Reservoir dangerous rock dumping into water induced surge scale evaluation system and method

Abstract

The application discloses a reservoir dangerous rock dumping into water induced surge scale evaluation system and method. The method comprises the following steps: determining the rock body submergence state according to the relative position relationship between the rock body base bottom elevation and the reservoir still water surface elevation; judging the rock body and water body contact position at the corresponding moment according to the rock body dumping process at different moments and the position, determining the rock body drainage volume and deducing the external force; calculating the acceleration, speed and displacement of different parts of the rock body in the movement process, and constructing a mechanical model containing dynamic pressure and static pressure coupling; embedding the mechanical model into the iSquares numerical framework, establishing an RGW-Squares dangerous rock dumping induced surge numerical model, and calculating the surge dynamic wave height to evaluate the dangerous rock dumping induced surge scale. The application provides a reservoir dangerous rock dumping into water induced surge scale evaluation system and method, fills the gap of the reservoir dangerous rock dumping induced surge dynamics model, and solves the problem of inaccurate surge scale evaluation.

Description

Technical Field

[0001] This invention belongs to the field of surge disaster scale assessment technology, specifically a system and method for assessing the scale of surges induced by the collapse of unstable rocks into the water of a reservoir. Background Technology

[0002] Rockfall collapse refers to the phenomenon where rock masses located on steep slopes, during their long-term evolution, are affected by factors such as crack propagation and weathering, eventually tilting and collapsing under their own weight, ultimately bending and becoming unstable along the direction of freefall. If high-level rock masses fall into the water, they will trigger severe secondary surge disasters, posing a serious threat to the geological safety of waterways, coastal infrastructure, and the lives of residents. Therefore, accurately assessing the failure mechanism of unstable rock masses and the surge disasters induced by collapses is a critical technical problem that urgently needs to be solved.

[0003] Currently, research on the instability and failure modes of unstable rock masses is relatively mature both domestically and internationally, and studies on the interaction between rock and soil and water are also extensive, mainly focusing on the process of rock mass intrusion and disintegration followed by water ingress. However, research on surge waves induced by unstable rock mass toppling into water remains significantly insufficient. Traditional methods do not fully consider the stage characteristics of rock mass movement under different inundation states, leading to large errors in surge wave height prediction. There is a lack of corresponding dynamic models to support accurate prediction and assessment of this type of surge wave disaster. Therefore, there is an urgent need to establish an assessment system and method for the scale of surge waves induced by unstable rock mass toppling into water in reservoirs. Summary of the Invention

[0004] According to one aspect of this application, a method for assessing the scale of swell induced by the toppling of unstable rock in a reservoir is provided to fill the gap in the dynamic model of swell induced by unstable rock in the prior art and to solve the problem of inaccurate assessment of swell scale. The method includes the following steps:

[0005] The method for assessing the scale of swell induced by the collapse of unstable rocks into the reservoir includes the following steps:

[0006] S1: Determine the submergence state of the rock mass based on the relative positional relationship between the bottom elevation of the rock mass foundation and the still water level of the reservoir;

[0007] S2: Based on the submerged state, according to the tilt angle and location of the rock mass at different times during the rock mass tilting process, determine the specific location of the rock mass in contact with the water body at the corresponding time, determine the drainage volume of the rock mass based on the specific location of the rock mass in contact with the water body, and deduce the external force on the rock mass.

[0008] S3: Using Newton's second law, calculate the acceleration, velocity, and displacement of the rock mass at different locations and at different times during its motion.

[0009] S4: Based on the velocity and displacement, construct a mechanical model that includes the coupling effect of dynamic pressure and static pressure to quantify the pressure distribution of the rock mass on the water body;

[0010] S5: Embed the aforementioned mechanical model into the iSquares numerical framework to establish the RGW-Squares rockfall-induced surge numerical model, and calculate the surge wave height to evaluate the rockfall-induced surge numerical model.

[0011] Preferably, in S1, the flooding state is defined based on the relative positional relationship between the rock mass and the water surface before the collapse, and the flooding state includes:

[0012] First submerged state: Elevation of the bottom surface of the rock mass foundation h p Below the elevation of still water surface wl The bottom of the rock mass is below the still water level;

[0013] Second submerged state: Elevation of the bottom surface of the rock mass foundation h p Equal to the elevation of still water surface wl The bottom surface of the rock mass is aligned with the still water surface;

[0014] Third submerged state: Elevation of the bottom surface of the rock mass foundation h p Elevation above still water surface wl The bottom of the rock mass is located above the water.

[0015] Preferably, in S2, the calculation process of the external force is as follows:

[0016] First submerged state: By assigning an initial rotational angular velocity and an initial tilting angle, the position of the rock mass in the unit area underwater at the corresponding moment is determined based on the angle of rock mass rotation, and the drainage volume of the unit area underwater is calculated to determine the external forces acting on the rock mass during the interaction between the rock mass and the water body.

[0017] Second and third submerged states: By calculating the initial rotational linear velocity of the rock mass at different positions when it reaches the water surface, the position of the unit area in contact with the water body at the corresponding moment is determined, the drainage volume at different positions of the underwater part is calculated, and the external forces acting on the rock mass during the interaction between the rock mass and the water body are determined.

[0018] Preferably, the selection of the calculation method for the specific location of the rock mass in contact with the water body at different times follows the following principles:

[0019] like h p <wl ,and > For the length of a unit area of ​​rock mass, the first inundation state calculation method is selected;

[0020] like h p=wl , and < the length of the unit area of the rock mass or > the height of the rock mass, then select the second submerged state calculation method;

[0021] If h p >wl [[ID=1"]], and | wl-h p | <H, then select the third submerged state calculation method;

[0022] The first submerged state calculation method is: by assigning an initial rotational angular velocity and an initial tipping angle, and based on the angle of rotation of the rock mass, determine the position of the rock mass underwater at the corresponding moment, calculate the drainage volume of the unit area of the part of the rock mass underwater, and thus determine the external force exerted on the rock mass during the interaction with the water body;

[0023] For the second and third submerged states, by calculating the initial rotational linear velocity at different positions when the rock mass reaches the water surface, determine the position of the square block in contact with the water body at the corresponding moment, calculate the drainage volume at different positions of the underwater part, and determine the external force exerted on the rock mass during the interaction with the water body.

[0024] Preferably, the external force includes gravity, buoyancy and resistance;

[0025] Among them, the gravity exerted on a single rock mass Fg is expressed as: ;

[0026] The buoyancy exerted on the rock mass at position r at time t is expressed as: ;

[0027] The water resistance exerted on the rock mass at position r at time t is expressed as: ;

[0028] Among them, is the density of the rock mass; is the density of water; g [[ID=[]is the acceleration due to gravity; is the volume of the rock blocks at each position. For the sake of easy estimation, in all three states can be calculated according to ; A is the area of the rock blocks at each position in contact with the water surface, ; C d is the water resistance coefficient; the drainage volume of the rock mass at different positions underwater The different flooding states are represented as follows:

[0029] First state of flooding:

[0030] Due to the elevation of the bottom surface of the rock mass foundation h p Less than the height of the still water surface wl ,but:

[0031] Given the initial angular velocity of rotation Initial tilt angle The initial linear velocity of rotation can then be expressed as: ; Water-facing side of the rock mass n The straight-line distance between the position and the base rotation point; where n It is an integer, and If the initial rotational angular velocity If the initial tilt angle is 0, then the initial tilt angle must satisfy the following condition: ;

[0032] When the rock mass rotates at an angle At that time, the vertical distance between different positions on the water-facing surface of the rock mass and the bottom surface of the base. Represented as:

[0033] ,in The value is updated in real time based on the linear velocity and angular velocity;

[0034] if That is, during the process of the rock mass rotating from its initial position to a horizontal position, the portion of the rock mass whose water-facing surface is underwater includes: The number of water blocks covered by the water-facing surface m for: Discharge volume at different underwater locations Expressed as:

[0035] ;

[0036] if Then the rock mass stops rotating and begins to move vertically downwards. The volume of water discharged at different underwater locations for:

[0037] ;

[0038] This expression means that the smaller of the two values ​​in parentheses is taken, where It represents the downward displacement of the rock mass at position r on the water-facing side at time t;

[0039] Second flooding state:

[0040] According to the kinetic energy theorem, the initial linear velocity of the rock mass when it reaches the water surface is... Represented as:

[0041] ;

[0042] Initial displacement of the rock mass when it reaches the water surface If the value is 0, then the drainage volume at different locations in the underwater part of the rock mass is... Represented as:

[0043] ;

[0044] Third state of flooding:

[0045] According to the kinetic energy theorem, the initial velocity of the rock mass when it reaches the water surface is... for:

[0046] ;

[0047] The initial position is the distance between different locations on the water-facing side of the rock mass and the water surface. Represented as:

[0048] ;

[0049] in θ The angle between the water-facing surface and the horizontal plane at the moment when the top of the rock mass comes into contact with the water surface;

[0050] From the above formula, we can see that In other words, initially all parts of the rock mass are above water, but after time iterations...

[0051] The volume of water discharged at different locations underwater. for: .

[0052] Preferably, the process in S3 for calculating the acceleration, velocity, and displacement of the rock mass at different locations r at different times in each stage, as well as the angle and angular velocity at each time under the first submerged state, is as follows:

[0053] Rock mass motion acceleration ;

[0054] The update speed at each time point is as follows: ;

[0055] The total displacement updated at each time step is: ;

[0056] The angle and angular velocity at each moment in the first submerged state can be updated based on the linear velocity, as follows:

[0057] , .

[0058] Preferably, the dynamic pressure in S4 is expressed as:

[0059] ;

[0060] Static pressure is expressed as:

[0061] ;

[0062] Total pressure is expressed as:

[0063] ;

[0064] if ,but ;

[0065] in, This represents the dynamic pressure exerted on the rock mass at position r at time t; This represents the static pressure exerted on the rock mass at position r at time t; This represents the total pressure exerted on the rock mass at position r at time t.

[0066] Preferably, the calculation process for the surge wave height in S5 is as follows:

[0067] The pressure exerted by the toppling rock mass on the water body is taken as the power source for the surge, and the gravity of the water body itself is taken as the power source for the propagation of the surge, which can be expressed as follows:

[0068] The power source of wave surge generation: ;

[0069] in: ; ;

[0070] The driving force of wave propagation: ;

[0071] in, During the generation of swells Time and location The total acceleration of the water body, for Time and location The acceleration caused by the total pressure when the rock mass interacts with the water body. for Time and location The acceleration of the water body due to gravity; for Time and location Total pressure gradient at the location; The water surface gradient;

[0072] Based on the initial velocity And based on the iSquares principle and method, the velocity of each tiny water body at each position r corresponding to each time t of the rock mass is updated. and water thickness ;

[0073] Based on the updated water thickness The water surface elevation at different locations and times of the rock mass was calculated. and surging waves ;

[0074] The water surface elevation The formula for calculation is: ;

[0075] The surge wave height The formula for calculation is: ;

[0076] in: For position Elevation of the riverbed bottom for Time and location The surging waves were high at that location. For position r The still water there is deep.

[0077] Preferably, the evaluation system includes:

[0078] The flooding status analysis module determines the flooding status based on the relationship between the bottom elevation of the rock mass foundation and the elevation of the still water surface.

[0079] The rock mass motion calculation module calculates the drainage volume and motion parameters based on the submerged state. The motion parameters include the acceleration, velocity and displacement at different times during the rock mass motion process.

[0080] The mechanical coupling module constructs a dynamic and static pressure coupling model.

[0081] The surge height calculation module is used to embed the iSquares framework to generate surge models and output surge wave height assessment results.

[0082] Preferably, the surge height calculation module is configured to: use rock pressure as the initial power source of the surge and water gravity gradient as the propagation power source; and use the time update and iterative solution of water acceleration through iSquares theory to update the real-time wave height and wave propagation process at different water areas.

[0083] Compared with the prior art, the present invention has the following beneficial technical effects:

[0084] This application determines the submergence state of the rock mass by comparing its relative elevation to the reservoir's still water level. This comprehensive approach considers the differences in the initial state of the rock mass under various submergence conditions, accurately defining the mechanical boundary conditions for different scenarios and avoiding model errors caused by ambiguous submergence state classifications in traditional methods. Based on this, the application analyzes the interaction between the rock mass and the water body during submergence under different submergence states. By determining the specific contact point between the rock mass and the water body at different times during the rock mass's tilting process, and based on this contact point, the application determines the drainage volume of the rock mass and derives the external forces acting on it. This precise quantification of the rock mass's pushing effect on the water body avoids the simplification errors of traditional single-stage models, providing crucial information for accurate subsequent analysis of rock mass movement and wave generation. Finally, based on Newton's second law, the application calculates the acceleration, velocity, and displacement of the rock mass during its movement, combining the contact area and drainage volume, and analyzes the impact of the rock mass movement on the water body. This study proposes a mechanical model combining dynamic and static pressure to realistically reflect the energy transfer and dissipation during rock mass movement, avoiding the subjectivity of empirical formulas. It fills a gap in existing research on mechanical models for rock mass toppling failure modes. By constructing a mechanical model that incorporates the coupling effects of dynamic and static pressures, the pressure distribution of the rock mass on the water body is quantified. This coupled model can simultaneously capture the impact effect of rock mass movement (dynamic pressure) and the stabilizing effect of water static pressure (static pressure), avoiding the limitations of a single pressure model and more accurately reflecting the pressure mechanism of rock mass movement on the water body. This mechanical model is embedded into the iSquares numerical framework to establish the RGW-Squares numerical model of rock mass toppling-induced surge waves. The dynamic sources in the generation and propagation of surge waves are analyzed, and the surge wave height is calculated based on the pressure exerted by the rock mass toppling on the water body and the propagation of the water's own gravity, to accurately assess the scale of surge waves induced by rock mass toppling. This provides reliable technical support for ensuring safe navigation in reservoirs and protecting people's lives, and provides an important technical foundation for subsequent analysis of the disaster chain of rock mass-induced surge waves. Attached Figure Description

[0085] Figure 1 This is a general framework diagram of a reservoir rockfall inrush surge scale assessment system according to the present invention;

[0086] Figure 2 This is a schematic diagram of the forces acting on the rock mass as it falls into the water and interacts with it under submerged conditions.

[0087] Figure 3 This is a schematic diagram of the forces acting on the rock mass as it falls into the water and interacts with the water body under three different submerged conditions.

[0088] Figure 4 This is a schematic diagram of the installation of pressure sensors on the rock mass;

[0089] Figure 5 This is a schematic diagram of the wave height meter installation during the experiment;

[0090] Figure 6 It is a comparison curve of test pressure and simulated pressure data under three flood conditions S1, S2 and S3;

[0091] Figure 7 The results are a comparison of numerical simulation and measured surge wave height data under three inundation conditions S1, S2 and S3. Detailed Implementation

[0092] The method for assessing the scale of swell induced by the collapse of unstable rocks into the reservoir includes the following steps:

[0093] S1: Determine the submergence state of the rock mass based on the relative positional relationship between the bottom elevation of the rock mass foundation and the still water level of the reservoir;

[0094] S2: Based on the submerged state, according to the tilt angle and location of the rock mass at different times during the rock mass tilting process, determine the specific location of the rock mass in contact with the water body at the corresponding time, determine the drainage volume of the rock mass based on the specific location of the rock mass in contact with the water body, and deduce the external force on the rock mass.

[0095] S3: Using Newton's second law, calculate the acceleration, velocity, and displacement of the rock mass at different locations and at different times during its motion.

[0096] S4: Based on the velocity and displacement, construct a mechanical model that includes the coupling effect of dynamic pressure and static pressure to quantify the pressure distribution of the rock mass on the water body;

[0097] S5: Embed the aforementioned mechanical model into the iSquares numerical framework to establish the RGW-Squares rockfall-induced surge numerical model, and calculate the surge wave height to evaluate the rockfall-induced surge numerical model.

[0098] It should be noted that:

[0099] In one embodiment of this application, the water-facing surface of the rock mass is divided into n unit square blocks according to a unit length Dc. Based on the submerged state, the position of the square block in contact with the water body at the corresponding moment can be determined according to the tilt angle and position of the rock mass at different moments during the rock mass tilting process, and the external forces on the rock mass can be deduced, wherein the external forces include gravity, buoyancy and resistance.

[0100] By combining Newton's second law, the acceleration, velocity and displacement of a unit square block at different times and locations on the rock mass during its motion are calculated, thereby obtaining the acceleration, velocity and displacement of the rock mass at different locations at different times during its motion.

[0101] In this application, based on the relative position of the bottom elevation of the rock mass foundation and the still water level of the reservoir, the rock mass is divided into completely submerged,

[0102] The study precisely defines the mechanical boundary conditions under three states: partially submerged and unsubmerged. For different submerged states, the rock mass entry process into water is divided into multiple stages, and the contact area, drainage volume, and motion parameters (acceleration, velocity, and displacement) of each stage are dynamically calculated. A coupled mechanical model combining dynamic pressure (determined by the rock mass velocity) and static pressure (determined by the hydrostatic pressure of the water body) is proposed to accurately quantify the pressure distribution of the rock mass on the water body. The mechanical model is embedded into the iSquares numerical framework to construct the RGW-Squares model, which enables efficient simulation of the generation and propagation of surge waves, significantly improving the accuracy and efficiency of calculation.

[0103] Furthermore, in S1, based on the relative positional relationship between the bottom elevation of the rock mass foundation and the elevation of the still water surface, the inundation state of the rock mass is classified, and the inundation state specifically includes:

[0104] Rock mass foundation bottom elevation h p Below the elevation of still water surface wl The bottom surface of the rock mass is below the still water level, meaning the bottom of the rock mass is submerged by water; this is recorded as the first submerged state. The elevation of the bottom surface of the rock mass foundation... h p Equal to the elevation of still water surface wl When the bottom surface of the rock mass is aligned with the still water surface, it is recorded as the second submerged state; the elevation of the bottom surface of the rock mass foundation... h p Elevation above still water surface wl The bottom surface of the rock mass is above the water, which is recorded as the third submerged state.

[0105] It should be noted that:

[0106] In one embodiment of this application, for a rectangular unstable rock mass with height H, thickness T, and width W, three submersion states can be classified based on the relative position of the rock mass and the water surface before it topples: the base elevation is higher than the still water surface elevation, meaning the unstable rock mass is not submerged; the base elevation is equal to the still water surface elevation, meaning the unstable rock mass is just in contact with the water surface; and the base elevation is lower than the still water surface elevation, meaning the unstable rock mass is partially or completely submerged. The submersion status of the unstable rock mass is determined based on these relative positional relationships. Different submersion states affect the energy transfer and surge generation mechanism when the unstable rock mass enters the water, and are important basic information for assessing the surge scale.

[0107] Furthermore, in S2, the calculation process for the external force is as follows:

[0108] First submerged state: By assigning an initial rotational angular velocity and an initial tilting angle, the position of the rock mass in the unit area underwater at the corresponding moment is determined based on the angle of rock mass rotation, and the drainage volume of the unit area underwater is calculated to determine the external forces acting on the rock mass during the interaction between the rock mass and the water body.

[0109] Second and third submerged states: By calculating the initial rotational linear velocity of the rock mass at different positions when it reaches the water surface, the position of the unit area in contact with the water body at the corresponding moment is determined, the drainage volume at different positions of the underwater part is calculated, and the external forces acting on the rock mass during the interaction between the rock mass and the water body are determined.

[0110] It should be noted that:

[0111] In one embodiment of this application, the unit area of ​​rock mass in contact with water under the first, second, and third flooding states refers to dividing the assessment area on a horizontal plane into multiple virtual, tiny square blocks, with a length of [missing information - likely a unit of measurement]. Dc At the same time, the water-facing surface of the rock mass is also calculated per unit length. Dc The rock mass is divided into n unit square blocks, the size of which changes in real time as the rock mass rotates. Based on the submerged state, the position of the square block in contact with the water at different times during the rock mass's collapse is determined according to the tilt angle and location. This allows us to obtain the position of the unit area of ​​the rock mass underwater at the corresponding time, thereby deriving the external forces acting on the rock mass, including gravity, buoyancy, and drag.

[0112] Furthermore, the rock mass is simulated based on its submerged state, specifically as follows:

[0113] For the first submerged state, at the initial moment of rock mass movement, by assigning an initial rotational angular velocity and an initial tilting angle, the underwater position of the rock mass at the corresponding moment is determined based on the angle of rotation. The drainage volume at different underwater locations is calculated, and the external forces acting on the rock mass during its interaction with the water are determined. These external forces include gravity, buoyancy, and water resistance. Typically, in the first submerged state, the submersion depth is... Greater than Dc If the flood depth Less than Dc If the submersion is very shallow, then the calculation is approximated according to the second type of submersion state.

[0114] For the second and third submerged states, the initial rotational linear velocity of the rock mass at different positions when it reaches the water surface is calculated to determine the position of the square block in contact with the water at the corresponding moment, calculate the drainage volume at different positions of the underwater part, and determine the external forces acting on the rock mass during the interaction between the rock mass and the water.

[0115] Furthermore, the calculation process for the external force under the first, second, and third flooding states is as follows:

[0116] ① First submerged state: Elevation of the bottom surface of the rock mass foundation h p Less than the height of the still water surface wl ,Right now h p <wl， but:

[0117] Given the initial angular velocity of rotation Initial tilt angle The initial linear velocity of rotation can then be expressed as: ; Water-facing side of the rock mass n The straight-line distance between the position and the base rotation point; where n It is an integer, and If the initial rotational angular velocity If the initial tilt angle is 0, then the initial tilt angle must satisfy the following condition: .

[0118] When the rock mass rotates by a certain angle At that time, the vertical distance between different positions on the water-facing surface of the rock mass and the bottom surface of the base. for:

[0119] ,in The value is updated in real time based on the linear velocity and angular velocity.

[0120] if That is, during the process of the rock mass rotating from its initial position to a horizontal position, the portion of the rock mass whose water-facing surface is underwater includes: The number of water blocks m covering the water-facing surface is: Discharge volume at different underwater locations Approximate expression: .

[0121] if Then the rock mass stops rotating and begins to move vertically downwards. The volume of water discharged at different underwater locations for: This expression means that the smaller of the two values ​​in parentheses is taken, where It represents the downward displacement of the rock mass at position r on the water-facing side at time t.

[0122] ② Second submerged state: Ground elevation of rock mass base h p equal to the height of the still water surface wl ,h p =wl or , then:

[0123] According to the kinetic energy theorem, the initial linear velocity of the rock mass when it reaches the water surface is:

[0124] The initial displacement of the rock mass when it reaches the water surface is: ;

[0125] The drainage volume at different positions of the underwater part is: ;

[0126] ③ The third submerged state: The elevation of the ground of the rock mass base h p is greater than the height of the static water surface wl， That is h p >] wl , then:

[0127] According to the kinetic energy theorem, the initial velocity of the rock mass when it reaches the water surface is:

[0128] ;

[0129] The distance between different positions on the water-facing surface of the rock mass and the water surface at the initial position is:

[0130] ;

[0131] Where θ is Figure 2 and Figure 3 the angle between the water-facing surface and the horizontal plane at the moment when the top of the rock mass shown in touches the water surface.

[0132] From the above formula, it can be seen that , that is, all parts of the rock mass are located above the water in the initial state. When time iteration is carried out,

[0133] , it means that the corresponding part of the block enters the water and generates pressure on the water body.

[0134] The drainage volume at different positions of the underwater part is: ;

[0135] The formula for the submerged state 3 is applicable to the case of | wl-h p | <H. For high-position dangerous rock masses, that is, | wl-hp |> H can be evaluated according to flooding state 2.

[0136] Under various submersion conditions, the gravitational force on a single rock mass is: ;

[0137] The buoyancy force on the rock mass at position r at time t for: ;

[0138] Water resistance experienced by the rock mass at position r at time t for: ;

[0139] in, The density of the rock mass; The density of water; g It is the acceleration due to gravity; Let represent the volume of the rock block at each location. For ease of estimation, the volumes under the three conditions are... All can be pressed Calculate; A represents the area of ​​the rock block at each location in contact with the water surface. ; C d This is the water resistance coefficient; Let r be the velocity of the rock mass at position r at time t. This velocity needs to be updated in real time according to the acceleration at different times.

[0140] Furthermore, in S3, the process of calculating the acceleration, velocity, and displacement of the rock mass at different locations r at different times in each stage, as well as the angle and angular velocity at each time under the first submerged state, is as follows:

[0141] Rock mass motion acceleration ;

[0142] The update speed at each time point is as follows: ;

[0143] The total displacement updated at each time step is: ;

[0144] The angle and angular velocity at each moment under submerged state 1 can be updated based on the linear velocity, as follows:

[0145] , .

[0146] Furthermore, in S4, based on the calculated velocity and displacement, the dynamic and static pressures during the rock mass movement are calculated, and a mechanical model combining dynamic and static pressures is constructed:

[0147] ; ;

[0148] The total pressure is: ;

[0149] if ,but .

[0150] in, This represents the dynamic pressure exerted on the rock mass at position r at time t; This represents the static pressure exerted on the rock mass at position r at time t; This represents the total pressure exerted on the rock mass at position r at time t.

[0151] Furthermore, the calculation process for the surge wave height in S5 is as follows:

[0152] The pressure exerted by the toppling rock mass on the water body is taken as the power source for the surge, and the gravity of the water body itself is taken as the power source for the propagation of the surge, which can be expressed as follows:

[0153] The power source of wave surge generation: ;

[0154] in: ; ;

[0155] Power source for wave propagation: ;

[0156] in, During the generation of swells Time and location The total acceleration of the water body, for Time and location The acceleration caused by the total pressure when the rock mass interacts with the water body. for Time and location The acceleration of the water body due to gravity; for Time and location Total pressure gradient at the location; This represents the surface gradient of the water body. When the rock mass interacts with the water body, the water is simultaneously subjected to pressure and gravity, which is the wave generation stage. When the rock mass sinks a certain distance underwater, the water-rock pressure ceases, and the water movement is driven solely by gravitational acceleration, entering the wave propagation stage, with an acceleration of... .

[0157] Given initial velocity Based on the iSquares principle and method, and the water acceleration obtained at the different stages mentioned above, the velocity of each tiny water block at each time t and each position r can be updated. and thickness Furthermore, the system maintains momentum and mass conservation during the update and iteration process.

[0158] When the updated water depth was obtained Then, the value at any given time can be obtained using the following formula. t any position r water surface elevation at the location and surging waves .

[0159] Water surface elevation: ;

[0160] Swell height: ;

[0161] in: For position Elevation of the riverbed bottom for Time and location The surging waves were high at that location. For position r The still water there is deep.

[0162] A system for assessing the scale of swell induced by a rockfall in a reservoir, comprising:

[0163] The flooding state analysis module is used to classify the rock mass into three flooding states based on the relative magnitude of the elevation of the base bottom surface and the elevation of the still water surface.

[0164] The rock mass motion calculation module calculates the drainage volume and motion parameters based on the submerged state. The motion parameters include the acceleration, velocity and displacement at different times during the rock mass motion process.

[0165] The mechanical coupling module is used to analyze the pressure effect of rock mass movement on water body based on the calculated velocity and displacement, and to construct a mechanical model that combines dynamic pressure and static pressure.

[0166] The surge height calculation module is used to embed the mechanical model into the iSquares numerical framework, establish the RGW-Squares rockfall-induced surge numerical model, take the pressure of the rockfall acting on the water as the power source of the surge, and the gravity of the water itself as the power source of the surge propagation, and decompose the two forces according to the water surface gradient to obtain the acceleration of the water movement. The surge wave height is calculated by the relationship between the water thickness and the water depth, thereby realizing the assessment of the surge scale induced by rockfall.

[0167] like Figure 1As shown, the specific implementation process of the system and method for assessing the scale of swell induced by the collapse of unstable rocks into water in one embodiment of this application is as follows:

[0168] 1) The flooding state analysis module is used to classify the rock mass into three flooding states based on the relative magnitude of the elevation of the base bottom surface and the elevation of the still water surface;

[0169] Specifically, when the elevation of the base of the rock mass is less than the elevation of the still water level, the bottom of the rock mass is submerged by water, which is recorded as the first submerged state (submerged state 1); when the elevation of the base of the rock mass is equal to the elevation of the still water level, the bottom of the rock mass is level with the water level, which is recorded as the second submerged state (submerged state 2); when the elevation of the base of the rock mass is greater than the elevation of the still water level, the bottom of the rock mass is above the water level, which is recorded as the third submerged state (submerged state 3).

[0170] 2) Rock mass motion calculation module, which calculates drainage volume and motion parameters based on the submerged state. The motion parameters include acceleration, velocity and displacement at different times during the rock mass motion process;

[0171] 3) Mechanical coupling module, used to analyze the pressure effect of rock mass movement on water body based on calculated velocity and displacement, and to construct a mechanical model that combines dynamic pressure and static pressure;

[0172] 4) The surge height calculation module is used to embed the mechanical model into the iSquares numerical framework, establish the RGW-Squares rockfall-induced surge numerical model, take the pressure of the rockfall acting on the water as the power source of the surge, and the gravity of the water itself as the power source of the surge propagation, and decompose the two forces according to the water surface gradient to obtain the acceleration of the water movement. The surge height is calculated by the relationship between the water thickness and the water depth, thereby realizing the assessment of the surge scale induced by rockfall.

[0173] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the following examples. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0174] Example 1

[0175] Surge assessment when the bottom of the rock mass is below the still water level

[0176] This embodiment uses a physical model test of rock mass toppling and surging waves as an example, with the still water surface elevation... wl =0.3m, Elevation of the bottom surface of the unstable rock base h p =0.25m (completely submerged state, corresponding to) Figure 3 Submerged state 1). Rock mass dimensions are height. H =0.5m, thickness T =0.1m, width W =0.1m, density ρ rock =2400kg / m 3 gravitational acceleration g =9.8m / s 2 .

[0177] Example 2

[0178] Surge assessment when the bottom of the rock mass is aligned with the still water surface

[0179] This embodiment uses a physical model test of rock mass toppling and surging waves as an example, with the still water surface elevation... wl =0.3m, Elevation of the bottom surface of the unstable rock base h p =0.3m (completely submerged state, corresponding to) Figure 3 Submerged state 2). Rock mass dimensions are height. H =0.5m, thickness T =0.1m, width W =0.1m, density ρ rock =2400kg / m 3 Gravitational acceleration g =9.8m / s 2 .

[0180] Example 3

[0181] Surge assessment of rock mass with bottom surface above still water level

[0182] still water surface elevation wl =0.3m, Elevation of the bottom surface of the unstable rock base h p =0.35m (corresponding to) Figure 3 Submerged state 3). Rock mass dimensions are height. H =0.5m, thickness T =0.1m, width W =0.1m, density ρ rock =2400kg / m 3 Gravitational acceleration g =9.8m / s 2 .

[0183] To verify the effectiveness of the method for assessing the scale of surge induced by rockfall in a reservoir as described in this application, the above three cases (i.e., three inundation conditions S1, S2, and S3) were calculated and evaluated based on the RGW-Squares rockfall-induced surge assessment model. The schematic diagrams of the installation of pressure sensors on the rock mass under the three inundation conditions S1, S2, and S3 are shown below. Figure 4 As shown in the diagram, the installation schematic of the wave height meter for the experimental species is as follows: Figure 5 As shown, the pressure data comparison results for the three flooding conditions S1, S2, and S3 are as follows: Figure 6 As shown, by Figure 6 It can be seen that under the three operating conditions S1, S2, and S3, the overall trends of the experimental and simulated pressures are basically consistent, both showing a trend of rapid rise to a peak followed by a gradual decline. Under the three submersion conditions S1, S2, and S3, the trends, peak values, and rates of pressure change between the simulated and experimental pressures show good consistency. This indicates that the simulation model can reflect the pressure changes in actual experiments to a certain extent and can help explore the mechanism by which submersion conditions affect pressure characteristics. Therefore, it can be concluded that the RGW-Squares rockfall-induced surge assessment model has a high degree of agreement with experimental data, can effectively simulate actual surge pressure changes, and possesses reliability. Furthermore, the model accurately reflects the differences in pressure characteristics under different submersion conditions.

[0184] Wave height data comparison results are as follows Figure 7 As shown, by Figure 7 It can be seen that the numerical simulations under all three operating conditions can reflect the fluctuation frequency and other characteristics of the surge wave height well. That is, the density (fluctuation frequency) of the simulated wave height and the measured wave height curves are basically consistent, and both can reflect the dynamic variation characteristics of the surge wave height under the corresponding inundation conditions. A comparison of the numerical simulation and measured surge wave height data under the three inundation conditions S1, S2, and S3 shows that the numerical simulation is in good agreement with the measured data in terms of overall trend and fluctuation characteristics, and can reflect the changes in surge wave height well. This indicates that the simulation method used can reflect the actual wave height variation pattern to a certain extent. Regardless of the inundation height conditions S1, S2, or S3, the simulation results can capture the approximate time points and fluctuation period characteristics of the peak and trough values ​​of the experimental wave height.

[0185] The numerical simulation and measured first wave height and error calculation are shown in Table 1.

[0186] Table 1. Numerical simulation and measured first wave height and error table

[0187]

[0188] As shown in Table 1, under condition S1, the minimum error is WG2 (-0.6%), the maximum error is WG3 (-6.1%), and the absolute value of the error at all measuring points is ≤6.1%, with no error exceeding ±10%. Under condition S2, the minimum error is WG7 (-2.5%), the maximum errors are WG3 (-11.3%) and WG6 (11.4%), and the absolute error at most monitoring points is ≤7.5%. Under condition S3, the minimum error is WG2 (0%), the maximum error is WG4 (14.3%), and the average error is approximately 6%. In summary, the RGW-Squares method exhibits high simulation accuracy in the first 5 seconds of surge propagation, and 88% of the data errors remain within 10%. Therefore, it can be concluded that the RGW-Squares rockfall-induced surge assessment model has a high degree of agreement with the experimental data, indicating that this numerical simulation method can accurately reflect the surge propagation characteristics induced by rockfall. The results further validate the rationality and reliability of the rock mass toppling surge dynamics model proposed in this study, providing important technical support for subsequent risk prediction of rock mass toppling surge disasters.

Claims

1. A method for assessing the scale of swell induced by the toppling of unstable rocks into the water of a reservoir, characterized in that, Includes the following steps: S1: Determine the submergence state of the rock mass based on the relative positional relationship between the bottom elevation of the rock mass foundation and the elevation of the still water surface of the reservoir; S2: Based on the submerged state, according to the tilt angle and location of the rock mass at different times during the rock mass tilting process, determine the specific location of the rock mass in contact with the water body at the corresponding time, determine the drainage volume of the rock mass based on the specific location of the rock mass in contact with the water body, and deduce the external force on the rock mass. S3: Using Newton's second law, calculate the acceleration, velocity, and displacement of the rock mass at different locations and at different times during its motion. S4: Based on the velocity and displacement, construct a mechanical model that includes the coupling effect of dynamic pressure and static pressure to quantify the pressure distribution of the rock mass on the water body; S5: Embed the mechanical model into the iSquares numerical framework, establish the RGW-Squares rockfall-induced surge numerical model, and calculate the surge wave height to evaluate the rockfall-induced surge numerical model. In S1, the flooding state is defined based on the relative positional relationship between the rock mass and the water surface before the collapse, and the flooding state includes: First submerged state: Elevation of the bottom surface of the rock mass foundation h p Below the elevation of still water surface wl The bottom of the rock mass is below the still water level; Second submerged state: Elevation of the bottom surface of the rock mass foundation h p Equal to the elevation of still water surface wl The bottom surface of the rock mass is aligned with the still water surface; Third submerged state: Elevation of the bottom surface of the rock mass foundation h p Elevation above still water surface wl The bottom of the rock mass is located above the water; The selection of the calculation method for the specific location of the contact between the rock mass and the water body at different times follows the following principles: like h p <wl ,and > For the length of a unit area of ​​rock mass, the first inundation state calculation method is selected; like h p =wl ,as well as < The length of a unit area of ​​rock mass or > For the height of the rock mass, the second inundation state calculation method is selected; If h p >wl , and | wl-h p | <H, then select the third submerged state calculation method; H is the height of the rock mass; The first submerged state calculation method is as follows: by assigning an initial rotational angular velocity and an initial tilting angle, the position of the rock mass underwater at the corresponding moment is determined according to the angle of rock mass rotation, and the drainage volume of a unit area of ​​the rock mass underwater is calculated, thereby determining the external force on the rock mass during the interaction between the rock mass and the water body; The second and third submerged states are determined by calculating the initial rotational linear velocity of the rock mass at different positions when it reaches the water surface, judging the position of the square block in contact with the water at the corresponding moment, calculating the drainage volume at different positions of the underwater part, and determining the external forces acting on the rock mass during the interaction between the rock mass and the water.

2. The method for assessing the scale of swell induced by the collapse of a dangerous rock into the water of a reservoir, as described in claim 1, is characterized in that... In S2, the calculation process for the external force is as follows: First submerged state: By assigning an initial rotational angular velocity and an initial tilting angle, the position of the rock mass in the unit area underwater at the corresponding moment is determined based on the angle of rock mass rotation, and the drainage volume of the unit area underwater is calculated to determine the external forces acting on the rock mass during the interaction between the rock mass and the water body. Second and third submerged states: By calculating the initial rotational linear velocity of the rock mass at different positions when it reaches the water surface, the position of the unit area in contact with the water body at the corresponding moment is determined, the drainage volume at different positions of the underwater part is calculated, and the external forces acting on the rock mass during the interaction between the rock mass and the water body are determined.

3. The method for assessing the scale of swell induced by the collapse of a dangerous rock into the water of a reservoir, as described in claim 1, is characterized in that... The external forces include gravity, buoyancy, and drag; Among them, the gravity of a single rock mass F g Represented as: ; The buoyancy force on the rock mass at position r at time t Represented as: ; Water resistance experienced by the rock mass at position r at time t Represented as: ; in, The density of the rock mass; The density of water; g It is the acceleration due to gravity; Let represent the volume of the rock block at each location. For ease of estimation, the volumes under the three conditions are... All can be pressed calculate; A This refers to the area of ​​the rock mass at each point in contact with the water surface. ; C d This is the water resistance coefficient; D C The unit length of the rock mass; T The thickness of the rock mass; Discharge volume at different locations in the underwater part of the rock mass The different flooding states are represented as follows: First state of flooding: Due to the elevation of the bottom surface of the rock mass foundation h p Less than the height of the still water surface wl ,but: Given the initial angular velocity of rotation Initial tilt angle The initial linear velocity of rotation can then be expressed as: ; Water-facing side of the rock mass n The straight-line distance between the position and the base rotation point; where n It is an integer, and If the initial rotational angular velocity If the initial tilt angle is 0, then the initial tilt angle must satisfy the following condition: ; When the rock mass rotates at an angle At that time, the vertical distance between different positions on the water-facing surface of the rock mass and the bottom surface of the base. Represented as: ,in The value is updated in real time based on the linear velocity and angular velocity; if That is, during the process of the rock mass rotating from its initial position to a horizontal position, the portion of the rock mass whose water-facing surface is underwater includes: The number of water blocks covered by the water-facing surface m for: Discharge volume at different underwater locations Expressed as: ； if Then the rock mass stops rotating and begins to move vertically downwards. The volume of water discharged at different underwater locations for: ； This expression means that the smaller of the two values ​​in parentheses is taken, where It represents the downward displacement of the rock mass at position r on the water-facing side at time t; Second flooding state: According to the kinetic energy theorem, the initial linear velocity of the rock mass when it reaches the water surface is... Represented as: ； Initial displacement of the rock mass when it reaches the water surface If the value is 0, then the drainage volume at different locations in the underwater part of the rock mass is... Represented as: ； Third state of flooding: According to the kinetic energy theorem, the initial velocity of the rock mass when it reaches the water surface is... for: ； The initial position is the distance between different locations on the water-facing side of the rock mass and the water surface. Represented as: ； in θ The angle between the water-facing surface and the horizontal plane at the moment when the top of the rock mass comes into contact with the water surface; From the above formula, we can see that In other words, initially all parts of the rock mass are above water, but after time iterations... The volume of water discharged at different locations underwater. for: 。 4. The method for assessing the scale of swell induced by the collapse of a dangerous rock into the water of a reservoir, as described in claim 3, is characterized in that... The process in S3 for calculating the acceleration, velocity, and displacement of the rock mass at different locations r at different times in each stage, as well as the angle and angular velocity at each time under the first submerged state, is as follows: Rock mass motion acceleration ; The update speed at each time point is as follows: ; The total displacement updated at each time step is: ; The angle and angular velocity at each moment in the first submerged state can be updated based on the linear velocity, as follows: ， 。 5. The method for assessing the scale of swell induced by the collapse of a dangerous rock into the water of a reservoir, as described in claim 3, is characterized in that... The dynamic pressure in S4 is expressed as: ； Static pressure is expressed as: ； Total pressure is expressed as: ； if ,but ; in, This represents the dynamic pressure exerted on the rock mass at position r at time t; This represents the static pressure exerted on the rock mass at position r at time t; This represents the total pressure exerted on the rock mass at position r at time t.

6. The method for assessing the scale of swell induced by the collapse of a dangerous rock into the water of a reservoir, as described in claim 3, is characterized in that... The calculation process for surge wave height in S5 is as follows: The pressure exerted by the toppling rock mass on the water body is taken as the power source for the surge, and the gravity of the water body itself is taken as the power source for the propagation of the surge, which can be expressed as follows: The power source of wave surge generation: ; in: ; ; The driving force of wave propagation: ; in, During the generation of surge waves Time and location The total acceleration of the water body, for Time and location The acceleration caused by the total pressure when the rock mass interacts with the water body. for Time and location The acceleration of water bodies caused by gravity; for Time and location Total pressure gradient at the location; The water surface gradient; Based on the initial velocity And based on the iSquares principle and method, the velocity of each tiny water body at each position r corresponding to each time t of the rock mass is updated. and water thickness ; Based on the updated water thickness The water surface elevation at different locations and times of the rock mass was calculated. and surging waves ; The water surface elevation The formula for calculation is: ; The surge wave height The formula for calculation is: ; in: For position Elevation of the riverbed bottom for Time and location The surging waves were high at that location. For position r The still water there is deep.

7. A system for assessing the scale of swell induced by a rockfall in a reservoir, characterized in that, The method for assessing the scale of swell induced by the overturning of unstable rocks into the water in reservoirs, as described in any one of claims 1 to 6, comprises: The flooding status analysis module determines the flooding status based on the relationship between the bottom elevation of the rock mass foundation and the elevation of the still water surface. The rock mass motion calculation module calculates the drainage volume and motion parameters based on the submerged state. The motion parameters include the acceleration, velocity and displacement at different times during the rock mass motion process. The mechanical coupling module constructs a dynamic and static pressure coupling model. The surge height calculation module is used to embed the iSquares framework to generate surge models and output surge wave height assessment results.

8. The system for assessing the scale of swell induced by a rockfall in a reservoir, as described in claim 7, is characterized in that... The surge height calculation module is configured to: use rock pressure as the initial power source of the surge and water gravity gradient as the propagation power source; and use the time update and iterative solution of water acceleration through iSquares theory to update the real-time wave height and wave propagation process at different water areas.

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