Cumulative damage evolution rule of rock slope based on shaking table test using VMD-HT

Cumulative damage can be produced within the slope under multiple earthquakes, including frequent earthquakes in earthquake-prone areas, foreshocks, and aftershocks of an earthquake event, which have great potential to trigger landslides. Consequently, clarifying the cumulative damage evolution rule subject to multiple earthquakes are of significance in identifying landslides. A large-scale shaking-table test was performed on a rock slope to investigate the rule. First, variational mode decomposition and Hilbert transform methods (VMD-HT) were proposed to recognize and extract the natural frequency of the slope. Then, the damage coefficient based on the first natural frequencies of the slope before and after loading were established, and the cumulative damage evolution of the slope during the test were investigated. The results showed that the root mean square (RMS) amplification factor was mainly distributed at the steep structural surfaces and outlet of the weak interlayer, and the factor decreases significantly at first, and then becomes stable with the increase in intensity. In addition, the marginal spectrum exhibited multiple peaks with the increase in elevation. The first peak (IMF1) mainly included the input signal information, which gradually dominates with damage accumulation under multiple earthquakes. Meanwhile, the second and third peaks (IMF2 and IMF3) mainly reflected the first and second natural characteristics of the slope and were amplified significantly with an increase in elevation. Moreover, with damage accumulation, the natural frequency of the slope gradually decreased. A large damage coefficient was mainly distributed at the steep structural plane and outlet of the weak interlayer, and the failure of the slope in the test was a progressive process which increased slightly at first (slow growth stage), then increased greatly (rapid growth stage), and finally remained approximately the same (destruction stages). The proposed method can properly evaluate the damage degree of a slope under earthquakes, which is meaningful for slope stability analysis, landslide monitoring, and early warning works.