库岸滑坡涌浪计算方法及物理模拟试验研究
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摘要
涌浪是伴随库岸滑坡而产生的一种次生灾害,滑坡高速入水激起巨大的涌浪,严重威胁库区水力工程、航行船只及沿岸居民的生命财产安全,往往带来比滑坡灾害本身更大的灾难。涌浪研究的关键是预测涌浪高度,分析其传播规律,进而才能评价涌浪对承灾体的危害。影响库岸滑坡涌浪的因素十分复杂,目前国内外对于涌浪高度的计算、传播规律分析已有初步研究,大部分计算方法都基于一定的假设条件,大大简化了涌浪的影响因素,计算模型过于理想化,都是基于单向流研究,与实际情况不符,计算参数的选取也大都根据经验而定,所得结果通常与实际值有较大出入。因此,通过物理模拟试验深入分析涌浪形成机制、探讨涌浪传播特点、验证并分析现有理论公式的适用性,对库区涌浪预测预报工作具有重要的理论和实践意义。
本论文在分析库岸滑坡变形破坏影响因素的基础上,介绍了滑坡速度计算方法,在考虑水阻力的基础上,对速度计算公式进行修正,并从波浪力学、水力学角度,分析了库岸滑坡涌浪的物理性质；从假设条件、边界条件及试验条件等方面总结了国内外现有涌浪计算方法,对比分析了各个方法的适用条件,从波浪变形的角度修正了传播浪相关计算公式；针对国内外模型试验中河道模型简化、单向流问题及考虑因素不全面的问题,本论文在遵守相似准则的前提下,以1：200的比例尺,建立了三峡库区白水河滑坡处4km河道的三维模型,合理布设相关测量仪器及数据采集设备,通过室内多组模型试验,测定了最大涌浪及传播浪高度,深入分析滑坡涌浪形成机制、涌浪形态特点,探讨了滑坡传播规律,并依次分析了各方法的适用特点；以水布垭库区大堰塘滑坡为计算实例,采用修正后的速度、涌浪计算公式,分别计算和分析了滑坡运动过程、涌浪高度及传播规律。
经过以上研究,论文得出以下几个方面的结论：
1.涌浪形成机制及性质
(1)从宏观角度来讲,涌浪的产生是由于一定体积的滑坡在以一定的速度扰动水体变形而产生。从波浪力学的角度来讲,滑坡涌浪产生时,既有水质点上下振动,也有水质点前后移动,属于振荡波和推移波叠加情况。此外涌浪波高受水深的影响,大部分情况下,滑坡涌浪的波形属于浅水非线性波研究范畴。
(2)通过试验分析,滑坡涌浪的形成过程为：水体在滑坡的的作用下沿前缘上爬而形成一个波峰,随着滑坡的运动,波峰达到最高直至变形破碎而涌入水体,随后形成第一列规则波波形,随着波浪的爬坡、反射变形而形成多个波列,且规则波的波幅均小于初始最大波峰的高度。
(3)综合分析试验现象及前人研究成果,提出初始涌浪高度是滑坡运动入水所引起的液面位移,当液面的位移在坡肩处形成尖陡波峰、波峰高度随着滑坡运动而达到极值,此时的涌浪高度就是初始最大涌浪高度。当液面位移没有形成尖陡的波峰,而是具有明显波峰及波谷的规则波时,最大涌浪高度是规则波列中的最大波幅,而这个最大波幅可能是第一列波的,也可能是后续的波列。能否在坡肩处形成波峰,与弗劳德数等因素密切相关。
(4)滑坡涌浪包括体积涌浪和冲击涌浪,两种涌浪同时存在,不同阶段各自所占比例不一样,涌浪产生初期以体积涌浪为主。通过试验分析,认为水平方向的运动主要引起液面位移而形成冲击涌浪,竖直方向的运动则主要引起“排水效应”,形成体积涌浪,竖直速度的大小则决定了滑坡在单位时间内能排开的水体体积。在其他因素一致的情况下,滑动面倾角越大,涌浪产生初期其体积涌浪高度越大,一定程度上也决定了其最大涌浪高度也较大。
2.各理论计算方法特点
(1)国外各种理论计算方法均以单向流为基础,即假设滑坡沿着河道轴向方向下滑或推进,这与涌浪产生的边界条件不符。实际中滑坡都是从两边的库岸下滑,涌浪在滑坡入水点产生以后先向对岸传播,然后通过波的扩散和反射,向上下游传播,不是简单的沿河道单向运动。
(2)潘家铮方法将整个涌浪过程视为一系列小波的线性叠加,假设每个小波都是孤立波。作者认为,波浪性质应根据Fritz提出的分区标准进行分析,将波浪全部假设为孤立波,与实际情况不符。且波浪传播到对岸反射后已经变形,高度发生变化,简单的线性叠加并不合理。
(3) Noda方法及潘家铮两种方法中涌浪高度只与滑坡速度、水深有关,都没有考虑滑坡规模大小对涌浪高度的影响。当滑坡厚度远小于水深时,其扰动范围与厚度密切相关,此时理论计算值明显偏大。
(4)根据波浪分区标准,1、2、4组试验所产生的波浪均为振荡波,3、5、6、7组试验则产生弱非线性过渡波。采用kamphuis方法中的稳定涌浪高度计算值近似代替最大浪高,其计算结果与试验测量最为接近。
(5) Ashtiani方法中考虑了滑动面倾角、滑坡水下运动时间这两个重要因素对滑坡涌浪高度的影响。从考虑的影响因素、河道规模、滑坡体材料及形状等方面比较,Ashtiani的模型试验条件与本试验最为接近。对比分析试验值和理论计算结果,Ashtiani方法的计算值和试验测量值较为接近。
(6) Fritz和Slingerland理论公式计算值相对于试验值都偏小,主要因为在试验中均采用了下滑过程中散体变形的柔性滑坡模型,滑坡变形导致其能量损失,从而使涌浪高度降低。其中,Slingerland方法适用于水深较小的情况下,通过本论文正交试验中的敏感性分析,该方法中水深的敏感区间为5m-30m。
(7)国内外模型试验都是在理想化的矩形水池中进行,水深、河道宽度、弯曲程度等始终保持不变,岸坡角度均为90°,波浪的浅水变形无从考虑,反射叠加也与实际情况不符。
3.涌浪影响因素的敏感性
通过正交试验的方差分析,得出最大浪高度影响因素的敏感性大小依次为：水深、滑坡速度、滑坡宽度、长度、厚度。涌浪预测中应重点考虑这些因素变化对指标值的影响。
4.涌浪传播规律
(1)沿岸传播浪是由多组波列传播、反射叠加而成。第一列波衰减较快,传播到对岸时高度不大,在岸坡上爬坡、反射回来后和后续的波列叠加,从而在沿岸形成较高的传播浪。
(2)传播浪高度随着传播距离的增加而逐渐减小,涌浪高度的衰减明显分为两个阶段,在第一阶段衰减速度极快,随后缓慢衰减。
5.速度及涌浪计算方法的修正
(1)在考虑水阻力的基础上,修正了美国土木工程师协会推荐公式及运动方程法。采用修正后的运动方程方法计算大堰塘滑坡运动速度,结果表明：滑坡所受水阻力在滑坡速度及迎水面积的动态变化下先增大后减小,导致加速度先减小后增大,滑坡先加速后减速。
(2)采用修正后的潘家铮初始最大涌浪计算方计算了大堰塘滑坡涌浪,结果表明,修正后的潘家铮方法和J.W.Kamphis方法最大涌浪计算结果相近,与实际情况比较符合；
(3)在考虑波浪的浅水变形及反射导致能损失的基础上,对潘家铮传播浪计算方法进行修正。计算表明：修正后的潘家铮传播浪、爬坡浪计算结果与调查值吻合较好,传播衰减规律一致。
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 factors
Basing 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.
本论文在分析库岸滑坡变形破坏影响因素的基础上,介绍了滑坡速度计算方法,在考虑水阻力的基础上,对速度计算公式进行修正,并从波浪力学、水力学角度,分析了库岸滑坡涌浪的物理性质；从假设条件、边界条件及试验条件等方面总结了国内外现有涌浪计算方法,对比分析了各个方法的适用条件,从波浪变形的角度修正了传播浪相关计算公式；针对国内外模型试验中河道模型简化、单向流问题及考虑因素不全面的问题,本论文在遵守相似准则的前提下,以1：200的比例尺,建立了三峡库区白水河滑坡处4km河道的三维模型,合理布设相关测量仪器及数据采集设备,通过室内多组模型试验,测定了最大涌浪及传播浪高度,深入分析滑坡涌浪形成机制、涌浪形态特点,探讨了滑坡传播规律,并依次分析了各方法的适用特点；以水布垭库区大堰塘滑坡为计算实例,采用修正后的速度、涌浪计算公式,分别计算和分析了滑坡运动过程、涌浪高度及传播规律。
经过以上研究,论文得出以下几个方面的结论：
1.涌浪形成机制及性质
(1)从宏观角度来讲,涌浪的产生是由于一定体积的滑坡在以一定的速度扰动水体变形而产生。从波浪力学的角度来讲,滑坡涌浪产生时,既有水质点上下振动,也有水质点前后移动,属于振荡波和推移波叠加情况。此外涌浪波高受水深的影响,大部分情况下,滑坡涌浪的波形属于浅水非线性波研究范畴。
(2)通过试验分析,滑坡涌浪的形成过程为：水体在滑坡的的作用下沿前缘上爬而形成一个波峰,随着滑坡的运动,波峰达到最高直至变形破碎而涌入水体,随后形成第一列规则波波形,随着波浪的爬坡、反射变形而形成多个波列,且规则波的波幅均小于初始最大波峰的高度。
(3)综合分析试验现象及前人研究成果,提出初始涌浪高度是滑坡运动入水所引起的液面位移,当液面的位移在坡肩处形成尖陡波峰、波峰高度随着滑坡运动而达到极值,此时的涌浪高度就是初始最大涌浪高度。当液面位移没有形成尖陡的波峰,而是具有明显波峰及波谷的规则波时,最大涌浪高度是规则波列中的最大波幅,而这个最大波幅可能是第一列波的,也可能是后续的波列。能否在坡肩处形成波峰,与弗劳德数等因素密切相关。
(4)滑坡涌浪包括体积涌浪和冲击涌浪,两种涌浪同时存在,不同阶段各自所占比例不一样,涌浪产生初期以体积涌浪为主。通过试验分析,认为水平方向的运动主要引起液面位移而形成冲击涌浪,竖直方向的运动则主要引起“排水效应”,形成体积涌浪,竖直速度的大小则决定了滑坡在单位时间内能排开的水体体积。在其他因素一致的情况下,滑动面倾角越大,涌浪产生初期其体积涌浪高度越大,一定程度上也决定了其最大涌浪高度也较大。
2.各理论计算方法特点
(1)国外各种理论计算方法均以单向流为基础,即假设滑坡沿着河道轴向方向下滑或推进,这与涌浪产生的边界条件不符。实际中滑坡都是从两边的库岸下滑,涌浪在滑坡入水点产生以后先向对岸传播,然后通过波的扩散和反射,向上下游传播,不是简单的沿河道单向运动。
(2)潘家铮方法将整个涌浪过程视为一系列小波的线性叠加,假设每个小波都是孤立波。作者认为,波浪性质应根据Fritz提出的分区标准进行分析,将波浪全部假设为孤立波,与实际情况不符。且波浪传播到对岸反射后已经变形,高度发生变化,简单的线性叠加并不合理。
(3) Noda方法及潘家铮两种方法中涌浪高度只与滑坡速度、水深有关,都没有考虑滑坡规模大小对涌浪高度的影响。当滑坡厚度远小于水深时,其扰动范围与厚度密切相关,此时理论计算值明显偏大。
(4)根据波浪分区标准,1、2、4组试验所产生的波浪均为振荡波,3、5、6、7组试验则产生弱非线性过渡波。采用kamphuis方法中的稳定涌浪高度计算值近似代替最大浪高,其计算结果与试验测量最为接近。
(5) Ashtiani方法中考虑了滑动面倾角、滑坡水下运动时间这两个重要因素对滑坡涌浪高度的影响。从考虑的影响因素、河道规模、滑坡体材料及形状等方面比较,Ashtiani的模型试验条件与本试验最为接近。对比分析试验值和理论计算结果,Ashtiani方法的计算值和试验测量值较为接近。
(6) Fritz和Slingerland理论公式计算值相对于试验值都偏小,主要因为在试验中均采用了下滑过程中散体变形的柔性滑坡模型,滑坡变形导致其能量损失,从而使涌浪高度降低。其中,Slingerland方法适用于水深较小的情况下,通过本论文正交试验中的敏感性分析,该方法中水深的敏感区间为5m-30m。
(7)国内外模型试验都是在理想化的矩形水池中进行,水深、河道宽度、弯曲程度等始终保持不变,岸坡角度均为90°,波浪的浅水变形无从考虑,反射叠加也与实际情况不符。
3.涌浪影响因素的敏感性
通过正交试验的方差分析,得出最大浪高度影响因素的敏感性大小依次为：水深、滑坡速度、滑坡宽度、长度、厚度。涌浪预测中应重点考虑这些因素变化对指标值的影响。
4.涌浪传播规律
(1)沿岸传播浪是由多组波列传播、反射叠加而成。第一列波衰减较快,传播到对岸时高度不大,在岸坡上爬坡、反射回来后和后续的波列叠加,从而在沿岸形成较高的传播浪。
(2)传播浪高度随着传播距离的增加而逐渐减小,涌浪高度的衰减明显分为两个阶段,在第一阶段衰减速度极快,随后缓慢衰减。
5.速度及涌浪计算方法的修正
(1)在考虑水阻力的基础上,修正了美国土木工程师协会推荐公式及运动方程法。采用修正后的运动方程方法计算大堰塘滑坡运动速度,结果表明：滑坡所受水阻力在滑坡速度及迎水面积的动态变化下先增大后减小,导致加速度先减小后增大,滑坡先加速后减速。
(2)采用修正后的潘家铮初始最大涌浪计算方计算了大堰塘滑坡涌浪,结果表明,修正后的潘家铮方法和J.W.Kamphis方法最大涌浪计算结果相近,与实际情况比较符合；
(3)在考虑波浪的浅水变形及反射导致能损失的基础上,对潘家铮传播浪计算方法进行修正。计算表明：修正后的潘家铮传播浪、爬坡浪计算结果与调查值吻合较好,传播衰减规律一致。
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 factors
Basing 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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