由於台灣深受地震與颱風等極端氣候影響，邊坡穩定問題一直是土木工程界被高度關注的課題，因此建立高效的防災與決策輔助工具非常重要。本研究以關子嶺邊坡為案例，以克服傳統邊坡滑動模擬在多尺度物理耦合與大變形分析上的技術瓶頸為目標，因傳統的邊坡穩定性分析方法如有限元素法（FEM）在處理邊坡破壞時，常會面臨網格嚴重扭曲而導致數值不穩定；而無網格的再生核粒子法（RKPM）雖能有效應用於大變形問題，但在三維大尺度的邊坡滑動模擬上卻常面臨計算成本過於昂貴的問題。為克服上述限制並兼顧精準度與運算效率，本研究致力於提出一項多階段整合運算框架：首先利用 RKPM 捕捉微觀尺度的起始破壞行為與固體-液體交互作用，接著導入 Support Vector Machine（SVM）演算法識別破壞面，最後結合理想曲面（ICS）方法與兩相土石流高效模擬淺水流動模型 (MoSES_2PDF)，進行宏觀尺度的加速崩塌溢淹動態模擬。此架構成功整合了從邊坡失穩破壞到土石流滑動傳播的完整機制，不僅突破了單一數值方法的限制，更能實現快速且全面的山崩危害評估，為未來的災害減緩與風險決策提供強而有力的科學支援

Taiwan is frequently affected by extreme weather events such as earthquakes and typhoons, making slope stability a critical issue in civil engineering. Therefore, developing efficient disaster prevention and decision-making auxiliary tools is of paramount importance. Taking the Guanziling slope as a case study, this research aims to overcome the technical bottlenecks of traditional slope stability simulations in multi-scale physical coupling and large deformation analysis. Traditional numerical methods, such as the Finite Element Method (FEM), often encounter numerical instability due to severe mesh distortion when processing slope failures. While the meshfree Reproducing Kernel Particle Method (RKPM) can effectively handle large deformation problems, it often faces prohibitively high computational costs in three-dimensional large-scale slope sliding simulations.
To address these limitations while balancing accuracy and computational efficiency, this study proposes a multi-stage integrated computational framework. First, RKPM is utilized to capture micro-scale failure initiation and solid-liquid interactions. Subsequently, a Support Vector Machine (SVM) algorithm is introduced to identify the failure surfaces. Finally, by integrating the Idealized Curved Surface (ICS) method with the MoSES_2PDF architecture, macro-scale accelerated simulations of landslide collapse and inundation dynamics are performed. This framework successfully integrates the complete mechanism from slope instability to landslide propagation. It not only breaks through the constraints of a single numerical method but also achieves rapid and comprehensive landslide hazard assessment, providing robust scientific support for future disaster mitigation and risk-based decision-making.

[1] Keita Abe, Kenichi Soga, and Samila Bandara. Material point method for coupled hydromechanical problems. Journal of Geotechnical and Geoenvironmental Engineering, 140(3):04013033, 2014.
[2] Christophe Ancey. Plasticity and geophysical flows: A review. Journal of non-Newtonian fluid mechanics, 142(1-3):4–35, 2007.
[3] Charles E. Augarde, Seung Jae Lee, and Dimitrios Loukidis. Numerical modelling of large deformation problems in geotechnical engineering: A state-of-the-art review. Soils and Foundations, 61(6):1718–1735, 2021.
[4] Francesca Aureli, Federico Prost, Renato Vacondio, Susanna Dazzi, and Alessia Ferrari. A gpu-accelerated shallow-water scheme for surface runoff simulations. Water, 12(3):637, 2020.
[5] Jonghyuk Baek, Ryan T. Schlinkman, Frank N. Beckwith, and Jiun-Shyan Chen. A deformation-dependent coupled lagrangian/semi-lagrangian meshfree hydromechanical formulation for landslide modeling. Advanced Modeling and Simulation in Engineering Sciences, 9(1):20, 2022.
[6] Samila Bandara and Kenichi Soga. Coupling of soil deformation and pore fluid flow using material point method. Computers and geotechnics, 63:199–214, 2015.
[7] Stephen Beissel and Ted Belytschko. Nodal integration of the element-free galerkin method. Computer methods in applied mechanics and engineering, 139(1-4):49–74, 1996.
[8] Ted Belytschko, Jiun-Shyan Chen, and Michael Hillman. Meshfree and particle methods: fundamentals and applications. John Wiley & Sons, 2023.
[9] Pavel B. Bochev, Clark R. Dohrmann, and Max D. Gunzburger. Stabilization of low-order mixed finite elements for the stokes equations. SIAM Journal on Numerical Analysis, 44(1):82–101, 2006.
[10] Javier Bonet and Sivakumar Kulasegaram. Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations. International journal for numerical methods in engineering, 47(6):1189–1214, 2000.
[11] Bernhard E. Boser, Isabelle M. Guyon, and Vladimir N. Vapnik. A training algorithm for optimal margin classifiers. In Proceedings of the fifth annual workshop on Computational learning theory, pages 144–152, 1992.
[12] André R. Brodtkorb, Martin L. Sætra, and Mustafa Altinakar. Efficient shallow water simulations on gpus: Implementation, visualization, verification, and validation. Computers & Fluids, 55:1–12, 2012.
[13] I. N. Bronstein, K. A. Semendjajew, G. Grosche, V. Ziegler, D. Ziegler, and E. Zeidler. Teubner-Taschenbuch der Mathematik. B.G. Teubner Verlagsgesellschaft, Leipzig, 1996.
[14] Ha H. Bui and Ryoichi Fukagawa. An improved sph method for saturated soils and its application to investigate the mechanisms of embankment failure: Case of hydrostatic pore-water pressure. International Journal for numerical and analytical methods in geomechanics, 37(1):31–50, 2013.
[15] Manuel J. Castro, Sergio Ortega, Marc De la Asuncion, José M. Mantas, and José M. Gallardo. Gpu computing for shallow water flow simulation based on finite volume schemes. Comptes Rendus Mécanique, 339(2-3):165–184, 2011.
[16] Jair Cervantes, Farid Garcia-Lamont, Lisbeth Rodríguez-Mazahua, and Asdrubal Lopez. A comprehensive survey on support vector machine classification: Applications, challenges and trends. Neurocomputing, 408:189–215, 2020.
[17] Jiun-Shyan Chen, Michael Hillman, and Sheng-Wei Chi. Meshfree methods: progress made after 20 years. Journal of Engineering Mechanics, 143(4):04017001, 2017.
[18] Jiun-Shyan Chen, Chunhui Pan, C. M. O. L. Roque, and Hui-Ping Wang. A lagrangian reproducing kernel particle method for metal forming analysis. Computational mechanics, 22:289–307, 1998.
[19] Jiun-Shyan Chen, Chunhui Pan, and Cheng-Tang Wu. Large deformation analysis of rubber based on a reproducing kernel particle method. Computational Mechanics, 19(3):211–227, 1997.
[20] Jiun-Shyan Chen, Chunhui Pan, Cheng-Tang Wu, and Wing Kam Liu. Reproducing kernel particle methods for large deformation analysis of non-linear structures. Computer methods in applied mechanics and engineering, 139(1-4):195–227, 1996.
[21] Jiun-Shyan Chen, Cheng-Tang Wu, Sangpil Yoon, and Yang You. A stabilized conforming nodal integration for galerkin mesh-free methods. International journal for numerical methods in engineering, 50(2):435–466, 2001.
[22] Jiun-Shyan Chen and Youcai Wu. Stability in lagrangian and semi-lagrangian reproducing kernel discretizations using nodal integration in nonlinear solid mechanics. In Advances in meshfree techniques, pages 55–76. Springer, 2007.
[23] Philippe Coussot. Mudflow Rheology and Dynamics. A. A. Balkema, Rotterdam, The Netherlands, 1997.
[24] Zili Dai, Yu Huang, Hualin Cheng, and Qiang Xu. 3d numerical modeling using smoothed particle hydrodynamics of flow-like landslide propagation triggered by the 2008 wenchuan earthquake. Engineering Geology, 180:21–33, 2014.
[25] Jia-Jyun Dong, Yun-Shan Li, Chih-Yu Kuo, Rui-Tang Sung, Ming-Hsu Li, Chyi-Tyi Lee, Chien-Chih Chen, and Wang-Ru Lee. The formation and breach of a short-lived landslide dam at hsiaolin village, taiwan—part i: post-event reconstruction of dam geometry. Engineering geology, 123(1-2):40–59, 2011.
[26] Harvey Dubner and Joseph Abate. Numerical inversion of laplace transforms by relating them to the finite fourier cosine transform. Journal of the ACM (JACM), 15(1):115–123, 1968.
[27] Carl T. Dyka and Robert P. Ingel. An approach for tension instability in smoothed particle hydrodynamics (sph). Computers & structures, 57(4):573–580, 1995.
[28] Delwyn G. Fredlund and R. E. G. Scoular. Using limit equilibrium concepts in finite element slope stability analysis. International Simposium on Slope Stability Engineering, pages 31–47, 1999.
[29] Pai-Chen Guan, Jiun-Shyan Chen, Y. Wu, H. Teng, J. Gaidos, K. Hofstetter, and M. Alsaleh. Semi-lagrangian reproducing kernel formulation and application to modeling earth moving operations. Mechanics of Materials, 41(6):670–683, 2009.
[30] Pai-Chen Guan, Sheng-Wei Chi, Jiun-Shyan Chen, Thomas R. Slawson, and Michael J. Roth. Semi-lagrangian reproducing kernel particle method for fragment-impact problems. International Journal of Impact Engineering, 38(12):1033–1047, 2011.
[31] Fausto Guzzetti, Francesca Ardizzone, Mauro Cardinali, Mauro Rossi, and Daniela Valigi. Landslide volumes and landslide mobilization rates in umbria, central italy. Earth and Planetary Science Letters, 279(3-4):222–229, 2009.
[32] Julian Heß, Yih-Chin Tai, and Yongqi Wang. Debris flows with pore pressure and intergranular friction on rugged topography. Computers & Fluids, 190:139–155, 2019.
[33] Michael Hillman and Jiun-Shyan Chen. An accelerated, convergent, and stable nodal integration in galerkin meshfree methods for linear and nonlinear mechanics. International Journal for Numerical Methods in Engineering, 107(7):603–630, 2016.
[34] Chih-Wei Hsu and Chih-Jen Lin. A comparison of methods for multiclass support vector machines. IEEE transactions on Neural Networks, 13(2):415–425, 2002.
[35] Xin Huang and Marcelo H. Garcia. A herschel–bulkley model for mud flow down a slope. Journal of fluid mechanics, 374:305–333, 1998.
[36] Yu Huang, Weijie Zhang, Qiang Xu, Pan Xie, and Liang Hao. Run-out analysis of flow-like landslides triggered by the ms 8.0 2008 wenchuan earthquake using smoothed particle hydrodynamics. Landslides, 9:275–283, 2012.
[37] H. Iseno, H. Kohashi, K. Furumoto, H. Mori, and M. Ohno. Large model tests of levee reinforcement method with toe drain for seepage failure. In Proc., Annual Symp. of Japanese Geotechnical Society, volume 39, pages 1255–1256, 2004.
[38] Richard M. Iverson, David L. George, K. Allstadt, Mark E. Reid, Brian D. Collins, James W. Vallance, Steve P. Schilling, Jonathan W. Godt, C. M. Cannon, Christopher S. Magirl, et al. Landslide mobility and hazards: implications of the 2014 oso disaster. Earth and Planetary Science Letters, 412:197–208, 2015.
[39] A. R. Khoei and T. Mohammadnejad. Numerical modeling of multiphase fluid flow in deforming porous media: a comparison between two-and three-phase models for seismic analysis of earth and rockfill dams. Computers and Geotechnics, 38(2):142–166, 2011.
[40] Chi-Jyun Ko, Po-Chih Chen, Hock-Kiet Wong, and Yih-Chin Tai. Moses 2pdf: A gis-compatible gpu-accelerated high-performance simulation tool for grain-fluid shallow flows. arXiv preprint arXiv:2104.06784, 2021.
[41] Chih-Yu Kuo, Yih-Chin Tai, François Bouchut, Anne Mangeney, Marica Pelanti, Rou-Fei Chen, and K. J. Chang. Simulation of tsaoling landslide, taiwan, based on saint venant equations over general topography. Engineering Geology, 104(3-4):181–189, 2009.
[42] Chih-Yu Kuo, Yih-Chin Tai, C. C. Chen, K. J. Chang, A. Y. Siau, Jia-Jyun Dong, R. H. Han, T. Shimamoto, and Chyi-Tyi Lee. The landslide stage of the hsiaolin catastrophe: Simulation and validation. Journal of Geophysical Research: Earth Surface, 116(F4), 2011.
[43] Land Eng. Consultants. Monitoring and early warning system for landslide-prone slopes in tainan city (110–112): First semi-annual report (rev. 1). Technical report, Land Engineering Consultants, Co., Ltd., Tainan, Taiwan, September 2022.
[44] Weijian Liang, Jidong Zhao, Huanran Wu, and Kenichi Soga. Multiscale, multiphysics modeling of saturated granular materials in large deformation. Computer Methods in Applied Mechanics and Engineering, 405:115871, 2023.
[45] Ching-Weei Lin, Wei-Shu Chang, Shou-Heng Liu, Tsai-Tsung Tsai, Shin-Pin Lee, Yun-Chung Tsang, Chjeng-Lun Shieh, and Chih-Ming Tseng. Landslides triggered by the 7 august 2009 typhoon morakot in southern taiwan. Engineering Geology, 123(1-2):3–12, 2011.
[46] Wing Kam Liu, Herman Chang, Jiun-Shyan Chen, and Ted Belytschko. Arbitrary lagrangian-eulerian petrov-galerkin finite elements for nonlinear continua. Computer methods in applied mechanics and engineering, 68(3):259–310, 1988.
[47] Wing Kam Liu, Jiun-Shyan Chen, Ted Belytschko, and Yi Fei Zhang. Adaptive ale finite elements with particular reference to external work rate on frictional interface. Computer Methods in Applied Mechanics and Engineering, 93(2):189–216, 1991.
[48] Wing Kam Liu, Sukky Jun, Shaofan Li, Jonathan Adee, and Ted Belytschko. Reproducing kernel particle methods for structural dynamics. International Journal for Numerical Methods in Engineering, 38(10):1655–1679, 1995.
[49] Wing Kam Liu, Sukky Jun, and Yi Fei Zhang. Reproducing kernel particle methods. International journal for numerical methods in fluids, 20(8-9):1081–1106, 1995.
[50] Leon B. Lucy. A numerical approach to the testing of the fission hypothesis. Astronomical Journal, vol. 82, Dec. 1977, p. 1013-1024., 82:1013–1024, 1977.
[51] Martin Mergili, Michel Jaboyedoff, José Pullarello, and Shiva P. Pudasaini. Back calculation of the 2017 piz cengalo–bondo landslide cascade with r. avaflow: what we can do and what we can learn. Natural Hazards and Earth System Sciences, 20(2):505–520, 2020.
[52] Hirotoshi Mori. SPH method to simulate river levee failures. PhD thesis, University of Cambridge, Cambridge, 2008.
[53] Hirotoshi Mori, N. Fukuhara, A. Hattori, R. Kuwano, Kenichi Soga, Y. Saito, and T. Sasaki. The sph method for simulating the progressive sliding failure of a river levee. Jpn Geotech J, 9(4):687–96, 2014.
[54] P. W. Randles and L. D. Libersky. Normalized sph with stress points. International Journal for Numerical Methods in Engineering, 48(10):1445–1462, 2000.
[55] Amit Saxena, Mukesh Prasad, Akshansh Gupta, Neha Bharill, Om Prakash Patel, Aruna Tiwari, Meng Joo Er, Weiping Ding, and Chin-Teng Lin. A review of clustering techniques and developments. Neurocomputing, 267:664–681, 2017.
[56] Martin Schanz and A. H.-D. Cheng. Transient wave propagation in a one-dimensional poroelastic column. Acta Mechanica, 145(1):1–18, 2000.
[57] Adrian E. Scheidegger. On the prediction of the reach and velocity of catastrophic landslides. Rock Mechanics and Rock Engineering, 5(4):231–236, 1973.
[58] Kenichi Soga, E. Alonso, Alba Yerro, K. Kumar, and Samila Bandara. Trends in large-deformation analysis of landslide mass movements with particular emphasis on the material point method. Géotechnique, 66(3):248–273, 2016.
[59] Deborah Sulsky, Zhen Chen, and Howard L. Schreyer. A particle method for history-dependent materials. Computer methods in applied mechanics and engineering, 118(1-2):179–196, 1994.
[60] Deborah Sulsky, Shi-Jian Zhou, and Howard L. Schreyer. Application of a particle-in-cell method to solid mechanics. Computer physics communications, 87(1-2):236–252, 1995.
[61] WaiChing Sun, Jakob T. Ostien, and Andrew G. Salinger. A stabilized assumed deformation gradient finite element formulation for strongly coupled poromechanical simulations at finite strain. International Journal for Numerical and Analytical Methods in Geomechanics, 37(16):2755–2788, 2013.
[62] Jeff W. Swegle, Darrell L. Hicks, and Steve W. Attaway. Smoothed particle hydrodynamics stability analysis. Journal of computational physics, 116(1):123–134, 1995.
[63] Yih-Chin Tai, Julian Heß, and Yongqi 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.
[64] Yih-Chin Tai, Chi-Jyun Ko, Kun-Ding Li, Yu-Chen Wu, Chih-Yu Kuo, Rou-Fei Chen, and Ching-Weei Lin. An idealized landslide failure surface and its impacts on the traveling paths. Frontiers in Earth Science, 8:313, 2020.
[65] Yih-Chin Tai, Chih-Yu Kuo, and Wai-How Hui. An alternative depth-integrated formulation for granular avalanches over temporally varying topography with small curvature. Geophysical & Astrophysical Fluid Dynamics, 106(6):596–629, 2012.
[66] Lauren E. D. Talbot, Joel Given, Ezra Y. S. Tjung, Yong Liang, Khaled Chowdhury, Raymond Seed, and Kenichi Soga. Modeling large-deformation features of the lower san fernando dam failure with the material point method. Computers and Geotechnics, 165:105881, 2024.
[67] Antonello Troncone, Luigi Pugliese, Andrea Parise, and Enrico Conte. A simple method to reduce mesh dependency in modelling landslides involving brittle soils. Géotechnique Letters, 12(3):167–173, 2022.
[68] Antonello Troncone, Luigi Pugliese, Andrea Parise, Pietro Mazzuca, and Enrico Conte. Post-failure stage analysis of flow-type landslides using different numerical techniques. Computers and Geotechnics, 182:107152, 2025.
[69] M. Th. van Genuchten. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil science society of America journal, 44(5):892–898, 1980.
[70] Vladimir N. Vapnik. The Nature of Statistical Learning Theory. Springer, New York, second edition, 1995.
[71] Yanran Wang, Jonghyuk Baek, Yichun Tang, Jing Du, Mike Hillman, and Jiun-Shyan Chen. Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures. Computational Mechanics, 73(4):907–942, 2024.
[72] Haoyan Wei, Jiun-Shyan Chen, Frank Beckwith, and Jonghyuk Baek. A naturally stabilized semi-lagrangian meshfree formulation for multiphase porous media with application to landslide modeling. Journal of Engineering Mechanics, 146(4):04020012, 2020.
[73] Haoyan Wei, Jiun-Shyan Chen, and Michael Hillman. A stabilized nodally integrated meshfree formulation for fully coupled hydro-mechanical analysis of fluid-saturated porous media. Computers & Fluids, 141:105–115, 2016.
[74] Joshua A. White and Ronaldo I. Borja. Stabilized low-order finite elements for coupled solid-deformation/fluid-diffusion and their application to fault zone transients. Computer Methods in Applied Mechanics and Engineering, 197(49-50):4353–4366, 2008.
[75] Hock-Kiet Wong, Yih-Chin Tai, Haruka Tsunetaka, and Norifumi Hotta. Two-phase approach to modeling the grain-fluid flows with deposition and entrainment over rugged topography. Advances in Water Resources, 188:104691, 2024.
[76] Fengyuan Wu, Wei Sun, Xinchao Li, Yongping Guan, and Manman Dong. Material point method-based simulation of dynamic process of soil landslides considering pore fluid pressure. International Journal for Numerical and Analytical Methods in Geomechanics, 47(13):2385–2404, 2023.
[77] Z. H. Yao, M. W. Yuan, H. W. Zhang, K. P. Wang, and Z. Zhang. Material point method for numerical simulation of failure phenomena in multiphase porous media. In Computational Mechanics: Proceedings of “International Symposium on Computational Mechanics” July 30–August 1, 2007, Beijing, China, pages 36–47. Springer, 2009.
[78] Duan Z. Zhang, Qisu Zou, W. Brian VanderHeyden, and Xia Ma. Material point method applied to multiphase flows. Journal of Computational Physics, 227(6):3159–3173, 2008.
[79] W. J. Zhang and K. Maeda. The model test and sph simulations for slope and levee failure under heavy rainfall considering the coupling of soil, water and air. In Soil Behavior and Geomechanics, pages 538–547. American Society of Civil Engineers, 2014.
[80] Olgierd C. Zienkiewicz, A. H. C. Chan, M. Pastor, B. A. Schrefler, and T. Shiomi. Computational geomechanics, volume 613. Citeseer, 1999.
[81] Olgierd Cecil Zienkiewicz, C. Humpheson, and R. W. Lewis. Associated and non-associated visco-plasticity and plasticity in soil mechanics. Géotechnique, 25(4):671–689, 1975.
[82] Olgierd Cecil Zienkiewicz, Y. M. Xie, B. A. Schrefler, A. Ledesma, and N. Bićanić. Static and dynamic behaviour of soils: a rational approach to quantitative solutions. ii. semi-saturated problems. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 429(1877):311–321, 1990.