| Landslide surge is a huge wave generated by landslide mass slipping into rivers,lakes and seas and the energy it carried being sufficiently converted in water.Landslide surge is a secondary disaster caused by landslide,and it causes huge damages to area where the surge is generated and propagated,sometimes even severer than the landslide itself.Throughout the whole process from the landslide mass entering the water and being generated to its propagation,three key points should be looked at in order to systematically study the mechanism of landslide surge in a river-type reservoir.First,the head wave height of surge represents the total energy of the landslide surge,and it controls the severity of the overall disaster.Second,the propagation pattern of the landslide surge represents the range of influence and also the highest possible degree of disaster.Third,the law of action of the river boundary on the propagation of surge represents the degree of reflection and stacking of landslide surge and also the follow-up propagation direction.On the basis of analyzing the progress of domestic and foreign research,this paper was supported by the National Natural Science Foundation project “Research on the Features of Landslide Surge on Curve Channels of River-type Reservoirs in Mountainous Areas and the Influence to Channel Navigation(51479015)”.Concerning the three key points of landslide surge,i.e.landslide surge’s head wave height,law of propagation and the river boundary’s effect on the propagation of surge,this research conducted tests and research.Landslide surge is generated by land slipping into water,and the features of the landslide has an inevitable cause-and-effect relationship with the features of follow-up surge.This paper firstly started from the rock soil structure of landslide mass and the mechanics properties of the slip surface,studied the movement mechanism of landslide in river-type reservoirs by three steps which were the start-up of landslide,the accelerated slipping of landslide and the landslide mass entering the water,and analyzed the features of landslide to uncover the conditions for the generation of surge.The typical curve channels in the Yangtze River Three Gorges Reservoir area were taken as the prototype,and they were conceptualized into a model of curve river-type reservoir.The landslide mass was simulated in terms of the geometric size of the landslide,the structure of the inner granular structure and the physical indicators,and the testing parameters included water depth,angle of slipping surface,thickness and width of the landslide mass,by-water status and the slope of the riverbed at the site where the landslide mass entered the water,and by letting the landslide mass entering the water from both concave and convex banks,physical model tests were carried out.The features of the head wave’s form was analyzed,statistics about the head wave height was collected,and based on the energy conservation concept,throughout the whole process from the start-up of the landslide to the conversion of energy generated by surge,this paper conducted research on the landslide’s head wave on the basis of energy conversion mechanism.Moreover,this paper analyzed the propagation features of landslide surge,collected data about the maximum wave height at different observation points,and adopted the tensor analysis method to study the general pattern of propagation and attenuation of landslide surge and accurately measured the influence scope of landslide surge and the maximum degree of damages along the flow-course.In addition,this paper established a three-dimensional landslide surge numerical model which could study the effect of complicated river boundaries on the propagation of landslide surge in scenarios with different bank slopes,surface curvature and wave steepness,aiming at finding out the pattern of how the height of back wave,wave cycle and propagation direction changed.The following innovative results were achieved:(1)Based on the motion mechanism of river-type reservoir landslide,the total mechanical energy of landslide mass before entering water was derived.Following the wave energy flow and according to the distribution features of head wave’s crest line,the head wave’s total wave energy was derived.On the basis of physical model test,the three-dimensional surface model between energy conversion coefficient and slipping surface angle,water depth and area of landslide mass under water was derived.Finally,the model for calculating the height of landslide surge’s head wave based on energy conservation and exchange mechanism was established.Starting from the concept of energy conservation,the relationship among the total head wave energy of the landslide mass after entering the water,the total mechanical energy before entering the water and the energy conversion coefficient were established.Through studying the motion features of the landslide from its start-up to entering the water,taking the moment when the landslide mass was separated from the spout as the key time node,and based on the rock-soil theory and Newton’s law of motion,the landslide’s kinetic motion formula and potential energy formula were theoretically derived,and the total mechanical energy formula of landslide mass before entering the water was established.The distribution of the head wave’s line of crest was analyzed through the contour map,following the flow of the wave energy,the wave energy theory was used to analyze the wave’s kinetic energy,potential energy and the work of pressure,so that the total wave energy formula was derived theoretically.On the basis of the testing data and calculation analysis,the energy conversion coefficient formula was established as well as the three-dimensional curved surface model among the energy conversion coefficient,slipping surface angle,water depth of reservoir,the area of landslide mass in water.Finally,the model for calculating the head wave height based on energy conversion and exchange mechanism was derived.(2)Based on the tensor analysis method,the tensor expressions demonstrating the negative exponential function between the maximum wave height transmissibility and the relative distance,the secondary function between the maximum wave height transmissibility and the azimuth angle,and the linear function between the maximum wave height transmissibility and the working condition(the ratio of initial wave height to water depth)were derived.A four-dimensional mathematical model pertaining the transmissibility of the maximum wave height,water depth,azimuth angle and propagation distance was established,and an experience wave field that covered the whole propagation area was established to reflect how the surge wave elements changed along the flow-course.On the basis of testing and analyzing the features of landslide surge propagation and collecting the statistics about the maximum wave height along the flow-course,the classification of experience wave field was performed on the landslide surge on curved river channel.Based on the maximum wave height along the flow-course,the initial maximum wave height,water depth of channel,azimuth angle and nondimensionalization of propagation distance,the research indicators were defined.First,a two-dimensional model between wave height propagation rate and relative distance was established,which showed a pattern of negative exponential curve-line distribution between them,and with the increase in the relative distance,the wave height propagation rate was monotonically decreasing;second,a three-dimensional model was established among wave height propagation rate,azimuth angle and relative distance,which found out the pattern that,the wave height propagation rate was in negative exponential curve-surface distribution with the azimuth angle and the relative distance;finally,a four-dimensional model among wave height propagation rate,working condition,azimuth angle,relative distance,which formed an experience wave field that covered the whole propagation area and comprehensively reflected the changes of landslide surge’s maximum wave along the flow-course,and the propagation and attenuation features of landslide surge in each area of curved river-type reservoir.(3)The regularity of effect on the propagation direction of landslide surge’s back wave by straight channels,concave banks and convex banks was explored.The relation diagram between spectrum intensity and frequency of waves was established,and the regularity of how bank slope gradient,surface curvature and arc angle influenced surge’s back wave cycle was obtained.The radial basis function expression between the wave height reflection rate and surface curvature,bank slope gradient,wave steepness and roughness coefficient was derived,and the model for calculating the back wave height of landslide surge on curved river channels was established.A three-dimensional numerical model of the landslide surge was established,and it was in good compliance with the physical testing model.According to the three working conditions of the point where the landslide mass entering the water,which were on the straight channels of the river,the vertex point of the convex bank on curved channels and the vertex point of the concave bank on curved channels,the pattern of complicated river boundaries’ effect on the direction of surge back wave and the cycle of back wave was obtained.By doing research according to different degrees of curve channel surface curvature,slope of river banks and location of landslide mass slipping into water,the regularity of how the single factor of river boundaries influenced the height of back waves,and the wave height reflection rate was in a negative exponential curve-line relationship with river surface curvature,sloping coefficient of banks and slopes as well as wave steepness.With the increase of surface curvature,sloping coefficient of banks and slopes and surge wave steepness,the wave height reflection rate was monotonically decreasing.Finally,based on the radial basis function,the model for calculating the back wave height of landslide surge on curved river channels was established. |
