High rock slope stability analysis using the enriched meshless shepard and least squares method

International Journal of Computational Methods

Volumn 8, Issue 2, 2011, Pages 209-228

  Zhu, Hehua ^a   Zhuang, Xiaoying ^a   Cai, Yongchang ^a   Ma, Guowei ^b  

^a Tongji University   (China)

^b UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

Crack; high rock slope; meshless; MLS; MSLS; slope stability

Indexed keywords

HIGH ROCK SLOPE; JINPING HYDROPOWER STATION; JOINTED ROCK MASS; LEAST SQUARE; LEAST SQUARES METHODS; MESH-LESS METHODS; MESHLESS; MLS; MODELING PROBLEMS; MSLS; NEAR-FIELD; POTENTIAL SLIP SURFACE; ROCK MASS; ROCK SLOPE STABILITY; SLICE METHOD;

LEAST SQUARES APPROXIMATIONS; ROCKS; SAFETY FACTOR;

SLOPE STABILITY;

EID: 79960119063     PISSN: 02198762     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219876211002551     Document Type: Conference Paper

References (63)

1. Alejano, L. R. and Alonso, E. [2005] Application of the "shear and tensile strength reduction technique" to obtain factors of safety of toppling and footwall rock slopes, EUROCK 2005: Impact of Human Activity on the Geological Environment, 7-13.
2. Atluri, S. N., Kim, H. G. and Cho, J. Y. [1999] A critical assessment of the truly meshless local Petrov-Galerkin and local boundary integral equation methods, Comput. Mech. 24, 348-372. (Pubitemid 30546709)
3. Atluri, S. N. and Zhu, T. [1998] A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics, Comput. Mech. 21, 117-127. (Pubitemid 128620889)
4. Belytschko, T. and Fleming, M. [1999] Smoothing, enrichment and contact in the element-free Galerkin method, Comput. Struct. 71, 173-195.
5. Belytschko, T., Krongauz, Y. and Organ, D. [1996] Meshless methods: an overview and recent developments, Comput. Meth. Appl. Mech. Eng. 139, 3-47. (Pubitemid 126382692)
6. Belytschko, T., Lu, Y. Y. and Gu, L. [1994] Element-free Galerkin method, Int. J. Numer. Meth. Eng. 37, 229-256.
7. Belytschko, T., Organ, D. and Gerlach, C. [2000] Element-free Galerkin methods for dynamic fracture in concrete, Comput. Meth. Appl. Mech. Eng. 187, 385-399.
8. Belytschko, T., Organ, D. and Krongauz, Y. [1995] A coupled finite element-element free Galerkin method, Comput. Mech. 17, 186-195.
9. 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, J. Geotech. Geoenvir. Eng. 135, 1547-1561.
10. Breitkopf, P., Rassine, A. and Touzot, G. [2000] Explicit form and efficient computation of MLS shape functions and their derivatives, Int. J. Numer. Meth. Eng. 48, 451-466.
11. Cho, J. Y., Song, Y. M. and Choi, Y. H. [2008] Boundary locking induced by penalty enforcement of essential boundary conditions in mesh-free methods, Comput. Meth. Appl. Mech. Eng. 197, 1167-1183.
12. Cai, Y. C. and Zhu, H. H. [2008] A local meshless Shepard and least square interpolation method based on local weak form, Comput. Model. Eng. Sci. 34, 179-204.
13. Chen, J. C. and Wang, H. P. [2000] New boundary condition treatment in meshfree computation of contact problems, Comput. Meth. Appl. Mech. Eng. 187, 441-468.
14. China Academy of Aerospace. [1993] Handbook of Stress Intensity Factor, Science Press, Beijing.
15. Chung, H. J. [2000] Adaptive nodal generation with the element-free Galerkin method, Struct. Eng. Mech. 10, 635-650.
16. Cundall, P. A. and Strack, O. D. L. [1979] A discrete numerical model for granular assemblies, Géotechnique 29, 47-65. (Pubitemid 9433658)
17. Dawson, E. M., Roth, W. H. and Drescher, A. [1999] Slope stability analysis by strength reduction, Géotechnique, 49, 835-840. (Pubitemid 30102457)
18. Dolbow, J. and Belytschko, T. [1998] An introduction to programming the meshless element-free Galerkin method, Arch. Comput. Meth. Eng. 5, 207-241.
19. Donald, B. and Chen, Z. Y. [1997] Slope stability analysis by the upper bound approach: fundamentals and methods, Can. Geotech. J. 34, 853-862.
20. Fan, C. and Yang, J. Y. [2009] Numerical modeling of mode I crack propagation in rocks with meshless method, Controlling Seismic Hazard and Sustainable Development of Deep Mines, 7th International Symposium on Rockburst and Seismicity in Mines (RASIM7), 1235-1238.
21. Fleming, M., Chun, Y. A., Moran, B. and Belytschko, T. [1997] Enriched element-free Galerkin methods for crack tip fields, Int. J. Numer. Meth. Eng. 40, 1483-1504.
22. Giani, G. P. [1992] Rock Slope Stability Analysis, Balkema, Rotterdam.
23. Goodman, R. E. [1980] Introduction to Rock Mechanics, Wiley, New York.
24. Griffiths, D. V. and Lane, P. A. [1999] Slope stability analysis by finite elements, Géotechnique 49, 387-403. (Pubitemid 29324467)
25. Gu, Y. T. and Zhang, L. C. [2008] Coupling of the meshfree and finite element methods for determination of the crack tip fields, Eng. Fract. Mech. 75, 986-1004. (Pubitemid 350215361)
26. Gu, Y. T. and Liu, G. R. [2002] A boundary point interpolation method for stress analysis of solids, Comput. Mech. 28, 47-54.
27. Hoek, E. and Bray, J. [1974] Rock Slope Engineering, Institution of Mining and Metallurgy, London.
28. Jing, L. and Hudson, J. A. [2002] Numerical methods in rock mechanics, Int. J. Rock Mech. Min. Sci. 39, 409-427. (Pubitemid 34923559)
29. Jing, L. [2003] A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering, Int. J. Rock Mech. Min. Sci. 40, 283-353. (Pubitemid 36580062)
30. John, E. S. [1976] Wide range stress intensity factor expressions for ASTME 399 standard fracture toughness specimens, Int. J. Fract. 12, 475-476.
31. Lancaster, P. and Salkauskas, K. [1981] Surfaces generated by moving least squares methods, Math. Comput. 37, 141-158.
32. Lee, A. H. and Yoon, Y. C. [2004] Numerical prediction of crack propagation by an enhanced element-free Galerkin method, Nucl. Eng. Des. 227, 257-271.
33. Lin, C. T., Amadei, B., Jung, J. and Dwyer, J. [1996] Extensions of discontinuous deformation analysis for jointed rock masses, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 33, 671-694.
34. Lin, J. S. and Ku, C. Y. [2006] Two-scale modeling of jointed rock masses, Int. J. Rock Mech. Min. Sci. 43, 426-436.
35. Liu, G. R. and Gu, Y. T. [2001a] A point interpolation method for two-dimensional solids, Int. J. Numer. Meth. Eng. 50, 937-951. (Pubitemid 32192399)
36. Liu, G. R. and Gu, Y. T. [2001b] A local point interpolation method for stress analysis of two-dimensional solids, Struct. Eng. Mech. 11, 221-236. (Pubitemid 32189184)
37. Liu, G. R., Gu, Y. T. and Dai, K. Y. [2004] Assessment and applications of point interpolation methods for computational mechanics, Int. J. Numer. Meth. Eng. 59, 1373-1397. (Pubitemid 38335662)
38. Liu, G. R. [2008] A generalized gradient smoothing technique and the smoothed bilinear form for Galerkin formulation of a wide class of computational methods, Int. J. Comput. Meth. 5, 199-236.
39. Liu, W. K., Han, W. M., Lu, S. H., Li, S. and Cao, J. [2004] Reproducing kernel element method, Part I: theoretical formulation, Comput. Meth. Appl. Mech. Eng. 193, 933-951. (Pubitemid 38439201)
40. Lu, X. Z., Jiang, J. J. and Ye, L. P. [2006] A composite crack model for concrete based on meshless method, Struct. Eng. Mech. 23, 217-232.
41. Lu, Y. Y. and Belytschko, T., et al. [1994] A new implementation of the element free Galerkin method, Comput. Meth. Appl. Mech. Eng. 113, 397-414.
42. Marc, D. and Huang, N. D. [2004] A meshless method with enriched weight functions for fatigue crack growth, Int. J. Numer. Meth. Eng. 59, 1945-1961.
43. Matsui, T. and San, K. C. [1992] Finite element slope stability analysis by shear strength reduction technique, Soils Found. 32, 59-70.
44. Nayroles, B., Touzot, G. and Villon, P. [1992] Generalizing the finite element method: diffuse approximation and diffuse elements, Comput. Mech. 10, 307-318. (Pubitemid 23570159)
45. Oden, J. T., Durate, C. A. and Zienkiewicz, O. C. [1998] A new cloud-based hp finite element method, Comput. Meth. Appl. Mech. Eng. 153, 117-126. (Pubitemid 128402596)
46. Oñate, E., Idelsohn, S., Zienkiewicz, O. C. and Taylor, R. L. [1996] A finite point method in computational mechanics: applications to convective transport and fluid flow, Int. J. Numer. Meth. Eng. 39, 3839-3866.
47. Osada, M., Shrestha, S. K., Kajiyama, T. and Yamaguchi, K. [2004] Application of rock mass integration method (RMIM) with DDA modeling in rock slope stability, Contribution of Rock Mechanics to the New Century, 1257-1262.
48. Potyondy, D. O. and Cundall, P. A. [2004] A bonded-particle model for rock, Int. J. Rock Mech. Min. Sci. 41, 1329-1364. (Pubitemid 39615643)
49. Rajendran, S. and Zhang, B. R. [2007] A "FE-meshfree" QUAD4 element based on partition of unity, Comput. Meth. Appl. Mech. Eng. 197, 128-147. (Pubitemid 47570884)
50. Shi, G. H. and Goodman, R. E. [1985] Two dimensional discontinuous deformation analysis, Int. J. Numer. Anal. Meth. Geomech. 9, 541-556.
51. Shi, G. H. and Goodman, R. E. [1989] Generalization of two-dimensional discontinuous deformation analysis for forward modelling, Int. J. Numer. Anal. Meth. Geomech. 13, 359-380.
52. Stern, M., Becker, E. B. and Dunham, R. S. [1976] A contour integral computation of mixed-mode stress intensity factors, Int. J. Fract. 12, 359-368.
53. Ugai, K. [1989] A method of calculation of total factor of safety of slopes by elasto-plastic FEM, Soils Found. 29, 190-195.
54. Williams, J. R. and O'Connor, R. [1999] Discrete element simulation and the contact problem, Arch. Comput. Meth. Eng. 6, 279-304.
55. Wuhan University, China [2005] The internal research report on the slope stability and scheme of supporting structure at the left bank of hydro-junction of Jinping hydropower station, School of Water Conservancy and Hydropower Engineering, Wuhan.
56. Xu, Y. and Saigal, S. [1998] An element-free Galerkin formulation for stable crack growth in an elastic solid, Comput. Meth. Appl. Mech. Eng. 154, 331-343. (Pubitemid 128402413)
57. Yeung, M. R., Sun, N., Lee, Y. S. and Jiang, Q. H. [2004] Factor of safety against wedge failure calculated by three-dimensional discontinuous deformation analysis, Contribution of Rock Mechanics to the New Century, 1263-1266.
58. Zhang, X., Lu, M. W. and Wegner, J. L. [2000] A 2-D meshless model for jointed rock structures, Int. J. Numer. Meth. Eng. 47, 1649-1661. (Pubitemid 30221826)
59. Zhang, Z., Liew, K. M., Cheng, Y. M., et al. [2008] Analyzing 2D fracture problems with the improved element-free Galerkin method, Eng. Anal. Bound. Elem. 32, 241-256.
60. Zhuang, X., Cai, Y. C. and Zhu, H. H. [2008a] Rock slope stability analysis based on meshless method and shortest path algorithm, Chin. Q. Mech. 29, 537-543.
61. Zhuang, X., Cai, Y. C. and Zhu, H. H. [2008b] An FEM modeling method for anchored slope stability analysis and discussions on anchoring effect, Chin. J. Geotech. Eng. 30, 1099-1104.
62. Zhuang, X. and Augarde, C. [2010] Aspects of the use of orthogonal basis functions in the element free Galerkin method, Int. J. Numer. Meth. Eng. 81, 366-380.
63. Zhu, T. and Atluri, S. N. [1998] A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method, Comput. Mech. 21, 211-222. (Pubitemid 128566411)