System and method for evaluating scale of surge induced by dumping of reservoir dangerous rock into water

Abstract

The invention discloses a system and a method for evaluating the scale of surge induced by reservoir dangerous rock pouring into water. The method comprises the steps that the rock mass submerging state is determined according to the relative position relation between the rock mass base bottom face elevation and the reservoir still water face elevation; judging the contact position of the rock mass and the water body at the corresponding moment according to the inclination angles and the positions of the rock mass at different moments in the dumping process of the rock mass, determining the drainage volume of the rock mass and deducing the external force borne by the rock mass; calculating the acceleration, the speed and the displacement of different parts of the rock mass in the movement process, and constructing a mechanical model containing a dynamic pressure and static pressure coupling effect; and the mechanical model is embedded into an iSquare numerical framework, an RGW-Square dangerous rock dumping induced surge numerical model is established, and the dynamic wave height of the surge is calculated to evaluate the scale of the dangerous rock dumping induced surge. The invention provides a system and a method for evaluating the scale of surge induced by reservoir dangerous rock dumping into water, fills the gap of a dynamic model of surge induced by reservoir dangerous rock dumping, and solves the problems of inaccurate surge scale evaluation and the like.

Description

Technical Field

[0001] The present invention belongs to the technical field of surge disaster scale assessment, and in particular relates to a system and method for assessing the scale of surges induced by the dumping of dangerous rocks into water in a reservoir. Background Art

[0002] The collapse of dangerous rocks refers to the phenomenon that the rock mass located on the steep hillside collapses and collapses under the action of its own weight during the long-term evolution process, affected by factors such as crack expansion and weathering deterioration, and eventually bends and collapses in the air-facing direction. If the high-level rock mass collapses into the water, it will cause severe secondary surge disasters, posing a serious threat to the geological safety of the waterway, coastal infrastructure and the lives of residents. On October 20, 2011, a dangerous rock collapsed in the Yangtze River section of Wangxia Village, Liangping Township, Wushan County, Chongqing, causing the waterway to be blocked and more than 2,000 passengers to be stranded. On July 27, 2022, a local collapse and rockfall occurred at the Diaozui dangerous rock on the right bank of the Qutang Gorge of the Yangtze River, with a rockfall volume of about 30m 3 The height difference from the Yangtze River is approximately 160 meters, and the vertical impact caused a splash of approximately 25 meters. On January 8, 2022, a rock face suddenly broke in the Furnas Canyon in Brazil, sending a 5-meter-high rock mass crashing into the water and onto three tourist boats. The accident killed 10 people and injured 32. Therefore, accurately assessing the failure mechanisms of dangerous rock masses and the resulting surge hazards induced by collapse are critical technical issues that urgently need to be addressed.

[0003] Currently, research on the instability and failure modes of dangerous rock masses is relatively mature, and research on rock-soil-water interactions is also extensive. This research primarily focuses on the process of rock mass disintegration and subsequent entry into water. However, research on the surge waves induced by the collapse of dangerous rock masses into water remains significantly insufficient. Traditional methods fail to fully consider the stage-specific characteristics of rock mass movement under different submergence states, resulting in large errors in the prediction of surge heights. There is a lack of corresponding dynamic models to accurately predict and assess this type of surge disaster. Therefore, there is an urgent need to establish a system and method for assessing the scale of surge waves induced by the collapse of dangerous rock masses into water in reservoirs. Summary of the Invention

[0004] According to one aspect of the present application, a method for assessing the scale of surges induced by the collapse of dangerous rocks in a reservoir is provided to fill the gap in the existing dynamic model of surges induced by the collapse of dangerous rocks in a reservoir and to solve the problem of inaccurate surge scale assessment. The method comprises the following steps:

[0005] The method for assessing the scale of surge waves induced by the dumping of dangerous rocks into the reservoir includes the following steps:

[0006] S1: Determine the submerged state of the rock mass based on the relative positional relationship between the bottom elevation of the rock mass base and the elevation of the reservoir's still water surface;

[0007] S2: Based on the submerged state, according to the inclination angle and position of the rock mass at different moments during the rock mass collapse process, determining the specific contact position between the rock mass and the water body at the corresponding moment, and determining the displacement volume of the rock mass and deriving the external force acting on the rock mass based on the specific contact position between the rock mass and the water body;

[0008] S3: Combined with 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: constructing a mechanical model including the coupling of dynamic pressure and static pressure based on the velocity and displacement to quantify the pressure distribution of the rock mass on the water body;

[0010] S5: The mechanical model is embedded in the iSquares numerical framework to establish the RGW-Squares dangerous rock collapse-induced surge wave numerical model, and the surge wave height is calculated to evaluate the dangerous rock collapse-induced surge wave numerical model.

[0011] Preferably, in S1, the submerged state is divided according to the relative position relationship between the rock mass and the water surface before the collapse, and the submerged state includes:

[0012] First flooding state: rock mass base bottom elevation h p Below the still water level wl, the bottom of the rock mass is below the still water level;

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

[0014] The third submerged state: rock mass base bottom elevation h p Above the still water level wl, the bottom of the rock mass is above the water.

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

[0016] First submerged state: By assigning an initial rotational angular velocity and an initial tilting angle, the position of the unit area of ​​the rock mass under water at the corresponding moment is determined according to the angle of rotation of the rock mass. The displacement volume of the unit area of ​​the rock mass under water is calculated to determine the external force exerted on the rock mass during the interaction between the rock mass and the water.

[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 where the rock mass contacts the water at the corresponding moment is determined, the displacement volume at different positions of the underwater part is calculated, and the external force acting on the rock mass during the interaction between the rock mass and the water is determined.

[0018] Preferably, the method for calculating the specific contact position between the rock mass and the water body at different times follows:

[0019] If h p <wl,且|wl-h p |>the length of the rock mass unit area, the first flooding state calculation method is selected;

[0020] If h p =wl, and |wl-h p |<length of rock mass unit area or |wl-h p |> the height of the rock mass, the second flooding state calculation method is selected;

[0021] If h p >wl, and |wl-h p | <H,则选择第三淹没状态计算方法;

[0022] 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 a corresponding moment is determined according to the angle of rotation of the rock mass, and the displacement volume of the unit area of ​​the rock mass underwater is calculated, thereby determining the external force applied during the interaction between the rock mass and the water body;

[0023] For the second and third submerged states, the initial linear velocity of rotation of the rock mass at different positions when it reaches the water surface is calculated, the position of the square block in contact with the water body at the corresponding moment is determined, the displacement volume at different positions of the underwater part is calculated, and the external force exerted on the rock mass during the interaction between the rock mass and the water body is determined.

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

[0025] Among them, the gravity Fg of a single rock mass is expressed as: F g =ρ s V s g;

[0026] The buoyancy F acting on the rock mass at position r at time t b (r,t) is expressed as: F b (r,t)=ρ w gV 排 (r,t);

[0027] The water resistance F of the rock mass at position r at time t d (r,t) is expressed as:

[0028] Among them, ρ s is the density of the rock mass; ρ w is the density of water; g is the acceleration due to gravity; V s is the volume of the rock at each position. For the convenience of estimation, V in three states s You can press Calculation: A is the area of ​​the rock mass at each location in contact with the water surface, C d is the water resistance coefficient; the displacement volume V of the rock mass at different positions under water 排 (r, t) in different submerged states are expressed as:

[0029] First flooding state:

[0030] Since the bottom elevation of the rock mass base hp is less than the still water level wl, then:

[0031] Given the initial rotation angular velocity w0(t) and the initial tilting angle α0, the initial rotation linear velocity can be expressed as v0(r,t)=w0(t)L(n); L(n) is the linear distance between the rock mass surface n and the base rotation point; where n is an integer, and If the initial rotation angular velocity w0(t) = 0, the initial tilt angle must satisfy

[0032] When the rock mass rotates by an angle α(t), the vertical distance h(n) between different positions on the water-facing surface of the rock mass and the bottom surface of the base can be expressed as:

[0033] h(n)=L(n)cosα(t), where the value of α(t) is updated in real time according to the linear velocity and angular velocity;

[0034] if That is, when the rock mass rotates from its initial position to the horizontal position, the part of the rock mass facing the water that is underwater is: h(n)∈[0,|wl-h p |], then the number of water blocks m covering the water-facing surface is: Displacement volume V at different underwater locations 排 (r,t) is expressed as:

[0035]

[0036] if The rock mass stops rotating and moves vertically downward. At this time, w(r, t) = 0. The displacement volume V at different underwater positions is 排 (r,t) is:

[0037]

[0038] This formula means that the values ​​in the brackets are smaller, where z s (r, t) represents the downward displacement of the rock mass at position r facing the water at time t;

[0039] Second flooding state:

[0040] According to the kinetic energy theorem, the initial linear velocity v0(r,t) of the rock mass when it reaches the water surface is expressed as:

[0041]

[0042] The initial displacement z of the rock mass when it reaches the water surface s (r, t0) is 0, then the displacement volume V of the rock mass at different positions under water is 排 (r,t) is expressed as:

[0043]

[0044] The third flooding state:

[0045] According to the kinetic energy theorem, the initial velocity v0(r,t) of the rock mass when it reaches the water surface is:

[0046]

[0047] The distance z between different positions on the rock mass facing the water surface and the water surface at the initial position s (r,t0) is expressed as:

[0048]

[0049] Where θ is the angle between the water-facing surface and the horizontal plane when the top of the rock mass contacts the water surface;

[0050] From the above formula, we can see that z s (r,t0)≤0, that is, in the initial state, all parts of the rock mass are located above the water. After time iteration,

[0051] z s (r, t0)>0, then the displacement volume V at different positions of the underwater part 排 (r,t) is:

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

[0053] Rock mass movement acceleration

[0054] The update speed at each moment is: v s (r,t+1)=v s (r,t)+a s (r,t)dt;

[0055] The total displacement updated at each moment is: s (r,t+1)=z s (r,t)+vs (r,t)dt+0.5a s (r,t)dt 2 ;

[0056] The angle and angular velocity at each moment in the first submerged state can be updated according to the linear velocity, respectively:

[0057] α(t)=α0+w(t)dt,w(t)=v s (r,t) / L(n).

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

[0059]

[0060] Static pressure is expressed as:

[0061] P s (r,t)=ρ w g|z s (r,t)|;

[0062] The total pressure is expressed as:

[0063]

[0064] If z s (r,t)≥min[2T,h w (r)], then P(r,t)=0;

[0065] Among them, P d (r, t) represents the dynamic pressure on the rock mass at position r at time t; P s (r, t) represents the static pressure on the rock mass at position r at time t; P(r, t) represents the total pressure on the rock mass at position r at time t.

[0066] Preferably, the calculation process of the surge wave height in S5 is:

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

[0068] The power source of the surge generation process: a w (r,t)=a p (r,t)+a gw (r,t);

[0069] Among them: a p (r,t)=-▽P(r,t) / ρ w ;a gw (r,t)=-g▽ h ζ(r,t);

[0070] The source of power in surge propagation: a gw (r,t)=-g▽ h ζ(r,t);

[0071] Among them, a w (r,t) is the total acceleration of the water body at position r at time t during the surge generation process, a p (r,t) is the acceleration generated by the total pressure when the rock mass and water body interact at position r at time t, a gw (r, t) is the acceleration of the water body caused by gravity at position r at time t; ▽P(r, t) is the total pressure gradient at position r at time t; ▽ h ζ(r,t) is the water surface gradient;

[0072] According to the initial velocity v0(r,t) and the water acceleration obtained at different stages, the velocity v of each tiny water body at each position r corresponding to each moment t is updated according to the iSquares principle and method. w (r, t) and water thickness H w (r,t);

[0073] According to the updated water thickness H w (r, t), calculate the water surface elevation ζ(r, t) and surge height η(r, t) at different positions of the rock mass at different times respectively;

[0074] The calculation formula of the water surface elevation ζ(r, t) is: ζ(r, t) = H w (r,t)+T0(r);

[0075] The calculation formula of the surge wave height η(r, t) is: η(r, t) = H w (r,t)-h w (r);

[0076] Where: T0(r) is the elevation of the riverbed at position r, η(r,t) is the surge height at position r at time t, h w (r) is the still water depth at position r.

[0077] Preferably, the evaluation system comprises:

[0078] The submergence state analysis module determines the submergence state based on the relationship between the bottom elevation of the rock mass base and the elevation of the still water surface;

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

[0080] Mechanical coupling module, building dynamic and static pressure coupling model;

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

[0082] Preferably, the surge height calculation module is configured as follows: using rock pressure as the initial surge power source and water body gravity gradient as the propagation power source; solving water body acceleration through time update and iteration of iSquares theory, and updating the real-time wave height and wave propagation process in different water areas.

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

[0084] The relative position relationship between the bottom elevation of the rock mass base and the elevation of the static water surface of the reservoir in this application determines the submerged state of the rock mass, which can comprehensively consider the differences in the initial state of the rock mass entering the water under different submerged conditions, accurately define the mechanical boundary conditions under different scenarios, and avoid the model errors caused by the fuzzy division of submerged states in traditional methods; on this basis, by analyzing the interaction process between the rock mass and the water body during the process of rock mass entering the water under different submerged states, according to the inclination angle and position at different moments in the process of rock mass tipping, the specific contact position between the rock mass and the water body at the corresponding moment is judged, and the drainage volume of the rock mass is determined based on the specific contact position between the rock mass and the water body, and the external force acting on the rock mass is deduced; the pushing effect of the rock mass on the water body is accurately quantified, avoiding the simplified assumption errors of the traditional single-stage model, and providing an important basis for the subsequent accurate analysis of rock mass movement and surge generation; according to Newton's second law, the acceleration, velocity and displacement of the rock mass movement are calculated in combination with the contact area and drainage volume, and the impact of the rock mass movement on the water body is analyzed. The authors propose a mechanical model combining dynamic and static pressure to accurately reflect the energy transfer and dissipation during rock mass movement and avoid the subjectivity of empirical formulas. This model addresses the lack of mechanical models for the failure mode of dangerous rock mass collapse in existing research. By constructing a mechanical model that incorporates the coupled dynamic and static pressures, they quantify the pressure distribution of rock mass on water. This coupled model simultaneously captures the impact effect of rock mass movement (dynamic pressure) and the stabilizing effect of water static pressure (static pressure), avoiding the one-sidedness of a single pressure model and more accurately reflecting the pressure mechanism of rock mass movement on water. This mechanical model is embedded in the iSquares numerical framework to establish the RGW-Squares numerical model of dangerous rock collapse-induced surge waves. This model analyzes the dynamic sources of surge generation and propagation, and calculates surge height based on the pressure exerted on water by the rock collapse and the propagation of the water's own gravity, allowing for an accurate assessment of the scale of surge waves induced by dangerous rock collapse. This provides reliable technical support for ensuring safe navigation in reservoirs and the safety of people, and lays an important technical foundation for subsequent analysis of the dangerous rock collapse-induced surge wave disaster chain. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 This is the overall framework diagram of a system for assessing the scale of surges induced by dumping of dangerous rocks into water in a reservoir according to the present invention;

[0086] Figure 2 It is a schematic diagram of the forces acting on the rock mass when it is dumped into water and interacts with the water body under submerged conditions;

[0087] Figure 3 It is a schematic diagram of the forces acting on the rock mass when dumped into water and interacting with the water under three submerged states;

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

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

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

[0091] Figure 7 It is the comparison result of numerical simulation and measured surge wave height data under three submergence conditions S1, S2 and S3. DETAILED DESCRIPTION

[0092] The method for assessing the scale of surge waves induced by the dumping of dangerous rocks into the reservoir includes the following steps:

[0093] S1: Determine the submerged state of the rock mass based on the relative positional relationship between the bottom elevation of the rock mass base and the elevation of the reservoir's still water surface;

[0094] S2: Based on the submerged state, according to the inclination angle and position of the rock mass at different moments during the rock mass collapse process, determining the specific contact position between the rock mass and the water body at the corresponding moment, and determining the displacement volume of the rock mass and deriving the external force acting on the rock mass based on the specific contact position between the rock mass and the water body;

[0095] S3: Combined with 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: constructing a mechanical model including the coupling of dynamic pressure and static pressure based on the velocity and displacement to quantify the pressure distribution of the rock mass on the water body;

[0097] S5: The mechanical model is embedded in the iSquares numerical framework to establish the RGW-Squares dangerous rock collapse-induced surge wave numerical model, and the surge wave height is calculated to evaluate the dangerous rock collapse-induced surge wave numerical model.

[0098] It should be noted that:

[0099] In one embodiment of the present application, the water-facing surface of the rock mass is divided into n unit square blocks according to the unit length Dc. Based on the submerged state, the position of the square block in contact with the water at the corresponding moment is determined according to the inclination angle and position at different moments during the rock mass toppling process, and the external force acting on the rock mass is deduced, where the external force includes gravity, buoyancy, and resistance.

[0100] Combined with Newton's second law, the acceleration, velocity and displacement of the unit square block at different positions on the rock mass at different times during the movement process are calculated, so as to obtain the acceleration, velocity and displacement of the rock mass at different positions at different times during the movement process. In this application, according to the relative position of the bottom elevation of the rock base and the static water surface of the reservoir, the rock mass is divided into three states: completely submerged, partially submerged and unsubmerged, and the mechanical boundary conditions under different states are accurately defined; for different submerged states, the rock mass entry process is divided into multiple stages, and the contact area, drainage volume and motion parameters (acceleration, velocity, displacement) of each stage are dynamically calculated; a coupled mechanical model combining dynamic pressure (determined by the rock mass movement speed) and static pressure (determined by the static 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 in the iSquares numerical framework to construct the RGW-Squares model to achieve efficient simulation of the surge generation and propagation process, significantly improving the calculation accuracy and efficiency.

[0101] Furthermore, in S1, based on the relative positional relationship between the bottom elevation of the rock mass base and the elevation of the still water surface, the submerged state of the rock mass is classified. The submerged state specifically includes:

[0102] Elevation of rock mass base bottom h p Below the still water level wl, the bottom of the rock mass is below the still water level, that is, the bottom of the rock mass is submerged by water, which is recorded as the first submerged state; the bottom elevation of the rock mass base h p = equal to the still water surface elevation wl, the bottom of the rock mass is aligned with the still water surface, which is recorded as the second submerged state; the bottom elevation of the rock mass base h p Above the still water level wl, the bottom of the rock mass is above the water, which is recorded as the third submerged state.

[0103] It should be noted that:

[0104] In an embodiment of the present application, for a rectangular dangerous rock mass with a height H, a thickness T and a width W, three submerging states are divided according to the relative position relationship between the rock mass and the water surface before the rock mass collapses, that is, the base bottom elevation is higher than the static water surface elevation, the dangerous rock is not submerged; the base bottom elevation is equal to the static water surface elevation, the dangerous rock just contacts the water surface; and the base bottom elevation is lower than the static water surface elevation, the dangerous rock is partially or totally submerged. According to the above relative position relationship, the submerging state of the dangerous rock is determined. Different submerging states will affect the energy transmission and the generation mechanism of the surge when the dangerous rock enters the water, and are important basic information for evaluating the scale of the surge.

[0105] Further, in S2, the calculation process of the external force is as follows:

[0106] The first submerging state: by assigning an initial rotational angular velocity and an initial collapse angle, the position of the unit area of the rock mass under water at the corresponding time is determined according to the angle of the rotation of the rock mass, the drainage volume of the unit area of the rock mass under water is calculated, and the external force of the rock mass in the interaction process with the water is determined;

[0107] The second submerging state and the third submerging state: by calculating the initial rotational linear velocity at different positions of the rock mass when the rock mass reaches the water surface, the position of the unit area of the rock mass contacting the water at the corresponding time is determined, the drainage volume at different positions under water is calculated, and the external force of the rock mass in the interaction process with the water is determined.

[0108] It should be noted that:

[0109] In an embodiment of the present application, the unit area of the rock mass contacting the water in the first submerging state, the second submerging state and the third submerging state refers to that the evaluation area is divided into a plurality of virtual small square blocks on the horizontal plane according to the range of the evaluation area and the scale of the collapsed rock mass, and the length of the square block is Dc. Meanwhile, the water-facing surface of the rock mass is also divided into n unit square blocks with a unit length Dc, and the size of n changes in real time with the rotation of the rock mass. Based on the submerging state, the position of the square block contacting the water at the corresponding time is determined according to the inclination angle and the position of the rock mass at different times in the collapse process, so as to obtain the position of the unit area of the rock mass under water at the corresponding time, and the external force of the rock mass is derived, which includes the gravity, the buoyancy and the resistance.

[0110] Further, the rock mass is simulated according to the submerging state of the rock mass, and specifically:

[0111] For the first submerged state, at the initial moment of rock mass movement, by assigning the initial rotation angular velocity and the initial tilting angle, the rock mass's underwater position at the corresponding moment is determined according to the rock mass rotation angle, the displacement volume at different positions of the underwater part is calculated, and the external forces acting on the rock mass during the interaction with the water body are determined, including gravity, buoyancy and water resistance. Usually in the first submerged state, the submerged depth is |wl-h p |greater than Dc; if the submergence depth |wl-h p | is less than Dc, that is, the submergence is very shallow, then the second submergence state is used for approximate calculation.

[0112] 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, the position of the square block in contact with the water body at the corresponding moment is determined, the displacement volume at different positions of the underwater part is calculated, and the external force exerted on the rock mass during the interaction between the rock mass and the water body is determined.

[0113] Furthermore, in the first submerged state, the second submerged state, and the third submerged state, the calculation process of the external force is specifically as follows:

[0114] ① The first submerged state: the bottom elevation of the rock mass base h p Less than the still water height wl, that is, h p <wl,则:

[0115] Given the initial rotation angular velocity w0(t) and the initial tilting angle α0, the initial rotation linear velocity can be expressed as v0(r,t)=w0(t)L(n); L(n) is the linear distance between the rock mass surface n and the base rotation point; where n is an integer, and If the initial rotation angular velocity w0(t) = 0, the initial tilt angle must satisfy

[0116] Then, when the rock mass rotates by a certain angle α(t), the vertical distance h(n) between different positions on the water-facing surface of the rock mass and the bottom surface of the base is:

[0117] h(n)=L(n)cosα(t), where the value of α(t) is updated in real time according to the linear velocity and angular velocity.

[0118] if That is, when the rock mass rotates from its initial position to the horizontal position, the part of the rock mass facing the water that is underwater is: h(n)∈[0,|wl-h p |], then the number of water blocks m covering the water-facing surface is: Displacement volume V at different underwater locations 排 (r,t) is approximately expressed as:

[0119] if The rock mass stops rotating and moves vertically downward. At this time, w(r, t) = 0. The displacement volume V at different underwater positions is 排 (r,t) is: This formula means that the values ​​in the brackets are smaller, where z s (r,t) represents the downward displacement of the rock mass at position r facing the water at time t.

[0120] ② Second submerged state: rock mass base ground elevation h p Equal to the height of the still water surface wl, h p =wl or |wl-h p |≤D c ,but:

[0121] According to the kinetic energy theorem, the initial linear velocity v0(r,t) of the rock mass when it reaches the water surface is:

[0122] The initial displacement z0(r,t) of the rock mass when it reaches the water surface is: s (r,t0)=0;

[0123] Displacement volume V at different positions of the underwater part 排 (r,t) is:

[0124] ③ The third submerged state: rock mass base ground elevation h p Greater than the still water surface height wl, that is, h p >wl, then:

[0125] According to the kinetic energy theorem, the initial velocity v0(r,t) of the rock mass when it reaches the water surface is:

[0126]

[0127] The distance z between different positions on the rock mass facing the water surface and the water surface at the initial position s (r,t0) is:

[0128]

[0129] where θ is Figure 2 and Figure 3 The angle between the water-facing surface and the horizontal plane when the top of the rock mass contacts the water surface is shown in FIG.

[0130] From the above formula we can know that z s (r,t0)≤0, that is, in the initial state, all parts of the rock mass are located above the water. After time iteration, z s If (r, t0)>0, it means that the corresponding part of the block enters the water, generating pressure on the water.

[0131] Displacement volume V at different positions of the underwater part 排 (r,t) is:

[0132] The formula for flooding state 3 applies to |wl-h p | <H的情况,对于高位危岩体,即|wl-h p |>H, it can be evaluated according to flooding state 2.

[0133] Under each submerged state, the gravity acting on a single rock mass is: F g =ρ s V s g;

[0134] The buoyancy F acting on the rock mass at position r at time t b (r,t) is: F b (r,t)=ρ w gV 排 (r,t);

[0135] The water resistance F acting on the rock mass at position r at time t d (r,t) is:

[0136] Among them, ρ s is the density of the rock mass; ρ w is the density of water; g is the acceleration due to gravity; V s is the volume of the rock at each position. For the convenience of estimation, V in three states s You can press Calculation: A is the area of ​​the rock mass at each location in contact with the water surface, C d is the water resistance coefficient; v s (r, t) is the velocity of the rock mass at position r at time t, which needs to be updated in real time according to the acceleration at different times.

[0137] Furthermore, in S3, the process of calculating the acceleration, velocity and displacement at different positions r of the rock mass at different times in each stage, as well as the angle and angular velocity at each time in the first submerged state is as follows:

[0138] Rock mass movement acceleration

[0139] The update speed at each moment is: v s (r,t+1)=v s (r,t)+a s (r,t)dt;

[0140] The total displacement updated at each moment is: z s (r,t+1)=z s(r,t)+v s (r,t)dt+0.5a s (r,t)dt 2 ;

[0141] The angle and angular velocity at each moment in submerged state 1 can be updated according to the linear velocity, which are:

[0142] α(t)=α0+w(t)dt,w(t)=v s (r,t) / L(n).

[0143] Furthermore, in S4, based on the calculated velocity and displacement, the dynamic pressure and static pressure during the rock mass movement are calculated, and a mechanical model combining dynamic pressure and static pressure is constructed:

[0144] P s (r,t)=ρ w g|z s (r,t)|;

[0145] The total pressure is:

[0146] If z s (r,t)≥min[2T,h w (r)], then P(r,t)=0.

[0147] Among them, P d (r, t) represents the dynamic pressure on the rock mass at position r at time t; P s (r, t) represents the static pressure on the rock mass at position r at time t; P(r, t) represents the total pressure on the rock mass at position r at time t.

[0148] Furthermore, the calculation process of surge wave height in S5 is as follows:

[0149] The pressure of the rock mass on the water body is regarded as the power source of the surge, and the gravity of the water body itself is regarded as the power source of the surge propagation, which can be expressed as follows:

[0150] The power source of the surge generation process: a w (r,t)=a p (r,t)+a gw (r,t);

[0151] Among them: a p (r,t)=-▽P(r,t) / ρ w ;a gw (r,t)=-g▽ h ζ(r,t);

[0152] Surge propagation power source: agw (r,t)=-g▽ h ζ(r,t);

[0153] Among them, a w (r,t) is the total acceleration of the water body at position r at time t during the surge generation process, a p (r,t) is the acceleration generated by the total pressure when the rock mass and water body interact at position r at time t, a gw (r, t) is the acceleration of the water body caused by gravity at position r at time t; ▽P(r, t) is the total pressure gradient at position r at time t; ▽ h ζ(r, t) is the surface gradient of the water body. When the rock body interacts with the water body, the water body is simultaneously subjected to pressure and gravity, which is the surge generation stage; when the rock body sinks a certain distance underwater, the water-rock pressure stops, and the movement of the water body is driven only by gravity acceleration, which enters the surge propagation stage, with an acceleration of a gw (r,t).

[0154] Given the initial velocity v0(r,t) and the water accelerations obtained at the different stages above, the velocity v of each tiny water block at each time t and each position r can be updated according to the iSquares principle and method. w (r, t) and thickness H w (r, t), and the momentum and mass of the system are conserved during the update and iteration process.

[0155] When the updated water thickness H is obtained w (r, t), the water surface elevation ζ(r, t) and surge height η(r, t) at any position r at any time t can be obtained according to the following formula.

[0156] Water surface elevation: ζ(r,t) = H w (r,t)+T0(r);

[0157] Surge height: η(r,t) = H w (r,t)-h w (r);

[0158] Where: T0(r) is the elevation of the riverbed at position r, η(r,t) is the surge height at position r at time t, h w (r) is the still water depth at position r.

[0159] A system for assessing the scale of surges induced by the dumping of dangerous rocks into water in a reservoir, comprising:

[0160] The submergence state analysis module is used to classify the rock mass into three submergence states based on the relative size relationship between the base bottom elevation and the still water surface elevation;

[0161] a rock mass movement calculation module, configured to calculate a drainage volume and movement parameters based on the submergence state, the movement parameters including acceleration, velocity and displacement at different time points in the rock mass movement process;

[0162] a mechanical coupling module, configured to analyze a pressure effect of the rock mass movement on the water body based on the calculated velocity and displacement, and construct a mechanical model combining dynamic pressure and static pressure;

[0163] a surge height calculation module, configured to embed the mechanical model into an iSquares numerical framework, establish an RGW-Squares numerical model of surge induced by rockfall, take the pressure of the rock mass on the water body as a dynamic source of surge generation, take gravity of the water body as a dynamic source of surge propagation, decompose the two forces according to a water body surface gradient, solve the acceleration of the water body movement, and calculate a surge wave height through a relationship between water body thickness and water depth, thereby realizing evaluation of a surge scale induced by rockfall.

[0164] As shown in FIG. 1, a specific embodiment process of a reservoir dangerous rockfall into water induced surge scale evaluation system and method provided in an embodiment of the present application is as follows: Figure 1

[0165] 1) a submergence state analysis module, configured to divide the rock mass into three submergence states based on a relative size relationship between a base bottom elevation and a still water surface elevation;

[0166] Specifically, when the base bottom elevation of the rock mass is less than the still water surface elevation, the bottom of the rock mass is submerged by the water body, which is recorded as a first submergence state (submergence state 1); when the base bottom elevation of the rock mass is equal to the still water surface elevation, the bottom of the rock mass is level with the water level, which is recorded as a second submergence state (submergence state 2); and when the base bottom elevation of the rock mass is greater than the still water surface elevation, the bottom of the rock mass is higher than the water level, which is recorded as a third submergence state (submergence state 3);

[0167] 2) a rock mass movement calculation module, configured to calculate a drainage volume and movement parameters based on the submergence state, the movement parameters including acceleration, velocity and displacement at different time points in the rock mass movement process;

[0168] 3) a mechanical coupling module, configured to analyze a pressure effect of the rock mass movement on the water body based on the calculated velocity and displacement, and construct a mechanical model combining dynamic pressure and static pressure;

[0169] ​4) The surge height calculation module is used to embed the mechanical model into the iSquares numerical framework and establish the RGW-Squares numerical model of surge waves induced by dangerous rock toppling. The pressure exerted by the rock toppling on the water body is used as the power source of the surge wave, and the gravity of the water body itself is used as the power source of the surge wave propagation. The two forces are decomposed according to the gradient of the water body surface to obtain the acceleration of the water body movement. The surge wave height is calculated based on the relationship between the water body thickness and water depth, thereby realizing the scale assessment of the surge wave induced by dangerous rock toppling.

[0170] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the following embodiments. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0171] Example 1

[0172] Surge assessment where the bottom of the rock mass is below the still water level

[0173] This embodiment takes the physical model test of rock overturning surge as an example, the still water surface elevation wlevel = 0.3m, the bottom surface elevation of the dangerous rock base h p =0.25m (completely submerged, corresponding to Figure 3 Submerged state 1). The rock mass dimensions are height H = 0.5 m, thickness T = 0.1 m, width W = 0.1 m, and density ρ rock =2400kg / m 3 , gravitational acceleration g = 9.8 m / s 2 .

[0174] Example 2

[0175] Surge assessment when the bottom of the rock mass is aligned with the still water surface

[0176] This embodiment takes the physical model test of rock overturning surge as an example, the still water surface elevation wlevel = 0.3m, the bottom surface elevation of the dangerous rock base h p =0.3m (completely submerged, corresponding to Figure 3 Submerged state 2). The rock mass dimensions are height H = 0.5 m, thickness T = 0.1 m, width W = 0.1 m, and density ρ rock =2400kg / m 3 , gravitational acceleration g = 9.8 m / s 2 .

[0177] Example 3

[0178] Surge assessment where the bottom of the rock mass is above the still water level

[0179] Still water surface elevation wlevel = 0.3m, dangerous rock base bottom elevation h p =0.35m(corresponding to Figure 3 Submerged state 3). The rock mass dimensions are height H = 0.5 m, thickness T = 0.1 m, width W = 0.1 m, and density ρ rock =2400kg / m 3 , gravitational acceleration g = 9.8 m / s 2 .

[0180] In order to verify the effectiveness of the method for assessing the scale of surge induced by the collapse of dangerous rocks in the reservoir described in this application, the above three cases (i.e., the three submerged conditions S1, S2, and S3) were calculated and evaluated based on the RGW-Squares model for assessing the scale of surge induced by the collapse of dangerous rocks. The schematic diagram of the installation of pressure sensors on the rock mass under the three submerged conditions S1, S2, and S3 is shown in the figure below. Figure 4 The installation diagram of the wave height meter for the test is shown in Figure 5 As shown, the comparison results of pressure data of three submerged working conditions S1, S2, and S3 are as follows: Figure 6 As shown by Figure 6 It can be seen that under the three working conditions S1, S2, and S3, the overall change trends of the test pressure and the simulated pressure are basically the same, showing a trend of first rapidly rising to a peak and then gradually decreasing. Under the three submergence working conditions S1, S2, and S3, the change trends, peak values, and pressure change rates of the simulated and test pressures are all highly consistent. This shows that the simulation model can, to a certain extent, reflect the pressure changes in actual tests and can assist in exploring the mechanism of the effect of submergence conditions on pressure characteristics. This shows that the simulation of the RGW-Squares dangerous rock collapse-induced surge assessment model is highly consistent with the test data, can well simulate the actual surge pressure changes, and is reliable. Moreover, the pressure characteristics of different submergence working conditions are different, and the simulation can accurately present them.

[0181] The comparison results of wave height data are as follows Figure 7 As shown by Figure 7 It can be seen that the numerical simulations under the three working conditions can well reflect the characteristics of the surge wave height, such as the fluctuation frequency. 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 change characteristics of the surge wave height under the corresponding submergence conditions. By comparing the numerical simulations and the measured surge wave height data under the three submergence conditions S1, S2, and S3, it can be seen that the numerical simulations are relatively consistent with the measured data in terms of overall trends and fluctuation characteristics, and can well reflect the changes in surge wave height. This shows that the simulation method adopted can, to a certain extent, reflect the variation law of actual wave height. Regardless of the submergence height conditions S1, S2, or S3, the simulation results can capture the approximate time nodes and fluctuation period characteristics of the peak and trough values ​​of the test wave height.

[0182] The numerical simulation and measured head wave heights and error calculations are shown in Table 1.

[0183] Table 1 Numerical simulation and measured head wave height and error table

[0184]

[0185] As shown in Table 1, under the S1 condition, the minimum error is WG2 (-0.6%), and the maximum error is WG3 (-6.1%). The absolute error of all measuring points is ≤6.1%, and no point has an error exceeding ±10%. Under the S2 condition, the minimum error is WG7 (-2.5%), and the maximum errors are WG3 (-11.3%) and WG6 (11.4%). The absolute error of most measuring points is ≤7.5%. Under the S3 condition, the minimum error is WG2 (0%), and the maximum error is WG4 (14.3%), with an average error of approximately 6%. In summary, the RGW-Squares method demonstrates high simulation accuracy within the first 5 seconds of surge propagation, with 88% of the data errors remaining within 10%. This indicates that the RGW-Squares model for assessing surge waves induced by rock collapse has a high degree of agreement with the experimental data, demonstrating that this numerical simulation method can accurately reflect the propagation characteristics of surge waves induced by rock collapse. The results further verified the rationality and reliability of the rockfall surge dynamics model proposed in this study, and provided important technical support for the subsequent prediction of dangerous rockfall surge disaster risks.

Claims

1. A method for assessing the scale of surge waves induced by dumping of dangerous rocks into water in a reservoir, characterized by: The following steps are involved: S1: Determine the submerged state of the rock mass based on the relative positional relationship between the bottom elevation of the rock mass base and the elevation of the reservoir's still water level; S2: Based on the submerged state, according to the inclination angle and position of the rock mass at different moments during the rock mass collapse process, determining the specific contact position between the rock mass and the water body at the corresponding moment, and determining the displacement volume of the rock mass and deriving the external force acting on the rock mass based on the specific contact position between the rock mass and the water body; S3: Combined with 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: constructing a mechanical model including the coupling of dynamic pressure and static pressure based on the velocity and displacement to quantify the pressure distribution of the rock mass on the water body; S5: The mechanical model is embedded in the iSquares numerical framework to establish the RGW-Squares dangerous rock collapse-induced surge wave numerical model, and the surge wave height is calculated to evaluate the dangerous rock collapse-induced surge wave numerical model.

2. The method for assessing the scale of surge waves induced by dumping dangerous rocks into water in a reservoir according to claim 1, characterized in that: In S1, the submerged state is divided according to the relative position relationship between the rock mass and the water surface before the collapse, and the submerged state includes: First flooding state: rock mass base bottom elevation h p Below the still water level wl, the bottom of the rock mass is below the still water level; Second submerged state: rock mass base bottom elevation h p Equal to the still water surface elevation wl, the bottom of the rock mass is aligned with the still water surface; The third submerged state: the bottom surface elevation of the rock mass base h p Above the still water level wl, the bottom of the rock mass is above the water.

3. The method for assessing the scale of surge caused by dumping of dangerous rocks into water in a reservoir according to claim 2, characterized in that: In S2, the calculation process of the external force is: First submerged state: By assigning an initial rotational angular velocity and an initial tilting angle, the position of the unit area of ​​the rock mass under water at the corresponding moment is determined according to the angle of rotation of the rock mass. The displacement volume of the unit area of ​​the rock mass under water is calculated to determine the external force exerted on the rock mass during the interaction between the rock mass and the water. 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 where the rock mass contacts the water at the corresponding moment is determined, the displacement volume at different positions of the underwater part is calculated, and the external force acting on the rock mass during the interaction between the rock mass and the water is determined.

4. The method for assessing the scale of surge caused by dumping dangerous rocks into water in a reservoir according to claim 2, characterized in that: The calculation method for the specific location of contact between rock mass and water body at different times follows: If h p <wl, and |wl - h p | > the length of the unit area of the rock mass, then select the first submerged state calculation method; If h p =wl, and |wl-h p |<length of rock mass unit area or |wl-h p |> the height of the rock mass, the second flooding state calculation method is selected; If h p > wl, and |wl - h p | < H, then select the third submergence state calculation method; 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 a corresponding moment is determined according to the angle of rotation of the rock mass, and the displacement volume of the unit area of ​​the rock mass underwater is calculated, thereby determining the external force applied during the interaction between the rock mass and the water body; For the second and third submerged states, the initial linear velocity of rotation of the rock mass at different positions when it reaches the water surface is calculated, the position of the square block in contact with the water body at the corresponding moment is determined, the displacement volume at different positions of the underwater part is calculated, and the external force exerted on the rock mass during the interaction between the rock mass and the water body is determined.

5. The method for assessing the scale of surge waves induced by dumping dangerous rocks into water in a reservoir according to claim 1, characterized in that: The external forces include gravity, buoyancy and resistance; Among them, the gravity Fg of a single rock mass is expressed as: F g =ρ s V s g; The buoyancy F acting on the rock mass at position r at time t b (r,t) is expressed as: F b (r,t)=ρ w gV 排 (r,t); The water resistance F acting on the rock mass at position r at time t d (r,t) is expressed as: Among them, ρ s is the density of the rock mass; ρ w is the density of water; g is the acceleration due to gravity; V s is the volume of the rock at each position. For the convenience of estimation, V in three states s You can press Calculation: A is the area of ​​the rock mass at each location in contact with the water surface, C d is the water resistance coefficient; the displacement volume V of the rock mass at different positions under water 排 (r, t) in different submerged states are expressed as: First flooding state: Since the bottom elevation of the rock mass base hp is less than the still water level wl, then: Given the initial rotation angular velocity w0(t) and the initial tilting angle α0, the initial rotation linear velocity can be expressed as v0(r,t)=w0(t)L(n); L(n) is the linear distance between the rock mass surface n and the base rotation point; where n is an integer, and If the initial rotation angular velocity w0(t) = 0, the initial tilt angle must satisfy When the rock mass rotates by an angle α(t), the vertical distance h(n) between different positions on the water-facing surface of the rock mass and the bottom surface of the base can be expressed as: h(n)=L(n)cosα(t), where the value of α(t) is updated in real time according to the linear velocity and angular velocity; if That is, when the rock mass rotates from its initial position to the horizontal position, the part of the rock mass facing the water that is underwater is: h(n)∈[0,|wl-h p |], then the number of water blocks m covering the water-facing surface is: Displacement volume V at different underwater locations 排 (r,t) is expressed as: if The rock mass stops rotating and moves vertically downward. At this time, w(r, t) = 0. The displacement volume V at different underwater positions is 排 (r,t) is: This formula means that the values ​​in the brackets are smaller, where z s (r, t) represents the downward displacement of the rock mass at position r facing the water at time t; Second flooding state: According to the kinetic energy theorem, the initial linear velocity v0(r,t) of the rock mass when it reaches the water surface is expressed as: The initial displacement z of the rock mass when it reaches the water surface s (r, t0) is 0, then the displacement volume V of the rock mass at different positions under water is 排 (r,t) is expressed as: The third flooding state: According to the kinetic energy theorem, the initial velocity v0(r,t) of the rock mass when it reaches the water surface is: The distance z between different positions on the rock mass facing the water surface and the water surface at the initial position s (r,t0) is expressed as: Where θ is the angle between the water-facing surface and the horizontal plane when the top of the rock mass contacts the water surface; From the above formula, we can see that z s (r,t0)≤0, that is, in the initial state, all parts of the rock mass are located above the water. After time iteration, z s (r, t0)>0, then the displacement volume V at different positions of the underwater part 排 (r,t) is:

6. The method for assessing the scale of surge caused by dumping dangerous rocks into water in a reservoir according to claim 1, characterized in that: The process of calculating the acceleration, velocity and displacement of the rock mass at different positions r at different times in each stage, as well as the angle and angular velocity at each time in the first submerged state in S3 is as follows: Rock mass movement acceleration The update speed at each moment is: v s (r,t+1)=v s (r,t)+a s (r,t)dt; The total displacement updated at each moment is: s (r,t+1)=z s (r,t)+v s (r,t)dt+0.5a s (r,t)dt 2 ; The angle and angular velocity at each moment in the first submerged state can be updated according to the linear velocity, respectively: α(t)=α0+w(t)dt,w(t)=v s (r,t) / L(n).

7. The method for assessing the scale of surge caused by dumping dangerous rocks into water in a reservoir according to claim 1, characterized in that: The dynamic pressure in S4 is expressed as: Static pressure is expressed as: P s (r,t)=ρ w g|z s (r,t)|; The total pressure is expressed as: If z s (r,t)≥min[2T,h w (r)], then P(r,t)=0; Among them, P d (r, t) represents the dynamic pressure on the rock mass at position r at time t; P s (r, t) represents the static pressure on the rock mass at position r at time t; P(r, t) represents the total pressure on the rock mass at position r at time t.

8. The method for assessing the scale of surge waves induced by dumping dangerous rocks into water in a reservoir according to claim 1, characterized in that: The calculation process of surge wave height in S5 is: The pressure of the rock mass on the water body is regarded as the power source of the surge, and the gravity of the water body itself is regarded as the power source of the surge propagation, which can be expressed as follows: The power source of the surge generation process: a w (r,t)=a p (r,t)+a gw (r,t); in: Power sources in swell propagation: Among them, a w (r,t) is the total acceleration of the water body at position r at time t during the surge generation process, a p (r,t) is the acceleration generated by the total pressure when the rock mass and water body interact at position r at time t, a gw (r,t) is the acceleration of the water body at position r at time t due to gravity; is the total pressure gradient at position r at time t; is the water surface gradient; According to the initial velocity v0(r,t) and the water acceleration obtained at different stages, the velocity v of each tiny water body at each position r corresponding to each moment t is updated according to the iSquares principle and method. w (r, t) and water thickness H w (r,t); According to the updated water thickness H w (r, t), calculate the water surface elevation ζ(r, t) and surge height η(r, t) at different positions of the rock mass at different times respectively; The calculation formula of the water surface elevation ζ(r, t) is: ζ(r, t) = H w (r,t)+T0(r); The calculation formula of the surge wave height η(r, t) is: η(r, t) = H w (r,t)-h w (r); Where: T0(r) is the elevation of the riverbed at position r, η(r,t) is the surge height at position r at time t, h w (r) is the still water depth at position r.

9. A system for assessing the scale of surges induced by the dumping of dangerous rocks into water in a reservoir, characterized in that: The evaluation system comprises: The submergence state analysis module determines the submergence state based on the relationship between the bottom elevation of the rock mass base and the elevation of the still water surface; A rock mass motion calculation module calculates the displacement volume and motion parameters based on the submerged state. The motion parameters include acceleration, velocity, and displacement at different moments during the rock mass motion process. Mechanical coupling module, building dynamic and static pressure coupling model; The surge height calculation module is used to embed the iSquares framework to generate a surge model and output surge height assessment results.

10. The system according to claim 9, characterized in that The surge height calculation module is configured to use rock pressure as the initial surge power source and water body gravity gradient as the propagation power source; solve water body acceleration through time update and iteration of iSquares theory, and update the real-time wave height and wave propagation process in different water areas.

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