Energy analysis of living stumps slope based on Hilbert-Huang Transform and marginal spectrum

A large-scale shaking table model test on a slope with living stumps was designed and conducted. Under various types of seismic waves and excitation intensities, acceleration data from monitoring points on both sides of the living stumps were collected. Hilbert-Huang Transform (HHT) was innovatively applied to study the dynamic response of slopes with living stumps under seismic loading, overcoming the limitations of traditional Fourier Transform and Wavelet Transform. The variation patterns of Hilbert energy and marginal spectral characteristics under different seismic excitations were analyzed, providing new insights from both time-frequency domain and energy perspectives. The research conclusion showed that: (1) Under different seismic waves, the horizontal peak acceleration inside the living stumps slope shows the elevation amplification effect, and increases with the intensity of excitation. Additionally, the existence of living stumps causes a difference in horizontal acceleration on both sides, and the absolute value of the difference is positively correlated with elevation and excitation intensity. (2) Under different seismic waves, Peak of Hilbert energy spectrum (PSHEA) is positively correlated with excitation intensity and elevation. With the increase of elevation, the increase of PSHEA increases gradually when the excitation intensity increases. PMSA is positively correlated with excitation intensity, but at low frequencies (1-3 Hz), Peak of marginal spectrum (PMSA) is negatively correlated with elevation; while at high frequencies (7-11 Hz), PMSA is positively correlated with elevation. (3) With increasing elevation and excitation intensity, the total seismic Hilbert energy continues to accumulate and reaches the maximum at the top of the slope. During the propagation of seismic waves, the living stumps and the rock-soil composite play the characteristics of filtering the low-frequency components and amplifying the high-frequency components, causing the total seismic Hilbert energy in the low-frequency (1-3 Hz) component to gradually decrease and transfer to the high-frequency (7-11 Hz) component, resulting in a significant increase in seismic Hilbert energy in the high-frequency component. (4) The superposition of incident wave and reflected wave near the living stumps, and the absorption of seismic Hilbert energy by the living stumps make the PSHEA, PMSA, and total seismic Hilbert energy on the outside of the living stumps always smaller than the inside, resulting in different dynamic responses on either side of the living stumps. The living stumps show attenuation effect on seismic Hilbert energy, and the attenuation degree increases with the increase of excitation intensity and elevation. The study provides a theoretical basis for the seismic design of living stumps slopes.