
系統識別號 
U00260901202017384500 
論文名稱(中文) 
以DDA模擬與落門試驗探討地下開挖引致地表沉陷與地滑之研究 
論文名稱(英文) 
DDA Simulation and Trapdoor Modeling for Underground Excavation Induced Subsidence and Landslide 
校院名稱 
成功大學 
系所名稱(中) 
土木工程學系 
系所名稱(英) 
Department of Civil Engineering 
學年度 
108 
學期 
1 
出版年 
109 
研究生(中文) 
杜崇楠 
研究生(英文) 
Trong Nhan Do 
電子信箱 
luckyluke7979@yahoo.com 
學號 
N68037013 
學位類別 
博士 
語文別 
英文 
論文頁數 
256頁 
口試委員 
口試委員田永銘 口試委員黃燦輝 口試委員王泰典 口試委員廖志中 口試委員潘以文 口試委員壽克堅 口試委員李德河 口試委員張文忠 指導教授吳建宏

中文關鍵字 
None

英文關鍵字 
Discontinuous Deformation Analysis (DDA)
physical trapdoor model
tunnel
landslide

學科別分類 

中文摘要 
None

英文摘要 
Complicated behaviors of rock mass during underground excavations, namely mining and tunnel, have been a challenging topic to many researchers due to the complicated behaviors. Geometry and mechanical properties of joints in a rock mass significantly affect surface subsidence and stress distribution around the underground excavations. The physical trapdoor models are applied to validate the correctness of using DDA to simulate the tunnels in blocky rock mass. Then, a actual case study is investigated by DDA to show the applicability of using DDA to solve practical problems.
In the trapdoor model, a rocky block mass is presented by precisedimension aluminum blocks and aluminum rods. Different shapes of aluminum blocks are used to form different kinds of rock geometry. To simulate the excavation process, the trap door is lowered with assigned distances, and the surface subsidence and the stress distribution are determined by a highaccuracy laser displacement sensor and stress measurement devices, respectively.
There are two numerical simulation approaches for rock mechanics, namely continuous and discontinuous simulations. Finite Element Method (FEM) can be a representative method for continuous simulation, which is limited to the simulation of discontinuous environments with large displacements. Discontinuous Deformation Analysis (DDA), a discrete element method, is a numerical simulation method developed by Dr. Shi 1989. This method simulates the behavior of jointed rock mass with large displacement and has achieved many advancements. Therefore, DDA is applied to simulate the underground structures in the trapdoor tests. By using the results from the trapdoor model to verify the correctness of those from DDA simulations, DDA is a very useful tool for the prediction of surface subsidence and stress distribution in the future underground constructions.
Therefore, the failure process of a mininginduced landslide at Nattai North, Australia is numerically simulated by DDA. Results obtained using Discontinuous Deformation Analysis (DDA) matched the conceptual failure process suggested by local geologists and the observed maximum runout distance. The maximum velocity of the sliding rocks exceeded 40 m/s. Computational results showed that the slope with inward subhorizontal bedding planes and subvertical discontinuities remained stable if the mininginduced high principle stresses did not fracture the rocks near the slope toe. Failure of the rocks near the toe of the slope was a key causal factor in the subsequent landslide. The research presents the first numerical simulation of the postfailure behavior of the mininginduced landslide at the Nattai North site. It also represents the first DDA simulation to clarify the chain reaction of a mininginduced landslide and demonstrate its applicability in such investigations.
In addition, the block size is one of the key characteristics affecting the mechanical behaviors of a rock mass during mining extraction. DDA is used to demonstrate that position with the same case study above, a mininginduced landslide in Nattai North of Australia. The effect of the block size on the stability of a slope is investigated. The study emphasizes the effect of four cases of block size on the movement of the escarpment, stress distribution around the mining, and the failure mode of the landslide. The results show that mining operations in both four cases of block size initiated the largest contemporary landslide and mass movement known in Australia. The size effect was proved to be a significant effect on the surface subsidence, arching effect as well as the landslide mode. Different block sizes produce an apparently different arching effect, which causes the difference in the landslide mode.

論文目次 
ACKNOWLEDGEMENTS I
ABSTRACT III
CONTENTS VI
LIST OF TABLES VIII
LIST OF FIGURES IX
LIST OF NOMENCLATURE XV
CHAPTER 1 INTRODUCTION 1
1.1 Research background and objectives 1
1.2 Methods for investigation of tunnelinginduced ground deformation 4
1.3 Flow chart of the research 6
CHAPTER 2 LITERATURE REVIEW 9
2.1 Discontinuum approaches 9
2.2 Physical trapdoor model 22
2.3 Mechanical behaviors of rock mass during tunneling 27
CHAPTER 3 THEORY OF DDA 34
CHAPTER 4 PHYSICAL TRAPDOOR MODEL 47
4.1 Physical trapdoor model 47
4.1 Earth pressure signal 61
CHAPTER 5 SINGLE TUNNEL 66
5.1 The physical trapdoor model 66
5.2 DDA simulation 70
5.3 Results 76
5.4 Discussions 93
CHAPTER 6 TWIN TUNNELS 96
6.1 The physical trapdoor model 96
6.2 DDA simulation 102
6.3 Results and discussions 105
CHAPTER 7 MININGINDUCED LANDSLIDE CASE STUDY 123
7.1 Introduction 123
7.2 Landslide case study: Nattai North at Australia 126
7.3 Small scale model of the study site 130
7.4 Fullscale model of Nattai North landslide with DDA simulation 137
7.5 Effect of the block size in Nattai North landslide with DDA simulation 173
CHAPTER 8 CONCLUSIONS AND FUTURE STUDIES 195
8.1 Conclusions 195
8.2 Future studies 196
APPENDIX 199
REFERENCES 211

參考文獻 
1. Adachi, T., Kimura, M., Kishida, K., 2003. Experimental study on the distribution of earth pressure and surface settlement through threedimensional trapdoor tests. Tunn. Undergr. Sp. Technol. 18, 171–183.
2. Addenbrooke, T.I., and Potts, D.M., 2001. Twin Tunnel Interaction: Surface and Subsurface Effects. Int. J. Geomech. 1, 249–271.
3. Alejano, L.R., Ramõâ RezOyanguren, P., Taboada, J., 1999. FDM predictive methodology for subsidence due to at and inclined coal seam mining. Int. J. Rock Mech. Min. Sci., 36(4), 475491.
4. Aleshina, I.N., Snytko, V.A., Szczypek, S., 2008. Mininginduced ground subsidences as the reliefforming factor on the territory of the Silesian Upland (Southern Poland). Geogr Nat Resour 29:288–291
5. AlNaddaf, M., Han, J., Jawad, S., Abdulrasool, G., Xu, C., 2017. Investigation of stability of soil arching under surface loading using trapdoor model tests. In: Proc., 19th Int. Conf. on Soil Mechanics and Geotechnical Engineering. 889–892.
6. Amadei, B., Lin, C.T., Sture, S., Jung, J., 1994. Modeling fracturing of rock masses with the DDA method. In 1st North American Rock Mechanics Symposium. American Rock Mechanics Association.
7. Amadei, B., Swolfs, H.S., Savage, W.Z., 1988. Gravityinduced stresses in stratified rock masses. Rock Mechanics and Rock Engineering, 21(1), 120.
8. Amir Reza Beyabanaki, S., Jafari, A., Omid Reza Biabanaki, S., Ronald Yeung, M., Reza Beyabanaki, A., Rah Mandegar, P., 2009. A Coupling Model Of 3D Discontinuous Deformation Analysis (3D DDA) And Finite Element Method. Arab. J. Sci. Eng. 34.
9. Asadi, A., Shakhriar, K., Goshtasbi, K., 2004. Profiling function for surface subsidence prediction in mining inclined coal seams. J. Min. Sci.
10. Atkinson, J.H., Potts, D.M., Schofield, A.N., 1977. Centrifugal model tests on shallow tunnels in sand. Tunnels Tunn 9:59–64.
11. BagherzadehKhalkhali, A., Mirghasemi, A.A., Mohammadi, S., 2008. Micromechanics of breakage in sharpedge particles using combined DEM and FEM. Particuology 6, 347361.
12. Bahuguna, P.P., Srivastava, A.M.C., Saxena, N.C., 1991. A critical review of mine subsidence prediction methods. Min. Sci. Technol. 13, 369–382.
13. Bandis, S.C., 2004. Numerical modelling of discrete materials in rock mechanics: developments and engineering applications. 1st Int. UDEC/3DEC Symp., Bochum, Germany
14. Bao, H., and Zhao, Z., 2010. An alternative scheme for the corner–corner contact in the twodimensional discontinuous deformation analysis. Advances in Engineering Software, 41(2), 206212.
15. Bao, H., and Zhao, Z., 2012. The vertextovertex contact analysis in the two dimensional discontinuous deformation analysis. Advances in Engineering Software, 45(1), 110.
16. Barla G, Debernardi D, Perino A., 2015. Lessons learned from deepseated landslides activated by tunnel excavation. Geomech Tunn 8:394–401
17. Barton, N., and Bandis, S., 1982. Effects of block size on the shear behavior of jointed rock. The 23rd US symposium on rock mechanics (USRMS). American Rock Mechanics Association.
18. Barton, N., Lien, R., Lunde, J., 1974. Engineering classification of rock masses for the design of tunnel support. Rock mechanics, 6, 189236
19. Bayer, B., Simoni, A., Schmidt, D., Bertello, L., 2017. Using advanced InSAR techniques to monitor landslide deformations induced by tunneling in the Northern Apennines, Italy. Eng. Geol. 226, 20–32.
20. Bell, F.G., Stacey, T.R., Genske, D.D., 2000. Mining subsidence and its effect on the environment: some differing examples. Environ Geol 40:135–152
21. Bhardwaj, G.S., Mehta, M., Ahmed, M.Y., Evans, R., 2014. Landslide Sensitivity Assessment of Existing Twin Tunnels: A Case Study of National Highway76 between Udaipur Pindwara, Rajasthan, India. Int. J. Adv. Earth Sci. Eng. 3, 201–210.
22. Bhasin, R., and Høeg, K. 1997. Numerical modelling of block size effects and influence of joint properties in multiply jointed rock. Tunnelling and Underground Space Technology, 12, 407415
23. Bi, Y., Zhang, J., Song, Z., Wang, Z., Qiu, L., Hu, J., Gong, Y., 2019. Arbuscular mycorrhizal fungi alleviate root damage stress induced by simulated coal mining subsidence ground fissures. Sci Total Environ 652:398–405
24. Bieniawski, Z., 1973. Engineering classification of jointed rock masses. Civil Engineer in South Africa, 15.
25. Blivet, J.C., Khay, M., Villard, P., Gourc, J.P., 2000. Experiment and design of geosynthetic reinforcement to prevent localised sinkholes. In: ISRM International Symposium. International Society for Rock Mechanics and Rock Engineering.
26. Bobet, A., Fakhimi, A., Johnson, S., Morris, J., Tonon, F., Yeung, M. R., 2009. Numerical models in discontinuous media: review of advances for rock mechanics applications. Journal of geotechnical and geoenvironmental engineering, 135(11), 15471561.
27. Boon, C.W., Neo, C.W., Ng, D.C.C., Ong, V.C.W., 2018. Discontinuum analyses of openings constructed with side drift and limited rock cover. J Zhejiang Univ A 19:255–265
28. Brady, B.H.G., 1987. Boundary element and linked methods for underground excavation. Analytical and computational methods in engineering rock mechanics, E. T. Brown, ed., Allen and Unwin, London, 164–204
29. Brideau, M., A., and Stead, D., 2010. Controls on Block Toppling Using a ThreeDimensional Distinct Element Approach. Rock Mech Rock Eng, 43:241260.
30. Britton, E.J., and Naughton, P.J., 2011. The arching phenomena observed in experimental trap door model tests. In: GeoFrontiers 2011: Advances in Geotechnical Engineering, 788797.
31. Bull, J.W., 2002. SoilStructure interaction: numerical analysis and modelling. CRC Press.
32. Burd, H.J., Houlsby, G.T., Augarde, C.E., Liu G., 2000. Modelling tunnellinginduced settlement of masonry buildings. Proc. Inst. Civ. Eng. Eng. 143, 17–29.
33. Byerlee, J.D., 1968. Brittleductile transition in rocks. J Geophys Res 73:4741–4750
34. Cao, W., Li, W., Tang, B., Dend, G., Li, J., 2017. PFC study on building of 2D and 3D landslide models [J]. Journal of Engineering Geology, 25(2): 455462.
35. Carnec, C, Delacourt, C., 2000. Three years of mining subsidence monitored by SAR interferometry, near Gardanne, France. J Appl Geophys 43:43–54
36. Castañeda, C, Gutiérrez, F, Manunta, M, Galve, J.P., 2009. DInSAR measurements of ground deformation by sinkholes, mining subsidence, and landslides, Ebro River, Spain. Earth Surf Process Landforms 34:1562–1574
37. Chakeri, H, Hasanpour, R, Hindistan, MA, Ünver, B., 2011. Analysis of interaction between tunnels in soft ground by 3D numerical modeling. Bull Eng Geol Environ.
38. Chalhoub, M., and Pouya, A., 2008. Numerical homogenization of a fractured rock mass: a geometrical approach to determine the mechanical representative elementary volume. Electron J Geotech Eng, 13, 112.
39. Chambon, P., Corte, J.F., 1994. Shallow tunnels in cohesionless soil: stability of tunnel face. J. Geotech. Eng. 120, 11481165.
40. Chapman, D.N., Ahn, S.K., Hunt, D.V., 2007. Investigating ground movements caused by the construction of multiple tunnels in soft ground using laboratory model tests. Canadian Geotechnical Journal, 44(6), 631643.
41. Chehade, F.H., Shahrour, I., 2008. Numerical analysis of the interaction between twintunnels: Influence of the relative position and construction procedure. Tunn Undergr Sp Technol 23:210–214
42. Chen, G., Ohnishi, Y., 1999. A nonlinear model for discontinuities in DDA. In: Proceedings of the 3rd International Conference on Analysis of Discontinuous Deformation, 57–64.
43. Chen, G., Wang, X., Wang, R., Liu, G., 2019. Health risk assessment of potentially harmful elements in subsidence water bodies using a Monte Carlo approach: An example from the Huainan coal mining area, China. Ecotoxicol Environ Saf 171:737–745
44. Chen, G., Zheng, L., Zhang, Y., Wu, J., 2013. Numerical simulation in rockfall analysis: A close comparison of 2D and 3D DDA. In: Rock Mechanics and Rock Engineering
45. Chen, H.M., Yu, H.S., Smith, M.J., 2016. Physical model tests and numerical simulation for assessing the stability of bricklined tunnels. Tunn Undergr Sp Technol.
46. Chen, K.T., and Wu, J.H., 2018. Simulating the failure process of the Xinmo landslide using discontinuous deformation analysis. Eng Geol 239:269–281
47. Chen, Q., Yin, T., Niu, W., Zheng, W., Liu, J., 2018. Study of the geometrical size effect of a fractured rock mass based on the modified blockiness evaluation method. Arabian Journal of Geosciences, 11, 286, doi: 10.1007/s1251701836459.
48. Chen, X., Liao, Z., Li, D.J., 2011. Experimental study on the effect of joint orientation and persistence on the strength and deformation properties of rock masses under uniaxial compression. Chin. J. Rock Mech. Eng, 30, 781789.
49. Chen, Y.F., and Wang, T.T., 2012. Historical Construction and Maintenance of Suhua Highway and associated Influence by Geotechnical Characteristics. SinoGeotechnics 131:47–58
50. Cheng, X., Xiao, J., Miao, Q., Wang, Y., 2015. Design and implementation of a software architecture for 3DDDA. Science China Technological Sciences, 58(9), 16041608.
51. Chevalier, B, Combe, G, Villard, P., 2009. Experimental and Numerical Study of the Response of Granular Layer in the Trapdoor Problem. In: AIP Conference Proceedings, 649–652.
52. Chiu, C.C., Weng, M.C., Huang, T.H., 2016. Modeling rock joint behavior using a roughjoint model. International Journal of Rock Mechanics and Mining Sciences, 89, 1425
53. Choi, J.K., Kim, K.D., Lee, S., Won, J.S., 2010. Application of a fuzzy operator to susceptibility estimations of coal mine subsidence in Taebaek City, Korea. Environ Earth Sci 59:1009–1022.
54. Chuanyong, H., 2008. Redevelopment of DDA program and its application. Rock and soil mechanics, 29, 166170.
55. Chrzanowski, A., Monahan, C., Roulston, B., SzostakChrzanowski, A., 1997. Integrated monitoring and modelling of ground subsidence in potash mines. Int. J. Rock Mech. Min. Sci. 34(34), 55e1.
56. Crouch, S.L., and Starfield, A.M., 1983. Boundary element methods in solid mechanics. Allen &, Unwin, London
57. Cui, Z., Liu, D., Wu, F., 2014. Influence of dip directions on the main deformation region of layered rock around tunnels. Bull. Eng. Geol. Environ. 73, 441–450.
58. Cundall, P.A., 1971. A computer model for simulating progressive, largescale movement in blocky rock system, in: Proceedings of the International Symposium on Rock Mechanics.
59. Cundall, P. A., 1978. BALL  A program to model granular media using the distinct element method. Dames and Moore Advanced Technology Group, London.
60. Cundall, P. A., 1980. UDEC  A generalized distinct element program for modeling jointed rock. Final Technical Rep. Prepared for European Research Office, PCAR180, Defense Technical Inforamtion Center
61. Cundall, P.A., 1987. Distinct element models of rock and soil structure. Analytical and computational methods in engineering rock mechanics, 129163.
62. Cundall, P.A., 1988. Formulation of a threedimensional distinct element model  Part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks. In International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Pergamon, 25(3), 107116
63. Cundall, P.A., and Strack, O.D.L., 1979. The development of constitutive laws for soil using the distinct element method. Numerical methods in geomechanics, 1, 289317.
64. Cunningham, DM., 1988. A rockfall avalanche in a sandstone landscape, Nattai North, NSW. Aust Geogr 19:221–229
65. Dai, H, Ren, L, Meng, W, Xue, H., 2011. Water distribution extracted from mining subsidence area using Kriging interpolation algorithm. Trans Nonferrous Met Soc China 21: 723726
66. Das, R., Singh, P.K., Kainthola, A., Panthee, S., Singh, T.N., 2017. Numerical analysis of surface subsidence in asymmetric parallel highway tunnels. J Rock Mech Geotech Eng 9:170–179
67. Deere, D.U., Hendron, A.J., Patton, F.D., Cording, E.J., 1966. Design Of Surface And NearSurface Construction In Rock. The 8th U.S. Symposium on Rock Mechanics (USRMS). American Rock Mechanics Association, Minneapolis, Minnesota, 66.
68. Dewoolkar, M.M., Santichaianant, K, Ko, H.Y., 2007. Centrifuge modeling of granular soil response over active circular trapdoors. Soils Found 47:931–945
69. Ding, X., Zhang, L., Zhu, H., Zhang, Q., 2014. Effect of model scale and particle size distribution on PFC3D simulation results. Rock mechanics and rock engineering, 47(6), 21392156.
70. Do, N.A., Dias, D., Oreste, P., DjeranMaigre, I., 2014. Threedimensional numerical simulation of a mechanized twin tunnels in soft ground. Tunn Undergr Sp Technol.
71. Do, T.N., and Wu, J.H., 2020. Simulation of the inclined jointed rock mass behaviors in a mountain tunnel excavation using DDA. Comput. Geotech. 117, 103249.
72. Do, T.N. and Wu, J.H., 2020. Simulating a miningtriggered rock avalanche using DDA: A case study in Nattai North, Australia. Engineering Geology, 264, 105386.
73. Do, T.N., Wu, J.H., Lin, H.M., 2017. Investigation of sloped surface subsidence during inclined seam extraction in a jointed rock mass using discontinuous deformation analysis. Int. J. Geomech. 17
74. Dunrud, C.R., and Osterwald, F.W., 1980. Effects of coal mine subsidence in the Sheridan, Wyoming, area (No. 1164). US Govt. Print. Off.
75. Elmo, D., Vyazmensky, A., Stead, D., Rance, J.R., 2007. A hybrid FEM/DEM approach to model the interaction between openpit and underground blockcaving mining. In 1st CanadaUS Rock Mechanics Symposium. American Rock Mechanics Association.
76. Fan, H., and He, S., 2015. An anglebased method dealing with vertex–vertex contact in the twodimensional discontinuous deformation analysis (DDA). Rock Mechanics and Rock Engineering, 48(5), 20312043.
77. Fan, X., Kulatilake, P.H.S.W., Chen, X., 2015. Mechanical behavior of rocklike jointed blocks with multinonpersistent joints under uniaxial loading: A particle mechanics approach. Engineering Geology, 190, 1732
78. Fathi Salmi, E., Nazem, M., Karakus, M., 2016. Numerical analysis of a large landslide induced by coal mining subsidence.
79. Franks, C.A.M., Geddes, J.D., 1986. Subsidence on steep slopes due to longwall mining. Int. J. Min. Geol. Eng. 4, 291–301.
80. Franzius, J.N., and Potts, D.M., 2005. Influence of mesh geometry on threedimensional finiteelement analysis of tunnel excavation. International Journal of Geomechanics, 5(3), 256266.
81. Franzius, J.N., Potts, D.M., Burland, J.B., 2006. The response of surface structures to tunnel construction. Proc. Inst. Civ. Eng. Eng. 159, 3–17.
82. Fu, G.Y., Ma, G.W., 2014. Extended key block analysis for support design of blocky rock mass. Tunn. Undergr. Sp. Technol. 41, 1–13.
83. Ghabraie, B., Ren, G., Zhang, X. and Smith, J., 2015. Physical modelling of subsidence from sequential extraction of partially overlapping longwall panels and study of substrata movement characteristics. International Journal of Coal Geology, 140, 7183.
84. Ghazvinian, A., Sarfarazi, V., Schubert, W., Blumel, M., 2012. A study of the failure mechanism of planar nonpersistent open joints using PFC2D. Rock mechanics and rock engineering, 45(5), 677693.
85. Gilbride, L.J., Free, K.S., Kehrman, R., 2005. Modeling Block Cave Subsidence at the Molycorp, Inc., Questa Mine? A Case Study. Alaska Rocks 2005, The 40th U.S. Symposium on Rock Mechanics (USRMS). American Rock Mechanics Association, Anchorage, Alaska, 14.
86. GonzálezPalacio, C., MenéndezDíaz, A., ÁlvarezVigil, A.E., GonzálezNicieza, C., 2005. Identification of nonpyramidal key blocks in jointed rock masses for tunnel excavation. Computers and Geotechnics, 32(3), 179200.
87. Goodman, R.E., and Shi, G.H., 1985. Block Theory and its Application to Rock
Engineering. PrenticeHall Press, New Jersey.
88. Goodman, R. E., Taylor, R. L., Brekke, T. L., 1968. A Model for the Mechanics of Jointed Rock. Journal of the Soil Mechanics and Foundations Div., ASCE, Vol. 94, No SM3, 637659
89. Grayeli, R., and Hatami, K., 2008. Implementation of the finite element method in the three‐dimensional discontinuous deformation analysis (3D‐DDA). International journal for numerical and analytical methods in geomechanics, 32(15), 18831902.
90. Great Britain. National Coal Board. Mining Department., 1975. Subsidence engineers' handbook. [London]. The Board.
91. Greif, V., and Vlčko, J., 2013. Key block theory application for rock slope stability analysis in the foundations of medieval castles in Slovakia. Journal of cultural heritage, 14(4), 359364.
92. Griffiths, D.V., 1985. Numerical modelling of interfaces using conventional finite elements, Proc. 5th. Int. Conf. Num. Meth. in Geomech. (Kawamoto, T. and Ichikawa, Y. Eds.), Nagoya, 2, 837844.
93. Guan, P.B., Tingatinga, E.A., Longalong, R.E., Saguid, J., 2016. Governing equations of multicomponent rigid bodyspring discrete element models of reinforced concrete columns. Journal of Physics: Conference Series, IOP Publishing, 744(1), 012021
94. Guan, Z., Deng, T., Du, S., Li, B., Jiang, Y., 2012. Markovian geology prediction approach and its application in mountain tunnels. Tunn Undergr Sp Technol 31:6167.
95. Guoxin, Z., and Xiaofeng, W., 2003. Influence Of Seepage On The Stability Of Rock SlopeCoupling Of Seepage And Deformation By DDA Method [J]. Chinese J. Rock Mech. Eng. 8.
96. Gurung, N., and Iwao, Y., 1998. Observations of deformation and engineering geology in the Lam Ta Khong tunnel, Thailand. Eng. Geol. 51, 55–63.
97. Hada, M., Taguchi, Y., Kagawa, K., 1988. Application of RBSM analysis to earth reinforcement method. International geotechnical symposium on theory and practice of earth reinforcement, 395400.
98. Han, J., Wang, F., Xu, C., AlNaddaf, M., 2016. Fullymobilized soil arching versus partiallymobilized soil arching. DEStech Trans Eng Technol Res.
99. Hart, R.D., 1988. An overview of methods for discontinuum analysis.
100. Hasan, H., 2006. Aluminum. The Rosen Publishing Group, Inc.
101. Hashimoto, R., Koyama, T., Kikumoto, M., Yamada, S., Araya, M., Iwasaki, Y., Ohnishi, Y., 2013. Application of coupled elastoplastic NMM–DDA procedure for the stability analysis of Prasat Suor Prat N1 Tower, Angkor, Cambodia. Geosystem Engineering, 16(1), 6274.
102. Hatzor, Y.H., Arzi, A.A., Zaslavsky, Y., Shapira, A., 2004. Dynamic stability analysis of jointed rock slopes using the DDA method: King Herod’s Palace, Masada, Israel. Int J Rock Mech Min Sci 41:813–832
103. He, M., Jia, X., Gong, W., Faramarzi, L., 2010. Physical modeling of an underground roadway excavation in vertically stratified rock using infrared thermography. Int J Rock Mech Min Sci.
104. He, M.C., Gong, W.L., Zhai, H.M., Zhang, H.P., 2010. Physical modeling of deep ground excavation in geologically horizontal strata based on infrared thermography. Tunn. Undergr. Sp. Technol.
105. Heliot, D., 1988. Generating a blocky rock mass. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 25, 3, 127138
106. Hoek, E., Marinos, P., Benissi, M., 1998. Applicability of the geological strength index (GSI) classification for very weak and sheared rock masses. The case of the Athens Schist Formation. Bulletin of Engineering Geology and the Environment, 57, 151160
107. Hokuriku Region Development Bureau., 2017. Design guideline (Highway). Minist Land, 397 Infrastructure, Transp Tour Niigata, Japan (In Japanese)
108. Holla, L., 1997. Ground movement due to longwall mining in high relief areas in New South Wales, Australia. Int J Rock Mech Min Sci 34:775–787
109. Hsiung, S.M., 2001. Discontinuous deformation analysis (DDA) with nth order polynomial displacement functions. In DC Rocks 2001, The 38th US Symposium on Rock Mechanics (USRMS). American Rock Mechanics Association.
110. Hsu, W.S., Huang, Y.H., Shen, T.S., Cheng, C.Y., Chen, T.Y., 2017. Analysis of the
hsuehshan tunnel fire in Taiwan. Tunn. Undergr. Sp. Technol. 69, 108–115.
111. Huang, F., Wang, Y., Wen, Y., Lin, Z., Zhu, H., 2019. The Deformation and Failure Analysis of Rock Mass Around Tunnel by Coupling Finite Difference Method and Discrete Element Method. Indian Geotechnical Journal, 49(4), 421436.
112. Huang, M., and Jia, C.Q., 2009. Strength reduction FEM in stability analysis of soil slopes subjected to transient unsaturated seepage. Comput. Geotech. 36, 93–101.
113. Huang, X., and Zhang, Z., 2012. Stress arch bunch and its formation mechanism in blocky stratified rock masses. J. Rock Mech. Geotech. Eng. 4, 19–27
114. Ikuma, M., 2005. Maintenance of the undersea section of the Seikan Tunnel. Tunn. Undergr. Sp. Technol. 20, 143–149.
115. Islam, M.R., Hayashi, D., Kamruzzaman, A.B.M., 2009. Finite element modeling of stress distributions and problems for multislice longwall mining in Bangladesh, with special reference to the Barapukuria coal mine. Int. J. Coal Geol. 78, 91–109.
116. Jansen, H.A., 1895. Versuche über Getreidedruck in Silozellen/HA Janssen. Zd VDI. Berlin, (35), 104.
117. Jeon, B., Jeon, S., Kim, J., Kim, T.H., 2012. Numerical evaluation of affecting parameters of surface subsidence in abandoned mine areas. Geosystem Engineering, 15, 299304
118. Jiang, Q., Zhou, C., Li, D., Yeung, M.R., 2012. A softening block approach to simulate excavation in jointed rocks. Bull Eng Geol Environ 71:747–759
119. Jiang, Q.H., Wei, W., Yao, C., Zhou, C.B., 2011. Failure mode analysis of jointed rock masses around underground opening under excavation unloading. Mater. Res. Innov. 15, s609s612.
120. Jianjun, S., Chunjian, H., Ping, L., Junwei, Z., Deyuan, L., Minde, J., Lin, Z., Jingkai, Z., Jianying, S., 2012. Quantitative prediction of mining subsidence and its impact on the environment. International Journal of Mining Science and Technology, 22(1), 6973.
121. Jing, L., Ma, Y., Fang, Z., 2001. Modeling of fluid flow and solid deformation for fractured rocks with discontinuous deformation analysis (DDA) method. Int. J. Rock Mech. Min. Sci.
122. Jing, Z, Wang, J, Zhu, Y, Feng, Y., 2018. Effects of land subsidence resulted from coal mining on soil nutrient distributions in a loess area of China. J Clean Prod 177:350–361
123. Jongpradist, P., Tunsakul, J., Kongkitkul, W., Fadsiri, N., Arangelovski, G., Youwai, S., 2015. High internal pressure induced fracture patterns in rock masses surrounding caverns: Experimental study using physical model tests. Engineering Geology, 197, 158171
124. Ju, Y., Zuo, J.P., Song, Z.D., Tian, L.L., Zhou, H.W., 2007. Numerical simulation of stress distribution and displacement of rock strata of coal mines by means of DDA method. Yantu Gongcheng Xuebao. Chinese Journal of Geotechnical Engineering, 29(2), 268273.
125. Kakurai, M., and Hori, J., 1990. Soilreinforcement with steel bars on a cut slope. Performance of Reinforced Soil Structures, British Geotechnical Society, Thomas Telford, 213217.
126. Karakus, M., Ozsan, A., Bacsarir, H., 2007. Finite element analysis for the twin metro tunnel constructed in Ankara Clay, Turkey. Bull. Eng. Geol. Environ. 66, 71–79.
127. Kawai T., 1977. New Element Models in Discrete Structural Analysis. Journal of the Society of Naval Architects of Japan, 141, 174180
128. Kim, B.H., Cai, M., Kaiser, P.K., Yang, H.S., 2006. Estimation of Block Sizes for Rock Masses with Nonpersistent Joints. Rock Mechanics and Rock Engineering, 40, 169
129. Koo, C.Y., and Chen, S., 1997. Development of second order displacement function for DDA and manifold method. In Working Forum on the Manifold Method of Material Analysis, 1, 183.
130. Kulatilake, P.H.S.W., Malama, B., Wang, J., 2001. Physical and particle flow modeling of jointed rock block behavior under uniaxial loading. International Journal of Rock Mechanics and Mining Sciences, 38, 641657
131. Le, L.A., Nguyen, G.D., Bui, H.H., Sheikh, A.H., Kotousov, A., Khanna, A., 2017. Modelling jointed rock mass as a continuum with an embedded cohesivefrictional model. Engineering Geology, 228, 107120,
132. Leca, E., and New, B., 2007. Settlements induced by tunneling in soft ground. Tunn. Undergr. Sp. Technol. 22, 119–149.
133. Lee, J.S., 2009. An application of threedimensional analysis around a tunnel portal under construction. Tunnelling and Underground Space Technology, 24, 731738
134. Lemos, J.V., 2008. Block modelling of rock masses  Concepts and application to dam foundations. European Journal of Environmental and Civil Engineering, 12(78): 915949.
135. Lemos, J.V., 2012. Explicit codes in geomechanics  FLAC, UDEC and PFC. In Innovative numerical modelling in geomechanics, CRC Press, 311328
136. Li, S., Yu, H., Liu, Y., Wu, F., 2008. Results from insitu monitoring of displacement, bolt load, and disturbed zone of a powerhouse cavern during excavation process. Int. J. Rock Mech. Min. Sci. 8, 1519–1525.
137. Li, S., Li, S., Zhang, Q., Xue, Y., Liu, B., Su, M., Wang, Z., Wang, S., 2010. Predicting geological hazards during tunnel construction. J. Rock Mech. Geotech. Eng. 2, 232–242.
138. Li, X.G., and Yuan, D.J., 2012. Response of a doubledecked metro tunnel to shield driving of twin closely undercrossing tunnels. Tunn Undergr Sp Technol 28:18–30
139. Lin, G, He, C., 2004. 3D FEM Numerical Simulation Analysis of Stratum Settlement of Twin Tunnel During Whole Construction Process [J]. Highway 39
140. Luding, S., 2006. About contact forcelaws for cohesive frictional materials in 2D and 3D. Behavior of granular media, 9, 137147.
141. Ma, L, Ding, L, Luo, H., 2014. Nonlinear description of ground settlement over twin tunnels in soil. Tunn Undergr Sp Technol 42:144–151
142. Ma, M.Y., Pan, A.D., Luan, M., Gebara, J.M., 1995. Stone arch bridge analysis by the DDA method. Arch bridges, 247256.
143. MacLaughlin, M.M., Doolin, D.M., 2006. Review of validation of the discontinuous deformation analysis (DDA) method. Int. J. Numer. Anal. Methods Geomech.
144. Maerz, N.H., and Germain, P. 1992. Block size determination around underground openings using simulations based on scanline mapping.
145. Matsuo, S., 1986. An overview of the Seikan Tunnel project. Tunn Undergr Sp Technol 1:323–331
146. Marinos, V., Marinos, P., Hoek, E., 2005. The geological strength index: applications and limitations. Bulletin of Engineering Geology and the Environment, 64, 5565
147. McBride, A., and Scheele, F., 2001a. Investigation of discontinuous deformation analysis using physical laboratory models. In: Proceedings of the fourth international conference on discontinuous deformation analysis, 73–82.
148. McBride, A.T., and Scheele, F., 2001b. Validation of discontinuous deformation analysis using a physical model. In: Structural Engineering, Mechanics and Computation. Elsevier, 719–726
149. McNulty, J.W., 1965. An experimental study of arching in sand (No. Aewestr1674). Army engineer waterways experiment station vicksburg ms.
150. Meguid, M.A., Saada, O., Nunes, M.A., Mattar, J., 2008. Physical modeling of tunnels in soft ground: A review. Tunn. Undergr. Sp. Technol.
151. Mirghasemi, A.A., and Mohammadi, S., 2011. Numerical simulation of particle breakage of angular particles using combined DEM and FEM. Powder technology.
152. Mohamad, H., Soga, K., Bennett, P.J., Mair, R.J., Lim, C.S., 2011. Monitoring twin tunnel interaction using distributed optical fiber strain measurements. J. Geotech. Geoenvironmental Eng. 138, 957–967.
153. Momma, K, Wu, J, Ohnishi, Y, Nishiyama, S., 2002. The three. dimensional Discontinuous Deformation Analysis (3D DDA) and its application to rock toppling. Landslides 39:48–52
154. Monserud, R.A., Haynes, R.W., Johnson, A.C., 2013. Compatible forest management. Springer Science & Business Media.
155. Mostyn, G, Helgstedt, MD, Douglas, KJ., 1997. Towards field bounds on rock mass failure criteria. Int J Rock Mech Min Sci 34:208e1
156. Ng, R.M.C., Lo, K.Y., Rowe, R.K., 1986. Analysis of field performance—the Thunder Bay tunnel. Can. Geotech. J. 23, 30–50.
157. Paikowsky, S.G., Palmer, C.J., Rolwes, L.E., 2006. The use of tactile sensor technology for measuring soil stress distribution. In: GeoCongress 2006: Geotechnical Engineering in the Information Technology Age, 1–6
158. Panthee, S., Singh, P.K., Kainthola, A., Singh, T.N. 2016. Control of rock joint parameters on deformation of tunnel opening. Journal of Rock Mechanics and Geotechnical Engineering, 8, 489498
159. Papamichos, E., Vardoulakis, I., Heil, L.K., 2001. Overburden modeling above a compacting reservoir using a trap door apparatus. Phys Chem Earth, Part A Solid Earth Geod 26:69–74
160. Pardo, G.S., Sáez, E., 2014. Experimental and numerical study of arching soil effect in coarse sand. Comput Geotech 57:75–84
161. Park, K.H., 2005. Analytical solution for tunnellinginduced ground movement in clays. Tunn Undergr Sp Technol 20:249–261
162. Park, S.H., 2001. Mechanical behavior of ground with inclined layers during tunnel excavation. Ph. D. Thesis, Department of Civil Engineering, Kyoto University, Japan
163. Park, S.H., and Adachi, T., 2002. Laboratory model tests and FE analyses on tunneling in the unconsolidated ground with inclined layers. Tunn. Undergr. Sp. Technol. 17, 181193.
164. Pells, P.J.N., 2008. Assessing parameters for computations in rock mechanics. In: Proceedings First Southern Hemisphere International Rock Mechanics Symposium (SHIRMS), Y. Potvin, J. Carter, A. Dyskin and R. Jeffrey (eds), 39–54
165. Pells, P.J.N., Braybrooke, J.C., Mong, J., Kotze, G.P., 1987. Cliff line collapse associated with mining activities. Soil Slope Instability and Stabilisation Balkema, Rotterdam, 359385.
166. Prudencio, M., and Van Sint Jan, M., 2007. Strength and failure modes of rock mass models with nonpersistent joints. International Journal of Rock Mechanics and Mining Sciences, 44, 890902
167. Ren, G., Whittaker, B.N., Reddish, D.J., 1989. Mining subsidence and displacement prediction using influence function methods for steep seams. Min. Sci. Technol. 8, 235–251
168. Reinke, P., and Ravn, S., 2004. Twintube, singletrack highspeed rail tunnels and consequences for aerodynamics, climate, equipment and ventilation. HBI Haerter Ltd, Thunstrasse 9.
169. Rojek, J., 2018. Contact Modeling in the Discrete Element Method. In Contact Modeling for Solids and Particles, Springer, Cham, 177228
170. Rose, B., Verreault, M., Andrieux, P., O’Connor, C., 2011. A systematic approach to rock mechanics challenges at Xstrata Zinc Brunswick Mine. In Sainsbury, Hart, Detournay & Nelson (eds), Continuum and Distinct Element Numerical Modeling in Geomechanics  2011, Minneapolis: Itasca, 0203
171. Sainsbury, D.P., Sainsbury, B.L., Lorig, L.J., 2010. Investigation of caving induced subsidence at the abandoned Grace Mine. Min Technol 119:151–161
172. Sakurai, S., and Shimizu, N., 1992. Reviews on Computational Methods in Rock Mechanics, Tsuchitokiso, Vol. 40, No. 11, Ser. No. 418, the Japanese Society of Soil Mechanics and Foundation Engineering, 3944
173. Salmi, E.F., Karakus, M., Nazem, M., 2019. Assessing the effects of rock mass gradual deterioration on the longterm stability of abandoned mine workings and the mechanisms of postmining subsidence  A case study of Castle Fields mine. Tunn Undergr Sp Technol 88:169–185
174. Sahu, P., Lokhande, R.D., 2015. An Investigation of Sinkhole Subsidence and its Preventive Measures in Underground Coal Mining. Procedia Earth Planet Sci 11:63–75
175. Sasaoka, T., Takamoto, H., Shimada, H., Oya, J., Hamanaka, A., Matsui, K., 2015. Surface subsidence due to underground mining operation under weak geological condition in Indonesia. Journal of Rock Mechanics and Geotechnical Engineering, 7(3), 337344.
176. Shahin, H.M., Nakai, T., Ishii, K., Iwata, T., Kuroi, S., 2016. Investigation of influence of tunneling on existing building and tunnel: Model tests and numerical simulations. Acta Geotech.
177. Shangyi, Z., Weimin, S., Yingren, Z., 2001. FEM for analysis of slope stability [J]. Undergr. Sp., 21(5), 450454.
178. Sharifzadeh, M, Daraei, R, Broojerdi, M.S., 2012. Design of sequential excavation tunneling in weak rocks through findings obtained from displacements based back analysis. Tunn Undergr Sp Technol 28:10–17
179. Sharma, K.G., 2009. Numerical analysis of underground structures. Indian Geotechnical Journal, 39(1), 163.
180. Shi, G.H., 1989. Discontinuous Deformation Analysis A New Numerical Model for the Static and Dynamics of Block Systems. PhD Diss. Dept. Civ. Eng.
181. Shi G.H., 1992. Discontinuous deformation analysis: a new numerical model for the statics and dynamics of deformable block structures. Eng Comput 9:157–168
182. Shi G.H., 1993. Block System Modeling by Discontinuous Deformation Analysis. Computational Mechanics Publication: Southampton, U.K.
183. Shi G.H., 2001. Three dimensional discontinuous deformation analyses. In Proceeding of the Fourth International Conference on Analysis of Discontinuous Deformation, Bicanic N (ed.). University of Glascow: Scotland, U.K., 1–21
184. Shi, G., Goodman, R.E., 1989. Generalization of twodimensional discontinuous deformation analysis for forward modelling. Int. J. Numer. Anal. Methods Geomech
185. Shimizu, Y., 2004. Fluid coupling in PFC2D and PFC3D. In Numerical Modeling in Micromechanics Via Particle Methods. Proc. of the 2nd International PFC Symposium, Kyoto, Japan, Leiden, Netherlands: AA Balkema, 281287
186. Shu, D.M., Bhattacharyya, A.K., 1992a. Modification of subsidence parameters for sloping ground surfaces by the rays projection method. Geotech Geol Eng 10:223–248
187. Shu, D.M., Bhattacharyya, A.K., 1992b. Influence of the sloping of ground surfaces on mine subsidence. Proc 11th Int Cong Gr Control mining, Wollongong, Aust July, Australas Inst Min Metall 475–482
188. Singh, R, Singh, T.N., Bajpai, R.K., 2018. The investigation of twin tunnel stability: Effect of spacing and diameter. J Geol Soc India 91:563–568
189. Singh, R.P., Yadav, R.N., 1995. Prediction of subsidence due to coal mining in Raniganj coalfield, West Bengal, India. Eng Geol 39:103–111
190. Someehneshin, J., OraeeMirzamani, B., Oraee, K., 2015. Analytical Model Determining the Optimal Block Size in the Block Caving Mining Method. Indian Geotechnical Journal, 45, 156168
191. Soren, K., Budi, G., Sen, P., 2014. Stability analysis of open pit slope by finite difference method. Int. J. Res. Eng. Technol, 3(5), 326334
192. Sridevi, J., and Sitharam, T.G., 2000. Analysis of strength and moduli of jointed rocks. Geotechnical & Geological Engineering, 18, 321
193. Stead, D., Eberhardt, E., Coggan, J.S., 2006. Developments in the characterization of complex rock slope deformation and failure using numerical modelling techniques. Engineering Geology, 83(13), 217235.
194. Sun, J., Ning, Y., Zhao, Z., 2011. Comparative study of Sarma’s method and the discontinuous deformation analysis for rock slope stability analysis. Geomech. Geoengin. 6, 293–302.
195. Tanaka, K., 2001. Numerical and experimental studies for the impact of projectiles on granular materials. Handbook of Conveying and Handling of Particulate Solids, 263270.
196. Tanaka, T., Sakai, T., 1993. Progressive failure and scale effect of trapdoor problems with granular materials. Soils Found 33:11–22
197. Tang, Y.G., Kung, G.T.C., 2009. Application of nonlinear optimization technique to back analyses of deep excavation. Comput. Geotech. 36, 276–290.
198. Tarrio, I., and DeJong, M.J., 2016. Two approaches to modelling the stability of the basilica of Vezelay. Structural Analysis of Historical Constructions 2016, 299306
199. Terzaghi, K., 1936. Stress distribution in dry and in saturated sand above a yielding trap door.
200. Terzaghi, K., 1943. Theoretical soil mechanics. J. Wiley and Sons, inc.
201. Thomas, A.H., Banyai, J.P., 2007. Risk management of the construction of tunnels using Tunnel Boring Machines (TBMs). Undergr. Spacethe 4th Dimens. Metropolises. London Taylor Fr. 1613–1618.
202. Thongprapha, T., Fuenkajorn, K., Daemen, J.J.K., 2015a. Study of surface subsidence above an underground opening using a trap door apparatus. Tunn. Undergr. Sp. Technol. https://doi.org/10.1016/j.tust.2014.11.007
203. Thongprapha, T, Fuenkajorn, K, Daemen, J.J.K., 2015b. Study of Surface Subsidence due to Underground Opening under Supercritical Condition Using Trap Door Apparatus. Sci Technol Asia 53–62
204. Tsesarsky, M., 2004. Stability of underground openings in stratified and jointed Rock, Ph.D. Dissertation, Department of Geological and Environmental Sciences, Ben Gurion University of the Negev,BeerSheva, Israel
205. Tsesarsky, M, Hatzor, Y.H., 2006. Tunnel roof deflection in blocky rock masses as a function of joint spacing and friction  A parametric study using discontinuous deformation analysis (DDA). Tunn Undergr Sp Technol
206. Tsesarsky, M, Hatzor, Y.H, Sitar, N., 2005. Dynamic displacement of a block on an inclined plane: analytical, experimental and DDA results. Rock Mech Rock Eng 38:153–167
207. Vardoulakis, I., Graf, B., Gudehus, G., 1981. Trapdoor problem with dry sand: A statical approach based upon model test kinematics. Int. J. Numer. Anal. Methods Geomech. 5, 57–78
208. Villard, P., Gourc, J.P., Giraud, H., 2000. A geosynthetic reinforcement solution to prevent the formation of localized sinkholes. Can. Geotech. J. 37, 987–999
209. Vlachopoulos, N, Vazaios, I, Madjdabadi, B.M., 2018. Investigation into the influence of excavation of twinbored tunnels within weak rock masses adjacent to slopes. Can Geotech J 55:1533–1551
210. Walton, O.R., 1995. Force models for particledynamics simulations of granular materials. In Mobile particulate systems, Springer, Dordrecht, 367380
211. Walton, O.R., and Braun, R.L., 1986. Viscosity, granulartemperatures, and stress calculations for shearing assemblies of inelastic, frictional disks. Rheology, 60(5):949980
212. Wang, C.Y., Chuang, C.C., Sheng, J., 1996. Time integration theories for the DDA method with finite element meshes. In: Proceedings of 1st Int. Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media, 263–287.
213. Wang, J., Feng, B., Zhang, X., Tang, Y., Yang, P., 2010. A case study on middle wall stress transformation in shallow buried twinarch tunnel, in: 2010 International Conference on Mechanic Automation and Control Engineering, 4571–4574.
214. Wang, S, Yang, J, Yang, Y, Zhong, F., 2014a. Construction of largespan twin tunnels below a highrise transmission tower: A case study. Geotech Geol Eng 32:453–467
215. Wang, S.H., Yang, Y., Wang, Y., Zhang, S.L., Guo, M.D., 2009. Numerical Method of Key Block Identification for Jointed Rock Tunnel Construction [J]. Chinese Journal of Underground Space and Engineering, 5.
216. Wang, W., Chen, G., Zhang, H., Zhou, S., Liu, S., Wu, Y., Fan, F., 2016. Analysis of landslide generated impulsive waves using a coupled DDASPH method. Eng. Anal. Bound. Elem. 64, 267–277.
217. Wang, Z., Qiao, C., Song, C., Xu, J., 2014. Upper bound limit analysis of support pressures of shallow tunnels in layered jointed rock strata. Tunn. Undergr. Sp. Technol. 43, 171–183.
218. Warburton, P.M., 1981. Vector stability analysis of an arbitrary polyhedral rock
block with any number of free faces. Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
18 (5), 415–427.
219. Warburton P. M., 1983. Application of a new computer model for reconstructing blocky rock geometryanalysing single block stability and identifying keystone. Proc. 5th Congr. ISRM, Melbourne.
220. Warburton P. M., 1985. A computer program for reconstructing blocky rock geometry and analysing single block stability. Comput. Geosci. 11, 707712.
221. Wei, P.H., and Yanlong, S.J., 2009. Study on distortion mechanism of mined slope affected by openpit and underground mining [J]. Metal Mine, 11.
222. White, D.J., Take, W.A., 2002. Particle Image Velocimetry (PIV) software for use in geotechnical testing. University of Cambridge, Department of Engineering
223. Wibowo, J.L., 1997. Consideration of secondary blocks in keyblock analysis. International Journal of Rock Mechanics and Mining Sciences, 34(34), 333 e1.
224. Williams, J.R., 1985. The theoretical basis of the discrete element method. In Proc. of the NUMETA'85 Conference, 897906
225. Windsor, C.R., and Thompson, A.G., 1993. SAFEXStability Assessment for Excavations in Rock. Rock Technology Software, Perth, Western Australia.
226. Wu, B.R, and Lee, C.J., 2003. Ground movements and collapse mechanisms induced by tunneling in clayey soil. Int J Phys Model Geotech 3:15–29
227. Wu, J.H., 2015. The elastic distortion problem with large rotation in discontinuous deformation analysis. Comput. Geotech. 69, 352–364.
228. Wu, J.H., Do, T.N., Chen, C.H., Wang, G., 2017. New geometric restriction for the displacement constraint points in discontinuous deformation analysis. Int. J. Geomech. 17
229. Wu, J.H., and Lin, H.M., 2013. Improvement of openclose iteration in DDA. Front. Discontinuous Numer. methods Pract. simulations Eng. disaster Prev. Fukuoka 185–191.
230. Wu, J.H., Ohnishi, Y., Nishiyama, S., 2004. Simulation of the mechanical behavior of inclined jointed rock masses during tunnel construction using Discontinuous Deformation Analysis (DDA). Int. J. Rock Mech. Min. Sci.
231. Wu, J.H., Chen, C.H., 2011. Application of DDA to simulate characteristics of the Tsaoling landslide. Comput Geotech.
232. Wu, W., Wang, X., Zhu, H., Shou, K.J., Lin, J.S., Zhang, H., 2020. Improvements in DDA program for rockslides with local incircle contact method and modified openclose iteration. Engineering Geology, 265, 105433.
233. Xiang, J., Munjiza, A., Latham, J.P., Guises, R., 2009. On the validation of DEM and FEM/DEM models in 2D and 3D. Eng. Comput. 26, 673–687.
234. Xianguo, C., and Bo, G., 2002. 2D Fem Numerical Simulation For CloselySpaced Parallel Tunnels In Metro [J]. Chinese J Rock Mech Eng 9:1330–1334
235. Xie, Y.Y., Hu, Z.R., Lu, G.J., Zhang, X.M., Zhao, C.M., Lai, K.C., 2013. Instant numerical simulation research on fire ventilation in extralong highway tunnel in zhongnanshan section of qinlin mountains. Procedia Engineering, 52, 468474.
236. Xu, N., Kulatilake, P.H.S.W., Tian, H., Wu, X., Nan, Y., Wei, T., 2013. Surface subsidence prediction for the WuTong mine using a 3D finite difference method. Comput. Geotech. 48, 134–145.
237. Yagi, T., Takeuchi, N., Yamamura, K., Hamasaki, E., 2013. Combined Method for Rigid BodiesSpring Model and Discrete Element Method. APCOM & ISCM, Singapore.
238. Yalcin, E., Gurocak, Z., Ghabchi, R., Zaman, M., 2016. Numerical analysis for a realistic support design: Case study of the Komurhan tunnel in eastern Turkey. Int. J. Geomech. 16.
239. Yang, X, and Ho, P., 2019. Is mining harmful or beneficial? A survey of local community perspectives in China. Extr Ind Soc 6:584–592
240. Yang, X.X., Jing, H.W., Tang, C.A., Yang, S.Q. 2017. Effect of parallel joint interaction on mechanical behavior of jointed rock mass models. International Journal of Rock Mechanics and Mining Sciences, 92, 4053
241. Yeung, M.R., Leong, L.L., 1997. Effects of joint attributes on tunnel stability. Proc. 1997 36th US Rock Mech. ISRM Int. Symp. 34, 505.
242. Yingren, Z., and Shangyi, Z., 2004., Calculation of inner force of support structure for landslide/slope by using strength reduction FEM [J]. Chinese J. Rock Mech. Eng. 20.
243. Yu, N., and Zhu, H., 2004. Analysis of earth deformation caused by shield tunnel construction and 3DFEM simulation. Rock Soil Mech. 25, 1330–1334.
244. Yu, P., Zhang, Y., Peng, X., Chen, G., Zhao, J.X., 2019. Distributedspring edgetoedge contact model for twodimensional discontinuous deformation analysis. Rock Mechanics and Rock Engineering, 118.
245. Zhai, S., Gao, Q., Song, J., 2006. Genetic programming approach for predicting surface subsidence induced by mining. J. China Univ. Geosci. 17, 361–366.
246. Zhang, H., Liu, S.G., Chen, G.Q., Zheng, L., Zhang, Y.B., Wu, Y.Q., Jing, P.D., Wang, W., Han, Z., Zhong, G.H., Lou, S., 2016a. Extension of threedimensional discontinuous deformation analysis to frictionalcohesive materials. International Journal of Rock Mechanics and Mining Sciences, 86, 6579
247. Zhang, J.J., Li, Y.L., Guo, L., Liu, Y., 2010. Design and Application of Rock Tunnel Visualization Procedures Based on Key Block Theory [J]. Journal of Water Resources and Architectural Engineering, 2.
248. Zhang, X, Jiao, Y.Y., Liu, Q., Chen, W.Z., 2007. Modeling of stability of a highway tunnel by using improved DDA method. Yantu Lixue Rock Soil Mech 28:1710–1714
249. Zhang, Y., Wang, J., Zhao, J.X., Chen, G., Yu, P., Yang, T., 2019. Multispring edgetoedge contact model for discontinuous deformation analysis and its application to the tensile failure behavior of rock joints. Rock Mechanics and Rock Engineering, 115.
250. Zhang, Y., Yang, J., Yang, F., 2015. Field investigation and numerical analysis of landslide induced by tunneling. Eng. Fail. Anal. 47, 25–33.
251. Zhang, Z., Zhang, M., Jiang, Y., Bai, Q., Zhao, Q., 2017. Analytical prediction for ground movements and liner internal forces induced by shallow tunnels considering nonuniform convergence pattern and groundliner interaction mechanism. Soils Found. 57, 211–226.
252. Zhao, G.F., Khalili, N., Zhao, X.B., Tu, X.B., 2012. Development of graphic user interface for Discontinues Deformation Analysis (DDA). Advances in Discontinuous Numerical Methods and Applications in Geomechanics and Geoengineering, 175180.
253. Zheng, L, Liu, X, Tang, Q, Ou, J., 2019. Lead Pollution and Isotope Tracing of Surface Sediments in the Huainan Panji Coal Mining Subsidence Area, Anhui, China. Bull Environ Contam Toxicol, 1–6
254. Zhou, J., Wei, J., Yang, T., Zhu, W., Li, L., Zhang, P., 2018. Damage analysis of rock mass coupling joints, water and microseismicity. Tunnelling and Underground Space Technology, 71, 366381
255. Zhu, H., Li, X., Cai, Y., Ding, W.Q., 2005. 3D Nonlinear FEM analysis on the Stability of the Slope at Tunnel Face During the Construction of the Twin Tunnels. J Highw Transp Res Dev 22:119–122
256. Zhu, H., Wu, W., Chen, J., Ma, G., Liu, X. and Zhuang, X., 2016. Integration of three dimensional discontinuous deformation analysis (DDA) with binocular photogrammetry for stability analysis of tunnels in blocky rockmass. Tunnelling and Underground Space Technology, 51, 3040.
257. Zhu, H., Wu, W., Zhuang, X., Cai, Y., Rabczuk, T., 2016. Method for estimating normal contact parameters in collision modeling using discontinuous deformation analysis. Int. J. Geomech. 17, E4016011.

論文全文使用權限 
同意授權校內瀏覽/列印電子全文服務，於20201206起公開。同意授權校外瀏覽/列印電子全文服務，於20201206起公開。 


