| Landslides falling into reservoirs generate impulsive waves which can cause hazard due to run-up along the shoreline and overtopping of dams. The impulsive waves result severe threat to coastal life, property and navigation. The result can even be worse. Calculation of the wave height is critical. Then the propagation law can be analyzed to evaluate the hazard. The influence factors of the wave height are complicated. Basing on assumptions, studies about the height calculation and propagation law have been performed. Most of them are simplyfied. The most important point is that the present research derives from unidirectional flow, which has sharp difference with the actual conditions. The empirical parameters can always result inaccuracy or errors. Therefor, laboratory model tests are appropriated ways to analyze the mechanism and propagation laws of landslides generated waves. It is theoretical and practical significant for the hazard prediction.Firstly, the influence factors of reservoir landslide deformation and failure are discussed. The velocity calculation is modified basing on considering water resistance. The characteristics of impulsive waves are analyzed basing on wave mechanics and hydraulics. Then, the present methods and their applicability are summarized from assumption conditions, boundary conditions and experimental conditions. The calculation method of propagation wave is modified according to wave transformation. Finally, taking the channel near Bai Shuihe landslide as a prototype, a three-dimensional laboratory model has been built basing on similarity criterion. The mechanism and propagation laws of impulsive waves are studied according to laboratory tests. Taking Da Yantang landslide as an example, the velocity and initial wave height are calculated by modified methods.Basing on the research, it is concluded as follows.1. Mechanism of the impulsive waves(1) The impulsive waves are the deformation of water caused by the moving landslide. On the other hand, it is a phenomenon of vibration and deformation of water particles. Therefore, it is superposition of oscillatory waves and transferring waves. Whatever, the wave height is always affected by water depth. It belongs to nonlinear shallow water wave. (2) The formation progress is observed during the model tests. The water runs up along the penetrating landslides forming a crest on the shoulder. The crest collapses after it reaches its maximum height. The collapsing in water results a positive and negative leading wave. The run-up of the wave on inclined ramp and the subsequent run-down forms the secondary wave system. The amplitude of the waves is lower than the fist wave crest.(3) Basing on the analysis of test phenomenon and present research, it is concluded that the initial wave height is the deformation of water body caused by falling landslides. When the crest forms on the landslide shoulder, reaching to its maximum height, it is the initial maximum wave height. However, when there is no crest on the shoulder, the maximum wave height is the maximum wave amplitude of wave systems. It can be the first wave and the others. It depends on the Froude number wether the crest forms on the shoulder.(4) The impulsive waves are composed with volume and impulsive waves. They exist simultaneously, but different from proportion. The volume waves are dominant during the initial stage. The horizontal motion contributes to impulsive waves. However, the vertical motion contributes to volume waves. The vertical velocity determines the water volume expelled during unit time. The wave height increases with the inclination of slide surface with other factors are the same.2. Characteristics of calculation methods(1) Most of the research derives from unidirectional flow, which has sharp difference with the actual conditions. When the impulsive waves have been generated, they propagate to opposite bank firstly, and to upstream and downstream, with dispersion and attenuation.(2) Pan Jiazeng assumed that the waves are linear superposition of several solitary-like waves. The wave properties should be distinguished by criterion advised by Fritz. The wave height varies with propagation because of the reflection and dispersion. It is included that linear superposition is unreasonable.(3) Noda and Pan Jiazeng methods are related with slide velocity and water depth, without considering landslide scale. When the water is deep, the calculation results are unreasonable because of the limited effective depth of landslide.(4) The waves generated in the first, second and fourth tests are oscillatory waves. However, the third, fifth, sixth, seventh are nonlinear transition waves. The initial maximum wave is replaced by stable wave calculated by kamphuis method. It indicates that the calculation results are consistent with tests value.(5) Basing on considering the inclination of slide surface and motion time under water, the Ashtiani method includes comprehensive influence factors. The tests conditions are similar to tests herein. The results calculated by Ashtiani method are consistent with tests value.(6) The wave heights calculated by Fritz and Slingerland methods are relatively low. The main reasons are the landslide model is deformable, which will result in energy loss during the motion of landslide. The Slingerland method is applicable when the water depth is shallow. Basing on orthogonal experiment analysis, the sensitivity interval for water depth is varies from 5m to 30m.(7) Most of the tests were performed in a rectangular channel model, without considering the variation of water depth, channel direction and width. All of the bank angles are 90°. Shallow water dispersion and reflection are neglected, and it will cause inaccuracy.3. Sensitivity of wave influence factorsBasing on variance analysis of orthogonal experiment, it is included that the sensitivity order is water depth, slide velocity, length and thickness. Those factors should be considered during prediction.4. Propagation laws(1) The propagation waves are composed with several wave systems, with transmission and superposition. The leading wave attenuation is faster, with low height to opposite bank. The propagation waves forms because of the reflection on the ramp and superposition of waves.(2) The wave height decreases with propagation distance. The attenuation is divided into two stages, and the first is faster.5. Modification of Calculation methods of velocity and impulsive waves(1) On the basis of considering water resistance, the advised and motion equation methods are modified. Da Yantang landslide is used as an example. It is concluded that the acceleration decreases firstly and increases later because of the variation of water resistance. The landslide velocity firstly increases and decreases later.(2) The modified Pan Jiazheng method is used to calculate the maximum wave height. It is concluded that the initial maximum wave height calculated by modified method and Kamphis J.W method are close, which are consistent with actual condition.(3) On the basis of considering shallow water dispersion and energy loss caused by reflection, the Pan Jiazheng method of propagation is modified. It indicates that the propagation and climbing waves calculated by modified method are consistent with investigation, and the attenuation law is the same. |
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