Method for predicting disaster-causing range of collapsed rockfall

Abstract

The invention provides a method for predicting a calamity-causing range of collapsed rockfall. The method comprises the following steps: triggering prediction evaluation of a collapsed dangerous rock body; triggering flight phase calculation; collision stage calculation; calculating a slope motion stage; and calculating a rockfall disaster-causing range. The method has the beneficial effects that the interception energy level of the stone blocking net is determined according to the impact kinetic energy, and the impact force serves as the basis of structural design of a stone blocking wall and the like. The protection system is arranged at the position with low bounce height and small motion kinetic energy according to geological conditions, and the height of the protection system is determined according to the bounce height.

Description

Technical Field

[0001] This invention belongs to the fields of engineering survey, geotechnical design, and disaster prevention and mitigation, and in particular relates to a method for predicting the disaster range caused by landslides and rockfalls. Background Technology

[0002] Rockfalls are a serious global mountain hazard with widespread distribution. Rockfall instability is often sudden, rapid, and highly destructive, but pre-disaster signs are usually subtle, making prevention in practical engineering very difficult. Especially in mountainous and hilly areas, strong river or valley incision leads to weathering and gravity unloading of the riverbank rock mass. Some areas also have alternating hard and soft strata or "hard on top, soft on the bottom," providing favorable conditions for rockfall development. Furthermore, high-intensity rainfall in a short period, large diurnal temperature variations, earthquakes, and human engineering activities such as excavation and unloading can all be significant contributing factors to rockfalls, posing a great threat to life and property. Many areas are limited by natural conditions and cannot implement active protection. If the trajectory and timing of rockfalls can be accurately predicted, their impact range can be determined, allowing for the delineation of safe zones and the implementation of passive protective engineering measures. In engineering practice, it is often necessary to predict and assess the potential threats of landslide disasters to prevent geological disaster accidents and to provide a basis for subsequent protective engineering design and construction, safe operation and maintenance, emergency rescue and safety avoidance. Summary of the Invention

[0003] In view of this, the present invention aims to propose a method for predicting the disaster range caused by rockfalls, so as to solve the problem that the existing technology cannot accurately predict rockfall disasters.

[0004] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0005] A method for predicting the disaster area caused by landslides and rockfalls includes the following steps:

[0006] S1. Prediction and assessment of triggering unstable rock mass collapse;

[0007] S2, Triggering flight phase calculations;

[0008] S3, Collision Phase Calculation;

[0009] S4. Calculation of slope motion stage;

[0010] S5. Calculation of the disaster area caused by falling rocks;

[0011] In step S1, the prediction and assessment of the triggering of the collapse of the unstable rock mass includes:

[0012] S11. Obtain deformation monitoring data of collapsed and unstable rocks through GNSS and generate an index data sequence;

[0013] S12. Accumulate once, perform catastrophe mapping, and establish a trigger assessment model;

[0014] S13, Quadratic fitting estimation;

[0015] S14, Error Inspection;

[0016] S15, Trigger judgment;

[0017] In step S2, flight phase calculations are triggered, including:

[0018] S21. Establish the slope equation for the movement of falling rocks and decompose it into linear slopes piece by piece.

[0019] S22. Determine the predictive evaluation conditions and provide initial motion parameters;

[0020] S23. Triggering flight phase A is divided into two phases: the AI ​​phase is the upward oblique projection before returning to the initial height, and the phase A-II is the downward oblique projection motion from the initial height before colliding with the ground.

[0021] S24. Calculate the horizontal movement distance based on the trajectory equation of the falling rocks in the AI ​​stage;

[0022] S25, Search for collision points;

[0023] S26. Calculate the equivalent slope length for the trigger flight phase;

[0024] In step S3, the collision phase calculation includes:

[0025] S31, Input the initial conditions for the collision phase;

[0026] S32. Calculate the horizontal and vertical rebound velocities of the collapsed rocks after impact and the angle between them and the horizontal direction.

[0027] S33. Calculate the maximum rebound height after the collision and determine the next motion stage based on it. The next motion stage is either the slope motion stage or the collision flight stage. The slope motion stage is stage C, and the collision flight stage is stage B.

[0028] S34. The collision flight phase B is divided into two phases: the phase B1 is the upward oblique projectile motion before returning to the initial height, and the phase B-II is the downward oblique projectile motion from the initial height before colliding with the ground.

[0029] S35. Calculate the horizontal movement distance based on the trajectory equation of the falling rocks in stage BI.

[0030] S36. Search for collision points;

[0031] S37. Calculate the horizontal and vertical movement distances and oblique lengths;

[0032] S38. Calculate the equivalent slope length during the collision flight phase;

[0033] In step S4, the slope motion stage calculation includes:

[0034] S41. Input the initial conditions for the slope motion stage;

[0035] S42. Calculate the translational kinetic energy and rotational kinetic energy;

[0036] S43. Calculate the angular velocity in reverse;

[0037] S44. Calculate the equivalent slope length during the slope movement stage.

[0038] Furthermore, in step S11, an indicator data sequence is generated, including:

[0039] The indicator data sequence is denoted as Θ (0) The expression is as follows:

[0040] Θ (0) =(Θ (0) (1), Θ (0) (2), …, Θ (0) (n)), n≥2;

[0041] In step S12, a single accumulation is performed, a catastrophe mapping is executed, and a trigger assessment model is established, including:

[0042] A single accumulation is denoted as Θ (1) The expression is as follows:

[0043] Θ (1) =(Θ (1) (1), Θ (1) (2), …, Θ (1) (n)), n≥2;

[0044] The trigger evaluation model is denoted as the GM(1,1) model, and the corresponding whitening differential equation is expressed as follows:

[0045]

[0046] In the formula, a and b are undetermined parameters. The parameter series a and b are solved using the following formula: [ab] T =(Δ T Δ) -1 Δ T Y N ;

[0047] In the formula, Δ and Y NThe expression is as follows:

[0048]

[0049] Y N =[Θ (0) (2), Θ (0) (3), …, Θ (0) (n)] T n≥2;

[0050] In the formula, Δ represents the data matrix composed of monitoring data obtained from a single accumulation; Y N This represents a data matrix composed of raw monitoring data;

[0051] The time response function expression for the GM(1,1) model is as follows:

[0052]

[0053] In the formula, Representing the whitening differential equation The solution is the fitting function expression, where E and Z represent two fitting parameters of the quadratic fitting function, obtained by fitting and transforming the equation of the monitoring data series, a is the undetermined parameter obtained from the first estimation in the above steps, and t represents time.

[0054] Furthermore, in step S13, the quadratic fitting estimation includes:

[0055] The quadratic fitting estimation expression is as follows:

[0056]

[0057] In the formula, K is expressed as follows:

[0058]

[0059] In the formula, K represents the constructed parameter matrix with the exponent e as the base;

[0060] For a series of numbers with equal time intervals, the formula can be derived by reversing the summation formula as follows:

[0061]

[0062] In the formula, This represents the (t+1)th simulated value being restored; This represents the (t+1)th simulated value; This represents the t-th simulated value.

[0063] Furthermore, in step S14, the error check includes:

[0064] The error expression is as follows:

[0065]

[0066] If q i If the value is ≤0.1, the model meets the requirements; otherwise, the model should be rebuilt.

[0067] In step S15, the determination is triggered, including:

[0068] If the displacement value exceeds the allowable displacement value, that is If a collapse is detected, the process begins to calculate the trajectory of the falling rocks.

[0069] Furthermore, in step S22, the predicted evaluation condition is determined, and initial motion parameters are given, including: an initial linear velocity of θ. x0 θ y0 The angular velocity is ω0, and the initial kinetic energy is E0;

[0070] In step S24, the horizontal movement distance is calculated, including:

[0071] The equation for the trajectory of the falling rocks during the AI ​​phase is as follows:

[0072] x (A-I)i =θ0cosα·Δt (A-I) ;

[0073]

[0074] In the formula, y (A-I)i This indicates that the AI ​​stage moved for a time Δt. (A-I) The longitudinal displacement of the collapsed rocks after reaching a certain point i; x (A-I)i This indicates that the AI ​​stage moved for a time Δt. (A-I) The lateral displacement after reaching a certain point i; g represents the gravitational acceleration; α represents the angle between the initial velocity θ0 and the horizontal direction;

[0075] In the formula, Δt (A-I) The total motion time for the AI ​​phase is expressed as follows:

[0076]

[0077] The expression for the horizontal movement distance in the AI ​​stage is as follows:

[0078]

[0079] In the formula, L (A-I)x This represents the distance traveled in the horizontal direction.

[0080] Furthermore, in step S25, the search for collision points includes:

[0081] The equation for the trajectory of the falling rocks in stage A-II is as follows:

[0082]

[0083] In the formula, x j This represents the lateral displacement of point j in stage A-II;

[0084] The slope surface of the landslide and rockfall movement is decomposed into a series of linear single slope surfaces, and the coordinates of each inflection point of the landslide and rockfall movement slope surface (a) are obtained. j b j If the slope of segment j is j, then the expression for the slope equation is as follows:

[0085]

[0086] x j ∈(a j a j+1 By combining the expressions for the trajectory equations of the falling rocks in stage A-II and the equations for the slope in segment j, the coordinates of the collision point are obtained as (x...). p y p If there is no solution, continue searching for a collision point on the next slope.

[0087] In step S26, the equivalent slope length for triggering the flight phase is calculated, including:

[0088] The expression for the duration of phase A-II is as follows:

[0089]

[0090] The expressions for the horizontal and vertical movement distances in stage A-II are as follows: L (A-II)x =x p -L (A-I)x ;

[0091]

[0092] The expression for the oblique length of the motion in stage A-II is obtained as follows:

[0093]

[0094] The expression for the equivalent wavelength in stage A is as follows:

[0095]

[0096] Furthermore, in step S31, the initial conditions for the collision phase are input, including:

[0097] The expression for the input conditions during the collision phase is as follows:

[0098] θ xp =θ0cosα;

[0099]

[0100] In the formula, θ xp θ yp The input velocity at the point of collision;

[0101] In step S32, the horizontal and vertical rebound velocities of the collapsed rocks after impact and the resulting rebound, as well as their angles with the horizontal direction, are calculated, including:

[0102] The expressions for the horizontal rebound velocity, vertical rebound velocity, and the angle between the rebounding rock and the horizontal direction after impact are as follows:

[0103]

[0104]

[0105] In the formula, ζ is the angle between the collapsed rocks after the rebound and the horizontal direction;

[0106] In the formula, e t and e n These are the restitution coefficients for the tangential and normal directions, respectively. For hard rock, e t and e n The values ​​are taken as 0.86 and 0.4 respectively; if it is soft rock, e t and e n The values ​​are taken as 0.84 and 0.35 respectively; if it is hard soil, e t and e n The values ​​are taken as 0.81 and 0.3 respectively; for ordinary soil, e t and e n The values ​​are 0.75 and 0.26 respectively; if it is loose soil, e t and e n The values ​​are 0.65 and 0.22 respectively;

[0107] In step S33, the maximum rebound height after the collision is calculated, including:

[0108] The expression for the maximum bounce height after a collision is as follows:

[0109]

[0110] In the formula, R is the radius of the equivalent cylinder of the collapsed rock;

[0111] If h max If h ≤ 2R, then the next stage is stage C. max If the value is greater than 2R, then the next stage is stage B.

[0112] Furthermore, in step S35, the horizontal movement distance is calculated, including:

[0113] The expression for the horizontal movement distance in the BI phase is as follows:

[0114]

[0115] In step S36, the search for collision points includes:

[0116] The equation for the trajectory of the falling rocks in stage B-II is as follows:

[0117]

[0118] The slope surface of the landslide and rockfall movement is decomposed into a series of linear single slope surfaces, and the coordinates of each inflection point of the slope surface of the rockfall movement are obtained as (a j b j The equations for the slope and the trajectory of the falling rocks are combined to obtain the coordinates of the collision point (x). pi y pi If there is no solution, continue searching for a collision point on the next slope.

[0119] In step S37, the horizontal and vertical movement distances and oblique lengths are calculated, including:

[0120] The expression for the duration of phase B-II is as follows:

[0121]

[0122] The expressions for the horizontal and vertical movement distances are as follows:

[0123] L (B-II)x =x pi -L (B-I)x ;

[0124]

[0125] The expression for the oblique length of the motion is as follows:

[0126]

[0127] In step S38, the equivalent slope length during the collision flight phase is calculated, including:

[0128] The expression for the equivalent slope length during the collision flight phase is as follows:

[0129]

[0130] Furthermore, in step S41, the initial conditions for the slope motion stage are input, including:

[0131] The expression for the initial conditions during the slope motion stage is as follows:

[0132] θ (C)x =θ (B)x ;

[0133]

[0134] In step S42, the translational kinetic energy and rotational kinetic energy are calculated, including:

[0135] The expressions for translational kinetic energy and rotational kinetic energy are as follows:

[0136] E va =0.5m(θ) (C)x 2 +θ (C)y 2 );

[0137] E ra =[0.5m(θ) (C)x 2 +θ (C)x 2 )]·ψ;

[0138] In the formula, m is the mass of the falling rock, and ψ is a function related to the angle ζ between the rebounding rock and the horizontal direction. If 0 ≤ ζ ≤ 36°, ψ takes the value of m. If 36° < ζ ≤ 74°, then ψ is taken as... In step S43, the angular velocity is calculated in reverse, including:

[0139] The expression for angular velocity is as follows:

[0140]

[0141] In step S43, the equivalent slope length during the slope movement stage is calculated, including:

[0142] The expression for the equivalent slope length in stage C is as follows:

[0143]

[0144] In the formula, Γ is the angle between the slope and the horizontal plane where the rolling motion occurs. is the rolling friction coefficient.

[0145] Furthermore, in step S5, the calculation of the disaster area caused by the rockfall includes:

[0146] S51. Calculate the total length of the equivalent slope, as shown in the following expression:

[0147] L = L (A) +L (B) +L (C) ;

[0148] S52. Calculate the disaster-causing area of ​​falling rocks, using the following expression:

[0149] D = η·2L;

[0150] In the formula, L is the maximum slope length of the movement, and η is the offset ratio of the rockfall movement.

[0151] This invention provides a method for predicting the disaster-causing range of landslides, used to predict the movement trajectory and impact area of ​​landslides. The behavioral characteristics of landslide rockfall movement are that the threatened area depends on the movement characteristics, and the threat capability comes from the impact kinetic energy. This invention uses impact kinetic energy to determine the interception energy level of rockfall barriers, and uses impact force as the basis for the design of rockfall barriers and other structures. This invention combines geological conditions to select locations with low bounce height and low kinetic energy for setting up protective systems, and determines the height of the protective system based on the bounce height. Attached Figure Description

[0152] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0153] Figure 1 This is the overall flowchart described in the embodiments of the present invention;

[0154] Figure 2 for Figure 1 Flowchart of the assessment process for triggering unstable rock masses;

[0155] Figure 3 for Figure 1 Flowchart of the triggering flight phase;

[0156] Figure 4 for Figure 1 Flowchart of the collision phase;

[0157] Figure 5 for Figure 1 Flowchart of the slope movement stages in the process;

[0158] Figure 6 for Figure 1 A flowchart for predicting the disaster area caused by rockfalls. Detailed Implementation

[0159] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0160] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0161] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0162] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0163] like Figures 1 to 6 As shown, a method for predicting the disaster area caused by landslides and rockfalls includes the following steps:

[0164] S1. Prediction and assessment of triggering unstable rock mass collapse;

[0165] S2, Triggering flight phase calculations;

[0166] S3, Collision Phase Calculation;

[0167] S4. Calculation of slope motion stage;

[0168] S5. Calculation of the disaster area caused by falling rocks;

[0169] The specific implementation method is as follows:

[0170] Step 1: Prediction and Assessment of Collapsed Rock Mass A1: Obtain deformation monitoring data of the collapsed rock mass, and record the changes in its displacement over time to form an index data sequence Θ. (0) , recorded as

[0171] Θ (0) =(Θ (0)(1), Θ (0) (2), …, Θ (0) (n)), n≥2;

[0172] A2: To reduce the randomness of the original data series, the original GNSS displacement monitoring data series is generated by 1-AGO accumulation, and Θ is obtained by one accumulation. (1) , recorded as

[0173] Θ (1) =(Θ (1) (1), Θ (1) (2), …, Θ (1) (n)), n≥2;

[0174] A3: Based on the monitoring data, a catastrophic mapping is performed, and a GM(1,1) model is established. The corresponding whitening differential equation is:

[0175] Where a and b are undetermined parameters. The parameter list is solved according to the following formula.

[0176] [ab] T =(Δ T Δ) -1 Δ T Y N ;

[0177] in,

[0178]

[0179] Y N =[Θ (0) (2), Θ (0) (3), …, Θ (0) (n)] T n≥2;

[0180] The corresponding time response function of the GM(1,1) model is:

[0181]

[0182] A4: To improve the accuracy of the model, based on the first estimated value of 'a' and the 1-AGO sequence X... (1) (k) Perform a second-order fitting estimation.

[0183]

[0184] in,

[0185]

[0186] For a series of numbers with equal time intervals, we can deduce the result by reversing the summation formula.

[0187]

[0188] in, It is Θ (0) The restored simulated value of t(k), where t(k) is... Corresponding raw data Θ (0) (k) and Θ (0) (1) The total time interval between them, k = 1, 2, ..., n.

[0189] A5: Generation error check.

[0190]

[0191] When q i If the value is ≤0.1, the model meets the requirements and can be used for prediction; otherwise, the model should be rebuilt.

[0192] A6: Trigger Decision: When the displacement value exceeds the allowable displacement value, i.e. At that time, the collapse occurred, and the calculation of the trajectory of the falling rocks began.

[0193] Step 2: Triggering Flight Phase Calculation B1: Based on field surveys, on-site borehole data, and remote sensing mapping results, determine the initial location of the landslide, estimate the mass of the falling rocks, establish the slope equation for the movement of the landslide, and decompose it piecewise into linear slope equations.

[0194] B2: Determine the predictive assessment conditions and provide initial motion parameters. The falling rock enters the triggered flight phase with an initial linear velocity of θ. x0 θ y0 The angular velocity is ω0, and the initial kinetic energy is E0. At this point, the collapsing rock is only subject to gravity, and its acceleration is gravitational acceleration g. The direction of the velocity is not in the same straight line as the direction of gravity, so the rock undergoes projectile motion, which is uniformly accelerated curvilinear motion. During the motion, the change in velocity is equal in any equal time interval, Δθ = gΔt, and the direction of the velocity change is always downward. In projectile motion, the horizontal and vertical components are independent of each other. Each component is not affected by the existence of the other. The two component motions and their resultant motion are simultaneous; the same time interval is the bridge connecting the two component motions and their resultant motion.

[0195] B3: In this invention, based on the guiding principle of "converting curves into straight lines", the oblique projectile motion is decomposed into uniform linear motion in the horizontal direction and vertical upward projectile motion in the vertical direction according to the laws of motion composition and classification.

[0196] The triggering flight phase A is divided into two stages: phase AI, which is the upward oblique projectile motion before returning to the initial height; and phase A-II, which is the downward oblique projectile motion from the initial height before colliding with the ground. If it is determined that the falling rock does not have an upward oblique projectile motion phase, then the calculation starts from the downward oblique projectile motion phase.

[0197] B4: At any moment during the AI ​​phase, the equation of motion for the center of mass of the collapsed rock is:

[0198] x (A-I)i =θ0cosα·Δt (A-I) ;

[0199]

[0200] If the rockfall is formed under conditions such as natural weathering, it generally undergoes free fall during its flight phase and is only subject to gravity. x =0, which is uniformly accelerated linear motion with an initial velocity of 0. At this time, the initial acceleration in both the horizontal and vertical directions is 0, and the motion is in free fall from the initial position.

[0201] If the projectile motion is caused by geological forces such as earthquakes, the initial velocity is upward, and the total motion time in the AI ​​phase is... The horizontal movement distance of the AI ​​stage is obtained as follows:

[0202]

[0203] After this point in time, the downward projectile motion enters stage A-II.

[0204] B5: At any moment during the downward oblique throwing A-II stage, the trajectory equation of the center of mass of the collapsed rock is:

[0205] B6: Find the collision point

[0206] Based on field surveys, on-site reconnaissance, and remote sensing mapping results, the rockfall movement slope was decomposed into segmented linear single slopes. The coordinates of each inflection point of the rockfall movement slope were obtained as (a j b j If the slope is such that the slope is j-th segment, then the expression for the slope equation is:

[0207]

[0208] x j ∈(a j a j+1 If both of the above equations are satisfied, then by combining the two equations, the coordinates of the collision point are obtained as (x...). p y pIf there is no solution within the current slope segment, the search for a collision point continues to the next slope segment.

[0209] B6: Calculate the equivalent slope length

[0210] After Phase A-II concludes, the duration of this phase is...

[0211]

[0212] The horizontal and vertical movement distances during this stage are as follows:

[0213] L (A-II)x =x p -L (A-I)x ;

[0214]

[0215] The oblique length of the motion in the A-II stage of the downward throw can be obtained as follows:

[0216]

[0217] The equivalent slope length for stage A is:

[0218]

[0219] Step 3: Collision Phase Calculation

[0220] C1: After the collapsed rocks collide with the slope, the collision phase begins. The input conditions for the collision phase are the same as the conditions at the end of the flight phase.

[0221] θ xp =θ0cosα;

[0222]

[0223] Where, θ xp θ yp It is the input velocity at the point of collision.

[0224] C2: During the collision, the motion of the falling rock changes drastically. The rock rebounds after contact with the surface, entering stage B. The slope angle of the collision surface is β. The horizontal and vertical components of the rebound velocity after the rebound are as follows:

[0225]

[0226] Where ζ is the angle between the collapsed rocks after the rebound and the horizontal direction.

[0227] Among them, e t and e nThese are the restitution coefficients for the tangential and normal directions, respectively. Based on the results of the preliminary comprehensive geological survey, the surface lithology of the slope is determined, thereby determining the restitution coefficients for the tangential and normal directions. If it is hard rock, e t and e n The values ​​are taken as 0.86 and 0.4 respectively; if it is soft rock, e t and e n The values ​​are taken as 0.84 and 0.35 respectively; for hard soil, e t and e n The values ​​are taken as 0.81 and 0.3 respectively; for ordinary soil, e t and e n The values ​​are taken as 0.75 and 0.26 respectively; for loose soil, e t and e n The values ​​were set to 0.65 and 0.22 respectively.

[0228] C3: Calculate the maximum bounce height h after the collision. max .

[0229]

[0230] Where R is the radius of the equivalent cylinder of the collapsed rocks, which can be used to determine the height of the interception net.

[0231] If h max If the value is ≤2R, then bouncing calculations are no longer performed, and the collapsed rocks enter the slope rolling state, i.e., stage C.

[0232] If h max If the value is greater than 2R, then the calculation is repeated according to the upward projectile motion. ζ is the angle between the falling rock and the horizontal plane at the beginning of the collision flight B stage, and the collision flight B stage begins.

[0233] C4: Re-enter the projectile motion calculation.

[0234] The collision flight B is divided into two stages: stage BI is the upward projectile motion before returning to the initial height; stage B-II is the downward projectile motion from the initial height before colliding with the ground again.

[0235] In the BI phase, the horizontal displacement of the rock as it falls back to the point on the same horizontal plane as the point of origin is:

[0236]

[0237] After this point in time, the downward projectile motion enters stage B-II.

[0238] At any moment during the downward oblique projection phase B-II, the equation of motion for the center of mass of the collapsed rock is:

[0239]

[0240] C5: Find the collision point

[0241] Based on field surveys, on-site reconnaissance, and remote sensing mapping results, the rockfall movement slope was decomposed into segmented linear single slopes, and the coordinates of each inflection point of the rockfall movement slope were obtained as (a j b j The equations for the slope and the trajectory of the center of mass of the collapsed rockfall are combined to obtain the coordinates of the collision point (x). pi y pi If there is no solution within the current slope segment, the search for a collision point continues to the next slope segment.

[0242] C6: After the completion of Phase B-II, the duration of this phase is...

[0243]

[0244] The horizontal and vertical movement distances during this stage are as follows:

[0245] L (B-II)x =x pi -L (B-I)x ;

[0246]

[0247] The oblique length of the motion during the downward throw phase is:

[0248]

[0249] C7: The equivalent slope length for phase B of the flight after the collision is:

[0250]

[0251] Step 4: Calculation of Slope Movement Stages

[0252] D1: After a rockfall collides with another rock, it will begin its next flight or enter a slope motion state, starting from the point of impact. If h max If the value is ≤2R, then bouncing calculations are no longer performed, and the collapsed rocks enter the slope rolling state, i.e., stage C. The input conditions for the slope rolling stage C are the same conditions at the end of the collision flight stage B-II.

[0253] θ (C)x =θ (B)x ;

[0254]

[0255] D2: After entering the slope motion, the falling rock accelerates and rolls on the slope until rolling friction causes all kinetic energy to be lost and it stops. The translational kinetic energy after the collision is:

[0256] E va =0.5m(θ) (C)x 2 +θ (C)y 2 );

[0257] D3: The corresponding rotational kinetic energy is:

[0258] E ra =[0.5m(θ) (C)x 2 +θ (C)x 2 )]·ψ;

[0259] Where m is the mass of the falling rock, and ψ is a function relating to the angle ζ between the rebounding rock and the horizontal direction. If 0 ≤ ζ ≤ 36°, ψ is taken as... If 36° < ζ ≤ 74°, then ψ is taken as... D4: Angular velocity is calculated in reverse:

[0260]

[0261] D5: The equivalent slope length L3 of the rolling phase C is:

[0262]

[0263] Where Γ is the angle between the slope and the horizontal plane that are rolling. This is the rolling friction coefficient. Its value is determined based on the slope and slope characteristics.

[0264] Step 5: Calculation of the disaster area caused by rockfall E1: Calculate the total length of the equivalent slope

[0265] The rockfall threat zone is a radial area controlled by an offset ratio, extending from the rockfall source to the toe of the slope. The final equivalent slope length is:

[0266] L = L (A) +L (B) +L (C) ;

[0267] E2: Calculate the disaster area caused by rockfall.

[0268] The disaster-causing area D of the falling rocks can be represented as:

[0269] D = η·2L;

[0270] Where L is the maximum slope length calculated from the rockfall, i.e., the total length of the equivalent slope, and η is the offset ratio of the rockfall movement. In actual engineering landslide disaster prevention, the offset ratio for landslide and rockfall prevention projects with a safety level of 1 is taken as 0.3, correspondingly 0.2 for level 2, and 0.1 for level 3. The higher the safety level, the larger the value.

[0271] Advantages of this invention:

[0272] This invention provides a method for predicting the disaster-causing range of landslides, used to predict the movement trajectory and impact area of ​​landslides. The behavioral characteristics of landslide rockfall movement are that the threatened area depends on the movement characteristics, and the threat capability comes from the impact kinetic energy. This invention uses impact kinetic energy to determine the interception energy level of rockfall barriers, and uses impact force as the basis for the design of rockfall barriers and other structures. This invention combines geological conditions to select locations with low bounce height and low kinetic energy for setting up protective systems, and determines the height of the protective system based on the bounce height.

[0273] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the disaster area caused by landslides and rockfalls, characterized in that: Includes the following steps: S1. Prediction and assessment of triggering unstable rock mass collapse; S2, Triggering flight phase calculations; S3, Collision Phase Calculation; S4. Calculation of slope motion stage; S5. Calculation of the disaster area caused by falling rocks; In step S1, the prediction and assessment of the triggering of the collapse of the unstable rock mass includes: S11. Obtain deformation monitoring data of collapsed and unstable rocks through GNSS and generate an index data sequence; S12. Accumulate once, perform catastrophe mapping, and establish a trigger assessment model; S13, Quadratic fitting estimation; S14, Error Inspection; S15, Trigger judgment; In step S2, flight phase calculations are triggered, including: S21. Establish the slope equation for the movement of falling rocks and decompose it into linear slopes piece by piece. S22. Determine the predictive evaluation conditions and provide initial motion parameters; S23. Triggering flight phase A is divided into two phases: the AI ​​phase is the upward oblique projectile motion before returning to the initial height, and the phase A-II is the downward oblique projectile motion from the initial height before colliding with the ground. S24. Calculate the horizontal movement distance based on the trajectory equation of the collapsed rocks in the AI ​​stage; S25, Search for collision points; S26. Calculate the equivalent slope length for the trigger flight phase; In step S4, the slope motion stage calculation includes: S41. Input the initial conditions for the slope motion stage; S42. Calculate the translational kinetic energy and rotational kinetic energy; S43. Calculate the angular velocity in reverse; S44. Calculate the equivalent slope length during the slope movement stage.

2. The method for predicting the disaster area caused by landslides and rockfalls according to claim 1, characterized in that: In step S11, an indicator data sequence is generated, including: The indicator data sequence is denoted as Θ (0) The expression is as follows: I (0) =(Θ (0) (1),Θ (0) (2),…,Θ (0) (n)), n≥2; In step S12, a single accumulation is performed, a catastrophe mapping is executed, and a trigger assessment model is established, including: A single accumulation is denoted as Θ (1) The expression is as follows: I (1) =(Θ (1) (1),Θ (1) (2),…,Θ (1) (n)), n≥2; The trigger evaluation model is denoted as the GM(1,1) model, and the corresponding whitening differential equation is expressed as follows: In the formula, a and b are undetermined parameters. The parameter series a and b are solved using the following formula: [ab] T =(Δ T Δ) -1 Δ T Y N ; In the formula, Δ and Y N The expression is as follows: Y N =[Θ (0) (2),Θ (0) (3),…,Θ (0) (n)] T n≥2; In the formula, Δ represents the data matrix composed of monitoring data obtained from a single accumulation; Y N This represents a data matrix composed of raw monitoring data; The time response function expression for the GM(1,1) model is as follows: In the formula, Representing the whitening differential equation The solution is the fitting function expression, where E and Z represent two fitting parameters of the quadratic fitting function, obtained by fitting and transforming the equation of the monitoring data column, a is the undetermined parameter obtained from the first estimation in the above steps, and t represents time. In step S13, the quadratic fitting estimation includes: The quadratic fitting estimation expression is as follows: In the formula, K is expressed as follows: In the formula, K represents the constructed parameter matrix with the exponent e as the base; For a series of numbers with equal time intervals, the formula can be derived by reversing the summation formula as follows: In the formula, This represents the (t+1)th simulated value being restored; This represents the (t+1)th simulated value; This represents the t-th simulated value.

3. The method for predicting the disaster area caused by landslides and rockfalls according to claim 2, characterized in that: In step S14, the error check includes: The error expression is as follows: If q i If the value is ≤0.1, the model meets the requirements; otherwise, the model should be rebuilt. In step S15, the determination is triggered, including: If the displacement value exceeds the allowable displacement value, that is If a collapse is detected, the process begins to calculate the trajectory of the falling rocks.

4. The method for predicting the disaster area caused by landslides and rockfalls according to claim 3, characterized in that: In step S22, the predicted evaluation condition is determined, given initial motion parameters, including: The initial linear velocity is θ x0 θ y0 The angular velocity is ω0, and the initial kinetic energy is E0; In step S24, the horizontal movement distance is calculated, including: The equation for the trajectory of the falling rocks during the AI ​​phase is as follows: x (A-I)i =θ0cosα·Δt (A-I) ; In the formula, y (A-I)i This indicates that the AI ​​stage moved for a time Δt. (A-I) The longitudinal displacement of the collapsed rocks after reaching a certain point i; x (A-I)i This indicates that the AI ​​stage moved for a time Δt. (A-I) The lateral displacement after reaching a certain point i; g represents the gravitational acceleration; α represents the angle between the initial velocity θ0 and the horizontal direction; In the formula, Δt (A-I) The total motion time for the AI ​​phase is expressed as follows: The expression for the horizontal movement distance in the AI ​​stage is as follows: In the formula, L (A-I)x This represents the distance traveled in the horizontal direction.

5. The method for predicting the disaster area caused by landslides and rockfalls according to claim 4, characterized in that: In step S25, the search for collision points includes: The equation for the trajectory of the falling rocks in stage A-II is as follows: In the formula, x j This represents the lateral displacement of point j in stage A-II; The slope surface of the landslide and rockfall movement is decomposed into a series of linear single slope surfaces, and the coordinates of each inflection point of the landslide and rockfall movement slope surface (a) are obtained. j b j If the slope of segment j is j, then the expression for the slope equation is as follows: x j ∈(a j a j+1 By combining the expressions for the trajectory equations of the falling rocks in stage A-II and the equations for the slope in segment j, the coordinates of the collision point are obtained as (x...). p y p If there is no solution, continue searching for a collision point on the next slope. In step S26, the equivalent slope length for triggering the flight phase is calculated, including: The expression for the duration of phase A-II is as follows: The expressions for the horizontal and vertical movement distances in stage A-II are as follows: L (A-II)x =x p -L (A-I)x ; The expression for the oblique length of the motion in stage A-II is obtained as follows: The expression for the equivalent wavelength in stage A is as follows:

6. The method for predicting the disaster area caused by landslides and rockfalls according to claim 5, characterized in that: In step S3, the collision phase calculation includes: S31, Input the initial conditions for the collision phase; S32. Calculate the horizontal and vertical rebound velocities of the collapsed rocks after impact and the angle between them and the horizontal direction. S33. Calculate the maximum rebound height after the collision and determine the next motion stage based on it. The next motion stage is either the slope motion stage or the collision flight stage. The slope motion stage is stage C, and the collision flight stage is stage B. S34. The collision flight phase B is divided into two phases: the phase B1 is the upward oblique projectile motion before returning to the initial height, and the phase B-II is the downward oblique projectile motion from the initial height before colliding with the ground. S35. Calculate the horizontal movement distance based on the trajectory equation of the falling rocks in stage BI. S36. Search for collision points; S37. Calculate the horizontal and vertical movement distances and oblique lengths; S38. Calculate the equivalent slope length during the collision flight phase.

7. The method for predicting the disaster area caused by landslides and rockfalls according to claim 6, characterized in that: In step S31, the initial conditions for the input collision phase include: The expression for the input condition during the collision phase is as follows: i xp =θ0cosα; In the formula, θ xp θ yp The input velocity at the point of collision; In step S32, the horizontal and vertical rebound velocities of the collapsed rocks after impact and the resulting rebound, as well as their angles with the horizontal direction, are calculated, including: The expressions for the horizontal rebound velocity, vertical rebound velocity, and the angle between the rebounding rock and the horizontal direction after impact are as follows: In the formula, ζ is the angle between the collapsed rocks after the rebound and the horizontal direction; In the formula, e t and e n These are the restitution coefficients for the tangential and normal directions, respectively. For hard rock, e t and e n The values ​​are taken as 0.86 and 0.4 respectively; if it is soft rock, e t and e n The values ​​are taken as 0.84 and 0.35 respectively; if it is hard soil, e t and e n The values ​​are taken as 0.81 and 0.3 respectively; for ordinary soil, e t and e n The values ​​are 0.75 and 0.26 respectively; if it is loose soil, e t and e n The values ​​are 0.65 and 0.22 respectively; In step S33, the maximum rebound height after the collision is calculated, including: The expression for the maximum bounce height after a collision is as follows: In the formula, R is the radius of the equivalent cylinder of the collapsed rock; If h max If h ≤ 2R, then the next stage is stage C. max If the value is greater than 2R, then the next stage is stage B.

8. The method for predicting the disaster area caused by landslides and rockfalls according to claim 7, characterized in that: In step S35, the horizontal movement distance is calculated, including: The expression for the horizontal movement distance in the BI phase is as follows: In step S36, the search for collision points includes: The equation for the trajectory of the falling rocks in stage B-II is as follows: The slope surface of the landslide and rockfall movement is decomposed into a series of linear single slope surfaces, and the coordinates of each inflection point of the slope surface of the rockfall movement are obtained as (a j b j The equations for the slope and the trajectory of the falling rocks are combined to obtain the coordinates of the collision point (x). pi y pi If there is no solution, continue searching for a collision point on the next slope. In step S37, the horizontal and vertical movement distances and oblique lengths are calculated, including: The expression for the duration of phase B-II is as follows: The expressions for the horizontal and vertical movement distances are as follows: L (B-II)x =x pi -L (B-I)x ; The expression for the oblique length of the motion is as follows: In step S38, the equivalent slope length during the collision flight phase is calculated, including: The expression for the equivalent slope length during the collision flight phase is as follows:

9. The method for predicting the disaster area caused by landslides and rockfalls according to claim 8, characterized in that: In step S41, the initial conditions for the slope motion stage are input, including: The expression for the initial conditions during the slope motion stage is as follows: i (C)x =θ (B)x ; In step S42, the translational kinetic energy and rotational kinetic energy are calculated, including: The expressions for translational kinetic energy and rotational kinetic energy are as follows: E va =0.5m(θ (C)x 2 +θ (C)y 2 ); E ra =[0.5m(θ (C)x 2 +θ (C)x 2 )]·ψ; Where m is the mass of the falling rock, ψ is a function related to the angle ζ between the collapsed falling rock after bouncing and the horizontal direction. If 0 ≤ ζ ≤ 36°, ψ takes If 36° < ζ ≤ 74°, ψ takes In step S43, the angular velocity is calculated by back-calculation, including: The expression for angular velocity is as follows: In step S43, the equivalent slope length during the slope movement stage is calculated, including: The expression for the equivalent slope length in stage C is as follows: In the formula, Γ is the angle between the slope and the horizontal plane where the rolling motion occurs. is the rolling friction coefficient.

10. The method for predicting the disaster area caused by landslides and rockfalls according to claim 9, characterized in that: In step S5, the calculation of the disaster area caused by falling rocks includes: S51. Calculate the total length of the equivalent slope, as shown in the following expression: L=L (A) +L (B) +L (C) ; S52. Calculate the disaster-causing area of ​​falling rocks, using the following expression: D = η·2L; In the formula, L is the maximum slope length of the movement, and η is the offset ratio of the rockfall movement.

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