Abstract
This paper presents a combined spheropolyhedral discrete element (DE)–finite element (FE) computational approach to simulating vertical plate loading on cohesionless soils such as gravels. The gravel particles are modeled as discrete elements, and the plate is modeled as a deformable FE continuum. The simulations provide a meaningful step toward better understanding how deformable bodies transmit loads to granular materials. The DE–FE contact algorithm is verified through comparison with an analytical solution for impact between two symmetric bars. A parametric study is conducted to ensure boundary effects are not significantly influencing the simulations. Numerical simulations are compared to experimental test results of lightweight deflectometer loading on a gravel base course with satisfactory agreement. Future developments of the approach intend to simulate wheel loading of military aircraft on unsurfaced airfields.
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References
Adam C, Adam D, Kopf F (2009) Computational validation of static and dynamic plate load testing. Acta Geotech 4(1):35–55
ASTM (2013) Annual book of standards. Volume 04.03, road and paving materials. ASTM International, West Conshohocken, Pennsylvania
Carpenter NJ, Taylor RL, Katona MG (1991) Lagrange constraints for transient finite element surface contact. Int J Numer Methods Eng 32(1):103–128
Chen H, Lei Z, Zang M (2014) LC-Grid: a linear global contact search algorithm for finite element analysis. Comput Mech 54(5):1285–1301
Cho G-C, Dodds J, Santamarina JC (2006) Particle shape effects on packing density, stiffness, and strength: natural and crushed sands. J Geotech Geoenviron Eng 132(5):591–602
Cundall PA, Strack OD (1979) A discrete numerical model for granular assemblies. Geotechnique 29(1):47–65
Dang HK, Meguid MA (2013) An efficient finite–discrete element method for quasi-static nonlinear soil–structure interaction problems. Int J Numer Anal Methods Geomech 37(2):130–149
Effeindzourou A, Chareyre B, Thoeni K, Giacomini A, Kneib F (2016) Modelling of deformable structures in the general framework of the discrete element method. Geotext Geomembr 44(2):143–156
Evans DJ, Murad S (1977) Singularity free algorithm for molecular dynamics simulation of rigid polyatomics. Mol Phys 34(2):327–331
Fakhimi A (2009) A hybrid discrete–finite element model for numerical simulation of geomaterials. Comput Geotech 36(3):386–395
Fleming PR (2000) Small-scale dynamic devices for the measurement of elastic stiffness modulus on pavement foundations. In: Tayabji SD, Lukanen EO (eds) Nondestructive testing of pavements and backcalculation of moduli: third volume, ASTM STP 1375. ASTM, West Conshohocken, pp 41–59
Galindo-Torres SA, Pedroso DM, Williams DJ, Li L (2012) Breaking processes in three-dimensional bonded granular materials with general shapes. Comput Phys Commun 183(2):266–277
Guo N, Zhao J (2014) A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media. Int J Numer Methods Eng 99(11):789–818
Guo N, Zhao J (2016) Multiscale insights into classical geomechanics problems. Int J Numer Anal Methods Geomech 40:367–390
Grasmick JG, Mooney MA, Surdahl RW, Voth M, Senseney C (2015) Capturing a layer response during the curing of stabilized earthwork using a multiple sensor lightweight deflectometer. J Mater Civ Eng 27(6):1–12
Hopkins MA (2014) Polyhedra faster than spheres? Eng Comput 31(3):567–583
Hughes TJR, Taylor RL, Sackman JL, Curnier A, Kanoknukulchai W (1976) A finite element method for a class of contact-impact problems. Comput Methods Appl Mech Eng 8(3):249–276
Hughes TJR (2000) The finite element method: linear static and dynamic finite element analysis. Dover, Mineola
Johnson KL (1987) Contact mechanics. Cambridge University Press, Cambridge
Kawamoto R, Ando E, Viggiani G, Andrade JE (2016) Level set discrete element method for three-dimensional computations with triaxial case study. J Mech Phys Solids 91:1–13
Li X, Wan K (2011) A bridging scale method for granular materials with discrete particle assembly—cosserat continuum modeling. Comput Geotech 38(4):1052–1068
Lim K-W, Kawamoto R, Ando E, Viggiani G, Andrade JE (2016) Multiscale characterization and modeling of granular materials through a computational mechanics avatar: a case study with experiment. Acta Geotech 11(2):243–253
Lin X, Ng TT (1997) A three-dimensional discrete element model using arrays of ellipsoids. Geotechnique 47(2):319–329
Matsushima T, Chang CS (2011) Quantitative evaluation of the effect of irregularly shaped particles in sheared granular assemblies. Granular Matter 13(3):269–276. doi:10.1007/s10035-011-0263-6
Onate E, Rojek J (2004) Combination of discrete element and finite element methods for dynamic analysis of geomechanics problems. Comput Methods Appl Mech Eng 193(27–29):3087–3128
Pournin L, Liebling TM (2005) A generalization of distinct element method to tridimensional particles with complex shapes. In: García-Rojo R, Herrmann HJ, McNamara S (eds) Powders and grains (2005), vol 2. A.A.Balkema Publishers, Rotterdam, pp 1375–1378
Regueiro RA (2007) Coupling particle to continuum regions of particulate material. In: Proceedings of IMECE2007, No. 42717, Seattle, WA, pp 1–6
Regueiro RA, Duan Z, Yan B (2016) Overlapped coupling between spherical discrete elements and micropolar finite elements in one dimension using a bridging-scale decomposition for statics. Eng Comput 33(1):28–63
Senseney CT, Mooney MA (2010) Characterization of a two-layer soil system using a light weight deflectometer with radial sensors. Transp Res Rec J Transp Res Board 2186:21–28
Senseney CT, Grasmick J, Mooney MA (2015) Sensitivity of lightweight deflectometer deflections to layer stiffness via finite element analysis. Can Geotech J 52(7):961–970
Smith IM, Griffiths DV (1998) Programing the finite element method. Wiley, New York
Stamp DH, Mooney MA (2013) Influence of lightweight deflectometer characteristics on deflection measurement. Geotech Test J 36(2):216–226
Szuladzinski G (2009) Formulas for mechanical and structural shock and impact. CRC Press, Boca Raton
Terzaghi K, Peck RB, Mesri G (1996) Soil mechanics in engineering practice. Wiley, New York
Timoshenko S, Goodier J (1951) Theory of elasticity. McGraw-Hill, New York
Vennapusa P, White D (2009) Comparison of light weight deflectometer measurements for pavement foundation materials. ASTM Geotech Test J 32(3):239–251
Walton OR (1982) Explicit particle-dynamics model for granular materials. Lawrence Livermore National Lab, Livermore
Walton O, Braun R (1993) Simulation of rotary-drum and repose tests for frictional spheres and rigid sphere clusters. In: Joint DOE/NSF workshop on flow of particulates and fluids, Ithaca, NY
Wellmann C, Wriggers P (2012) A two-scale model of granular materials. Comput Methods Appl Mech Eng 205–208(1):46–58
Yan B, Regueiro RA, Sture S (2010) Three-dimensional ellipsoidal discrete element modeling of granular materials and its coupling with finite element facets. Eng Comput 27(4):519–550
Zhao C, Zang M (2014) Analysis of rigid tire traction performance on a sandy soil by 3D finite element–discrete element method. J Terrramech 55:29–37. doi:10.1016/j.jterra.2014.05.005
Acknowledgements
The authors gratefully acknowledge support from the Department of Defense (DoD) High Performance Computing Modernization Office (HPCMO) to the USAFA which funded hardware, and Grant FA7000-15-2-005 to the University of Colorado Boulder. The authors thank Cadet Pawin Sarabol for running numerous simulations during a summer internship at the University of Colorado Boulder. ZD, BZ, and RAR also acknowledge partial funding from ONR MURI Grant N00014-11-1-0691.
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Disclaimer: The views expressed in this paper are those of the authors and do not reflect the official policy or position of the United States Air Force, Department of Defense, or the U.S. Government.
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Senseney, C.T., Duan, Z., Zhang, B. et al. Combined spheropolyhedral discrete element (DE)–finite element (FE) computational modeling of vertical plate loading on cohesionless soil. Acta Geotech. 12, 593–603 (2017). https://doi.org/10.1007/s11440-016-0519-8
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DOI: https://doi.org/10.1007/s11440-016-0519-8