Calibration of Microscopic Penalty Parameters in the Combined Finite–Discrete-Element Method
Publication: International Journal of Geomechanics
Volume 20, Issue 7
Abstract
With unique advantages in simulating solid fracture, the combined finite–discrete-element method has become increasingly popular in the rock mechanics field. Nevertheless, a large number of microscopic parameters in the method need to be specified and many of them cannot be directly measured via laboratory tests. Therefore, these parameters must be determined via a calibration procedure. To calibrate appropriate microscopic parameters, we should find the relationship between them and the macroscopic mechanical response. In these microscopic parameters, the normal and tangential penalty parameters play a very important role. Thus, in this paper we study the effect of penalty parameters on macroscopic mechanical parameters in the combined finite–discrete-element method. It is found that as the penalty parameters increase, the elastic modulus and Poisson's ratio gradually approach the experimental values. However, the further increase of penalty parameters has little effect on the elastic modulus and Poisson's ratio when they reach 100 times the elastic modulus. Based on this conclusion, a simple method for the calibration of penalty parameters is proposed, which can be used to quickly determine the penalty parameters according to the uniaxial compression test.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grant Numbers 11872340 and 11602006, the Xiangjiang Scholars Program (XJ2019040), the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (CUG170657, CUGGC09), and the National Natural Science Foundation of China under Grant Numbers 41731284 and 41920104007.
References
Baoquan, A., and D. D. Tannant. 2007. “Discrete element method contact model for dynamic simulation of inelastic rock impact.” Comput. Geosci. 33 (4): 513–521.
Cheng, G., T. Ma, C. Tang, H. Liu, and S. Wang. 2017. “A zoning model for coal mining-induced strata movement based on microseismic monitoring.” Int. J. Rock. Mech. Min. Sci. 94: 123–138.
Cundall, P. A. 1971. “A computer model for simulating progressive, large-scale movement in blocky rock system.” In Vol. 1 of Proc., Int. Symp. on Rock Mechanics, 2–8. Nancy, France: Proceedings of Symposium of International Society of Rock Mechanics.
Cundall, P. A. 1988. “Formulation of a three-dimensional distinct element model—Part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks.” Int. J. Rock Mech. Min. Sci. Geomech. Abst. 25 (3): 107–116.
Cundall, P. A., and O. D. L. Strack. 1979. “A discrete numerical model for granular assemblies.” Geotechnique 29 (1): 47–65.
Dorren, L. K. A. 2003. “A review of rockfall mechanics and modelling approaches.” Prog. Phys. Geogr.: Earth Environ. 27 (1): 69–87.
Fukuda, D., M. Mohammadnejad, H. Liu, Q. Zhang, J. Zhao, S. Dehkhoda, A. Chan, J.-I. Kodama, and Y. Fujii. 2020. “Development of a 3D hybrid finite-discrete element simulator based on GPGPU-parallelized computation for modelling rock fracturing under quasi-static and dynamic loading conditions.” Rock Mech. Rock Eng. 53: 1079–1112.
Gao, F. Q., and D. Stead. 2014. “The application of a modified Voronoi logic to brittle fracture modelling at the laboratory and field scale.” Int. J. Rock Mech. Min. Sci. 68: 1–14.
Gao, K., Q. Lei, N. Bozorgzadeh, V. J. Chau. 2019. “Can we estimate far-field stress using the mean of local stresses? An examination based on numerical simulations.” Comput. Geotech. 116: 103188.
Ghaboussi, J. 1988. “Fully deformable discrete element analysis using a finite element approach.” Comput. Geotech. 5 (3): 175–195.
Ghazvinian, E., M. S. Diederichs, and R. Quey. 2014. “3D random Voronoi grain-based models for simulation of brittle rock damage and fabric-guided micro-fracturing.” J. Rock Mech. Geotech. Eng. 6 (6): 506–521.
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 (3): 283–353.
Kazerani, T., and J. Zhao. 2010. “Micromechanical parameters in bonded particle method for modelling of brittle material failure.” Int. J. Numer. Anal. Methods Geomech. 34 (18): 1877–1895.
Lei, Z., E. Rougier, E. E. Knight, and A. Munjiza. 2015. “FDEM simulation on fracture coalescence in brittle materials.” In 49th US Rock Mechanics/Geomechanics Symp. San Francisco: American Rock Mechanics Association.
Lei, Z., E. Rougier, A. Munjiza, H. Viswanathan, and E. E. Knight. 2019. “Simulation of discrete cracks driven by nearly incompressible fluid via 2D combined finite-discrete element method.” Int. J. Numer. Anal. MethodsGeomech. 43 (9): 1724–1743.
Li, X., E. Kim, and G. Walton. 2019. “A study of rock pillar behaviors in laboratory and in-situ scales using combined finite-discrete element method models.” Int. J. Rock Mech. Min. Sci. 118: 21–32.
Lisjak, A., D. Figi, and G. Grasselli. 2014. “Fracture development around deep underground excavations: Insights from FDEM modelling.” J. Rock Mech. Geotech. Eng. 6 (6): 493–505.
Lisjak, A., and G. Grasselli. 2010. “Rock impact modelling using FEM/DEM.” Proc., 5th Int. Conf. on Discrete Element Methods, 269–274. London: Engineering and Materials Science, Queen Mary Univ. of London.
Lisjak, A., and G. Grasselli. 2014. “A review of discrete modeling techniques for fracturing processes in discontinuous rock masses.” J. Rock Mech. Geotech. Eng. 6 (4): 301–314.
Liu, Q., and P. Deng. 2019. “A numerical investigation of element size and loading/unloading rate for intact rock in laboratory-scale and field-scale based on the combined finite-discrete element method.” Eng. Fract. Mech. 211: 442–462.
Mahabadi, O. K. 2012. “Investigating the influence of micro-scale heterogeneity and microstructure on the failure and mechanical behaviour of geomaterials.” Philosophy, Civil Engineering, Univ. of Toronto.
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.
Mahabadi, O. K., B. S. A. Tatone, and G. Grasselli. 2014. “Influence of microscale heterogeneity and microstructure on the tensile behavior of crystalline rocks.” J. Geophys. Res.: Solid Earth 119 (7): 5324–5341.
Munjiza, A. 2004. The combined finite-discrete element method. London: John Wiley & Sons.
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.
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.
Munjiza, A., K. R. F. Andrews, and J. K. White. 1999a. “Combined single and smeared crack model in combined finite-discrete element analysis.” Int. J. Numer. Methods Eng. 44 (1): 41–57.
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.
Munjiza, A., J. P. Latham, and K. R. F. Andrews. 1999b. “Challenges of a coupled combined finite-discrete element approach to explosive induced rock fragmentation.” Fragblast 3 (3): 237–250.
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.
Potyondy, D. O., and P. A. Cundall. 2004. “A bonded-particle model for rock.” Int. J. Rock Mech. Min. Sci. 41 (8): 1329–1364.
Rougier, E., E. E. Knight, S. T. Broome, A. J. Sussman, and A. Munjiza. 2014. “Validation of a three-dimensional Finite-Discrete Element Method using experimental results of the Split Hopkinson Pressure Bar test.” Int. J. Rock Mech. Min. Sci. 70: 101–108.
Shi, G.-H. 1992a. “Discontinuous deformation analysis: A new numerical model for the statics and dynamics of deformable block structures.” Eng. Comput. 9 (2): 157–168.
Shi, G. H. 1992b. Manifold method of material analysis. Triangle Park, NC: Army Research Office Research.
Tang, X., J. Rutqvist, M. Hu, and N. M. Rayudu. 2019. “Modeling three-dimensional fluid-driven propagation of multiple fractures using TOUGH-FEMM.” Rock Mech. Rock Eng. 52: 611–627.
Tatone, B. S. A., and G. Grasselli. 2015. “A calibration procedure for two-dimensional laboratory-scale hybrid finite–discrete element simulations.” Int. J. Rock Mech. Min. Sci. 75: 56–72.
Vazaios, I., N. Vlachopoulos, and M. S. Diederichs. 2019. “Assessing fracturing mechanisms and evolution of excavation damaged zone of tunnels in interlocked rock masses at high stresses using a finite-discrete element approach.” J. Rock Mech. Geotech. Eng. 11 (4): 701–722.
Williams, J. R. 1988. “Contact analysis of large numbers of interacting bodies using discrete modal methods for simulating material failure on the microscopic scale.” Eng. Comput. 5 (3): 198–209.
Williams, J. R., and G. G. W. Mustoe. 1987. “Modal methods for the analysis of discrete systems.” Comput. Geotech. 4 (1): 1–19.
Wu, Z., H. Sun, and L. N. Y. Wong. 2019. “A cohesive element-based numerical manifold method for hydraulic fracturing modelling with voronoi grains.” Rock Mech. Rock Eng. 52: 2335–2359.
Yan, C., and Y.-Y. Jiao. 2018. “A 2D fully coupled hydro-mechanical finite-discrete element model with real pore seepage for simulating the deformation and fracture of porous medium driven by fluid.” Comput. Struct. 196: 311–326.
Yan, C., and Y.-Y. Jiao. 2019a. “FDEM-TH3D: A three-dimensional coupled hydrothermal model for fractured rock.” Int. J. Numer. Anal. Methods Geomech. 43: 415–440.
Yan, C., and Y.-Y. Jiao. 2019b. “A 2D discrete heat transfer model considering the thermal resistance effect of fractures for simulating the thermal cracking of brittle materials.” Acta Geotech. https://doi.org/10.1007/s11440-019-00821-x.
Yan, C., Y.-Y. Jiao, and S. Yang. 2019a. “A 2D coupled hydro-thermal model for the combined finite-discrete element method.” Acta Geotech. 14 (2): 403–416.
Yan, C., Y.-Y. Jiao, and H. Zheng. 2018. “A fully coupled three-dimensional hydro-mechanical finite discrete element approach with real porous seepage for simulating 3D hydraulic fracturing.” Comput. Geotech. 96: 73–89.
Yan, C., Y.-Y. Jiao, and H. Zheng. 2019b. “A three-dimensional heat transfer and thermal cracking model considering the effect of cracks on heat transfer.” Int. J. Numer. Anal. Methods Geomech. 43 (10): 1825–1853.
Yan, C., Y. Ren, and Y. Yang. 2019c. “A 3D thermal cracking model for rockbased on the combined finite–discrete element method.” Comput. Part. Mech. https://doi.org/10.1007/s40571-019-00281-w.
Yan, C., and H. Zheng. 2016. “A two-dimensional coupled hydro-mechanical finite-discrete model considering porous media flow for simulating hydraulic fracturing.” Int. J. Rock Mech. Min. Sci. 88: 115–128.
Yan, C., and H. Zheng. 2017a. “Three-dimensional hydromechanical model of hydraulic fracturing with arbitrarily discrete fracture networks using finite-discrete element method.” Int. J. Geomech. 17 (6): 04016133. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000819.
Yan, C., and H. Zheng. 2017b. “A coupled thermo-mechanical model based on the combined finite-discrete element method for simulating thermal cracking of rock.” Int. J. Rock Mech. Min. Sci. 91: 170–178.
Yan, C., and H. Zheng. 2017c. “FDEM-flow3D: A 3D hydro-mechanical coupled model considering the pore seepage of rock matrix for simulating three-dimensional hydraulic fracturing.” Comput. Geotech. 81: 212–228.
Yan, C., H. Zheng, G. Sun, and X. Ge. 2016. “Combined finite-discrete element method for simulation of hydraulic fracturing.” Rock Mech. Rock Eng. 49 (4): 1389–1410.
Yan, C. Z., and H. Zheng. 2017d. “A new potential function for the calculation of contact forces in the combined finite-discrete element method.” Int. J. Numer. Anal. Methods Geomech. 41 (2): 265–283.
Yang, Y., X. Tang, H. Zheng, Q. Liu, and L. He. 2016. “Three-dimensional fracture propagation with numerical manifold method.” Eng. Anal. Bound. Ele. 72: 65–77.
Yang, Y., D. Xu, and H. Zheng. 2018. “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.
Zhang, C., X. Cheng, and J. Hou. 2010. “Study of mechanical behavior of deep-buried marble at jinping ii hydropower station.” Chin. J. Rock Mech. Geotech. Eng. 29 (10): 1999–2009.
Zhou, J., L. Zhang, A. Braun, and H. Zhenhua. 2017. “Investigation of processes of interaction between hydraulic and natural fractures by PFC modeling comparing against laboratory experiments and analytical models.” Oil Gas Eng. 10 (7): 1001.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 20 • Issue 7 • July 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Mar 7, 2019
Accepted: Nov 12, 2019
Published online: Apr 22, 2020
Published in print: Jul 1, 2020
Discussion open until: Sep 22, 2020
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.