Study on dynamic mechanical properties of phosphate rock through experimental tests and mesoscale simulation


Dynamic characteristics of rock masses are an important part of the safety and stability analysis in rock mass engineering. The split Hopkinson pressure bar (SHPB) tests on the phosphate rock in Yichang are conducted, combined with the Split-desktop digital image method and mesoscopic discrete element method (DEM). Both macroscopic and mesoscopic characteristics of the phosphate rock have been studied from such perspectives as stress and strain, fractal characteristics of fragment size, and the spatial and temporal evolution of cracks. The research results show that the dynamic strength of the phosphate rock presents obvious strain rate effect, but the dynamic elasticity modulus is not so sensitive to the strain rate. There is a great correlation between the failure degree of rock specimens and the strain rate. The fractal characteristics of specimen fragments can be used to quantitatively evaluate the rock failure degree under impact loading. According to the characteristics of crack propagation, the rock failure process under the impact can be divided into four stages, namely the elastic crack-free stage, the crack initiation stage, the rapid crack growth stage, and the slow crack development stage. Moreover, with the increase of impact loading, micro-cracks are activated in large quantities. The specimens gradually change from the local damage mode to the axial splitting failure mode and to the crushing failure mode, and in this process, the number of tensile cracks takes an absolute advantage compared with the number of shear cracks.

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Acoustic emission


Computed tomography

D :

Fractal dimension


Discrete element method


Dynamic increase factor


Discrete fracture net


Particle flow code


Scanning electron microscopy


Split Hopkinson pressure bar

a :

The length of fragment

b :

The width of fragment

A :

The cross-sectional area of the contact

β :

The contributing factor of the moment

F n :

The real-time normal force on the contact

Fn :

Compressive strength

F s :

The real-time tangential force on the contact

Fs :

Tensile strength

I :

The moment of inertia of the contact cross section on the bond

J :

The polar moment of inertia of the contact cross-sectional area on the bond

M b :

The bending moment on the bond

M s :

The torque on the bond

N :

The number of fragments whose equivalent grain size is greater than Req

N 0 :

The number of fragments with maximum equivalent grain size Reqmax

\( N\left(\overline{\varepsilon}\right) \) :

The measured result on the scale \( \overline{\varepsilon} \)

R :

The radius of the bond

R eq :

Equivalent grain size

ε :

The strain

\( \dot{\varepsilon} \) :

The strain rate

\( \overline{\varepsilon} \) :

The scale

σ :

The stress

\( \overline{\sigma} \) :

The real-time normal stress

\( \overline{\tau} \) :

The real-time tangential stress


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The research was supported by the National Natural Science Foundation of China (No. 51609183), the National Natural Science Foundation of China (No. 51504176), and the Fundamental Research Funds for the Central Universities (No. 2017-YB-022).

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Correspondence to Gang Wang.

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Responsible Editor: Zeynal Abiddin Erguler

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Liu, X., Wang, G., Liu, T. et al. Study on dynamic mechanical properties of phosphate rock through experimental tests and mesoscale simulation. Arab J Geosci 13, 969 (2020).

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  • Rock dynamics
  • Phosphate rock
  • Split Hopkinson pressure bar
  • Fractal dimension
  • Mesoscopic particle flow discrete element