Abstract
Calcareous sand (CS) is a special geomaterial that is susceptible to particle breakage. In order to clarify the effects of coarse-particle content (CC) and impact energy (Eb) on CS particle breakage, multiple impact tests were conducted on CS, and fractal dimension (α) and relative breakage ratio (Br) were introduced to quantitatively assess the CS particle breakage under varying conditions. According to the results, (I) the CS particle breakage during impact testing caused an increase in α. (II) The ultimate fractal dimension for CS under impact loading ranged from 2.16 to 2.73 and was only related to its initial fractal dimension. (III) A mathematical model capable of predicting the α of CS according to its initial median particle size and Eb was built, and the rationality of this model was validated. (IV) The Br of CS increased following a logarithm function with increasing CC and a hyperbolic function with increasing Eb. (V) The relationship between α and Br was established for CS under impact loading. These results can provide a theoretical basis for further research on the influence of particle breakage on strength parameters of CS under impact loading.
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Abbreviations
- CS:
-
Calcareous sand
- CC :
-
Coarse-particle content (unit: %)
- E b :
-
Impact energy (Unit: KJ)
- α :
-
Fractal dimension
- Br :
-
Relative breakage ratio
- Δα :
-
Fractal dimension increment
- α u :
-
Ultimate fractal dimension
- α 0 :
-
Initial fractal dimension
- d 50 :
-
Initial median particle size (unit: mm)
- a 1 :
-
Parameter related to material properties
- b 1 :
-
Parameter related to material properties
- a 2 :
-
Parameter related to material properties
- b 2 :
-
Parameter related to material properties
- c 2 :
-
Parameter related to material properties
- a 3 :
-
Parameter related to material properties
- b 3 :
-
Parameter related to material properties
- c 3 :
-
Parameter related to material properties
- Gs :
-
Specific gravity
- e max :
-
Maximum void ratio
- e min :
-
Minimum void ratio
- ρ dmax :
-
Maximum dry density (unit: g/cm3)
- ρ dmin :
-
Minimum dry density (unit: g/cm3)
- d 10 :
-
Diameter that corresponds to an 10% finer in the particle size distribution curve (unit: mm)
- d 30 :
-
Diameter that corresponds to an 30% finer in the particle size distribution curve (unit: mm)
- d 60 :
-
Diameter that corresponds to an 60% finer in the particle size distribution curve (unit: mm)
- C u :
-
Nonuniformity coefficient
- C c :
-
Curvature coefficient
- ω :
-
Hammering frequency (unit: blows/min)
- t :
-
Hammering time (unit: min)
- M :
-
Mass of the driving hammer (unit: kg)
- g :
-
Gravitational acceleration (unit: m/s2)
- h :
-
Falling height of the driving hammer (Unit: m)
- m :
-
Sample mass (unit: g)
- n :
-
Numbers of sample loading
- PSDC:
-
Particle size distribution curve
- V :
-
Sample volume (unit: cm3)
- S :
-
Sample area (unit: cm2)
- d :
-
Particle size (unit: mm)
- N :
-
Particle number
- N(d > d i):
-
Number of particles above di in size
- C :
-
Fitting parameter
- P :
-
Mass percentage of particles less than di in size
- m(d < d i):
-
Mass of particles less than di in size (unit: g)
- d max :
-
Maximum particle size (unit: mm)
- PSFC:
-
Particle size fractal curve
- R 2 :
-
Correlation coefficient
- a 4 :
-
Fitting parameter
- b 4 :
-
Fitting parameter
- a 5 :
-
Fitting parameter
- b 5 :
-
Fitting parameter
- k 1 :
-
Fitting parameter
- m 1 :
-
Fitting parameter
- k 2 :
-
Fitting parameter
- m 2 :
-
Fitting parameter
- k 3 :
-
Fitting parameter
- m 3 :
-
Fitting parameter
- n 3 :
-
Fitting parameter
- l 3 :
-
Fitting parameter
- B t :
-
Total breakage
- B p :
-
Breakage potential
- p 1 :
-
Fitting parameter
- p 2 :
-
Fitting parameter
- p 3 :
-
Fitting parameter
- p 4 :
-
Fitting parameter
- δ 1 :
-
Fitting parameter
- δ 2 :
-
Fitting parameter
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Funding
This research was funded by the National Key Research and Development Program of China (No. 2017YFC1500400), the Major International (Regional) Joint Research Project (No. 52020105002), the China Postdoctoral Science Foundation (Nos. 2020M682653 & 2021T140142), and the Guangdong Basic and Applied Basic Research Foundation (No. 2020A1515110663).
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Wang, X., Cui, J., Shen, JH. et al. Particle breakage behavior of a foundation filling material on island-reefs in the South China Sea under impact loading. Bull Eng Geol Environ 81, 345 (2022). https://doi.org/10.1007/s10064-022-02844-3
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DOI: https://doi.org/10.1007/s10064-022-02844-3