地下水的運動――水文地質(zhì)學(xué)基礎(chǔ)

1、 第四章地下水的運動Groundwater FlowBasis of Hydrogeology 水文地質(zhì)學(xué)基礎(chǔ)環(huán)境與土木工程學(xué)院地質(zhì)災(zāi)害防治與地質(zhì)環(huán)境保護國家重點實驗室吳勇博士、教授本章內(nèi)容4.1 達西定律(Darcys Law4.2 達西定律討論(Discussing4.3 流網(wǎng)(Flow Nets實習(xí)實驗達西實驗與應(yīng)用第四章地下水的運動滲流地下水在巖石空隙中的運動稱為滲流 地下水滲流遵循水力學(xué)基本原理(復(fù)習(xí)差異水力學(xué)研究水在管、渠明流多孔介質(zhì),空隙細小,水流很緩慢滲流從流態(tài)來看地下水多為層流(除巖溶管道外層流紊流側(cè)重穩(wěn)定流(不討論非穩(wěn)定流4.1達西定律(Darcys law達西定律線性滲透

2、定律(linear lawH.Darcy法國水力學(xué)家,1856年(以實驗為基礎(chǔ)研究時期通過大量的室內(nèi)實驗得出的4.1.1 實驗條件:裝置圖P36,圖4-11等徑圓筒裝入均勻砂樣(uniform sand,斷面為2上(下各置一個穩(wěn)定的溢水裝置保持穩(wěn)定水流3實驗時上端進水,下端出水示意流線4砂筒中安裝了2個測壓管5下端測出水量(outflowQCompany Logo First systematic study of the movement of water through a porous medium Henry Darcy Frenchman from DijonEngineerWate

3、r Distribution System “The Public Fountains Of the City of Dijon ”(1856ConditionsIn General, Darcys Law holds for:1. Saturated flow and unsaturated flow2. Steady-state and transient flow3. Flow in aquifers and aquitards4. Flow in homogeneous andheteogeneous systems5. Flow in isotropic or anisotropic

4、 media6. Flow in rocks and granular media4.1.1 達西試驗裝置QO O斷面1斷面2h H 2H 1LLh K Q =達西試驗裝置_兩種1常水頭裝置2變水頭裝置Darcys Experiment He investigated the flow of water in a column of sand He varied:Length and diameter of the columnPorous material in the columnWater levels in inlet and outlet reservoirs Measured th

5、e rate of flow (Q: volume / time4.1.2達西定律(Darcys law 通過變水頭,多次實驗得出:出水端的流量Q與砂柱、測壓管水頭之間的關(guān)系為:(1Lh K Q =gradient hydraulic J I Lh 水力梯度= Q 滲流量;砂柱斷面面積;h 水頭損失(m;L 滲流途徑;K 與試樣有關(guān)的比例常數(shù)。v 由水力學(xué)中水動力學(xué)基本原理:(2Q = K I 4.1.2達西定律(Darcys law 滲透流速根據(jù)水力學(xué)流速與流量的關(guān)系對上式轉(zhuǎn)化:Q = ·V與(2式比較V = K ·I -(3稱為滲透流速(seepage velocity

6、 Darcy velocity specific discharge 上式為單位面積上的流量-稱比流量達西定律中由此看出:滲透流速與水力梯度是一次方成正比故達西定律又稱為線性滲透定律A Q U =VI 關(guān)系圖轉(zhuǎn)下頁VI 曲線砂樣VIO 12V = K ·I (34.2達西定律討論4.2.1 滲透流速(V與過水?dāng)嗝?Q = K I = V過水?dāng)嗝媾c水力學(xué)中的水流過斷面是否一致?否 過水?dāng)嗝?假想的斷面實際孔隙斷面n 孔隙度 實際水流斷面n 有效孔隙度Q/=V 比照水力學(xué),實際流速Q(mào)/= u關(guān)系:地下水滲透流速V = u n e 滲透流速V :是假設(shè)水流通過整個巖層斷面(骨架+空隙時所具

7、有的虛擬的平均流速。意義:研究水量時,只考慮水流通過的總量與平均流速,而不去追蹤實際水質(zhì)點的運移軌跡簡化的研究A QU =過水?dāng)嗝姹容^Q = -KA (h / Lx y負(fù)號的含義是什么?流動方向總是指向水頭低的方向。x yh 1h 2+h 2h 1= 負(fù)數(shù)但流向是有h 1到h 2因此負(fù)號代表流動方向總是指向水頭低的方向。L 3x L T x L 2x L K 是什么?K = 水力傳導(dǎo)性= 滲透系數(shù)Q = -KA (h / L改寫成K = QL / A (-h/LT K 的單位是什么?=K 越大, 流量(Q也愈大。過水?dāng)嗝媾c實際過水?dāng)嗝孢^水?dāng)嗝?實際過斷面(4.2.2水力梯度水力梯度(I(hyd

8、raulic gradient v水力學(xué)中水力坡度(J:單位距離上的水頭損失v是沿滲流途徑上的水頭損失與相應(yīng)的滲流長度之比v vLhLHLHHI2121=gvpZH22+=v物理涵義上來看I:代表著滲流過程中,機械能的損失率,由水力學(xué)中水頭的概念加以分析:v在地下水滲流研究中任意點的水頭表達式總水頭測壓水頭速度水頭機械能勢能動能水力梯度(I 在達西實驗中:4.2.2水力梯度g up Z H 221111+=111p Z H +其原因是u 2/2g 很小而忽略v 在地下水滲流研究中常:總水頭測壓水頭(這是習(xí)慣用法我們?nèi)匀挥肏 = H 1-H 2代表該程L 12 上的總水頭損失,I 則為總能量損失

9、率v 滲流過程中總機械能的損耗原因(與水力學(xué)相近流體的粘滯性引起的內(nèi)摩擦阻力(分子間固體顆粒表面對水流的反作用力4.2.2水力梯度水力梯度(I從達西公式: V = KI來看:當(dāng)I 增大時,V 也愈大;即流速V 愈大,單位滲流途徑上損失的能量也愈大;反過來,水力梯度I愈大時,驅(qū)動水流運動與速度也愈大注意:水頭損失一定要與滲流途徑相對應(yīng)4.2.3滲透系數(shù)滲透系數(shù)K(coefficient of permeability在有些教科書中也稱為水力傳導(dǎo)率(hydraulic conductivity定義:水力梯度為I =1 時的滲透流速(V=KI具有速度量綱L2 T-1VI關(guān)系圖 由公式V = K I

10、分析當(dāng)I一定時,巖層的K愈大,則V也愈大,Q大因此,滲透系數(shù)K是表征巖石透水性的定量指標(biāo)4.2.3滲透系數(shù)滲透系數(shù)K影響因素:以松散巖石,等徑孔隙為例來分析水的重率;動力粘滯系數(shù)從公式即得出: K 與巖石性質(zhì)有關(guān)K (d 02,n e 與流體物理性質(zhì)有關(guān)K (/表4-1列出常見巖石滲透系數(shù)的參考值4.2.4 達西定律的適用范圍(自學(xué)P38中間一段雷諾數(shù)數(shù)介于110 之間e 20n d 32K = The bigger the cross sectional area, the more water will flow th rough (QQ directly proportional to

11、the cross sectional areaCross Sectional Area (AAs the length increases, the Q decreases.Q is inversely proportional to the length of the pipe.Length of the Column (LDifference in height of the water (head from when it begins fl owingthrough the column (h in to when it comes out of the column (h out

12、As the head difference increases, the flow rate increases(QFlow rate is directly proportional to the head differenceHead Difference (h in h out Hydraulic Gradient = Change in Head / Lengthrate at which water flows through is proportional to gradientHydraulic GradientContour Map Maps Topographic Grad

13、ientIn hydrogeology, hydraulic head gradient is driving force HighLowh 2h 1=99 96 = 3(mL =100(mGradient = 3 / 100 = .03NO UNITS!Darcys LawQ = -KA (h / LEmpirical Law Derived from Observation, not from Theory Q = flow rate; volume per time (L3/TA = cross sectional area (L2h = change in head (LL = len

14、gth of column (LK = constant of proportionalityQ = -KA (h / Lx yWhats with the negative sign?Flow is in direction of decreasing hydraulic head x yh 1h 2+h 2h 1= negative number But flow goes from h 1to h 2So negative sign added to indicate that flowis always in the direction of decreasing headL 3x L

15、 T x L 2x L What is K?K = Hydraulic Conductivity = coefficient of permeabilityQ = -KA (h / LRearrange K = QL / A (-h/LT What are the units of K?=The larger the K, the greater the flow rate (Qfunctions of temperature How do we calculateK? K is a function of both:Porous medium The Fluid Porous medium

16、Intrinsic Permeability (k i (function of size of pore openingsFluid Density (Viscosity (K = k i (g / Smaller the sediment, smaller the openings, smaller k i and K 部分介質(zhì)經(jīng)驗滲透系數(shù)值Clay SiltSediments have wide range of values for K (cm/sClay10-910-6Silt10-610-4Silty Sand10-510-3Sands10-310-1Gravel10-21Sand

17、 GravelConstant Head Permeameter Used for sands, noncohesive sediment Cylindrical chamber to hold sample Maintain a constant headWater moves through sampleat constant rateMeasure Q (volume / timeQ = -KA (h/ LRearrangeK = QL / A (-hFalling Head Permeameter Used for low K sedimentsSet up similar to co

18、nstant headDo not provide constant supply of waterMeasure initial head (hoMeasure head after some time t (htContinuity: flow in = flow outd t 2L d c 2t ln h 0hK = K = hydraulic conductivityL = sample lengthh 0= initial head in falling tubeh = final head in falling tubet = timed t = diameter of falli

19、ng head tubed c = diameter of chamberNot a true velocity as part of the column is filled with sedimen tQ = -KA (h / LRearrangeQ A q = -K (h / Lq = specific discharge (Darcian velocity“apparent velocity ”velocity water would move through an aquiferif it were an open conduit Average linear velocity =

20、v =True Velocity Average Mean Linear Velocity?Q Aq = -K (h / LOnly account for area through which flow is occurringFlow area = porosity x areaWater can only flow through the poresQ nAq n =4.3 流網(wǎng)(Flow net4.3.1 基本概念(concept滲流場:地下水流動(運動的空間流網(wǎng)是描述滲流場中地下水流動狀況的有效工具流網(wǎng):是由一系列等水頭線(equipotential lines與流線(flow li

21、nes組成的網(wǎng)格,稱流網(wǎng)(flow net流線:某時刻在滲流場中畫出的一條空間曲線,該曲線上各個水質(zhì)點的流速方向都與這條曲線相切(某時刻各點流向的連線(跡線:流體水質(zhì)點在滲流場中某一時間段內(nèi)的運動軌跡trace line等水頭線:在某時刻,滲流場中水頭相等各點的連線(水勢場的分布4.3.1 基本概念基本概念二維流網(wǎng)圖:平面流網(wǎng):潛水等水位線圖,承壓水等測壓水位線圖 剖面流網(wǎng):含水量厚度較大時,常需要刻畫剖面的水流 流網(wǎng)特點:在各向同性介質(zhì)中,流線與等水頭線正交;在各向異性介質(zhì)中,流線與等水頭線斜交是按一定規(guī)則繪制的,等水頭線(等水頭差繪制,流線(等流量寬,單寬流量相等4.3.2 定性流網(wǎng)繪制定

22、性流網(wǎng)的繪制-(各向同性介質(zhì)中在許多實際工作中,繪制定性流網(wǎng)分析問題很重要 精確流網(wǎng)受許多條件(資料不足等制約,很難辦到 思考回答:邊界條件?有哪幾類?流線起點和終點?等水頭線如何控制?等流量如何確定?“源”resource (發(fā)散流線處“匯”sink (吸收流線處“地下分水線”divide line(分水或分流處為“流線”4.3.2 定性流網(wǎng)繪制繪制步驟(簡要:1尋找已知邊界(濕周,隔水邊界,水位線2分水線、源、匯的確定3畫出滲流場周邊流線與條件4中間內(nèi)插流量等單寬量流量控制流線根數(shù)確定等水頭差間隔參見河間地塊流網(wǎng)圖P40,圖4-4邊界性質(zhì)圖河間地塊流網(wǎng)等水頭線、流線與各類邊界的關(guān)系已知邊界a濕周b隔水邊界cd水位線河間地塊流網(wǎng)的繪制1尋找已知邊界(濕周,隔水邊界,水位線2分水線、源、匯的確定3畫出滲流場周邊流線與條件, 4確定等水頭值,中間內(nèi)插4.3.3 流網(wǎng)的應(yīng)用流網(wǎng)圖的應(yīng)用它反映了滲流