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Relating discrete element method parameters to rock properties using classical and micropolar elasticity theories
Author(s) -
Alassi Haitham Tayseer,
Holt Rune
Publication year - 2012
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.1056
Subject(s) - discrete element method , elasticity (physics) , mathematics , element (criminal law) , poisson's ratio , macro , linear elasticity , elastic modulus , poisson distribution , mathematical analysis , mechanics , classical mechanics , physics , finite element method , structural engineering , engineering , computer science , statistics , thermodynamics , political science , law , programming language
SUMMARY Micro–macro relations for discrete element method (DEM) media are derived using both classical and micropolar elasticity theories. The DEM media are classified into two main categories: dense packing, and loose packing. For both categories, relations for Young modulus ( E ), Poisson's ratio ( ν ) to represent static behaviors, and wave velocities (P‐wave and S‐wave) to represent dynamic behaviors are derived using the internal DEM parameters (k n , k s ) and compared with values obtained from static and dynamic numerical tests. Whereas the dynamic behaviors for the two categories and the static behaviors for the dense packing match the analytical relations, the static behavior for the loose packing does not. Micropolar elasticity theory is also used to study the behaviors of the DEM media, where it is shown that if element rotation is included, DEM media behave according to linear elasticity theory. However, if element rotation is constrained, asymmetrical stresses arise in the DEM media, and a new expression is derived for the S‐wave, which allows it, under certain conditions, to travel faster than the P‐wave. Copyright © 2011 John Wiley & Sons, Ltd.