A method for analyzing rockfall trajectory

Abstract

The present invention provides a method for analyzing rockfall trajectory, belonging to the field of engineering geology and geological disaster prevention. The method comprises the following steps: obtaining rockfall characteristic parameters and slope characteristic parameters of a dangerous rock mass in a study area, constructing a three-dimensional model of the dangerous rock mass in the study area based on the rockfall characteristic parameters and slope characteristic parameters; simulating the rockfall motion process when the three-dimensional model of the dangerous rock mass in the study area collapses, constructing a rockfall motion equilibrium equation taking into account air resistance and the vertical downward Magnus force generated by the rockfall's self-rotation in mid-air; applying an initial velocity in the vertical direction to the rockfall, calculating the acceleration of the rockfall on the slope using the rockfall motion equilibrium equation, analyzing the rockfall motion characteristic parameters based on the acceleration, and analyzing the rockfall motion trajectory based on the motion characteristic parameters. The present invention can obtain more reliable motion characteristic parameters, and the motion characteristic parameters can accurately analyze the rockfall trajectory.

Description

Technical Field

[0001] The present invention belongs to the field of engineering geology and geological disaster prevention and control, and particularly relates to a rockfall motion trajectory analysis method. Background Art

[0002] The development of dangerous rock is influenced by many factors, including topography, lithology, geological structure, earthquakes, rainfall, and groundwater. Loose and broken areas, well-developed joints, steep terrain, and areas with soil-rock interlayers are particularly susceptible to rockfall collapses. Currently, there are several models for calculating rockfall trajectories, including empirical models, rigid-body motion models, GIS-based prediction models, and three-dimensional coupled discrete element models. Current GIS-based prediction models offer significant advantages in regional assessments, enabling repeated testing to address safety concerns during research, reduce research costs, and provide a reference for the prediction and management of landslide geological hazards. However, when calculating rockfall trajectories, these models typically simplify the rocks into spherical particles and use the principles of normal distribution to generate random seeds. These models simulate the random paths of dangerous rockfalls of different sizes and locations after collapse, thereby analyzing the threatened areas.

[0003] However, in actual cases, large, nearly spherical, and highly threatening falling rocks spend most of their time in the air from the time they break away from the parent rock to the time they stop moving. Their trajectory is affected not only by air resistance but also by their own rotation. GIS-based prediction models often ignore the influence of self-rotation when calculating the trajectory of falling rocks, resulting in inaccurate calculations of the trajectory of falling rocks. Summary of the Invention

[0004] In order to overcome the above-mentioned shortcomings of the prior art, the present invention provides a method for analyzing the trajectory of falling rocks, comprising the following steps:

[0005] Obtain the rockfall characteristic parameters and slope characteristic parameters of the dangerous rock mass in the study area, and construct a three-dimensional model of the dangerous rock mass in the study area based on the rockfall characteristic parameters and slope characteristic parameters;

[0006] The rockfall motion process during the collapse of a three-dimensional model of a dangerous rock mass in the study area was simulated. The equilibrium equation of rockfall motion was constructed by considering air resistance and the vertical downward Magnus force generated by the rockfall's self-rotation in the air.

[0007] An initial velocity is applied to the falling rock in the vertical direction, and the acceleration of the falling rock on the slope is calculated using the rockfall motion equilibrium equation. The motion characteristic parameters of the falling rock are analyzed based on the acceleration, and the motion trajectory of the falling rock is analyzed based on the motion characteristic parameters.

[0008] Preferably, the construction of the rockfall motion equilibrium equation comprises the following steps:

[0009] Obtain the translational velocity and rotational tangential velocity of the rockfall, and obtain the combined velocity of any two points of the rockfall during high-speed rotation based on the translational velocity and rotational tangential velocity of the rockfall;

[0010] Obtain the spin angular velocity and density of the falling rock, and obtain the pressure difference between any two points of the falling rock based on the spin angular velocity, density and the combined velocity of any two points of the falling rock;

[0011] obtaining a thickness of a flow layer attached to the rockfall, and calculating a Magnus force exerted by the rockfall in a vertical downward direction based on the thickness of the flow layer attached to the rockfall and the pressure difference;

[0012] Obtain the mass of the falling rock and the air resistance it experiences; construct a motion equilibrium equation based on the mass of the falling rock, the air resistance it experiences, and the Magnus force exerted on the falling rock in the vertical downward direction.

[0013] Preferably, the method for obtaining the spin angular velocity of the falling rock is specifically as follows: obtaining the viscosity coefficient of the air, the windward area of ​​the falling rock, the mass of the falling rock, the time of the falling rock and the rotation radius of the falling rock, and obtaining the spin angular velocity of the falling rock through the viscosity coefficient of the air, the windward area of ​​the falling rock, the mass of the falling rock, the time of the falling rock and the rotation radius of the falling rock.

[0014] Preferably, the rockfall motion equilibrium equation is as follows:

[0015]

[0016] Where m is the mass of the rockfall; g is the acceleration due to gravity, usually 9.81 m / s 2 ;f x 、f y are the components of air resistance in the horizontal and vertical directions respectively; F y is the Magnus force of the falling rock in the vertical downward direction, v x 、v y are the components of the translational velocity of the falling rock in the horizontal and vertical directions, are the horizontal and vertical components of the rockfall acceleration, respectively.

[0017] Preferably, the rockfall characteristic parameters include: rockfall shape, rockfall diameter and rockfall density.

[0018] Preferably, the slope characteristic parameters include normal restitution coefficient, tangential restitution coefficient and dynamic friction coefficient.

[0019] Preferably, the motion characteristic parameters of the falling rocks on the slope include: maximum motion energy, speed and bounce height.

[0020] The rockfall motion trajectory analysis method provided by the present invention has the following beneficial effects:

[0021] The present invention can construct a three-dimensional model of a dangerous rock mass in a study area based on rockfall characteristic parameters and slope characteristic parameters; by simulating the rockfall motion process when the three-dimensional model of the dangerous rock mass in the study area collapses, it can construct a rockfall motion equilibrium equation. When calculating the rockfall motion characteristic parameters, the equilibrium equation can take into account air resistance and the Magnus effect generated by the self-rotational motion of the rockfall, thereby obtaining more reliable motion characteristic parameters; and the motion characteristic parameters can be used to accurately analyze the motion trajectory of the rockfall. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] To more clearly illustrate the embodiments of the present invention and its design, the following briefly introduces the drawings required for this embodiment. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be derived from these drawings without inventive effort.

[0023] Figure 1 Flowchart of a rockfall motion trajectory analysis method according to an embodiment of the present invention;

[0024] Figure 2 It is a three-dimensional model of dangerous rock mass;

[0025] Figure 3 is the wind resistance condition of falling rocks of different shapes; Figure 3 (a) is a flat-plate-shaped falling rock. Figure 3 (b) is a cone-shaped rockfall. Figure 3 (c) is a long strip of fallen rock. Figure 3 (d) is a falling rock with a streamline shape.

[0026] Figure 4 It is the self-rotating motion of falling rocks after being ejected;

[0027] Figure 5 The simulation results of the kinetic energy, bounce height and stopping position of WY01 after it breaks away from the dangerous rock area; Figure 5 (a) is the energy change diagram without considering the Magrus effect; Figure 5 (b) is the energy change diagram after considering the Magrus effect; Figure 5 (c) is the change diagram of bounce height without considering the Magrus effect; Figure 5 (d) is the change diagram of bounce height after considering the Magrus effect; Figure 5 (e) is the stopping position change diagram without considering the Magrus effect; Figure 5 (f) is the stopping position change diagram after considering the Magrus effect;

[0028] Figure 6 The simulation results of the kinetic energy, bounce height and stopping position of WY02 after it breaks away from the dangerous rock area; Figure 6 (a) is the energy change diagram without considering the Magrus effect; Figure 6 (b) is the energy change diagram after considering the Magrus effect; Figure 6 (c) is the change diagram of bounce height without considering the Magrus effect; Figure 6 (d) is the change diagram of bounce height after considering the Magrus effect; Figure 6 (e) is the stopping position change diagram without considering the Magrus effect; Figure 6 (f) is the stopping position change diagram after considering the Magrus effect;

[0029] Figure 7 The simulation results of the kinetic energy, bounce height and stopping position of WY03 after it breaks away from the dangerous rock area; Figure 7 (a) is the energy change diagram without considering the Magrus effect; Figure 7 (b) is the energy change diagram after considering the Magrus effect; Figure 7 (c) is the change diagram of bounce height without considering the Magrus effect; Figure 7 (d) is the change diagram of bounce height after considering the Magrus effect; Figure 7 (e) is the stopping position change diagram without considering the Magrus effect; Figure 7 (f) is the stopping position change diagram after considering the Magrus effect. DETAILED DESCRIPTION

[0030] In order to enable those skilled in the art to better understand the technical solution of the present invention and to be able to implement it, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solution of the present invention and are not intended to limit the scope of protection of the present invention.

[0031] Example

[0032] The present invention provides a method for analyzing the trajectory of falling rocks, specifically Figure 1 As shown, the following steps are included:

[0033] Step 1: Obtain the rockfall characteristic parameters and slope characteristic parameters of the dangerous rock mass in the study area, and construct a three-dimensional model of the dangerous rock mass in the study area based on the rockfall characteristic parameters and slope characteristic parameters.

[0034] The present invention selects site A as the study area. The study area is located on steep cliffs and slopes, with an altitude between 700 and 1000 meters. The relative height difference of the steep cliff is 180 to 310 meters. The slope of the upper cliff is about 70° to 80°. The cover layer is relatively thin, about 0.5 meters long, and consists of flint fragments and clay powder; the terrain below the steep cliff is characterized by a stepped slope with a slope of about 30° to 50°, and the thickness varies from 0.5 meters to 3.5 meters. The central portion of the steep cliff is composed of gray, massive flint, while the lower portion is dominated by a dark gray, medium-thick microcrystalline flint layer, interwoven with bioclasts and a thin layer of brownish-gray marl. Due to intense weathering and rain erosion, this stratum is highly unstable and subject to frequent rockfalls. These rockfalls typically measure 1.5 cubic meters or less in volume and appear as angular, wedge-shaped and rectangular boulders, accompanied by debris drops with a volume of approximately 0.2-0.3 cubic meters. The foot of the slope has become a reservoir for rockfalls, and nearby residential buildings are under a constant threat of rockfall hazards. The lithologies of the strata are primarily Quaternary artificial fill, landslide deposits, and Silurian strata. Furthermore, the study area is located in an open mountainous environment characterized by complex topography and significant relief. Convergence of cold and warm air there is influenced by a range of factors, including climate and topography. This results in strong winds with wind speeds reaching 14 to 24 m / s.

[0035] This study utilized drone photogrammetry, using a DJI drone to collect slope features in the study area. The image measurement software Agisoft Photoscan was used to generate elevation data from the collected slope features. The 3D rock modeling software Rocpro3D was then used to construct a 3D model of the dangerous rock mass. This modeling required two types of parameters: rockfall characteristic parameters and slope surface characteristic parameters. Rockfall characteristic parameters include rockfall shape, rockfall diameter, and rockfall density, while slope surface characteristic parameters include the normal restitution coefficient (Rn), the tangential restitution coefficient (Rt), and the kinetic friction coefficient k. Details of the rockfall characteristic parameters, derived from field surveys, are shown in Table 1, and the slope surface characteristic parameters are shown in Table 2.

[0036] Table 1 Values ​​of rockfall characteristic parameters in dangerous rock areas

[0037]

[0038] Table 2 Values ​​of characteristic parameters of slope in dangerous rock area

[0039] Slope characteristic parameters <![CDATA[R n ]]> <![CDATA[R t ]]> k Moderately weathered hard rock surface 0.27 0.81 0.50 Hard soil slope with sparse vegetation 0.22 0.74 0.61 Soft soil slope with no vegetation 0.17 0.60 0.67

[0040] The final three-dimensional model of the dangerous rock mass can be roughly divided into three dangerous rock areas according to the surface characteristics: the moderately weathered hard rock surface area, the hard soil slope with sparse vegetation area, and the soft soil slope with no vegetation area. Figure 2 shown.

[0041] Step 2: Simulate the rockfall motion process when the three-dimensional model of the dangerous rock mass in the study area collapses, consider the air resistance and the vertical downward Magnus force generated by the rockfall's self-rotation in the air, and construct the rockfall motion equilibrium equation.

[0042] RocPro3D is a professional 3D modeling software specifically designed for rockfall analysis. It uses a probabilistic approach to comprehensively consider the impact of rockfall shape, soil properties, and terrain irregularities on rockfall trajectories. The software boasts efficient grids and computational algorithms, enabling the construction of soil models with varying geomechanical characteristics and multiple starting surfaces. Furthermore, RocPro3D can rapidly calculate rockfall trajectories of various sizes and shapes and visualize them in a variety of formats. By importing terrain data and automatically generating a grid using the Delaunay algorithm, it enables efficient and accurate model construction. Therefore, the present invention employs RocPro3D to model rockfall trajectories.

[0043] When an object moves relative to an air flow, the air flow will produce resistance to the object in the opposite direction of movement, referred to as wind resistance (or flow resistance). Based on this, the air resistance formula is introduced: f = -Cρsv 2 / 2, where v is the relative speed of the falling rock; ρ is the air density; s is the windward area of ​​the falling rock when it moves forward; and C is the air resistance coefficient, which is related to the shape of the falling rock. Figure 3 As shown in the figure, four types of rockfalls with the same windward side but different shapes are taken as examples. Figure 3 (a) is a flat-plate-shaped falling rock. Figure 3 (b) is a cone-shaped rockfall. Figure 3 (c) is a long strip of falling rock. When it moves relative to the rock, it is in a local vacuum state. When the flow rate is too high, the "Carl vortex street" effect is generated, and the wind resistance is large. Figure 3 (d) is a streamlined rockfall. The presence of the tail vertebra eliminates the vortex and reduces the wind resistance.

[0044] The protruding dangerous rocks on the slope often form loose rocks of various shapes due to the effects of physical and mechanical weathering. After becoming unstable, they perform free fall motion on the air-facing surface. In particular, plate-shaped and block-shaped rocks usually have a large windward area and a high movement speed, and are significantly affected by air resistance. The initial equation for rockfall motion is established as follows:

[0045]

[0046]

[0047] Where m is the mass of the rockfall; g is the acceleration due to gravity, usually 9.81 m / s 2;f x 、f y are the decomposition of air resistance in the horizontal and vertical directions respectively.

[0048] In the process of falling rocks, in addition to being affected by air resistance, they are also accompanied by high-speed self-rotation. Due to the influence of uneven slopes, collisions, friction, etc., the rotational angular velocity vector of the falling rocks does not coincide with the translational velocity vector and forms a plane. A vertical downward Magnus force is generated in the direction perpendicular to this plane, which is called the Magnus effect. This phenomenon will cause the trajectory of the falling rocks to deflect during the descent, affecting the movement state of the falling rocks in the air, such as Figure 4 As shown, taking a rectangular rockfall as an example, the length of the rockfall is e, the width is h, and the thickness is n. Due to the viscosity effect, the attached fluid on the surface of the rockfall will move with the rockfall, and the movement trajectory of the attached fluid is similar to that of a circle. Figure 4 Where v represents the translational velocity of the rockfall (the direction of its motion), ω is the angular velocity of its spin, r is the distance between the particle and the axis of rotation, α is the rockfall's rotation angle, u represents the rockfall's tangential velocity (i.e., the velocity of the fluid attached to its surface), and can be expressed as u = rω. F is the Magnus force. Assuming the rockfall is in laminar flow, the Newtonian viscosity formula is introduced:

[0049]

[0050] Where, f z is the rotational resistance to the falling rock; η is the viscosity coefficient of air; (du / dr) r is the velocity gradient at the rotation radius r; s is the frontal area; the rotating rockfall is considered as a circle on the xoy plane, r is the rotation radius; the rotational resistance torque of the rockfall is:

[0051]

[0052] Where M is the rotational resistance torque; η is the viscosity coefficient of air; (du / dr) r is the velocity gradient at the turning radius r; s is the frontal area; r is the turning radius.

[0053] Consider the rotating rockfall as a thin disk with a rotation radius of r and ignore the thickness. The moment of inertia of the rockfall is J = mr 2 / 3, by M=Jd ω / d t The rate of change of the angular velocity of the falling rock with time is:

[0054]

[0055] Where m is the mass of the rockfall; ω is the angular velocity of the rockfall; η is the viscosity of the air; (du / dr) ris the velocity gradient at the turning radius r; s is the frontal area; r is the turning radius.

[0056] To facilitate calculation, the velocity gradient is quantified and the differential approximation is obtained:

[0057]

[0058] Where u represents the tangential linear velocity of the falling rock; r is the rotation radius; ω is the spin angular velocity of the falling rock; and Δr is the radius increment.

[0059] Substituting equation (6) into equation (5) and integrating it, we can obtain the relationship between angular velocity ω and time t:

[0060] ω=ω0exp(-3ηst / mr) (7);

[0061] Where ω is the angular velocity of the rockfall; ω0 is the initial angular velocity; m is the mass of the rockfall; η is the viscosity coefficient of the air; s is the windward area; r is the rotation radius; and t is the time.

[0062] Then the relationship between the tangential linear velocity u of the dangerous rock rotation and time t can be expressed as:

[0063] u=rω=rω0exp(-3ηst / mr) (8);

[0064] Where ω is the angular velocity of the rockfall; ω0 is the initial angular velocity; m is the mass of the rockfall; η is the viscosity coefficient of the air; s is the windward area; r is the rotation radius; and t is the time.

[0065] During the high-speed rotation of the falling rock, take points a and b and get the total velocity v a 、v b :

[0066]

[0067] Where v is the translational velocity of the rockfall, u is the tangential linear velocity of the rockfall, and α is the rotation angle of the rockfall.

[0068] The pressure difference between two points can be obtained from Bernoulli's equation:

[0069]

[0070] Where p a 、p b are the pressures at points a and b respectively; ρ is the air density; v a and v b are the combined velocities of point a and point b respectively; r is the rotation radius; ω is the angular velocity of the rockfall; v is the translational velocity of the rockfall; α is the rotation angle of the rockfall.

[0071] From dF = Δpds, we can get: n is the thickness of the vesicle (approximately the thickness of the rockfall), and the Magnus force F in the x and y directions can be obtained by substituting the equation into the integral. x With F y :

[0072]

[0073] Where Δp is the pressure difference; ρ is the air density; n is the thickness of the velocities; r is the radius of rotation; ω is the angular velocity of the rockfall; v is the translational velocity of the rockfall; and α is the rotation angle of the rockfall.

[0074] From Equations (12) and (13), we can see that the Magnus force acts in the vertical direction and is zero in the horizontal direction. Combined with the air resistance, the equilibrium equation is established, as shown in Equations (14) and (15):

[0075]

[0076] In the formula, m is the mass of the falling rock; g is the acceleration due to gravity, usually 9.81 m / s 2 ;f x 、f y are the components of air resistance in the horizontal and vertical directions respectively; F y is the Magnus force of the falling rock in the vertical downward direction, v x 、v y are the components of the translational velocity of the falling rock in the horizontal and vertical directions, are the horizontal and vertical components of the rockfall acceleration, respectively.

[0077] Step 3: Apply an initial velocity to the rockfall in the vertical direction, use the rockfall motion equilibrium equation to calculate the acceleration of the rockfall on the slope, analyze the motion characteristic parameters of the rockfall based on the acceleration, and analyze the motion trajectory of the rockfall based on the motion characteristic parameters.

[0078] Combining equations (14), (15) and Table 2, and considering the effects of air resistance and the vertical downward Magnus force generated by falling rocks rotating at high speed in the air, the present invention uses RocPro3D software to simulate the possible collapse motion of the three dangerous rock areas of the dangerous rock mass three-dimensional model, and sets the number of falling rocks in each dangerous rock area to 500. In addition, considering that the area is affected by valley winds, the influence of the Magnus effect on falling rocks cannot be ignored. Therefore, initial velocities are given to falling rocks of different diameters in the vertical direction to study the influence of the Magnus effect on falling rocks. The present invention analyzes the falling rock motion in the three dangerous rock areas by giving the falling rocks in the three dangerous rock areas vertical initial velocities of 2m / s, 2m / s and 1m / s respectively. Figure 5 、 Figure 6 and Figure 7 The motion characteristics of the three simulated dangerous rock areas WY01, WY02 and WY03 after collapse are shown respectively. Figure 5 (a) is the energy change diagram without considering the Magrus effect; Figure 5 (b) is the energy change diagram after considering the Magrus effect; Figure 5 (c) is the change diagram of bounce height without considering the Magrus effect; Figure 5 (d) is the change diagram of bounce height after considering the Magrus effect; Figure 5 (e) is the stopping position change diagram without considering the Magrus effect; Figure 5 (f) is the stopping position change diagram after considering the Magrus effect; Figure 6 (a) is the energy change diagram without considering the Magrus effect; Figure 6 (b) is the energy change diagram after considering the Magrus effect; Figure 6 (c) is the change diagram of bounce height without considering the Magrus effect; Figure 6 (d) is the change diagram of bounce height after considering the Magrus effect; Figure 6 (e) is the stopping position change diagram without considering the Magrus effect; Figure 6 (f) is the stopping position change diagram after considering the Magrus effect; Figure 7 (a) is the energy change diagram without considering the Magrus effect; Figure 7 (b) is the energy change diagram after considering the Magrus effect; Figure 7 (c) is the change diagram of bounce height without considering the Magrus effect; Figure 7 (d) is the change diagram of bounce height after considering the Magrus effect; Figure 7 (e) is the stopping position change diagram without considering the Magrus effect; Figure 7 (f) is the stopping position change diagram after considering the Magrus effect. Figures 5 to 7 It can be seen that although the dangerous rock areas WY01 and WY03 have the same shape, they have different diameters. The impact of the Magnus effect is analyzed by comparing whether or not the Magnus effect is considered. Figure 5 and Figure 7 It shows that after considering the Magnus effect, the motion characteristic parameters of falling rocks change significantly, and the motion energy, bounce height and displacement all decrease to varying degrees.

[0079] Theoretical analysis indicates that, when the Magnus effect is considered, falling rocks are subjected to a vertical downward Magnus force, which results in greater impact energy, greater bounce height, and longer travel distance. However, simulation results show that the impact energy, bounce height, and travel distance of rockfalls WY01 and WY03 all decrease to varying degrees. The decreases in impact energy, bounce height, and travel distance are most pronounced in rockfall WY01, where the impact energy decreases from a maximum of 3010 kJ to 2705 kJ, the maximum bounce height decreases from 2.484 m to 2.145 m, and the maximum travel distance decreases accordingly. This phenomenon suggests that, when the Magnus effect is considered, the energy loss of falling rocks increases, the number of collisions with the slope increases, and thus the maximum travel distance decreases. A comparative analysis of rocks with diameters of 1 m and 1.5 m shows that, when the Magnus effect is considered, the larger the rock diameter, the greater the energy loss during movement and the more collisions with the slope.

[0080] Depend on Figure 6 It can be seen that the cylindrical rock of WY02 exhibits different kinematic characteristics from the spherical rocks (WY01 and WY03). The location of the maximum impact energy and the maximum travel distance of the rockfall remain unchanged, while the impact energy increases from 5122 kJ to 5164 kJ, the number of rocks with the maximum travel distance decreases from 39 to 37, and the maximum bounce height of the rockfall decreases from 4.81 m to 4.536 m. Compared with spherical rocks, cylindrical rocks primarily roll during their fall, and their bouncing and collision time is relatively shorter than that of spherical rocks. The Magnus effect has little influence on cylindrical rocks.

[0081] In summary, this paper theoretically analyzes the motion characteristics of falling rocks in midair, considers the Magnus force generated by the self-rotation of falling rocks in midair based on the principle of pressure difference, and establishes an equilibrium equation based on air resistance and the Magnus effect. Using RocPro3D, a landslide hazard at Site A was simulated and the impact of the Magnus effect was compared and analyzed. The main conclusions are as follows:

[0082] (1) In the process of studying rockfall geological disasters, the greater the relative speed of the rockfall and the air, the angular velocity, the thickness of the attached fluid (the thickness of the air moving with the rockfall), and the air density, the greater the Magnus force it is subjected to.

[0083] (2) After considering the Magnus effect, the falling rocks are subjected to a vertical downward force, the speed of the falling rocks increases, the number of collisions between the spherical falling rocks and the slope surface increases, the energy loss is greater, the impact energy, bounce height and horizontal movement distance of the falling rocks will decrease, and the threat to residents at the foot of the slope will decrease.

[0084] The above embodiments are only preferred specific implementation methods of the present invention, and the protection scope of the present invention is not limited thereto. Any simple changes or equivalent replacements of the technical solutions that can be obviously obtained by any technician familiar with the field within the technical scope disclosed in the present invention fall within the protection scope of the present invention.

Claims

1. A rockfall trajectory analysis method, characterized in that: The steps include: Obtain the rockfall characteristic parameters and slope characteristic parameters of the dangerous rock mass in the study area, and construct a three-dimensional model of the dangerous rock mass in the study area based on the rockfall characteristic parameters and slope characteristic parameters; The rockfall motion process during the collapse of a three-dimensional model of a dangerous rock mass in the study area was simulated. The equilibrium equation of rockfall motion was constructed by considering air resistance and the vertical downward Magnus force generated by the rockfall's self-rotation in the air. Applying an initial velocity to the falling rock in the vertical direction, calculating the acceleration of the falling rock on the slope using the rockfall motion equilibrium equation, analyzing the motion characteristic parameters of the falling rock based on the acceleration, and analyzing the motion trajectory of the falling rock based on the motion characteristic parameters; The step of constructing the rockfall motion equilibrium equation comprises the following steps: Obtain the translational velocity, tangential linear velocity, and rotation angle of the rockfall, and obtain the combined velocity of any two points of the rockfall during its high-speed rotation based on the translational velocity, tangential linear velocity, and rotation angle; wherein the tangential linear velocity is obtained based on the rockfall's spin angular velocity and rotation radius; Get the density of air, and then get the pressure difference between any two points of the rockfall based on the density of air and the combined velocity of any two points of the rockfall. obtaining a thickness of a flow layer attached to the rockfall, and calculating a Magnus force exerted by the rockfall in a vertical downward direction based on the thickness of the flow layer attached to the rockfall and the pressure difference; Obtain the mass of the falling rock and the air resistance it experiences; construct a motion equilibrium equation based on the mass of the falling rock, the air resistance it experiences, and the Magnus force exerted on the falling rock in the vertical downward direction.

2. The rockfall trajectory analysis method according to claim 1, characterized in that: The method for obtaining the spinning angular velocity of the falling rock is specifically as follows: obtaining the viscosity coefficient of the air, the windward area of ​​the falling rock, the mass of the falling rock, the time of the falling rock and the rotation radius of the falling rock, and obtaining the spinning angular velocity of the falling rock through the viscosity coefficient of the air, the windward area of ​​the falling rock, the mass of the falling rock, the time of the falling rock and the rotation radius of the falling rock.

3. The rockfall trajectory analysis method according to claim 2, characterized in that: The equilibrium equation of rockfall motion is as follows: ； ； Where, is the mass of the rockfall; is the acceleration due to gravity, usually taken as 9.81m / s 2 ; 、 are the components of air resistance in the horizontal and vertical directions respectively; is the Magnus force of the falling rock in the vertical downward direction, 、 are the components of the translational velocity of the falling rock in the horizontal and vertical directions, 、 are the horizontal and vertical components of the rockfall acceleration, respectively.

4. The rockfall trajectory analysis method according to claim 1, characterized in that: The rockfall characteristic parameters include rockfall shape, rockfall diameter and rockfall density.

5. The rockfall motion trajectory analysis method according to claim 1, characterized in that: The slope characteristic parameters include normal restitution coefficient, tangential restitution coefficient and dynamic friction coefficient.

6. The rockfall trajectory analysis method according to claim 1, characterized in that: The motion characteristic parameters of the falling rock falling on the slope include: maximum motion energy, speed and bounce height.

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