本文以破裂面幾何參數（破裂面長、破裂面方位、破裂面內寬與破裂面中心位置）為基礎，考慮破裂面長度為負指數分布、方位為均佈分布、破裂面內寬為對數常態分布及破裂面中心位置為卜松分佈。本文建立二維隨機離散破裂面模式，並採達西定律與質量平衡觀念，代入特定邊界條件以及水平衡方程式求得破裂面相交各節點之水頭，依其數值解可得節點之流量，再依其比例進行蒙地卡羅法之質點追蹤技術，得質點濃度累積穿透曲線，並以穿透曲線方程式驗證。
　　破裂岩體地下水流之研究為—假設情況下，其破裂面數越多的情況及破裂面越長時，地下水流量分佈行為經Chi-square檢定最適分佈為常態分佈。在不同內寬的情況下，其地下水流量分佈行為為常態分佈。在破裂面數較少且破裂面長較短時，其地下水流量分佈行為有一明顯的偏態。破裂岩體邊界露頭對地下水流量關係，以地質統計方法計算破裂岩體兩端露頭對流量因子之碎形維度值，發現於邊界露頭輸入端其碎形維度值相對較小，代表邊界露頭輸入端對流量相關性較大，經多次模擬結果發現其地下水流量最大時，其露頭數將會存在於某一區間。
　　污染物於破裂岩體中傳輸研究，本研究假設不同破裂面相交角度下，可發現其在傳輸維度方面，其污染物運動距離（ln<r2>）與時間（ln<t>）之關係呈線性相關，其斜率值約為1.4~1.64間。百分之五十傳輸時間（T50）與百分之九十之傳輸時間（T90）隨破裂面角度變化於相同之角度時，其傳輸時間於正負角度偏差時相同。在整體岩體延散度性質，其性質也隨破裂面相交角度變化而有對稱行為，另外假設案例下，平均傳輸時間也隨破裂面數少與破裂面長度較短時，其分佈行為有一明顯向左偏態行為。
　　應用蘭嶼地區破裂面資料，地下水流量之統計分佈行為，經Chi-square檢定出最適分佈為Beta分佈，而污染物平均傳輸時間分佈行為，經Chi-square檢定出最適分佈為Logistic分佈。而經本模式預測污染物傳輸特性，顯示污染物平均傳輸速率在0.528 m/day、污染物運動距離（ln<r2>）與傳輸時間（ln<t>）之斜率值為1.64，平均延散度為0.91m。當考慮現地以釷-234放射性元素貯放時，當外洩時，其放射性污染物平均傳輸時間（T50，百分之五十污染物到達時間）為0.92，也就是到達全部ㄧ半濃度之機率有九成；磷-32時，當外洩時，平均傳輸時間（T50，百分之五十污染物到達時間）累積到達機率為0.18，也就是到達全部ㄧ半濃度之機率有一成八。

　　In this study, the discrete fracture model was performed to investigate the behaviors of the fluid flow and particle transport in the fracture network. A field case study was also provided in low-level nuclear waste repository site in Lan-Yu area, Taiwan. Several procedures are executed to investigate the phenomenon of the flow and particle transport in the fracture rock. In order to construct the fracture network, called as the discrete fracture mode, fracture parameters are generated by the specific distribution accompany with the Mote Carlo method. For instance, the centers of fractures, fracture lengths and apertures are assumed to be the Poisson’s distribution, negative exponential distribution and lognormal distribution, respectively. Furthermore, the flow field in the rock was solved using the mass-balance equation with specified boundary conditions. Moreover, the particle transport field was solved under the assumption that the amount of particles is proportional to the flow rate and the particles are released under the up-stream flow field. The breakthrough curve related to accumulated percentage of the particles can be obtained. The geostatic method was also applied to calculate the fractal value related to the outcrops against the flow
　　In our study cases, results showed that when the fracture network was involved more numbers of fractures and longer length of fractures, the groundwater flow is to be distributed as normal . By the way, the groundwater flow against the aperture is also to be distributed as normal. However, in the case of less fractures and shorter fracture length, the flow distribution seems apparently to be biased as compared with normal distribution. The impact of the input boundary outcrops for groundwater flow was more significant than that of the output boundary outcrops.
　　Under the various fracture angle, simulation results for particle transport showed that the distance particles traveling and the traveling time is positively linear and the slope value is from 1.4 to 1.64. The dispersivity and the average traveling time of particles traveling were dependent on the fractures interception angle.
　　From the data in Lan-Yu area, our simulation results indicated that the groundwater flow distribution is to distribute as Beta distribution, and the particles average traveling time trend to be Logistic distribution . The average traveling velocity is to be 0.528 m/day. The slope of the distance particles traveling with the traveling time is the value of 1.64, and the dispersivity is the value of 0.91m as comparing to the value of 1m using the Sauty method. The average traveling time accumulated probability of the radioactive element 234Th is the value of 0.92 and the average traveling time accumulated probability of 32P is the value of 0.18.

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