Skip to main content
SpringerLink
Log in

Fractal dimension, particle shape, and particle breakage analysis for calcareous sand

  • Original Paper
  • Published:
Bulletin of Engineering Geology and the Environment Aims and scope Submit manuscript

A Correction to this article was published on 21 April 2022

This article has been updated

Abstract

To explore the fractal dimension, particle shape, and particle breakage of calcareous sand (CS) under multi-level ending pressure, a series of one-dimensional compression experiments along with microscope image recognition tests were performed. Test results demonstrated that compression behavior of CS was similar to that of silt soil for the reason that considerable particle breakage occurred under high-stress level. In unloading process, rebound index of tested specimens was in the range of 0.0027–0.0052 which suggested that irrecoverable plastic deformation consists of the main part of compression. The shape index sphericity (\({S}_{C}\)), aspect ratio (\({A}_{R}\)), convexity (\({C}_{X}\)), and overall regularity (\({O}_{R}\)) increased as increasing axial stress or decreasing average grain size. Besides, there existed a turning point of axial stress of 3200 kPa; these shape indexes increased rapidly first and then approached to a stable value after that. At present study, the surface and mass fractal dimension of tested specimens were in the range of 1.12–1.93 and 2.14–2.92, respectively. Both fractal dimension and relative breakage ratio increased logarithmically as increasing axial stress from 0 to 6400 kPa. In addition, an increase in the average grain size led to an increase in the relative breakage ratio and a decrease in fractal dimension which indicated that larger particles are more easily broken for the reason that the stress concentration between granular grains. Furthermore, there existed approximate linear relations between surface or mass fractal dimension with relative breakage ratio which might be helpful to quantitate the particle breakage of granular materials.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Change history

References

  • Al Hattamleh O, AlShalabi F, Al Qablan H (2010) Effect of grain crushing and bedding plane inclination on Aqaba sand behavior. Bull Eng Geol Environ 69(1):41–49

    Article  Google Scholar 

  • Altun S, Göktepe B, Sezer A (2011) Relationships between shape characteristics and shear strength of sands. Soils Found 51(5):857–871

    Article  Google Scholar 

  • Assadi Langroudi A, Jefferson I, O’Hara-Dhand K (2014) Micromechanics of quartz sand breakage in a fractal context. Geomorphology 211:1–10

    Article  Google Scholar 

  • Azam S (2000) Collapse and compressibility behaviour of arid calcareous soil formations. Bull Eng Geol Env 59(3):211–217

    Article  Google Scholar 

  • Boubrit H, Melbouci B (2020) Quantification of the crushing of grains by the calculation of the surfaces. Eur J Environ Civ Eng 24(13):2284–2305

    Article  Google Scholar 

  • Bouzeboudja A, Melbouci B (2016) Etude De L’Evolution De La Dimension Fractale Des Grains De Materiaux Granulaires Soumis a Des Essais Mecaniques. Bull Eng Geol Environ 75(2):821–839

    Article  Google Scholar 

  • Bouzeboudja H, Melbouci B, Bouzeboudja A (2018) Fractal dimension of roughness: influence of grain size and granular class. J Build Mater Struct 5(1):147–156

    Article  Google Scholar 

  • Bouzeboudja H, Melbouci B, Bouzeboudja A (2021) Experimental study of crushed granular materials by the notion of fractal dimension in 2D and 3D. Geotech Geol Eng. https://doi.org/10.1007/s10706-021-02007-3

    Article  Google Scholar 

  • Bowman ET, Soga K, Drummond W (2001) Particle shape characterisation using Fourier descriptor analysis. Géotechnique 51(6):545–554

    Article  Google Scholar 

  • Cai ZY, Li XM, Guan YF, Huang YH (2016) Particle breakage rules of rockfill materials. Chinese J Geotech Eng 38(05):923–929

  • Casini F, Viggiani GMB (2013) Breakage of an artificial crushable material under loading. Granular Matter 15(5):661–673

    Article  Google Scholar 

  • Chen Q, Peng W, Yu R (2021) Laboratory investigation on particle breakage characteristics of calcareous sands. Adv Civ Eng 2021(4):1–8

    Google Scholar 

  • Cheng L, Shahin MA, Cord-ruwisch R (2014) Bio-cementation of sandy soil using microbially induced carbonate precipitation for marine environments. Géotechnique 64(12):1010–1013

    Article  Google Scholar 

  • Clarke KC (1986) Computation of the fractal dimension of topographic surfaces using the triangular prism surface area method. Comput Geosci 12(5):713–722

    Article  Google Scholar 

  • de Bono JP, McDowell GR (2016) The fractal micro mechanics of normal compression. Comput Geotech 78:11–24

    Article  Google Scholar 

  • Donaldson CAMC (1995) Quantifying soil microstructure using fractals. Geotechnique 45(1):105–116

    Article  Google Scholar 

  • Einav I (2007) Breakage mechanics—part i: theory. J Mech Phys Solids 55(6):1274–1297

    Article  Google Scholar 

  • Eshghinezhad H, Shariatmadari N, Askari Lasaki B (2020) Influence of adding tire chips on the mechanical behavior of calcareous sands. Geotech Geol Eng 39:2147–2160

    Article  Google Scholar 

  • Etienne Guyon J (1994) Du Sac De Billes Au Tas De Sable. Nat Sci Soc (montrouge) 5(2):77

    Google Scholar 

  • Fan Z, Hu C, Zhu Q (2021) Three-dimensional pore characteristics and permeability properties of calcareous sand with different particle sizes. Bull Eng Geol Environ 80(3):2659–2670

    Article  Google Scholar 

  • Gang Wang ZWQY (2020) Particle breakage evolution of coral sand using triaxial compression test. J Rock Mech Geotech Eng 13(2):321–334

    Article  Google Scholar 

  • Hardin BO (1985) Crushing of Soil Particles. J Geotech Eng 111(10):1177–1192

    Article  Google Scholar 

  • Huang JY, Hu SS, Xu SL (2017) Fractal crushing of granular materials under confined compression at different strain rates. Int J Impact Eng 106:259–265

    Article  Google Scholar 

  • Jiabo Wang PFFM (2020) Experimental study of one-dimensional compression creep in crushed dry coral sand. Can Geotech J. https://doi.org/10.1139/cgj-2019-0406

    Article  Google Scholar 

  • Kuang D, Long Z, Guo R (2020) Experimental and numerical investigation on size effect on crushing behaviors of single calcareous sand particles. Mar Georesources & Geotechnol 1–11

  • Kuang D, Long Z, Guo R (2021) Experimental and numerical study on the fragmentation mechanism of a single calcareous sand particle under normal compression. Bull Eng Geol Environ 80(4):2875–2888

    Article  Google Scholar 

  • Kulatilake PHSW, Um J (1997) Requirements for accurate estimation of fractal parameters for self-affine roughness profiles using the line scaling method. Rock Mech Rock Eng 30(4):181–206

    Article  Google Scholar 

  • Lade PV, Yamamuro JA, Bopp PA (1996) Significance of particle crushing in granular materials. J Geotech Eng 122(4):309–316

  • Lee SD, Lee CI, Park Y (1997) Characterization of joint profiles and their roughness parameters. Int J Rock Mech Min Sci 34(3–4):171–174

  • Li HY, Chai HW, Xiao XH (2020) Fractal breakage of porous carbonate sand particles: microstructures and mechanisms. Powder Technol 363:112–121

    Article  Google Scholar 

  • Lin L, Li S, Sun L (2020) Evolution of particle size distribution for carbonate sand under impact load. Powder Technol 376:549–564

    Article  Google Scholar 

  • Li X, Liu J (2021) One-dimensional compression feature and particle crushability behavior of dry calcareous sand considering fine-grained soil content and relative compaction. Bull Eng Geol Environ 80(5):4049–4065

    Article  Google Scholar 

  • Linjian M, Li Z, Wang M (2018) Effects of size and loading rate on the mechanical properties of single coral particles. Powder Technol 342(15):961–971

  • Liu X, Li S, Sun L (2020) The study of dynamic properties of carbonate sand through a laboratory database. Bull Eng Geol Environ 79(7):3843–3855

    Article  Google Scholar 

  • Lv Y, Li X, Wang Y (2020) Particle breakage of calcareous sand at high strain rates. Powder Technol 366:776–787

    Article  Google Scholar 

  • Lv Y, Wang Y, Zuo D (2019) Effects of particle size on dynamic constitutive relation and energy absorption of calcareous sand. Powder Technol 356:21–30

    Article  Google Scholar 

  • Ma L, Li Z, Wang M, Wei H, Fan P (2019) Effects of size and loading rate on the mechanical properties of single coral particles. Powder Technol 342:961–971

    Article  Google Scholar 

  • Ma G, Zhou W, Zhang Y (2018) Fractal behavior and shape characteristics of fragments produced by the impact of quasi-brittle spheres. Powder Technol 325:498–509

    Article  Google Scholar 

  • Marsal RJ (1967) Large scale testing of rockfill materials. J Soil Mech Found Div 93(2):27–43

    Article  Google Scholar 

  • Miao G, Airey D (2013) Breakage and ultimate states for a carbonate sand. Géotechnique 63(14):1221–1229

    Article  Google Scholar 

  • Muir Wood D, Maeda K (2008) Changing grading of soil: effect on critical states. Acta Geotech 3(1):3–14

    Article  Google Scholar 

  • Nakata Y, Hyodo M, Hyde AFL (2001) Microscopic particle crushing of sand subjected to high pressure one-dimensional compression. Soils Found 41(1):69–82

    Article  Google Scholar 

  • Nie J, Cao Z, Li D (2021) 3D DEM insights into the effect of particle overall regularity on macro and micro mechanical behaviours of dense sands. Comput Geotech 132: 103965

  • Peleg S, Naor J, Hartley R (1984) Multiple resolution texture analysis and classification. IEEE Trans Pattern Anal Mach Intell PAMI-6(4):518–523

  • Perfect E (1997) Fractal models for the fragmentation of rocks and soils: a review. Eng Geol 48(3):185–198

    Article  Google Scholar 

  • Rasouli MR, Moradi M, Ghalandarzadeh A (2020) Effects of initial static shear stress orientation on cyclic behavior of calcareous sand. Mar Georesources Geotechnol 1–15

  • Rousé PC, Fannin RJ, Shuttle DA (2008) Influence of roundness on the void ratio and strength of uniform sand. Géotechnique 58(3):227–231

    Article  Google Scholar 

  • Rui S, Guo Z, Si T (2020) Effect of particle shape on the liquefaction resistance of calcareous sands. Soil Dyn Earthq Eng 137:106302

  • Russell DA, Hanson JD, Ott E (1980) Dimension of time in strange attractors. Phys Rev Lett 45(14):1175–1178

  • Salem M, Elmamlouk H, Agaiby S (2013) Static and cyclic behavior of north coast calcareous sand in Egypt. Soil Dyn Earthq Eng 55:83–91

    Article  Google Scholar 

  • Sandoval EA, Pando MA (2012) Experimental assessment of the liquefaction resistance of calcareous biogenous sands. Earth Sci Res J 16(1):55–63

    Google Scholar 

  • Shahnazari H, Rezvani R (2013) Effective parameters for the particle breakage of calcareous sands: an experimental study. Eng Geol 159:98–105

    Article  Google Scholar 

  • Shen Y, Zhu Y, Liu H (2018) Macro-meso effects of gradation and particle morphology on the compressibility characteristics of calcareous sand. Bull Eng Geol Environ 77(3):1047–1055

    Article  Google Scholar 

  • Shi J, Haegeman W, Cnudde V (2019) Anisotropic small-strain stiffness of calcareous sand affected by sample preparation, particle characteristic and gradation. Géotechnique 1–15

  • Souley TBH (1997) Fractal analysis of shear joint roughness. Int J Rock Mech Min Sci 34(3–4):130–131

    Google Scholar 

  • Sun Y, Nimbalkar S, Chen C (2019) Particle breakage of granular materials during sample preparation. J Rock Mech Geotech Eng 11(2):417–422

    Article  Google Scholar 

  • Tyler SW, Wheatcraft SW (1992) Fractal Scaling of soil particle-size distributions analysis and limitations. Soil Sci Soc Am J 56:362–369

    Article  Google Scholar 

  • Wang X, Cui J, Zhu C (2021) Experimental study of the mechanical behavior of calcareous sand under repeated loading-unloading. Bull Eng Geol Environ 80(4):3097–3113

    Article  Google Scholar 

  • Wang X, Wu Y, Cui J (2020) Shape characteristics of coral sand from the South China Sea. JMSE 8(10):803

    Article  Google Scholar 

  • Wang Y, Ma L, Wang M (2018) A creep constitutive model incorporating deformation mechanisms for crushable calcareous sand. Arabian J Geosci 11(20)

  • Xiao Y, Liu H, Chen Q (2017) Evolution of particle breakage and volumetric deformation of binary granular soils under impact load. Granul Matter 19(4)

  • Xiao Y, Long L, Evans TM  et al (2019) Effect of particle shape on stress-dilatancy responses of medium-dense sands. J Geotech Geoenviron Eng 145(2): 04018105. https://ascelibrary.org/doi/10.1061/(ASCE)GT.1943-5606.0001994

  • Xiao Y, Yuan Z, Lv Y (2018) Fractal crushing of carbonate and quartz sands along the specimen height under impact loading. Constr Build Mater 182:188–199

    Article  Google Scholar 

  • Xiao Y, Yuan Z, Lin J (2019) Effect of particle shape of glass beads on the strength and deformation of cemented sands. Acta Geotech 14(6):2123–2131

    Article  Google Scholar 

  • Xiao Y, Wang C, Wu H (2021) New simple breakage index for crushable granular soils. Int J Geomech 21(8):4021136

    Article  Google Scholar 

  • Xu D, Huang M, Zhou AY (2020a) One-dimensional compression behavior of calcareous sand and marine clay mixtures. Int J Geomech 20(9)

  • Xu Y, Ge J, Li H (2020b) Relationship between fractal dimension of fragmentation degree and energy dissipation of rock-like materials under initial stress. Shock Vib 2020:1–10

    Google Scholar 

  • Yang Xiao AWSJ (2019) Effect of particle shape on strength and stiffness of biocemented glass beads. J Geotech Geoenviron Eng 145(11):6019016

    Article  Google Scholar 

  • Yang G, Jiang Y, Nimbalkar S (2019) Influence of particle size distribution on the critical state of rockfill. Adv Civ Eng 2019:1–7

    Google Scholar 

  • Yang J, Luo XD (2015) Exploring the relationship between critical state and particle shape for granular materials. J Mech Phys Solids 84:196–213

    Article  Google Scholar 

  • Yang J, Wei LM (2012) Collapse of loose sand with the addition of fines: the role of particle shape. Géotechnique 62(12):1111–1125

    Article  Google Scholar 

  • Yu B, Li J (2011) Some fractal characters of porous media. Fractals 09(03):365–372

    Article  Google Scholar 

  • Yu D, Ye J, Yao L (2020) Prediction of the long-term settlement of the structures built on a reclaimed coral reef island: an aircraft runway. Bull Eng Geol Environ 79(9):4549–4564

    Article  Google Scholar 

  • Yu Q, Liu J, Patil UD (2019) Two-dimensional fractal model for ultimate crushing state of coarse aggregates. Fractals 27(07):1950109

    Article  Google Scholar 

  • Zeng L, Hong Z, Gao Y (2017) One-dimensional compression behaviour of reconstituted clays with and without humic acid. Appl Clay Sci 144:45–53

    Article  Google Scholar 

  • Zhang H, Luo Z, Qiu Y (2020) Experimental and mathematical modeling of monotonic behavior of calcareous sand. Adv Civ Eng 2020:1–14

    Google Scholar 

  • Zhang J, Li M, Liu Z (2017) Fractal characteristics of crushed particles of coal gangue under compaction. Powder Technol 305:12–18

    Article  Google Scholar 

  • Zhang S, Tong CX, Li X (2015) A new method for studying the evolution of particle breakage. Géotechnique 65(11):911–922

    Article  Google Scholar 

  • Zhang X, Hu W, Scaringi G (2018) Particle shape factors and fractal dimension after large shear strains in carbonate sand. Géotech Lett 8(1):73–79

    Article  Google Scholar 

  • Zheng B, Qi S, Luo G (2021) Characterization of discontinuity surface morphology based on 3D fractal dimension by integrating laser scanning with ArcGIS. Bull Eng Geol Environ 80(3):2261–2281

    Article  Google Scholar 

  • Zhi Ding SHYS (2021) Comparative study on cyclic behavior of marine calcareous sand and terrigenous siliceous sand for transportation infrastructure applications. Constr Build Mater (283):122740

  • Zhou B, Ku Q, Wang H (2020) Particle classification and intra-particle pore structure of carbonate sands. Eng Geol 279:105889

  • Zhou B, Wang J, Wang H (2014) A new probabilistic approach for predicting particle crushing in one-dimensional compression of granular soil. Soils Found 54(4):833–844

    Article  Google Scholar 

Download references

Funding

This work was funded by the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2020B1515120083), National Natural Science Foundation of China (Grant No. 42171130, 41731281), and Industry-Academia-Research Cooperation Program of Zhuhai City (ZH22017001200149PWC).

Author information

Authors and Affiliations

  1. School of Civil Engineering, Sun Yat-Sen University, Guangzhou, 510275, China

    Xue Li, Jiankun Liu & Jinze Li

  2. Southern Marine Science and Engineering Guangdong Laboratory, Zhuhai, 519082, China

    Jiankun Liu

Authors
  1. Xue Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiankun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jinze Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiankun Liu.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Additional information

The original online version of this article was revised: In Table 8, Chen et al. 2021 should be added in the caption. In the Eq. 18, the author name citation should be change to “Chen et al. 2021”.

Appendix

Appendix

Table 9 Standard deviation of sphericity (\({S}_{C}\)), aspect ratio (\({A}_{R}\)), convexity (\({C}_{X}\)), and overall regularity (\({O}_{R}\))
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, X., Liu, J. & Li, J. Fractal dimension, particle shape, and particle breakage analysis for calcareous sand. Bull Eng Geol Environ 81, 106 (2022). https://doi.org/10.1007/s10064-022-02585-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10064-022-02585-3

Keywords

Search

Navigation