<p>The macroscopic mechanical characteristics of a material can be influenced by the complex microstructural interactions within the medium, which trigger scale effects and deformation localization. The impact of these microstructural interactions on seismic wave propagation can be described by the higher-order derivatives of state variables and the scale parameter related to the microstructural properties of the material, as outlined in the second-order strain gradient (SSG) theory. Research shows that microstructural interactions cause new perturbations to emerge in the P- and S-wavefields. Rayleigh waves, which propagate near the surface, are generated by the interference of P- and S-waves, and their dispersive characteristics can provide notable insights into the shallow geological structure. Therefore, investigating the propagation characteristics of seismic waves, particularly the scale effects of Rayleigh waves, under the SSG theory, is necessary. This study first introduces the nonlocal effects into the constitutive relationship of the conventional wave equations, derives expressions for the nonlocal strain/stress, and formulates the generalized wave equations under the SSG theory. Then, the study presents the free-surface conditions for the generalized wave equations and conducts numerical experiments to explore the scale effects on the propagation of surface and body waves. Results of these numerical experiments show that the heterogeneity introduced by the complex microstructural properties within the medium leads to observable scale effects in the propagation of P-, S-, and Rayleigh waves. Moreover, the dispersive characteristics of Rayleigh waves are modified when considering the nonlocal strain gradient effects, which are dependent on frequency and scale parameters.</p>

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Characteristic analysis of seismic wave propagation at the free surface under the second-order strain gradient theory

  • Chao-pu Chen,
  • Wen-lei Bai,
  • Hong Liu,
  • You-ming Li,
  • Zhi-yang Wang

摘要

The macroscopic mechanical characteristics of a material can be influenced by the complex microstructural interactions within the medium, which trigger scale effects and deformation localization. The impact of these microstructural interactions on seismic wave propagation can be described by the higher-order derivatives of state variables and the scale parameter related to the microstructural properties of the material, as outlined in the second-order strain gradient (SSG) theory. Research shows that microstructural interactions cause new perturbations to emerge in the P- and S-wavefields. Rayleigh waves, which propagate near the surface, are generated by the interference of P- and S-waves, and their dispersive characteristics can provide notable insights into the shallow geological structure. Therefore, investigating the propagation characteristics of seismic waves, particularly the scale effects of Rayleigh waves, under the SSG theory, is necessary. This study first introduces the nonlocal effects into the constitutive relationship of the conventional wave equations, derives expressions for the nonlocal strain/stress, and formulates the generalized wave equations under the SSG theory. Then, the study presents the free-surface conditions for the generalized wave equations and conducts numerical experiments to explore the scale effects on the propagation of surface and body waves. Results of these numerical experiments show that the heterogeneity introduced by the complex microstructural properties within the medium leads to observable scale effects in the propagation of P-, S-, and Rayleigh waves. Moreover, the dispersive characteristics of Rayleigh waves are modified when considering the nonlocal strain gradient effects, which are dependent on frequency and scale parameters.