Measurements on the structural contribution to friction in granular media [Elektronische Ressource] / Wolfgang Eber

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• Publié par: technische_universitat_munchen
• Publié le: 01 janvier 2007
• Nombre de lectures: 8
• Langue: English
• Poids de l'ouvrage: 5 Mo

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Measurements on Friction in Granular Media Dipl.-Phys.W. Eber, Technische Universität München
Institut für Geologie, Geotechnik und Baubetrieb
Technische Universität München
Measurements on the Structural
Contribution to Friction in
Granular Media
Wolfgang Eber
Vollständiger Abdruck der von der Fakultät für Bauingenieur- und Vermessungswesen der
Technischen Universität München zur Erlangung des akademischen Grades eines
Doktors der Naturwissenschaften (Dr. rer. nat.)
genehmigten Dissertation.
Vorsitzender: Univ.-Prof. Dr.-Ing. J. Zimmermann
Prüfer der Dissertation: 1. Univ.-Prof. Dr.-Ing. N. Vogt
2. Univ.-Prof. Dr. rer. nat. H. Herrmann,
Eidgenössische Technische Hochschule
Zürich/Schweiz
Die Dissertation wurde am 06.12.2006 bei der Technischen Universität eingereicht und durch
die Fakultät für Bauingenieur- und Vermessungswesen am 12.03.2007 angenommen.Measurements on Friction in Granular Media Dipl.-Phys.W. Eber, Technische Universität München
Excerpts of this paper have been published in the journal Physical Review E [67] with
permission of the Fakultät für Bauingenieur- und Vermessungswesen, Technische Universität
München, dated 29.05.2001.Measurements on Friction in Granular Media Dipl.-Phys.W. Eber, Technische Universität München
Abstract
In this paper, some experimental results are presented, estimating the lateral
stress response to a longitudinal stress applied to an ideal granular system as
a function of friction parameters. Structural effects are taken into account
through the use of angle of contact distributions. The two-dimensional
model, based on mainly equally sized cylinder granules allows to derive a
dependency of the friction between single granules and the overall angle of
friction, which is commonly used to describe the macroscopic behaviour of
granular material.
This approach is valid for materials that have been subjected to some unidi-
rectional deformation, which enables shearing joints to establish. Such
behaviour is compatible with classic theories derived from the basic Rankine
concept.
In contrast to this, stochastically mixed materials with no deformation
history exhibit somewhat different characteristics since the deformation is
not concentrated to shearing joints. They can be described with good success
by a purely statistical approach. For this case the importance of small irregu-
larities on the surface of the model grains is pointed out.
Concerning the impact of the inner structure of a granular system, a scale
can be determined, where three classes are defined. At the first level single
particles are described, while the building of a network of force bearing
chains is addressed at the second level. A rough estimation of the mesh size
is given and confirmed by experimental results. At the third level the granu-
lar structure of a medium can be neglected and continuous theories work
well.
Classification of the subject according to the Physics and Astronomy Classification
Scheme® (PACS®), prepared by the American Institute of Physics (AIP): PACS 45.70.QjMeasurements on Friction in Granular Media Dipl.-Phys.W. Eber, Technische Universität München
Table of Contents
1 Introduction ........................................................ 9
2 Granular Parameters in Soil Mechanics .............................. 11
2. 1 General Remarks on Approaches to Soil Mechanics .................... 11
2. 2 Angle of Friction and Cohesion of Natural Soil ......................... 14
2. 2. 1 Experiments with an undefined shear joint 14
2. 2. 2 Experiments with a fixed shear joint 15
2. 3 Porosity/Packing Fraction ......................................... 16
2. 4 Particle Properties and Distribution in Natural Soils ..................... 18
2. 5 Motivation for a Granular Model and Restrictions ....................... 20
3 Experimental Setup ................................................ 23
3. 1 The Frame ..................................................... 23
3. 2 The Granular System ............................................. 24
3. 3 The Polariscope 25
3. 4 The Force Transmission .......................................... 26
3. 5 Universality .................................................... 26
4 Measurements of Averaged Forces ................................. 27
4. 1 Friction Measurements ........................................... 27
4. 2 Estimation of Unevenness ........................................ 30
4. 3 Coefficient of Lateral Stress ....................................... 31
4. 3. 1 Coordinate System .......................................... 31
4. 3. 2 Constructing an Unambiguous State .............................. 31
4. 3. 3 Measuring the Lateral Stress Factors ............................. 37
4. 3. 4 Side Effects ................................................ 39
4. 3. 5 Final Readings ............................................. 42
4. 4 First Discussion of Results, General Remarks ......................... 43
4. 5 Excursion: Confirmation of Active State .............................. 44
5 Measurement of Porosity rsp. Packing Fraction ..................... 48
5. 1 Minimum Porosity/Maximum Packing Fraction 48
5. 2 Packing Fraction after Unidirectional Deformation ...................... 49Measurements on Friction in Granular Media Dipl.-Phys.W. Eber, Technische Universität München
6 Survey of the Macroscopic Structure ................................ 52
6. 1 Image Processing ............................................... 52
6. 2 Visualisation Results ............................................. 54
6. 3 Approval of Linearity 55
6. 4 Distribution of Intensities and Forces 57
6. 5 Mesh Size Acquisition ............................................ 60
7 Discussion of Results: Overview .................................... 64
8 Discussion of Porosity Measurements ............................... 66
8. 1 Theoretical Limiting Densities ...................................... 66
8. 2 Referring to Measurements ........................................ 68
8. 3 The Granular State prior to Force Measurements ....................... 71
9 Discussion of Results: Well Organised Granular Material ............. 74
9. 1 The Mohr-Coulomb Concept ....................................... 74
9. 2 Comparison to the Rankine Border States: Structural Contribution ........ 76
9. 3 Estimation of Self Organising Effects ................................ 80
9. 3. 1 Consequence of continuous deformation .......................... 80
9. 3. 2 Influence of varying diameters of elements ......................... 82
9. 3. 3 Estimated structural impact .................................... 83
10 Discussion of Results: Less Organised Granular Material ........... 86
10. 1 Assumed Self Organising Process based on Unevenness ............... 88
10. 2 Quantitative Estimation of the Self Organised Stability .................. 88
10. 3 Descriptive Parameterizing Approach ............................... 91
11 Statistical Approach: Less Organised Granular Material ............. 93
11. 1 Preliminary Test Using a Highly Simplified Model ...................... 93
11. 2 Monte Carlo Modelling .......................................... 97
11. 2. 1 Modelling Force Chains ...................................... 97
11. 2. 2 Simulational Approach ....................................... 98
11. 2. 3 Software Aspects ........................................... 99
11. 2. 4 Proceeding .............................................. 100
11. 3 The Stochastic Model in Detail ................................... 101
11. 3. 1 The Basic Cell ............................................ 101Measurements on Friction in Granular Media Dipl.-Phys.W. Eber, Technische Universität München
11. 3. 2 Limit of Possible Angles ..................................... 101
11. 4 Modelling a Frictionless Chain ................................... 103
11. 4. 1 Equilibrium of Forces on a Single Cylinder ....................... 103
11. 4. 2 Basic Solution: Propagation of a Longitudinal Force ................. 105
11. 5 Introduction of Torsional Moments ................................ 106
11. 5. 1 Unloading Lateral Contacts .................................. 107
11. 5. 2 Unloading Lateral Forces in Symmetric Cases ..................... 108
11. 6 Coefficient of Geometry ........................................ 113
11. 6. 1 Parameters .............................................. 113
11. 6. 2 Definition of a Cell ......................................... 115
11. 6. 3 General Formulation of the Form Factor: ......................... 115
11. 6. 4 Packing Ratios ........................................... 117
11. 7 Building Mean Values .......................................... 118
11. 7. 1 Generating Force Chains ...