Translated Titles

Numerical Simulation of Debris Flows with Weighted Moving-least-square Local Approximation





Key Words

淺水波方程式 ; 土石流 ; 本構關係 ; 局部多項式近似 ; 權重最小二乘法 ; 無網格數值方法 ; shallow water equations ; debris flow ; constitutive relation ; local polynomial approximation ; weighted moving-least-square method (WLS) ; mesh-less method



Volume or Term/Year and Month of Publication


Academic Degree Category




Content Language


Chinese Abstract

台灣位於板塊交界帶,於板塊推擠作用下,使得台灣地質狀態相當脆弱,加上降雨集中、氣候變遷以及人為山坡地開發等影響,導致土石災害發生更加頻繁,每當土石災害發生,不僅造成下游地區人民之生命財產損失,災後的整治也造成社會資源上極大負擔。 本研究主要以無網格數值計算方法中權重最小二乘局部近似法,分析土石流於堆積段(即山坡地、河谷等)之運動情形,並以解析解及室內實驗結果來驗證本模式的精準度。試圖建立一套土石流數值模式,作為土石流防治工程及土石流預警之應用工具。本研究以淺水波方程式為基礎,結合O’Brien & Julien (1985)提出之土石流本構關係式,建構用以描述土石流之數學模型。 本模式之正確性,由黃 (2003)推導之解析解及洪 (2011)室內實驗,得到良好驗證。配合土石流潛勢溪流調查及航空攝影測量取得現場數值高程模型資料,無須網格建置,即能快速求得土石流動情形及其漫淹範圍,藉以提供土石流防治工程及土石流預警之參考依據。

English Abstract

Taiwan is located in the convergence of tectonic plates. The plate-tectonic movement makes Taiwan’s geological status quite vulnerable. On top of that, the concentrated rainfall, climate change, hillside development, and other influences cause the land disasters to occur more frequently. In the land disaster, it not only causes the loss of life or property of the local resident, but the remediation also is a huge burden for the society. In this research, the weighted moving-least-square local approximation method of the mesh-less method is used to analyze the debris flow in the movements of the deposition regions (mountain slopes, valleys, etc.). An analytical solution and laboratory experimental results are introduced to verify present model’s accuracy. This research uses the shallow water equations as the bases, combining the constitutive relation model of debris flow proposed by O’Brien & Julien (1985) to construct the mathematical model to characterize debris flows. The model has a good verification performance comparing with the analytical solution derived by 黃 (2003) and the laboratory experiments conducted by 洪 (2011). The established numerical model of debris flow can be used in debris flow prevention schemes and debris flow warning tools. Combining the data of potential debris flow stream and on-site DEM from authority, the debris flow movements and influence range can be rapidly obtained, without numerical grid construction. The model can efficiently provide information for the provision of debris flow hazard.

Topic Category 工學院 > 土木工程學研究所
工程學 > 土木與建築工程
  1. 1. Bagnold, R. A., “Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear,” Proc. of the Royal Soc. of London, Vol. 225, pp. 49-63, 1954.
  2. 4. Hung, C. Y., and Capart, H., “Rotating laser scan method to measure the transient free-surface topography of small-scale debris flows,” Experiments in Fluids, 54: 1544, 2013.
  3. 5. Julien, P. Y., and Lan, Y., “Rheology of hyperconcentrations,” Journal of Hydraulic Engineering, Vol. 117, pp. 346-353, 1991.
  4. 7. Mei, C. C., and Yuhi, M., “Slow flow of a Bingham fluid in a shallow channel of finite width,” Journal of Fluid Mechanics, Vol. 431, pp. 135-159, 2001.
  5. 9. O’Brien, J. S., and Julien, P. Y., “Laboratory Analysis of Mudflow Properties,” J. Hydraul. Eng., ASCE, 114(8), pp. 877-887, 1988.
  6. 10. O’Brien, J. S., Julien, P. Y., and Fullerton, W. T., “Two-dimensional water flood and mudflow simulation,” Journal of Hydraulic Engineering, Vol. 119, No. 2, pp. 224-261, Feb., 1993.
  7. 12. Oñate, E., Idelsohn, S., Zienkiewicz, O. C., and Taylor, R. L., “A finite point method in computational mechanics. Applications to convective transport and fluid flow,” International Journal for Numerical Methods in Engineering, 39: 3839-3866, 1996.
  8. 14. Pierson, T. C., “Erosion and deposition by debris flows at Mt. Thomas, north Canerbury, New Zealand,” Earth Surface Processes, Vol. 5, pp. 227-247, 1980.
  9. 16. Takahashi, T., “Mechanical characteristics of debris flow,” Journal of Hydraulic Engineering, Vol. 104(HY8), pp. 1153-1169, 1978.
  10. 20. Wu, N. J. and Tsay, T. K., “A robust local polynomial collocation method,” International Journal for Numerical Method in Engineering, 93: pp. 355-375, 2011.
  11. 24. 洪啟耀,「以小尺度模型實驗模擬土石流形貌變化與流變參數之關係」,國立台灣大學土木工程學研究所碩士論文,2011。
  12. 25. 姜國正,「以修正有限配點法模擬水波港池共振問題」,國立台灣大學土木工程學研究所碩士論文,2012。
  13. 2. Chen, B. S., Tsay, T. K., Chiang, K. C., and Yang, C. W., “Regional connectivity in Modified Finite Point Method,” Engineering Analysis with Boundary Elements, 47, pp. 21-31, 2014.
  14. 3. Coe, J., “Debris Flow in Action,” U.S. Geological Survey, 2009.
  15. 6. Jan, C. D., “A study on the numerical modeling of debris flows,” Proceedings of the 1st International Conference on Debris Flow Hazards Mitigation, pp. 771-726, 1997.
  16. 8. O’Brien, J. S., and Julien, P. Y., “Physical properties and mechanics of hyperconcentrated sediment flows,” Proc. ASCE Hyd. Div. Spec. Conf. on Delineation of Landslides, Flash Flood and Debris Flow Hazards, Logan Utah, June 1984, pp. 260-279, 1985.
  17. 11. O’Brien, J. S., “FLO-2D User’s Manual,” 2009.
  18. 13. Oñate, E., Idelsohn, S., Zienkiewicz, O. C., and Taylor, R. L., C. Sacco, “A stabilized finite point method for analysis of fluid mechanics problems,” Computer Methods in Applied Mechanics and Engineering, 139: 315-346, 1996.
  19. 15. Schamber, D. R., and MacArthur, R. C., “One-dimensional model for mudflows,” Proc. ASCE specialty conference on hydr. and hydro. in the small comp. age., Vol. 2, ASCE, New York, N.Y., pp. 1334-1339, 1985.
  20. 17. Takahashi, T., “Debris flow on prismatic open channel,” Journal of the Hydraulics Division, Vol. 106, No. 3, pp. 381-396, March, 1980.
  21. 18. Takahashi, T., and Tsujimoto, H., “Delineation of the debris flow hazardous zone by a numerical simulation method,” Proc. Int. Symp. on Erosion, Debris Flow and Disaster Prevention, Tsukuba, Japan, pp. 457-462, 1985.
  22. 19. Woolhiser, D. A., “Simulation of unsteady overland floe,” in K. Mahmood, and V. Yevjevich(eds.), Unsteady Flow in Open Channels, Water Resources Publications, Fort Collins, CO, Vol. 2, pp. 485-508, 1975.
  23. 21. 行政院農業委員會水土保持局,「土石流潛勢溪流分布」,土石流防災資訊網,2015。
  24. 22. 余昌益、吳雲瑞、詹錢登,「含砂濃度對含砂水體流變參數的影響之初步研究」,第一屆土石流研討會論文集,第179-190頁,1997。
  25. 23. 李咸亨、Budijanto Widjaja、曹家文、謝宗榮,「以室內實驗和現場模擬方式研究土石流之黏滯係數」,中華水土保持學會102年年會論文集,編號1-2,2013。
  26. 26. 涂冠宇,「土石流數值模擬之初步研究」,逢甲大學水利工程學研究所碩士論文,2005。
  27. 27. 陳盈守、陳振宇、賴承農、鍾佩蓉,「探討土石流堆積物分布範圍與體積濃度推算之關係」,第二十屆水利工程研討會,2011。
  28. 28. 黃名村,「土石流災害範圍之數值模擬及利用微波偵測土石流之研究」,國立台灣大學土木工程學研究所博士論文,2003。
  29. 29. 蔡元芳,「土石流扇狀地形狀特性之研究」,國立成功大學水利及海洋工程研究所博士論文,1999。
  30. 30. 賴桂文,「一維變密度土石流模式」,國立台灣大學土木工程學研究所碩士論文,1999。
  31. 31. 謝正倫,「土石流預警系統之研究」,研究報告,第130號,國立成功大學台南水工試驗所,1991。