Discontinuous Deformation Analysis with Potential Contact Forces
Publication: International Journal of Geomechanics
Volume 19, Issue 10
Abstract
In conventional discontinuous deformation analysis (DDA), the procedure called open–close iteration is adopted to enforce the contact condition, which needs to repeatedly fix and remove the artificial springs between blocks in contact to determine real contact states. The open–close iteration belongs to the category of trial-and-error methods, in which convergence cannot be always guaranteed. Meanwhile, the contact force is treated as concentrated force, leading to the difficulties in determining the shear strength from cohesion and stresses in the contact area. The so-called potential contact force concept adopted in the combined finite-element method and discrete-element method (FEM-DEM) has been proved efficient and robust. In the FEM-DEM the contact force is treated as a distributed contact force, which is more realistic and was utilized in this study to tackle contacts. A major advantage over the conventional DDA lies in the elimination of the need to handle singular contact types that would incur huge difficulties in three-dimensional simulations. Therefore, a contact potential–based DDA (CPDDA) was developed by introducing potential contact forces. Some typical examples, including those originally designed by the DDA inventor, are reanalyzed, proving the feasibility of CPDDA.
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Acknowledgments
This study was supported by the National Key Research and Development Program of China (Grant 2018YFC0407002) and the National Natural Science Foundation of China (Grants 11502033 and 51579016).
References
Bao, H. R., Z. Y. Zhao, and Q. Tian. 2014. “On the implementation of augmented Lagrangian method in the two-dimensional discontinuous deformation analysis.” Int. J. Numer. Anal. Methods Geomech. 38 (6): 551–571. https://doi.org/10.1002/nag.2217.
Barla, M., G. Piovano, and G. Grasselli. 2012. “Rock slide simulation with the combined finite-discrete element method.” Int. J. Geomech. 12 (6): 711–721. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000204.
Bobet, A., A. Fakhimi, S. Johnson, J. Morris, F. Tonon, and M. R. Yeung. 2009. “Numerical models in discontinuous media: review of advances for rock mechanics applications.” J. Geotech. Geoenviron. Eng. 135 (11): 1547–1561. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000133.
Bui, T. Q., N. T. Nguyen, L. Van Lich, M. N. Nguyen, and T. T. Truong. 2018. “Analysis of transient dynamic fracture parameters of cracked functionally graded composites by improved meshfree methods.” Theor. Appl. Fract. Mech. 96 (Aug): 642–657. https://doi.org/10.1016/j.tafmec.2017.10.005.
Cai, Y. E., G. P. Liang, G. H. Shi, and N. G. W. Cook. 1996. “Studying an impact problem by using LDDA method.” In Proc., First Int. Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media, edited by M. R. Salami, and D. Banks, 288–294. Albuquerque, NM: TSI Press.
Chen, L., G. R. Liu, Y. Jiang, K. Zeng, and J. Zhang. 2011. “A singular edge-based smoothed finite element method (ES-FEM) for crack analyses in anisotropic media.” Eng. Fract. Mech. 78 (1): 85–109. https://doi.org/10.1016/j.engfracmech.2010.09.018.
Cheng, Y. M. 1998. “Advancements and improvement in discontinuous deformation analysis.” Comput. Geotech. 22 (2): 153–163. https://doi.org/10.1016/S0266-352X(98)00002-0.
Cundall, P. A. 1971. “A computer model for simulating progressive, large scale movements in blocky rock systems.” In Vol. 1 of Proc., Symp. of the Int. Society for Rock Mechanics, II-8, 1–8. Nancy, France: International Society for Rock Mechanics and Rock Engineering.
Desai, C. S., M. M. Zaman, J. G. Lightner, and H. J. Siriwardane. 1984. “Thin-layer element for interfaces and joints.” Int. J. Numer. Anal. Methods Geomech. 8 (1): 19–43. https://doi.org/10.1002/nag.1610080103.
Doolin, D. M., and N. Sitar. 2004. “Time integration in discontinuous deformation analysis.” J. Eng. Mech. 130 (3): 249–258. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:3(249).
Duarte, C. A., O. N. Hamzeh, T. J. Liszka, and W. W. Tworzydlo. 2001. “A generalized finite element method for the simulation of three-dimensional dynamic crack propagation.” Comput. Methods Appl. Mech. Eng. 190 (15–17): 2227–2262. https://doi.org/10.1016/S0045-7825(00)00233-4.
Elguedj, T., R. P. de Saint Maurice, A. Combescure, V. Faucher, and B. Prabel. 2018. “Extended finite element modeling of 3D dynamic crack growth under impact loading.” Finite Elem. Anal. Des. 151 (Oct): 1–17. https://doi.org/10.1016/j.finel.2018.08.001.
Goodman, R. E., and S. T. John. 1977. “Finite element analysis for discontinuous rocks.” In Numerical methods in geotechnical engineering, edited by C. S. Desai, and J. T. Christian, 148–175. New York: McGraw-Hill.
Goodman, R. E., R. Taylor, and T. L. Brekke. 1968. “A model for the mechanics of jointed rock.” J. Soil Mech. Found. Div. 94 (3): 637–660.
Hsiung, S. M. 2001. “Discontinuous deformation analysis (DDA) with nth order polynomial displacement functions.” In Proc., 38th US Rock Mechanics Symp. Rock Mechanics in the National Interest, edited by D. Elsworth, J. P. Tinucci, and K. A. Heasley, 1413–1420. Rotterdam, Netherlands: A. A. Balkema.
Jiang, Q. H., Y. F. Chen, C. B. Zhou, and M. R. Yeung. 2013. “Kinetic energy dissipation and convergence criterion of discontinuous deformations analysis (DDA) for geotechnical engineering.” Rock Mech. Rock Eng. 46 (6): 1443–1460. https://doi.org/10.1007/s00603-012-0356-5.
Jiang, Q. H., and M. R. Yeung. 2004. “A model of point-to-face contact for three-dimensional discontinuous deformation analysis.” Rock Mech. Rock Eng. 37 (2): 95–116. https://doi.org/10.1007/s00603-003-0008-x.
Jiang, W., and H. Zheng. 2015. “An efficient remedy for the false volume expansion of DDA when simulating large rotation.” Comput. Geotech. 70 (Oct): 18–23. https://doi.org/10.1016/j.compgeo.2015.07.008.
Jiang, Q. H., C. B. Zhou, and D. Q. Li. 2009. “A three-dimensional numerical manifold method based on tetrahedral meshes.” Comput. Struct. 87 (13–14): 880–889. https://doi.org/10.1016/j.compstruc.2009.03.002.
Jiao, Y. Y., H. Q. Zhang, X. L. Zhang, H. B. Li, and Q. H. Jiang. 2015. “A two-dimensional coupled hydromechanical discontinuum model for simulating rock hydraulic fracturing.” Int. J. Numer. Anal. Methods Geomech. 39 (5): 457–481. https://doi.org/10.1002/nag.2314.
Jing, L. R., Y. Ma, and Z. L. Fang. 2001. “Modeling of fluid flow and solid deformation for fractured rocks with discontinuous deformation analysis (DDA) method.” Int. J. Rock Mech. Min. Sci. 38 (3): 343–355. https://doi.org/10.1016/S1365-1609(01)00005-3.
Katona, M. G. 1983. “A simple contact-friction interface element with applications to buried culverts.” Int. J. Numer. Anal. Methods Geomech. 7 (3): 371–384. https://doi.org/10.1002/nag.1610070308.
Koo, C. F., J. C. Chern, and S. Chen, 1995. “Development of second order displacement function for DDA.” In Proc., 1st Int. Conf. on Analysis of Discontinuous Deformation, edited by J. C. Li, C. Y. Wang, and J. Sheng, 21–23. Chungli, Taiwan, China: National Central Univ.
Lin, C. T., B. Amadei, J. Jung, and J. Dwyer. 1996. “Extensions of discontinuous deformation analysis for jointed rock masses.” Int. J. Rock Mech. Min. Geomech. Abstr. 33 (7): 671–694. https://doi.org/10.1016/0148-9062(96)00016-2.
Lin, S. Z., and Z. Q. Xie. 2015. “Performance of DDA time integration.” Sci. China Technol. Sci. 58 (9): 1558–1566. https://doi.org/10.1007/s11431-015-5893-1.
Liu, F., and K. W. Xia. 2017. “Structured mesh refinement in MLS-based numerical manifold method and its application to crack problems.” Eng. Anal. Boundary Elem. 84 (Nov): 42–51. https://doi.org/10.1016/j.enganabound.2017.08.004.
Ma, M. Y., M. Zaman, and J. H. Zhou, 1996. “Discontinuous deformation analysis using the third-order displacement function.” In Proc., 1st Int. Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media, edited by M. R. Salami, and D. Banks, 383–394. Albuquerque, NM: TSI Press.
Mahabadi, O. K., A. Lisjak, A. Munjiza, and G. Grasselli. 2012. “Y-Geo: New combined finite-discrete element numerical code for geomechanical applications.” Int. J. Geomech. 12 (6): 676–688. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000216.
Morris, J. P., M. B. Rubin, G. I. Block, and M. P. Bonner. 2006. “Simulations of fracture and fragmentation of geologic materials using combined FEM/DEM analysis.” Int. J. Impact Eng. 33 (1–12): 463–473. https://doi.org/10.1016/j.ijimpeng.2006.09.006.
Munjiza, A. 2004. The combined finite-discrete element method. Hoboken, NJ: John Wiley & Sons.
Munjiza, A., and K. R. F. Andrews. 2000. “Penalty function method for combined finite-discrete element systems comprising large number of separate bodies.” Int. J. Numer. Methods Eng. 49 (11): 1377–1396. https://doi.org/10.1002/1097-0207(20001220)49:11%3C1377::AID-NME6%3E3.3.CO;2-2.
Munjiza, A., K. R. F. Andrews, and J. K. White. 1999. “Combined single and smeared crack model in combined finite-discrete element analysis.” Int. J. Numer. Methods Eng. 44 (1): 41–57. https://doi.org/10.1002/(SICI)1097-0207(19990110)44:1%3C41::AID-NME487%3E3.3.CO;2-1.
Munjiza, A., T. Bangash, and N. W. M. John. 2004. “The combined finite–discrete element method for structural failure and collapse.” Eng. Fract. Mech. 71 (4–6): 469–483. https://doi.org/10.1016/S0013-7944(03)00044-4.
Munjiza, A., D. R. J. Owen, and N. Bicanic. 1995. “A combined finite-discrete element method in transient dynamics of fracturing solids.” Eng. Comput. 12 (2): 145–174. https://doi.org/10.1108/02644409510799532.
Ooi, E. T., S. Natarajan, C. Song, and E. H. Ooi. 2017. “Crack propagation modelling in concrete using the scaled boundary finite element method with hybrid polygon–quadtree meshes.” Int. J. Fract. 203 (1–2): 135–157. https://doi.org/10.1007/s10704-016-0136-4.
Perrone, N., and R. Kao. 1975. “A general finite difference method for arbitrary meshes.” Comput. Struct. 5 (1): 45–57. https://doi.org/10.1016/0045-7949(75)90018-8.
Rabczuk, T., and T. Belytschko. 2004. “Cracking particles: a simplified meshfree method for arbitrary evolving cracks.” Int. J. Numer. Methods Eng. 61 (13): 2316–2343. https://doi.org/10.1002/nme.1151.
Rabczuk, T., and T. Belytschko. 2007. “A three-dimensional large deformation meshfree method for arbitrary evolving cracks.” Comput. Methods Appl. Mech. Eng. 196 (29–30): 2777–2799. https://doi.org/10.1016/j.cma.2006.06.020.
Salimzadeh, S., and N. Khalili. 2016. “Fully coupled XFEM model for flow and deformation in fractured porous media with explicit fracture flow.” Int. J. Geomech. 16 (4): 04015091. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000623.
Shi, G. H. 1988. “Discontinuous deformation analysis: A new numerical model for the statics and dynamics of block systems.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of California.
Shi, G. H. 1991. “Manifold method of material analysis.” In Transactions of the 9th Army Conf. on Applied Mathematics and Computing, Rep. No. 92–1, 51–76. Research Triangle Park, NC: US Army Research Office.
Shi, G. H. 2015. “Contact theory.” Sci. China Technol. Sci. 58 (9): 1450–1498. https://doi.org/10.1007/s11431-015-5814-3.
Wang, X., P. Yu, J. Yu, Y. Yu, and H. Lv. 2018. “Simulated crack and slip plane propagation in soil slopes with embedded discontinuities using XFEM.” Int. J. Geomech. 18 (12): 04018170. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001290.
Wei, W., Q. H. Jiang, and J. Peng. 2017. “New rock bolt model and numerical implementation in numerical manifold method.” Int. J. Geomech. 17 (5): E4016004. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000669.
Wei, W., Q. Zhao, Q. H. Jiang, and G. Grasselli. 2018. “Three new boundary conditions for the seismic response analysis of geomechanics problems using the numerical manifold method.” Int. J. Rock Mech. Min. Sci. 105 (May): 110–122. https://doi.org/10.1016/j.ijrmms.2018.03.009.
Wu, Z., L. F. Fan, Q. S. Liu, and G. W. Ma. 2017. “Micro-mechanical modeling of the macro-mechanical response and fracture behavior of rock using the numerical manifold method.” Eng. Geol. 225 (Jul): 49–60. https://doi.org/10.1016/j.enggeo.2016.08.018.
Wu, Z., and L. N. Y. Wong. 2014. “Extension of numerical manifold method for coupled fluid flow and fracturing problems.” Int. J. Numer. Anal. Methods Geomech. 38 (18): 1990–2008. https://doi.org/10.1002/nag.2293.
Xu, D. D., G. H. Sun, and H. Zheng. 2013. “Application of Munjiza’s algorithm to contact treatment in numerical manifold method.” [In Chinese.] Rock Soil Mech. 34 (2): 526–534. https://doi.org/10.16285/j.rsm.2013.02.001.
Xu, D. D., Y. T. Yang, H. Zheng, and A. Q. Wu. 2017. “A high order local approximation free from linear dependency with quadrilateral mesh as mathematical cover and applications to linear elastic fractures.” Comput. Struct. 178 (Jan): 1–16. https://doi.org/10.1016/j.compstruc.2016.10.001.
Yang, Y. T., H. W. Guo, X. D. Fu, and H. Zheng. 2018a. “Boundary settings for the seismic dynamic response analysis of rock masses using the numerical manifold method.” Int. J. Numer. Anal. Methods. Geomech. 42 (9): 1095–1122. https://doi.org/10.1002/nag.2786.
Yang, Y. T., X. H. Tang, H. Zheng, Q. S. Liu, and L. He. 2016. “Three-dimensional fracture propagation with numerical manifold method.” Eng. Anal. Boundary Elem. 72 (Nov): 65–77. https://doi.org/10.1016/j.enganabound.2016.08.008.
Yang, Y. T., X. H. Tang, H. Zheng, Q. S. Liu, and Z. J. Liu. 2018b. “Hydraulic fracturing modeling using the enriched numerical manifold method.” Appl. Math. Modell. 53 (Jan): 462–486. https://doi.org/10.1016/j.apm.2017.09.024.
Yang, Y. T., D. D. Xu, and H. Zheng. 2018c. “Explicit discontinuous deformation analysis method with lumped mass matrix for highly discrete block system.” Int. J. Geomech. 18 (9): 04018098. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001234.
Yang, Y. T., and H. Zheng. 2017. “Direct approach to treatment of contact in numerical manifold method.” Int. J. Geomech. 17 (5): E4016012. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000714.
Yang, Y. T., H. Zheng, and M. V. Sivaselvan. 2017. “A rigorous and unified mass lumping scheme for higher-order elements.” Comput. Methods Appl. Mech. Eng. 319 (Jun): 491–514. https://doi.org/10.1016/j.cma.2017.03.011.
Yeung, M. R., Q. H. Jiang, and N. Sun. 2007. “A model of edge-to-edge contact for three-dimensional discontinuous deformation analysis.” Comput. Geotech. 34 (3): 175–186. https://doi.org/10.1016/j.compgeo.2006.11.001.
Zárate, F., A. Cornejo, and E. Oñate. 2018. “A three-dimensional FEM–DEM technique for predicting the evolution of fracture in geomaterials and concrete.” Comput. Part. Mech. 5 (3): 411–420. https://doi.org/10.1007/s40571-017-0178-z.
Zeng, W., and G. R. Liu. 2018. “Smoothed finite element methods (S-FEM): An overview and recent developments.” Arch. Comput. Methods Eng. 25 (2): 397–435. https://doi.org/10.1007/s11831-016-9202-3.
Zhang, P., C. B. Du, X. R. Tian, and S. Y. Jiang. 2018. “A scaled boundary finite element method for modelling crack face contact problems.” Comput. Methods Appl. Mech. Eng. 328 (Jan): 431–451. https://doi.org/10.1016/j.cma.2017.09.009.
Zhang, Y. H., X. D. Fu, and Q. Sheng. 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. https://doi.org/10.1016/j.tust.2013.10.012.
Zheng, H., and W. Jiang. 2009. “Discontinuous deformation analysis based on complementary theory.” Sci. China Ser. E. Technol. Sci. 52 (9): 2547–2554. https://doi.org/10.1007/s11431-009-0256-4.
Zheng, H., and X. K. Li. 2015. “Mixed linear complementarity formulation of discontinuous deformation analysis.” Int. J. Rock Mech. Min. Sci. 75 (Apr): 23–32. https://doi.org/10.1016/j.ijrmms.2015.01.010.
Zheng, H., D. F. Liu, C. F. Lee, and Z. Q. Yue. 2004. “A sophisticated node-pair model for interface problems.” Comput. Geotech. 31 (2): 137–153. https://doi.org/10.1016/j.compgeo.2003.11.004.
Zheng, H., and D. D. Xu. 2014. “New strategies for some issues of numerical manifold method in simulation of crack propagation.” Int. J. Numer. Methods Eng. 97 (13): 986–1010. https://doi.org/10.1002/nme.4620.
Zienkiewicz, O. C., and R. L. Taylor. 2000. Fluid dynamics. Vol. 3 of The finite element method. 5th ed. Oxford, UK: Butterworth–Heinemann.
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International Journal of Geomechanics
Volume 19 • Issue 10 • October 2019
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© 2019 American Society of Civil Engineers.
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Received: Oct 18, 2018
Accepted: Apr 8, 2019
Published online: Jul 17, 2019
Published in print: Oct 1, 2019
Discussion open until: Dec 17, 2019
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