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| Stress wave propagation under low frequency dynamic loading and simulation method with particle flow code#br# |
| ZHANG Shihuai，WU Shunchuan，CHEN Zijian |
(Key Laboratory of Ministry of Education for Efficient Mining and Safety of Metal Mine，University of Science and Technology，Beijing 100083，China)
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Abstract 1D and 2D particle flow numerical models were generated respectively based on the particle flow theory in order to study the stress wave propagation induced by the low frequency dynamic loading. Firstly，P wave propagation in the 1D particle string models were studied systematically from several aspects including the excitation types of source，bond model types，numerical dispersion effects and boundary conditions，which provided the reference data for simulating the propagation of stress wave in 2D particle flow model. The simulation results of large-scale 1D particle string model(6 400 m) indicate that it is better to choose the Ricker wavelet than the sine wave as the seismic source of wave field，because the Ricker wavelet has no high frequency corners；For the particle string model with contact bond，the amplitude of P wave decreased with the distance from source，but the velocity was almost constant，with the relative error of 0.12% compared with the theoretical result. For the particle string model with parallel bond，the waveform of P wave distorted intensely. Numerical results of the effects of dispersion increased with the dominant frequency of Ricker wavelet as well as distance from source. However，the wave frequency mainly reduced the amplitude，but the distance from source reduced both the amplitude and velocity. What?s more，for frequency f≤60.23 Hz，the relationship between the angular frequency and wave number is almost linear，and the dispersion in models is negligible. For the rigid boundary，the amplitude of reflected wave is identical to the incident wave and opposite in sign，and the displacement at the boundary is zero；For the free boundary，the amplitude of reflected wave is identical to the incident wave，and the amplitude at the boundary is twice that of the incident wave；For absorbing boundary，the amplitude of reflected wave was reduced about 96.8% relative to the incident wave，indicating that it the impact of reflected wave was reduced effectively. According to the above conclusions，the contact bond model was adopted and the absorbing boundary was applied in the large-scale 2D hexagonally packed particle flow model(3 000 m 3 000 m). The characteristics of P and S-wave front，waveform and wave velocity variations were analysed in details. When a concentrated force is applied to the source，there exists P wave and S wave excited by the point source in the model. The presence of S wave proves that geometrical arrangement of particles in the model has a tremendous influence on the propagation of stress wave. When the frequency of the source is constant，the amplitude and velocity of P wave and S wave decrease with the increase of the distance from source due to dispersion，and the dispersive effects of S wave are greater. When a concentrated force is applied to the source，the amplitude of P wave displacement field reaches a maximum along and zero perpendicular to the axis of the applied force，while the amplitude of S wave displacement field reaches zero along and maximum perpendicular to the axis of the applied force.
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| Cite this article: |
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ZHANG Shihuai,WU Shunchuan,CHEN Zijian. Stress wave propagation under low frequency dynamic loading and simulation method with particle flow code#br#[J]. , 2016, 35(8): 1555-1568.
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| URL: |
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http://www.rockmech.org/EN/Y2016/V35/I8/1555 |
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2016, Vol. 35 
