邊坡埋設排水管對於地下水位差異分析之水文模式改進研究

A Study on Improving Hydrologic Simulation Model Algorithms for Groundwater Table Analysis in Slopeland with Drain Pipes

洪國展(Kuo-Chan Hung)

指導教授 ： 李天浩

國立臺灣大學/工學院/土木工程學研究所/博士(2007年)

https://doi.org/10.6342/NTU.2007.01341

摘要

本研究的目的是以水文模式探討邊坡中含有埋設排水管時，對於坡地地下水位差異的影響。坡地中地下水位與孔隙水壓的變化，為影響坡地是否穩定的主因之一，為了促進地下水排除以降低孔隙水壓，進而使坡地較為穩定，於邊坡處埋設排水管為最常見的工程處理方式，但其實際降低地下水位的效益卻難以利用經驗加以衡量。本研究針對此項問題，建立能夠描述含埋設排水管之坡地地下水位變化的模式，以探討在不同排水管設置方式下對於降低地下水位的效益。
在含有排水管的坡地地下水問題中，可分為三項主要議題：1.變飽和度地下水問題在數值模式計算時具有質量不守恆的特性，且於坡地下游端具有特殊的滲流面問題，若無法解決質量不守恆與滲流面估計，便難以獲得正確的地下水位與孔隙水壓分佈；2.三維模式可描述不規則模擬域，但其大量的網格將使計算效率降低，若可以在含有排水管坡地的問題中將三維模式進行簡化，並同時符合可容許誤差，便能夠提高計算效率；3.排水管水流與坡地地下水水流為兩種不同的流動機制，將其耦合時排水管對於坡地而言具有匯聚水流的效應，並在周圍土壤中形成類似奇異點的效應，此外，當大量水體積進入排水管而形成滿管時，排水管中水體積可能透過管上孔洞回到周圍土壤之中，因此對於排水管而言，在滿管之後並非為一般壓力管流的流動方式，必須在排水管與周圍土壤之間，尋求一種符合物理行為的水量交換估計與邊界條件對應，才能良好解決在坡地地下水模式與管路傳輸模式之間的耦合。
針對坡地地下水問題，本研究引用Celia等人(1990)與Neuman(1973)的研究，解決質量不守恆與滲流面估計的問題。同時提出沿坡面方向將三維坡地劃分為多層垂直二維模擬域的方式，建立準三維變飽和度地下水模式以改進三維模擬的效率問題，並在含有排水孔位置的每一垂直二維模擬域上，引用Fipps等人(1986)的研究，以兼顧計算精度與效率。對於含排水管的坡地問題中，本研究提出「虛擬管柱」的觀念，解決排水管水流傳輸時可能在明渠╱滿管流流況之間的切換，以及將準三維變飽和度地下水模式與明渠╱滿管流模式耦合時所面對的邊界條件對應問題。
在變飽和度地下水模式的問題中，具有因為數值計算所造成質量不守恆的問題，以及在坡地下游所特有的滲流面邊界。本研究以有限元素法結合Galerkin的數值技巧，建立三維與垂直二維變飽和度地下水流數值模式，在三維模式中將模擬域劃分為多數個四面體元素，而在二維模式中將模擬域劃分為多數個三角形元素，同時針對質量不守恆與下游滲流面位置估計的問題，分別採用Celia等人(1990)所提出質量守恆處理方式與Neuman(1973)所提出滲流面位置迭代求解技巧加以解決。研究結果發現，利用有限元素法結合上述兩項改進技術，能夠獲得正確描述孔隙水壓分佈與滲流面邊界位置的變飽和度地下水模式。
本研究提出將坡地沿坡面方向劃分成數個垂直剖面的方式，利用垂直二維變飽和度地下水模式模擬每一垂直剖面，並配合剖面之間交換量的計算，構築準三維變飽和度地下水模式，模式中同時提出於最下游剖面處建立一虛擬剖面的方式，以解決滲流面的問題。研究結果顯示，利用以上技術所建立的準三維變飽和度地下水模式，可以獲得與三維變飽和度地下水模式相近的模擬結果，並能夠提高計算效率。
對單層垂直二維地下水模式而言，當模擬域中具有排水孔位置時，排水孔具有匯聚水流的效應，並在鄰近土壤造成高水力梯度，且在此區域中的數值模擬誤差較大，要減少計算誤差，必須在近排水管區布置細化網格。本研究利用Fipps等人(1986)的作法，以簡化網格配置及單點代表排水孔位置的方式，結合電阻調整法所推求的簡化網格等價飽和水力傳導係數加以模擬，並將電阻調整法擴充至完全飽和╱未飽和土層同時存在的情況。研究結果顯示，結合以上的改進技術可以獲得與細化網格佈置模擬下所得的相同結果，其無論在地下水位面位置、孔隙水壓分佈或是排水節點排水量上都相當接近，並且能夠大幅降低電腦計算時間。
本研究提出「虛擬管柱」的概念，解決在明渠╱滿管流流況之間轉換的問題，並作為耦合準三維變飽和度地下水模式與明渠╱滿管流模式的基礎。藉由此虛擬管柱設定，便可以利用相同的演算邏輯穩定計算明渠╱滿管流流況之間的變換，而在選擇適當的虛擬管柱底面積下，可以使得滿管後進入虛擬管柱內的水量變化等於排水節點代表網格的含水量變化，並且虛擬管柱內水位的差異等於排水節點水頭的差異，進而獲得兩模式狀態變數的對應。研究結果顯示，此耦合模式能夠以前人實驗良好驗證，並可以在明渠╱滿管流之間良好切換，對於土層進水╱退水的反應也能穩定描述。
本研究同時利用此耦合模式分析在排水管長度、排水管埋設高度、排水管直徑、排水管埋設間距、坡地基質飽和水力傳導係數以及坡地坡度六項因子不同設定下，對於坡地中最高地下水位面位置、管段進水╱滿管時刻以及排水管排水能力的影響。此外，本研究也針對在不同排水管長度、排水管埋設高低、排水管直徑的設定下，分析與未埋設排水管情況相比時，所能降低的地下水位面程度。結果顯示，長度愈長，埋設深度愈深的排水管，其降低地下水位面的程度愈高，而在未滿管情況下，管徑的影響並不顯著。

關鍵字

排水管 ； 邊坡 ； 地下水位 ； 水文模式

並列摘要

The research studies the effects of drainage pipes on the groundwater table in slopelands with pipes using a hydrologic model. The variations of groundwater table and pore water pressure are the ones of major factors in the view of slope stability. Embedding drainage pipes at the side slope to facilitate groundwater drainage and to reduce the pore water pressure is a common method in engineering aspect. However, it is difficult to estimate the efficiency in lowering the groundwater table by experiences. The object of this research is establishing a numerical model describing the variation of groundwater table in slopelands with pipes, furthermore, studying the efficiency of different setting scenarios in lowering the groundwater table.
There are the main aspects in the issue of the slopelands with pipes: 1. the numerical modeling in variably saturated groundwater flow is charactered by mass unbalance and specific seepage face flow at downstream. It is difficult to obtain the accurate groundwater table and the distribution of pore water pressure unless conquers the problem of mass unbalance and seepage face estimation; 2. A 3-dimentional (3D) model is capable in simulating an irregular domain, however, the efficiency lowers. The calculating efficiency can be improved by simplified the 3D model and matching the tolerance; and 3. The pipe flow and groundwater flow are different flow mechanisms. The pipes have effect in converging water flow and make a singular-like point in soil when coupling the two mechanisms. Furthermore, when mass of water flow in the pipes, the pipes become full, and some of the water in pipes may feedback to the surrounding soil matrix through the holes on the pipes. Based on the above, the full pipe flow does not present a pressurized pipe flow. It also needs a physical-based method to estimate the interchange flow and make the boundary conditions consistency between the two flow mechanisms.
The research solves the mass unbalance and seepage face estimation using the method proposed by Celia(1990) and Neuman(1973), respectively. The research proposes a quasi-3D model to improve the efficiency in 3D simulating. The method divides the slope with a few vertical 2D simulating domain along the slope, and ensures the calculating accuracy and efficiency in simulating a 2D simulating domain with a drainage hole using the method proposed by Fippes(1986). To deal with the problem in simulating the water flow in slopelands with pipes, the research proposes the idea of “virtual pipes”. With the virtual pipes, the problems of the switch between channel flow/full pipe flow in pipe flow simulation and the boundary condition consistency in coupling the quasi-3D model and pipe flow model can be solved.
The numerical modeling in variably saturated groundwater flow is charactered by mass unbalance and specific seepage face flow at downstream. The research established a 3D and a vertical 2D model by finite element method (FEM) with Galerkin technique. The domain divides into some pyramids and some triangles in 3D and 2D domains, respectively. Also, the research solves the mass unbalance and seepage face estimation using the method proposed by Celia(1990) and Neuman(1973), respectively. The study concludes the distribution of pore water pressure and seepage face in variably saturated groundwater flow can be simulated correctly by FEM combining the above two techniques.
The research proposes a quasi-3D model to improve the efficiency in 3D simulating. In the quasi-3D model, the 3D domain divides into few vertical 2D domains. Each vertical 2D domain is simulated by the vertical 2D model, the interchanging quantities between adjacent vertical 2D domains are also calculated and a virtual slice at the most downstream position is added to solve the seepage face. The study concludes the simulating results of the established quasi-3D model are close to that of the 3D model. The quasi-3D model can improve the efficiency significantly.
With regard to the vertical 2D model, the existing drainage hole has the effect of convergent water flow, and results high hydraulic gradient in surrounding soil. The error in simulating this zone is larger. It needs fine grids configuration in this zone to lower the calculating error. The research uses a simplified gird configuration and single drainage point proposed by Fipps(1986). Based on the above, the model simulates using an equivalent hydraulic conductivity in simplified gird, which is called the resistance adjusted method. The research extents the resistance adjusted method into saturated/unsaturated soil. The study concludes the above combination can obtain similar groundwater table, distribution of pore water pressure and drainage water flow rate compared with the simulated results with fine grid configuration. The method can also improve the efficiency significantly.
The research proposes the concept of “virtual pipes” to solve the switch between the channel flow/full pipe flow and to be the basis of coupled model of the quasi-3D model and pipe flow model. With the virtual pipes, the channel flow and the full pipe flow can be solved by the same algorithm. With a proper area of virtual pipe, the water volume into the virtual pipe after the full pipe regime happened in the pipe flow model can equal to the water content in soil bulk representing by the calculating node in the quasi-3D model, furthermore, the water level in the virtual pipe can equal to the head value of the calculating node. Therefore, the state variables in the two models are consistent. The study concludes the coupled model can be validated with the previously flume experiment. The coupled model can also switch between channel flow/full pipe flow stably and describe the hydrologic response in soil.
The research simulates the effects of the different lengths, embedded heights, diameters, embedded intervals of pipe, the different saturated hydraulic conductivities of soil matrix and the different slopes on the highest groundwater table, the time of water flowing into pipes, the time of full pipes happened and the drainage flow rate. Besides, the research compares the simulating results with the cases of slopelands without pipes. The study concludes, the longer pipes, the deeper embedded pipes can lower much more groundwater table. The effect of diameter of pipes affects less under channel flow regime.

並列關鍵字

Drain Pipes ； Slopeland ； Groundwater Table ； Hydrologic Simulation Model

參考文獻

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