A method for determining the collapse state of slope landslide during dam break

Abstract

The present invention discloses a method for determining the collapse state of a slope landslide during a dam break process, comprising the steps of: establishing a mathematical model of the area of ​​the slope landslide and performing grid division; selecting each grid unit as a central grid, comparing it with adjacent grids one by one, and judging whether the central grid and the corresponding adjacent grids meet the landslide condition; determining the minimum sliding height for stopping the landslide process that satisfies at least one grid unit, for iterative calculation, determining the sliding height of each grid unit as the central grid and the rising height of the adjacent grids, and updating the elevations of all grid units; until all central grids have no adjacent grids that meet the landslide condition, the iteration is stopped, and the slope landslide reaches a balanced state. The determination method of the present invention is more in line with the actual landslide process, and each grid simultaneously considers the effect of its own downward sliding and the effect of being lifted as an adjacent grid to generate a superimposed rising height, which is updated at the same time, greatly improving the processing efficiency.

Description

Technical Field

[0001] The invention relates to the technical field of geotechnical engineering, and in particular to a method for determining the collapse state of a slope landslide during a dam breach. Background Art

[0002] A large number of dam-break model tests and field observations have shown that the mechanism of dam-break damage, in addition to the effect of water flow entraining sand, also involves the phenomenon of slope landslide collapse. Therefore, the corresponding slope landslide collapse calculation must be included in the numerical simulation calculation of the dam-break process. The slope landslide mechanism of dam materials with different properties is also different. The slope of viscous dam materials usually slides in blocks, while the slope of inviscid dam materials is usually steeper and slides in particles. Whether horizontally or vertically, when the slope gradient exceeds a certain critical angle, the particles of inviscid dam materials will slide to the foot of the slope to form a new slope with a residual angle, which is manifested in the macroscopic view as the slope collapses to form a new slope. In 2007, Wu et al. published [Document 1] (Wu W. Computational River Dynamics [M]. London, UK: CRC Press, 2007.), which proposed a slope landslide calculation method suitable for a two-dimensional center-defined rectangular grid. This method considers the instability condition between the central grid and the surrounding 8 adjacent grids in a local 3×3 grid: exceeding the critical angle. If the instability condition is met, the elevation of the central element and the corresponding adjacent grid in the local 3×3 grid will change until the new slope angle is equal to the residual angle. The algorithm disclosed is only a landslide processing method for the central grid and its adjacent grids within the local 3×3 range. For the entire two-dimensional grid plane, an iterative solution is required: first, the landslide calculation of each 3×3 local grid is performed in sequence according to row priority, and then the landslide calculation of each 3×3 local grid is performed in sequence according to column priority. Iterate the above steps until the landslide calculation is stable. This algorithm has the following problems:

[0003] 1. The "chain" reaction between unit landslide and adjacent units requires repeated iterative calculations. The calculation mode cannot be parallelized and the amount of calculation cannot be estimated, resulting in extremely low numerical calculation efficiency and difficulty in popularization in practical applications.

[0004] 2. The convergence of the algorithm has no theoretical support;

[0005] 3. There is a difference from the actual landslide mode: the actual landslide mode is that landslides occur simultaneously in the entire two-dimensional plane area that meets the landslide conditions, and then a "chain" reaction occurs; while the calculation method of the algorithm is to start the landslide from one point, and then promote the "chain" reaction of the entire grid in turn. Summary of the invention

[0006] Technical purpose: In view of the above-mentioned shortcomings, the present invention provides a method for determining the collapse state of slope landslide during dam break, which can quickly determine whether the equilibrium state of stopping landslide is reached during dam break.

[0007] Technical solution: To achieve the above technical objectives, the present invention adopts the following technical solution:

[0008] A method for determining the collapse state of a slope during a dam breach is characterized in that a mathematical model of a dam slope landslide area is established under a two-dimensional central rectangular grid, comprising the steps of:

[0009] S1. Select each grid unit as a central grid for processing at the same time: the central grid includes a plurality of corresponding adjacent grids, and calculates the slope angle, the tangent value of the repose angle, and the tangent value of the residual angle between each selected central grid and the adjacent grids;

[0010] S2, comparing the selected central grid with the adjacent grids one by one: judging whether the central grid and the corresponding adjacent grids meet the landslide condition according to the tangent value of the slope angle and the tangent value of the repose angle between the central grid and the adjacent grids; judging whether the central grid and the corresponding adjacent grids meet the residual angle condition according to the tangent value of the slope angle and the tangent value of the residual angle between the central grid and the adjacent grids;

[0011] S3, if at least one grid unit in the landslide area satisfies the landslide condition, the minimum sliding height that satisfies at least one grid unit to stop the landslide process is used as the iterative sliding height Drop for iterative calculation;

[0012] In each iteration, each grid cell that meets the landslide condition is independently calculated to determine the sliding height of each grid cell as the central grid and the rising height of the adjacent grid. The difference between the rising height and the sliding height is used as the superimposed rising height of the grid cell, and the elevation of all grid cells is updated.

[0013] The iteration stops when all the central grids have no adjacent grids that meet the landslide conditions;

[0014] S4. There are no grid cells that meet the landslide conditions in the slope landslide area, and the slope landslide reaches a balanced state.

[0015] Preferably, in step S3, the method for determining the sliding height of each grid unit as the central grid is as follows:

[0016] The iterative sliding height Drop is used as the sliding height of the central grid, and the area Area of ​​the central grid, the area sum LArea of ​​the adjacent grids that meet the landslide conditions, and the rising height Drop*α of the adjacent grids that meet the landslide conditions are calculated, where α=Area / LArea;

[0017] The rising height of each grid unit as an adjacent grid is: ∑ i Drop×α i ×M i , the superimposed rising height is (∑ i Drop×α i ×M i )-Drop×M;α i It represents the height of each grid cell as the rise of the ith adjacent grid, which does not meet the landslide condition. i is 0;

[0018] If the central grid landslide condition is met, M is 1, otherwise it is 0; if the neighboring grid landslide condition is met, the corresponding M i The value of is 1, otherwise it is 0.

[0019] Preferably, in step S3, the adjacent grid is an 8-neighborhood or a 4-neighborhood. If a 4-neighborhood is adopted, the value of i is from 1 to 4; if an 8-neighborhood is adopted, the value of i is from 1 to 8.

[0020] Preferably, the horizontal plane is taken as the xy plane, the elevation direction is taken as the z-axis direction, and the slope landslide area is divided into a plurality of adjacent grid units in the xy plane.

[0021] Preferably, in step S2, the residual angle condition is satisfied when: the elevation difference between the central grid and the neighboring grid is equal to the product of the grid spacing and the residual angle tangent value tanRs of the grid unit.

[0022] Preferably, in step S2, the method for determining the tangent value of the repose angle is as follows:

[0023] In the dam model, if the grid cell is covered by water, the wet repose angle and the tangent of the wet repose angle are used; if the grid cell is not covered by water, the dry repose angle and the tangent of the dry repose angle are used; if one of two adjacent grid cells is covered by water and the other is not covered by water, the average of the dry repose angle and the wet repose angle, and the average of the dry repose angle and the wet repose angle are used.

[0024] Beneficial effects: Compared with the prior art, the invention provides an efficient algorithm for slope landslide in a two-dimensional central rectangular grid, which has the following beneficial effects:

[0025] (1) The simulation of the landslide process in the method proposed by the present invention will start the landslide at the first time as long as the landslide conditions are met, which is more consistent with the actual landslide process.

[0026] (2) In the method of the present invention, the landslide calculation is performed as a whole, which ensures that each iteration process will make the elevation value of the two-dimensional grid plane smoother as a whole, and will always tend to a stable state after multiple iterations.

[0027] (3) The calculation method of the method of the present invention is parallel. Each grid simultaneously considers the effect of its own downward sliding and the effect of being lifted up as an adjacent grid to generate a superimposed rising height. All grids update the grid height at the same time.

[0028] (4) The present invention is based on a two-dimensional central rectangular grid, and the two-dimensional grid can be stored in a matrix form. Therefore, the parallel computing method of the present invention is particularly suitable for matrix vectorized programming optimization technology, which can greatly improve computing efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 A three-dimensional schematic diagram of a dam model in the present invention established by a two-dimensional center-defined rectangular grid model;

[0030] Figure 2 A grid diagram of the dam model in the present invention represented by a two-dimensional central rectangular grid;

[0031] Figure 3 is a schematic diagram of a central grid and eight adjacent grids in the present invention;

[0032] Figure 4 for Figure 3 Schematic diagram of the slope angle formed between the central grid and any adjacent grid;

[0033] Figure 5 It is a flow chart of the method for determining the collapse state of a slope landslide during a dam-breaking process of the present invention;

[0034] Figure 6 is the initial elevation value of the grid in the first embodiment;

[0035] Figure 7 is the water depth of the grid in Example 1;

[0036] Figure 8 is the tangent value of the repose angle of the grid in the first embodiment;

[0037] Fig. 9 is the residual tangent value of the grid in Example 1;

[0038] Fig.10 This is a schematic diagram of the situation where the central grid in the first embodiment slides toward the neighboring grid;

[0039] Fig.11 is the grid elevation value after the first iteration in the first embodiment;

[0040] Fig.12 is the grid elevation value after the second iteration in the first embodiment;

[0041] Fig.13 It is a schematic diagram of the embankment before the landslide and the embankment after being determined by the method of the present invention;

[0042] Fig.14 for Fig.13 Front view of

[0043] Fig.15 A schematic diagram of the evolution process of the breach determined by the method of the present invention;

[0044] Fig.16 This is a time statistical result diagram of the first 130 landslide calculations determined using the method of the present invention. DETAILED DESCRIPTION

[0045] The present invention provides a method for determining the collapse state of a slope landslide during a dam-breaking process under a two-dimensional central rectangular grid. The method simulates the landslide process, determines the grids that meet the landslide conditions, and performs landslide calculations as a whole, ensuring that each iteration process makes the elevation value of the two-dimensional grid plane smoother as a whole, and tends to a stable state after multiple iterations. The determination method is parallel, and each grid simultaneously considers the effect of its own downward sliding and the effect of being lifted as an adjacent grid to generate a superimposed rising height, and all grids simultaneously update the grid heights.

[0046] 1. Dam model

[0047] In the present invention, a matrix is ​​used to represent the dam represented by a two-dimensional center-defined rectangular grid model. The horizontal plane is used as the xy plane, the elevation direction is the z-axis direction, and the xy plane is discretized into a series of squares. The elevation of the dam is equal to the elevation at the center position of the two-dimensional rectangular grid in the xy plane, that is, the dam is discretized into a series of cuboids.

[0048] like Figure 1 The embodiment shown is a three-dimensional display of a dam built by defining a rectangular grid model with a two-dimensional center. The low-lying area in the middle is formed by the impact of the flood at the breach. The rectangular grid does not have to be divided evenly, but it can be divided evenly. The numbers in the grid represent the elevation of the center of the grid, such as Figure 2 shown.

[0049] 2. Landslide conditions

[0050] by Figure 3 The example shown is used to illustrate the landslide condition. The network center point p is represented by a shadow, and the eight adjacent grid cells are used as adjacent cells.

[0051] The landslide condition is: if the slope formed by grid cell p and any adjacent cell exceeds the angle of repose, the embankment between the two cells will collapse.

[0052] like Figure 4 As shown, Rp and Rs represent the stationary angle and the residual angle respectively, Zp and Zi represent the elevations of the centers of two adjacent grid units p and i respectively, ΔZp and ΔZi represent the changes in the elevations of the center points of the grid unit p and the grid unit i respectively.

[0053] If θ is the slope angle of grid p and grid i, if the slope angle θ is greater than the repose angle Rp, grid unit p will collapse, and the collapsed material will fall into grid i, so that the elevation of grid p will decrease and the elevation of grid i will increase. However, when the new slope angle θ reaches the residual angle Rs, the collapse process will stop and a new stable state will be formed.

[0054] The change in elevation needs to satisfy the law of conservation of mass: ΔZp*Ap+ΔZi*Ai=0, where Ap and Ai represent the areas of grid p and grid i, respectively. In actual simulation calculations, it is necessary to consider the landslide conditions between a grid and the eight grids around it at the same time, and the height of grid collapse and elevation needs to satisfy the law of conservation of mass overall.

[0055] In actual simulation calculations, the repose angle and the repose angle need to be considered separately under dry and wet conditions. If the current grid is covered by water, the wet repose angle and the wet repose angle are used for calculation. If the current grid is not covered by water, the dry repose angle and the dry repose angle are used for calculation. If one of two adjacent grids is covered by water and the other is not covered by water, the repose angle used in calculating the landslide condition between them is the average of the dry repose angle and the wet repose angle, and the repose angle is the average of the dry repose angle and the wet repose angle.

[0056] 3. Methods for determining the collapse state of slope landslide

[0057] When judging the collapse conditions, the angle comparison can be equivalently converted into the comparison of the tangent value of the angle, that is, if the condition is met: tanθ is greater than tanRp, the adjacent grid will collapse, where tanθ and tanRp represent the tangent values ​​of the slope angle and the rest angle, respectively. When the new slope angle tangent value tanθ is equal to the residual angle tangent value tanRs, the collapse process stops and a new stable state is formed.

[0058] like Figure 5 As shown, the method for determining the collapse state of a slope landslide under a two-dimensional central rectangular grid of the present invention specifically comprises the following steps:

[0059] Step 1: Calculate the tangent of the static angle and the residual tangent of each grid cell.

[0060] tanRp represents the tangent value of the grid cell, tanRs represents the residual tangent value, h represents the water depth value, th1 represents the threshold value of the water depth, tanWRp represents the input parameter - wet tangent value of the repose angle, tanDRp represents the input parameter - dry tangent value of the repose angle, tanWRs represents the input parameter - wet residual tangent value, tanDRs represents the input parameter - dry residual tangent value, and th1 represents the input parameter - threshold value.

[0061]

[0062] Step 2: For each grid in the 3×3 grid centered on it, find the adjacent grids between the central grid and any adjacent grid that meet the landslide conditions. The "adjacent grid" can be an 8-neighborhood or a 4-neighborhood.

[0063] Step 3: If a grid (i, j) has at least one adjacent grid that meets the landslide condition, the numbers of these adjacent grids are recorded as a set L(i, j), then the area of ​​all adjacent grids that meet the landslide condition is calculated, LArea(i, j), and the area of ​​the grid is recorded as Area(i, j). Consider that the material of grid (i, j) slides evenly on the adjacent grid that meets the landslide condition. Assuming that the sliding height of grid (i, j) is Drop (a very small value, not meeting the residual angle condition), the rising height of the grid set L(i, j) is:

[0064] Drop*Area(i,j) / LArea(i,j) (Formula 2)

[0065] Here, α=Area(i, j) / LArea(i, j), which is the ratio of the area of ​​the central grid to the sum of the areas of the neighboring grids that meet the landslide conditions.

[0066] Step 4: Assume that the landslide speed of all central grids that meet the landslide conditions is equal, that is, the sliding height per unit time is equal. Calculate the rising height of each grid as the adjacent grid ∑ i Drop×α i , where α i It represents the area ratio of the grid as the different positions of the neighborhood grid. Only those that meet the above landslide conditions have corresponding α i Value, α that does not meet the landslide condition i is 0. If a 4-neighborhood is used, i ranges from 1 to 4. If an 8-neighborhood is used, i ranges from 1 to 8. The area ratio is calculated as shown in Formula 2.

[0067] Step 5: Calculate the stacking height of each grid as follows:

[0068] (∑ i Drop×αi ×M i )-Drop×M (Formula 3)

[0069] Where M and M i The value is 0 or 1, and the value rules are as follows:

[0070] If the central grid landslide condition is met, M is 1, otherwise it is 0; if the neighboring grid landslide condition is met, the corresponding M i The value of is 1, otherwise it is 0.

[0071] Step 6: Determine the Drop value of the current iteration in a way that the residual angle tangent value is reached first.

[0072] The process is explained as follows: As Drop increases, higher grids will be lowered, while lower grids will be raised. In this process, the height of some grids will meet the landslide stop condition, which will trigger a chain reaction. Therefore, the Drop value cannot be too large in the current calculation process. The Drop value is determined by the following method: the minimum Drop value that can stop the landslide process of at least one grid. The condition for landslide stop is: center grid - neighboring grid == grid spacing * tanRs.

[0073] Step 7: Update the elevation of all grids according to formula 3.

[0074] Step 8: Repeat the process from step 2 to step 7. If the result of step 2 shows that all central grids have no adjacent grids that meet the landslide conditions, then stop the iteration. It is determined that there are no grid cells that meet the landslide conditions in the slope landslide area, and the slope landslide reaches a balanced state.

[0075] Embodiment 1

[0076] like Figure 6 As shown in the figure, 4 neighborhoods are used as the neighborhood definition method. The grid is evenly divided into 4×4 areas, the size of each grid is 1×1, and the input parameters are as follows: tanWRp=0.8, tanDRp=1, tanWRs=0.2, tanDRs=0.3, th1=0.01. Figure 6 Indicates the initial elevation value of the grid, Figure 7 Represents the water depth of the grid.

[0077] (1) Tangent value calculation

[0078] First, calculate the tangent of the rest angle and the residual tangent of each grid cell as follows: Figure 8 and Fig. 9 shown.

[0079] Since there are 4 neighborhoods and the grid size is 1×1, the horizontal distance between the centers of adjacent grids is 1. According to the landslide condition: center grid - adjacent grid > grid center horizontal distance * center grid's tangent angle of rest, the elevation difference between the center grid and the neighboring grid is equal to the product of the grid spacing and the residual tangent value of the grid unit, tanRs. The case of landslide from the center grid to the neighboring grid is as follows: Fig.10 As indicated by the arrow in .

[0080] (2) Iterative calculation

[0081] Assuming the grid is numbered according to the upper left grid coordinate (0,0), the x-axis is to the right, and the y-axis is downward, then Fig.10 This means that the grid (2,2) will slide toward the grid (2,3), and the grid (3,2) will slide toward the grid (3,3).

[0082] According to the formula (∑ i Drop×α i ×M i )-Drop×M, the superimposed rising height of each grid is as follows:

[0083] Grid(2,2): -Drop, Grid(2,3): Drop, Grid(3,2): -Drop, Grid(3,3): Drop

[0084] The grid-adjusted elevation values ​​are as follows:

[0085] Grid (2,2): 5-Drop, Grid (2,3): 3+Drop, Grid (3,2): 5-Drop, Grid (3,3): 2+Drop.

[0086] To stop the process of grid (2,2) sliding toward grid (2,3), it must satisfy: 5-Drop-(3+Drop)=0.3, and the calculated value is Drop=0.85.

[0087] To stop the process of grid (3,2) sliding toward grid (3,3), it must satisfy: 5-Drop–(2+Drop)=0.3, and the calculated value is Drop=1.35.

[0088] Obviously, the process of mesh (2,2) sliding to mesh (2,3) ends before the process of mesh (3,2) sliding to mesh (3,3). So set Drop = 0.85.

[0089] Thus, the grid elevation value after the first iteration is obtained as follows Fig.11 shown.

[0090] Entering the second iteration.

[0091] According to the landslide condition, grid (3,2) will slide toward grid (3,3), and the superimposed rise heights of each grid are as follows:

[0092] Grid(3,2):-Drop, Grid(3,3):Drop;

[0093] The grid-adjusted elevation values ​​are as follows:

[0094] Grid (3,2): 4.15-Drop, Grid (3,3): 2.85+Drop;

[0095] To stop the process of grid (3,2) sliding toward grid (3,3), it must satisfy: 4.15-Drop–(2.85+Drop)=0.3, and the calculated value is Drop=0.5.

[0096] The grid elevation value after the second iteration is obtained as follows: Fig.12 shown.

[0097] At this point, all the central grids have no adjacent grids that meet the landslide conditions, so the iteration stops. Fig.12 The result is the final output.

[0098] 4. Display of landslide effects

[0099] The present invention is based on a planar two-dimensional central rectangular grid, and the two-dimensional grid can be stored in a matrix form. The parallel computing method of the present invention is particularly suitable for matrix vectorized programming optimization technology, which can greatly improve computing efficiency.

[0100] Fig.13 The left picture in the middle is the dam before the landslide, and the right picture is the dam after the landslide calculation by this method. The dam is divided into 40×80 grids. In the initial state, the landslide amount is large. Fig.14 for Fig.13 Front view of.

[0101] Fig.15 Shown from top to bottom is a schematic diagram of the evolution process of the breach when the landslide algorithm of the present invention is added to the dam breach simulation calculation.

[0102] Fig.16 The time statistics of the first 130 landslide calculations are shown in the figure. The hardware configuration is CPU: i7 7700HQ and 16G memory. The program is written in python + numpy library. It can be seen that the time for each landslide calculation is less than 0.1s. The first landslide is large, and the time taken for the later landslide is small is basically less than 0.03s, which is less time-consuming.

[0103] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for determining the collapse state of a slope during a dam breach, characterized in that: Under the plane two-dimensional central rectangular grid, the mathematical model of the embankment slope landslide area is established, including the following steps: S1. Select each grid unit as a central grid for processing at the same time: the central grid includes a plurality of corresponding adjacent grids, and calculates the slope angle, the tangent value of the repose angle, and the tangent value of the residual angle between each selected central grid and the adjacent grids; S2, comparing the selected central grid with the adjacent grids one by one: judging whether the central grid and the corresponding adjacent grids meet the landslide condition according to the tangent value of the slope angle and the tangent value of the repose angle between the central grid and the adjacent grids; judging whether the central grid and the corresponding adjacent grids meet the residual angle condition according to the tangent value of the slope angle and the tangent value of the residual angle between the central grid and the adjacent grids; S3, if at least one grid unit in the landslide area satisfies the landslide condition, the minimum sliding height that satisfies at least one grid unit to stop the landslide process is used as the iterative sliding height Drop for iterative calculation; In each iteration, each grid cell that meets the landslide condition is independently calculated to determine the sliding height of each grid cell as the central grid and the rising height of the adjacent grid. The difference between the rising height and the sliding height is used as the superimposed rising height of the grid cell, and the elevation of all grid cells is updated. The iteration stops when all the central grids have no adjacent grids that meet the landslide conditions; The method for determining the sliding height of each grid unit as the central grid is as follows: The iterative sliding height Drop is used as the sliding height of the central grid, and the area Area of ​​the central grid, the area sum LArea of ​​the adjacent grids that meet the landslide conditions, and the rising height Drop*α of the adjacent grids that meet the landslide conditions are calculated, where α=Area / LArea; The rising height of each grid unit as an adjacent grid is: ∑ i Drop×α i ×M i , the superimposed rising height is (∑ i Drop×α i ×M i )-Drop×M;α i It represents the area ratio of each grid unit as the i-th adjacent grid, which does not meet the landslide condition. i is 0; If the central grid landslide condition is met, M is 1, otherwise it is 0; if the neighboring grid landslide condition is met, the corresponding M i The value of is 1, otherwise it is 0; S4. There are no grid cells that meet the landslide conditions in the slope landslide area, and the slope landslide reaches a balanced state.

2. The method for determining the collapse state of a slope during a dam break according to claim 1, characterized in that: In step S3, the adjacent grid is an 8-neighborhood or a 4-neighborhood. If a 4-neighborhood is used, the value of i ranges from 1 to 4. If an 8-neighborhood is used, the value of i ranges from 1 to 8.

3. The method for determining the collapse state of a slope during a dam break according to claim 1, characterized in that: In the step S1, the horizontal plane is taken as the xy plane, the elevation direction is taken as the z-axis direction, and the slope landslide area is divided into a plurality of adjacent grid units in the xy plane.

4. The method for determining the collapse state of a slope during a dam break according to claim 1, characterized in that: In step S2, the residual angle condition is satisfied when the elevation difference between the central grid and the neighboring grid is equal to the product of the grid spacing and the residual angle tangent value tanRs of the grid unit.

5. The method for determining the collapse state of a slope during a dam break according to claim 1, characterized in that: In step S2, the method for determining the tangent value of the repose angle is as follows: In the dam model, if the grid cell is covered by water, the wet repose angle and the tangent of the wet repose angle are used; if the grid cell is not covered by water, the dry repose angle and the tangent of the dry repose angle are used; if one of two adjacent grid cells is covered by water and the other is not covered by water, the average of the dry repose angle and the wet repose angle, and the average of the dry repose angle and the wet repose angle are used.

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