This research investigates the post-failure behavior of the Yang Ming Chiao-Tung University slope using the Discontinuous Deformation Analysis (DDA) method. A series of parametric case studies were conducted to evaluate the effects of friction angle variations and joint or discontinuity orientations on slope stability and deformation mechanisms in National Yang Ming Chiao Tung University slope as the study site. Previously, there were three major disasters reported in the study site, mostly consist of shallow landslide caused by colluvium failure after natural disasters happening. Each case incorporated different combinations of material properties and geometric discontinuities to simulate possible failure scenarios based on field conditions.
The results demonstrate that in the present condition, the slope is in stable condition and significant block movements were not found, however, when natural hazard that caused reductions in joint friction angle in both colluvium and sandstone layer, the slope may slide and fail, especially in the lower slope regions. The presence and orientation of discontinuities were also found to strongly influence the failure pattern, often shifting behavior from sliding to rotational collapse. The DDA simulation outcomes were validated through real-world risk maps and previous disaster record occurred at the study site. It is found that the simulations aligned well with observed hazard zones, especially in critical areas with low factor of safety. The study concludes that both material strength parameters and structural discontinuities play essential roles in post-failure behavior, and that DDA is a reliable tool for evaluating these processes.

1. 台灣世曦工程顧問股份有限公司 (2020)，109年山坡地總體檢及設施檢測委託技術服務案期末報告書。國立陽明交通大學委託之山坡地總體檢期末報告。國立陽明交通大學，台北，台灣。
2. 吳振瑋 (2023)， 大規模順向坡滑動機制受岩層弱面分布與力學性質之影響。 國立中央大學土木工程學系碩士論文，桃園，台灣。
3. 陳美彣 (2025)， 探討岩心資料模擬岩層裂隙分佈對大規模順向坡滑動機制與機率之影響。 國立中央大學土木工程學系碩士論文，桃園，台灣。
4. Aaron, J., and McDougall, S. (2019). “Rock Avalanche Mobility: The Role of Path Material.”.Engineering.Geology,.257:.105-126. https://doi.org/10.1016/j.enggeo.2019.05.003.
5. Abramson, L., Lee, T. Boyce, G., and Sharma, S. (2002). “Slope Stability and Stabilization Methods (2nd Edition)”. Wiley. New York, United States of America.
6. Ataei, M., and Bodaghabadi, S. (2008). “Comprehensive Analysis of Slope Stability and Determination of Stable Slopes in the Chador-Malu Iron Ore Mine Using Numerical and Limit Equilibrium Methods.” Journal of China University of Mining and Technology 18 (4): 488–493. https://doi.org/10.1016/S1006-1266(08)60281-3.
7. Arbanas, M., Snježana, and Arbanas, Z. (2015). “Landslides: A Guide to Researching Landslide Phenomena and Processes”. IGI Global Scientific Publishing. Hershey, United States of America. https://doi.org/10.4018/978-1-4666-7336-6.
8. Bahabadi, K., Mohsen, Bafghi, A. Y., Marji, M. F., Shahami, H., and Abolfazl, A. (2024). “A Hybridized DDA-DDM for Modeling Jointed Rock Masses.” Theoretical and Applied Fracture Mechanics 131: 104-445. https://doi.org/10.1016/j.tafmec.2024.104445.
9. Barton, N., Lien, R., and Lunde, J. (1974). “Engineering Classification of Rock Masses for the Design of Tunnel Support.” Rock Mechanics Felsmechanik Mécanique Des Roches 6 (4): 189–236. https://doi.org/10.1007/BF01239496.
10. Barton, N. (1998). “Quantitative Description of Rock Masses for the Design of NMT Reinforcement” International Conference on Hydro Power Development in Himalayas, Shimla, India., January 1998: 379–400.
11. Bobet, A., Fakhimi, A., Johnson, S., Morris, J., Tonon, F., and Yeung, M. R. (2009). “Numerical Models in Discontinuous Media: Review of Advances for Rock Mechanics Applications.” Journal of Geotechnical and Geoenvironmental Engineering 135 (11): 1547–1561. https://doi.org/10.1061/(asce)gt.1943-5606.0000133.
12. Chen, H., Crosta, G. B., and Lee, C. F. (2006). “Erosional Effects on Runout of Fast Landslides, Debris Flows and Avalanches: A Numerical Investigation.” Geotechnique 56 (5): 305–322. https://doi.org/10.1680/geot.2006.56.5.305.
13. Cheng, Y. M., and Yip, C. J. (2007). “Three-Dimensional Asymmetrical Slope Stability Analysis Extension of Bishop’s, Janbu’s, and Morgenstern–Price’s Techniques.” Journal of Geotechnical and Geoenvironmental Engineering 133 (12): 1544–1555. https://doi.org/10.1061/(asce)1090-0241(2007)133:12(1544).
14. Christian, J. T., Charles, C. L., and Gregory B. B.. (1994). “Reliability Applied to Slope Stability Analysis.” Journal of Geotechnical Engineering 120 (12): 2180–2207. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:12(2180)
15. Chung, M. C., Chen, C. H., Lee, C. F., Huang, W. K., and Tan, C. H. (2018). “Failure Impact Assessment for Large-Scale Landslides Located near Human Settlement: Case Study in Southern Taiwan.” Journal of Sustainability 10 (5): 1005 - 1091. https://doi.org/10.3390/su10051491.
16. Crosta, G. B., Imposimato, S., and Roddeman, D. G. (2003). “Numerical Modelling of Large Landslides Stability and Runout.” Natural Hazards and Earth System Science 3 (6): 523–538. https://doi.org/10.5194/nhess-3-523-2003.
17. Crozier, M. J. (2010). “Deciphering the Effect of Climate Change on Landslide Activity: A Review.” Geomorphology 124 (3–4): 260–267. https://doi.org/10.1016/j.geomorph.2010.04.009.
18. Cruden, D. M. (1991). “A Simple Definition of a Landslide.” Bulletin of the International Association of Engineering Geology - Bulletin de l’Association Internationale de Géologie de l’Ingénieur 43 (1): 27–29. https://doi.org/10.1007/BF02590167.
19. Cruden, D. M,, and Varnes, D. J. (1996). “Landslide Types and Processes, Special Report ” National Academy of Sciences, 247:36-75. https://www.researchgate.net/publication/269710355_CrudenDM_Varnes_DJ_1996_Landslide_Types_and_Processes_Special_Report_Transportation_Research_Board_National_Academy_of_Sciences_24736-75.
20. Das, B. M., and Sobhan, K. (2013). “Principles of Geotechnical Engineering 8th Edition.” Cengage Learning. Stamford, United States of America. ISBN-13: 9780357420553
21. Deng, D. P., Lian H. Z., and Li, L. (2017). “Limit Equilibrium Analysis for Rock Slope Stability Using Basic Hoek–Brown Strength Criterion.” Journal of Central South University 24 (9): 2154–2163. https://doi.org/10.1007/s11771-017-3624-4.
22. Doolin, D. M., and Sitar, N. (2002). “Displacement Accuracy of Discontinuous Deformation Analysis Method Applied to Sliding Block.” Journal of Engineering Mechanics 128 (11): 1158–1168. https://doi.org/10.1061/(asce)0733-9399(2002)128:11(1158).
23. Doolin, D. M., and Sitar, N. (2004). “Time Integration in Discontinuous Deformation Analysis.” Journal of Engineering Mechanics 130 (3): 249–258. https://doi.org/10.1061/(asce)0733-9399(2004)130:3(249). 2004.
24. Fu, X. D., Qian S., Zhang, Y. H., Chen, J., Zhang, S. K., and Zhang, Z. P. (2017). “Computation of the Safety Factor for Slope Stability Using Discontinuous Deformation Analysis and the Vector Sum Method.” Computers and Geotechnics 92: 68–76. https://doi.org/10.1016/j.compgeo.2017.07.026.
25. Giordano, A., Mele, E., and Luca, A. D. (2002). “Modelling of Historical Masonry Structures: Comparison of Different Approaches through a Case Study.” Engineering Structures 24 (8): 1057–1069. https://doi.org/10.1016/S0141-0296(02)00033-0.
26. Goodman, R. E. (1989). “Introduction to Rock Mechanics. 2nd Edition.” Wiley. New York, United States of America, 1-273. https://doi.org/10.1061/9780784484036.036.
27. Gong, S., Hu, C. B., Guo, L. X., Ling, D. S., Chen, G. Q., and Zhang, X. L. (2022). “Extended DDA with Rotation Remedies and Cohesive Crack Model for Simulation of the Dynamic Seismic Landslide.” Engineering Fracture Mechanics 266: 108-395. https://doi.org/10.1016/j.engfracmech.2022.108395.
28. Griffiths, D. V., and Lane, P. A. 2001. “Slope Stability Analysis by Finite Elements.” Géotechnique 51 (7): 653–654. https://doi.org/10.1680/geot.51.7.653.51390.
29. Guo, L. X., Chen G. Q., Gong S. L., Sun, H., and Chantat, K. (2021). “Analysis of Rainfall-Induced Landslide Using the Extended DDA by Incorporating Matric Suction.” Computers and Geotechnics 135: 104-145. https://doi.org/10.1016/j.compgeo.2021.104145.
30. Hashimoto, R., Koyama, T., Kikumoto, M., Saito, T., and Mimura, M. (2014). “Stability Analysis of Masonry Structure in Angkor Ruin Considering the Construction Quality of the Foundation.” Journal of Civil Engineering Research 4: 78–82. https://doi.org/10.5923/c.jce.201402.13.
31. Hencher, S. (2004). “Weathering and Erosion Processes in Rocks – Implications for Geotechnical Engineering.” Proceedings Symposium on Hong Kong Soils and Rocks, March, Hong Kong, 29–79.
32. Highland, L. M., and Bobrowsky, P. (2008). “The Landslide Handbook - A Guide to Understanding Landslides.” Landslides: Global Risk Preparedness 1: 1–147.
33. Hoek, E., and Brown, E. T. (2019). “The Hoek–Brown Failure Criterion and GSI – 2018 Edition.” Journal of Rock Mechanics and Geotechnical Engineering 11 (3): 445–463. https://doi.org/10.1016/j.jrmge.2018.08.001.
34. Hong, Z., Liu, S. G., Zheng, L., Zhu, H. H., Zhuang, X. Y., Zhang, Y. B., and Wu, Y. Q. (2018). “Method for Resolving Contact Indeterminacy in Three-Dimensional Discontinuous Deformation Analysis.” International Journal of Geomechanics 18 (10): 1–19. https://doi.org/10.1061/(asce)gm.1943-5622.0001259
35. Hungr, O., Leroueil, S., and Picarelli, L. (2014). “The Varnes Classification of Landslide Types, an Update.” Journal of Landslides 11 (2): 167–194. https://doi.org/10.1007/s10346-013-0436-y.
36. Ibrahim, D., Rebecca, D., Robert, L. J., and George, T. F. (2011). “Measurements of the Static Friction Coefficient between Tin Surfaces and Comparison to a Theoretical Model.” Journal of Tribology 133 (3): 57-63. https://doi.org/10.1115/1.4004338.
37. Imre, B. (2004). “Numerical Slope Stability Simulations of the Northern Wall of Eastern Candor Chasma (Mars) Utilizing a Distinct Element Method.” Planetary and Space Science 52 (14): 1303–1319. https://doi.org/10.1016/j.pss.2004.09.001.
38. Israelsson, J. I. (1996). “Short Descriptions of UDEC and 3DEC.” Developments in Geotechnical Engineering 79 (C): 523–528. https://doi.org/10.1016/S0165-1250(96)80041-1.
39. Jiao, Y. Y., Huan Q. Z., Tang, H. M., Zhang, X. L., Adoko, A. C., and Hu N. T. (2014). “Simulating the Process of Reservoir-Impoundment-Induced Landslide Using the Extended DDA Method.” Engineering Geology 182 : 37–48. https://doi.org/10.1016/j.enggeo.2014.08.016.
40. Jeng, C. J., Tan C. H., Chung M. C., Lee J. F., and Fei, L. Y. (2010). “Monitoring and Numerical Analysis for Typhoon Morakot Induced Landslide in Cau-Pin Area.” 4th Japan-Taiwan Joint Workshop on Geotechnical Hazards from Large Earthquakes and Heavy Rainfall, Sendai, Japan., October, 2010.
41. Juang, C. H., Yuin Y. J., and Lee, D. H. (1998). “Stability Analysis of Existing Slopes Considering Uncertainty.” Engineering Geology 49 (2): 111–122. https://doi.org/10.1016/S0013-7952(97)00078-1.
42. Khan, M. S., Riahi, A., and Curran, J. H. (2010). “Effects of Time-Step Size on the Efficiency of Discontinious Deformation Analysis.” ISRM International Symposium - 6th Asian Rock Mechanics Symposium, October, New Delhi, India: 45-68.
43. Langfelder, L. J., and Nivargikar, V. R. (1967). “Some Factors Influencing Shear Strength and Compressibility of Compacted Soils.” Highway Research Board 177: 4–21. http://onlinepubs.trb.org/Onlinepubs/hrr/1967/177/177-002.pdf.
44. Li, J. Y., Wang, W. D., Chen, G. Q., and Zheng, H. (2022). “Simulating the Impact of Highway Construction to Landslides with Creep Deformation Using DDA: A Case Study of Qinglong Landslide in Guizhou Province, China.” Arabian Journal of Geosciences 15 (2): 1-40. https://doi.org/10.1007/s12517-021-09287-2.
45. Liu, C., Liu, X. L., Peng, X. C., Wang, E. Z., and Wang, S. J. (2019). “Application of 3D-DDA Integrated with Unmanned Aerial Vehicle–Laser Scanner (UAV-LS) Photogrammetry for Stability Analysis of a Blocky Rock Mass Slope.” Landslides 16 (9): 1645–1661. https://doi.org/10.1007/s10346-019-01196-6.
46. Liu, K. F., and Huang, M. C. (2009). “Numerical Simulation of Debris Flows.” Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering 6. Virtual, Online, 375–382. https://doi.org/10.1115/OMAE2009-79197.
47. Liu, Z. Y., Su, L. J., Zhang, C. L., Iqbal, J., Hu, B. L., and Dong, Z. B. (2020). “Investigation of the Dynamic Process of the Xinmo Landslide Using the Discrete Element Method.” Computers and Geotechnics 123: 103-561. https://doi.org/10.1016/j.compgeo.2020.103561.
48. Lo, C. M., Lin, M. L., Tang, C. L., and Hu, J. C. (2011). “A Kinematic Model of the Hsiaolin Landslide Calibrated to the Morphology of the Landslide Deposit.” Engineering Geology 123 (1–2): 22–39. https://doi.org/10.1016/j.enggeo.2011.07.002.
49. Lu, C. Y., Tang, C. L., Chan, Y. C., Hu, J. C., and Chi, C. C. (2014). “Forecasting Landslide Hazard by the 3D Discrete Element Method: A Case Study of the Unstable Slope in the Lushan Hot Spring District, Central Taiwan.” Engineering Geology 183: 14–30. https://doi.org/10.1016/j.enggeo.2014.09.007.
50. Ma, S., He, C., Zhao, Z. Y., Wen N., Xing Z., and Zhang, Z. Y. (2017). “Modeling of Rock Joints Under Cyclic Loading Conditions Using Discontinuous Deformation Analysis.” Rock Mechanics and Rock Engineering 50 (5): 1205–1215. https://doi.org/10.1007/s00603-016-1158-y.
51. MacLaughlin, M. M., and Doolin, D. M., (2006). “Review of Validation of the Discontinuous Deformation Analysis (DDA) Method.” International Journal for Numerical and Analytical Methods in Geomechanics 30 (4): 271–305. https://doi.org/10.1002/nag.427.
52. MacLaughlin, M. M., Sitar, N., Doolin, D. M. and Abbot, T. (2001). “Investigation of Slope-Stability Kinematics Using Discontinuous Deformation Analysis.” International Journal of Rock Mechanics and Mining Sciences 38 (5): 753–762. https://doi.org/10.1016/S1365-1609(01)00038-7.
53. Mikola, R. G., Hatami, K., and Doolin, D. M. (2011). “Elastic-Plastic Discontinuous Deformation Analysis Using Mohr-Coulomb Model.” Transactions of the Institutions of Mining and Metallurgy, Section A: Mining Technology 120 (3): 148–157. https://doi.org/10.1179/1743286311Y.0000000006.
54. Ning, Y. J., Xin, M. A., Qing, L., and Ma, G. W. (2012). “Modeling Rock Failure Using the Numerical Manifold Method Followed by the Discontinuous Deformation Analysis.” Acta Mechanica Sinica/Lixue Xuebao 28 (3): 760–773. https://doi.org/10.1007/s10409-012-0055-1.
55. Ning, Y. J., and Zhao, Z. Y. (2013). “A Detailed Investigation of Block Dynamic Sliding by the Discontinuous Deformation Analysis.” International Journal for Numerical and Analytical Methods in Geomechanics 30 (13): 1303–1336. https://doi.org/10.1002/nag.
56. Niroumand, H., Kassim, K. A., Ghafooripour, A., Nazir, R., and Far, S. Y. Z. (2012). “Investigation of Slope Failures in Soil Mechanics.” Electronic Journal of Geotechnical Engineering 17: 2703–2720.
57. Oktarianty, H. (2019). “Influence of DifferenceDip Direction on the Relationship of Friction Angel and Factor of Safety in Wedge Failure for Rock Slope.” IOP Conference Series: Earth and Environmental Science 353, October, Pangkal Pinang, Indonesia, 352-356. https://doi.org/10.1088/1755-1315/353/1/012028.
58. Pan, J. H., Peng Y., and Xiao, P. Z. (2024). “Numerical Modeling of Earthquake-Induced Landslides Using Updated Lagrangian Nonlocal General Particle Dynamics Method.” Engineering Geology 340: 107-131. https://doi.org/10.1016/j.enggeo.2024.107641.
59. Peng, X. Y., Yu, P. C., Chen, G. Q., Xia, M. Y., and Zhang, Y. B. (2020). “Development of a Coupled DDA–SPH Method and Its Application to Dynamic Simulation of Landslides Involving Solid–Fluid Interaction.” Rock Mechanics and Rock Engineering 53 (1): 113–131. https://doi.org/10.1007/s00603-019-01900-x.
60. Phoon, K. K., Zi, J. C., Jian, J., Yat, F. L., Najjar, S, Takayuki S., Tang, C., Zhen Y. Y., Yoshida, I., and Ching, J. Y. (2022). “Geotechnical Uncertainty, Modeling, and Decision Making.” Soils and Foundations 62 (5): 101-189. https://doi.org/10.1016/j.sandf.2022.101189.
61. Pradhan, P. S., and Siddique, T. (2020). “Stability Assessment of Landslide-Prone Road Cut Rock Slopes in Himalayan Terrain: A Finite Element Method Based Approach.” Journal of Rock Mechanics and Geotechnical Engineering 12 (1): 59–73. https://doi.org/10.1016/j.jrmge.2018.12.018.
62. Rockscience. (2004). “Application of the Finite Element Method to Slope Stability.” Rocscience Inc. 8 (5–6): 553–579. https://doi.org/10.1080/12506559.1999.10511397.
63. Sarhosis, V., Bagi, K., Lemos, J. V., and Milani, G. (2016). “Computational Modeling of Masonry Structures Using the Discrete Element Method.” IGI Global. Newcastle, United Kingdom, 1-60. http://services.igi-global.com/resolvedoi/resolve.aspx?doi=10.4018/978-1-5225-0231-9.
64. Salunkhe, D. P., Guruprasd C., Rupa N. B., and Pooja R. K. (2017). “An Overview on Methods for Slope Stability Analysis.” International Journal of Engineering Research 6 (03): 528–535. https://doi.org/10.17577/ijertv6is030496.
65. Schofield, A. N. (1968). “Critical State Soil Mechanics.” Engineer 16 (3–4): 53–66.
66. Schuster, R. L., and Fleming, R. W. (1986). “Economic Losses and Fatalities Due To Landslides.” Environmental & Engineering Geoscience 23 (1): 11–28 https://doi.org/10.2113/gseegeosci.xxiii.1.11.
67. Shi, G. H. (2014). “Application of Discontinuous Deformation Analysis on Stability Analysis of Slopes and Underground Power Houses.” Geomechanics and Geoengineering 9 (2): 80–96. https://doi.org/10.1080/17486025.2013.871065.
68. Shi, G.H. (2007). “Applications of Discontinuous Deformation Analysis (DDA) to Rock Engineering.” Computational Mechanics, July, Beijing, China, 136–147. https://doi.org/10.1007/978-3-540-75999-7_12.
69. Shi, G. H., and Goodman, R. E. (1985). “Two Dimensional Discontinuous Deformation Analysis.” International Journal for Numerical and Analytical Methods in Geomechanics 9 (6): 541–556. https://doi.org/10.1002/nag.1610090604.
70. Shi, G. H. (1992). “Discontinuous Deformation Analysis: A New Numerical Model for the Statics and Dynamics of Deformable Block Structures.” Engineering Computations 9 (2): 157–168. https://doi.org/10.1108/eb023855.
71. Sitar, N., MacLaughlin, M. M., and Doolin, D. M. (2005). “Influence of Kinematics on Landslide Mobility and Failure Mode.” Journal of Geotechnical and Geoenvironmental Engineering 131 (6): 716–728. https://doi.org/10.1061/(asce)1090-0241(2005)131:6(716).
72. Song, Y. X., Huang, D., and Zeng, B. (2017). “GPU-Based Parallel Computation for Discontinuous Deformation Analysis (DDA) Method and Its Application to Modelling Earthquake-Induced Landslide.” Computers and Geotechnics 86: 80–94. https://doi.org/10.1016/j.compgeo.2017.01.001.
73. Thavalingam, A., Bicanic, N., Robinson, J. I., and Ponniah, D. A. (2001). “Computational Framework for Discontinuous Modelling of Masonry Arch Bridges.” Computers and Structures 79 (19): 1821–1830. https://doi.org/10.1016/S0045-7949(01)00102-X.
74. Tseng, C. H., Yu C. C., Jeng, C. J., and Hsieh, Y. C. (2017). “Slip Monitoring of a Dip-Slope and Runout Simulation by the Discrete Element Method: A Case Study at the Huafan University Campus in Northern Taiwan.” Natural Hazards 89 (3): 1205–1225. https://doi.org/10.1007/s11069-017-3016-y.
75. Tsesarsky, M., Hatzor, Y. H., and Sitar, N. (2005). “Dynamic Displacement of a Block on an Tnclined Plane: Analytical, Experimental and DDA Results.” Rock Mechanics and Rock Engineering 38 (2): 153–167. https://doi.org/10.1007/s00603-004-0043-2.
76. Varnes, D.J. (1978). “Slope Movement Types and Processes.” Transportation Research Board 229: 276.
77. Wang, W., Chen, G. Q., Zhang, H., Zhou, S. H., Liu, S. G., Wu, Y. Q., and Fu, S. F. 2016. “Analysis of Landslide-Generated Impulsive Waves Using a Coupled DDA-SPH Method.” Engineering Analysis with Boundary Elements 64: 267–277. https://doi.org/10.1016/j.enganabound.2015.12.014.
78. Whitman, R. V. (1984). “The Seventeenth Terzaghi Lecture Introduction of the Seventeenth.” Geotechnical. Engrg 110 (2): 143–188.
79. Wu, J. H., Ohnishi, Y., Shi, G. H., and Nishiyama, S. (2005). “Theory of Three-Dimensional Discontinuous Deformation.” International Journal of Geomechanics 5: 179–195. https://doi.org/10.1061/(ASCE)1532-3641(2005)5.
80. Wu, J. H. (2010). “Seismic Landslide Simulations in Discontinuous Deformation Analysis.” Computers and Geotechnics 37 (5): 594–601. https://doi.org/10.1016/j.compgeo.2010.03.007.
81. Wu, J. H., and Chen, C. H. (2011). “Application of DDA to Simulate Characteristics of the Tsaoling Landslide.” Computers and Geotechnics 38 (5): 741–750. https://doi.org/10.1016/j.compgeo.2011.04.003.
82. Wu, J. H., Chen, J. H., and Lu, C. W. (2013). “Investigation of the Hsien-Du-Shan Rock Avalanche Caused by Typhoon Morakot in 2009 at Kaohsiung County, Taiwan.” International Journal of Rock Mechanics and Mining Sciences 60: 148–159. https://doi.org/10.1016/j.ijrmms.2012.12.033.
83. Wu, J. H., Ohnishi, Y., and Nishiyama, S. (2004). “Simulation of the Mechanical Behavior of Inclined Jointed Rock Masses during Tunnel Construction Using Discontinuous Deformation Analysis (DDA).” International Journal of Rock Mechanics and Mining Sciences 41 (5): 731–743. https://doi.org/10.1016/j.ijrmms.2004.01.010.
84. Wu, J. H., Ohnishi, Y., and Nishiyama, S. (2005). “A Development of the Discontinuous Deformation Analysis for Rock Fall Analysis.” International Journal for Numerical and Analytical Methods in Geomechanics 29 (10): 971–988. https://doi.org/10.1002/nag.429.
85. Wu, J. H., Wang, W. N., Chang, C. S., and Wang, C. L. (2005). “Effects of Strength Properties of Discontinuities on the Unstable Lower Slope in the Chiu-Fen-Erh-Shan Landslide, Taiwan.” Engineering Geology 78 (3–4): 173–186. https://doi.org/10.1016/j.enggeo.2004.12.005.
86. Wyllie, D. C., and Mah, C. W. (2005). “Rock Slope Engineering: Civil and Mining, 4th Edition.” CRC Press. London, United Kingdom, 1–432. https://doi.org/10.1201/9781315274980.
87. Yu, P. C., Chen, G. Q., Peng, X. Y., Guo, L. X., and Zhang, Y. B. (2019). “Extension and Application of Discontinuous Deformation Analysis with a Damped Contact Spring Model.” International Journal of Rock Mechanics and Mining Sciences 123: 104-123. https://doi.org/10.1016/j.ijrmms.2019.104123.