Effect of arc cracks in composite rock strata on ground vibration under SH wave

The existence of cracks complicates the scattering wave field in composite rock strata. The cracks not only affect the dynamic features of the site but also influence the displacement amplitude of the ground vibration. Therefore, it is of engineering significance to study the crack scattering in composite rock strata. Based on the function of complex variables (CVF) and big circle method, this paper constructs a series solution to the scattering wave field of the arc crack in composite rock strata. Specifically, a series of equations were established according to the continuous conditions of stress and displacement at the boundaries of the rock layer and the crack. Then, the model was solved by Fourier series and truncating finite terms, followed by the discussion of the calculation error. Through programming calculations, the authors analyzed the impact of two arc cracks in the “upper-hard and lower-soft” composite rock strata on the ground vibration under incident SH wave. The results show that the magnitude of ground displacement depends on the following factors: the medium parameters of the rock layer, the frequency of the incident wave, and the depth and direction of the cracks; compared with the lower rock layer, the surface rock layer can obviously amplify the amplitude of the ground displacement; with the growing frequency of the incident wave, the influence of horizontal and vertical cracks on the amplitude of the ground displacement first increased and then decreased; the shallower the crack, the greater the impact on ground displacement amplitude; the horizontal crack had a greater influence on the ground displacement amplitude than the vertical crack.