Abstract
The shape of granular materials is one of the effective parameters in determining mechanical behavior. This property affects the fracture strength, compressibility, maximum friction angle and the distribution of contact stresses. So far, laboratory studies on the effect of shape on the behavior of granular materials have focused mostly on comparing the results of angular and rounded grains. Due to the distribution of different shapes in natural grain materials, experimental studies of the effect of sphericity index are of great importance. On the other hand, it is necessary to investigate the grain shape on the compression model parameters comprehensively. Therefore, based on the energy conservation equation and the use of statistical Weibull and fractal theory, the compressibility model of granular materials under uniaxial loading conditions is obtained by taking into account the quantitative parameters related to the shape of grain. Then, in order to evaluate the analytical model, three stages of laboratory tests are performed. In the first stage, uniaxial loading tests are performed on four different shapes of concrete grains of the same size under the same conditions. In the second stage, similar experiments are performed on angular granite grains to check the applicability of the model to natural materials with different shapes. In the third stage, the sleeper loading modeling is performed on granite grains of real ballast dimensions. The results of large-scale tests are compared with the compressibility model obtained from the results of small-scale tests. Finally, an empirical relationship is proposed to determine the amount of breakage factor based on the energy applied to the grains. The results show that the empirical relationship in combination with the analytical solution can accurately predict the stress-breakage-void ratio behavior of granular materials at each loading step.
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Abbreviations
- BH :
-
Hardin breakage factor
- c :
-
Convexity coefficient
- D :
-
Fractal dimension
- d :
-
Grain diameter
- dmin :
-
Smallest grain size
- dmax :
-
Largest grain size
- d0 :
-
Average of grain diameters
- ds :
-
Change of surfaces created in grains due to breakage
- e :
-
Void ratio
- E :
-
Applied energy per unit volume
- E 50 :
-
Elasticity modulus
- K 0 :
-
Horizontal stress coefficient due to vertical stress
- M :
-
Coefficient of grain friction
- m :
-
Weibull modulus
- n d :
-
Geometric similarity
- P s :
-
Survival probability
- P’ :
-
Isotropic stress
- q :
-
Deviatoric stress
- S :
-
Sphericity index
- S 0 :
-
Sum of side surfaces of grains
- V s :
-
Volume of grains
- α :
-
Coefficient of grain strength
- β :
-
Coefficient of grain geometry
- \({\beta }_{s}\) :
-
Surface shape factor
- \({\beta }_{v}\) :
-
Volume shape factor
- \(\Gamma\) :
-
Surface-free energy
- \(\delta {\varepsilon }_{q}^{P}\) :
-
Plastic shear strain increment
- \(\delta {\varepsilon }_{v}^{P}\) :
-
Plastic volumetric strain increment
- \(\delta {e}^{P}\) :
-
Plastic void ratio increment
- \(\mu\) :
-
Coefficient of grain friction
- \(\upsigma\) :
-
Induced tensile stress
- \({\sigma }_{y}\) :
-
Stress corresponding to point with the greatest curvature in the e-log σ plot
- \({\sigma }_{0}\) :
-
Characteristic stress
- \({\sigma }_{a}\) :
-
Vertical stress
- \(\phi\) :
-
Angle of internal friction
- \(\Psi\) :
-
State parameter
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This study was supported by the research grant of the Sahand University of Technology (SUT) (GN. 30.13766).
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Gorbanpoor, V., Emami Tabrizi, M. & Afshin, H. Experimental investigation of the shape effect on the mechanical behavior of granular materials under uniaxial loading with lateral confinement. Bull Eng Geol Environ 81, 292 (2022). https://doi.org/10.1007/s10064-022-02751-7
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DOI: https://doi.org/10.1007/s10064-022-02751-7