A method for judging the type of surge induced by water area landslide and predicting wave height

Abstract

The application discloses a water area landslide induced surge type judgment and wave height prediction method, which comprises the following steps: a dynamic model of slope body instability is established, the speed u(t) and the displacement s(t) process of the landslide body are obtained, the dimensionless parameters Fr and S are calculated, the surge wave type is distinguished, and the wave height A of the corresponding wave type is calculated by calling the oscillation wave / single wave formula. z The application has very important engineering application value. m Through the classification and discrimination of the landslide surge wave, the wave height prediction method is proposed for different surge waves, reliable technical support is provided for the determination of relevant disaster prevention and mitigation measures and the formulation of emergency plans, and the application has very important engineering application value.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of water conservancy and hydropower engineering, and particularly relates to a type judgment and wave height prediction method for landslide-induced surge waves in water areas. BACKGROUND

[0002] With the increasing demand for clean energy in China and the rapid development of hydropower construction technology, the height of most dams and slopes has exceeded 300 meters, and some has reached more than 500 meters. Most giant and large hydropower projects will be built on river sections with high seismic intensity, strong surface transformation of canyon slopes, and complex lithology and structure, which are directly or indirectly threatened by high-speed landslides. In order to evaluate the landslide surge disaster risk in the reservoir area, many scholars have carried out research. However, most of the research on the first wave or climbing height of landslide surge wave is based on one influencing factor or multiple influencing factors for analysis, thereby obtaining an empirical or semi-empirical formula of the surge wave, that is, most of the research does not specifically decompose and discuss the landslide surge wave problem. For different types of surge waves, it is obviously unreasonable to use one formula to predict the wave height or climbing height of different types of landslide surge waves. Therefore, it is necessary to classify and distinguish the landslide surge wave, and propose a wave height prediction method for different surge waves, so as to provide reliable technical support for the determination of relevant disaster prevention and mitigation measures and the formulation of emergency plans. SUMMARY

[0003] The application aims to provide a type judgment and wave height prediction method for landslide-induced surge waves in water areas, and solve the problem of large calculation error of surge wave height.

[0004] The application is achieved by the following technical means: a type judgment and wave height prediction method for landslide-induced surge waves in water areas, comprising the following steps:

[0005] Step 1: establishing a dynamics model of slope instability to obtain the speed u(t) and displacement s(t) process of the landslide body;

[0006] Step 2: calculating the dimensionless parameters Fr and S z to distinguish the type of surge wave;

[0007]

[0008]

[0009] In the formula, u is the speed of the landslide body, s z is the thickness of the landslide body, h is the static water depth, g is the acceleration of gravity, a is the angle between the slide bed and the horizontal plane, and S z is the component of the relative thickness of the landslide body in the vertical direction.

[0010] If formula (11) is satisfied, the surge wave is an oscillation wave:

[0011] Fr < (0.7 - 0.5S z ) (11)

[0012] If (12) is satisfied, the surge wave is single wave:

[0013] Fr > (0.7 - 0.5S z ) (12)

[0014] Step 3, call the oscillatory wave / single wave formula to calculate the wave height A corresponding to the wave type m ;

[0015] If the surge wave is single wave, then

[0016] The wave height A m and the nonlinear relationship of the water flow velocity v w :

[0017]

[0018] If the surge wave is oscillatory wave,

[0019] The wave height of the surge wave at any time and position, i.e. the wave height, is η(x, t);

[0020]

[0021] In the formula, ω 2 = gk tanh kh, indicating the dispersion relationship, k is the wave number, and g is the acceleration of gravity.

[0022] In the step 1, if the slope body has not entered the water, the landslide velocity u(t) and the landslide displacement s(t) are:

[0023]

[0024]

[0025] In the formula, a = g (sin α - C n cos α), which is the acceleration of the landslide body at the initial time, L1 is the sliding length of the landslide body on the slope when the slope body has not entered the water, and C n is the friction coefficient of the slope surface,

[0026] If the slope body contacts the water but has not all entered the water, the landslide velocity u(t) and the landslide displacement s(t) are solved as:

[0027]

[0028] In the formula, the coefficient the coefficient The coefficients a and b are functions of the displacement s(t) of the slope body in the stage of contacting with water but not being totally submerged, C d is the drag coefficient of the flow around, C m is the added mass coefficient, m b represents the mass of the slope body, p w is the density of water, V is the volume of the slide submerged in water, A is the projected area of the slope body in the direction of movement,

[0029] If the slope body is totally submerged in water, the velocity u(t) and the displacement s(t) of the slope body are solved as:

[0030]

[0031]

[0032] where C and C1 are integral constants,

[0033] C and C1 are respectively:

[0034]

[0035]

[0036] where T2 is the time at the end of the stage of contacting with water but not being totally submerged, and u2 and L2 are the corresponding velocity and displacement respectively, and L1 is the displacement of the slope in the stage of being above water.

[0037] In the step 1, the dynamics model of the instability of the slope body is:

[0038]

[0039] where m b represents the mass of the slope body, s represents the distance of the movement of the slope body on the slope, t represents the time of the movement of the slope body on the slope, F A is the added mass force, F g is the component of the gravity along the direction of movement, F b is the component of the buoyancy along the direction of gravity, F n is the Coulomb dynamic friction force along the direction of movement, F d is the hydrodynamic drag, F f is the lubrication force caused by the velocity gradient of the boundary layer.

[0040] In the step 3, the wave height η(x, t) of the surge wave at any time and position is further solved as:

[0041]

[0042]

[0043]

[0044] In the formula, x is the horizontal range of wave propagation direction, and T is the total calculated time.

[0045] The present application has the beneficial effect that by classifying and distinguishing the landslide surge wave, and proposing a wave height prediction method for different surge waves, reliable technical support is provided for the determination of relevant disaster prevention and mitigation measures and the formulation of emergency plans, and has very important engineering application value. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 Flow chart for water area landslide induced surge type judgment and wave height prediction method;

[0047] Figure 2 Wave making device diagram for example;

[0048] Figure 3 Comparison of calculated and experimental displacement values;

[0049] Figure 4 Comparison of calculated and experimental velocity values;

[0050] Figure 5 Comparison of theoretical classification limits and experimental observation values;

[0051] Figure 6 Comparison of single wave formula calculated and experimental values;

[0052] Figure 7 Comparison of oscillatory wave formula calculated and experimental values;

[0053] The present application will be further described in detail below in combination with the drawings and examples. DETAILED DESCRIPTION

[0054] Example 1

[0055] As shown in Figure 1 , a water area landslide induced surge type judgment and wave height prediction method includes the following steps:

[0056] Step 1, a dynamic model of slope body instability is established to obtain the speed u(t) and displacement s(t) process of the landslide body;

[0057] A model test device as shown in Figure 2 is established, including a left slope and a bottom horizontal bottom plate, a baffle is arranged at the connection between the slope and the bottom plate, the landslide body is placed on the top of the slope in the water tank, and is released at an initial speed u0, pushes away the water body after entering the water, and is stopped by the baffle at the bottom of the slope, the process takes the horizontal direction as the x axis and the vertical direction as the z axis, the speed process and displacement process in this coordinate system can be solved.

[0058] Specifically, according to Newton's law, the dynamics model of the bank slope body in the step 1 is,

[0059]

[0060] wherein, m b represents the mass of the landslide body, s represents the distance of the landslide body moving on the slope, t represents the time of the landslide body moving on the slope, F A is the additional mass force, F g is the component of gravity along the moving direction, F b is the component of buoyancy along the gravity direction, F n is the Coulomb dynamic friction force along the moving direction, F d is the hydrodynamic resistance, F f is the lubrication force caused by the velocity gradient of the boundary layer.

[0061] In the step 1, if the bank slope body has not entered the water, the velocity u(t) of the landslide body and the displacement s(t) of the landslide body are: Figure 3 and Figure 4 in the water stage,

[0062]

[0063]

[0064] wherein, a=g(sinα-C n cosα), is the acceleration of the landslide body at the initial moment, L1 is the sliding length of the landslide body on the slope when the bank slope body has not entered the water, C n is the friction coefficient of the slope surface,

[0065] If the bank slope body contacts the water but has not entered the water completely, the velocity u(t) of the landslide body and the displacement s(t) of the landslide body are solved as: Figure 3 and Figure 4 in the water stage,

[0066]

[0067] wherein, the coefficient is the coefficient In the stage that the bank slope body contacts the water but has not entered the water completely, the coefficients a and b are functions of the displacement s(t) of the landslide body, C d is the flow resistance coefficient, C m is the additional mass coefficient, m b represents the mass of the landslide body, p w is the density of the water, V is the volume of the landslide body submerged in the water, A is the projection area of the landslide body in the moving direction,

[0068] If the slope is totally submerged, the velocity u(t) and displacement s(t) of the landslide are given by Figure 3 and Figure 4 the underwater stage,

[0069]

[0070]

[0071] where C and C1 are integral constants,

[0072] C and C1 are given by

[0073]

[0074]

[0075] where T2 is the time at the end of the stage when the slope is in contact with water but not totally submerged, and u2 and L2 are the corresponding velocity and displacement, respectively, and L1 is the displacement of the landslide in the stage above water.

[0076] The displacement of the process is shown in Fig. 1, and the velocity is shown in Fig. 2. Figure 3 Figure 4

[0077] Step 2, dimensionless parameters Fr and S z are calculated to determine the type of surge wave.

[0078]

[0079]

[0080] where u is the velocity of the landslide, s z is the thickness of the landslide, h is the depth of the water, g is the acceleration of gravity, a is the angle between the slide bed and the horizontal plane, and S z is the component of the relative thickness of the landslide in the vertical direction.

[0081] If (11) is satisfied, the surge wave is an oscillatory wave:

[0082] Fr < (0.7 - 0.5S z ) (11)

[0083] If (12) is satisfied, the surge wave is a solitary wave:

[0084] Fr > (0.7 - 0.5S z ) (12)

[0085] Step 1 calculates the velocity process and displacement process of the landslide for different initial velocities u0. Step 2 extracts the velocity v at the time of entering water from the velocity process, and uses​​ Fr is calculated at each velocity, the type of surge is determined by the relationship between Fr and S, and the theoretical classification limit is compared with the observed value as shown in Figure 5 .

[0086] Step 3, call the oscillatory wave / single wave formula to calculate the wave height A corresponding to the wave type m ;

[0087] According to the type determined in step 2, the wave height formula of different wave types is called for calculation. The velocity process used in the calculation is the velocity curve calculated in step 1. Among them, the wave height calculation formula of single wave is an analytical solution, which can directly calculate the wave height by bringing in the velocity and landslide parameters. The wave height calculation formula of oscillatory wave needs to be solved numerically. The comparison process between the values calculated in step 3 and the test values is shown in Figure 6 for single wave and Figure 7 for oscillatory wave.

[0088] If the surge wave is a single wave, then

[0089] The velocity and water depth before and after the single wave are calculated using the mass conservation equation and momentum equation, and the formulas are as follows:

[0090] ch = (c - u w )(h + A m ) (13)

[0091]

[0092] Step 3.1.2: Solve the wave height A m and the nonlinear relationship of water flow velocity u w :

[0093] If the surge wave is a single wave, then

[0094] The nonlinear relationship of wave height A m and water flow velocity v w :

[0095]

[0096] The explicit expression of A m / h as a function of can be obtained as the unique positive solution of a third-order equation:

[0097]

[0098] Based on the known or previously obtained other parameters, the value of wave height A m when the surge wave is a single wave is calculated. The wave height is predicted.

[0099] If the surge wave is an oscillatory wave,

[0100] A two-dimensional coordinate system is established, with the wave propagation direction as the x-axis and the wave height direction as the z-axis. Then the velocity potential function φ can be given by the Laplace equation:

[0101]

[0102] According to the free water surface boundary condition, the topography boundary condition and the far-field radiation boundary condition, the boundary function expression of the calculation domain is determined as:

[0103]

[0104]

[0105]

[0106]

[0107] The Laplace transform method and the Fourier cosine transform about x are used to solve equation (17):

[0108]

[0109] The integral constants A and B are determined by the boundary conditions:

[0110]

[0111]

[0112] After the Laplace inverse transform and the Fourier cosine inverse transform, the wave height η(x, t) at any time and position of the surge wave is obtained,

[0113] If the surge wave is an oscillatory wave,

[0114] then the wave height η(x, t) at any time and position of the surge wave is obtained.

[0115]

[0116] In the formula, ω 2 = gk tanh kh, which represents the dispersion relation, k is the wave number, and g is the gravitational acceleration.

[0117] Given other parameters or based on previously obtained results, the wave height η at a specific position x and a specific time t when the surge wave is an oscillatory wave is calculated. The wave height is predicted.

[0118] In step 3, the wave height η(x, t) at any time and position of the surge wave is further solved as,

[0119]

[0120]

[0121]

[0122] where x is the horizontal extent of the wave propagation, T is the total time of computation.

[0123] In the actual prediction process, for example, s z h is the thickness of the landslide, g is the gravity acceleration, a is the angle between the landslide bed and the horizontal plane, S z These parameters can be obtained by measuring the landslide,

[0124] After obtaining the landslide velocity u(t) and the landslide displacement s(t) process according to step 1, then according to step 2, the dimensionless parameters Fr and S z are calculated, to determine whether the surge wave caused by the landslide is a single wave or an oscillatory wave, and finally according to the type of the surge wave, according to step 3, the corresponding wave height calculation formula is selected, and the finally calculated single wave height A m or the oscillatory wave height η is the predicted wave height value.

Claims

1. A method for judging the type of surge induced by landslide in water area and predicting the height of the surge, characterized in that, The method comprises the following steps: Step 1, establishing a dynamic model of the slope body instability to obtain the speed u(t) and displacement s(t) of the landslide body; Step 2, Calculate dimensionless parameters Fr and S z to determine the type of swell wave where u is the velocity of the landslide mass, s z is the thickness of the landslide mass, h is the static water depth, g is the acceleration of gravity, a is the angle between the slide bed and the horizontal, S z is the component of the relative thickness of the landslide mass in the vertical direction; If formula (11) is satisfied, the surge wave is an oscillation wave: Fr < (0.7 - 0.5S z ) (11) If formula (12) is satisfied, the surge wave is a single wave: Fr > (0.7 - 0.5S z ) (12) Step 3, call the oscillatory wave / single wave formula to calculate the wave height A of the corresponding wave type m ; If the surge wave is a single wave, then Wave height A m Non-linear relationship with the water flow velocity v w of the water If the surge wave is an oscillation wave, the wave height of the surge wave at any time and position, i.e. the wave height, is η(x, t); where ω 2 = gk tanh kh, represents the dispersion relation, k is the wave number, and g is the gravitational acceleration.

2. The method according to claim 1, characterized in that: In step 1, if the slope body has not entered the water, the speed u(t) and displacement s(t) of the landslide body are: In the formula, a=g(sinα-C n cosα), where L1 is the initial acceleration of the landslide body, and C is the sliding length of the landslide body on the slope before it enters the water. n The coefficient of friction of the slope surface. If the slope body contacts the water but has not entered the water completely, the speed u(t) and displacement s(t) of the landslide body are solved as: where the coefficients coefficients In the stage of the slope body contacting with water but not all entering water, the coefficients a and b are functions of the displacement s(t) of the slope body, C d is the flow resistance coefficient, C m is the added mass coefficient, m b represents the mass of the slope body, ρ w is the density of water, V is the volume of the sliding block submerged in water, A is the projected area of the slope body in the direction of motion, If the slope body is completely underwater, the speed u(t) and displacement s(t) of the landslide body are solved as: In the formula, C and C1 are integral constants, C and C1 are respectively: In the formula, the time at the end of the stage when the slope body contacts the water but has not entered the water completely is T2, and the corresponding speed and displacement are u2 and L2 respectively, and L1 is the displacement of the landslide in the water stage.

3. The method according to claim 1, characterized in that: In step 1, the dynamic model of the slope body instability is, where m b represents the landslide mass quality, s represents the distance of the landslide mass moving on the slope, t represents the time of the landslide mass moving on the slope, F A is the additional mass force, F g is the component of gravity along the direction of motion, F b is the component of buoyancy along the direction of gravity, F n is the Coulomb dynamic friction force along the direction of motion, F d is the hydrodynamic resistance, F f is the lubrication force of the boundary layer due to the velocity gradient.

4. The method according to claim 1, characterized in that: In step 3, the wave height η(x, t) of the surge wave at any time and position is further solved as, In the formula, x is the horizontal range of the wave propagation direction, and T is the total time calculated.

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