山區邊坡崩塌災害一直都是台灣面臨的一大問題，隨著工程分析軟體的發展，許多模擬方法已普遍應用到大地工程上，例如：極限平衡法(LEM)及有限元素法(FEM)，然而極限平衡法只能得到邊坡的破壞面以及安全係數，傳統的有限元素法在模擬大變形或應變問題時，容易發生網格扭曲造成模擬中止或數值解不精確，因此發展出了進階有限元素法，其中耦合歐拉-拉格朗日(CEL)技術結合了歐拉及拉格朗日技術的優點，解決網格扭曲的問題，得以模擬大變形或應變問題。
本文以CEL技術模擬國內兩起邊坡崩塌案例，分別是台北藝術大學填土邊坡崩塌事件以及高雄燕巢泥岩邊坡崩塌事件。首先以極限平衡法取得案例的地下水位以下之材料參數，再代入至CEL模型進行崩塌案例模擬，模擬滑動材料的滑動及堆積過程以及與結構物的互制行為。模擬結果顯示，堆積高度與材料參數的凝聚力與摩擦角有關；結構物的位移距離會受地形面摩擦性質及擋土設施幾何的影響。結果表示CEL不只呈現出崩塌的過程，在流固耦合方面有很好的應用。

Slope failure disasters have always been a major problem in Taiwan. With the development of engineering analysis software, lots of simulation methods, such as the limit equilibrium method (LEM) and the finite element method (FEM), have been widely applied to the geotechnical engineering field. However, LEM can only estimate the failure surface and factor of safety of the slope. When the traditional FEM is used to solve the large deformation problems, non-convergence or early termination of the FEM results may occur due to mesh distortion. Advanced FEMs, such as Coupled Eulerian-Lagrangian (CEL) method, were therefore developed. By combining the advantages of Lagrangian and Eulerian techniques, CEL can be used to solve the mesh distortion problems.
In this study, a CEL method was utilized to simulate two slope failure cases in Taiwan, which are Taipei National University of the Arts backfill slope failure and Yanchao mudstone slope failure. The LEM was firstly used to obtain the material properties below groundwater level, the obtained material properties were then applied to the CEL model to simulate the sliding and accumulation processes of the sliding material and the interaction behavior between the sliding material and the structure. Simulation results show that accumulation height is related to materials’ cohesion and friction angle, and structure displacement is affected by friction properties of the terrain and the size of the retaining facility. This study demonstrates that CEL technique can not only capture failure process of the slope bust also has a good application in aspect of fluid-solid coupling.

1. 台北市大地工程技師公會。國立台北藝術大學網球場下邊坡坍滑原因鑑定及長期整治方案建議工作報告書。(2001).
2. 徐采筠。驗證與應用耦合歐拉－拉格朗日技術：以顆粒流試驗為例。 國立成功大學土木系，碩士論文。(2019)
3. 陳時祖。台灣西南部地區泥(頁)岩之工程地質特性。地工技術 ； 48期 (1994 / 12 / 01) ， P25 – 33。(1994)
4. Cox, R., Lowe, D. R., & Cullers, R. L. The influence of sediment recycling and basement composition on evolution of mudrock chemistry in the southwestern United States. Geochimica et Cosmochimica Acta, 59(14), 2919-2940. (1995).
5. Chang, H. W., Tien, Y. M., & Juang, C. H. Formation of south-facing bald mudstone slopes in southwestern Taiwan. Engineering geology, 42(1), 37-49. (1996).
6. Dick, J. C., Shakoor, A., & Wells, N. A geological approach toward developing a mudrock-durability classification system. Canadian Geotechnical Journal, 31(1), 17-27. (1994).
7. Demers, D., Robitaille, D., Locat, P., & Potvin, J. Inventory of large landslides in sensitive clay in the province of Québec, Canada: preliminary analysis. In Landslides in sensitive clays (pp. 77-89). Springer, Dordrecht. (2014).

8. Dey, R., Hawlader, B., Phillips, R., & Soga, K. Stability analysis of a river bank slope with an existing shear band. In Proceedings of the 6th Canadian geohazards conference. (2014).
9. Dey, R., Hawlader, B., Phillips, R., & Soga, K. Large deformation finite-element modeling of progressive failure leading to spread in sensitive clay slopes. Géotechnique, 65(8), 657-668. (2015)
10. Dey, R., Hawlader, B., Phillips, R., & Soga, K. Modeling of large-deformation behaviour of marine sensitive clays and its application to submarine slope stability analysis. Canadian Geotechnical Journal, 53(7), 1138-1155. (2016).
11. Higuchi, K., Chigira, M., & Lee, D. H. High rates of erosion and rapid weathering in a Plio-Pleistocene mudstone badland, Taiwan. Catena, 106, 68-82. (2013).
12. Hung, C., Liu, C. H., & Chang, C. M. Numerical investigation of rainfall-induced landslide in mudstone using coupled finite and discrete element analysis. Geofluids. (2018).
13. Retallack, G. J. A paleopedological approach to the interpretation of terrestrial sedimentary rocks: The mid-Tertiary fossil soils of Badlands National Park, South Dakota. Geological Society of America Bulletin, 94(7), 823-840. (1983).
14. Richard E.. Goodman. Engineering Geology: Rock in Engineering Construction. J. Wiley. (1993).
15. Hu, P., Wang, D., Stanier, S. A., & Cassidy, M. J. Assessing the punch-through hazard of a spudcan on sand overlying clay. Géotechnique,65(11), 883-896. (2015).
16. Khoa, H. D. V., & Jostad, H. P. Application of coupled Eulerian- Lagrangian method to large deformation analyses of offshore foundations and suction anchors. International Journal of Offshore and Polar Engineering, 26(03), 304-314. (2016).
17. Locat, A., Leroueil, S., Bernander, S., Demers, D., Jostad, H. P., & Ouehb, L. Progressive failures in eastern Canadian and Scandinavian sensitive clays. Canadian Geotechnical Journal, 48(11), 1696-1712. (2011).
18. Locat, A., Leroueil, S., Locat, P., Demers, D., Robitaille, D., & Lefebvre, G. In situ characterization of the Saint-Jude landslide, Québec, Canada. In Geotechnical and Geophysical Site Characterization: Proceedings of the 4th International Conference on Site Characterization ISC-4 (Vol. 1, pp. 507-514). Taylor & Francis Books Ltd. (2013).
19. Locat, A., Locat, P., Demers, D., Leroueil, S., Robitaille, D., & Lefebvre, G. The Saint-Jude landslide of 10 May 2010, Quebec, Canada: Investigation and characterization of the landslide and its failure mechanism. Canadian geotechnical journal, 54(10), 1357-1374. (2017).
20. Lee, K., & Jeong, S. Large deformation FE analysis of a debris flow with entrainment of the soil layer. Computers and Geotechnics, 96, 258-268. (2018).
21. Lin, C. -H., Hung, -C., Hsu, T. -Y. Simulations of granular material behaviors using Coupled Eulerian-Lagrangian approach: From collapse to fluid-structure interaction. Computers and Geotechnics. (Prepared) (2019a).

22. Lin, C. H., Hung, C., Weng, M. C., Lin, M. L., & Uzuoka, R. Failure mechanism of a mudstone slope embedded with steep anti-dip layered sandstones: case of the 2016 Yanchao catastrophic landslide in Taiwan. Landslides, 16(11), 2233-2245. (2019b).
23. Moriguchi, S., Borja, R. I., Yashima, A., & Sawada, K. Estimating the impact force generated by granular flow on a rigid obstruction. Acta Geotechnica, 4(1), 57-71. (2009).
24. Pradhan, A. M. S., Kang, H. S., Lee, J. S., & Kim, Y. T. An ensemble landslide hazard model incorporating rainfall threshold for Mt. Umyeon, South Korea. Bulletin of Engineering Geology and the Environment, 78(1), 131-146. (2019).
25. Qiu, G., Henke, S., & Grabe, J. Application of a Coupled Eulerian- Lagrangian approach on geomechanical problems involving large deformations. Computers and Geotechnics, 38(1), 30-39. (2011).
26. Shakoor, A., & Smithmyer, A. J. An analysis of storm-induced landslides in colluvial soils overlying mudrock sequences, southeastern Ohio, USA. Engineering Geology, 78(3-4), 257-274. (2005).
27. Wang, C., Saha, B., & Hawlader, B. Some factors affecting retrogressive failure of sensitive clay slopes using large deformation finite element modeling. In Proceedings of the 68th Canadian Geotechnical Conference and the 7th Canadian Permafrost Conference, Quebec City, Canada, Sept (pp. 21-23). (2015).
28. Wang, C., Hawlader, B., & Perret, D. Finite element simulation of the 2010 Saint-Jude landslide in Quebec. In Proceedings of the 69th Canadian Geotechnical Conference, Quebec City, Quebec, Canada. (2016).
29. Yune, C. Y., Chae, Y. K., Paik, J., Kim, G., Lee, S. W., & Seo, H. S. Debris flow in metropolitan area—2011 Seoul debris flow. Journal of Mountain Science, 10(2), 199-206. (2013).