Scaling up of single fracture using a spectral analysis and computation of its permeability coefficient

스펙트럼 분석을 응용한 단일 균열 규모확장과 투수계수 산정

  • 채병곤 (한국지질자원연구원 지질환경재해연구부)
  • Published : 2004.03.01

Abstract

It is important to identify geometries of fracture that act as a conduit of fluid flow for characterization of ground water flow in fractured rock. Fracture geometries control hydraulic conductivity and stream lines in a rock mass. However, we have difficulties to acquire whole geometric data of fractures in a field scale because of discontinuous distribution of outcrops and impossibility of continuous collecting of subsurface data. Therefore, it is needed to develop a method to describe whole feature of a target fracture geometry. This study suggests a new approach to develop a method to characterize on the whole feature of a target fracture geometry based on the Fourier transform. After sampling of specimens along a target fracture from borehole cores, effective frequencies among roughness components were selected by the Fourier transform on each specimen. Then, the selected effective frequencies were averaged on each frequency. Because the averaged spectrum includes all the frequency profiles of each specimen, it shows the representative components of the fracture roughness of the target fracture. The inverse Fourier transform is conducted to reconstruct an averaged whole roughness feature after low pass filtering. The reconstructed roughness feature also shows the representative roughness of the target subsurface fracture including the geometrical characteristics of each specimen. It also means that overall roughness feature by scaling up of a fracture. In order to identify the characteristics of permeability coefficients along the target fracture, fracture models were constructed based on the reconstructed roughness feature. The computation of permeability coefficient was performed by the homogenization analysis that can calculate accurate permeability coefficients with full consideration of fracture geometry. The results show a range between $10^{-4}{\;}and{\;}10^{-3}{\;}cm/sec$, indicating reasonable values of permeability coefficient along a large fracture. This approach will be effectively applied to the analysis of permeability characteristics along a large fracture as well as identification of the whole feature of a fracture in a field scale.

균열을 따른 지하수 유동은 균열 기하양상에 의해 속도와 유동형태가 결정되므로, 암반 내 지하수 유동특성 해석 시 유동경로 역할을 하는 균열의 기하양상을 정확하게 파악하는 것은 중요하다. 그러나, 실제 현장규모에서는 노두의 불연속적 분포와 지표 하 정보의 연속적 획득이 불가능하기 때문에 전체적인 균열 정보를 얻기 어렵다. 따라서, 해석대상 균열 전체양상을 표현할 수 있는 방법의 개발이 요구된다. 이 연구는 퓨리에 변환을 토대로 해석대상 균열의 전체 기하양상을 파악하는 방법을 개발하고자 새로운 접근을 시도하였다. 시추코아로부터 해석대상 균열을 따라 시료를 채취한 후, 각 시료별로 퓨리에 변환을 통해 거칠기 구성성분 중 영향력이 큰 성분을 선택하였다. 그리고, 선정된 성분들을 평균하여 평균 스펙트럼을 구하였다. 평균 스펙트럼은 각 시료의 모든 성분을 포함하고 있으므로, 해석 대상 균열의 거칠기 성분 중 대표성분을 나타낸다. Low pass filtering을 수행한 후, 퓨리에 역변환을 실시하여 평균화 된 전체 균열의 거칠기 형상을 재현하였다. 재현된 거칠기 형상 또한 각 시료의 전체 기하특성을 포함하는 해석대상 지표하 균열의 대표적 거칠기 양상을 나타내는 것이다. 또한, 이는 규모확장을 통한 균열 전체의 거칠기 양상을 의미하는 것이다. 해석대상 균열을 따른 투수계수 특성을 파악하기 위해 재현된 거칠기 양상을 바탕으로 균열모델을 구성하였다. 투수계수는 균열 기하특성을 최대한 반영하여 정확한 투수계수를 구할 수 있는 균질화 해석법을 통해 산정 하였다. 해석결과는 $10^{-4}{\;}and{\;}10^{-3}{\;}cm/sec$ 범위의 투수계수 분포를 보이는데, 이는 큰 규모의 균열을 따른 투수계수 값이라 할 수 있다. 이러한 시도는 전술한 바와 같이 제한된 단속적 균열정보를 이용해 해석대상의 균열전체에 대한 기하양상은 물론 투수계수를 산정 할 수 있는 방법이 될 것이다.도는 매립된 폐기물의 성상과 밀접한 관계를 보이며 해안가를 따라 매립되어 있는 지역의 토양 내 중금속의 용출은 주변 환경에 대한 잠재적인 환경위험을 결정 시 중요한 역할을 한다.로 제거할 수 있는 것으로 나타났다. 오염 지도에 근거하여 산출된 복원 물량에 대하여 토양세척법을 이용하는 경우 복원 비용을 산출하였으며, 이와 같은 자료는 고로폐광산 주변 오염 토양에 대한 실제 복원 공정의 설계에 중요한 자료로 활용될 수 있을 것으로 판단된다.om the sampling and analytical procedures. There is a cost involved in order to improve the precision of sampling and analytical methods so as to decrease the degree of measurement uncertainty. The economical point of compromise in an investigation planning can be achieved when the allowable degree of uncertainty has been set before-hand. The investigation can then be planned accordingly not to exceed the uncertainty limit. Furthermore, if the measurement uncertainty estimated from the preliminary investigation can be separated into sampling and analytical uncertainties, it can be used as a criterion where the resources for the investigation should be allotted cost-effectively to reinforce the weakest link of

Keywords

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