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SIMULATIONS OF GRANULAR COLUMN COLLAPSE USING SMOOTHED PARTICLE HYDRODYNAMICS AND DISCRETE ELEMENT METHODS
ABSTRACT
Granular materials are an inseparable part of daily life. Granular flow is commonly encountered in nature (e.g., landslides, debris avalanches, active movement of retaining walls) and various industrial and engineering processes (e.g., hopper flow, conveyer belts, silo discharge). Granular material may exhibit both solid-like and fluidlike behaviors and due to this complexity, understanding of the behavior of granular materials under different flow conditions is of great importance and has been the subject of various experimental and numerical studies in recent years. Interesting cases of granular flow are dynamic (i.e. rapid) and quasi-static (i.e. slow) collapses of granular columns, which are relevant to landslides and active movement of retaining walls in geotechnical engineering, respectively, and provide invaluable insights into the mechanics of unsteady dense granular flow.
In this research, two numerical simulation techniques including Smoothed Particle Hydrodynamics (SPH) method from continuum framework and Discrete Element Method (DEM) from discrete framework have been employed to model three-dimensional (3D) quasi-static and dynamic collapses of cylindrical and rectangular granular columns and the transitional regime between quasi-static and dynamic collapses. The developed 3D models are initially validated against available experimental observations and are later used to provide better understandings of the collapse mechanisms including collapse pattern, deposit morphology, energy dissipations, non-deformed region, etc.
Results of the developed SPH and DEM models reveal that both continuum and discrete frameworks are qualitatively and quantitatively capable of capturing different aspects of granular collapse as long as appropriate constitutive models or contact behaviors are implemented. However, DEM simulations are better capable of capturing particle-level behaviors, such as the sharp edges of the free surface and flow front.
Results of the developed 3D SPH and DEM models under different flow
conditions show that quasi-static collapse is qualitatively similar to the dynamic collapse, with final profile height, runout distance, collapse pattern, and energy dissipation mainly depending on the initial aspect ratio of the columns. However, the quasi-static collapse results in shorter runout distances and less granular material distortion. It is also observed that transition between quasi-static and dynamic collapses occurs within a small range of Midi numbers. Furthermore, the developed models are used to conduct a parametric study on the effects of microscopic and macroscopic material properties (e.g., density, friction, rotational resistance and porosity) on flow behavior. For quasi-static granular column collapse, theoretical equations for final height, runout distance and energy dissipations for two conceptual cases (i.e., truncated cone-like/truncated wedge-like deposits for small aspect ratios and cone-like/wedge-like deposits for large aspect ratios) are derived, and it is shown that results of these equations are in good agreement with SPH and DEM simulations and experimental observations.
The dissertation also presents the results of SPH simulation of flow of water through non-deformable porous media, which can be considered as the first stage of developing a fully coupled SPH-DEM model to comprehensively study the flow of water through soil. The developed models are validated against the results of available numerical studies in the literature and an experimental study which was conducted as a part of this research.
TABLE OF CONTENTS
List of Figures ……………………………………………………………………………………………….. ix
List of Tables ………………………………………………………………………………………………… xiv
Acknowledgements ………………………………………………………………………………………… xv
Chapter 1 Introduction ……………………………………………………………………………………. 1
Motivation ………………………………………………………………………………………………. 1
Experimental studies ………………………………………………………………………………… 5
Dynamic collapse ……………………………………………………………………………… 6
Quasi-static collapse ………………………………………………………………………….. 10
Comparison between quasi-static and dynamic collapse ………………………… 13
Numerical methods ………………………………………………………………………………….. 14
SPH and DEM simulations of granular column collapse ………………………… 19
Aim and objectives ………………………………………………………………………………….. 21
Dissertation organization ………………………………………………………………………….. 23
References ………………………………………………………………………………………………. 25
Chapter 2 Simulation of Collapse of Granular Columns using Discrete Element Method …………………………………………………………………………………………………… 31
Abstract ………………………………………………………………………………………………….. 31
Introduction …………………………………………………………………………………………….. 32
DEM model ……………………………………………………………………………………………. 36
Numerical sample preparation …………………………………………………………….. 38
Material properties …………………………………………………………………………….. 39
Contact stiffness ……………………………………………………………………………….. 40
Rotational resistance ………………………………………………………………………….. 45
Results and discussions …………………………………………………………………………….. 46
Effect of rotational resistance on deposit morphology ……………………………. 52
Effect of initial porosity on deposit morphology …………………………………… 54
Energy dissipation …………………………………………………………………………….. 57
Conclusions …………………………………………………………………………………………….. 62
Acknowledgements ………………………………………………………………………………….. 64
References ………………………………………………………………………………………………. 64
Chapter 3 Simulation of Quasi-Static and Dynamic Collapses of Rectangular Granular Columns using Smoothed Particle Hydrodynamics Method …………….. 74
Abstract ………………………………………………………………………………………………….. 74Introduction …………………………………………………………………………………………….. 75
Numerical implementation ……………………………………………………………………….. 78
SPH method ……………………………………………………………………………………… 78
Governing equations ………………………………………………………………………….. 80
Constitutive model …………………………………………………………………………….. 80
Implementing governing equations in SPH formulation …………………………. 84
Boundary conditions ………………………………………………………………………….. 85
3D SPH model ………………………………………………………………………………….. 86
Results and discussions …………………………………………………………………………….. 88
Quasi-static collapse pattern ……………………………………………………………….. 88
Quasi-static final deposit profile …………………………………………………………. 92
Energy dissipation …………………………………………………………………………….. 97
Evolution of heights at the fixed and moving walls ……………………………….. 99
Effect of friction angle and bulk density on deposit morphology …………….. 102
Dynamic collapse pattern …………………………………………………………………… 102
Dynamic final deposit profile ……………………………………………………………… 105
Effect of wall velocity on deposit morphology ……………………………………… 107
Conclusions …………………………………………………………………………………………….. 109
Acknowledgements ………………………………………………………………………………….. 111
References ………………………………………………………………………………………………. 111
Chapter 4 Simulation of Quasi-Static Axisymmetric Collapse of Granular
Columns using Smoothed Particle Hydrodynamics and Discrete Element Methods …………………………………………………………………………………………………. 117
Abstract ………………………………………………………………………………………………….. 117
Introduction …………………………………………………………………………………………….. 118
Numerical implementations ………………………………………………………………………. 122
SPH method ……………………………………………………………………………………… 122
Discrete Element Method (DEM) ……………………………………………………….. 127
Quasi-static axisymmetric collapse ……………………………………………………… 131
Results and discussions …………………………………………………………………………….. 132
Collapse pattern ………………………………………………………………………………… 132
Non-deformed region ………………………………………………………………………… 138
Final deposit profile …………………………………………………………………………… 139
Energy dissipation …………………………………………………………………………….. 146
Evolution of heights at the center and moving walls ……………………………… 149
Conclusions …………………………………………………………………………………………….. 150
Acknowledgements ………………………………………………………………………………….. 152
References ………………………………………………………………………………………………. 152
Chapter 5 Simulation of Flow through Non-Deformable Porous Media using Smoothed Particle Hydrodynamics Method ………………………………………………… 159
Abstract ………………………………………………………………………………………………….. 159Introduction …………………………………………………………………………………………….. 160
SPH basic principles and formulations ……………………………………………………….. 163
SPH governing equations …………………………………………………………………… 164
Equation of state ……………………………………………………………………………….. 166
Averaged Navier-Stokes equations ……………………………………………………… 166
Solid-fluid coupling force …………………………………………………………………… 167
Density diffusion ………………………………………………………………………………. 168
Timestep ………………………………………………………………………………………….. 169
Boundary conditions ………………………………………………………………………….. 170
2D SPH model ………………………………………………………………………………………… 171
Model verification …………………………………………………………………………………… 175
Verification of fluid pressure distribution …………………………………………….. 175
Density diffusion effect ……………………………………………………………………… 177
Results ……………………………………………………………………………………………………. 178
SPH model validation against other numerical simulations …………………….. 178
SPH model validation against experimental data …………………………………… 181
Conclusions …………………………………………………………………………………………….. 185
Acknowledgements ………………………………………………………………………………….. 186
Reference ……………………………………………………………………………………………….. 186
Chapter 6 Conclusions and Recommendations …………………………………………………… 195
Conclusions …………………………………………………………………………………………….. 195
Recommendations for Future Work …………………………………………………………… 204
Alternate approaches for studying the effects of particle shape in DEM simulations and comparison with the artificial rotational resistance
approaches …………………………………………………………………………………. 204Study of the transitional regime using DEM model ……………………………….. 204
Simulating Cone Penetration Test (CPT) ……………………………………………… 205
Fully coupled DEM-SPH model to simulate flow through porous media …. 205
Chapter 1
Introduction
Motivation
This research focuses on the utilization of two computational methods from continuum and discrete frameworks to enhance the understanding of the behavior of granular materials under different flow conditions. Granular materials are an inseparable part of daily life since the beginning of history. From digging wells, building roads and passages and construction of adobe structures, to harvesting of crops and storing them in silos and even in hourglasses for measuring time, mankind has been trying to wield these materials to improve their lives. Nowadays, granular materials are used on a regular basis in every construction project (e.g., highway, railway and retaining wall construction), various industrial and mining processes (e.g., hopper flow, conveyer belts, chutes), and in pharmaceutical manufacturing (e.g., handling and storage of tablets).
Deformation/flow of granular materials is a very interesting topic in civil engineering as it is often encountered in nature in the form of rapid flow of soil grains (e.g., landslides, debris avalanches, etc.) or slow movement of soil particles (e.g., active movement of retaining walls, pile jacking, etc.). Figure 1-1 shows a few examples of granular flow. The importance of studying the flow of granular materials can be elaborated by the specific case of landslides, which are known as a potential threat to human lives and civil infrastructures (e.g., roads, pipelines, bridges, utilities, etc.). In order to assess the safety of existing facilities against possible landslides and to determine the safe location for future constructions, the accurate prediction of landslide runout is essential.
(a) (b) (c)
(d) (e)
(f) (g)
Figure 1-1. Examples of granular flow: (a) hourglass, goo.gl/m53LB5; (b) pill manufacturing, goo.gl/FZz3wc; (c) sand dunes, goo.gl/xE8pB9; (d) crushed aggregate conveyer, goo.gl/ifg4Zr; (e) grain handling in silo goo.gl/4g3Ked; (f) landslide, goo.gl/h45vpy; (g) snow avalanche, goo.gl/azQ88y
Granular materials in their static condition have been widely studied through the years, and good understanding of their properties are available. However, their behavior in motion vastly differs from those of the static condition and is a highly complex behavior which is yet to be fully understood. The behavior of moving granular materials depends on not only factors including grain properties (e.g., density, shape, friction angle, etc.), packing properties and dimensions (e.g., void ratio, relative density, aspect ratio), but also the flow characteristic (e.g., strain rate) (Vidyapati 2012; Redaelli et al. 2017).
In general, the flow of granular materials can be classified into three different regimes based on the strain rate and velocity of the particles (Jaeger et al 1996; Forterre and Pouliquen 2008; Owen et al. 2008). In one end, and in case of very low flow intensities, particles’ velocities are small, and they remain in constant contact throughout the flow, forming a perpetual force chain among granular particles. This flow regime is known as “Quasi-static regime”, in which the effect of inertia of individual grains can be neglected. As particles are in constant contact during the flow, the system energy dissipation occurs mainly due to friction of material grains and other dissipative mechanisms (e.g., inelastic collision, damping, etc.) do not affect the total energy dissipation of the system (Roux and Combes 2002; Forterre and Pouliquen 2008). This flow regime can be observed during various civil/geotechnical engineering phenomena, such as the active deformation of retaining walls and bridge abutments, pile jacking, CPT testing, etc. On the other end, and in case of very high flow intensities and in low material concentration, particle grains are apart from each other and move rapidly in a dilute environment and the flow is dominated by binary collision between material grains, resulting in a gaseous-like behavior. In this case, energy dissipation mainly occurs due to the inelastic collision of material; hence this flow is known as “Collisional regime” (Goldhirsch 2003; Forterre and Pouliquen 2008; Midi 2004). This type of flow can be observed during sand storms or dropping of granular materials from chutes. Finally, and between the aforementioned two extreme conditions, an intermediate behavior can be recognized, during which particles remain in contact during the flow, maintaining a force network between the particles, while the particle inertia is also important and affects the flow behavior. In this condition, the granular material demonstrates both fluid-like and solid-like behaviors, hence this regime is named “Dense Inertial regime” in the literature (Midi 2004). In this flow regime, energy of particles dissipates by the combined action of interparticle friction and surface collision. (Pouliquen and Chevoir 2002; Midi 2004; Forterre and Pouliquen 2008). This type of flow is encountered in variety of natural and industrial phenomena such as landslides, avalanches, grain handling, pharmaceuticals,
etc.
Figure 1-2 is a comparative demonstration of these three regimes for a granular flow that occurs while pouring beads on an existing bead-pile (Forterre and Pouliquen 2008). As can be noticed, the granular material can exhibit different states of matter based on the way they are handled: they can resist shear stresses similar to solids, while having the potential of flowing and spreading similar to fluids and gases (Jaeger et al.
1996; Andreotti et al 2013).
Figure 1-2. Example of three flow regimes obtained by pouring steel beads on a pile (Andreotti et al. 2013)
Granular flow has the potential of leading to catastrophic incidents such as landslides and snow avalanches. The complicated granular material behavior in such phenomena makes predicting the extent of damages difficult. Thus, understanding the behavior of granular materials under different flow conditions is of great importance and has been the subject of various experimental and numerical studies.
