二维盆地地下水流模式与转化规律分析
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摘要
托特(J. Toth)利用解析解在均质各项同性小型潜水盆地中绘制出了三个不同级次的地下水流系统,局部、中间及区域水流系统,以此为基础,托特(J. Toth)提出了地下水流系统理论。而后,托特(J. Toth)及以英格伦(G.B.Engelen)等为代表的后续研究者的共同努力下,地下水流系统理论的概念和方法得到不断完善和发展,这种以系统论的思想从整体角度分析和解决问题,将地下水流场、水化学场和温度场等各种问题纳入同一个框架下进行研究,成为水文地质学发展中的一个重大突破。
作为水文地质领域的一种新方法和新进展,广大水文地质工作者利用各种方法从不同角度丰富和完善了地下水流系统理论。但是,地下水流系统理论在实际应用中尚未完全发挥出自身优越性,在系统模式和理论研究中还存在一些不足,如：Toth潜水盆地模型中渗流区定为水平边界,模拟时上边界采用定水头边界的处理方法；后续研究者也延续了这些相同的假设条件。由此,在盆地地下水流系统级次发育特征和转化规律认识不足,地下水流系统的物理机制尚未完全揭示。针对以上问题,本文主要开展了以下研究：
(1)充分收集和分析前人研究成果,把握地下水流系统理论和地下水数值模拟研究现状、进展、主要趋势及存在的不足。重点分析托特(J. Toth)小型潜水盆地理论数学模型的建立方法、计算结果和地下水流系统级次发育模式,探讨控制盆地地下水流系统的主要影响因素。
(2)以小型潜水盆地模型为基础,运用Visual MODFLOW地下水流数值模拟软件求解Toth盆地模型,进一步分析Toth模型方法对地下水流模式形成、转化和控制因素的规律；针对Toth盆地模型中水平上边界渗流区处理问题,采用定义潜水面为渗流区的改进模拟。
(3)设计通量上边界条件的盆地地下水流模型,探讨盆地地下水流系统发育模式和控制因素；系统分析盆地地下流模式特征和转化规律,揭示地下水流系统的物理机制。
(4)在上述模拟基础上,利用不同条件地下水流系统速度场分析盆地水流特征,探讨盆地水流低速区的分布形式。
通过上述研究工作,得到下述主要认识与结论：
1、Toth盆地模型地下水流系统模式由盆地总斜率与局部变化斜率共同决定。
倾斜正弦定水头条件下,Toth盆地模型中,盆地总斜率(代表盆地的整体坡度)控制中间和区域地下水流系统发育,局部变化斜率(代表正弦曲线振幅大小引起的局部地形起伏)控制局部地下水流系统发育；通过数值模拟,以水平上边界为渗流区的Toth盆地模型中,地下水流模式的发育与转化规律表现为：①盆地总斜率小于局部变化斜率时,发育简单局部一级地下水流系统；②两者相等时,发育局部和中间二级嵌套地下水流系统；③盆地总斜率大于局部变化斜率时,发育复杂的局部、中间和区域三级嵌套地下水流系统；④单一倾斜盆地,才能够发育简单区域地下水流系统。
2、针对Toth盆地模型中的不足,定义潜水面为渗流区上边界的模型更合理。
Toth盆地模型采用水平上边界渗流区和倾斜正弦曲线定水头条件,水平上边界渗流区导致盆地地下水流渗流区为承压模式,而非潜水盆地；倾斜正弦曲线定水头条件则将补给和排泄两大因素人为组合在一起,使得Toth盆地模型在改变盆地深度或者介质渗透性时,盆地通量(补给量和排泄量)发生改变,研究者难以把握单一因素对盆地地下水系统发育的影响和控制作用。对于水平上边界渗流区,改进Toth盆地渗流区为潜水面,使模型成为真正的潜水盆地,模拟得出的地下水流模式更准确。
3、改进的通量上边界盆地模型,得出了盆地地下水流完整模式及其影响因素。
设计通量上边界盆地模型与模拟方法,使入渗补给强度、介质渗透性、盆地形态(长度与深度)和可能势汇独立可控,探讨各因素对盆地地下水流模式发育及转化的影响。
保持通量上边界盆地其他条件一定,定向改变一种影响因素,盆地地下水流模式呈规律性改变：①入渗补给强度ε由强至弱改变,或渗透系数K由小到大改变,盆地地下水流模式由简单局部一级地下水流系统,转变局部和中间二级嵌套地下水流系统,然后转变为复杂的局部、中间和区域三级嵌套地下水流系统,继而演变为局部和区域二级嵌套地下水流系统,最后为简单区域一级地下水流系统。②盆地深度d由浅至深改变,或者盆地长度L由大到小改变,盆地地下水流模式由简单局部一级地下水流系统,转变局部和中间二级嵌套地下水流系统,然后转变为复杂的局部、中间和区域三级嵌套地下水流系统。
4、通量上边界盆地模型,揭示了影响因素对地下水流模式作用存在反向一致性。
对比分析通量上边界改变入渗补给强度ε、渗透系数K、盆地深度d和长度L因素的数值模拟结果,得出：
①盆地其他条件一定,单独由强到弱改变入渗补给强度ε与由小到大改变渗透系数K,盆地地下水流模式相同,定义两者的比值为入渗强度比Ric，该比值在均质各向同性盆地中与平均水力梯度I涵义相同,为地下水流的驱动力,是盆地地下水流模式发育的关键控制因素；保持其他条件不变,只要入渗强度比Ric相同,地下水流模式相同；
②盆地其他条件一定,等比例由浅至深改变盆地深度d和由大到小改变盆地长度L的地下了水流模式相同,定义两者之比为长深比Rld在其条件不变下,长深比Rld相同的盆地,地下水流模式相同；
③盆地可能势汇S是地下水流系统发育的必要条件,多个不同强度可能势汇S存在时,盆地在其他条件作用下可能发育多级地下水流模式；
④影响和控制盆地地下水流模式的各种因素相互影响和共同作用,盆地自组织形成相应的地下水流模式特征,这种自组织过程使得盆地地下水流在当前条件下呈现最优化运动。
本文创新点：通过分析Toth盆地模型与模拟方法的不足,设计通量上边界盆地数值模拟模型,提出了二维均质各向同性盆地地下水流的五种模式及其转化规律；揭示了入渗强度比Ric和长深比Rld对地下水流模式呈反向影响与控制,探究了地下水流模式转化的物理机制；研究结果充实与完善了地下水流系统理论。
J. Toth got three-order groundwater flow systems (local, intermediate and regional flow system) in small drainage basins with homogeneous isotropic medium by analytical solution and based on this study he proposed the theory of groundwater flow system (GWFS). Then with the efforts of J. Toth and G. B. Engelen etc. follow-up researchers, concepts and methods of GWFS develop gradually. The system theory turns out to be a breakthrough for hydrogeology which brings various problems (groundwater flow field, water chemistry field and temperature field etc.) into a frame to study.
As a new way and new trend of hydrogeology, many hydrogeologists utilize different methods to enrich and improve GWFS theory from different points. Yet the theory does not realize its merits completely in practice and the reasons are summarized as:there are defects in Toth's basin model and since the following researchers adopt the same propositions, it is hard to control the single influencing factor; the unclear function characteristics and rules of influential factors of groundwater flow pattern lead to insufficient understanding on order development characteristic and transformation rules of groundwater flow system; the physical mechanism of groundwater is not revealed completely.
The main contents and method of this thesis as follows:
(1) By collecting and analyzing previous research results, this thesis sums up the research status, development, future trends and deficiency of GWFS theory and groundwater numerical simulation.Through analyzing build method, computing results and GWFS order developing patterns of J. Toth's small drainage basin mathematical model, main influencing factors of basin GWFS control are discussed.
(2) Based on small drainage basin model, using Visual MODFLOW to solve Toth's model, the thesis analyzes inefficiencies of the model in formation, transformation and controlling factors of groundwater flow patterns.
(3) Basin groundwater flow model with flux upper-boundary is designed. The physical mechanism of GWFS is revealed by analyzing influencing and controlling factors of GWFS, pattern characteristics and transformation rules of groundwater flows, and making combinational analysis on different influencing and controlling factors.
(4) Presenting basin groundwater flow characteristics through the analysis of GWFS speed field, distribution ways of low-velocity zones of basin water flow are discussed.
We come to the following conclusion after above studies.
1. GWFS development patterns of Toth's basin model are codetermined by total slope and partial slope of basin. In Toth's model, with tilt sine constant head condition, total slope of basin (standing for the whole gradient) determines intermediate and regional GWFS development and partial slope (indicating partial topographic relief caused by sine curve amplitude) determines local GWFS development. In Toth's model with level upper boundary in flow field, Groundwater flow pattern development and transformation rules are shown by numerical simulation.①When total slope is smaller than partial slope, simple local systems are presented.②When total slope is equal to partial slope, local-intermediate nested systems are presented.③When total slope is bigger than partial slope, local-intermediate-regional nested systems are presented.
2. Changing flow field upper boundary into water table of Toth's model is more suitable to overcome defects of Toth's model.
In Toth's model, with the same tilt sine curve constant head upper boundary, basin flux (including recharging and discharge) changes when basin depth or medium permeability is changed. Toth and following researchers study influences of basin size and changing permeability use constant head condition, but defects of the model make researchers hard to study influences and control effects of single factor to groundwater system development. Changing flow field upper boundary into water table of Toth's model is to make the model nearer to the truth and to increase precision of groundwater flow pattern description.
3. Using flux upper boundary model and making infiltration intensity, hydraulic conductivity geometry (depth and length of basin) and potential sinks controlled independently, this thesis discusses influences of single factor change to groundwater flow pattern development and transformation.
Changing a factor while keeping flux upper boundary constant, groundwater flow patterns change regularly.①With a reduction of infiltration intensity or increase of hydraulic conductivity, groundwater flow patterns present similar changes, from simple local systems to local-intermediate nested systems(two real sinks), and then to local-intermediate-regional nested systems (three real sinks), and finally simple regional systems (one real sink only) while other conditions keep constant.②With an increase of basin depth or reduction of basin length, groundwater flow patterns present similar changes, from simple local systems to local-intermediate nested systems(two real sinks), and then to local-intermediate-regional nested systems (three real sinks) while other conditions keep constant.
4. Laws of influential factors effects of flux upper boundary basin correspond reversely. After comparative analysis and defining Ric and Rid, we can understand physical mechanism of GWFS.
Comparing and analyzing the numerical simulation results by changing infiltration intensityε, hydraulic conductivity K, depth d and length L of flux upper boundary basin respectively, we draw the following conclusions.①With a reduction of infiltration intensity or increase of hydraulic conductivity, groundwater flow patterns present similar changes while other conditions keep constant. Defining the ration of infiltration intensity to hydraulic conductivity as Ric, the ratio Ric may be considered as the rate of driven force for groundwater flow due to the same value and dimension with the average hydraulic gradient and is a key factor to groundwater flow pattern development. Characteristics of groundwater flow patterns are same as long as Ric is same, though infiltration intensity or hydraulic conductivity is changed while other conditions keep constant.
②With an increase of basin depth or reduction of basin length, groundwater flow patterns present similar changes, defining the ratio of depth and length as Rld. Same Rld results same pattern of groundwater flow while other conditions keep constant.
③Potential sinks S is a necessity for GWFS development. When Different potential sinks exist, multi-order groundwater flow patterns may be developed under other conditions' effects.
④With the interactions and coactions of various influential factors of groundwater flow patterns, groundwater flow pattern characteristics are self-organized and the process promotes optimizations of groundwater flows
Aiming at the limitation of Tothian modeling method, this study puts forward the modeling method using upper flux-boundary and discusses two-dimension groundwater flow patterns and transformation rules. After defining Rlc and Rid, the thesis examines influential factors which correspond reversely and their physical mechanism. It is not only a major innovation of this study, but also a perfection of groundwater flow system theory.
作为水文地质领域的一种新方法和新进展,广大水文地质工作者利用各种方法从不同角度丰富和完善了地下水流系统理论。但是,地下水流系统理论在实际应用中尚未完全发挥出自身优越性,在系统模式和理论研究中还存在一些不足,如：Toth潜水盆地模型中渗流区定为水平边界,模拟时上边界采用定水头边界的处理方法；后续研究者也延续了这些相同的假设条件。由此,在盆地地下水流系统级次发育特征和转化规律认识不足,地下水流系统的物理机制尚未完全揭示。针对以上问题,本文主要开展了以下研究：
(1)充分收集和分析前人研究成果,把握地下水流系统理论和地下水数值模拟研究现状、进展、主要趋势及存在的不足。重点分析托特(J. Toth)小型潜水盆地理论数学模型的建立方法、计算结果和地下水流系统级次发育模式,探讨控制盆地地下水流系统的主要影响因素。
(2)以小型潜水盆地模型为基础,运用Visual MODFLOW地下水流数值模拟软件求解Toth盆地模型,进一步分析Toth模型方法对地下水流模式形成、转化和控制因素的规律；针对Toth盆地模型中水平上边界渗流区处理问题,采用定义潜水面为渗流区的改进模拟。
(3)设计通量上边界条件的盆地地下水流模型,探讨盆地地下水流系统发育模式和控制因素；系统分析盆地地下流模式特征和转化规律,揭示地下水流系统的物理机制。
(4)在上述模拟基础上,利用不同条件地下水流系统速度场分析盆地水流特征,探讨盆地水流低速区的分布形式。
通过上述研究工作,得到下述主要认识与结论：
1、Toth盆地模型地下水流系统模式由盆地总斜率与局部变化斜率共同决定。
倾斜正弦定水头条件下,Toth盆地模型中,盆地总斜率(代表盆地的整体坡度)控制中间和区域地下水流系统发育,局部变化斜率(代表正弦曲线振幅大小引起的局部地形起伏)控制局部地下水流系统发育；通过数值模拟,以水平上边界为渗流区的Toth盆地模型中,地下水流模式的发育与转化规律表现为：①盆地总斜率小于局部变化斜率时,发育简单局部一级地下水流系统；②两者相等时,发育局部和中间二级嵌套地下水流系统；③盆地总斜率大于局部变化斜率时,发育复杂的局部、中间和区域三级嵌套地下水流系统；④单一倾斜盆地,才能够发育简单区域地下水流系统。
2、针对Toth盆地模型中的不足,定义潜水面为渗流区上边界的模型更合理。
Toth盆地模型采用水平上边界渗流区和倾斜正弦曲线定水头条件,水平上边界渗流区导致盆地地下水流渗流区为承压模式,而非潜水盆地；倾斜正弦曲线定水头条件则将补给和排泄两大因素人为组合在一起,使得Toth盆地模型在改变盆地深度或者介质渗透性时,盆地通量(补给量和排泄量)发生改变,研究者难以把握单一因素对盆地地下水系统发育的影响和控制作用。对于水平上边界渗流区,改进Toth盆地渗流区为潜水面,使模型成为真正的潜水盆地,模拟得出的地下水流模式更准确。
3、改进的通量上边界盆地模型,得出了盆地地下水流完整模式及其影响因素。
设计通量上边界盆地模型与模拟方法,使入渗补给强度、介质渗透性、盆地形态(长度与深度)和可能势汇独立可控,探讨各因素对盆地地下水流模式发育及转化的影响。
保持通量上边界盆地其他条件一定,定向改变一种影响因素,盆地地下水流模式呈规律性改变：①入渗补给强度ε由强至弱改变,或渗透系数K由小到大改变,盆地地下水流模式由简单局部一级地下水流系统,转变局部和中间二级嵌套地下水流系统,然后转变为复杂的局部、中间和区域三级嵌套地下水流系统,继而演变为局部和区域二级嵌套地下水流系统,最后为简单区域一级地下水流系统。②盆地深度d由浅至深改变,或者盆地长度L由大到小改变,盆地地下水流模式由简单局部一级地下水流系统,转变局部和中间二级嵌套地下水流系统,然后转变为复杂的局部、中间和区域三级嵌套地下水流系统。
4、通量上边界盆地模型,揭示了影响因素对地下水流模式作用存在反向一致性。
对比分析通量上边界改变入渗补给强度ε、渗透系数K、盆地深度d和长度L因素的数值模拟结果,得出：
①盆地其他条件一定,单独由强到弱改变入渗补给强度ε与由小到大改变渗透系数K,盆地地下水流模式相同,定义两者的比值为入渗强度比Ric，该比值在均质各向同性盆地中与平均水力梯度I涵义相同,为地下水流的驱动力,是盆地地下水流模式发育的关键控制因素；保持其他条件不变,只要入渗强度比Ric相同,地下水流模式相同；
②盆地其他条件一定,等比例由浅至深改变盆地深度d和由大到小改变盆地长度L的地下了水流模式相同,定义两者之比为长深比Rld在其条件不变下,长深比Rld相同的盆地,地下水流模式相同；
③盆地可能势汇S是地下水流系统发育的必要条件,多个不同强度可能势汇S存在时,盆地在其他条件作用下可能发育多级地下水流模式；
④影响和控制盆地地下水流模式的各种因素相互影响和共同作用,盆地自组织形成相应的地下水流模式特征,这种自组织过程使得盆地地下水流在当前条件下呈现最优化运动。
本文创新点：通过分析Toth盆地模型与模拟方法的不足,设计通量上边界盆地数值模拟模型,提出了二维均质各向同性盆地地下水流的五种模式及其转化规律；揭示了入渗强度比Ric和长深比Rld对地下水流模式呈反向影响与控制,探究了地下水流模式转化的物理机制；研究结果充实与完善了地下水流系统理论。
J. Toth got three-order groundwater flow systems (local, intermediate and regional flow system) in small drainage basins with homogeneous isotropic medium by analytical solution and based on this study he proposed the theory of groundwater flow system (GWFS). Then with the efforts of J. Toth and G. B. Engelen etc. follow-up researchers, concepts and methods of GWFS develop gradually. The system theory turns out to be a breakthrough for hydrogeology which brings various problems (groundwater flow field, water chemistry field and temperature field etc.) into a frame to study.
As a new way and new trend of hydrogeology, many hydrogeologists utilize different methods to enrich and improve GWFS theory from different points. Yet the theory does not realize its merits completely in practice and the reasons are summarized as:there are defects in Toth's basin model and since the following researchers adopt the same propositions, it is hard to control the single influencing factor; the unclear function characteristics and rules of influential factors of groundwater flow pattern lead to insufficient understanding on order development characteristic and transformation rules of groundwater flow system; the physical mechanism of groundwater is not revealed completely.
The main contents and method of this thesis as follows:
(1) By collecting and analyzing previous research results, this thesis sums up the research status, development, future trends and deficiency of GWFS theory and groundwater numerical simulation.Through analyzing build method, computing results and GWFS order developing patterns of J. Toth's small drainage basin mathematical model, main influencing factors of basin GWFS control are discussed.
(2) Based on small drainage basin model, using Visual MODFLOW to solve Toth's model, the thesis analyzes inefficiencies of the model in formation, transformation and controlling factors of groundwater flow patterns.
(3) Basin groundwater flow model with flux upper-boundary is designed. The physical mechanism of GWFS is revealed by analyzing influencing and controlling factors of GWFS, pattern characteristics and transformation rules of groundwater flows, and making combinational analysis on different influencing and controlling factors.
(4) Presenting basin groundwater flow characteristics through the analysis of GWFS speed field, distribution ways of low-velocity zones of basin water flow are discussed.
We come to the following conclusion after above studies.
1. GWFS development patterns of Toth's basin model are codetermined by total slope and partial slope of basin. In Toth's model, with tilt sine constant head condition, total slope of basin (standing for the whole gradient) determines intermediate and regional GWFS development and partial slope (indicating partial topographic relief caused by sine curve amplitude) determines local GWFS development. In Toth's model with level upper boundary in flow field, Groundwater flow pattern development and transformation rules are shown by numerical simulation.①When total slope is smaller than partial slope, simple local systems are presented.②When total slope is equal to partial slope, local-intermediate nested systems are presented.③When total slope is bigger than partial slope, local-intermediate-regional nested systems are presented.
2. Changing flow field upper boundary into water table of Toth's model is more suitable to overcome defects of Toth's model.
In Toth's model, with the same tilt sine curve constant head upper boundary, basin flux (including recharging and discharge) changes when basin depth or medium permeability is changed. Toth and following researchers study influences of basin size and changing permeability use constant head condition, but defects of the model make researchers hard to study influences and control effects of single factor to groundwater system development. Changing flow field upper boundary into water table of Toth's model is to make the model nearer to the truth and to increase precision of groundwater flow pattern description.
3. Using flux upper boundary model and making infiltration intensity, hydraulic conductivity geometry (depth and length of basin) and potential sinks controlled independently, this thesis discusses influences of single factor change to groundwater flow pattern development and transformation.
Changing a factor while keeping flux upper boundary constant, groundwater flow patterns change regularly.①With a reduction of infiltration intensity or increase of hydraulic conductivity, groundwater flow patterns present similar changes, from simple local systems to local-intermediate nested systems(two real sinks), and then to local-intermediate-regional nested systems (three real sinks), and finally simple regional systems (one real sink only) while other conditions keep constant.②With an increase of basin depth or reduction of basin length, groundwater flow patterns present similar changes, from simple local systems to local-intermediate nested systems(two real sinks), and then to local-intermediate-regional nested systems (three real sinks) while other conditions keep constant.
4. Laws of influential factors effects of flux upper boundary basin correspond reversely. After comparative analysis and defining Ric and Rid, we can understand physical mechanism of GWFS.
Comparing and analyzing the numerical simulation results by changing infiltration intensityε, hydraulic conductivity K, depth d and length L of flux upper boundary basin respectively, we draw the following conclusions.①With a reduction of infiltration intensity or increase of hydraulic conductivity, groundwater flow patterns present similar changes while other conditions keep constant. Defining the ration of infiltration intensity to hydraulic conductivity as Ric, the ratio Ric may be considered as the rate of driven force for groundwater flow due to the same value and dimension with the average hydraulic gradient and is a key factor to groundwater flow pattern development. Characteristics of groundwater flow patterns are same as long as Ric is same, though infiltration intensity or hydraulic conductivity is changed while other conditions keep constant.
②With an increase of basin depth or reduction of basin length, groundwater flow patterns present similar changes, defining the ratio of depth and length as Rld. Same Rld results same pattern of groundwater flow while other conditions keep constant.
③Potential sinks S is a necessity for GWFS development. When Different potential sinks exist, multi-order groundwater flow patterns may be developed under other conditions' effects.
④With the interactions and coactions of various influential factors of groundwater flow patterns, groundwater flow pattern characteristics are self-organized and the process promotes optimizations of groundwater flows
Aiming at the limitation of Tothian modeling method, this study puts forward the modeling method using upper flux-boundary and discusses two-dimension groundwater flow patterns and transformation rules. After defining Rlc and Rid, the thesis examines influential factors which correspond reversely and their physical mechanism. It is not only a major innovation of this study, but also a perfection of groundwater flow system theory.
引文
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[9]E.拉兹洛(闵家胤译).从贝塔朗菲的著述看一般系统论的起源[J].系统辩证学学报,1993,2：60-64.
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[22]Toth J, Miller R F. Possible effects of erosional changes of the topographic relief on pore pressures at depth. Water Resources Research.1983,19(6):1587-1597.
[23]Toth J, Sheng G. Enhancing safety of nuclear waste disposal by exploiting regional groundwater flow:the recharge area concept. Hydrogeology Journal.1996,4(4):4-25.
[24]Zijl W, Scale aspects of groundwater flow and transport systems. Hydrogeology Journal.1999,7(1),139-150.
[25]Jiang XW, Wan L, Wang XS, Ge SM. Effect of exponential decay in hydraulic conductivity with depth on regional groundwater flow. Geophysical Research Letters,2009,36(24), L24402.
[26]陈梦熊,许志荣.地下水系统论文选编[M].地矿部科技顾问委员会,河南地矿部环境水文地质总站编印,1984：1-15.
[27]韩再生.从局部到区域尺度认识地下水流——第33届国际水文地质大会综述[J].水文地质工程地质,2005,2：118-120.
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