An algorithm for generating mechanically sound sphere packings in geological models

The discrete element method (DEM) is a powerful tool for simulating complex mechanical behaviors which discretizes the targeted medium with particles. The properties of particle assemblies used in DEM simulations directly impact the behavior of the simulated medium. It is thus of critical importance to generate particle assemblies so as to (1) avoid any bias induced by their fabric and (2) conform with the structural discontinuities of the medium under consideration. The main objective of this work is to propose an algorithm, inspired by the space-filling Apollony fractal, to generate sphere packings in geological objects as a first step toward their mechanical modeling with the DEM. In particular, we assess the relevance of the generated packings for simulating the behavior of a rocklike material, and we discuss the ability of the proposed approach to discretize geological models. The algorithm ensures the tangential conformity of spheres with the model boundaries internal and external, and enables to adapt the particle size distribution in the vicinity of structures of interest such as fractures or faults.

[1]  Jian Lu,et al.  Geometrical modeling of granular structures in two and three dimensions. Application to nanostructures , 2009 .

[2]  A. Eulitz,et al.  Yade Documentation 2nd ed , 2015 .

[3]  Gaël Combe,et al.  Experimental micromechanical analysis of a 2D granular material: relation between structure evolution and loading path , 1997 .

[4]  F. Donze,et al.  A DEM model for soft and hard rocks: Role of grain interlocking on strength , 2013 .

[5]  J. Walsh,et al.  The impact of porosity and crack density on the elasticity, strength and friction of cohesive granular materials : insights from DEM modelling , 2009 .

[6]  Anuraag R. Kansal,et al.  Computer generation of dense polydisperse sphere packings , 2002 .

[7]  Carlos Alexander Recarey Morfa,et al.  Modified algorithm for generating high volume fraction sphere packings , 2015, CPM 2015.

[8]  Márcio Muniz de Farias,et al.  Systemic characterization and evaluation of particle packings as initial sets for discrete element simulations , 2018 .

[9]  P. Sanz,et al.  Overview of continuum and particle dynamics methods for mechanical modeling of contractional geologic structures , 2014 .

[10]  Vincent Richefeu,et al.  Study of cold powder compaction by using the discrete element method , 2011 .

[11]  Rene Weller,et al.  Fast sphere packings with adaptive grids on the gpu , 2013 .

[12]  Gabriel Zachmann,et al.  ProtoSphere: a GPU-assisted prototype guided sphere packing algorithm for arbitrary objects , 2010, SIGGRAPH ASIA.

[13]  Lei Yang,et al.  Implementing discrete element method for large-scale simulation of particles on multiple GPUs , 2017, Comput. Chem. Eng..

[14]  H. Herrmann,et al.  Searching for the perfect packing , 2003 .

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

[16]  F. Donze,et al.  Necking and fracking may explain stationary seismicity and full degassing in volcanic silicic spine extrusion , 2018, Earth and Planetary Science Letters.

[17]  L. Scholtès,et al.  Influence of stress induced microcracks on the tensile fracture behavior of rocks , 2018, Computers and Geotechnics.

[18]  Daisuke Nishiura,et al.  ppohDEM: Computational performance for open source code of the discrete element method , 2014, Comput. Phys. Commun..

[19]  J. C. Jaeger,et al.  Fundamentals of rock mechanics , 1969 .

[20]  Katalin Bagi,et al.  An algorithm to generate random dense arrangements for discrete element simulations of granular assemblies , 2005 .

[21]  Stuart Hardy,et al.  Structural evolution of calderas: Insights from two-dimensional discrete element simulations , 2008 .

[22]  Waldemar Celes Filho,et al.  An efficient algorithm to generate random sphere packs in arbitrary domains , 2016, Comput. Math. Appl..

[23]  Ching S. Chang,et al.  Packing Structure and Mechanical Properties of Granulates , 1990 .

[24]  Karim Hitti,et al.  Optimized Dropping and Rolling (ODR) method for packing of poly-disperse spheres , 2013 .

[25]  R. Peikert,et al.  THE FRACTAL DIMENSION OF THE APOLLONIAN SPHERE PACKING , 1994 .

[26]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[27]  Daniel N. Wilke,et al.  Collision detection of convex polyhedra on the NVIDIA GPU architecture for the discrete element method , 2015, Appl. Math. Comput..

[28]  Bruno Chareyre,et al.  Intensity and volumetric characterizations of hydraulically driven fractures by hydro-mechanical simulations , 2017 .

[29]  M. Stroeven,et al.  Assessment of packing characteristics by computer simulation , 1999 .

[30]  Guillaume Caumon,et al.  RINGMesh: A programming library for developing mesh-based geomodeling applications , 2017, Comput. Geosci..

[31]  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 .

[32]  David R. Owen,et al.  Filling domains with disks: an advancing front approach , 2003 .

[33]  George T. Hahn,et al.  Influence of microstructure on fracture propagation in rock , 1973 .

[34]  Brian McPherson,et al.  The Role of Particle Packing in Modeling Rock Mechanical Behavior using Discrete Elements , 2002 .

[35]  Hai-Sui Yu,et al.  A particle refinement method for simulating DEM of cone penetration testing in granular materials , 2012 .

[36]  P. Cundall,et al.  A bonded-particle model for rock , 2004 .

[37]  Liang Cui,et al.  Analysis of a triangulation based approach for specimen generation for discrete element simulations , 2003 .

[38]  J. Jerier,et al.  Packing spherical discrete elements for large scale simulations , 2010 .

[39]  Diego Mas Ivars,et al.  The synthetic rock mass approach for jointed rock mass modelling , 2011 .

[40]  J. Morgan,et al.  Controls on Fore‐Arc Deformation and Stress Switching After the Great 2011 Tohoku‐Oki Earthquake From Discrete Numerical Simulations , 2018, Journal of Geophysical Research: Solid Earth.

[41]  David Oskar Potyondy,et al.  The bonded-particle model as a tool for rock mechanics research and application: current trends and future directions , 2015 .

[42]  F. Donze,et al.  Modelling progressive failure in fractured rock masses using a 3D discrete element method , 2012 .

[43]  Tom Shire,et al.  Numerical techniques for fast generation of large discrete-element models , 2018 .

[44]  J. Jerier,et al.  A geometric algorithm based on tetrahedral meshes to generate a dense polydisperse sphere packing , 2009 .

[45]  C. O’Sullivan.  Particulate Discrete Element Modelling: A Geomechanics Perspective , 2011 .

[46]  J. Yliruusi,et al.  Particle packing simulations based on Newtonian mechanics , 2007 .

[47]  G. Caumon,et al.  Surface-Based 3D Modeling of Geological Structures , 2009 .