滑坡体与非线性浅水波的相互作用
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摘要
滑坡体产生的海啸或涌浪造成惨重人员伤亡和经济损失的灾害在世界各地时有报道。为了适应防灾减灾的需要，各国学者综合采用灾后实地调查、物理模型实验、解析求解和数值模拟的研究方法，对滑坡体兴波问题开展了大量研究工作，以往研究表明滑坡体的高度、体积、密度、滑动距离、滑动面倾角、水深等对波峰高度有显著影响，相关研究成果也已经应用于灾害风险评估和早期预警之中。然而，在已经建立的许多波峰高度估计公式中，还没有一个公式能涵盖所有关键物理参数。这是因为目前的数学模型中多直接设定滑坡体运动过程，忽略了滑坡体和水波之间的相互作用复杂。这类模型虽经人为调整参数可应用于灾害后报，但对潜在滑坡体造成灾害的预测能力不足。
本论文建立了滑坡体和水波相互作用的耦合数学模型。假设滑坡体兴波区域内水波横向能量扩散可忽略，在立面二维的简化下应用非线性浅水方程描述水波过程；假设滑坡体底部流体法向流速为零，应用简化的N-S方程描述底部流动；在滑坡体的运动方程中考虑了惯性力、水波波动压力、底部流体对滑坡体的阻力和浮托力、以及滑坡体和滑动面间的库仑摩擦力等。与线性浅水波理论解、物理模型实验结果和灾后调查资料对比表明，本论文的模型能很好的预测滑坡体运动和水波波峰高度，并能捕捉到向岸传播波峰、近岸水位降落等实际灾害过程。
本论文首先通过设定滑坡体运动过程的方式研究了滑坡体兴波作用，数值结果表明，Fr数、水波非线性、滑坡体形状的非对称性对波峰高度有显著影响：当滑坡体高度和体积保持不变，波峰高度随滑坡体前端坡度的增大而增大；当Fr>1，波峰高度随滑坡体运动速度的减小而增大，并且水波非线性会进一步放大波峰高度。水波线性假设，及以往对滑坡体形状非对称性的忽视，都导致波峰高度的低估，不利于防灾减灾。
随后，本论文通过理论分析和数值计算研究了水波对滑坡体运动的反作用，研究表明，水波对滑坡体上表面作用有直接的切向阻力，并通过法向压力和对滑坡体底部流动的驱动改变着滑坡体和滑动面间的库仑摩擦力。
最后，对水波和滑坡体相互作用的数值模拟结果表明，库仑摩擦系数、滑坡体的入水速度等对相互作用有显著影响。耦合计算结果进一步表明，以往研究中忽视的Fr数和滑坡体形状的非对称性同样是影响波峰高度的关键因素。
Landslide generated tsunami has caused human life losses and devastating damagearound the world. Researchers have studied this problem through hazard investigation,experiment modeling, analytical solution, and numerical simulation. It was found thatthe height of wave crest depends strongly on the height, volume, density, traveldistance of landslide, slope angle, and water depth, etc. A lot of correspondingestimation equations are developed using different sets of parameters mentioned above,and research achievement is applied to risk assessment and early warning system. Buttill now, none of these estimation equations include all the major parameters. Moreover,due to the complex interaction between landslide and waves generated, the motion oflandslide is always prescribed a priori in numerical simulations. Hence, thesenumerical models are limited to wave hindcasting by artificially fitting parameters, andmay not be used to predict real event.
A mathematical model is derived to describe the dynamic interaction betweenlandslide and water waves. Wave energy propagation in the transverse direction isreasonably neglected in the landslide disturbance zone. Hence, under vertical2dimensional assumptions, nonlinear shallow water wave equations are implemented togovern wave generation process; under the assumptions that fluid velocity in thenormal direction is zero, N-S equations are simplified to govern the flow underneathlandslide; inertial force, water wave pressures along the surface of landslide, togetherwith lubrication resistance, floating force, coulomb friction force acting on the bottomare included in the force balance equation of landslide. Validation with analyticalsolution of linear shallow water waves and experimental results indicate that the modelpresented here can predict landslide motion and wave crest height. The model can alsocapture wave crest propagating onshore and recession of water surface along thecoastline which are recorded in hazard investigation documents.
Wave generation by landslide disturbance is studied first by prescribing differentlandslide motion. The significant effect of Froude number, nonlinearity of waves, andasymmetry of landslide shape on wave crest height is discussed. For landslide withsame height and volume, the steeper landslide front, the larger wave crest height. If Fr>1, Wave crest height increases when velocity of landslide is reduced. Further more,if Fr>1, wave nonlinearity will amplify wave crest. So wave crest may beunderestimated, when linear wave assumption is used or asymmetry of landslide isignored.
Then, based on theoretical analysis and numerical simulation, the effect of waterwaves on landslide motion is studied. Dynamic water wave pressures along the surfacecause resistance to landslide motion. And waves also affect both flow underneathlandslide, and normal effective force between landslide and the slope, so will changethe coulomb friction force.
In the end, dynamic coupling simulations of landslide motion and water wavesshows that, coulomb friction coefficient, entry velocity of landslide into water alsoplay a key role in the dynamic interaction between landslide and water waves. Casescomparison verifies again, that, Froude number and asymmetry of landslide areessential to wave crest height prediction, which researchers failed to notice in the past.
本论文建立了滑坡体和水波相互作用的耦合数学模型。假设滑坡体兴波区域内水波横向能量扩散可忽略，在立面二维的简化下应用非线性浅水方程描述水波过程；假设滑坡体底部流体法向流速为零，应用简化的N-S方程描述底部流动；在滑坡体的运动方程中考虑了惯性力、水波波动压力、底部流体对滑坡体的阻力和浮托力、以及滑坡体和滑动面间的库仑摩擦力等。与线性浅水波理论解、物理模型实验结果和灾后调查资料对比表明，本论文的模型能很好的预测滑坡体运动和水波波峰高度，并能捕捉到向岸传播波峰、近岸水位降落等实际灾害过程。
本论文首先通过设定滑坡体运动过程的方式研究了滑坡体兴波作用，数值结果表明，Fr数、水波非线性、滑坡体形状的非对称性对波峰高度有显著影响：当滑坡体高度和体积保持不变，波峰高度随滑坡体前端坡度的增大而增大；当Fr>1，波峰高度随滑坡体运动速度的减小而增大，并且水波非线性会进一步放大波峰高度。水波线性假设，及以往对滑坡体形状非对称性的忽视，都导致波峰高度的低估，不利于防灾减灾。
随后，本论文通过理论分析和数值计算研究了水波对滑坡体运动的反作用，研究表明，水波对滑坡体上表面作用有直接的切向阻力，并通过法向压力和对滑坡体底部流动的驱动改变着滑坡体和滑动面间的库仑摩擦力。
最后，对水波和滑坡体相互作用的数值模拟结果表明，库仑摩擦系数、滑坡体的入水速度等对相互作用有显著影响。耦合计算结果进一步表明，以往研究中忽视的Fr数和滑坡体形状的非对称性同样是影响波峰高度的关键因素。
Landslide generated tsunami has caused human life losses and devastating damagearound the world. Researchers have studied this problem through hazard investigation,experiment modeling, analytical solution, and numerical simulation. It was found thatthe height of wave crest depends strongly on the height, volume, density, traveldistance of landslide, slope angle, and water depth, etc. A lot of correspondingestimation equations are developed using different sets of parameters mentioned above,and research achievement is applied to risk assessment and early warning system. Buttill now, none of these estimation equations include all the major parameters. Moreover,due to the complex interaction between landslide and waves generated, the motion oflandslide is always prescribed a priori in numerical simulations. Hence, thesenumerical models are limited to wave hindcasting by artificially fitting parameters, andmay not be used to predict real event.
A mathematical model is derived to describe the dynamic interaction betweenlandslide and water waves. Wave energy propagation in the transverse direction isreasonably neglected in the landslide disturbance zone. Hence, under vertical2dimensional assumptions, nonlinear shallow water wave equations are implemented togovern wave generation process; under the assumptions that fluid velocity in thenormal direction is zero, N-S equations are simplified to govern the flow underneathlandslide; inertial force, water wave pressures along the surface of landslide, togetherwith lubrication resistance, floating force, coulomb friction force acting on the bottomare included in the force balance equation of landslide. Validation with analyticalsolution of linear shallow water waves and experimental results indicate that the modelpresented here can predict landslide motion and wave crest height. The model can alsocapture wave crest propagating onshore and recession of water surface along thecoastline which are recorded in hazard investigation documents.
Wave generation by landslide disturbance is studied first by prescribing differentlandslide motion. The significant effect of Froude number, nonlinearity of waves, andasymmetry of landslide shape on wave crest height is discussed. For landslide withsame height and volume, the steeper landslide front, the larger wave crest height. If Fr>1, Wave crest height increases when velocity of landslide is reduced. Further more,if Fr>1, wave nonlinearity will amplify wave crest. So wave crest may beunderestimated, when linear wave assumption is used or asymmetry of landslide isignored.
Then, based on theoretical analysis and numerical simulation, the effect of waterwaves on landslide motion is studied. Dynamic water wave pressures along the surfacecause resistance to landslide motion. And waves also affect both flow underneathlandslide, and normal effective force between landslide and the slope, so will changethe coulomb friction force.
In the end, dynamic coupling simulations of landslide motion and water wavesshows that, coulomb friction coefficient, entry velocity of landslide into water alsoplay a key role in the dynamic interaction between landslide and water waves. Casescomparison verifies again, that, Froude number and asymmetry of landslide areessential to wave crest height prediction, which researchers failed to notice in the past.
引文
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