CN111950168A - Rolling stone track calculation method - Google Patents
Rolling stone track calculation method Download PDFInfo
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- CN111950168A CN111950168A CN202010894268.XA CN202010894268A CN111950168A CN 111950168 A CN111950168 A CN 111950168A CN 202010894268 A CN202010894268 A CN 202010894268A CN 111950168 A CN111950168 A CN 111950168A
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Abstract
The invention discloses a method for calculating a rolling stone track, which adopts equipment comprising a nine-axis sensor, a wireless communication module and a computer, wherein the nine-axis sensor is installed in dangerous rock of a side slope and is communicated with the computer through the wireless communication module, a digital model of a target side slope is prestored in the computer to obtain a slope surface equation f (x, y), the calculation method comprises the steps of establishing a coordinate system with the dangerous rock as an original point on the side slope, dividing the rolling stone formed by the dangerous rock on the side slope into a sliding stage, a flying stage, a collision and bounce stage and a rolling stage, respectively calculating the displacement and the speed of the rolling stone of each stage, and finally comprehensively calculating the final position of the synthesized rolling stone to finish the calculation of the rolling stone track. The invention can accurately position the position corresponding to each time in the process of starting and falling the rolling stones, and simultaneously uses computer-aided simulation to ensure that the model can quickly and accurately predict the falling stone position so as to reduce the effect of disaster.
Description
Technical Field
The invention belongs to the field of slope prevention and control, and particularly relates to a method for calculating a rock rolling track, which is used for predicting the position of a rock falling point of a slope, giving an alarm in advance and reducing harm. The method is mainly used for side slopes which are easy to slide and have dangerous rocks. Especially for mountain and hillside with large dangerous rock.
Background
The research and analysis methods for the slope rolling stone movement problem can be summarized into two types, namely an empirical method mainly based on experimental research and a theoretical derivation method. The former mainly includes field test research and indoor scale model test research. The experimental research data has the characteristics of accuracy, objectivity and comprehensiveness. The method of experimental research is also an important method for determining basic physical mechanical parameters and deeply understanding the problem of the side slope rock rolling. It goes without saying that a certain amount of experimental data is indispensable for studying the rolling stone problem and is the basis for a correct understanding of the rolling stone problem. However, the data of experimental research is lack of systematicness and has the characteristic of strong regional limitation, so that the result of the experimental method has no wide engineering significance. The theoretical derivation method is mainly based on kinematics and dynamics theory to establish a reasonable mathematical calculation model. With the development of computer technology, there is a great development in the computer-aided analysis method in rock research, and the research in this area has been started in the last 80 th century abroad and is still in depth at present. And (3) using a computer to assist in analyzing the motion track of the rolling stone, and firstly establishing a reasonable calculation model. Whether the calculation model is correct or not needs to be judged and adjusted through test data, so that a dialectic method from practice to theory to practice needs to be adhered to correctly estimate the motion track of the rolling stone.
The currently accepted main factors influencing the motion trail of the slope rolling stones are as follows: the shape of the side slope (such as the slope of the side slope and the length of the side slope), the geomechanical properties of the slope surface of the side slope (such as the roughness of the slope surface, the vegetation coverage degree of the slope surface, the softness of the soil covered by the slope surface and the softness of the bedrock exposed out of the slope surface), the physical and mechanical properties (such as the strength) of the rolling stone, the size and the shape of the rolling stone and the like, and the influence factors have great uncertainty, so that the calculation of the motion track of the rolling stone becomes very complicated. Foreign literature describes model input parameters by means of probability, and for parameters such as the size of the rolling stone and the initial velocity vector, a function of probability distribution is given instead of a determined value, and the uncertainty is reflected by the means. The present invention does not discuss this aspect, but still treats these input parameters as deterministic values. This is for mathematical simplicity.
Disclosure of Invention
The invention aims to provide a method for calculating a rolling stone track. The invention relates to a rolling stone track calculation method which mainly comprises a nine-axis sensor, an energy supply battery and a computer.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a method for calculating a rolling stone track is characterized by comprising the following steps: the method comprises the steps that the nine-axis sensor is installed in dangerous rock of a side slope and is communicated with a computer through the wireless communication module, a digital model of a target side slope is prestored in the computer to obtain a slope surface equation f (x, y), a coordinate system with the dangerous rock as an original point is established on the side slope, then rolling stones formed by the dangerous rock on the side slope are divided into a sliding stage, a flying stage, a collision and bounce stage and a rolling stage, rolling stone displacement and speed of each stage are respectively calculated, and finally the final position of the synthesized rolling stone is comprehensively calculated to finish rolling stone track calculation.
Further, for the sliding phase, the rolling stone starts to slide from the rest, and the sliding distance is calculated according to the following formula:
in the above formula, s is the sliding distance of the rolling stones in the sliding stage, v0The speed of the rolling stone at the end of sliding is measured and obtained by a nine-axis sensor positioned in the rolling stone; g is the acceleration of gravity; mu is a sliding friction coefficient and is obtained by a field friction test or experience; alpha is the gradient of the sliding section of the side slope and is obtained by field measurement; gamma is a slope vegetation correction coefficient and is obtained by adopting a field contrast test;
determining the coordinate P at the end of the sliding phase of the rolling stone through the formula (1)0(x0,y0) Wherein x is0＝scosα，y0＝-ssinα。
Further, for the flying and falling stage, the distance calculation formula of the roller rock flying is as follows:
x＝v0x·Δt+x0formula (2)
Wherein v is0xVelocity v for the end of the slip phase0Component in the direction of the x-axis, v0yVelocity v for the end of the slip phase0A component in the y-axis direction;
and (3) combining the formula (2) and the formula (3) to eliminate delta t to obtain a motion trail equation of the free flying and falling of the rolling stones:
obtaining a coordinate P at the end of the flying and falling stage through a motion track equation and a slope equation of the free flying and falling of the rolling stones1(x1,y1)。
Further, in the flying stage, the influence of the rotational kinetic energy on the falling of the rock is considered, a kinetic energy correction coefficient sigma is introduced into the formula (4), and the value of the sigma is compared according to a small stone block to obtain a corrected formula:
further, for the collision bounce phase, the calculation formula is as follows:
obtaining the speed v before the first collision by a nine-axis sensor in the rolling stone1The position at collision, i.e. the position P at the end of the flight phase1(x1,y1)；
Will velocity v before first impact1Decomposed into v along the x and y axesxbAnd vybThen the velocity v is adjustedxbAnd vybThe normal direction and the tangential direction of the slope surface where the first collision is located are decomposed, and the formula is as follows:
vnb＝vybcosθ-vxbsinθ
vtb＝vybsinθ+vxbcosθ
in the above formula, vnbNormal velocity component, v, of rolling stone before impact with slopetbThe tangential velocity component of the rolling stone and the slope surface before the collision of the rolling stone and the slope surface, and the slope surface angle of the current slope surface theta;
and (3) solving the speed of the rolling stone after the rolling stone collides with the slope surface according to a collision formula as follows:
vna＝Rnvnb
vta＝Rtvtb
vnavelocity component, v, in the direction normal to the slope surface after the rolling stone collides with the slope surfacetaComponent of velocity in slope tangential direction after impact of rolling stone with slope surface, RnIs the normal reduction coefficient of the slope surface of the side slope, RtTangential reduction coefficient of slope surface, RnAnd RtSelecting according to the geological conditions of the side slope;
according to the velocity v after the first collisionnaAnd vtaCalculating a parabolic track after the first collision, then calculating the position of a second collision point by combining a slope equation, and then repeatedly calculating according to the steps until the speed after the collision is not enough to throw the rolling stone again, wherein the position of the collision is the end position P of the collision bounce stage2(x2,y2) Velocity is decomposed into v along the x and y axes2xAnd v2y。
Further, the method for judging the end of the collision bounce stage comprises the following steps:
definition of
Wherein v isnaAnd vtaThe normal component and the tangential component of the bouncing speed of the roller stone after collision are respectively, lambda is called as the collision bounce angle of the roller stone, and when tan lambda is less than xi after the roller stone collides, the roller stone is considered to enter a rolling state without bounce; otherwise, continuing to analyze and calculate according to the bounce; xi is a constant which is arbitrarily larger than 0, and the size of xi is determined according to the calculation precision.
Further, for the scrolling phase, the calculation formula is as follows:
for rolling stones, the dynamic balance equation yields:
N-mgcos＝0
ms″＝mgsin-f
Is″＝fτ-Nd
in the formula:
is a slope angle; n is the supporting force of the slope surface to the rolling stones; f is the friction force of the slope surface to the rolling stones; m is the mass of the rolling stone; tau is a correction coefficient; s is the displacement vector of the rolling stone, and I is the moment of inertia; s "is the second derivative of the displacement vector with respect to time, i.e. the acceleration;
from the above formula
Definition of
B is a correction relating to the quality and shape of the rolling stone, d is the diameter of the rolling stone; definition of mur＝dτ＝tanβrCalled coefficient of rolling friction, betarReferred to as the rolling friction angle;
there is s ″ ═ Bg (sin-dcos),so that the obtained rolling stone can roll at any position S on the slope2Velocity V of
V2The speed in the direction of the slope at the beginning of the rolling phase,
if s' < 0, i.e., tan < tan betarWhen the rolling stone rolls at a reduced speed and finally stops under the action of rolling friction, namely V is 0, and the displacement when the rolling stone stops is as follows:
at this time, the position P of the roller stone at the stop is obtained3(x3,y3) Wherein x is3＝S2cos+x2，y3＝S2sin+y2。
The working principle of the invention is as follows:
the method simplifies the rolling stones into a two-dimensional motion model, and decomposes the complex rolling stone motion into permutation and combination of several stages. Each stage has its corresponding features and assumptions.
Since the rock movement is very complex, for theoretical analysis, the following assumptions need to be made:
(1) the rolling stones are mass points, but the influence of fine factors such as the size and the shape of the rolling stones on the movement track of the rolling stones is not ignored.
(2) The mass of the rolling stones is constant, i.e. the rolling stones are hard enough not to break apart during collision.
(3) Neglecting the effect of air resistance.
(4) The slope surface of the side slope uses the idea of differentiation, and the collision point of the rolling stones is regarded as a continuous straight line.
(5) Neglecting the influence of the roughness of the slope surface of the side slope.
Through data of the nine-axis sensor, the field parameters such as friction coefficient, gradient change and the like can be known more accurately by experiments. In the prior art, all complex factors need to be summarized, and the factors influencing the movement of the rolling stones can be refined as much as possible in the invention so as to meet the actual situation to the greatest extent.
The mathematical model of the invention can be divided into the following four steps
1. Sliding phase
The sliding stage is the initial stage of the displacement of the rolling stones and is the stage of kinetic energy accumulation, in this stage, we need to obtain the sliding distance of the rolling stones and the initial speed for ending the stage and entering the next stage
2. Stage of flying down
The flying and falling stage is a falling motion curve of the rolling stone, in the stage, an inclined throwing line of the rolling stone is placed into a coordinate system, and the motion of the rolling stone is decomposed into superposition of uniform deceleration motion of an x axis and free falling motion of a y axis.
3. Stage of collision bounce
The collision bounce stage is a stage of converting the gravitational potential energy of the rolling stone into elastic potential energy, the incident speed and the rock slope surface are decomposed into normal speed, and the emergent speed of the bouncing rolling stone can be obtained after the correction of the coefficient of restitution
4. Scrolling phase
The rolling stage is the end stage of the movement of the rolling stone, and the rolling distance of the rolling stone at the final standstill can be obtained according to the gradient and the previously obtained speed vector.
Firstly, determining the position of dangerous rocks, collecting slope measurement data, arranging a protective net, then placing the nine-axis sensor into the dangerous rocks through drilling holes, and sealing after determining that a signal receiver receives signals. And the dangerous rock state is judged through the signal receiver, and real-time monitoring is carried out. Once the dangerous rock displacement is found, the computer is used for simulating and predicting the falling point of the rolling rock by the calculation method provided by the invention, and alarming is carried out to minimize the damage caused by the rolling rock.
The invention has the advantages that
Firstly, when dangerous rocks roll to form falling rocks, the movement track can be simulated by a computer, so that related personnel can predict a disaster area in advance
(II) the positioning system is arranged, so that once a disaster happens, related personnel can quickly position the scene
And (III) the calculation speed is high, and an alarm can be given out in time before the rolling stones are not damaged.
And (IV) helping us to understand the movement of the rolling stones and verifying theoretical results through actual situation reversal.
And (V) collecting data in a large range to prepare for constructing a database.
And (VI) compared with the existing model, the influence factors are refined, so that the simulated curve is more in line with the actual situation.
Drawings
Fig. 1 is a structural block diagram of a slope rolling stone early warning system of the invention.
Fig. 2 is a schematic view of the site layout of the slope rolling stone early warning system of the invention.
Fig. 3 is a schematic diagram of the sliding phase movement of the present invention.
Fig. 4 is a schematic diagram of the movement of the present invention in the flying stage.
FIG. 5 is a schematic diagram of the motion of the present invention during the bounce phase of collision.
Fig. 6 is a schematic diagram of the scrolling phase motion of the present invention.
FIG. 7 is a schematic view of the hole formation in step 2 according to the embodiment of the present invention.
Fig. 8 is a schematic view of a nine-axis sensor embedded in step 3 according to an embodiment of the present invention.
Fig. 9 is a schematic diagram of testing the communication signals of the nine-axis sensor in step 4 according to the embodiment of the present invention.
FIG. 10 is a schematic view of the operation of closing the via holes in step 5 according to the embodiment of the present invention.
In the figure, 1-nine-axis sensor, 2-dangerous rock, 3-mountain, 4-guardrail, 5-highway, 6-computer, 8-drill bit, 9-pore forming, 10-concrete backfill area, S1-sliding stage, S2-flying stage, S3-collision bounce stage, and S4-rolling stage.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
The invention is further described with reference to the following drawings and specific examples, which are not intended to be limiting.
As shown in fig. 1, the slope rolling stone early warning system based on the nine-axis sensor of the rolling stone track calculation method of the invention comprises a remote control system, a data transmission subsystem and a field data acquisition subsystem; the data transmission subsystem is used for realizing data transmission between the remote control system and the field data acquisition subsystem; the remote control system comprises a geographic information subsystem, a rolling stone track calculation subsystem and a model early warning subsystem, wherein the geographic information subsystem is used for storing a digital model of the target slope; the rolling stone track calculation subsystem is used for establishing a rolling stone landslide track calculation model library and calculating the track of the rolling stone according to different initial boundary conditions; the model early warning subsystem is used for predicting a rock rolling falling point according to the triggering of landslide and the rock rolling track simulated and calculated by the rock rolling track calculation subsystem, judging an influence area by combining nearby houses and roads and sending early warning information; the field data acquisition subsystem comprises a nine-axis sensor 1 installed in a slope dangerous rock 2.
As a specific embodiment, the geographic information subsystem obtains the topographic information of the field area through a laser radar and an oblique photography technology, and the topographic information includes a slope model and information of road houses and roads around the slope.
As a specific embodiment, the model early warning subsystem includes an automatic early warning system and a manual early warning system, the automatic early warning system notifies an operator monitoring the remote control system, and the manual early warning system includes a telephone notification and a short message notification.
As a specific embodiment, the data transmission subsystem performs data transmission by using a GPRS signal, a 3G signal, a 4G signal, or a 5G signal, and specifically uses a GPRS chip, a 3G chip, a 4G chip, or a 5G chip.
As a specific example, the nine-axis sensor 1 is powered by a micro battery.
As a specific example, the remote control system is installed on a computer 6 in a remote control room.
The method for establishing the slope rolling stone early warning system comprises the following steps:
step 1, scanning a target area by using an unmanned aerial vehicle carrying terrain scanning equipment (such as a three-dimensional laser scanner), collecting terrain data, and determining the position of dangerous rock 2;
step 3, connecting the nine-axis sensor 1 with a communication module for data transmission and embedding the nine-axis sensor into a hole 9, as shown in fig. 8;
step 5, after the signal is confirmed and can be normally received by the remote control system, closing the pore-forming hole 9 on the dangerous rock 2, as shown in fig. 10;
step 6, testing whether the signals sent by the nine-axis sensor 1 can be received by the computer 6 again;
7, when rockfall occurs, triggering the nine-axis sensor 1 in the dangerous rock 2, and sending a dangerous rock 2 moving signal to a remote control system;
and step 10, after receiving the alarm signal, the monitoring personnel immediately report the disaster area and send dangerous area information to related personnel to inform the disaster occurrence situation, the rescue work is immediately carried out, and the related area, particularly the road, is temporarily blocked.
Particularly, when the remote control system monitors that the displacement of the rolling stones stops through the nine-axis sensor 1, the rescue work is immediately carried out in the corresponding area, and rescue workers can be told that the rolling stones move at any place, so that secondary disasters can be effectively avoided.
The method for calculating the rolling stone track by using the rolling stone track calculating subsystem comprises the following steps:
the computer 6 prestores a digital model of a target side slope to obtain a slope surface equation f (x, y), the calculation method is to establish a coordinate system with the dangerous rock 2 as an origin on the side slope, divide the rolling stones formed by the dangerous rock 2 on the side slope into a sliding stage S1, a flying stage S2, a collision and bounce stage S3 and a rolling stage S4, respectively calculate the displacement and the speed of the rolling stones at each stage, and finally comprehensively calculate the final position of the synthesized rolling stones to complete the calculation of the rolling stone track.
1. For rolling stone sliding on slope
We assume that the slope shape is known, the slope equation is f (x, y), and the initial conditions for the rolling stone motion are determined by field investigation as known conditions in the fall.
As shown in fig. 3, when the rolling stones start to slide from a standstill, the following calculation formula is applied:
in the above formula, S is the sliding distance of the rolling stones in the sliding stage S1, v0The speed of the rolling stone at the end of sliding is measured and obtained by a nine-axis sensor 1 positioned in the rolling stone; g is gravity acceleration, and can be 9.8m/s2(ii) a Mu is a sliding friction coefficient and is obtained by a field friction test or experience; alpha is a sliding section of the slopeSlope, obtained by field measurements; gamma is a slope vegetation correction coefficient and is obtained by adopting a field contrast test;
the sliding distance calculation formula is as follows:
the coordinate P of the rolling stone at the end of the sliding stage S1 is determined by formula (1)0(x0,y0) Wherein x is0＝scosα，y0＝-ssinα。
2. Flying stage for rolling stones S2
As shown in fig. 4, where the slope angle of the side slope changes, and after a collision occurs, a falling of the rolling stones tends to be formed. Under the action of gravity, the gravitational potential energy of the rolling stone is converted into kinetic energy. Neglecting the influence of air resistance when the rolling stone flies, the free flying of the rolling stone can be described as a simple parabolic motion, and the motion track is a parabola among a series of collision points. For free-fall of the roller stones, the design concerns are the location of the point of impact, the incident velocity of the impact, and the impact velocity and height of the roller stones in the subsequent bounce.
The invention uses the following calculation formula:
x＝v0x·Δt+x0formula (2)
Wherein v is0xVelocity v for the end of the slip phase S10Component in the direction of the x-axis, v0yVelocity v for the end of the slip phase S10A component in the y-axis direction;
and (3) combining the formula (2) and the formula (3) to eliminate delta t to obtain a motion trail equation of the free flying and falling of the rolling stones:
obtaining a coordinate P when the flying and falling stage S2 is finished through a motion trail equation and a slope equation of the free flying and falling of the rolling stones1(x1,y1)。
In the process of free falling of the rolling stones, the rotational energy accounts for 10% of the total kinetic energy, so that the curve is influenced to a certain extent, a kinetic energy correction coefficient sigma is taken, and the value of the sigma can be obtained by a comparison experiment according to smaller stones, so that the corrected formula is as follows:
3. for rolling stone collision bounce
As shown in fig. 5, the roller stone inevitably generates energy loss after colliding with the slope surface in the bouncing stage (the energy loss can be reflected by the change of the speed of the roller stone), that is, each time the roller stone bounces, the roller stone is equivalent to be in an initial state again, and initial conditions are provided for the calculation of the next bounce. Therefore, the whole bounce stage of the rolling stones can be divided into the bounce processes which are connected with each other. After the parameters of the slope surface of the side slope and the initial state of the rolling stones are known (the initial state of the rolling stones is generally static in nature), the calculation of the motion trail of the first bounce can be carried out. And then, calculating the second bounce motion trail based on the result of the first bounce motion trail calculation, and so on until the rolling stone bounce motion is finished.
The essence of the calculation of the track of the bouncing movement stage of the rolling stone is to find out the intersection point of a parabola and each line segment of the slope surface of the side slope and the time of each parabolic movement when the rolling stone bounces each time, and once the time of the contact point and the time of the rolling stone doing the parabolic movement are determined, the movement track of the rolling stone can be determined by applying the following formula.
Since the present invention is installed with the nine-axis sensor 1 in the rock mass, the position P of the rolling stone before collision can be obtained1(x1,y1) And velocity v1In order to further simplify the calculation process of the invention, the rolling stones and the slope surface of the side slope are subjected to the speed before the first collisionDegree v1Decomposed into v along the x and y axesxbAnd vybThen the velocity v is adjustedxbAnd vybThe normal direction and the tangential direction of the slope surface where the first collision is located are decomposed, and the formula is as follows:
vnb＝vybcosθ-vxbsin theta equation (6)
vtb＝vybsinθ+vxbcos θ equation (7)
In the above formula, vnbNormal velocity component, v, of rolling stone before impact with slopetbThe tangential velocity component of the slope at the front of the collision of the rolling stone and the slope, and the slope angle of the slope at the current stage;
and (3) solving the speed of the rolling stone after the rolling stone collides with the slope surface according to a collision formula as follows:
vna＝Rnvnb
vta＝Rtvtb
vnavelocity component, v, in the direction normal to the slope surface after the rolling stone collides with the slope surfacetaComponent of velocity in slope tangential direction after impact of rolling stone with slope surface, RnIs the normal reduction coefficient of the slope surface of the side slope, RtTangential reduction coefficient of slope surface, RnAnd RtAnd selecting according to the geological conditions of the side slope.
According to the velocity v after the first collisionnaAnd vtaCalculating a parabolic track after the first collision, then calculating the position of a second collision point by combining a slope equation, and then repeatedly calculating according to the steps until the speed after the collision is not enough to throw the rolling stone again, wherein the position of the collision is the end position P of the collision bounce stage S32(x2,y2) Velocity is decomposed into v along the x and y axes2xAnd v2yThe concrete formula is as follows:
v2x＝vnasinθ+vtacos theta equation (8)
v2y＝vtasinθ-vnacos theta equation (9)
The following provides a better method for judging the end of the collision bounce stage S3:
definition of
Wherein v isnaAnd vtaThe normal component and the tangential component of the bouncing speed of the roller stone after collision are respectively, lambda is called as the collision bounce angle of the roller stone, and when tan lambda is less than xi after the roller stone collides, the roller stone is considered to enter a rolling state without bounce; otherwise, continuing to analyze and calculate according to the bounce; xi is a constant which is arbitrarily larger than 0, and the size of xi is determined according to the calculation precision.
4. For rolling stone
As shown in fig. 6, when it is difficult to continue the bouncing movement by the remaining kinetic energy after the rolling stone collision, the rolling (sliding) movement stage is shifted. The rolling of the rolling stone mainly occurs at the beginning and the end of the movement, and in some slope sections with steeper slope, sliding rolling is also possible. Design concerns are when the rolling stones enter the rolling state during movement, and the final distance of the rolling.
In reality, the model is always different from the actual situation, the rolling stones do not exist in a regular geometric shape, and therefore a correction coefficient tau is introduced to correct calculation errors caused by the shapes and sizes of the rolling stones. Because the nine-axis sensor 1 can capture the position of the rolling stone in the motion curve at each moment, the value of tau can be adjusted according to the field situation, so that the rolling stone is closer to the actual situation. And the correction accuracy will be higher and higher in case large data collection is sufficient.
For rolling analysis of the rolling stone, as shown in the figure, assuming that the rolling stone enters the rolling state at the point O, at this time, for any time t, the dynamic equilibrium equation can be obtained
Formula (10) of N-mgcos ═ 0
ms' ═ mgsin-f formula (11)
Is ″ ═ f τ -Nd equation (12)
Wherein, the slope angle is a slope surface slope angle; n is the supporting force of the slope surface to the rolling stones; f is the friction force of the slope surface to the rolling stones; m is the mass of the rolling stone; tau is a correction coefficient; s is the displacement vector of the rolling stone, and I is the moment of inertia; s "is the second derivative of the displacement vector with respect to time, i.e. the acceleration;
from the above formula
Definition of
B is a correction relating to the quality and shape of the rolling stone, d is the diameter of the rolling stone; definition of mur＝dτ＝tanβrCalled coefficient of rolling friction, betarReferred to as the rolling friction angle;
because S ″ -Bg (sin-dcos) exists, the rolling stone can roll at any position S on the slope surface2Velocity V of
V2For the speed in the ramp direction at the beginning of the scrolling phase S4,
if s' < 0, i.e., tan < tan betarWhen the rolling stone rolls at a reduced speed and finally stops under the action of rolling friction, namely V is 0, and the displacement when the rolling stone stops is as follows:
at this time, the position P of the roller stone at the stop is obtained3(x3,y3) Wherein x is3＝S2cos+x2，y3＝S2sin+y2。
This equation can be used to evaluate the impact of a rolling stone disaster.
At the same time have
Like the coefficient of restitution RnAnd RtSame coefficient of rolling friction murIs also an important parameter for correctly estimating the motion trail of the rolling stone. The rolling friction coefficient is related to the size, shape and speed of the rolling stone, the slope gradient and the slope geomechanical property. In the case of sufficient experimental data, μ can be back-calculated from equation (16)rThe value of (c). The results of the field test show that the rolling stone has a rolling friction coefficient murBetween 0.3 and 1.0 (beta)rBetween 16 deg. and 45 deg.).
Due to the uncertainty of the main factors for controlling the motion of the side slope rolling stones, the estimation of the motion trail of the side slope rolling stones is very complicated. From the engineering point of view, the main contradiction of the problem is grasped, and on the basis of a certain assumption, a set of simple calculation formula for estimating the motion of the rolling stone is necessary and can meet the engineering requirements. Whether the real motion track of the actual side slope rolling stone can be correctly estimated by the formulas depends on the collision recovery coefficient R in the calculation to a great extentnAnd RtAnd coefficient of rolling friction murReliability of isoparametric values. Therefore, detailed on-site investigation of slopes that may cause a rolling rock disaster is essential before analysis. In the invention, the nine-axis sensor 1 can be used for testing the field environment, and if necessary, a field test in a certain range is supplemented, so that accurate parameter values can be obtained, which cannot be achieved by the model at the present stage, and influence factors can be refined through the obtained data, so that the maximum coincidence with the actual situation is achieved.
It should be noted that although the direction of the rolling stones is uncertain, once the rolling stones start to roll and fly, the direction is basically determined, and the deviation of the direction in the subsequent rolling and flying processes is negligible relative to the distance of rolling out or flying out, so the track of the rolling stones can be simplified into the motion in the two-dimensional plane coordinate system, and the two-dimensional coordinate system is determined according to the direction of the rolling stones start to roll, and at this time, the slope equation is the intersection line equation obtained by intersecting the vertical plane in which the rolling direction is located and the three-dimensional slope, which is f (x, y).
The above embodiments are merely illustrative of the present invention and are not to be construed as limiting the invention. Although the present invention has been described in detail with reference to the embodiments, it should be understood by those skilled in the art that various combinations, modifications or equivalents may be made to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention, and the technical solution of the present invention is covered by the claims of the present invention.
Claims (7)
1. A method for calculating a rolling stone track is characterized by comprising the following steps: the method comprises the steps that the nine-axis sensor is installed in dangerous rock of a side slope and is communicated with a computer through the wireless communication module, a digital model of a target side slope is prestored in the computer to obtain a slope surface equation f (x, y), a coordinate system with the dangerous rock as an original point is established on the side slope, then rolling stones formed by the dangerous rock on the side slope are divided into a sliding stage, a flying stage, a collision and bounce stage and a rolling stage, rolling stone displacement and speed of each stage are respectively calculated, and finally the final position of the synthesized rolling stone is comprehensively calculated to finish rolling stone track calculation.
2. The method of calculating a stone rolling trajectory of claim 1, wherein: for the sliding stage, the rolling stone starts to slide from a rest state, and the sliding distance is calculated according to the following formula:
in the above formula, s is the sliding distance of the rolling stones in the sliding stage, v0The speed of the rolling stone at the end of sliding is measured and obtained by a nine-axis sensor positioned in the rolling stone; g is the acceleration of gravity; mu is a sliding friction coefficient and is obtained by a field friction test or experience; alpha is a slope sliding sectionThe gradient of (d) is obtained by field measurement; gamma is a slope vegetation correction coefficient and is obtained by adopting a field contrast test;
determining the coordinate P at the end of the sliding phase of the rolling stone through the formula (1)0(x0,y0) Wherein x is0＝scosα，y0＝-ssinα。
3. The method of calculating a stone rolling trajectory of claim 2, wherein: for the flying and falling stage, the distance calculation formula of the flying of the rolling stone is as follows:
x＝v0x·Δt+x0formula (2)
Wherein v is0xVelocity v for the end of the slip phase0Component in the direction of the x-axis, v0yVelocity v for the end of the slip phase0A component in the y-axis direction;
and (3) combining the formula (2) and the formula (3) to eliminate delta t to obtain a motion trail equation of the free flying and falling of the rolling stones:
obtaining a coordinate P at the end of the flying and falling stage through a motion track equation and a slope equation of the free flying and falling of the rolling stones1(x1,y1)。
4. The method of calculating a stone rolling trajectory of claim 3, wherein: in the flying stage, the influence of the rotational kinetic energy on the falling of the rolling stone is considered, a kinetic energy correction coefficient sigma is introduced into the formula (4), and the value of the sigma is compared according to a small stone block to obtain a corrected formula:
5. the method of calculating a stone rolling trajectory of claim 3, wherein: for the collision bounce stage, the calculation formula is as follows:
obtaining the speed v before the first collision by a nine-axis sensor in the rolling stone1The position at collision, i.e. the position P at the end of the flight phase1(x1,y1)；
Will velocity v before first impact1Decomposed into v along the x and y axesxbAnd vybThen the velocity v is adjustedxbAnd vybThe normal direction and the tangential direction of the slope surface where the first collision is located are decomposed, and the formula is as follows:
vnb＝vybcosθ-vxbsinθ
vtb＝vybsinθ+vxbcosθ
in the above formula, vnbNormal velocity component, v, of rolling stone before impact with slopetbThe tangential velocity component of the rolling stone and the slope surface before the collision of the rolling stone and the slope surface, and the slope surface angle of the current slope surface theta;
and (3) solving the speed of the rolling stone after the rolling stone collides with the slope surface according to a collision formula as follows:
vna＝Rnvnb
vta＝Rtvtb
vnavelocity component, v, in the direction normal to the slope surface after the rolling stone collides with the slope surfacetaComponent of velocity in slope tangential direction after impact of rolling stone with slope surface, RnIs the normal reduction coefficient of the slope surface of the side slope, RtTangential reduction coefficient of slope surface, RnAnd RtSelecting according to the geological conditions of the side slope;
according to the velocity v after the first collisionnaAnd vtaCalculating a parabolic track after the first collision, then calculating the position of a second collision point by combining a slope equation, and then repeatedly calculating according to the steps until the speed after the collision is not enough to throw the rolling stone again, wherein the position of the collision is the end position P of the collision bounce stage2(x2,y2) Velocity is decomposed into v along the x and y axes2xAnd v2y。
6. The method of calculating a stone rolling trajectory of claim 5, wherein: the method for judging the end of the collision bounce stage comprises the following steps:
definition of
Wherein v isnaAnd vtaThe normal component and the tangential component of the bouncing speed of the roller stone after collision are respectively, lambda is called as the collision bounce angle of the roller stone, and when tan lambda is less than xi after the roller stone collides, the roller stone is considered to enter a rolling state without bounce; otherwise, continuing to analyze and calculate according to the bounce; xi is a constant which is arbitrarily larger than 0, and the size of xi is determined according to the calculation precision.
7. The method of calculating a stone rolling trajectory of claim 5, wherein: for the rolling phase, the calculation formula is as follows:
for rolling stones, the dynamic balance equation yields:
N-mgcos＝0
ms″＝mgsin-f
Is″＝fτ-Nd
in the formula:
is a slope angle; n is the supporting force of the slope surface to the rolling stones; f is the friction force of the slope surface to the rolling stones; m is the mass of the rolling stone; tau is a correction coefficient; s is the displacement vector of the rolling stone, and I is the moment of inertia; s "is the second derivative of the displacement vector with respect to time, i.e. the acceleration;
from the above formula
Definition of
B is equal to the mass of the rockA correction relating to shape, d is the diameter of the stone; definition of mur＝dτ＝tanβrCalled coefficient of rolling friction, betarReferred to as the rolling friction angle;
because S ″ -Bg (sin-dcos) exists, the rolling stone can roll at any position S on the slope surface2Velocity V of
V2The speed in the direction of the slope at the beginning of the rolling phase,
if s' < 0, i.e., tan < tan betarWhen the rolling stone rolls at a reduced speed and finally stops under the action of rolling friction, namely V is 0, and the displacement when the rolling stone stops is as follows:
at this time, the position P of the roller stone at the stop is obtained3(x3,y3) Wherein x is3＝S2cos+x2，y3＝S2sin+y2。
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