本研究探討土壤異質性對地下水滲流之影響。本研究首先建立一非飽和土壤水數值模式，經由實測資料驗證，將此模式應用於地下水入滲模擬，本文以蒙地卡羅法產生土壤物理特性隨機參數，以序率模擬探討土壤異質性之影響，並與定率模擬結果做一比較。模擬結果顯示，土壤水分受土壤異質性之影響會有減緩之現象，當土層中同時存在滲透性較小與滲透性較大之土壤時，垂直入滲率受到滲透性較小土壤之影響較鉅。經由序率模擬，可得到入滲率之平均值、範圍及分布情形，並發現入滲率符合常態分布。本研究另以序率模擬之入滲率累積機率曲線探討定率模擬或經驗公式之計算結果，結果顯示定率模擬或經驗公式高估入滲之機率相當高。

This study investigates the influence of soil heterogeneity on groundwater seepage flow. An unsaturated groundwater flow model is developed; the model is calibrated with field data and then applied in seepage flow simulation. This study adopts Monte Carlo simulation to generate stochastic parameters of soil characteristics and investigate the influence of soil heterogeneity on seepage flow. The results of stochastic simulation are compared with those of conventional deterministic approach. The results reveal that soil heterogeneity inhibits seepage flow. The seepage flow is governed by the soil with less permeability rather than that with greater one when various soil classes exist. The range, mean value, and distribution pattern of infiltration rate can be obtained with the stochastic simulations. It is also found that the infiltration rate is normal-distributed. The cumulative probability curves of infiltration rate are used to investigate the results from deterministic simulation as well as empirical formula. The results indicate that the probability for the deterministic simulation and empirical formula to overestimate infiltration rate is rather high.

第一章 緒論…………………………………………………………1
1-1 前言……………………………………………………………1
1-2 文獻回顧………………………………………………………2
1-3 研究目的與方法………………………………………………6
第二章 非飽和土壤水模式………………………………………8
2-1 二維非飽和土壤水模式………………………………………8
2-2 數值方法………………………………………………………10
2-3 導水係數 ……………………………………………………14
2-4 邊界條件………………………………………………………15
2-5 網格大小與時間差分間距……………………………………16
2-6 數值模式驗證…………………………………………………17
第三章 蒙地卡羅模擬……………………………………………19
3-1 獨立變數之蒙地卡羅模擬……………………………………19
3-2 相關變數之蒙地卡羅模擬……………………………………22
第四章 案例研究……………………………………………………25
4-1 案例一：飽和導水係數 之異質性…………………………26
4-2 案例二：土壤特性參數之異質性……………………………30
4-3 案例三：異質性土壤之非等向性……………………………34
4-4 案例四：實際案例之探討……………………………………36
4-5 入滲率之分布型態……………………………………………39
第五章 結論與建議………………………………………………40
5-1 結論…………………………………………………………………40
5-2 建議…………………………………………………………………41
參考文獻…………………………………………………………………42
附表………………………………………………………………………47
附圖………………………………………………………………………57

1、 Ang, A. H-S., and W. H. Tang, Probability concepts in engineering planning and design, Vol. II:Decision, risk, and reliability. John Wiley and Sons, Inc., New York, N.Y., 1984.
2、 Belmans, C., J.G. Wesseling and R.A. Feddes, Simulation model of the water balance of a cropped soil:SWATRE. Journal of Hydrology, 63, pp271-286, 1981.
3、 Bornhoft, D., A simulation model for the description of the one-dimensional vertical soil water flow in the unsaturated zone. Ecological Modelling, 75/76, pp269-278, 1994.
4、 Broadbridge, P. and I. White, Constant rate rainfall infiltration : a versatile nonlinear model. Water Resour. Res., 24, pp145-154, 1988.
5、 Brown, L. C., Uncertainty analysis in water quality modeling using QUAL2E, system analysis in water quality management, IAWAPRC, Pergamon Press., pp309-319, 1987.
6、 Celia, M.A., L. R. Ahuja, and G.F. Pinder, Orthogonal collocation and alternating-direction procedures for unsaturated flow problems. Adv. Water Resour., 10, pp178-187, 1987.
7、 Chang, Che-Hao, Tung Yeou-Koung, Yang Jinn-Chuang, Monte carlo simulation for correlated variables with marginal distributions. J. Hydr. Engrg, ASCE,120(3) ,pp313-331, 1994.
8、 Der Kiureghian, A., and Liu, P. L., Structural reliability under incomplete probability information. J. Engrg. Mech., ASCE, 112(1), pp85-104,1985.
9、 Franke, H.-J. and G. Teutsch, Stochastic simulation of the regional pesticide transport including the unsaturated and the saturated zone. Ecological Modelling,75/76, pp529-539, 1994.
10、 Freeze, R. A., Three-dimensional, transient, saturated-unsaturated flow in a groundwater basin. Water Resour. Res., 7(2), pp347-366, 1971.
11、 Haverkamp, R., M. Vauclin, J. Touma, P. J. Wierenga, and G. Vachaud, A comparison of numerical simulation models for one-dimensional infiltration. Soil Sci. Soc. Am. J., 41, pp285-293, 1977.
12、 Hillel, D., Fundamentals of soil physics, Academic, San Diego, Calif., 1980.
13、 Liu, P. L., and Der Kiureghian, A. Multivariate distribution models with prescribed marginals and covariances. Probabilistic Engrg. Mech., 1(2), pp105-112, 1986.
14、 Li, S.-G., Feng, R., and M. Dennis, A space-time accurate mothod for solving solute transport problems. Water Resour. Res., 28(9), pp2297-2306, 1992.
15、 Mantoglou, A., and L. W. Gelhar, Stochastic modeling of large-scale transient unsaturated flow systems. Water Resour. Res., 23(1), pp37-46, 1987.
16、 Melching, C. S., and S. Anmangandla. Improved first-order uncertainty mehtod for water-quality modeling. J. Envir. Engrg., ASCE, 118(5), pp791-805, 1992.
17、 Mualem, Y., A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res., 12, pp513-522, 1976.
18、 Nataf, A., Détermination des distribution don’t les marges sont données. Comptes Rendus de l’Academie des Sciences, 225, Paris, France, pp42-43, 1962.
19、 Parrish, R. S. Generating random deviates from multivariate Pearson distributions. Comutational Statistics and Data Analysis, 9, pp283-296, 1990.
20、 Philip, J.R., The theory of infiltration 1.,Soil Sci., 83,pp345-357, 1957.
21、 Rajesh, S., and T.-C. Jim Yeh, Analytical solutions for one-dimensional, transient infiltration toward the water table in homogeneous and layered soil. Water Resour. Res., 27, pp753-762, 1991.
22、 Stauffer, F., and M. Rauber, Stochastic macrodispersion models for gravel aquifers. J. Hydraul. Res, 36, pp885-896, 1998.
23、 Ten Berge, H.F.M., K. Metselaar, M.J.W. Hansen, and E.M. de San Aqustin, The SAWAH riceland hydrology model. Water Resour. Res., 31(11), pp2721-2732, 1995.
24、 Touma, J., and Vauclin, M., Experimental and numerical analysis of two phase infiltration in partially saturated soil. Transport in Porous Media, 1, pp28-55, 1986.
25、 Van der Zee, S. and Boesten, J., Effects of soil heterogeneity on pesticide leaching to groundwater. Water Resour. Res., 27, pp3051-3063, 1991.
26、 van Genuchten, M. Th., A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J., 44, p892-898,1980.
27、 Young, D. M., Jr., The numerical solution of elliptic and parabolic partial differential equations. in Survey of Numerical Analysis, edited by J. Todd, pp380-438, McGraw-Hill, New York, 1962.
28、 Warrick, A. W., An analytical solution to richard’s equation for time-varying infiltration. Water Resour. Res., 27, pp763-766, 1991.
29、 Yeh G. T., 3DFMWATER：A three-dimensional finite element model of water flow through saturate-unsaturated media. ORNL- 6386, Union Carbide Corp., Nuclear Div., Oak Ridge Natl. Lab., 1987.
30、 Zabra, R. L., A general mass-conservation numerical solution for the unsaturated flow equation. Water Resour. Res., 26, pp1483-1496, 1990.
31、 歐明謙，『地下水人工補注垂直數學模式之研究』，國立台灣大學農業工程學研究所碩士論文，民國七十五年。
32、 林清敏，『自動網格形成法在地下水數值模擬之應用研究』，國立台灣大學土木工程研究所碩士論文，民國八十年。
33、 蘇燕珠，『土壤滲透性與孔隙分布相關性之研究』，國立台灣大學農業工程研究所碩士論文，民國八十二年。
34、 王德宜，『地下水數學模式於雲林地區邊界補注量推估之研究』，國立台灣大學農業工程學研究所碩士論文，民國八十三年。
35、 李清水，『雲彰地區深淺層抽水量之模擬』，國立台灣大學農業工程學研究所碩士論文，民國八十三年。
36、 蕭偉松，『未飽和層入滲模擬問題之研究』，國立台灣大學土木工程研究所碩士論文，民國八十五年。
37、 林鈺，『水質模擬之不確定性分析』，國立台灣大學土木工程研究所碩士論文，民國八十六年。
38、 黃志華，『急水溪水質模擬與風險分析』，國立台灣大學土木工程研究所碩士論文，民國八十六年。
39、 劉振宇，『增加水田地下水涵養補注方法之評估』，農委會研究計劃報告，台大農工系，民國八十七年。
40、 許瑞昌，『未飽和層土壤水份垂直入滲之數值模擬』，國立台灣大學農業工程學研究所碩士論文，民國八十七年。