# Study on the Steepness of Landslide-Induced Wave and Nonlinear Motion of Container Ships
## 4 The Propagation Law of Landslide-Induced Surges
### The Test Study of First Wave Height  
When a bank slope is unstable, the landslide body will slide into water at a high speed and exchange energy with the water body, and the water quality points in the free surface will implicate with each other. The water level in the river course will also fluctuate. Therefore, the movement of a landslide into water is a process of energy transfer, transformation, and dissipation. This paper explores the influence law of the volume amount of a landslide and the ratio of the thickness of a landslide to the height of the first wave, thus revealing the morphological characteristics of the initial movement of landslide surges.  
During the test, it was observed that the slide body was sliding at high speed and had instantaneous interaction with the water body. The landslide-induced surge expanded naturally in a fan shape. The propagation of the landslide-induced surge is mainly divided into two stages. The first stage is the occurrence stage of the landslide surge. In this stage, the wave parameters of the landslide surge change in a complex manner, and the regularity is not strong. This is related to the shape of the channel, the sliding speed of the landslide, and the property of the landslide. The second stage is the expansion and development stage of the landslide-induced surge. As the energy of the surge gradually decreases during its propagation, it gradually tends toward a stable state. The stable wave height is less than the maximum initial wave height, accompanied by certain obstruction and climbing phenomena.  
As can be seen in Figure 6, the free liquid level of the landslide presents a static state before entering the water. As the landslide body enters water at high speed, it generates a three-dimensional nonlinear landslide-induced surge, which occurs on one side of the bank and gradually spreads to the other side. The wave generation is messy, and the development process is complex and  
Figure 4: The schematic drawing of the experimental model.  
Figure 5: Comparison the free surface between Henrich and model at t = 1.0 s.  
random. The landslide-induced surge then reaches its peak in a very short time, with a steep peak and asymmetrical wave axis. Moreover, the first peak energy of the landslide-induced surge is relatively large. With the increase of time, the peak of the landslide-induced surge declines exponentially, the amplitude decreases, and the wavelength increases. The wave period gradually increases in the case of 1 m \(\times\) 1.5 m \(\times\) 0.4 m. In the others, the change of wave period is not obvious at the back of the curve.  
The comparison between Working Condition 4 and Working Condition 5 shows that, with the same test water depth and landslide inclination, the larger the landslide volume, the faster the landslide-induced surge propagation speed, and the shorter the propagation time required for the same distance. In other words, the peak value appeared first in Working Condition 5 compared with Working Condition 4, and the height of the first wave in Working Condition 5 was also higher than that in Working Condition 4.  
The comparison between Working Condition 2 and Working Condition 4 shows that, with the same landslide volume, the larger the ratio of width to thickness of the landslide, the larger the effective contact area between the landslide and water, the more sufficient the energy transfer, and the faster the landslide-induced surge propagation speed. That is, the peak appeared earlier in Working Condition 4, and the height of the first wave in this condition was higher than that in Working Condition 2.