Simulations of Fracture and Fragmentation of Geologic Materials using Combined FEM/DEM Analysis

Results are presented from a study investigating the effect of explosive and impact loading on geological media using the Livermore Distinct Element Code (LDEC). LDEC was initially developed to simulate tunnels and other structures in jointed rock masses with large numbers of intact polyhedral blocks. However, underground structures in jointed rock subjected to explosive loading can fail due to both rock motion along preexisting interfaces and fracture of the intact rock mass itself. Many geophysical applications, such as projectile penetration into rock, concrete targets, and boulder fields, require a combination of continuum and discrete methods in order to predict the formation and interaction of the fragments produced. In an effort to model these types of problems, we have implemented Cosserat point theory and cohesive element formulations into the current version of LDEC, thereby allowing for dynamic fracture and combined finite element/discrete element simulations. Results of a large-scale LLNL simulation of an explosive shock wave impacting an elaborate underground facility are also discussed. It is confirmed that persistent joints lead to an underestimation of the impact energy needed to fill the tunnel systems with rubble. Non-persistent joint patterns, which are typical of real geologies, inhibit shear within the surrounding rock mass and significantly increase the load required to collapse a tunnel.

[1]  J. Monaghan Simulating Free Surface Flows with SPH , 1994 .

[2]  M. Rubin Numerical solution of two- and three-dimensional thermomechanical problems using the theory of a Cosserat point , 1995 .

[3]  M. Ortiz,et al.  Computational modelling of impact damage in brittle materials , 1996 .

[4]  P. A. Cundall,et al.  NUMERICAL MODELLING OF DISCONTINUA , 1992 .

[5]  D. S. Dugdale Yielding of steel sheets containing slits , 1960 .

[6]  Roger D. Hart,et al.  Development of Generalized 2-D and 3-D Distinct Element Programs for Modeling Jointed Rock , 1985 .

[7]  P. Cundall,et al.  FORMULATION OF A THREE-DIMENSIONAL DISTINCT ELEMENT MODEL - PART II. MECHANICAL CALCULATIONS FOR MOTION AND INTERACTION OF A SYSTEM COMPOSED OF MANY POLYHEDRAL BLOCKS , 1988 .

[8]  Joseph P. Morris,et al.  The Distinct Element Method — Application to Structures in Jointed Rock , 2003 .

[9]  J. Monaghan Smoothed particle hydrodynamics , 2005 .

[10]  G. I. Barenblatt THE MATHEMATICAL THEORY OF EQUILIBRIUM CRACKS IN BRITTLE FRACTURE , 1962 .

[11]  David D. Pollard,et al.  Distinct element modeling of deformation bands in sandstone , 1995 .

[12]  J. Morris,et al.  Modeling Low Reynolds Number Incompressible Flows Using SPH , 1997 .

[13]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[14]  P. A. Cundall,et al.  A DISCONTINUOUS FUTURE FOR NUMERICAL MODELLING IN GEOMECHANICS , 2001 .

[15]  F. E. Heuze,et al.  Simulations of Underground Structures Subjected to Dynamic Loading Using the Distinct Element Method , 2002 .

[16]  P. A. Cundall,et al.  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 , 1988 .

[17]  Xiaopeng Xu,et al.  Numerical simulations of fast crack growth in brittle solids , 1994 .

[18]  F. E. Heuze,et al.  Analysis of Explosions in Hard Rocks: The Power of Discrete Element Modeling , 1993 .

[19]  John W. Hutchinson,et al.  Dynamic Fracture Mechanics , 1990 .

[20]  John A. Hudson,et al.  Comprehensive rock engineering , 1993 .

[21]  J. Fineberg,et al.  Microbranching instability and the dynamic fracture of brittle materials. , 1996, Physical review. B, Condensed matter.

[22]  M. B. Rubin,et al.  Simulations of dynamic crack propagation in brittle materials using nodal cohesive forces and continuum damage mechanics in the distinct element code LDEC , 2006 .

[23]  J. Morgan,et al.  Numerical simulations of granular shear zones using the distinct element method: 1. Shear zone kinematics and the micromechanics of localization , 1999 .

[24]  O. T. Nguyen,et al.  Coarse-graining and renormalization of atomistic binding relations and universal macroscopic cohesive behavior , 2002 .

[25]  M. Rubin Cosserat Theories: Shells, Rods and Points , 2000 .

[26]  J. Monaghan,et al.  SPH elastic dynamics , 2001 .

[27]  J. Morris Simulating surface tension with smoothed particle hydrodynamics , 2000 .

[28]  Michael Ortiz,et al.  Three‐dimensional finite‐element simulation of the dynamic Brazilian tests on concrete cylinders , 2000 .

[29]  M. B. Rubin,et al.  Cosserat Theories: Shells, Rods and Points. Solid Mechanics and its Applications, Vol 79 , 2002 .

[30]  J P Morris Review of Rock Joint Models , 2003 .

[31]  Stephen A. Vavasis,et al.  Time continuity in cohesive finite element modeling , 2003 .

[32]  Julia K. Morgan,et al.  Numerical simulations of granular shear zones using the distinct element method: 2. Effects of particle size distribution and interparticle friction on mechanical behavior , 1999 .