本文主要分為兩個部分，第一部分為理想化破壞曲面、第二部分為使用 GPU 進 行二相流模擬。在第一部分中以 Tai et al.(2020) 所提出理想化曲面法進行崩塌破壞深 度及量體之估算，當現地資料較為不足時此方法能夠對於破壞面進行快速的評估， 且若缺少相關潛勢範圍資料時，以橢圓投影方式進行潛在崩塌範圍之選取，經過驗 證後也找出此方法於現地上的應用性。另一方面將破壞面假設為圓弧形破壞後，能 夠搭配切片法進行安全係數的計算，以此分析坡面的穩定型態，並與現地資料進行 比較推測出可能產生破壞之深度。在進行砂堆崩塌實驗時，觀察到砂堆在產生崩塌 前其表面會累積至特定量體後才會產生崩塌，並且為序列式從坡腳開始產生破壞， 這也與現地觀察到的崩塌現象相似，因此本文將此概念以理想曲面進行實驗的二維 分析，找出可能產生破壞之曲面。同時此方法也能夠考慮不同的地下水位分佈對於 安全係數影響，本文也嘗試建構可能地下水分佈對於坡面的安全係數影響進行分析。
在第一部分中使用理想化破壞曲面進行破壞面之建構後，第二部分將所估算之 量體使用 GPU 進行土石流運移行為之計算，本文以 Tai et al.(2019) 所提出於地形座 標上的二相流數值方法為基礎，使用 CUDA 架構進行 GPU 計算，計算效率上以小林 村崩塌事件為例，從原先使用 CPU 單核進行 180 秒的情境模擬中，其運算時間從大 約 2.5 小時增快至 90 秒內即可完成計算，提升大約 100 倍之計算效率;若使用國網 中心之高速電腦甚至只需 60 秒即能完成計算，提升大約 150 倍之計算效率，使模式 在情境模擬中能接近即時演算，並且與實際土石流災害進行比較在運移路徑及土體 堆積上，都有一定的相似性以此驗證此模式的應用性，並進行參數率定推測出較適 當的參數範圍。本文同時使用 OpenGL 將數值計算結果進行三維呈現並使用 PyQt 進 行介面化之設計，使模式在應用上朝向更便利之方向。

This paper is mainly divided into two parts, the first part is devoted to the idealized curved surface for mimicking the slope failure surface, and the second part focuses on the two-phase debris flow simulation using GPU. In the first part, the idealized curved surface method proposed by Tai et al. (2020) is used to estimate the landslide damage depth and the associated volume. When the on-site data is lacking or incomplete for a precise prediction, this method can roughly estimate the landslide surface at the first time, where the ellipse projection method can be utilized to select the potential landslide range. As well, assuming a circular arc for the failure surface, the thickness of the landslide body is considered in computing the safety factor with the method of slice for the analysis of a slope stability.
Once the failure surface is constructed by using the idealized curved failure surface, the GPU-accelerated simulation tool can be used to predict the plausible flow paths of the released mass or the consequential debris flow. This study uses the terrain coordinates proposed by Tai et al. (2019). Based on the numerical method of two-phase debris flow, the CUDA architecture is used for GPU computation to improve the computation efficiency, so that the computational efficiency can be close to real-time calculation in the scenario simulation. In comparison with the actual debris flow disaster, the similar paths as shown in the ortho-photo reveals the applicability of this model.
Finally, a Graphical User Interface (GUI) using the technique of PyQt is developed for the operation of the model, an illustrating tool is developed (by OpenGL) for a user- interactive three-dimensional rendering toward a more complete disaster prevention system.

[1] F. Aureli, F. Prost, R. Vacondio, S. Dazzi, and A. Ferrari. A GPU-Accelerated Shallow- Water Scheme for Surface Runoff Simulations. Water, 12(3):637, 2020.
[2] A.W.Bishop.Theuseoftheslipcircleinthestabilityanalysisofslopes.Geotechnique, 5(1):7–17, 1955.
[3] A. Breuer and M. Bader. Teaching parallel programming models on a shallow-water code. In 2012 11th International Symposium on Parallel and Distributed Computing, pages 301–308. IEEE, 2012.
[4] B. M. Das and N. Sivakugan. Fundamentals of geotechnical engineering. Cengage Learning, 2016.
[5] S. Dazzi, R. Vacondio, and P. Mignosa. Integration of a levee breach erosion model in a GPU-accelerated 2D shallow water equations code. Water Resources Research, 55(1):682–702, 2019.
[6] S. Dazzi, R. Vacondio, and P. Mignosa. Internal boundary conditions for a GPU- accelerated 2D shallow water model: implementation and applications. Advances in Water Resources, 137:103525, 2020.
[7] J. Gan, Z. Zhou, and A. Yu. A GPU-based DEM approach for modelling of particulate systems. Powder Technology, 301:1172–1182, 2016.
[8] R. Gandham, D. Medina, and T. Warburton. GPU accelerated discontinuous Galerkin methods for shallow water equations. Communications in Computational Physics, 18(1):37–64, 2015.
[9] F. Guzzetti, F. Ardizzone, M. Cardinali, M. Rossi, and D. Valigi. Landslide volumes and landslide mobilization rates in Umbria, central Italy. Earth and Planetary Science Letters, 279(3-4):222–229, 2009.
[10] M. Harris. Optimizing parallel reduction in CUDA. Nvidia developer technology, 2(4):1–39, 2007.
[11] P. S. Heckbert. A seed fill algorithm. Graphics gems, 275:721–722, 1990.
[12] C.-C. Huang and C.-C. Tsai. New method for 3D and asymmetrical slope stability analysis. Journal of Geotechnical and Geoenvironmental Engineering, 126(10):917– 927, 2000.
[13] M. Jaboyedoff, F. Baillifard, R. Couture, J. Locat, and P. Locat. Toward preliminary hazard assessment using DEM topographic analysis and simple mechanical modeling by means of sloping local base level. Landslides evaluation and stabilization. Balkema, pages 199–205, 2004.
[14] C.-Y. Kuo, P.-W. Tsai, Y.-C. Tai, Y.-H. Chan, R.-F. Chen, and C.-W. Lin. Application Assessments of Using Scarp Boundary-Fitted, Volume Constrained, Smooth Minimal Surfaces as Failure Interfaces of Deep-Seated Landslides. Rock Avalanches, 2021.
[15] J. Liu, K. Nakatani, and T. Mizuyama. Effect assessment of debris flow mitigation works based on numerical simulation by using Kanako 2D. Landslides, 10(2):161–173, 2013.
[16] M.Mergili,J.-T.Fischer,J.Krenn,andS.P.Pudasaini.r.avaflowv1,anadvancedopen- source computational framework for the propagation and interaction of two-phase mass flows. Geoscientific Model Development, 10(2):553–569, 2017.
[17] K. Nakatani, S. Hayami, Y. Satofuka, and T. Mizuyama. Case study of debris flow disaster scenario caused by torrential rain on Kiyomizu-dera, Kyoto, Japan-using Hyper KANAKO system. Journal of Mountain Science, 13(2):193–202, 2016.
[18] K. Nakatani, T. Wada, Y. Satofuka, and T. Mizuyama. Development of “Kanako 2d (ver. 2.00),”a user-friendly one-and two-dimensional debris flow simulator equipped with a graphical user interface. International Journal of Erosion Control Engineering, 1(2):62–72, 2008.
[19] C. NVIDIA. Nvidia cuda compute unified device architecture programming guide. NVIDIA Corporation, 2007.
[20] M. E. Reid, S. B. Christian, D. L. Brien, and S. Henderson. Scoops3D—software to analyze three-dimensional slope stability throughout a digital landscape. US Geological Survey Techniques and Methods, book, 14, 2015.
[21] Y. Tai and C. Kuo. Modelling shallow debris flows of the Coulomb-mixture type over temporally varying topography. Natural Hazards and Earth System Sciences, 12(2):269–280, 2012.
[22] Y.-C. Tai, J. Heß, and Y. Wang. Modeling Two-Phase Debris Flows With Grain-Fluid Separation Over Rugged Topography: Application to the 2009 Hsiaolin Event, Taiwan. Journal of Geophysical Research: Earth Surface, 124(2):305–333, 2019.
[23] Y.-C. Tai, C.-J. Ko, K.-D. Li, Y.-C. Wu, C.-Y. Kuo, R.-F. Chen, and C.-W. Lin. An idealized landslide failure surface and its impacts on the traveling paths. Frontiers in Earth Science, 8:313, 2020.
[24] X. Wu, E. J. Kubatko, and J. Chan. High-order entropy stable discontinuous Galerkin methods for the shallow water equations: curved triangular meshes and GPU accelera- tion. Computers & Mathematics with Applications, 82:179–199, 2021.
[25] 池谷浩 and 水山高久. 土石流の流動と堆積に関する研究. 土木研究所報告, (157):p88–153, 1982.
[26] 黃郁婷. 剪力強度折減法應用於動態邊坡穩定性之研究. 國立成功大學資源工程 學系碩博士班碩士論文, 2011.