Interaction Between Landslide And Nonlinear Shallow Water Waves

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.