摘要
基于颗粒流理论,分别建立大尺度一维、二维颗粒流数值模型,研究低频动载应力波的传播规律。在一维颗粒链模型中,分别从震源激发方式、黏结模型、数值弥散、边界条件的角度系统地研究P波在数值模型中的传播规律,为模拟动载应力波在二维颗粒流模型中的传播提供了参考数据。大尺度一维颗粒链模型(6 400 m)研究结果表明:(1)雷克子波不存在高频角点,比正弦波更适合模拟波场震源;(2)当颗粒链模型采用接触黏结时,P波振幅随距离的增大而衰减,但波速基本不变,与理论值的相对误差为0.12%;(3)当颗粒链模型采用平行黏结时,P波波形产生强烈扭曲;(4)数值弥散分析表明,雷克子波峰值频率的增大和震中距的增大均会使弥散程度增大,但峰值频率的增大主要使波的振幅降低,震中距的增大使振幅和波速均降低。当频率f≤60.23 Hz,角频率?与波数k近似成线性关系,弥散现象可忽略;(5)边界条件分析表明,对于刚性边界,反射波与入射波的振幅大小相等,符号相反,边界处质点的位移等于0;对于自由边界,反射波与入射波的振幅完全相等,符号相同,边界处质点的振幅为入射波的2倍;对于吸收边界,反射波振幅比入射波相比大约减少了96.8%,能有效降低反射波的影响。根据以上结论,在大尺度二维六角形排列颗粒流模型(3 000 m?3 000 m)中,采用接触黏结模型,并施加吸收边界条件,分别探讨了P波和S波波阵面特征及波形与波速的变化,并定性地分析了远场条件下的场源效应。结果表明:(1)当在震源处施加集中力时,模型中出现由点震源激发的P波和S波。考虑到颗粒间的切向刚度为零,S波的存在说明颗粒几何排布对应力波在颗粒模型中的传播规律影响很大;(2)当震源频率一定时,震中距越大,P波和S波的振幅及波速均因弥散作用而降低,且S波弥散程度更大;(3)场源效应分析表明,在震源处施加集中力时,P波位移场在力的方向上幅值最大,在垂直于力的方向上无位移;S波位移场在垂直于力的方向上幅值最大,在力的方向上无位移。上述研究得到了应力波在大尺度一维、二维颗粒流模型中传播的规律,与理论分析结果较为吻合,对进一步模拟研究岩石的动态力学行为及其细观机制具有重要的参考价值。
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 w and wave number k 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.
出处
《岩石力学与工程学报》
EI
CAS
CSCD
北大核心
2016年第8期1555-1568,共14页
Chinese Journal of Rock Mechanics and Engineering
基金
科技北京百名领军人才培养工程(Z151100000315014)
国家自然科学基金资助项目(51074014
51174014)~~
关键词
岩石力学
颗粒流理论
动载
应力波
数值弥散
边界条件
集中力
场源效应
rock mechanics
particle flow theory
dynamic load
stress wave
numerical dispersion
boundary conditions
concentrated force
source effects
