25(1):29-33.[JIANG H T.Problems and discussions in the study of land subsidence in the suzhou-wuxi-changzhou area[J].Quaternary Sciences,2005,25(1):29-33.(in Chinese)]
[11]胡蓓蓓,姜衍祥,周俊,等.天津市滨海地区地面沉降灾害风险评估与区划[J].地理科学,2008,28(5):693-697.[HU B B,JANG Y X,ZHOU J,et al.Assessment and zonation of land subsidence disaster risk of Tianjin Binhai area[J].Scientia Geographica Sinica,2008,28(5):693-697.(in Chinese)]
[12]陈崇希,裴顺平.地下水开采—地面沉降模型研究[J].水文地质工程地质,2001,28(2):5-8.[CHEN C X,PEI S P.Study on model of groundwater exploitation and ground subsidence[J].Hydrogeology&Engineering Geology,2001,28(2):5-8.(in Chinese)]
[13]沈孝宇,孙愫文,周国云,等.宁波城市地面沉降物理数学模型及沉降预测[J].地球科学,1989,14(2):135-144.[SHEN X Y,SUN S W,ZHOU G Y,et al.Physical mathematics model and prediction on subsidence of Ningbo city[J].Earth Science,1989,14(2):135-144.(in Chinese)]
[14]陈武,裴万胜,李双洋,等.饱和多孔介质流-固耦合的数值模型及工程应用[J].岩石力学与工程学报,2013,32(增刊2):3346-3354.[CHEN W,PEI W S,LI S Y,et al.Numerical simulation and engineering application of solid-fluid coupled model for saturated porous media[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(Sup2):3346-3354.(in Chinese)]
[15]金玮泽,骆祖江,陈兴贤,等.地下水渗流与地面沉降耦合模拟[J].地球科学-中国地质大学学报,2014,39(5):611-619.[JIN W Z,LUO Z J,CHEN X X,et al.Coupling simulation of groundwater seepage and land subsidence[J].Earth Science Journal of China University of Geosciences,2014,39(5):611-619.(in Chinese)]
[16]安庆军.太沙基固结理论的若干问题研究[D].南京:南京工业大学,2007.[AN Q J.Study on someproblems of Terzaghi consolidation theory[D].Nanjing:Nanjing University of Technology,2007.(in Chinese)]
[17]Terzaghi K.Principle of soil mechanics IV:settlement and consolidation of Clay[J].Engineering News Record,1925,5(8):874-878.
[18]Biot M A.General theory of three-dimensional consolidation[J].Journal of Applied Physics,1941,38(12):155-164.
[19]Seelheim F.Methoden zur bestimmung der durchlssigkeit des bodens[J].Zeitschrift für Analytische Chemie,1880,19(1):387-402.
[20]Carman P C.Fluid flow through granular beds[J].Transactions-Institution of Chemical Engineeres,1937,15:150-166.
[21]刘波,张功,江永华,等.基于变渗透系数的深基坑单井抽水沉降研究[J].工程地质学报,2014,22(6):1123-1127.[LIU B,ZHANG G,JIANG Y H,et al.Settlement research on single pumping well of foundation pit using changeable permeability coefficient model[J].Journal of Engineering Geology,2014,22(6):1123-1127.(in Chinese)]
[22]刘江涛,廖东良,葛新民.基于Kozeny-Carman方程的水相相对渗透率计算方法[J].科学技术与工程,2012,12(29):7500-7504.[LIU J T,LIAO D L,GE X M.Water Phase Relative Permeability Calculation Based on Kozeny-Carman Equation[J].Science Technology and Engineering,2012,12(29):7500-7504.(in Chinese)]
[23]徐鹏,邱淑霞,姜舟婷,等.各向同性多孔介质中Kozeny-Carman常数的分形分析[J].重庆大学学报,2011,34(4):78-82.[XU P,QIU S X,JIANG Z T,et al.Fractal analysis of Kozeny-Carman constant in the homogenous porous media[J].Journal of Chongqing University,2011,34(4):78-82.(in Chinese)]
[24]郑斌,李菊花.基于Kozeny-Carman方程的渗透率分形模型[J].天然气地球科学,2015,26(1):193-198.[ZHENG B,LI J H.A New fractal permeability model for porous media based on KozenyCarman equation[J].Natural Gas Geoscience,2015,26(1):193-198.(in Chinese)]
[25]Dvorkin J,Gvirtzman H,Nur A.Kozeny-Carman Relation for a Medium with Tapered Cracks[J].Geophysical Research Letters,1991,18(5):877-880.
[26]Zhu L,Gong H,Li X,et al.Land subsidence due to groundwater withdrawal in the northern Beijing plain,China[J].Engineering Geology,2015,193:243-255.
[27]王非,缪林昌,黎春林.抽水地面沉降中含水层渗流变形耦合模型研究[J].铁道工程学报,2011(7):1-5.[WANG F,MIAO L C,LI C L.Study on coupled model for aquifer seepage deformation during pumped ground subsidence[J].Journal of Railway Engineering Society,2011(7):1-5.(in Chinese)]
[28]熊小锋,施小清,吴剑锋,等.弹塑性变形条件下抽水引起的地面沉降三维数值模拟[J].水文地质工程地质,2017,44(2):151-159.[XIONG X F,SHI X Q,WU J F,et al.3D numerical simulation of elas to-plastic land subsidence induced by groundwater pumping[J].Hydrogeology&Engineering Geology,2017,44(2):151-159.(in Chinese)]
[29]苏晨,崔亚莉,邵景力,等.基于理论法的地面沉降数值模型进展[J].水文地质工程地质,2014,41(6):147-152.[SU C,CUI Y L,SHAO J L,et al.Advances in numerical models of land subsidence based on comprehensive theories[J].Hydrogeology&Engineering Geology,2014,41(6):147-152.(in Chinese)]