Theoretical study on the propagation characteristics of P-wave in oblique joints rock mass
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摘要: 为了探究非线性斜交节理岩体中纵波的传播特性，采用理论分析、对比验证、数值计算相结合的方法，首先引用双曲线本构模型，基于应力波与线性单节理的交互作用关系，根据叠加原理推导纵波入射非线性斜交节理的传播方程，其次依据文献的入射纵波参数与节理岩体条件，计算透反射系数发现结果非常接近，验证理论模型是准确可行的，然后选取δ函数的辅助函数作为入射纵波，参数分析波形、持时以及节理刚度对斜交节理岩体中纵波传播特性的影响规律。研究结果表明：δ函数的辅助函数入射斜交节理时具有明显地幅值降低、幅值时刻滞后以及持时延长的现象，更能体现纵波短时内的突变特性和非线性衰减特征；入射纵波持时的增加会明显提高P波的透射性能，稍微降低P波和S波的反射特性；随着节理初始法向刚度和切向刚度的增加，S波反射系数呈下凹曲面型衰减，P波透射系数呈上凸曲面型递增，P波的透射性能与节理法向刚度相关性密切，S波的反射特性受斜交节理中第2条节理影响显著。研究成果有益于开展天然节理岩体的力学特性和动力响应研究。Abstract: In order to investigate the propagation characteristics of P-wave in nonlinear oblique joints rock mass, a comprehensive approach integrating theoretical analysis, comparative validation and numerical calculation was employed. Initially, the hyperbolic joint constitutive model featuring normal nonlinear deformation and tangential linear deformation was presented. Based on the interaction relationship between stress waves and a linear single joint, the propagation equation for P-wave incident on oblique joints was derived according to superposition principle. Then, by using the parameters of the incident P-wave and the conditions of jointed rock mass reported in literature, the transmission and reflection coefficients were calculated and found to be in close agreement, verifying the accuracy and feasibility of the theoretical model. Furthermore, the auxiliary function of δ function was selected as the incident P-wave to analyze the influence rule of waveform, duration and joint stiffness on the propagation characteristics of P-wave in oblique joints rock mass through parameter study. The results demonstrated that the phenomenon of amplitude reduction, amplitude-time delay and duration extension is pronounced when the auxiliary function of δ function incident on oblique joints, which can better reflect the abrupt change characteristics and nonlinear attenuation behavior of P-wave in a short time. The duration of the incident P-wave in oblique joints rock mass can significantly enhance the transmission performance of P-wave and slightly reduce the reflection characteristics of P-wave and S-wave. As the initial normal stiffness and the shear stiffness of joint increase, the reflection coefficient of S-wave decays in a concave surface shape, while the transmission coefficient of P-wave increases in a convex shape. The transmission performance of P-wave is closely related to the normal stiffness of joints, whereas the reflection characteristics of S-waves are significantly influenced by the second joint in the oblique joints. These research findings offer valuable insights into the mechanical properties and dynamic response of natural jointed rock mass.
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图 1 应力波入射线性节理的传播模型
Figure 1. Propagation model of stress wave incident on linear joint
图 4 纵波入射非线性斜交节理的传播模型
Figure 4. Propagation model of P-wave incident on nonlinear oblique joints
图 5 验证纵波入射非线性斜交节理传播模型
Figure 5. Verification for the propagation model of P-wave incident on nonlinear oblique joints
图 6 不同入射波波形下横波全反射时反射波和透射波
Figure 6. Transmitted and reflected waves of S-wave total reflection under different incidence wave waveforms
图 7 不同入射波波形下反射波和透射波
Figure 7. Transmitted and reflected waves under different incidence wave waveforms
图 8 δ函数的辅助函数的持时对反射系数和透射系数的影响规律
Figure 8. Transmission and Reflection coefficients versus duration for auxiliary function of δ function
图 9 节理特性相同时kn0对反射系数和透射系数的影响规律
Figure 9. Transmission and Reflection coefficients versus kn0 for same joint characteristics
图 10 节理特性相同时ks对反射系数和透射系数的影响规律
Figure 10. Transmission and Reflection coefficients versus ks for same joint characteristics
图 11 节理特性相同时刚度对反射系数和透射系数的影响规律
Figure 11. Transmission and Reflection coefficients versus stiffness for same joint characteristics
图 12 节理特性不同时kn0对反射系数和透射系数的影响规律
Figure 12. Transmission and Reflection coefficients versus kn0 for different joint characteristics
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