Multi-fractal characteristics of particle size distribution of granular backfilling materials under different loads
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Hao Yan
, Jixiong Zhang , Jiaqi Wang , Nan Zhou and Sheng Zhang
Abstract
This study is focused on the inhomogeneity and local heterogeneity of the particle size distributions (PSD) of granular backfilling materials (eolian sands and loess) from western mines of China under overburden strata loads. The multi-fractal spectrum and variations in corresponding parameters of PSD of granular backfilling materials were obtained under different loads using a laser particle size analyzer and an environmental scanning electron microscope (ESEM). The results indicated that the load had negligible effects on the multi-fractal characteristics of PSD of eolian sand. There were no significant variations in the capacity dimension D(0), the information entropy dimension D(1) and the bandwidth of the multi-fractal spectra (Δα) as a function of the load. In contrast, the load significantly affected the multi-fractal characteristics of the PSD of loess, and D(0), D(1) and Δα increased and then decreased (maximized at 2 MPa) as the load increased. Furthermore, there was a correlation between structural morphology parameters and multi-fractal parameters in the particle breakage process, which demonstrated that D(0), D(1) and Δα of PSD of granular backfilling materials could effectively reflect the particle breakage and the change of structural morphology parameters of backfilling materials under different loads.
Kurzfassung
Die diesem Beitrag zugrundeliegende Studie konzentriert sich auf die Inhomogenität und die lokale Heterogenität von Partikelgrößenverteilungen (Particle Size Distributions (PSD)) von körnigen Verfüllmaterialien (Aeolische Sande und Löß) der westlichen Minen in China unter übergroßen Schichtbelastungen. Das multifraktale Spektrum und die Variationen der entsprechenden Parameter der PSD von körnigen Verfüllmaterialien wurden unter verschiedenen Lasten ermittelt, indem ein Laserpartikelgrößenmesser und ein Rasterelektronenmikroskop (ESEM) genutzt wurden. Die Ergebnisse deuten darauf hin, dass die Belastung einen vernachlässigbaren Effekt auf die multifraktalen Charakteristika der PSD von aeolischem Sand hat. Es ergaben sich keine signifikanten Variationen in der Kapazitätsdimension D(0), der Informationsentropiedimension D(1) und der Bandbreite der multfraktalen Spektren (Δα) als Funktion der Belastung. Im Gegensatz dazu wirkte sich die Belastung signifikant auf die multifraktalen Charakteristika der PSD von Löß aus, und D(0), D(1) und Δα nahmen zunächst zu und dann ab (mit einem Maximum bei 2 MPa), als die Belastung zunahm. Darüber hinaus bestand eine Korrelation zwischen den strukturellen Morphologie-Parametern und den multifraktalen Parametern im Prozess der Partikelbrechung, die zeigte, dass D(0), D(1) und Δαder PSD von körnigen Verfüllmaterialien die Partikelspaltung effektiv reflektieren können, ebenso wie die Veränderung der strukturellen Morphologie-Parameter von Verfüllmaterialien unter verschiedenen Belastungen.
References
1 J. X.Zhang, Q.Zhang, Q.Sun, R.Gao, D.Germain, S.Abro: Surface subsidence control theory and application to backfill coal mining technology, Environmental Earth Sciences74 (2015), No. 2, pp. 1439–144810.1007/s12665-015-4133-0Search in Google Scholar
2 R.Gao, J. X.Zhang, A. J. S.Spearing, M.Li, F.An, D. Y.Hao: Research into stope roof control of compound roof by solid backfilling mining, International Journal of Mining Science and Technology26 (2016), No. 4, pp. 609–61410.1016/j.ijmst.2016.05.012Search in Google Scholar
3 L.Zhao, W. J.Wang, Z.Li, Y. F.Chen: Microstructure and pore fractal dimensions of recycled thermal insulation concrete, Materials Testing57 (2015), No. 4, pp. 349–35910.3139/120.110713Search in Google Scholar
4 H.Zhu, F.Nicot, F.Darve: Meso-structure evolution in a 2D granular material during biaxial loading, Granular Matter18 (2016), No. 3, pp. 1–1210.1007/s10035-016-0608-2Search in Google Scholar
5 M.Grigoriu: Material responses at micro- and macro-scales, Computational Materials Science107 (2015), pp. 190–20310.1016/j.commatsci.2015.05.024Search in Google Scholar
6 T.Jiřina, J.Šperl: Reduction of surface subsidence risk by fly ash exploitation as filling material in deep mining areas, Natural Hazards53 (2010), No. 2, pp. 251–25810.1007/s11069-009-9425-9Search in Google Scholar
7 J. X.Zhang, M.Li, Z.Liu, N.Zhou: Fractal characteristics of crushed particles of coal gangue under compaction, Powder Technology305 (2017), pp. 12–1810.1016/j.powtec.2016.09.049Search in Google Scholar
8 X.Wei, X. G.Li, N.Wei: Fractal features of soil particle size distribution in layered sediments behind two check dams: Implications for the Loess Plateau, China, Geomorphology266 (2016), pp. 133–14510.1016/j.geomorph.2016.05.003Search in Google Scholar
9 E.Fernández, H. F.Jelinek: Use of fractal theory in neuroscience: Methods, advantages, and potential problems, Methods24 (2001), No. 4, pp. 309–32110.1006/meth.2001.1201Search in Google Scholar PubMed
10 E.Perfect, B. D.Kay: Fractal theory applied to soil aggregation, Soil Science Society of America Journal55 (1991), No. 6, pp. 309–32110.2136/sssaj1991.03615995005500060009xSearch in Google Scholar
11 P. D.Panagiotopoulos, O. K.Panagouli, E. S.Mistakidis: Fractal geometry and fractal material behaviour in solids and structures, Archive of Applied Mechanics63 (1993), No. 1, pp. 1–2410.1007/BF00787906Search in Google Scholar
12 K.Tsujii: Fractal materials and their functional properties, Polymer Journal40 (2008), No. 9, pp. 785–79910.1295/polymj.PJ2008053Search in Google Scholar
13 Y. X.Zhao, S.Chang, C.Liu: Multifractal theory with its applications in data management, Annals of Operations Research234 (2015), No. 1, pp. 133–15010.1007/s10479-014-1599-1Search in Google Scholar
14 J. M.Wang, M.Zhang, Z. K.Bai, L. L.Guo: Multi-fractal characteristics of the particle distribution of reconstructed soils and the relationship between soil properties and multi-fractal parameters in an opencast coal-mine dump in a loess area, Environmental Earth Sciences73 (2015), No. 8, pp. 4749–476210.1007/s12665-014-3761-0Search in Google Scholar
15 H. F.Huang, C. S.Wang, H. B.Bai, Z. H.Wang: Water protection in the western semiarid coal mining regions of China: A case study, International Journal of Mining Science and Technology22 (2012), No. 5, pp. 719–72310.1016/j.ijmst.2012.08.022Search in Google Scholar
16 L. Y.Guo, Z. Y.Ren, Y. S.Liu: The causes of land landscape changes in semi-arid area of Northwest China: A case study of Yulin city, Journal of Geographical Sciences16 (2006), No. 2, pp. 192–19810.1007/s11442-006-0207-ySearch in Google Scholar
17 E.Jankowski, S. C.Glotzer: Calculation of partition functions for the self-assembly of patchy particles, Journal of Physical Chemistry B115 (2011), No. 48, pp. 14321–1432610.1021/jp206430zSearch in Google Scholar PubMed
18 F. J.Caniego, R.Espejo, M. A.Martín, F. S.José: Multifractal scaling of soil spatial variability, Ecological Modelling182 (2005), No. 3–4, pp. 291–30310.1016/j.ecolmodel.2004.04.014Search in Google Scholar
19 Z. Y.Zhao, J.Zhu, B.Xia: Multi-fractal fluctuation features of thermal power coal price in China, Energy117 (2016), No. 1, pp. 10–1810.1016/j.energy.2016.10.081Search in Google Scholar
20 H. O.Peitgen, H.Jurgens, D.Saupe: Chaos and Fractals, Springer, New York, USA (2004)10.1007/b97624Search in Google Scholar
21 R. G.Zuo, J.Wang: Fractal/multifractal modeling of geochemical data: A review, Journal of Geochemical Exploration164 (2016), pp. 33–4110.1016/j.gexplo.2015.04.010Search in Google Scholar
22 F.Podczeck: A shape factor to assess the shape of particles using image analysis, Powder Technology93 (1997), No. 1, pp. 47–5310.1016/S0032-5910(97)03257-9Search in Google Scholar
© 2018, Carl Hanser Verlag, München
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Articles in the same Issue
- Inhalt/Contents
- Contents
- Fachbeiträge/Technical Contributions
- SteBLife – A new short-time procedure for the calculation of S-N curves and failure probabilities
- Surface treatment for effective bonding in the sports industry
- Effect of different rotational speeds on mechanical and metallurgical properties of friction welded dissimilar steels
- Comparison of titanium and FGM dental implants with different coating types
- Weld quality and productivity of AISI 4140 steel welded by unpulsed and pulsed GMAW
- Corrosion behavior of Hastelloy® C–4® Ni–Cr–Mo–Fe alloys for coal gasification syngas plants
- Application of FactSage® thermodynamic modeling for predicting the ash transformation with temperatures under partial slagging entrained flow coal gasification condition
- Röntgen- und Neutronentomographie am knöchernen Innenohr der Bartenwale
- Partial repair of thermally sprayed and sealed corrosion protection – Organic coating material or thermal spraying?
- Experimental study on solidification of Cu(II)-contaminated soil using red mud with cement and Ca(OH)2
- Tribological study of sintered iron based and copper based brake materials by pin-on-disc method
- Influence of drilling parameters on temperature and surface roughness of AISI O2 steel
- Multi-fractal characteristics of particle size distribution of granular backfilling materials under different loads
- Dry sliding behavior of aluminum alloy 8011 with 4 % fly ash
- Optimization of the milling parameters for an Al/Si3N4 functionally graded composite using grey relational analysis