1. Appropriate Applications for Discrete Element Geotechnical Modeling
John M. Ting ScD, PE
Professor & Head
Civil & Environmental Engineering
University of Massachusetts Lowell

2. What Discrete Element Method (DEM) is NOT
DEM is not a replacement for mainstream nonlinear Finite Element analysis
DEM should not be used without appropriate validation
comparison should be made with analytical, numerical or empirical solutions wherever possible
care should be taken to ensure macroscopic properties match between DEM and prototype systems

3. What Discrete Element Method CAN do:
Assist in developing continuum constitutive models
arbitrary stress path, micromechanics approach, statistical history, reproducible samples
Improve understanding of fundamental processes in granular media
mechanisms of strength and failure, material processes, multiphase materials
Model large-scale soil-structure interaction problems
geometric & material nonlinearity, bifurcation

4. Examples - modeling fundamental processes in granular media
Influence of particle flatness on strength of granular materials
Segregation of granular media by size
Flow of granular media into and out from bins & hoppers
Mechanical model for frozen soil (?)

5. Influence of particle flatness on strength of granular materials
Biaxial tests on 2D ellipses (from Ting et al 1995) σ θ σ

6. Shear banding • formation of shear bands detected during biaxial tests
• 60º bedding angle, shear plane at opposite 45+Ø/2 plane

7. Segregation of granular materials
• 700 uniformly distributed disks mixed with 1/2 turn of mixer
• note migration of larger particles to wall
• misses mechanism of sieving due to 2D limitations
• from Ting & Corkum 1988

8. Flow of granular media
• filling and discharge of dry granular materials into a silo
• modeled with round and 2D elliptical particles using scaled gravity
• evaluated lateral pressures on walls during filling
• observed failure and plugging mechanisms during discharge
• from Mischel 1998; also Rotter et al 1998

9. Mechanical model for frozen soil ?
Currently intractable problem in soil mechanics
• build DEM model for multiphase granular media?
• ice modeled as spring-dashpot system with tensile strength
• investigate presence of long term ultimate strength of frozen soil ?

10. Examples - DEM modeling of large-scale soil-structure interaction
behavior of rock blocks
mechanics of rock bolting
bearing plate resistance
mechanics of plowing ?

11. Stability of rock masses on a slope
note which blocks slide, and which topple
identical to Goodman & Bray’s analysis, except block #3 from bottom first slides and then topples (from Grabinsky 1989)

12. Mechanics of rock bolting
Simulated rock-bolting demonstration from WES

13. DEM simulation of rock bolting demonstration
Using 2D polygonal particles (from Grabinsky 1989)

14. DEM simulation of rock bolting demonstration
compared with full scale rock bolting demonstration experiment at University of Toronto
DEM correctly indicated that the system would FAIL at the initial configuration - ie for their rock bolt washer size and spacing, and shape, size and interparticle friction of granular material
after altering the washer size and spacing and the type of granular material, DEM correctly indicated that the system would SUCCEED

15. Modeling bearing capacity of shallow footings
Need to use scaled gravity and non-circular particles
results compared well with Terzaghi bearing capacity theory & confirm validity of DEM technique (Khwaja 1996)

16. Modeling mechanics of plowing?
need to scale gravity & use noncircular particles
need 3D to model tines
should be able to determine stresses in soil front of blade as well as shape of spoil pile next to blade

17. Conclusions
DEM is a powerful tool for modeling difficult problems with granular media
DEM can provide considerable insight into mechanics of granular media
care must be take in using DEM to ensure model accurately represents desired system
3D DEM requires enormous computing resources and comparable software to interpret results

18. What needs to be done
Validation of DEM with detailed 1-to-1 experiments, if interested in constitutive modeling
validation of 3D DEM with non-spherical particles - need to pay close attention to contact detection, less to contact relationships
development of graphical tools for extracting useful data from 3D data set
start funding some research!

19. Acknowledgments
Work done at University of Toronto ( ) funded by Natural Science & Engineering Research Council of Canada, and Cray Research
Work done at University of Massachusetts Lowell ( ) funded by Air Force Office of Scientific Research and DoD AASERT

20. Reference list
Ting, JM, Meachum, L.R. and J.D. Rowell (1995). "Effect of Particle Shape on the Strength and Deformation Mechanisms of Ellipse-shaped Assemblages," Engineering Computations: Int'l Journal of Computer-Aided Engineering and Software, ed. D.R.J. Owen and K.J. Bathe, 12(2):
Ting, JM, Khwaja, M., Meachum, L.R. and Rowell, J.D "An Ellipse-based Discrete Element Model for Granular Materials," Int'l Journal for Numerical and Analytical Methods in Geomechanics, 17(9):
Ting, J.M "A Robust Algorithm for Ellipse-based Modelling of Granular Materials," Computers and Geotechnics, 13(3):
Ting, J.M. and B.T. Corkum "A Computational Laboratory for Discrete Element Geomechanics," ASCE Journal of Computing in Civil Engineering, 6(2):
Ting, JM, B.T. Corkum, C.R. Kauffman and C. Greco "A Discrete Numerical Model for Soil Mechanics," ASCE Journal of Geotechnical Engineering, 115(3):
Ting, JM and J.D. Rowell, "Ellipse-based Discrete Element Model for Granular Materials: Validation Testing," Proc ASCE Engineering Mechanics Conference on Discontinuous Materials, Colorado, May 1995.
Ting, J.M. and L.R. Meachum, "Effect of Bedding Plane Orientation on the Behavior of Granular Systems," Mechanics of Materials with Discontinuities and Heterogeneities, ed. A. Misra and C.S. Chang, ASME AMD Vol 201:
Ting, JM, Rowell, J.D. and Meachum, L.R "Influence of Particle Shape on the Strength of Ellipse-shaped Granular Assemblages," Proc. Second Int'l Conf. Discrete Element Methods, Cambridge, Mass., pp
Ting, JM "An Ellipse-based Micromechanical Model for Angular Granular Materials," Proc. ASCE Engineering Mechanics Specialty Conference on Mechanics Computing in 1990's and Beyond, Columbus, Ohio, Vol. 2, pp

21. Reference list (con’td)
Ting, JM and B.T. Corkum "Discrete Element Models in Geotechnical Engineering," Proc. 3rd International Conference on Computing in Civil Engineering, Vancouver, Canada, Vol. 2, pp
Ting, J.M. and B.T. Corkum "Soil-structure Interaction by Discrete Numerical Modelling," Proc. Canadian Society for Civil Engineering Annual Conference, Calgary, Canada, Vol. 3, pp
Ting, J.M. and B.T. Corkum "Strength Behavior of Granular Materials Using Discrete Numerical Modelling," Proc. 6th Int'l Conference on Numerical Methods in Geomechanics, Innsbruck, Austria, Vol. 1, pp
Ting, JM, B.T. Corkum and C. Greco 1986. "Application of the Distinct Element Method in Geotechnical Engineering," Proc. Int'l Symp. Numerical Models in Geomechanics, Ghent, Belgium, pp
Mischel, G.A “Validation of an Ellipse-based Discrete Element Model with Application to Granular Material Pressures in Storage Silos,” M.S. thesis, Dept. Civil & Environmental Engineering, UMass Lowell, Lowell, MA.
Khwaja, M “Discrete Element Method: Micro-Mechanical and Large Scale Modeling,” M.S. thesis, Dept. Civil & Environmental Engineering, UMass Lowell , Lowell, MA.
Meachum, L.R “Influence of Particle Shape on the Mechanical Behavior of Granular Materials,” M.S. thesis, Dept. Civil & Environmental Engineering, UMass Lowell, Lowell, MA.
Grabinsky, M.w “An Angular Discrete Element Model for Geomechanics,” M.A.Sc. Thesis, Dept. Civil Eng., University of Toronto, Canada.