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Structure, equipment, statue or storage cask may experience free-standing rocking on slopes because of the nonuniform settlement of the base, construction error or foundation failure. The free-standing rigid block on a slope subjected to one-sine pulse excitation and earthquake motions is examined in this paper. First, considering the free-standing rigid block on a slope, the overturning acceleration spectrum under one-sine pulse is built. The spectrum covers two overturning modes, i.e. overturning with one impact either before or after the excitation and overturning without impact. Then the influences of the slope on the overturning acceleration spectrum are discussed in depth. The analytical solution is compared with the numerical solution based on both linear and nonlinear formulations. It reveals that the safe region of the minimum overturning acceleration spectrum between mode 1 and mode 2 depends on the angle of the slope. Further, the block on a slope is subjected to the Tianjin, Kobe and Northbridge earthquake motions. By simplifying the main pulse of the motions to one-sine pulse, although the overturning acceleration spectrum fails to predict the overturning acceleration of the block subjected to real earthquake motions, it can provide some guidelines to predict the practical performance of the rocking structures.

This study investigated the applicability of a nonlinear analysis method that considers progressive failure to evaluating the stability of rock slopes, including post-earthquake residual displacement. The vibration step of the nonlinear analysis, which begins after residual displacement occurs, was found to match that of a dynamic centrifugal model test. The nonlinear analysis was concluded to be relatively conservative because it calculated a slightly larger residual displacement than that observed during the model test. A real-scale soft rock slope was analyzed, and the results showed that the proposed analysis method is useful for evaluating slope seismic stability, including post-earthquake residual displacements.

A series of shaking table tests were conducted on reinforced slopes to study the slope dynamic characteristics. The influence of concrete-canvas tilt degrees on the seismic response was studied. By considering the effects of different concrete-canvas tilt degrees, the seismic responses of the reinforced slopes were analyzed, along with the accelerations, crest settlements, and horizontal displacements. The failure patterns of different model slopes were compared using white coral sand marks placed at designated elevations to monitor the internal slide of the reinforced slopes. Several round markers were placed on the slope surface to compare the deformation before and after shaking with different amplitudes. The results indicated that with the increase in concrete-canvas tilt degrees, a better reinforcing effect was obtained, and 30^° reinforcement reached a threshold level, the slide-out point shifts from the crest of the slope to the middle of the reinforced model. The bottom 2/7th zone of the slope was relatively stable during the earthquake and the reinforcement was ineffective at the bottom of the slope. When both considered the influence of reinforcing effect and construction difficulty, 20^° is the suitable tilt degree in concrete-canvas reinforced slopes. The characteristics of increasing strength of the concrete canvas make it suitable for the application in slope protection.

An experimental study was carried out to investigate the tsunami surge impacts on small balls climbing on different slopes. Dam-break flows were generated in a flume to simulate tsunami surge. The water surface profiles at the sluice gate were observed, the tsunami inundation height and the surge velocity in the flume were measured, and the maximum climbing heights of small balls on different slopes were recorded. Results show that the dam-break speed and the tsunami surge strength increase with increasing reservoir water level. The increasing tsunami inundation height, the decreasing ball density, and the decreasing ball diameter have positive effects on the maximum ball climbing height. Based on the normalized experimental data, equations for estimating the maximum ball climbing heights on different slopes were proposed as functions of the inundation height, the ball diameter, and the ball density. The calculated values from the equation are generally within $\pm 20$% of the measured values in the experimental ranges.