Propagation Characteristics Of Stress Wave In A Rock With Variable Cross-sectional Areas Under Axial Static Stresses

The geometric morphology of the natural rock blocks is various,and they are inevitably subjected to geostress.In order to achieve the best rock-breaking effect and facilitate the stability analysis of surrounding rock in blasting construction,research on the stress wave propagation in a rock with variable cross-sectional areas under initial stress was conducted in this paper.Firstly,the effects of stress-induced elastic deformation of bars on the transmission coefficient for ladder bars and the propagation coefficient for bars with continuously variable cross-sections were analytically explored.The results show that the initial stress can enhance the ability of stress wave propagation in the variable cross-section bar.Variation ratio of cross-sectional area,elastic modulus and Poisson's ratio determines the initial deformation of bar,thus affects the stress wave propagation.Secondly,considering that the density,the dynamic elastic modulus and the longitudinal wave velocity of rock are all influenced by the initial stress,the stress wave propagation models for the ladder rock and the rock with continuously variable cross-sectional areas were established,respectively.The evolution laws of the transmission coefficient and the amplitude attenuation under different initial stress-induced deformation were studied.The results show that in the time and frequency domain,the characteristics of stress wave propagation in the rock with variable cross-sectional areas are remarkably influenced by the axial static load.With the increase in axial static load,the transmission coefficient of the ladder rock and the amplitude attenuation coefficient of the rock with variable cross-sectional areas decrease firstly,and then increase.The magnitude of amplitude attenuation coefficient and its spatial distribution are dependent on the axial static load,the geometric morphology and the variation ratio of cross-sectional area.Thirdly,the one-dimensional stress wave propagation experiments were carried out for red sandstone bars with linearly increasing cross-sectional areas under different axial static stresses.The characteristics of the waveform,the amplitude attenuation and the frequency dispersion in the red sandstone were investigated.And the qualitative comparison between experimental results and analytical results was also made.The results show that the higher the initial stress is,the sharper the falling edge of waveform is,and the higher the peak stress of unloading is.With the increase of initial stress,the amplitudes of the same measuring point decrease rapidly at first and then change slowly.With the increase of initial stress,the response amplitudes and the amplitude attenuation coefficients first decrease rapidly and then change slowly.The response amplitudes are not sensitive to the changing ratio of cross-sectional areas of red sandstone,while the changing ratio of the amplitude attenuation coefficient versus initial stress are positively correlated with the variation ratio of cross-sectional areas of red sandstone.In the frequency domain,with the increase of the initial stress,the frequency spectrums change from steep to gentle,and the amplitudes of waves with different frequencies also present the characteristics of rapid reduction to slow change.Furthermore,compared with that of higher-frequency wave,the amplitudes of waves with lower frequencies are easier to be affected by initial stress.Finally,based on the analytical,experimental and numerical simulation results,the mechanism of amplitude attenuation of stress wave in the rock with variable cross-sectional areas was explored.Under axial static load,the reasons for stress wave amplitude attenuation in a rock with variable cross-sectional areas includes geometric attenuation and physical attenuation.The geometric attenuation is almost unrelated with the initial stress and the magnitude of disturbance.The initial stress affects the physical attenuation in the rock,and the geometric characteristics of the rock determine the spatial distribution of initial stress and micro pores,and the initial stress determines the compaction degree of the rock pores,which is the essential factor determining the energy attenuation of the stress wave.The geometric characteristics and the initial stress are the direct causes of the variation of stress wave propagation law.