Vibration of viscoelastic rock slope with a filled structural plane caused by incident P-wave

The dynamic response characteristic of a rock slope is a crucial factor in analyzing the dynamic stability of rock mass, which is essentially a vibration problem caused by stress wave propagation. In theoretical studies of stress wave propagation, the slope model is often simplified, neglecting the vibration superposition effect due to multiple reflections between the slope surface and structural planes, as well as the attenuation of stress wave caused by viscoelasticity of rock mass. Based on the time domain recursive analysis method, the stress wave propagation analysis model was established for a viscoelastic rock slope with filled structural planes. This model incorporated quality factors of the stress wave and derived both the analytical equation for slope vibration and the expression for the slope amplification coefficient. Assuming the slope behaves as a Kelvin viscoelastic body, the normal deformation of the contact interface on the filled structural surface conforms to a nonlinear hyperbolic model, whereas the tangential deformation follows a linear model. The results indicate that, although multiple reflection waves in the rock mass amplify the slope's vibration effect, the viscoelastic properties of rock mass dampen this amplification, making it less significant. Furthermore, as both the slope inclination and the inclination of the filled structural plane increase, the slope amplification coefficient undergoes significant and nonlinear variations. As the coordinates of the monitoring points increase, the slope amplification coefficient initially undergoes abrupt fluctuations, gradually decreasing towards stability. Additionally, as the thickness of the filled structural surface increases, the slope amplification coefficient decreases progressively.