Three-phase coupled falling type dangerous rock surge amplitude prediction method

Abstract

The invention discloses a three-phase coupled falling type dangerous rock surge amplitude prediction method which comprises the following steps: when a dangerous rock impacts a water body to form a cavitation bubble, the cavitation bubble is subjected to three stages of development, contraction and closing, and data of the thickness a of the dangerous rock, the length Lpot of the cavitation bubble and the water depth hw are acquired; the speed v0 and the initial potential energy Ec of the dangerous rock at the moment of making contact with the water surface and the initial kinetic energy Ek0 of the dangerous rock at the moment of impacting the water surface are calculated; iteratively solving the movement speed in all subsequent movement time, and establishing a speed-time relation curve after the dangerous rock enters water; according to the speed at any moment, the corresponding cavitation bubble diameter, the change rate and the change rule of the cavitation bubble potential energy along with time are obtained, and then the potential energy maximum value of the cavitation bubble above the closed point is obtained; the surge wave energy conversion rate is solved according to the maximum cavitation bubble potential energy value, and finally the maximum surge amplitude is solved. The method has the advantages that the energy conversion mechanism of the gas-phase substance in the wave making process is quantified by introducing the cavitation kinetic model, and the wave amplitude prediction precision is remarkably improved.

Description

Technical Field

[0001] This invention is a three-phase coupled method for predicting the amplitude of falling rock surge waves, belonging to the field of hydrogeological data processing technology. Background Technology

[0002] The reservoir areas in southwestern my country are mostly characterized by high mountains and deep valleys, steep banks, and complex geological conditions. Under the combined effects of internal and external dynamics such as reservoir water immersion, rainfall, and earthquakes, incidents of rockfalls into the water are frequent. The surge waves generated by the impact of falling debris are characterized by high energy, long propagation distance, and high elevation gain, posing a serious threat to the safety of reservoir waterways, riverside facilities, residential areas, and the dam itself. Therefore, conducting research on the prediction of rockfall surge waves, especially focusing on the propagation and evolution forecasting of surge waves under complex river conditions in reservoir areas (such as continuous bends, varying slopes, and varying widths), is a key technical link in achieving accurate early warning and disaster prevention and mitigation in reservoir areas. It has significant practical implications for ensuring the safety of people's lives and property and the stable operation of major projects.

[0003] Existing rockfall surge prediction models are mostly based on the solid-liquid two-phase coupling assumption. However, when a rockfall impacts water, cavitation bubbles form. The development, contraction, and collapse of these bubbles not only affect wave amplitude but also directly dominate wave evolution. Ignoring the contribution of gas-phase cavitation bubbles to surge energy leads to significant prediction errors, especially in deep water conditions. a <h w <L pot or a< L pot <h w The development, contraction, and collapse of cavitation bubbles have a dominant influence on the amplitude of swell waves, and existing swell wave prediction models for falling rocks cannot accurately reflect this physical mechanism. Furthermore, existing swell wave prediction models for falling rocks only solve for the extreme amplitudes before and after the split by the energy transfer relationship of solid-liquid interactions, and can only output static maximum amplitude values. They lack quantitative analysis of the morphological evolution during wave propagation and cannot simulate the morphological differences such as stretching, distortion, or attenuation of the waveform before and after the split. Summary of the Invention

[0004] The technical problem this invention aims to solve is to address the above-mentioned shortcomings by providing a three-phase coupled method for predicting the amplitude of swell waves caused by falling rocks, particularly applicable to the prediction of swell disasters generated after falling rocks into water in canyon and glacier areas. This method significantly improves the accuracy of amplitude prediction by introducing a cavitation dynamics model to quantify the energy conversion mechanism of gaseous substances during wave generation. The algorithm can be implemented through computer programming, providing important technical support for swell prediction and disaster prevention and mitigation in complex river channels in reservoir areas.

[0005] To solve the above technical problems, the present invention adopts the following technical solution: A three-phase coupled method for predicting the amplitude of falling rock surge waves includes the following steps: When a rock impacts a body of water and forms a cavitation bubble, the cavitation bubble will go through three stages: development, contraction and closure. Data on the rock thickness a, the cavitation length Lpot and the water depth hw can be obtained. Calculate the velocity v0 and initial potential energy E of the rock at the instant it contacts the water surface. c and the initial kinetic energy at the moment of impact with the water surface ; Iteratively solve for the velocity during all subsequent motion times to establish the velocity-time relationship curve after the rock enters the water; Based on the velocity at any given moment, determine the corresponding cavitation diameter, rate of change, and the change law of cavitation potential energy over time, and then calculate the maximum potential energy of the cavitation above the closure point. The surge wave energy conversion rate is calculated based on the maximum cavitation potential energy, and finally the maximum surge wave amplitude is solved.

[0006] Furthermore, the velocity v0 and initial potential energy E of the unstable rock at the instant it contacts the water surface... c and the initial kinetic energy at the moment of impact with the water surface The calculation formula is: Among them, the mass of the unstable rock m and the gravitational acceleration Fall height Hc.

[0007] Furthermore, the specific process of establishing the velocity-time relationship curve after the dangerous rock enters the water is as follows: The motion of the unstable rock is divided into 100 uniformly accelerated motion processes within 100 extremely short time intervals Δt, each denoted as i = 1, 2, 3... 100. During this process, the unstable rock is mainly affected by gravity and water resistance. The water resistance F at each iteration step i is... w (i) can be determined based on the impact velocity v(i) and water density. According to the formula for calculating water resistance Perform calculations, where C w is the water resistance coefficient, which can generally be taken as 1.26, v(i) is the velocity at the corresponding iteration step i, and S is the interaction area between the unstable rock and the water body; The velocity value in each iteration is obtained by iterative calculation based on the velocity v(i-1) from the previous iteration step. This allows us to obtain the velocity-time relationship curve of the unstable rock at any time i△t after it enters the water.

[0008] Furthermore, the calculation process for the cavitation diameter and rate of change is as follows: Based on the principle of independence of cavitation cross-section expansion, the Besant-Rayleigh problem, and the generalized Bernoulli equation, differentiating with respect to time t yields the relationship between point B, which is far from the cavitation, and point A, which is on the cavitation wall, at the same elevation, satisfying the following condition: Given any cross-sectional position z in the water and the impact velocity v of the unstable rock at time t, the radius R and rate of change of the cavitation bubble can be calculated. ; In the formula Let p be the velocity potential function; u be the velocity of the water body moving outward from the cavitation at the cross-section position; and p and Let B be the hydrostatic pressure and water density at point B, respectively; z be the depth of the cross-section; R0 be the initial cavitation diameter; at t=0, R=R0=b / 2, where b is the width of the rock; α is a constant less than 1, related to the shape of the object and the velocity of the impact on the water. From R=R0, we have... α is a correction factor, which can be taken as α = 0.1;

[0009] Furthermore, the calculation process for the change of the cavitation potential energy over time is as follows: Throughout the entire development and closure process of a cavitation bubble, the potential energy at any cross-section of the cavitation bubble can be obtained by integrating over dz. The cavitation energy E above the closure point of the cavitation bubble... pot The calculation is performed, and the potential energy of the entire cavitation bubble at any time t is the sum of the potential energies of all cross sections, which can be written as: In the formula, j is the cavitation section number, j=1,2,3....; The volume of the cavitation bubble. and These represent the pressure outside and inside the cavitation bubble, respectively. This indicates the pressure difference between the inside and outside of the cavitation bubble; Using the velocity-time relationship curve after the rockfall enters the water as the time reference, the cavitation dynamic parameters at each time t in step S4 are synchronously correlated. For each time node t, the formula for the sum of cavitation potential energy in step S5 is substituted to calculate the cavitation energy E corresponding to that time. pot Numerical value, establishing the cavitation potential energy E above the cavitation closure point. pot Correspondence with time; Iterate through the cavitation energy E corresponding to all time points pot The data is filtered to identify the peak value, which represents the maximum potential energy E during the entire cavitation development process. pot max .

[0010] Furthermore, the calculation process for the surge wave energy conversion rate is as follows: A loss factor k is used to simplify the energy loss caused by water collision and jet. Experiments show that a value of 0.53 can be taken. The energy E at the maximum cavitation development is then calculated. pot maxRatio to initial kinetic energy: The surge energy conversion rate can be calculated. .

[0011] Furthermore, the calculation process for the maximum amplitude of the surge is as follows: The surge wave of a falling rock is simplified into a damped sine wave. η(x,t) is the value at time t and position x. The potential energy of the surge wave can be determined based on the water density. Integrating with wavelength λ, we obtain the result, written as: Regarding the total energy possessed by the waves Then the wave energy within multiple periods can be summed. Calculations show that, under two-dimensional conditions, swell waves will be generated symmetrically on both sides of the cavitation bubble. Combining this with the formula for calculating cavitation potential energy, the correlation between the energy of the falling rock and the swell wave can be obtained. Solve for the amplitude in the formula This allows us to obtain the maximum amplitude of the surging waves from the falling rock.

[0012] The present invention adopts the above technical solution and has the following technical effects compared with the prior art: The three-phase coupled wave amplitude prediction method for falling rockfall surges described in this invention is particularly suitable for predicting surge disasters caused by falling rock masses into water in canyon and glacier areas. This method significantly improves wave amplitude prediction accuracy by introducing a cavitation dynamics model to quantify the energy conversion mechanism of gaseous substances during wave generation. The algorithm can be implemented through computer programming, providing important technical support for surge prediction and disaster prevention and mitigation in complex river channels in reservoir areas. Attached Figure Description

[0013] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0014] Figure 1 This diagram illustrates the expansion, contraction, and closure of cavitation bubbles after a dangerous rock falls into water, as described in this invention. Figure 2 This is a diagram showing the cavitation development under different water depth conditions in this invention; Figure 3 This is the logic diagram for calculating the surging waves from a falling rock in this invention; Figure 4 This is a diagram illustrating the expansion, contraction, and closure process of the cavitation bubble calculated in this invention. Figure 5This is a diagram illustrating the change in cavitation potential energy during the cavitation development-contraction-closure process in the present invention. Detailed Implementation

[0015] Examples, such as Figure 3 As shown, a three-phase coupled method for predicting the amplitude of falling rock surge waves includes the following steps:

[0016] Step S0, when the unstable rock impacts the water body and forms cavitation, such as Figure 1 and Figure 2 As shown, cavitation bubbles undergo three stages: development, contraction, and closure. Based on the thickness 'a' of the unstable rock and the cavitation length 'L'... pot and water depth h w It can calculate the swell problem of falling rocks in deep water, when the runout closure point is located below the rock: a <L pot <h w The wave-making process involves solid, liquid, and gas phases, and the surge waves are mainly formed by the contraction and collapse of cavitation bubbles created by the impact of unstable rocks on the water.

[0017] Step S1, based on Through the mass m of the unstable rock and the acceleration due to gravity Fall height H c Calculate the velocity v0 and initial potential energy of the rock at the instant it contacts the water surface. and the initial kinetic energy at the moment of impact with the water surface .

[0018] Step S2: Divide the motion of the unstable rock into 100 uniformly accelerated motion processes within a very small time interval Δt, denoted as i = 1, 2, 3...100. During this process, the unstable rock is mainly affected by gravity and water resistance. The water resistance F at each iteration step i is... w (i) can be determined based on the impact velocity v(i) and water density. According to the formula for calculating water resistance Perform calculations, where C w is the water resistance coefficient, which can generally be taken as 1.26, v(i) is the velocity at the corresponding iteration step i, and S is the interaction area between the unstable rock and the water body.

[0019] Step S3: Based on the velocity v(i-1) from the previous iteration step, obtain the velocity value in each calculation through iterative calculation. This allows us to obtain the velocity-time relationship curve of the unstable rock at any time i△t after it enters the water.

[0020] Step S4: Based on the principle of independence of cavitation cross-section expansion, the Besant–Rayleigh problem, and the generalized Bernoulli equation, differentiating with respect to time t yields the relationship between point B, which is far from the cavitation, and point A on the cavitation wall at the same elevation, satisfying the following condition: Given any cross-sectional position z in the water and the impact velocity v of the unstable rock at time t, the radius R and rate of change of the cavitation bubble can be calculated. ; In the formula Let p be the velocity potential function; u be the velocity of the water body moving outward from the cavitation at the cross-section position; and p and Let B be the hydrostatic pressure and water density at point B, respectively; z be the depth of the cross-section; R0 be the initial cavitation diameter; at t=0, R=R0=b / 2, where b is the width of the rock; α is a constant less than 1, related to the shape of the object and the velocity of the impact on the water. From R=R0, we have... α is a correction coefficient, which can be taken as α=0.1.

[0021] Step S5: During the entire development-closure process, the potential energy at any cross section of the cavitation bubble can be obtained by integrating over dz. For points above the cavitation closure point (z... <L pot Cavitation energy E pot The calculation is performed, and the potential energy of the entire cavitation bubble at any time t is the sum of the potential energies of all cross sections, which can be written as: In the formula, j is the cavitation section number, j=1,2,3....; The volume of the cavitation bubble. and These represent the pressure outside and inside the cavitation bubble, respectively. This indicates the pressure difference between the inside and outside of the cavitation bubble.

[0022] Step S6: Using the velocity-time relationship curve of the unstable rock after entering the water obtained in Step S3 as the time reference, synchronously correlate the cavitation dynamic parameters at each time t in Step S4, and for each time node t, substitute into the potential energy summation formula in Step S5 to calculate the cavitation energy E corresponding to that time. pot Numerical value, establishing the cavitation potential energy E above the cavitation closure point. pot Correspondence with time; Iterate through the cavitation energy E corresponding to all time points pot The data is filtered to identify the peak value, which represents the maximum potential energy E during the entire cavitation development process. pot max .

[0023] Step S7: A loss factor k is used to simplify the energy loss caused by water collision and jet. Experiments show that a value of 0.53 can be taken. The energy E at the maximum cavitation development is then calculated. pot max Ratio to initial kinetic energy: The surge energy conversion rate can be calculated. .

[0024] Step S8: Simplify the surge wave of the falling rock into the form of a damped sine wave. η(x,t) is the value at time t and position x. The potential energy of the surge wave can be determined based on the water density. Integrating with wavelength λ, we obtain the result, written as: Regarding the total energy possessed by the waves Then the wave energy within multiple periods can be summed. Calculations show that, under two-dimensional conditions, swell waves will be symmetrically generated on both sides of the cavitation bubble. Combining this with the formula for calculating cavitation potential energy, the correlation between the falling rock and the swell wave energy can be obtained. Solve for the amplitude in the formula This allows us to obtain the maximum amplitude of the surging waves from the falling rock.

[0025] Based on the initial velocity, iteratively solve for the velocity (velocity-time relationship curve) over all subsequent motion time intervals. Then, based on the velocity at any given moment, calculate the corresponding cavitation diameter, rate of change, and the change law of cavitation potential energy over time. Next, calculate the maximum potential energy of the cavitation above the closure point. Based on the maximum potential energy of the cavitation, calculate the conversion rate of the surge wave energy. Finally, calculate the maximum amplitude of the surge wave.

[0026] For example, consider a rock with a thickness of a = 0.13 cm, a width of b = 0.195 cm, and a drop height of H. c =180cm and water depth h w Substituting 70cm into the formula, we can obtain... Figure 4 and Figure 5 The diagram shows the development of cavitation bubbles and the pattern of cavitation potential energy changes. Figure 4 In the diagram, (a)~(f) represent the cavitation morphology at t=0.41, 0.46, 0.51, 0.55, 0.57, and 0.91s.

[0027] The same calculation method was used to calculate the surge waves from the 2022 Diaozui rockfall and collapse event and the July 10, 2020 rockfall and collapse event at the Yuxiakou section of the Qingjiang River in Changyang County, Three Gorges Reservoir Area, China. The calculation parameters, observations, calculation results, and errors are shown in the table below. Compared with field observations, the rockfall and collapse surge wave calculation method proposed in this study accurately reproduces the surge wave amplitude, with errors of +33% and -16%, respectively.

[0028]

[0029] The description of this invention is given for illustrative and descriptive purposes only and is not intended to be exhaustive or to limit the invention to the forms disclosed. Many modifications and variations will be apparent to those skilled in the art. The embodiments were chosen and described in order to better illustrate the principles and practical application of the invention and to enable those skilled in the art to understand the invention and design various embodiments with various modifications suitable for a particular purpose.

Claims

1. A three-phase coupled method for predicting the amplitude of falling rock surge waves, characterized in that: Includes the following steps: When a dangerous rock impacts a water body and forms a cavitation bubble, the cavitation bubble goes through three stages: development, contraction, and closure. The rock thickness *a* and the cavitation bubble length *L* are obtained from this process. pot and water depth h w Data; Calculate the velocity v0 and initial potential energy E of the rock at the instant it contacts the water surface. c and the initial kinetic energy at the moment of impact with the water surface ; Iteratively solve for the velocity during all subsequent motion times to establish the velocity-time relationship curve after the rock enters the water; Based on the velocity at any given moment, determine the corresponding cavitation diameter, rate of change, and the change law of cavitation potential energy over time, and then calculate the maximum potential energy of the cavitation above the closure point. The surge wave energy conversion rate is calculated based on the maximum cavitation potential energy, and finally the maximum surge wave amplitude is solved.

2. The method for predicting the amplitude of a falling rock surge wave as described in claim 1, characterized in that: The velocity v0 and initial potential energy E of the unstable rock at the instant it contacts the water surface c and the initial kinetic energy at the moment of impact with the water surface The calculation formula is: The parameters include the mass of the unstable rock (m), the acceleration due to gravity (g), and the fall height (H). c .

3. The method for predicting the amplitude of a falling rock surge as described in claim 1, characterized in that: The specific process of establishing the velocity-time relationship curve after the unstable rock enters the water is as follows: The motion of the unstable rock is divided into 100 uniformly accelerated motion processes within a very small time interval Δt, denoted as i = 1, 2, 3...

100. During this process, the unstable rock is mainly affected by gravity and water resistance. The water resistance F at each iteration step i is... w (i) can be determined based on the impact velocity v(i) and water density. According to the formula for calculating water resistance Perform calculations, where C w is the water resistance coefficient, which can generally be taken as 1.26, v(i) is the velocity at the corresponding iteration step i, and S is the interaction area between the unstable rock and the water body; The velocity value in each iteration is obtained by iterative calculation based on the velocity v(i-1) from the previous iteration step. This allows us to obtain the velocity-time relationship curve of the unstable rock at any time i△t after it enters the water.

4. The method for predicting the amplitude of a falling rock surge as described in claim 1, characterized in that: The calculation process for the cavitation diameter and rate of change is as follows: Based on the principle of independence of cavitation cross-section expansion, the Besant-Rayleigh problem, and the generalized Bernoulli equation, differentiating with respect to time t yields the relationship between point B, which is far from the cavitation, and point A, which is on the cavitation wall, at the same elevation, satisfying the following condition: Given any cross-sectional position z in the water and the impact velocity v of the unstable rock at time t, the radius R and rate of change of the cavitation bubble can be calculated. ； In the formula Let p be the velocity potential function; u be the velocity of the water body moving outward from the cavitation at the cross-section position; and p and Let B be the hydrostatic pressure and water density at point B, respectively; z be the depth of the cross-section; R0 be the initial cavitation diameter; at t=0, R=R0=b / 2, where b is the width of the rock; α is a constant less than 1, related to the shape of the object and the velocity of the impact on the water. From R=R0, we have... α is a correction coefficient, which can be taken as α=0.

1.

5. The method for predicting the amplitude of a falling rock surge wave as described in claim 4, characterized in that: The calculation process for the change of cavitation potential energy over time is as follows: Throughout the entire development and closure process of a cavitation bubble, the potential energy at any cross-section of the cavitation bubble can be obtained by integrating over dz. The cavitation energy E above the closure point of the cavitation bubble... pot The calculation is performed, and the potential energy of the entire cavitation bubble at any time t is the sum of the potential energies of all cross sections, which can be written as: In the formula, j is the cavitation section number, j=1,2,3....; The volume of the cavitation bubble. and These represent the pressure outside and inside the cavitation bubble, respectively. This indicates the pressure difference between the inside and outside of the cavitation bubble; Using the velocity-time relationship curve after the rockfall enters the water as the time reference, the cavitation dynamic parameters at each time t in step S4 are synchronously correlated. For each time node t, the formula for the sum of cavitation potential energy in step S5 is substituted to calculate the cavitation energy E corresponding to that time. pot Numerical value, establishing the cavitation potential energy E above the cavitation closure point. pot Correspondence with time; Iterate through the cavitation energy E corresponding to all time points pot The data is filtered to identify the peak value, which represents the maximum potential energy E during the entire cavitation development process. pot max .

6. The method for predicting the amplitude of a falling rock surge wave as described in claim 5, characterized in that: The calculation process for the surge wave energy conversion rate is as follows: A loss factor k is used to simplify the energy loss caused by water collision and jet. Experiments show that a value of 0.53 can be taken. The energy E at the maximum cavitation development is then calculated. pot max Ratio to initial kinetic energy: The surge energy conversion rate can be calculated. .

7. The method for predicting the amplitude of a falling rock surge wave as described in claim 6, characterized in that: The calculation process for the maximum wave amplitude of the surge is as follows: The surge wave of a falling rock is simplified into a damped sine wave. η(x,t) is the value at time t and position x. The potential energy of the surge wave can be determined based on the water density. Integrating with wavelength λ, we obtain the result, written as: Regarding the total energy possessed by the waves Then the wave energy within multiple periods can be summed. Calculations show that, under two-dimensional conditions, swell waves will be generated symmetrically on both sides of the cavitation bubble. Combining this with the formula for calculating cavitation potential energy, the correlation between the energy of the falling rock and the swell wave can be obtained. Solve for the amplitude in the formula This allows us to obtain the maximum amplitude of the surging waves from the falling rocks.

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