An Efficient Disk-Based Discontinuous Deformation Analysis Model for Simulating Large-Scale Problems
Publication: International Journal of Geomechanics
Volume 20, Issue 7
Abstract
Simulating large-scale problems are still challenging for discontinuous deformation analysis (DDA). To this end, this paper develops an efficient disk-based DDA (DDDA) model considering the efficiency in searching contact pairs and solving linear equations. First, an efficient contact search algorithm, namely the lattice search algorithm (LSA), is proposed, and efficiency tests of the LSA and direct search algorithm (DSA) demonstrate the high efficiency of the LSA. Second, three equations solvers, namely Jacobi iterative method (J), conjugate gradient method (CG), and preconditioned CG (PCG), are adopted to respectively solve the equations of the DDDA, and efficiency tests of these solvers show that the best solver is the PCG and the J is unsuited to solving the equations when using large penalty spring stiffness. Finally, a landslide simulation which includes 30,000 disks, 5,990 line segments, and 180,000 calculation steps is conducted, the result of which shows that: (1) up to 41.1 h, which is 99.2% of the time consumed in contact search using the DSA, is reduced by using the LSA; (2) up to 18.22 h, which is 69.8% of the time consumed in solving the equations using the CG, is reduced by using the PCG as the equation solver; (3) the time consumed in the simulation is 68.72 h when using the DSA to search contact pairs and using the CG to solve the equations; while the consumed time reduces to 9.4 h when using the LSA to search contact pairs and using the PCG to solve the equations, whose reduction proportion is 86.3%. The simulation indicates the large-scale computation capacity and further application in engineering with the DDDA.
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Acknowledgments
The authors are grateful to the support provided by the China National Natural Science Foundations (No. 51509242, 11702235, 51604109).
References
Ali, R. K., J. Ahmad, and J. H. Wu. 2008. “A new algorithm to identify contact patterns between convex blocks for three-dimensional discontinuous deformation analysis.” Comput. Geotech. 35 (5): 746–759. https://doi.org/10.1016/j.compgeo.2007.12.002.
Beyabanaki, S. A. R., and C. B. Amvrossios. 2012. “Three-dimensional discontinuous deformation analysis (3-D DDA) method for particulate media applications.” Geomech. Geoeng. 7 (4): 239–253. https://doi.org/10.1080/17486025.2012.714477.
Beyabanaki, S. A. R., and C. B. Amvrossios. 2013a. “Accuracy of dynamic disk-based DDA with respect to a single sliding disk cluster.” Geomech. Geoeng. 9 (3): 231–240. https://doi.org/10.1080/17486025.2013.838645.
Beyabanaki, S. A. R., and C. B. Amvrossios. 2013b. “Non-rigid disk-based DDA with a new contact model.” Comput. Geotech. 49: 25–35. https://doi.org/10.1016/j.compgeo.2012.11.004.
Beyabanaki, S. A. R., and C. B. Amvrossios. 2015. “Sphere-boundary edge and sphere-boundary corner contacts model in DDA for simulating particulate media in 3-D.” Geomech. Geoeng. 10 (2): 83–94. https://doi.org/10.1080/17486025.2014.933892.
Beyabanaki, S. A. R., C. B. Amvrossios, and L. B. Liu. 2015. “Applying disk-based discontinuous deformation analysis (DDA) to simulate Donghekou landslide triggered by the Wenchuan earthquake.” Geomech. Geoeng. 11 (3): 177–188. https://doi.org/10.1080/17486025.2015.1082647.
Beyabanaki, S. A. R., A. Jafari, and M. R. Yeung. 2010. “High-order three-dimensional discontinuous deformation analysis (3-D DDA).” Int. J. Numer. Methods Biomed. Eng. 26 (12): 1522–1547. https://doi.org/10.1002/cnm.1220.
Chen, G. Q., M. C. He, and F. S. Fan. 2018. “Rock burst analysis using DDA numerical simulation.” Int. J. Geomech. 18 (3): 04018001. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001055.
Chen, K. T., and J. H. Wu. 2018. “Simulating the failure process of the Xinmo landslide using discontinuous deformation analysis.” Eng. Geol. 239: 269–281. https://doi.org/10.1016/j.enggeo.2018.04.002.
Choo, L. Q., Z. Y. Zhao, H. M. Chen, and Q. Tian. 2016. “Hydraulic fracturing modeling using the discontinuous deformation analysis (DDA) method.” Comput. Geotech. 76: 12–22. https://doi.org/10.1016/j.compgeo.2016.02.011.
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).
Feng, Y. T., K. Han, and D. R. J. Owen. 2003. “Filling domains with disks: An advancing front approach.” Int. J. Numer. Methods Eng. 56 (5): 699–713. https://doi.org/10.1002/nme.583.
Fu, X. D., Q. Sheng, Y. H. Zhang, and J. Chen. 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. https://doi.org/10.1002/nag.2407.
Hatzor, Y. H., and A. Feintuch. 2001. “The validity of dynamic block displacement prediction using DDA.” Int. J. Rock Mech. Min. Sci. 38 (4): 599–606. https://doi.org/10.1016/S1365-1609(01)00026-0.
Huang, G. H., Y. Y. Jiao, L. Wang, and Q. Zhao. 2017. “Three-dimensional spherical DDA method for modeling friction problems.” Int. J. Geomech. 17 (5): E4016016. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000758.
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.
Jiao, Y. Y., G. H. Huang, Z. Y. Zhao, F. Zheng, and L. Wang. 2015. “An improved three-dimensional spherical DDA model for simulating rock failure.” Sci. China Technol. Sci. 58 (9): 1533–1541. https://doi.org/10.1007/s11431-015-5898-9.
Jiao, Y. Y., H. Q. Zhang, H. M. Tang, X. L. Zhang, A. C. Adoko, and H. N. Tian. 2014a. “Simulating the process of reservoir-impoundment-induced landslide using the extended DDA method.” Eng. Geol. 182: 37–48. https://doi.org/10.1016/j.enggeo.2014.08.016.
Jiao, Y. Y., H. Q. Zhang, X. L. Zhang, H. B. Li, and Q. H. Jiang. 2014b. “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.
Jiao, Y. Y., X. L. Zhang, and J. Zhao. 2012. “Two-dimensional DDA contact constitutive model for simulating rock fragmentation.” J. Eng. Mech. 138 (2): 199–209. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000319.
Jiao, Y. Y., Q. Zhao, L. Wang, G. H. Huang, and F. Tan. 2019. “A hybrid MPI/OpenMP parallel computing model for spherical discontinuous deformation analysis.” Comput. Geotech. 106: 217–227. https://doi.org/10.1016/j.compgeo.2018.11.004.
Jiao, Y. Y., Q. Zhao, F. Zheng, and L. Wang. 2017. “Latest advances in discontinuous deformation analysis method.” Sci. China Technol. Sci. 60 (6): 963–964. https://doi.org/10.1007/s11431-016-0634-y.
Ke, T.-C., and J. Bray. 1995. “Modeling of particulate media using discontinuous deformation analysis.” J. Eng. Mech. 121 (11): 1234–1243. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:11(1234).
Koyama, T., S. Nishiyama, M. Yang, and Y. Ohnishi. 2011. “Modeling the interaction between fluid flow and particle movement with discontinuous deformation analysis (DDA) method.” Int. J. Numer. Anal. Methods Geomech. 35 (1): 1–20. https://doi.org/10.1002/nag.890.
Li, X. P., S. M. He, Y. Luo, and Y. Wu. 2012. “Simulation of the sliding process of Donghekou landslide triggered by the Wenchuan earthquake using a distinct element method.” Environ. Earth Sci. 65 (4): 1049–1054. https://doi.org/10.1007/s12665-011-0953-8.
Munjiza, A., and K. R. F. Andrews. 1998. “NBS contact detection algorithm for bodies of similar size.” Int. J. Numer. Methods Eng. 43 (1): 131–149. https://doi.org/10.1002/(SICI)1097-0207(19980915)43:1%3C131::AID-NME447%3E3.0.CO;2-S.
Ning, Y. J., J. Yang, G. W. Ma, and P. Chen. 2011. “Modelling rock blasting considering explosion gas penetration using discontinuous deformation analysis.” Rock Mech. Rock Eng. 44 (4): 483–490. https://doi.org/10.1007/s00603-010-0132-3.
Ning, Y. J., Y. Zheng, and W. Bin. 2017. “Advances in two-dimensional discontinuous deformation analysis for rock-mass dynamics.” Int. J. Geomech. 17 (5): E6016001. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000654.
Perkins, E., and J. R. Williams. 2001. “A fast contact detection algorithm insensitive to object sizes.” Eng. Comput. 18 (1/2): 48–62. https://doi.org/10.1108/02644400110365770.
Peters, J. F., R. Kala, and R. S. Maier. 2009. “A hierarchical search algorithm for discrete element method of greatly differing particle sizes.” Eng. Comput. 26 (6): 621–634. https://doi.org/10.1108/02644400910975423.
Shi, G. H. 1988. “Discontinuous deformation analysis: A new model for the statics and dynamics of block systems.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of California.
Shi, G. H. 2015. “Contact theory.” Sci. China Technol. Sci. 58 (9): 1450–1496. https://doi.org/10.1007/s11431-015-5814-3.
Thomas, P. A. 1997. “Discontinuous deformation analysis of particulate media.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of California.
Thomas, P. A., and J. D. Bray. 1999. “Capturing nonspherical shape of granular media with disk clusters.” J. Geotech. Geoenviron. Eng. 125 (3): 169–178. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:3(169).
Wang, F., Q. Cheng, L. Highland, M. Miyajima, H. Wang, and C. Yan. 2009. “Preliminary investigation of some large landslides triggered by the 2008 Wenchuan earthquake, Sichuan Province, China.” Landslides 6 (1): 47–54. https://doi.org/10.1007/s10346-009-0141-z.
Wang, L., Y. Y. Jiao, G. H. Huang, F. Zheng, and Q. Zhao. 2017. “Model of sphere-to-edge contact for spherical discontinuous deformation analysis.” Int. J. Geomech. 17 (12): 04017110. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001021.
Wu, J. H., J. S. Lin, and C. S. Chen. 2009. “Dynamic discrete analysis of an earthquake-induced large-scale landslide.” Int. J. Rock Mech. Min. Sci. 46 (2): 397–407. https://doi.org/10.1016/j.ijrmms.2008.07.010.
Xiao, Y. F., Q. H. Miao, M. Huang, Y. Wang, and J. Xue. 2017. “Parallel computing of discontinuous deformation analysis based on graphics processing unit.” Int. J. Geomech. 17 (5): E4016010. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000717.
Yagoda-Biran, G., and Y. H. Hatzor. 2016. “Benchmarking the numerical discontinuous deformation analysis method.” Comput. Geotech. 71: 30–46. https://doi.org/10.1016/j.compgeo.2015.08.003.
Yin, Y., F. Wang, and P. Sun. 2009. “Landslide hazards triggered by the 2008 Wenchuan earthquake, Sichuan, China.” Landslide 6 (2): 139–152. https://doi.org/10.1007/s10346-009-0148-5.
Zhao, Z. Y., Y. Zhang, and H. R. Bao. 2011. “Tunnel blasting simulations by the discontinuous deformation analysis.” Int. J. Comput. Methods 8 (2): 277–292. https://doi.org/10.1142/S0219876211002599
Zheng, F., Y. Y. Jiao, Y. F. Leung, and J. B. Zhu. 2018. “Algorithmic robustness for contact analysis of polyhedral blocks in discontinuous deformation analysis framework.” Comput. Geotech. 104: 288–301. https://doi.org/10.1016/j.compgeo.2018.07.019.
Zheng, H., and X. K. Li. 2015. “Mixed linear complementarity formulation of discontinuous deformation analysis.” Int. J. Rock Mech. Min. Sci. 75: 23–32. https://doi.org/10.1016/j.ijrmms.2015.01.010.
Zheng, H., P. Zhang, and X. Du. 2016. “Dual form of discontinuous deformation analysis.” Comput. Methods Appl. Mech. Eng. 305: 196–216. https://doi.org/10.1016/j.cma.2016.03.008.
Zhu, H. H., W. Wu, J. Q. Chen, G. W. Ma, X. G. Liu, and X. Y. Zhuang. 2016. “Integration of three dimensional discontinuous deformation analysis (DDA) with binocular photogrammetry for stability analysis of tunnels in blocky rock mass.” Tunnelling Underground Space Technol. 51: 30–40. https://doi.org/10.1016/j.tust.2015.10.012.
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Published In
International Journal of Geomechanics
Volume 20 • Issue 7 • July 2020
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© 2020 American Society of Civil Engineers.
History
Received: Jul 18, 2019
Accepted: Dec 17, 2019
Published online: May 11, 2020
Published in print: Jul 1, 2020
Discussion open until: Oct 11, 2020
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