| 摘要: | 熱-水-力(Thermal-Hydraulic-Mechanical, THM)耦合模式，描述著熱學、水力學以及力學之間相互影響的行為，為地下工程中一項重要的安全評估技術；序率蒙地卡羅模式比起傳統定率模式，可以額外提供THM耦合複雜行為造成的不確定性與相關性評估。相依參數(dependent parameter,指參數值隨外在條件改變)模式當中的材料特性，能夠更完整的詮釋材料介質在THM耦合系統中的真實行為。目前國際上的相關研究在序率THM模式與相依參數THM模式的交互作用行為探討尚有不足，也尚未有完整的序率結合相依參數THM模式的探討。因此本研究使用有限元素軟體COMSOL MULTIPHYSICS，並以用過核子燃料最終處置場為例進行分析，使用台灣具有儲放潛力的母岩以及緩衝材料為標的，發展一維相依參數THM全耦合模式。本研究首先建立概念模型進行定率THM模式分析，接著以地質統計開源程式碼GSLIB以及本研究以Python開發的高斯序列模擬程式碼，分別產製水力參數、熱傳參數以及力學參數為隨機場的實現場(Realizations)，並將上述參數分成四個案例導入THM模式進行序率蒙地卡羅模擬。計算共變異函數和平均數來探討位移、孔隙水壓以及溫度等三變數的不確定性和各變數之間的交互作用行為，並比較相依參數模式(DPM)以及非相依參數模式(IPM)結果的差異。本研究結果顯示，DPM顯著影響了定率模式中孔隙水壓變化量的分布，而溫度以及位移則受到較少影響，然而部分參數不均勻的分布導致了DPM與IPM有不同的穩定狀態。序率模式案例當中顯示，水力參數、熱傳參數、力學參數的擾動對THM系統中的孔隙水壓影響最大，但是系統平衡之後，水力參數案例的變數不確定性會趨於0，熱傳參數以及力學參數案例的變數不確定性則會趨於一個穩定數值。此一現象代表熱傳參數以及力學參數的異質性影響了各實現場最終穩定狀態，另外，DPM也顯著影響了各案例當中不確定性的分布狀態以及數值。共變異數結果則顯示，不同的序率案例顯示出不同的物理行為，而這些物理行為除了因為受到THM耦合、異質參數的影響之外，也受到模式設定的影響。另外，DPM也因為相依參數在空間分布的趨勢而影響了部分變數之間交互作用的關係性。綜合以上結果可以得知，採用THM多重物理量耦合數值模式進行定率或是序率的分析時，採用相依參數能夠更詳細的分析且獲得較貼近實際行為的評估結果。
;For the issue of safety assessment of final disposal sites for spent nuclear fuel, the study on coupled thermal-hydraulic-mechanical (THM) simulation seldom discusses the cross-interactions between random variables by using the stochastic concept with dependent parameters, which is defined as parameter value changes with the changed environmental condition. Stochastic analysis is an important issue for the safety assessment whereas the THM system with dependent parameters are close to the reality. Therefore, this study used the software COMSOL Multiphysics to develop a fully-coupled THM model with dependent parameters and adopted Monte Carlo simulation with the hydraulic properties, thermal properties, and mechanical properties being the random variables to assess the covariance functions between all the variables. Geostatistical code, GSLIB, and the Python code developed in this study is used to generate the random fields for a 1D fully-coupled THM model. Three variables in the THM model are the displacement, pore water pressure, and temperature, which would interact with each other. The mean and covariance were calculated to evaluate the uncertainty and cross-interactions between these random variables. The results showed that DPM largely affects the distribution of pore water pressure but less for those of displacement and temperature. Non-uniform distributed parameters make the results of DPM and IPM become different when the system reach a stable condition. The stochastic results show that pore water pressure is the most sensitive variable under the perturbations of the hydraulic, thermal, and mechanical parameters. After the system reach the stable condition, the uncertainty will become 0 in the hydraulic variable, but not in thermal and mechanical variables. This indicates that heterogeneity of thermal and mechanical properties affects the stable condition in each realization for both IPM and DPM. The covariance results show that the coupled THM theory, heterogeneous parameters and model settings are the main reasons to induce different physical behavior in different stochastic cases. Morever, DPM also affects the coupled behavior due to the change of the parameters values. Therefore, DPM should be considered in the safety assessment of final disposal sites for spent nuclear fuel. |
