具不規則邊界且為非均質非等向水層的解析解

Abstract

本計畫的目的，係針對具有不規則邊界、非均質且非等向的含水層，提出一個推導方法或步 驟，透過適當的空間分割，推導描述該水層因抽水產生暫態水位變化的解析解。本計畫的研究動 機，來自於讀到兩篇文獻中提到含水層抽水的案例，一篇是Javandel 與Zaghi (1975)，此文與解析 解有關，是分析在伊朗的集水廊道因定水頭抽水產生的穩態水頭分佈；另一篇是Kihm et al. (2007)，與數值解有關，是探討在韓國京畿道的一個山腳沖積扇，因抽水所產生的地下水位變化 與地層下陷問題。這兩個案例所涉及的水層邊界，都呈現不規則的型態(凹角形)，而第一篇文獻 所考慮的水層水力特性具均質、等向性。 本計畫擬分成三年執行，第一年將探討集水廊道的案例，考慮一個徑向非均質、非等向之凹 角含水層，且水層為無限延伸，推求此集水廊道抽水問題的暫態解。目前南台灣很缺水，南部沖 積平原區可考慮設置集水廊道抽水，以因應缺水問題。第二、三年的計畫，將沿用韓國京畿道附 近凹角形沖積扇抽水產生地層下陷的案例，分析此類沖積扇含水層因抽水在不同邊界條件下所產 生的洩降變化。由於此現地案例的邊界較為複雜，第二年計畫先考慮簡化的問題，把原本河川所 在的定水頭邊界改為不透水邊界，以確認所建立的求解方法可行，可解得抽水時所造成的暫態水 頭分佈解析解。第三年仍探討韓國沖積扇問題，考慮該河川是凹角水層的定水頭邊界，且水頭會 隨距離呈線性變化，以符合該沖積扇的現地狀況，並推導出暫態的洩降分佈解。

The objective of this proposal is to provide a systematic way of derivation for obtaining analytical solutions of transient drawdown distribution in non-homogeneous and anisotropic aquifers due to pumping. By utilizing the method of domain decomposition in dividing the aquifer, the developed solutions can describe the transient groundwater flow for aquifers with irregular boundaries. This study is motivated by two cases involving pumping in aquifers with irregular boundary reported in journal articles. The first case was presented by Javandel and Zaghi (1975) in which they studied the steady groundwater flow in a collection well system under constant-head pumping in Iran. Another case was given by Kihm et al. (2007) in which they investigated the problem of land subsidence due to groundwater pumping from an alluvial aquifer in Gyeonggi-Do, Korea. This proposal is a three-year project. In the first year, a new transient solution will be developed for describing the groundwater flow pumped from an aquifer with a collection well system. The aquifer with a reentrant angle is considered to be non-homogeneous, anisotropic and infinite-extended in radial direction. In the second year, we will derive a solution for describing the groundwater flow in an alluvial aquifer with a reentrant angle in Korea due to pumping. The constant-head boundaries representing the rivers in the second case are replaced by no-flow boundaries. This simplification is to ensure that our approach can solve the problem successfully. In the last year, we will further consider the field problem of the alluvial aquifer in Korea, which has a reentrant angle and is bounded by sloping rivers.