Velocity equivalence-based discrete landslide surge test and whole-process amplitude prediction method

Abstract

The invention discloses a discrete landslide surge test and whole-process wave amplitude prediction method based on speed equivalence. According to the method, a three-dimensional physical model is established according to Froude similarity criteria, and accurate control over the water entering speed of the slip mass is achieved through speed equivalence. The high-position landslide movement is divided into an initial state, a sliding-out state, a water entering state, a sliding-out stage and a sliding stage, and the speed of a slide body in each state is calculated by adopting a structural strain energy method, an improved Pankend classification method and an energy method. Through a multi-factor orthogonal test, the influence rule of the landslide sliding speed, the water entry volume and the initial water depth on the surge characteristics is systematically analyzed, and a surge whole-process prediction model system covering the initial wave amplitude, the propagation attenuation and the dam front climbing height is constructed based on test data. According to the invention, the problems of insufficient sliding speed control precision and lack of prediction model systematicness in the prior art are effectively solved, the test accuracy and prediction reliability are significantly improved, and important technical support is provided for risk assessment of landslide surge disasters in the reservoir area.

Description

Technical Field

[0001] This invention relates to the field of landslide geological disaster prevention and mitigation technology, and in particular to a method for predicting the wave amplitude of a loose landslide based on velocity equivalence in a surge test. Technical Background

[0002] Landslide surges, as secondary disasters caused by landslides sliding into water, are often far more destructive than landslides themselves, posing a significant threat to engineering safety and ecological environment safety.

[0003] To minimize the risks of landslides and surges during the construction and operation of high dams and large reservoirs, and to reduce casualties and property losses, it is of great significance to conduct accurate and reliable surge prediction research.

[0004] Currently, existing physical model experiments have the following problems:

[0005] ① Landslides are often triggered by a combination of factors such as reservoir water level changes, rainfall infiltration, and earthquakes. It is difficult to accurately reproduce and simulate their coupling mechanism in an experimental environment.

[0006] ② To simplify operations, existing empirical formulas based on physical experiments mostly rely on rigid body or block models, and the data mostly comes from two-dimensional flume experiments, which makes it difficult to truly reflect the three-dimensional complexity of actual terrain and river conditions.

[0007] ③ Current test methods mostly rely on the landslide body accelerating its sliding under its own weight, making it difficult to accurately control its entry speed into the water, resulting in insufficient repeatability and accuracy of test results;

[0008] ④ Existing prediction formulas are mostly empirical relationships based on local stages or specific conditions, and a systematic and complete wave amplitude prediction system for the entire wave surge process has not yet been formed.

[0009] Numerical simulation is not limited by physical conditions, and can flexibly set measurement points and output full-process data. However, its calculation accuracy is often constrained by problems such as idealized assumptions of the algorithm, high parameter sensitivity, and difficulty in balancing calculation efficiency and accuracy. Summary of the Invention

[0010] The purpose of this invention is to provide a method for predicting wave amplitude during landslide surge tests and the entire process of landslide surges based on velocity equivalence. This invention establishes a set of initial condition setting methods applicable to landslide surge tests at high elevations. Through a series of physical experiments, it constructs wave amplitude prediction calculation formulas applicable to all stages of the landslide surge process, providing theoretical and technical support for the accurate prediction of landslide surge height.

[0011] A method for predicting the wave amplitude of a landslide based on velocity equivalence and slab landslide surges throughout the entire process, characterized by the following steps:

[0012] (1) Construct a three-dimensional physical model based on the Froude similarity criterion;

[0013] (2) Based on the principle of velocity equivalence, the range of landslide entry velocity is determined by theoretical calculation, and the entry velocity of the model landslide body into the water is controlled by adjusting the slope, length and bottom friction material of the chute;

[0014] (3) Set the inflow volume and initial water depth based on geological analysis and similarity ratio conversion;

[0015] (4) Perform orthogonal experiments and collect data;

[0016] (5) Based on experimental data, establish a full-process wave amplitude prediction system including an initial wave amplitude prediction model, a wave amplitude propagation attenuation prediction model, and a wave surge dam front run-up prediction model.

[0017] Furthermore, this invention establishes a three-dimensional physical model as an experimental system based on the Froude similarity criterion, including a landslide area and a river channel area. The landslide area is equipped with a tiltable sliding box, with an electrically controlled rotating baffle at its leading edge, and the bottom surface can be covered with materials of different friction coefficients;

[0018] Furthermore, regarding the design of key parameters:

[0019] Landslide velocity: Based on the velocity equivalence principle, the disturbance and weakening effects of external disaster-causing factors such as reservoir water level and rainfall on the landslide body are equivalently represented by velocity. During the experiment, precise control of the entry velocity into the water is sufficient to simulate the influence of external factors on the landslide. The structural deformation energy method is used to calculate the landslide initiation velocity, the modified Pan Jiazheng slice method is used to calculate the exit velocity, and the energy method is used to calculate the entry velocity into the water. In the experiment, the entry velocity of the model landslide body into the water is controlled by adjusting the slope, length, and bottom material of the chute.

[0020] Water inflow volume: The unstable volume is determined based on geological analysis. After conversion by similarity ratio, different volume conditions are achieved by adjusting the length of the sliding body. Furthermore, the water inflow volume is varied by fixing the initial width and thickness of the sliding body and adjusting its length.

[0021] Initial water depth: Multiple water depth conditions are set according to the characteristic water level of the reservoir;

[0022] Furthermore, regarding the experiment and data processing: a multi-factor orthogonal experiment was adopted, and data was collected using a wave height meter, video system, etc., and then processed by Fast Fourier Transform (FFT) filtering.

[0023] The formula for calculating the landslide initiation speed is as follows: .

[0024] The formula for calculating the landslide slip velocity is as follows: , The maximum velocity of all blocks in front of the block corresponding to the center of mass of the sliding body. The equivalent slip velocity of the entire landslide .

[0025] The formula for calculating the landslide entry velocity into water is as follows: .

[0026] Furthermore, for the establishment of the amplitude prediction model, the following model is established based on the fitting of experimental data:

[0027] The initial amplitude prediction model is as follows:

[0028]

[0029] Where, k d = 0.0964, a = 0.6366, b = 0.2022.

[0030] The preferred form of the amplitude propagation attenuation prediction model is a power function:

[0031]

[0032] Where a = 0.5829, b = -0.1150, c = 0.2305, k2 = -0.2026.

[0033] The aforementioned wave surge dam run-up prediction model is as follows:

[0034]

[0035] Where a = 0.817, b = -0.036, c = 0.051, d = 0.9035, e = 0.012.

[0036] This invention targets granular landslides. Based on the principle of velocity equivalence, it represents external influencing factors as the landslide's entry velocity into water. Precise velocity control is achieved by controlling the entry velocity in experiments and adjusting factors such as the length of the slide rail, the slope of the chute, and the coefficient of friction. Setting the landslide velocity is a crucial prerequisite for surge analysis, and the granular model more accurately reflects the disintegration and diffusion behavior of the landslide during its movement.

[0037] This invention enables precise control of the entry velocity of loose landslides into water, establishes a systematic and complete wave amplitude prediction model system for the entire process of swell, significantly improves the accuracy of experiments and the reliability of predictions, and provides an effective means for swell risk assessment of reservoir landslides. Attached Figure Description

[0038] Figure 1 The diagram shows three states of a landslide before it enters the water, where (a) is the initial state, (b) is the state of sliding out, and (c) is the state of entering the water.

[0039] Figure 2 This is a schematic diagram of the forces acting on the strip.

[0040] Figure 3 This is a schematic diagram of the energy method for calculating sliding speed.

[0041] Figure 4 The slope entry velocity under different kinetic friction coefficients;

[0042] Figure 5 This is a comparison between experimental values ​​and formula-predicted values ​​of relative wave amplitude along the surge path. Detailed Implementation

[0043] This invention relates to a method for predicting the wave amplitude of a granular landslide based on velocity equivalence through wave experiments. The technical solution of this invention is described in detail below through specific embodiments, but the scope of protection of this invention is not limited to these embodiments.

[0044] 1. Physical Model Construction

[0045] Based on the actual topographic map and the Froude similarity criterion, a three-dimensional physical model of landslide surge was constructed. The model system mainly includes the landslide area and the river channel area. A tiltable sliding box is installed in the landslide area, with a rotating baffle controlled by a motor at its front edge. Different materials (such as sheet metal, geotextile, or PVC board) can be laid on the bottom surface of the sliding box to set different bottom friction coefficients and meet the requirements of various test conditions.

[0046] 2. Landslide configuration and activation

[0047] Before the experiment, loose landslide material was filled into the sliding chamber. The sliding chamber was precisely adjusted to a predetermined tilt angle using a hydraulic pump. The rotating baffle at the front of the chamber, controlled by a motor, could rapidly tilt downwards at a set time, causing the landslide to initiate from its original position under gravity. Initially, the landslide slid as a whole; as the distance traveled increased, it gradually disintegrated and broke apart under the combined effects of gravity, bottom friction, and internal friction. The landslide material can be small-diameter pebbles, crushed stones, gravel, or 3D-printed polyethylene granules, etc., and must meet the requirements for similarity in rheological properties and geometric shape.

[0048] 3. Testing System

[0049] The testing and measurement equipment includes wave height meter, video acquisition system, slip speed measuring instrument and climbing height measuring instrument.

[0050] 4. Experimental Variable Design

[0051] The initial wave amplitude of the swell in a loose-body landslide is mainly affected by three key factors: the velocity of the landslide entering the water, the volume of water entering the water, and the initial water depth. Based on these factors, this experiment designed a multi-factor, multi-level test scheme.

[0052] (1) Landslide velocity design

[0053] like Figure 1 As shown, for high-altitude loose-body landslides, their motion is divided into three states: initial state, sliding out state, and water entry state, corresponding to two stages: sliding out and sliding phases. The velocity of each state is calculated separately.

[0054] 1) Startup speed

[0055] Creep landslides typically undergo creep and tensile fracturing stages before overall instability, a process in which energy gradually accumulates. As creep deformation increases, the length of the locked section gradually shortens. When the deformation reaches a critical point, the locked section fails brittlely, and the accumulated potential energy is instantly converted into kinetic energy, causing the landslide to slide down rapidly. Assuming the deformation within the landslide structure is linearly elastic, according to the generalized Hooke's law, its structural deformation energy can be expressed as:

[0056] (1)

[0057] In the formula, The structural deformation energy of the landslide; The volume of landslide deformation. , This represents the volume of the soil and rock mass that slid during the active sliding segment. This represents the volume of the soil and rock mass in the passive sliding section. The stress between deformed soil and rock particles inside the landslide; This represents the strain between deformed soil and rock particles within the landslide. It represents the elastic modulus of the landslide soil and rock mass.

[0058] Assume the kinetic energy of the soil and rock mass within the active sliding section of the landslide is Its quality is The mass of the soil and rock mass within the passive sliding section is Due to the release of deformation energy from the landslide structure, the initial velocity of the soil and rock mass in the active sliding section is... Simultaneously, during this process, the active sliding section of rock and soil will push the passive sliding section of rock and soil to move together. At this time, the sliding speeds of the two parts of rock and soil are the same, and this speed is the overall initiation speed of the landslide. .

[0059] Taking the rock and soil mass of the active sliding section as the calculation object when the locked section undergoes brittle failure, according to the kinetic energy law, we can obtain:

[0060] (2)

[0061] Taking the landslide as a whole as the calculation object, according to the momentum theorem, we can obtain:

[0062] (3)

[0063] By combining equations (2) and (3), the initiation velocity of the entire landslide due to the release of deformation energy of the soil and rock mass in the active sliding section can be obtained:

[0064] (4)

[0065] In the formula, the kinetic energy of the rock and soil mass within the active sliding section of the landslide is... At the moment of landslide failure, the deformation energy within the landslide structure... Equal. Typically, the volume of the soil and rock mass sliding in the active sliding segment is equal. Approximately the volume of the soil and rock mass in the passive sliding section twice that is .

[0066] 2) Slide speed

[0067] The basic principle of Pan Jiazheng's slice method is to perform force analysis in the horizontal and vertical directions, neglecting the shear force between the landslide blocks during the calculation. This invention improves upon Pan Jiazheng's slice method by adjusting the direction of force analysis and the establishment of equilibrium equations from the original horizontal and vertical directions to along and perpendicular to the landslide sliding direction. The modified slice method better reflects the actual motion state of landslides, improving the scientific rigor and applicability of the calculations. It assumes that the landslide blocks undergo rigid circular arc sliding, neglecting the vertical shear force between the blocks. Figure 2 As shown, a force analysis is performed on the block, and the corresponding dynamic equations are established:

[0068] Perpendicular to the sliding surface direction:

[0069] (5)

[0070] Along the direction of the slip surface:

[0071] (6)

[0072] Consider the Mohr-Coulomb strength criterion:

[0073] (7)

[0074] For the entire sliding deformation body Combining equations (5) to (7), we obtain the acceleration of the strip:

[0075] (8)

[0076] In equations (5) to (8), W i Let α be the weight of the i-th block; i U is the inclination angle of the bottom sliding surface of the i-th block;bi N is the water pressure acting at the bottom of the i-th block; i F is the normal force acting on the bottom of the i-th block; i U is the force acting on the side wall of the i-th block; i T is the water pressure acting on the side wall of the i-th block; i M is the frictional force acting on the bottom of the i-th block; i Let a be the mass of the i-th block; i Let b be the acceleration of the i-th block along the sliding surface direction; i c is the length of the bottom of the i-th block; i Let be the cohesive force of the bottom sliding strip of the i-th block; Let be the internal friction angle of the bottom sliding strip of the i-th block.

[0077] Assuming the blocks undergo uniformly accelerated motion on the bottom sliding surface, calculate the sliding velocity of each block after sliding a distance ΔLi using kinematic formulas:

[0078] (9)

[0079] In the formula, For the sliding speed of the strip, This represents the sliding distance.

[0080] The maximum velocity of all blocks in front of the block corresponding to the center of mass of the landslide is taken as the equivalent slip velocity of the entire landslide. .

[0081] 3) Calculation of landslide entry velocity into water

[0082] The energy method is based on the principle of energy conservation. It assumes the sliding body enters a semi-infinite boundary water area, treats the entire sliding body as a rigid body, neglects its deformation, and uses the center of gravity as a point mass for calculation, while ignoring air resistance. The sliding force consists of the gravitational component along the sliding direction minus the frictional force, such as... Figure 3 As shown.

[0083] From the energy conservation equation, we can obtain:

[0084] (10)

[0085] (11)

[0086] In equations (10) and (11), m s v is the mass of the sliding body; m H is the velocity of the sliding body's center of mass as it moves to the shear exit point; c denoted as , where is the vertical height from the shear outlet to the water surface; f is the frictional force experienced by the sliding body during the sliding phase; μ0 is the dynamic friction coefficient during the sliding phase; and k0 is the terrain correction coefficient (k0 > 1). It is the acceleration due to gravity; The angle of inclination of the smooth surface;

[0087] Combining equations (10) and (11), the landslide entry velocity into the water can be obtained as follows:

[0088] (12)

[0089] In the formula, The velocity at which the sliding body enters the water.

[0090] Since the coefficient of dynamic friction of the sliding surface has a significant impact on the sliding speed, a sensitivity analysis of the coefficient of dynamic friction is performed. For example... Figure 4 As shown, the entry velocity of the landslide body into the water is negatively correlated with the coefficient of kinetic friction; as the coefficient of kinetic friction increases, the entry velocity of the landslide body gradually decreases. When the coefficient of kinetic friction varies within the range of 0.1 to 0.5, the entry velocity of the landslide body in the A-A' profile varies between 51.16 and 91.49 m / s, and the entry velocity of the landslide body in the B-B' profile varies between 45.03 and 84.92 m / s.

[0091] The calculation results above show that the landslide entry velocity varies under different coefficients of dynamic friction. Therefore, a series of velocity values ​​were set within the possible velocity range for experimental simulation to investigate the impact of velocity on the surge.

[0092] (2) Inflow volume design

[0093] Based on on-site investigation and stability analysis, the potential instability volume of the landslide was determined and converted into a model volume using similarity criteria. To account for actual uncertainties, a series of inflow volumes of 0.10 m³, 0.30 m³, 0.50 m³, 0.90 m³, 1.50 m³, 2.00 m³, 3.00 m³, and 4.23 m³ were set. Volume variations were achieved by fixing the initial width and thickness of the landslide mass and adjusting its length.

[0094] (3) Initial water level design

[0095] According to the reservoir operation plan, six characteristic water levels, namely 2128 m, 2180 m, 2210 m, 2230 m, 2248 m and 2267 m, were selected for the test, covering a water depth range of 0.45–1.38 m.

[0096] 5. Test Plan and Operating Procedures

[0097] Sliding speed (10 levels), volume (8 levels), and water depth (6 levels) were selected as independent variables, and a multi-factor orthogonal experimental design was adopted. The specific scheme is shown in Table 2.2. The sliding speed control error should not exceed ±0.3 m / s. The single test procedure is as follows:

[0098] (1) Clear the river channel and reset the sliding box, fill it with sliding material, and adjust the box tilt angle through the hydraulic system;

[0099] (2) Adjust the river water level to the target depth, stabilize it, and then calibrate and zero all sensors;

[0100] (3) Start the camera system and begin recording;

[0101] (4) The motor starts, the baffle opens, the slide body slides down, and the test begins;

[0102] (5) The data acquisition system will automatically stop recording after 300 seconds of continuous recording. The recording can be stopped manually afterward.

[0103] (6) Clean up the site, prepare for the next set of experiments, and process the data obtained.

[0104] 6. Data Preprocessing

[0105] High-frequency noise (caused by sensor and environmental vibrations) was removed by Fast Fourier Transform (FFT) filtering, while low-frequency surge signals were preserved. The filtered data has the same characteristics as the original waveform, and subsequent analyses are based on the filtered data.

[0106] 7. Amplitude prediction formulas for each stage of the entire process

[0107] (1) Initial amplitude prediction

[0108] Establish a dimensionless empirical formula:

[0109] (13)

[0110] In the formula, This represents the maximum amplitude of the initial swell. This is the initial water depth; The relative volume of the sliding body; For Froude number, ; is the correction factor for the meandering river topography; a and b are the parameters to be determined.

[0111] Based on the experimental data, the values ​​of each parameter were obtained through multivariate nonlinear fitting analysis: k d = 0.0964, a = 0.6366, b = 0.2022, correlation coefficient R 2 The value is 0.88. The power exponent of the relative velocity of the sliding body is 0.6366, while the power exponent of the relative volume is 0.2022, indicating that the relative velocity of the sliding body has a significantly greater impact on the initial wave amplitude than the volume.

[0112] (2) Prediction of amplitude attenuation along the path

[0113] By introducing a generating function and a decay function, a formula for amplitude decay along the path is established:

[0114] (14)

[0115] In the formula, This represents the maximum wave amplitude propagating to a location x distance from the landslide source; For the wave generating function term, Let be the volume of the sliding body, and a, b, and c be undetermined coefficients. Let be the wave propagation attenuation function term, k2 be the attenuation coefficient, and x be the distance to the landslide source.

[0116] Substituting the experimental data, and using the principle of nonlinear regression, the undetermined parameters in equation (14) can be calculated as a = 0.5829, b = -0.1150, c = 0.2305, k2 = -0.2026, and the corresponding correlation coefficient R. 2 The value is 0.928. The experimentally measured data are compared with the predicted value calculated using equation (14), as shown below. Figure 5 As shown in the figure, the dashed line represents the ±30% error threshold, meaning the error between the measured and predicted values ​​is generally within 30%.

[0117] (3) Prediction of the rise of the swell dam

[0118] Establish a multi-factor elevation gain prediction formula:

[0119] (15)

[0120] In the formula, This represents the maximum elevation gain on the dam. This represents the maximum wave amplitude in front of the dam. denoted as the wave incident angle, which is the angle between the impact direction and the central axis of the dam; a, b, c, d, and e are the parameter coefficients to be determined.

[0121] Substituting the experimental data and applying the principle of nonlinear regression, the values ​​of the coefficients are: a = 0.817, b = -0.036, c = 0.051, d = 0.9035, e = 0.012, and the correlation coefficient R0 is... 2 It is 0.99.

Claims

1. A method for predicting the wave amplitude of a granular landslide based on velocity equivalence and slab surge, characterized in that, Includes the following steps: (1) Construct a three-dimensional physical model based on the Froude similarity criterion; (2) Based on the principle of velocity equivalence, the range of landslide entry velocity is determined by theoretical calculation, and the entry velocity of the model landslide body into the water is controlled by adjusting the slope, length and bottom friction material of the chute; (3) Set the inflow volume and initial water depth based on geological analysis and similarity ratio conversion; (4) Perform orthogonal experiments and collect data; (5) Based on experimental data, establish a full-process wave amplitude prediction system including an initial wave amplitude prediction model, a wave amplitude propagation attenuation prediction model, and a wave surge dam front run-up prediction model.

2. The method for predicting the wave amplitude of a granular landslide based on velocity equivalence and a swell test, as described in claim 1, is characterized in that... Based on the principle of velocity equivalence, the disturbance and weakening effects of external disaster-causing factors such as reservoir water level and rainfall on the landslide body are equivalently represented by velocity. During the test, the influence of external factors on the landslide can be realized by precisely controlling the water entry velocity. The landslide initiation velocity is calculated using the structural deformation energy method, the slide out velocity is calculated using the improved Pan Jiazheng slice method, and the water entry velocity is calculated using the energy method.

3. The method for predicting the wave amplitude of a granular landslide based on velocity equivalence and a swell test, as described in claim 1, is characterized in that... The water inflow volume is varied by fixing the initial width and thickness of the sliding body and adjusting its length.

4. The method for predicting the wave amplitude of a granular landslide based on velocity equivalence and a swell test, as described in claim 1, is characterized in that... The collected data needs to be filtered and denoised using Fast Fourier Transform (FFT).

5. The method for predicting the wave amplitude of a granular landslide based on velocity equivalence and a swell test, as described in claim 2, is characterized in that... The formula for calculating the landslide initiation speed is as follows: .

6. The method for predicting the wave amplitude of a granular landslide based on velocity equivalence and in sluice-scale landslides according to claim 2, characterized in that, The formula for calculating the landslide slip velocity is as follows: , The maximum velocity of all blocks in front of the block corresponding to the center of mass of the sliding body. The equivalent slip velocity of the entire landslide .

7. The method for predicting the wave amplitude of a granular landslide based on velocity equivalence and a swell test, as described in claim 2, is characterized in that... The formula for calculating the landslide entry velocity into water is as follows: .

8. The method for predicting the wave amplitude of a landslide based on velocity equivalence and a granular material landslide surge, as described in claim 1, is characterized in that... The initial amplitude prediction model is as follows: Where, k d = 0.0964, a = 0.6366, b = 0.2022.

9. The method for predicting the wave amplitude of a granular landslide based on velocity equivalence and a swell test throughout the entire process, as described in claim 1, is characterized in that... The preferred form of the amplitude propagation attenuation prediction model is a power function: Where a = 0.5829, b = -0.1150, c = 0.2305, k2 = -0.2026.

10. The method for predicting the wave amplitude of a granular landslide based on velocity equivalence and a swell test, as described in claim 1, is characterized in that... The aforementioned wave surge dam run-up prediction model is as follows: Where a = 0.817, b = -0.036, c = 0.051, d = 0.9035, e = 0.012.

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