Extension of the Discontinuous Deformation Analysis Method to Simulate Seismic Response of a Large Rock Cavern Complex
Publication: International Journal of Geomechanics
Volume 17, Issue 5
Abstract
The discontinuous deformation analysis (DDA) method calculates large deformations and discontinuous problems using time-step solving and provides an effective tool for analyzing the seismic response of rock mass engineering. In this paper, extensions of the DDA method to simulate the seismic response of a large rock cavern complex are carried out. First, applicability of the existing seismic input methods, including the multiblock Newmark method, large mass method, and large stiffness method, are discussed. Second, considering the characteristics of the seismic response of a large rock cavern complex, a new seismic DDA model that includes a coupling model and a force-input method is presented. Last, the extended DDA method is used for a case study. Simulations of the quasi-static and seismic dynamic stages for the large rock cavern complex of the Dagangshan hydropower station in southwest China are carried out. Considering the stress and displacement distributions in the quasi-static stage, the most unfavorable movable blocks are found. In the seismic dynamic stage, serious damage to the main machine building and local damage of the downstream sidewall of the main transformer chamber are observed, and the seismic response of the large rock cavern complex can be visually divided into four phases, which show that failures of the most unfavorable movable blocks are an early sign of collapse of a rock cavern complex.
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Acknowledgments
The authors thank Dr. Shi for his guidance in understanding the DDA method and providing the original DDA program. The work reported in this paper is financially supported by National Key Basic Research Program of China (973 Program) under Grant No. 2015CB057905 and the National Natural Science Foundation of China (Grant No. 51509241, 11272331, U1402231, and 11472292). We also thank the editor and two anonymous reviewers for their helpful and insightful comments.
References
Bao, H. R., Hatzor, Y. H., and Huang, X. (2012). “A new viscous boundary condition in the two-dimensional discontinuous deformation analysis method for wave propagation problems.” Rock Mech. Rock Eng., 45(5), 919–928.
Bao, H. R., and Zhao, Z. Y. (2012). “The vertex-to-vertex contact analysis in the two-dimensional discontinuous deformation analysis.” Adv. Eng. Software, 45(1), 1–10.
Cheng, Y. M., and Zhang, Y. H. (2002). “Coupling of FEM and DDA methods.” Int. J. Geomech., 503–517.
Doolin, D. M. (2005). “Unified displacement boundary constraint formulation for discontinuous deformation analysis (DDA).” Int. J. Numer. Anal. Methods Geomech., 29(12), 1199–1207.
Dowding, C. H., and Rozen, A. (1978). “Damage to rock tunnels from earthquake shaking.” J. Geotech. Eng. Div., 104(2), 175–191.
Fu, X. D., Sheng, Q., Zhang, Y. H., and Chen, J. (2015a). “Application of the discontinuous deformation analysis to stress wave propagation through a one-dimensional rock mass.” Int. J. Rock Mech. Min. Sci., 80, 155–170.
Fu, X. D., Sheng, Q., Zhang, Y. H., and Chen, J. (2016). “Investigation of highly efficient algorithms for solving linear equations in the discontinuous deformation analysis method.” Int. J. Numer. Anal. Methods Geomech., 40(4), 469–486.
Fu, X. D., Sheng, Q., Zhang, Y. H., Zhou, Y. Q., and Dai, F. (2015b). “Boundary setting method for the seismic dynamic response analysis of engineering rock mass structures using the discontinuous deformation analysis method.” Int. J. Numer. Anal. Methods Geomech., 39(15), 1693–1712.
Goodman, R. E., and Shi, G. H. (1985). Block theory and its applications to rock engineering, Prentice-Hall, Englewood Cliffs, NJ.
Gu, J., and Zhao, Z. Y. (2009). “Considerations of the discontinuous deformation analysis on wave propagation problems.” Int. J. Numer. Anal. Methods Geomech., 33(12), 1449–1465.
Hatzor, Y. H., Arzi, A. A., Zaslavsky, Y., and Shapirad, 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(5), 813–832.
Hsiung, S. M., and Shi, G. H. (1999). “Simulation of earthquake effects on underground excavations using discontinuous deformation analysis (DDA).” Proc., 38th U.S. Symp. on Rock Mechanics, American Rock Mechanics Association, Washington, DC, 1413–1420.
Irie, K., Koyama, T., Nishiyama, S., Yasuda, Y., and Ohnishi, Y. (2012). “A numerical study on the effect of shear resistance on the landslide by discontinuous deformation analysis (DDA).” Geomech. Geoeng., 7(1), 57–68.
Jiang, Q. H., Chen, Y. F., and Zhou, C. B. (2013). “Kinetic energy dissipation and convergence criterion of discontinuous deformations analysis (DDA) for geotechnical engineering.” Rock Mech. Rock Eng., 46(6), 1443–1460.
Jiang, Q. H., Wei, W., Yao, C., and Zhou, C. B. (2011). “Failure mode analysis of jointed rock masses around underground opening under excavation unloading.” Mater. Res. Innovations, 15(S1), 609–612.
Jiang, Q. H., and Yeung, M. R. (2004). “A model of point-to-face contact for three-dimensional discontinuous deformation analysis.” Rock Mech. Rock Eng., 37(2), 95–116.
Jiang, Q. H., Zhou, C. B., Li, D. Q., and Yeung, M. R. (2012). “A softening block approach to simulate excavation in jointed rocks.” Bull. Eng. Geol. Environ., 71(4), 747–759.
Jiao, Y. Y., Huang, G. H., Zhao, Z. Y., Zheng, F., and Wang, L. (2015). “An improved three-dimensional spherical DDA model for simulating rock failure.” Sci. China Tech. Sci., 58(9), 1533–1541.
Jiao, Y. Y., Zhang, X. L., and Zhao, J. (2012). “Two-dimensional DDA contact constitutive model for simulating rock fragmentation.” J. Eng. Mech., 199–209.
Jiao, Y. Y., Zhang, X. L., Zhao, J., and Liu, Q. S. (2007). “Viscous boundary of DDA for modeling stress wave propagation in jointed rock.” Int. J. Rock Mech. Min. Sci., 44(7), 1070–1076.
Jing, L. R. (1998). “Formulation of discontinuous deformation analysis (DDA)—An implicit discrete element model for block systems.” Eng. Geol., 49(3–4), 371–381.
Kaidi, S., Ouahsine, A., Sergent, P., and Rouainia, M. (2012). “Discontinuous deformation analysis to assess the stability of rockfill dams under seismic loading.” C.R. Mec., 340(10), 731–738.
Kamai, R., and Hatzor, Y. H. (2008). “Numerical analysis of block stone displacements in ancient masonry structures: A new method to estimate historic ground motion.” Int. J. Numer. Anal. Methods Geomech., 32(11), 1321–1340.
Ke, T. C., and Goodman, R. E. (1994). “Discontinuous deformation analysis and the artificial joint concept.” Proc., 1st North Am. Rock Mechanics Symp., American Rock Mechanics Association, Alexandria, VA, 599–646.
Kong, X. J., and Liu, J. (2002). “Dynamic failure numeric simulations of model concrete-faced rock-fill dam.” Soil Dyn. Earthquake Eng., 22(9–12), 1131–1134.
Li, T. B. (2012). “Damage to mountain tunnels related to the Wenchuan Earthquake and some suggestions for aseismic tunnel construction.” Bull. Eng. Geol. Environ., 71(2), 297–308.
Li, X. K., and Zheng, H. (2015). “Condensed form of complementarity formulation for discontinuous deformation analysis.” Sci. China Tech. Sci., 58(9), 1509–1519.
Lin, C. T., Amadei, B., Jung, J., and Dwyer, J. (1996). “Extensions of discontinuous deformation analysis for jointed rock mass.” Int. J. Rock Mech. Min. Sci., 33(71), 671–694.
Ma, M. Y. (1999). “Development of discontinuous deformation analysis the first ten years (1986 to 1996).” Proc., 3rd Int. Conf. on Analysis of Discontinuous Deformation: From Theory to Practice, B. Amadei, ed., American Rock Mechanics Association, Alexandria, VA, 17–32.
MacLaughlin, M. M., and Doolin, D. M. (2006). “Review of validation of the discontinuous deformation analysis (DDA) method.” Int. J. Numer. Anal. Methods Geomech., 30(4), 271–305.
Newmark, N. M. (1965). “Effects of earthquakes on dams and embankments.” Géotechnique, 15(2), 139–160.
Ning, Y. J., and Zhao, Z. Y. (2013). “A detailed investigation of block dynamic sliding by the discontinuous deformation analysis.” Int. J. Numer. Anal. Methods Geomech., 37(15), 2373–2393.
Sasaki, T., Hagiwara, I., Horikawa, S., Ohnishi, Y., Nishiyama, S., and Yoshinaka, R. (2005). “Earthquake response analysis of a rockfall by discontinuous deformation analysis.” Proc., 7th Int. Conf. on Analysis of Discontinuous Deformation, M. M. MacLaughlin and N. Sitar, eds., Honolulu, HI, 137–146.
Shi, G. H. (1988). “Discontinuous deformation analysis: A new numerical model for the statics and dynamics of block systems.” Ph.D. thesis, Univ. of California, Berkeley, CA.
Shi, G. H. (1999). “Application of discontinuous deformation analysis and manifold method.” Proc., 3rd Int. Conf. on Analysis of Discontinuous Deformation: From Theory to Practice, B. Amadei, ed., American Rock Mechanics Association, Alexandria, VA, 3–16.
Shi, G. H. (2009). “Rock stability analysis and three convergences of discontinuous deformation analysis (DDA).” Proc., 9th Int. Conf. on Analysis of Discontinuous Deformation: New Development and Application, Singapore, 1–11.
Shi, G. H. (2015). “Contact theory.” Sci. China Tech. Sci., 58(9), 1450–1496.
Shi, G. H., and Goodman, R. E. (1984). “Discontinuous deformation analysis.” Proc., 25th Symp. on Rock Mech., Society of Mining Engineers, Englewood, CO, 269–277.
State Economy and Trade Commission of the People's Republic of China. (1997). “Specifications for seismic design of hydraulic structures.” S. L. 203, China Water Power Press, Beijing.
Su, H. Z., Hu, J., Li, J. Y., and Wu, Z. R. (2013). “Deep stability evaluation of high-gravity dam under combining action of powerhouse and dam.” Int. J. Geomech., 257–272.
Wu, J. H. (2010). “Seismic landslide simulations in discontinuous deformation analysis.” Comput. Geotech., 37(5), 594–601.
Yang, W. D., Zhang, Q. Y., Li, S. C., and Wang, S. G. (2014). “Estimation of in situ viscoelastic parameters of a weak rock layer by time-dependent plate-loading tests.” Int. J. Rock Mech. Min. Sci., 66, 169–176.
Zhang, Y. B., Chen, G. Q., Zheng, L., and Wu, J. (2013). “Effects of near-fault seismic loadings on run-out of large-scale landslide: A case study.” Eng. Geol., 166(8), 216–236.
Zhang, Y. H., Fu, X. D., and Sheng, Q. (2014). “Modification of the discontinuous deformation analysis method and its application to seismic response analysis of large underground caverns.” Tunnelling Underground Space Technol., 40(Feb), 241–250.
Zhang, Y. T., Xiao, M., and Li, Y. J. (2010). “Effect of Wenchuan Earthquake on earthquake damage and dynamic response analysis of underground powerhouse of Yingxiuwan hydropower station.” Chin. J. Rock Mech. Eng., 29(S2), 3663–3671.
Zheng, L., Chen, G., Zhang, Y., and Zhang, H. (2013). “Review of rock stability analysis using discontinuous deformation analysis (DDA).” Proc., 3rd ISRM Symp. on Rock Mechanics, X. T. Feng, J. A. Hudson, and F. Tan, eds., International Society for Rock Mechanics, Lisbon, Portugal, 491–500.
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Published In
International Journal of Geomechanics
Volume 17 • Issue 5 • May 2017
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© 2016 American Society of Civil Engineers.
History
Received: Aug 7, 2015
Accepted: Apr 5, 2016
Published online: May 17, 2016
Discussion open until: Oct 17, 2016
Published in print: May 1, 2017
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