地下水流及其汙染傳輸在受外力影響下行為模式之序率分析

Abstract

地下含水層常因受外力的影響，造成孔隙水壓的變動。因而，破壞 土壤顆粒與水壓間的平衡，導致土壤顆粒的變形，更進一步影響到土壤 孔隙間的儲水量。因此，要有效率的規劃經營地下水資源，必須將孔彈 理論(poroelasticity theory)納入地下水流運算模式中，得以確切推估土壤 顆粒在受外力下的變化情形。 地下含水層特性參數的空間分佈，具有很大的變異性（formation heterogeneity），此變異性對地下水流動影響甚鉅。所以一般地下水流模 式所預測的結果，常常具有很大的空間不確定性。現有孔彈理，雖然提 供了預測地下含水層在受外力下所造成變形情形的理論基礎，但是此理 論基礎只限於評估在小尺度下（at local scale）土壤顆粒變形狀況。換言 之，並未將土壤特性的異質性納入模式中。然而，往往評估在大尺度下 （at field scale）的變化情形，才是實際運用上考量的重點。因此，如何 擴充現有小尺度下的孔彈理論，將地下含水層特性參數空間的異質性納 入模式的運算中，以做為地下水資源規劃上的重要參考依據，有實務上 的需要。 因此，本參年研究計劃的目的在於利用序率分析方式，擴充現有孔 彈理論，將土壤特性空間的異質性，納入模式的物理機制中，以探討地 下水流及其相關污染傳輸之問題。 (1)第壹年預期執行工作項目：  推導描述在大尺度下土壤顆粒變形的序率方程式  推導序率方程式的解析解  推導序率模式結果的可信度或不確定性 (2)第貳年預期執行工作項目：  推導描述土壤顆粒位移變化的解析解  推導非定常性流速統計特性(statistics for the nonstationary velocity field)  推導描述在大尺度及拉格朗日(Lagrangian)架構下擴散傳輸現象 的傳輸時間統計特性(travel time statistics)解 (3)第參年預期執行工作項目：  推導描述在大尺度及歐拉(Eulerian)架構下擴散傳輸現象的序率方 程式  推導序率方程式的解析解  推導在大尺度下擴散傳輸的係 數  推導在大尺度下污染物濃度變化的解析解

In general, the fluidfilled granular soils comprising the aquifers are deformable under applied stresses. Fluctuations in pore groundwater pressure in response to the changes in imposed stresses are often encountered in many practical problems of subsurface flow. Such interaction will cause the deformation of the solid matrix, which in turn affects the storage of groundwater in the void space. Thus, the assessment of the variability of the poroelastic response of the medium is essential for the planning and management of groundwater resources in aquifers. Natural porous earth materials are observed to display spatial variability of their properties. Heterogeneity has been shown to play an important role in influencing the behavior of groundwater flow in the field. There is therefore a great deal of uncertainty to be anticipated in the prediction of groundwater movement at the field scale. The poroelasticity theory has been developed at the local scale treating formations, layers or zones within the aquifer as being homogeneous. An important weakness to this classical approach is that it ignores the influence of the formation spatial variability. However, many practical problems of subsurface flow require predictions over relative large space scale, where a wide range of formation heterogeneities are included in the flow domain. Therefore, there arises a need to incorporate the influence of natural heterogeneity into the prediction of the poroelastic response of the heterogeneous medium in analysis of field-scale groundwater flow and solute transport, which is the objective undertaken here. A three-year research project is proposed to achieve the objective outlined above. The project is divided into three major components: (1) Specific tasks designed during the project’s first year  Development of stochastic model for two-way interaction between fluids and applied stress in the modeling process  Development of the closed-form solution for the stochastic perturbation model  Quantification of the spatial variability in excess pressure head (2) Specific tasks designed during the project’s second year  Quantification of the spatial variability in solid’s displacement  Evaluation of the covariance function of nonstationary velocity field  Evaluation of the solute travel time statistics within the Lagrangian framework (3) Specific tasks designed during the project’s third year  Development of field-scale stochastic solute concentration model within the Eulerian framework  Development of the closed-form solution of the concentration perturbation model  Quantification of the field-scale dispersive flux  Quantification of the spatial variability in plume concentration field