A two-way coupled method for calculating the motion of fluid landslide surges

Abstract

A two-way coupled flow landslide surge motion calculation method belongs to the field of civil engineering and water conservancy. This calculation method not only considers the combined effects of landslide / surge gravity, static soil / water pressure, and friction resistance, but also considers the strong coupling force between landslide and surge. According to the continuity principle of matter, Newton's second law, and the force of the unit body, the calculation equation of flow landslide surge motion is derived. The present invention is suitable for the calculation of flow landslide surge motion in reservoirs, and can calculate the movement process of the landslide under the strong coupling of landslide and surge and the movement process of the generated surge.

Description

Technical Field

[0001] The invention belongs to the field of civil engineering and is a method for calculating landslide surge motion based on the principle of material continuity and Newton's second law, while taking into account the strong coupling force between landslide surges. The method is suitable for calculating landslide surge motion in reservoir fluidity. Background Art

[0002] Landslide surge is one of the most common geological disasters in the reservoir area. It refers to a disaster in which a certain volume of landslide quickly impacts a certain volume of water body and generates an initial surge, which, after propagating in the water body, poses a threat to the safety of ships, coastal personnel and facilities in the water. Domestic and foreign scholars have carried out a lot of research on landslide surge disasters, but the proposed calculation methods mostly focus on the single-phase coupling of landslides to river water bodies, without considering the coupling force of water bodies to landslides. Therefore, Quecedo, Zhao Lanhao and others used three-phase flow to calculate the movement process of air, water and landslides, and used the level set method to track the free water surface. However, in reality, since the calculation domain of landslide surge is relatively large and the calculation amount of NS equation is relatively large, NS equation is not the most ideal calculation method for landslide surge. Therefore, it is more reasonable to use the depth average equation as the calculation method for landslide surge. Therefore, it is very necessary to establish a flow landslide surge motion calculation method based on the depth average equation and bidirectional coupling. Summary of the invention

[0003] Aiming at the shortcomings of the existing landslide surge motion calculation method, the present invention provides a method for calculating the fluid landslide surge motion taking into account the strong coupling force between landslide surges, which is suitable for calculating the fluid landslide surge motion of reservoirs.

[0004] In order to solve the above technical problems, the present invention adopts the following calculation scheme: (1)

[0005] A two-way coupled flow landslide surge motion calculation method, characterized in that the calculation method has a calculation equation,

[0006]

[0007]

[0008]

[0009]

[0010]

[0011]

[0012] Where η is the amplitude of the surge; Q 1x , Q1y are the fluxes of the surge in the x and y directions respectively; Z 2 is the riverbed elevation; g is the acceleration due to gravity; h is the 1 is the water body depth; They represent the frictional resistance of the water body in the x and y directions respectively; They represent the velocity components of the water body relative to the riverbed in the XOZ plane and the YOZ plane respectively; v 1z =(v 1x -v 2x )tanα 1 +(v 1y -v 2y )tanβ 1 represents the velocity of the water relative to the riverbed in the z direction, v 1x 、v 1y are the speeds of the water in the x and y directions, v 2x 、v 2y are the velocities of the sliding body in the x and y directions, α 1 , β 1 are the inclination angles of the riverbed and the XOZ and YOZ planes respectively; n is the Manning roughness coefficient; q 1 =tan 2 α 1 +tan 2 β 1 ; It represents the total velocity of the water body; represents the total velocity of the sliding body; ρ 1 is the density of water; ρ 2 is the density of the sliding body; C D is the drag force coefficient; h 2 is the thickness of the sliding body; Q 2x , Q 2y is the flux of the landslide in the x and y directions; represents the erosion rate of the landslide; Z 3 is the height of the slide bed; τ l =ρ 2 gh 2 tanφ' a +c represents the shear stress of the sliding body at the sliding surface, φ′ a is the internal friction angle of the sliding body, c is the cohesion of the sliding body; τ e =ρ 3 gh 2 tanφ'+c' represents the shear strength of the eroded layer, ρ 3 is the density of the erosion layer, φ' is the internal friction angle of the erosion layer, and c' is the cohesion of the erosion layer; k=1-sinφ' a is the landslide side pressure coefficient; They represent the velocity components of the sliding body in the XOZ plane and the YOZ plane respectively; v 2z =v 2x tanα 2 +v 2y tanβ 2 represents the velocity of the sliding body in the z direction; q 2 =tan 2 α 2 +tan 2 β 2 , α 2 , β 2 are the inclination angles of the slider bed and the XOZ and YOZ planes respectively; φ a is the apparent friction angle of the sliding body, B ss is the pore pressure coefficient, τ ss is the steady-state shear strength.

[0013] The specific steps include:

[0014] Step 1: Obtain the computational domain DEM data;

[0015] Step 2: Determine the landslide thickness h 2 , erosion layer thickness h 3 , water level Z 1 , Manning roughness coefficient n of the riverbed, drag coefficient C D ;

[0016] Step 3: Determine the river water density ρ 1 , landslide density ρ 2 , erosion layer density ρ 3 , landslide internal friction angle φ′ a , landslide cohesion c, landslide pore pressure coefficient B ss , internal friction angle φ' of the erosion layer, cohesion c' of the erosion layer;

[0017] Step 4: For the reservoir slope that has not experienced sliding, substitute the data in steps 1, 2, and 3 into the equation to calculate the thickness of the landslide at each moment. 2 , surge amplitude η.

[0018] Furthermore, the surge danger of the river section is judged according to the surge amplitude η value, and a red warning is issued for the river section with η≥3m, an orange warning is issued for the river section with 2m≤η<3m, and a blue warning is issued for the river section with 1m≤η<2m.

[0019] Beneficial effects:

[0020] (1) This calculation method takes into account the strong coupling force between landslide and surge, which is more in line with the actual situation of reservoir landslide and surge movement;

[0021] (2) This calculation method uses the depth average equation and the finite difference method for calculation, which is more efficient and economical.

[0022] (3) This calculation method uses the pore pressure coefficient B measured in the experiment ss , steady-state shear strength τ ss Calculate the movement process of the landslide, and the calculation results will be more reliable. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 : difference grid;

[0024] Figure 2 : River surge wave height;

[0025] Figure 3 : The height of the swell climbing along the coast; DETAILED DESCRIPTION

[0026] The present invention provides a bidirectionally coupled flow landslide surge motion calculation method, which specifically comprises the following steps:

[0027] (1) Obtaining computational domain DEM data: using drones or geospatial data cloud systems to obtain the above data;

[0028] (2) Determine the landslide thickness h 2 , erosion layer thickness h 3 , water level Z 1 , Manning roughness coefficient n of the riverbed, drag coefficient C D :Determine the above parameters based on on-site investigation and specification requirements;

[0029] (3) Determine the river water density ρ 1 , landslide density ρ 2 , erosion layer density ρ 3 , landslide internal friction angle φ a , landslide cohesion c, landslide pore pressure coefficient B ss , the internal friction angle of the erosion layer φ′ a , erosion layer cohesion c': the above parameters are determined by experiments;

[0030] (4) For the reservoir slope where no sliding occurs, substitute the data in steps 1, 2, and 3 into the equation to calculate the thickness of the landslide at each time point h. 2 , surge amplitude η, a red warning will be issued for river sections where η ≥ 3m, an orange warning will be issued for river sections where 2m ≤ η < 3m, and a blue warning will be issued for river sections where 1m ≤ η < 2m.

[0031] The derivation process of the control equation is as follows:

[0032] The governing equations of landslide surge are derived based on the material continuity principle and Newton's second law, and all derivations are performed in a three-dimensional Cartesian coordinate system.

[0033] Derivation of surge motion equation:

[0034] The acceleration of the surge unit in the x direction is a 1x and the y-direction acceleration a 1y It can be written as follows (ignoring the change in velocity in the depth Z direction):

[0035]

[0036]

[0037] In the formula, v 1x 、v 1y are the velocities of the water in the x and y directions respectively.

[0038] Considering the force balance of the unit body in the X and Y directions, all external forces are projected along the X and Y directions, and the following equation is obtained according to Newton's second law:

[0039]

[0040]

[0041] Where P 1x , P 1y is the projection of the lateral pressure on the unit body in the x and y directions, G 1x , G 1y is the projection of the gravity on the unit body in the x and y directions, S 1x , S 1y It is the projection of the friction force on the unit body in the x and y directions.

[0042] Water weight G 1 The direction of action is vertically downward, perpendicular to the XOY plane and the XOY plane, and the projection in the x and y directions is 0, so gravity is no longer analyzed separately.

[0043] (1) Acceleration caused by lateral pressure

[0044] Assuming that the lateral pressure of the unit body is distributed in a triangular shape along the depth direction, the acceleration generated by the lateral pressure is as follows:

[0045]

[0046]

[0047] In the formula, m 1 is the mass of water, ρ 1is the density of water, h 1 is the thickness of the water body, Δh 1 is the increment of water thickness, g is the acceleration due to gravity, and η is the water surface amplitude.

[0048] (2) Acceleration caused by drag force

[0049] The drag force is the resistance of the water body to the underwater landslide. From fluid mechanics, we know that the drag force on the landslide is:

[0050]

[0051] In the formula, C D is the drag coefficient, ρ 2 is the density of the landslide, is the total velocity of the water body, represents the total velocity of the sliding body, v 2x 、v 2y are the velocities of the sliding body in the x and y directions, q 1 =tan 2 α 1 +tan 2 β 1 , α 1 , β 1 are the inclination angles of the riverbed and the XOZ and YOZ planes, respectively.

[0052] According to the action and reaction, the drag force on the water is:

[0053]

[0054] The drag force produces accelerations in the X and Y directions as follows:

[0055]

[0056]

[0057] In the formula, They represent the velocity components of the water body relative to the riverbed in the XOZ plane and the YOZ plane, respectively. 1z =(v 1x -v 2x )tanα 1 +(v 1x -v 2x )tanβ 1 is the velocity of the water relative to the riverbed in the z direction.

[0058] (3) Acceleration caused by friction of the bed surface

[0059] The bed surface friction can be derived from the energy equation of uniform flow. The theoretical calculation formula of friction is:

[0060]

[0061] Where n is the Manning roughness coefficient of the riverbed.

[0062] The accelerations generated by the friction of the bed surface in the X and Y directions are as follows:

[0063]

[0064]

[0065] Combining equations (7), (8), (9), (10), (11), (12), (15), (16), (18) and (19), we can get the momentum equation of landslide motion as follows:

[0066]

[0067]

[0068] In the formula, Q 1x , Q 1y are the fluxes of the surge in the x and y directions respectively; Respectively represent water body x, y Frictional resistance term in direction;.

[0069] In any time step, the sum of the water volume flowing into and out of the unit body should be equal to the change in the water volume in the water column control body. The expression of the continuity equation is as follows:

[0070]

[0071] In the formula, Z 2 is the riverbed elevation.

[0072] Derivation of the landslide motion equation:

[0073] The acceleration of the landslide unit in the X direction is a 2x and the Y-direction acceleration a 2y It can be written as follows (ignoring the change in velocity in the depth Z direction):

[0074]

[0075]

[0076] Considering the force balance of the soil unit in the X and Y directions, all external forces are projected along the X and Y directions, and the following equation is obtained according to Newton's second law:

[0077]

[0078]

[0079] Where P 2x , P 2y are the projections of the lateral pressure on the unit body in the x and y directions, N 2x 、N 2y are the projections of the support force on the unit body in the x and y directions, S 2x , S 2y are the projections of the friction force on the unit body in the x and y directions, respectively, 2x 、F 2y are the projections of the drag force on the unit body in the x and y directions, respectively, m 2 is the mass of the sliding body.

[0080] (1) Acceleration caused by lateral pressure

[0081] Considering the force of the overlying water body on the soil unit, assuming that the lateral pressure of the soil unit is distributed in a trapezoidal shape along the depth direction, the lateral pressure coefficient k is the same on the left and right sides of the soil unit, and does not change in the depth direction, the acceleration generated by the lateral pressure is as follows:

[0082]

[0083]

[0084] Where k is the lateral pressure coefficient of the landslide, k = 1-sinφ' a ,φ′ a is the internal friction angle of the landslide, h 2 is the thickness of the landslide, Δh 2 is the increment of landslide thickness,

[0085] (2) Acceleration generated by the supporting force

[0086] During the movement of the landslide, each unit body is balanced in the normal direction. All forces are projected in the normal direction of the riverbed surface. The resultant force in the normal direction of the riverbed surface is 0. The acceleration generated by the supporting force is as follows:

[0087]

[0088] In the formula, α 2 , β 2 It is the angle between the slider bed and the XOZ and YOZ planes.

[0089] make q 2 =tan 2 α 2 +tan2 β 2 , the acceleration generated by the supporting force is simplified as follows:

[0090]

[0091] The acceleration components of the support force in the X and Y directions are:

[0092]

[0093]

[0094] (3) Acceleration caused by sliding surface resistance

[0095] The Mohr-Coulomb model is used to calculate the sliding resistance, and its expression is as follows:

[0096]

[0097] In the formula, φ a is the apparent friction angle of the sliding body, and c is the cohesion of the sliding body.

[0098] Apparent friction angle calculation:

[0099] τ(h 2 ,B ss )=τ ss +(σ(h 2 )tanφ-τ ss )(1-B ss ) (34)

[0100] σ(h 2 )=ρ 1 gh 1 cos 2 θ 1 +ρ 2 gh 2 cos 2 θ 2 (35)

[0101]

[0102]

[0103] In the formula, τ ss is the steady-state shear strength, σ(h 2 ) is the normal pressure of the sliding body, φ' a is the internal friction angle of the sliding body, B ss is the pore pressure coefficient, which indicates the degree of excess pore water pressure accumulation. It is affected by factors such as the properties of the sliding zone soil, the degree of saturation and the drainage conditions of the sliding bed. Its value range is shown in Table 1.

[0104] Table 1 B ss Value range

[0105]

[0106] The acceleration components of the sliding surface resistance in the x and y directions are:

[0107]

[0108]

[0109] In the formula, They represent the velocity components of the sliding body in the XOZ and YOZ planes respectively; v 2z =v 2x tanα 2 +v 2y tanβ 2 represents the velocity of the sliding body in the z direction, and c is the cohesion of the sliding body.

[0110] (4) Acceleration caused by drag force

[0111] The drag force is the resistance of the water body to the underwater landslide. From fluid mechanics, we know that the drag force on the landslide is:

[0112]

[0113] The drag force produces accelerations in the X and Y directions as follows:

[0114]

[0115]

[0116] Combining equations (23), (24), (25), (26), (27), (28), (31), (32), (38), (39), (41), and (42), we can get the momentum equation of landslide motion as follows:

[0117]

[0118]

[0119] In the formula, Q 2x , Q 2y is the flux of the landslide in the x and y directions.

[0120] In any time step, the sum of the sliding volume flowing into and out of the unit body should be equal to the change of the soil volume in the soil column control body. The expression of the continuity equation is as follows:

[0121]

[0122] Where E is the erosion rate of the slider bed.

[0123] Erosion rate calculation:

[0124]

[0125] In the formula, Z 3 is the height of the slide bed; τ l =ρ 2 gh 2 tanφ′ a +c represents the shear stress of the sliding body at the sliding surface, τ e =ρ 3 gh 2 tanφ'+c' represents the shear strength of the eroded layer, ρ 3 is the density of the erosion layer, φ' is the internal friction angle of the erosion layer, and c' is the cohesion of the erosion layer.

[0126] Discrete method:

[0127] The finite difference method is used to discretize the calculation equation of landslide surge motion, such as Figure 1 As shown in Figure 1, the thickness of the landslide or water body is located at the center of the grid, and the fluxes in the x and y directions are located on the unit grid lines. The thickness of the landslide or water body at the center of the grid is calculated by the flux changes on the unit lines. The convection term in the control equation is discretized using the third-order upwind difference method, and the other terms on the right side of the momentum equation are discretized using the central difference method.

[0128] Examples:

[0129] The Gongjiafang landslide is located on the north bank of the Yangtze River in Wuxia Town, Wushan County, Chongqing. The Yangtze River flows from west to east through this area. The landslide is 120 km from the Three Gorges Dam downstream and 4 km from the Wushan urban area upstream. The reservoir water level was about 173 m when the landslide occurred. The initial surge height caused by the landslide was about 13 m, and the surge height on the opposite bank was about 10 m. The Wuxia Town Wharf 3.5 km upstream and the Shiziwan Wharf on the opposite bank were both affected by the surge. The specific surge height observation values ​​are shown in Table 2.

[0130] Table 2 List of the climbing heights of the Gongjiafang landslide surge

[0131]

[0132]

[0133] The DEM data downloaded from the geospatial data cloud platform (http: / / www.gscloud.cn) was used as the post-slide terrain of the landslide. The pre-slide terrain of the landslide was restored according to the post-slide terrain and the elevation of the two side walls of the landslide. The landslide model was established based on the DEM data of the pre-slide terrain and post-slide terrain of the landslide. The water level when the landslide was unstable was 173m. The points with a pre-slide terrain elevation less than 173m were set as water coverage areas. The water depth was the difference between the elevation and 173m. The surge model was established based on the DEM data and water depth data of the pre-slide terrain. Then the calculation domain was divided into 394×145 differential grids on the XOY plane. The actual size of the differential grid was 30m×30m, and the actual calculation range was 11.82km×4.35km.

[0134] According to the existing research on the Gongjiafang landslide surge, the density of the sliding body is 2100kg / m 3 , combined with multiple back-calculations of the internal friction angle φ′ during sliding motion a Take 32°, the cohesion C of the sliding body and sliding belt is 0, and the landslide does not liquefy B ss The calculation parameters of the surge model are determined by existing studies combined with multiple back calculations. The specific calculation parameters during the landslide surge movement are shown in Table 3. The initial states of the landslide and the water body are both stationary, the calculation time step is 0.1s, and the total calculation time is 3000s.

[0135] Depend on Figure 2 , Figure 3 It can be seen that the simulated value of the maximum surge climbing height near the shore is 20.4m, and the simulated value of the maximum surge climbing height on the opposite bank is 18.5m. The field observation values ​​of the surge climbing height on the shore are all within the simulation range. According to the correlation analysis, the simulation results are basically consistent with the field observation results, and the numerical simulation is reliable.

[0136] Table 3. Gongjiafang landslide surge simulation parameters

[0137]

Claims

1. A bidirectionally coupled flow landslide surge motion calculation method, characterized in that: The calculation equation used is: Where η is the amplitude of the surge; Q 1x , Q 1y are the fluxes of the surge in the x and y directions respectively; Z2 is the riverbed elevation; g is the gravitational acceleration; h1 is the water depth; They represent the frictional resistance of the water body in the x and y directions respectively; They represent the velocity components of the water body relative to the riverbed in the XOZ plane and the YOZ plane respectively; v 1z =(v 1x -v 2x )tanα1+(v 1y -v 2y )tanβ1 represents the velocity of water relative to the riverbed in the z direction, v 1x 、v 1y are the speeds of the water in the x and y directions, v 2x 、v 2y are the velocities of the sliding body in the x and y directions respectively, q1 = tan 2 α1+tan 2 β1, α1, β1 are the inclination angles between the riverbed and the XOZ and YOZ planes, respectively; n is the Manning roughness coefficient; It represents the total velocity of the water body; represents the total velocity of the sliding body; ρ1 is the density of the water body; ρ2 is the density of the sliding body; C D is the drag coefficient; h2 is the thickness of the sliding body; Q 2x , Q 2y is the flux of the landslide in the x and y directions; represents the erosion rate of the landslide; Z3 is the elevation of the sliding bed; τ s =ρ2gh2tanφ′ a +c represents the shear stress of the sliding body at the sliding surface, φ' a is the internal friction angle of the sliding body, c is the cohesion of the sliding body; τ b =ρ3gh2tanφ′+c′ represents the shear strength of the erosion layer, ρ3 is the density of the erosion layer, φ' is the internal friction angle of the erosion layer, and c' is the cohesion of the erosion layer; k=1-sinφ′ a is the landslide side pressure coefficient; They represent the velocity components of the sliding body in the XOZ and YOZ planes respectively; v 2z =v 2x tanα2+v 2y tanβ2 represents the speed of the sliding body in the z direction; q2 = tan 2 α2+tan 2 β2, α2, β2 are the inclination angles of the slider bed and the XOZ and YOZ planes respectively; φ a is the apparent friction angle of the sliding body, B ss is the pore pressure coefficient, τ ss is the steady-state shear strength; The specific steps include: Step 1: Obtain the computational domain DEM data; Step 2: Determine the thickness of the landslide h2, the thickness of the erosion layer h3, the water level Z1, the Manning roughness coefficient n of the riverbed, and the drag coefficient C D ; Step 3: Determine the river water density ρ1, landslide density ρ2, erosion layer density ρ3, and landslide internal friction angle φ a ', landslide cohesion c, landslide pore pressure coefficient B ss , internal friction angle φ' of the erosion layer, cohesion c' of the erosion layer; Step 4: For the reservoir slope where no sliding occurs, substitute the data in the above steps 1, 2 and 3 into the equation for calculation to obtain the landslide thickness h2 and surge amplitude η at each moment.

2. The method for calculating fluid landslide surge motion according to claim 1, characterized in that: The surge danger of the river section is judged according to the value of the surge amplitude η. A red warning is issued for the river section with η≥3m, an orange warning is issued for the river section with 2m≤η<3m, and a blue warning is issued for the river section with 1m≤η<2m.

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