岩石动力学计算中的网格效应及机理研究

岩石动力学计算中，网格尺寸对数值计算结果的可靠性有重要影响。采用数值实验的方法，对岩石爆炸应力波传播数值计算中的网格尺寸效应及其敏感性机理进行了研究。研究结果表明：合适的网格尺寸要根据载荷特征和波传播介质的属性来决定；当一个载荷波长内的网格数达到16个以上时，计算得到的各物理量的波形和峰值基本趋于稳定；计算还给出了各物理量与网格密度的关系；随着爆心距的增加，物理量对网格尺寸的敏感性降低，其机理是载荷中的高频成分逐渐衰减、载荷的波长变大，模型所需的网格尺寸变大；时间步长系数对计算结果的影响也非常明显，当时间步长系数取0.05时，位移稳态值趋于收敛值。

Mesh Size Effect and Its Mechanism Research in Numerical Calculation of Rock Dynamics

In rock dynamics calculation, the mesh size has an important influence on the reliability of numerically calculated results. A numerical experimental method is used to research the mesh size effect and its sensitivity mechanism in the numerical simulation of propagation of explosion stress wave in rock. The research results show that a proper mesh size should be specified both by the load characteristics and the property of wave propagation medium. When the number of mesh is up to 16 within one load wavelength, the waveforms and peak values of all calculated physical quantities trend to be stable.The relationships between the values of physical quantities and the different mesh densities are also presented. With the increase in distance from explosive source, the sensitivity of physical quantities to mesh size decreases. This is because high-frequency components attenuate gradually, and the wavelength of load becomes longer with the increase in distance from explosive source. The time step coefficient also has a great influence on computational results. When the time step coefficient equals to 0.05, the stable value of displacement tends to converge.