Abstract
This paper is mainly aimed to present an improved DDA (discontinuous deformation analysis) that can deal well with both shear and tensile failure problems. Firstly, the shear mechanism of DDA is detailed investigated. The results show that when handling the frictional interface, the critical shear resistance can be accurately determined only if the penalty value is carefully selected, however, when handling the cohesive interface, the critical shear resistance is significantly underestimated. The inaccurate prediction is due to the inconsistent distribution of normal force and shear force between the two vertex-to-edge contacts in one edge-to-edge contact. Here an edge-to-edge treatment is introduced into DDA. Secondly, to moderately reflect the tensile failure process of rock masses, a two-phase constitutive model is introduced into the DDA with edge-to-edge treatment, and the improved DDA is obtained. Finally, the improved DDA is used to simulate the failure process of gypsum centrifuge model. The results show the improved DDA can deal well with rock failure problems by shear or tension failure.
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Bakun-Mazor, D., Hatzor, Y. H., and Glaser, S. D. (2012). “Dynamic sliding of tetrahedral wedge: The role of interface friction.” International Journal for Numerical and Analytical Method in Geomechanics, Vol. 36, No. 3, pp. 327–343, DOI: 10.1002/nag.1009.
Barton, N. and Bandis. S. (1982). “Effects of block size on the shear behavior of jointed rock.” Proc. 23th US Symp. on Rock Mechanics., Berkeley, CA, USA, pp. 739–760.
Doolin, D. M. and Sitar, N. (2002). “Displacement accuracy of discontinuous deformation analysis method applied to sliding block.” Journal of Engineering Mechanics, Vol. 128, No. 11, pp. 1158–1168, DOI: 10.1061/(ASCE)0733-9399(2002)128:11(1158).
Goodman, R. E. and Bray, J. W. (1976). “Toppling of rock slopes.” Proc. The Specialty Conference on Rock Engineering for Foundations and Slopes, American Society of Civil Engineering, Boulder, CO, USA, pp. 739–760.
Hillerbora, A., Modeer, M., and Petersson, P. E. (1976). “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite element.” Cement and Concrete Research, Vol. 6, No. 6, pp. 773–781, DOI: 10.1016/0008-8846(76)90007-7.
Hsiung, S. M. (2001). “Discontinuous deformation analysis (DDA) with nth order polynomial displacement functions.” Proc. 38th US Rock Mechanics Symposium, Washington D.C., USA, pp. 1437–1444.
Huang, D., Song, Y. X., Cen, D. F., and Fu, G. Y. (2016). “Numerical modeling of earthquake-induced landslide using an improved discontinuous deformation analysis considering dynamic friction degradation of joints.” Rock Mechanics & Rock Engineering, Vol. 49, No. 12, pp. 4767–4786, DOI: 10.1007/s00603-016-1056-3.
Jiang, Q. H., Cheng, Y. F., Zhou, C. B., and Yeung, M. C. R. (2013). “Kinetic energy dissipation and convergence criterion of discontinuous deformation analysis (DDA) for geotechnical engineering.” Rock Mechanics and Rock Engineering, Vol. 46, No. 6, pp. 1443–1460, DOI: 10.1007/s00603-012-0356-5.
Jiao, Y. Y., Zhang, X. L., and Zhao, J. (2012). “Two-dimensional DDA contact constitutive model for simulating rock fragmentation.” Journal of Engineering Mechanics, ASCE, Vol. 138, No. 2, pp. 199–209, DOI: 10.1061/(ASCE)EM.1943-7889.0000319.
Jing, L. R. (1998). “Formulation of discontinuous deformation analysis (DDA)—An implicit discrete element model for block systems.” Engineering Geology, Vol. 49, No. 3, pp. 371–381, DOI: 10.1016/S0013-7952(97)00069-0.
Kitoh, H., Takeuchi, N., Ueda, M., Higuchi, H., Kambayashi, A., and Tomida, M. (1997). “Size effect analysis of plain concrete beams by using RBSM.” Proc. 2nd International Conference on Analysis of Discontinuous Deformation, Japan Institute of Systems Research, Kyoto, Japan, pp. 373–382.
Ma, S. Q., Zhao, Z. Y., Nie, W., Nemcik, J., Zhang Z. Y., and Zhu, X. (2017). “Implementation of displacement-dependent Barton-Bandis rock joint model into discontinuous deformation analysis” Computers and Geotechnics, Vol. 86, pp. 1–8, DOI: 10.1016/j.compgeo.2016.12.030.
Maclaughlin, M. M. (1997). Discontinuous deformation analysis of the kinematics of landslides. PhD Thesis, University of California, Berkeley, CA, USA.
Maclaughlin, M. M. and Doolin, D. M. (2006). “Review of validation the discontinuous deformation analysis (DDA) method.” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 30, No. 4, pp. 271–305, DOI: 10.1002/nag.427.
Pyrak-Nolte, L. J., Myer, L. R., and Cook, N. G. W. (1990). “Anisotropy in seismic velocities and amplitudes from multiple parallel fractures.” Journal of Geophysical Research, Vol. 95, No. 87, pp. 11345–11358, DOI: 10.1029/JB095iB07p11345.
Rousseau, J., Frangin, E., Marin, P., and Daudeville, L. (2008). “Damage prediction in the vicinity of an impact on a concrete structure: A combined FEM/DEM approach.” Computers and Concrete, Vol. 5, No. 4, pp. 343–358, DOI: 10.12989/cac.2008.5.4.343.
Scholtes, L. and Donze, F. V. (2012). “Modelling progressive failure in fractured rock masses using a 3D discrete element method.” International Journal of Rock Mechanics and Mining Sciences, Vol. 52, pp. 18–30, DOI: 10.1016/j.ijrmms.2012.02.009.
Shi, G. H. (1988). Discontinuous deformation analysis–A new numerical model for the statics and dynamics of block systems. PhD Thesis, University of California, Berkeley, CA, USA.
Sitar, N. S., Maclaughlin, M. M., and Doolin, D. M. (2005). “Influence of kinematics on landslide mobility and failure mode.” Journal of Geotechnical and Geoenvironmental Engineering, Vol. 131, No. 6, pp. 716–728, DOI: 10.1061/(ASCE)1090-0241(2005)131:6(716).
Wang, L. Z., Jiang, H. Y., Yang, Z. X., Xu, Y. C., and Zhu, X. B. (2013). “Development of discontinuous deformation analysis with displacementdependent interface shear strength.” Computers and Geotechnics, Vol. 47, pp. 91–101, DOI: 10.1016/j.compgeo.2012.06.006.
Wong, L. N. Y. and Wu, Z. J. (2014). “Application of the numerical manifold method to model progressive failure in rock slopes” Engineering Fracture Mechanics, Vol. 119, No. 3, pp. 1–20, DOI: 10.1016/j.engfracmech.2014.02.022.
Yeung, M. C. R. (1991). Application of Shi’s discontinuous deformation analysis to the study of rock behavior. PhD Thesis, University of California, Berkeley, CA, USA.
Zhang, J. H., Chen, Z. Y., and Wang, X. G. (2007). “Centrifuge modeling of rock slopes susceptible to block toppling.” Rock Mechanics and Rock Engineering, Vol. 40, No. 4, pp. 363–382, DOI: 10.1007/s00603-006-0112-9.
Zhang, Y. B., Xu, Q., Chen, G. Q., Zhao, J. X., and Zheng, L. (2014). “Extension of discontinuous deformation analysis and application in cohesive-friction slope analysis.” International Journal of Rock Mechanics and Mining Sciences, Vol. 70, No. 9, pp. 533–545, DOI: 10.1016/j.ijrmms.2014.06.005.
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Gong, W., Hu, J. & Tao, Z. An Improved Discontinuous Deformation Analysis to Solve Both Shear and Tensile Failure Problems. KSCE J Civ Eng 23, 1974–1989 (2019). https://doi.org/10.1007/s12205-019-2019-5
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DOI: https://doi.org/10.1007/s12205-019-2019-5