Fluid boundary prediction method for waste slag field instability outburst

Abstract

The invention discloses a fluid boundary prediction method for waste slag field instability outburst, and relates to the field of disaster monitoring, and the method comprises the steps: S1, carrying out the initial waste slag fluid motion prediction, and marking the initial boundary line of all waste slag fluids; s2, waste slag parameters are collected, geological parameters are obtained, and the downstream area is divided into downstream land parcels; s3, screening out risk plots with potential collapse, and calculating a critical sliding depth by using a limit equilibrium method; and S4, updating all the critical sliding depths to the digital elevation model so as to resolve the waste slag fluid motion prediction, and marking a corrected boundary line. According to the method, the digital elevation model is updated by calculating the volume of the potential collapse area, so that the prediction result is continuously adjusted along with the burst process, and the problem that the prediction accuracy of the waste slag fluid coverage range is relatively low due to fixed terrain hypothesis is avoided; the method has the advantages of dynamically correcting the waste slag outburst fluid track boundary and improving the outburst disaster prevention capacity.

Description

Technical Field

[0001] The present invention relates to the field of disaster monitoring, and particularly relates to a method for predicting the fluid boundary of the instability and collapse of a waste dump. Background Art

[0002] A waste dump is a special artificial landform formed by loose accumulations such as waste soil, gravel, etc. generated during activities such as mine exploitation, tunnel construction, and water conservancy projects. Due to its loose structure, complex material composition, and lack of natural geological stability, it is extremely prone to instability and collapse under the action of external factors such as heavy rainfall, earthquake, or human disturbance, forming a high-speed moving debris flow or debris flow, which poses a serious threat to downstream residential areas, infrastructure, and the ecological environment. The accumulations in the waste dump are mainly artificial loose accumulations, characterized by a large particle size span, high porosity, and no natural consolidation process. Compared with the progressive erosion of natural soil and water loss, the collapse of the waste dump is more of a sudden instability situation. Most waste dumps are located in artificially modified terrains, such as valley filling areas and slope foot accumulations, and are affected by both artificial roads or building structures and natural terrain after collapse.

[0003] Existing static stability assessment methods for waste dumps mostly use computational fluid dynamics models to simulate the flow process of debris flows. When the waste dump undergoes instability and collapse, in the case of a soil-type waste dump, progressive damage to the land is likely to occur when the debris flows downstream after collapse. During progressive collapse, the fluid erodes the base or accumulates coarse particles, which will dynamically change the terrain. Currently, during the process of disaster warning and assessment of the instability and collapse of waste dumps, existing conventional fluid mechanics waste prediction methods usually calculate a fixed terrain boundary, but lack consideration of the change in the fluid coverage boundary caused by terrain changes during fluid flow. Using a fixed terrain boundary causes existing models to have problems in simulating the fluid offset caused by the formation of a new terrain by fluid scouring, which may lead to a lower prediction of the fluid coverage range of the debris flow fluid in the waste dump than the actual flow velocity peak, and further lead to insufficient estimation of the impact kinetic energy of the collapsing fluid, and ultimately easily result in a lower prediction of the accident destructiveness of the instability and collapse of the waste dump than the actual occurrence. Summary of the Invention

[0004] The present invention provides a method for predicting the fluid boundary of the instability and collapse of a waste dump, which solves the problem that the existing fluid prediction process has poor prediction effect due to the lack of correction of the debris fluid trajectory boundary caused by terrain changes during the collapse of the waste dump.

[0005] The present invention is achieved by the following technical solutions: A method for predicting the fluid boundary of the instability and collapse of a waste dump, the method comprising: Step S1: Construct a digital elevation model for the target waste dump and the downstream area, perform an initial prediction of the movement of the waste fluid for the target waste dump, and mark the initial boundary line of all the predicted waste fluid on the digital elevation model; Step S2: Collect the waste residue parameters of all waste residue accumulations in the target waste residue site, obtain the geological parameters of the downstream area of the target waste residue site from the digital elevation model, and divide the downstream area into a certain number of downstream plots each containing several grid cells; Step S3: Screen out the downstream plots with potential collapses based on the waste residue parameters and geological parameters and label them as risk plots, and use the limit equilibrium method to calculate the critical sliding depth indicating potential soil collapse in all risk plots; Step S4: Update all the critical sliding depths to the digital elevation model and label it as the corrected elevation model, use the corrected elevation model to re-solve the prediction of waste residue fluid movement, and label the corrected boundary line indicating the updated waste residue fluid.

[0006] Currently, in the process of disaster warning and assessment of the instability and breach of waste residue sites, existing hydrodynamic models usually fix the terrain boundary. The boundary prediction by conventional hydrodynamic models can predict the fluid boundary based on the fixed terrain, but usually lacks consideration of the changes in the fluid coverage boundary caused by terrain changes during fluid flow. Using a fixed terrain boundary causes problems in existing models where it is difficult to simulate the potential impact energy generated after the formation of a new terrain by fluid erosion, which may lead to the prediction of the downstream flow velocity peak and the fluid coverage range of the debris flow fluid in the waste residue site being lower than the actual flow velocity peak, and further lead to insufficient estimation of the impact kinetic energy of the breach fluid, and ultimately easily result in the prediction of the accident destructiveness of the instability and breach of the waste residue site being lower than the actual occurrence level. Based on this, the present invention provides a method for predicting the fluid boundary of the instability and breach of a waste residue site, which solves the problem that the existing fluid prediction process has poor prediction effect due to the lack of correction of the waste residue fluid trajectory boundary caused by terrain changes during the breach of the waste residue site.

[0007] Further, the process of screening out risk plots includes: based on the waste residue parameters and geological parameters, calculating the fluid shear stress and critical shear stress of each downstream plot, where the fluid shear stress represents the shear force exerted by the breach of the waste residue fluid on the surface of the downstream area of the target waste residue site, and the critical shear stress represents the minimum shear stress threshold for the surface of the downstream area of the target waste residue site to resist erosion; when the fluid shear stress of the downstream plot is greater than the critical shear stress, label the downstream plot as a risk plot.

[0008] Further, the waste residue parameters collected in each downstream plot of the target waste residue site include, all taking average values: The unit weight value of the waste residue fluid, which represents the gravity value of the solid particles and pore water contained in the waste residue fluid per unit volume; The density of the waste residue fluid, which represents the mass of the entire waste residue fluid per unit volume; The depth of the waste residue fluid, which represents the vertical height of the waste residue fluid perpendicular to the surface in the flow direction; The geological parameters collected in each downstream plot of the target waste dump include: Average slope angle, which represents the slope angle of the average slope of the surface downstream of the waste dump; Bulk density value of soil particles, which represents the gravity value of soil solid particles in a unit volume; Median soil particle size, which represents the median value of particle sizes in the particle size distribution of soil; Internal friction angle of soil, which represents the amplitude of the internal friction characteristics between soil particles;

[0009] Furthermore, assume that the waste fluid is a uniform laminar flow; assume that the bulk density value of the waste fluid is denoted as γ1, the density of the waste fluid is denoted as ρ1, and the depth of the waste fluid is denoted as h; the bulk density value of soil particles is denoted as γ2, the median soil particle size is denoted as d, and the internal friction angle of soil is denoted as θ; assume that the average slope angle is denoted as φ; assume that the fluid shear stress and the critical shear stress are denoted as τ1 and τ2 respectively, Then the calculation formula of the fluid shear stress is expressed as: , The calculation formula of the critical shear stress is expressed as: , where sinφ represents the average slope value of the downstream area, and K represents the adjustment coefficient of soil particles in the downstream area of the target waste dump.

[0010] Furthermore, assume that the critical sliding depth representing the critical state in the limit equilibrium method in each downstream plot is denoted as hc, and the calculation content of the critical sliding depth includes: Assume that the calculation formula of the critical sliding depth hc is expressed as: .

[0011] Furthermore, calculate the potential collapse volume of each risk plot, and update the collapse volume as auxiliary data to the digital elevation model; assume that the size of the collapse volume is the product of the critical sliding depth and the sliding area; assume that the acquisition process of the sliding area includes: Mark the size data of the grid cells in the digital elevation model, calculate the slope area of each grid cell on the surface downstream of the waste dump, and sum all the grid cells for each downstream plot and set the result as the sliding area.

[0012] Furthermore, the update process of the corrected elevation model includes: Convert the calculated critical sliding depth into topographic elevation changes, update it to the initial elevation data points in the digital elevation model, and correct it to the elevation modification data points in the modified elevation model; perform Gaussian filtering on the modified elevation model to eliminate the jagged edges caused by discrete distribution; add a Boolean field to the attribute table of the digital elevation model to mark the elevation modification data points; the process of converting the critical sliding depth into topographic elevation changes is as follows: use the vertical projection method to convert the critical sliding depth.

[0013] Further, when using the Boolean field to mark the elevation modification data points in each downstream plot, mark the modified elevation model according to the quadtree structure, and the process includes: Take all the elevation modification data points of the entire modified elevation model as the root node of the quadtree structure, with the coverage range being the entire geographical range of the modified elevation model, and recursively divide all the root nodes of the modified elevation model; set the marking screening conditions, mark the child nodes that meet the marking screening conditions after division with the Boolean field, and continue to recursively divide the remaining child nodes until convergence, and perform hydrodynamic calculations on the grid cells with marked elevation modification data points in each downstream plot to complete the process of re-solving the prediction of the movement of waste slag fluid.

[0014] Further, estimate the energy contributions of the root nodes and child nodes after subdivision before each division, set an energy threshold, and stop dividing if the energy contributions of each root node and child node are lower than the energy threshold.

[0015] Compared with the prior art, the present invention updates the digital elevation model by calculating the critical sliding depth of the potential collapse area, and calculates the critical sliding depth of the downstream area of the waste dump to correct the digital elevation model, so that the prediction result is continuously adjusted with the breach process, avoiding the problem of low prediction accuracy of the coverage range of waste slag fluid caused by the fixed terrain assumption, realizing the real-time interaction between fluid movement and topographic erosion, having the advantages of dynamically correcting the trajectory boundary of waste slag breach fluid and the beneficial effect of improving the disaster prevention ability of the breach. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, form a part of this application, and do not constitute a limitation on the embodiments of the present invention. In the drawings: Figure 1 It is a flowchart of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0017] To make the objectives, technical solutions, and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with the embodiments and the drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and do not limit the present invention. Embodiment

[0018] As Figure 1 shown, this embodiment is a method for predicting the fluid boundary of the instability and collapse of a waste dump, and the method includes: Step S1: Construct a digital elevation model for the target waste dump and the downstream area, implement an initial prediction of the waste fluid movement for the target waste dump, and mark the initial boundary line of all predicted waste fluids in the digital elevation model; Step S2: Collect the waste parameters of all waste deposits in the target waste dump, obtain the geological parameters of the downstream area of the target waste dump from the digital elevation model, and divide the downstream area into a certain number of downstream plots containing a number of grid cells; Step S3: Screen out the downstream plots with potential collapses based on the waste parameters and geological parameters and mark them as risk plots, and use the limit equilibrium method to calculate the critical sliding depth representing potential soil collapse in all risk plots; Step S4: Update all the critical sliding depths to the digital elevation model and mark it as the corrected elevation model, and use the corrected elevation model to re-solve the waste fluid movement prediction and mark the corrected boundary line representing the updated waste fluid.

[0019] The target waste dump refers to a specific area where waste soil, gravel, etc. accumulate during activities such as mine exploitation, tunnel construction, and water conservancy projects. The accumulated materials mainly include soil, gravel, clay, sand, etc., and are usually loose materials without natural consolidation. The waste dump accumulations generally have characteristics such as a large particle size span, high porosity, and low density, and are prone to instability and collapse under the influence of external forces. Due to the lack of natural consolidation process, the waste dump accumulations are prone to secondary disasters such as landslides and debris flows under conditions such as heavy rainfall, earthquakes, and artificial disturbances; the erosion of the waste fluid leads to the weakening of the bottom, gradually triggering local or overall collapse. The digital elevation model is a three-dimensional terrain model constructed based on ground height data, which can accurately describe the terrain undulations, including slopes, valleys, ridges, etc., and is usually stored and calculated in the form of regular grids or triangular meshes, providing a digital way to describe the terrain undulations and is widely used in fields such as terrain analysis, watershed modeling, landslide prediction, fluid simulation, and disaster warning. In the prior art, the digital elevation model is mainly collected and constructed through satellite remote sensing data, lidar, or unmanned aerial vehicle photogrammetry, etc. The prediction of the waste fluid movement is completed using a conventional fluid calculation model. The initial prediction of the waste fluid movement means using the conventional model calculation method to complete a conventional prediction of the fluid movement direction of the waste dump accumulations in the target waste dump "without considering the influence of terrain changes on the waste fluid". Preferably, in specific implementations, the conventional fluid dynamics models or prediction methods selected may include the FLO-2D two-dimensional model based on the shallow water equation, the Debris flow debris flow dynamic simulation software based on debris flow analysis, and the RAMMS software for rapid assessment of debris fluid dynamic simulation, etc. The initial boundary line refers to the area that the fluid is initially expected to cover after it starts to move at the initial stage of the collapse of the waste dump, and is used to represent the initial range of the potential influence area of the fluid. The waste parameters of the waste dump accumulations refer to various physical and engineering property parameters related to the waste dump accumulations, which are used to describe the basic characteristics of the waste dump accumulations. The process of collecting waste parameters can be carried out by surveying the terrain and accumulation characteristics on site, collecting waste samples and conducting physical and chemical analyses. The geological parameters of the downstream area refer to using the terrain information in the digital elevation model to extract geological parameters such as soil, rock, and groundwater related to the downstream area of the waste dump. Among them, the geographical information system GIS software can automatically extract these terrain information from the digital elevation model. The downstream area refers to the range where the fluid may spread and flow after the collapse of the waste dump; according to the terrain size and prediction accuracy requirements of the downstream area, it is divided into multiple grid units of equal or unequal size. In each grid unit of the grid, parameters such as the flow velocity, erosion effect, and impact energy of the fluid are measured and interact with adjacent units to simulate the dynamic behavior of the fluid; according to the fluid simulation results of each grid, the boundary of the grid is dynamically adjusted to adapt to the terrain changes during the collapse process and improve the prediction accuracy of the overall fluid trajectory.

[0020] The risk plot refers to the downstream plot with potential soil collapse or other geological instability risks during the breach of the waste dump. Once the waste fluid breaches, its impact force will affect the downstream area, especially the areas prone to erosion; if infrastructure such as buildings, roads, and bridges is located on the risk plot, it may be impacted by the waste fluid, resulting in damage to the infrastructure. The critical sliding depth represents the thickness perpendicular to the ground surface of the damaged ground surface assuming a shallow sliding failure occurs. Identifying the risk plot and its potential critical sliding depth in advance can identify the threatened areas in advance and provide a basis for engineering design, early warning systems, and the deployment of emergency measures. The limit equilibrium method is a commonly used method for stability analysis, mainly used to evaluate the landslide, collapse, or caving risks of soil or rock masses. Update the calculated critical sliding depth into the digital elevation model as part of the correction content of the modified elevation model to reflect the potential terrain changes that may occur. By calculating the potential critical sliding depth and dynamically modifying the terrain, it is possible to more accurately predict the spread range, flow velocity, and impact energy of the waste fluid, avoiding underestimating the impact of the breach on the downstream area. Re-solving the waste fluid movement prediction using the modified elevation model means that after considering the potential terrain change factors, re-performing the fluid movement simulation and prediction based on the updated elevation data. With the real-time simulation of the dynamic terrain changes, it is possible to more accurately predict the flow path, flow velocity, and impact range of the fluid during the breach process, thereby improving the disaster early warning and prevention capabilities. The modified boundary line represents the boundary range of the fluid movement updated and adjusted based on the initial boundary line of the initial prediction result, combined with the impact of the potential collapse area on the waste fluid.

[0021] Further, the process of screening out the risk plots includes: calculating the fluid shear stress and the critical shear stress of each downstream plot based on the waste dump parameters and geological parameters, where the fluid shear stress represents the shear force exerted by the breach of the waste fluid on the ground surface in the downstream area of the target waste dump, and the critical shear stress represents the minimum shear stress threshold for the ground surface in the downstream area of the target waste dump to resist erosion; when the fluid shear stress of the downstream plot is greater than the critical shear stress, mark the downstream plot as a risk plot.

[0022] The fluid shear stress refers to the shear force exerted by a fluid on the solid surface it contacts during the flow process; during the instability and collapse process of the waste dump, the waste fluid will scour the surface of the downstream area. The critical shear stress refers to the minimum shear stress value required to cause the sliding, collapse, or erosion of the soil or rock surface. During the process of screening risk plots, the role of the fluid shear stress is to measure the scouring and erosion ability of the waste fluid on the downstream surface; the fluid shear stress refers to the tangential force exerted by the waste fluid on the surface, representing the scouring intensity of the waste fluid on the surface during the flow process. The larger the value, the stronger the erosion effect exerted by the fluid on the surface, and the more likely it is to cause soil erosion and collapse. The critical shear stress represents the minimum shear stress that the surface soil of this plot can resist external shear forces without being eroded or scoured, and is used to measure the anti-erosion ability of the downstream plot. When the fluid shear stress of the downstream plot is greater than the critical shear stress, it indicates that the surface of this plot cannot resist fluid scouring and may undergo erosion or collapse, and is marked as a risk plot; when the fluid shear stress of the downstream plot is less than the critical shear stress, it indicates that the surface of this plot is still stable enough and will not be marked as a risk plot. Example

[0023] Further, the waste parameters collected in each downstream plot of the target waste dump include the following values taken as averages: The unit weight value of the waste fluid, which represents the gravity value of the solid particles and pore water contained in the waste fluid per unit volume; The density of the waste fluid, which represents the mass of the entire waste fluid per unit volume; The depth of the waste fluid, which represents the vertical height perpendicular to the surface of the waste fluid in the flow direction; The geological parameters collected in each downstream plot of the target waste dump include: The average slope angle, which represents the slope angle of the average slope of the downstream surface of the waste dump; The unit weight value of soil particles, which represents the gravity value of the soil solid particles themselves per unit volume; The median particle size of the soil, which represents the median value of the particle size distribution of the soil particles; The internal friction angle of the soil, which represents the amplitude of the internal friction characteristics between the particles within the soil.

[0024] As a feasible implementation method, assume that the waste fluid is a uniform laminar flow; assume that the unit weight value of the waste fluid is represented as γ1, the density of the waste fluid is represented as ρ1, and the depth of the waste fluid is represented as h; the unit weight value of soil particles is represented as γ2, the median particle size of the soil is represented as d, and the internal friction angle of the soil is represented as θ; assume that the average slope angle is represented as φ; assume that the fluid shear stress and the critical shear stress are represented as τ1 and τ2 respectively, Then the calculation formula for the fluid shear stress is expressed as: , The calculation formula for the critical shear stress is expressed as: , where sinφ represents the average slope value of the downstream area, and K represents the adjustment coefficient of soil particles in the downstream area of the target waste dump site.

[0025] The unit weight value of the waste dump fluid refers to the weight of the waste dump fluid per unit volume (i.e., the mixture of waste dump and water) under the action of gravity. It is a physical quantity used to describe the density and fluid characteristics of the waste dump fluid, that is, the relationship between the mass of the waste dump fluid per unit volume and gravity. The density of the waste dump fluid refers to the mass of the waste dump fluid per unit volume. The depth of the waste dump fluid refers to the vertical height of the waste dump fluid relative to the ground surface in the flow direction in the waste dump site. The slope angle refers to the angle between the ground surface and the horizontal plane, which measures the degree of terrain inclination; the larger the slope angle, the steeper the ground surface. The average slope angle is the average value of the overall inclination of the area. The unit weight value of soil particles refers to the mass of soil particles per unit volume, which reflects the weight of the solid particles in the soil itself. The median particle size of the soil represents the particle size at the median position in the particle size distribution of the soil. The internal friction angle of the soil refers to the angle between the shear resistance and the normal force generated between soil particles when they come into contact and slide, which can usually be measured by a shear test.

[0026] The fluid shear stress is the mutual force that appears on both sides of any cross-section inside an object when it deforms due to external factors, which is called internal force; the intensity of the internal force, that is, the internal force per unit area, is called "stress". Its calculation relationship is expressed as shear stress equals the ratio of force to unit area. It should be noted that both pressure and shear stress describe the average value of force on a surface, and their dimensional forms are the same. The difference is that pressure is the average value of "external force" on a surface, and shear stress is the average value of "internal force" caused by external force on a surface; pressure is a normal effect, which causes a certain cross-section to produce pressure deformation in the direction perpendicular to the cross-section; shear stress is a tangential effect, which causes the cross-section to produce dislocation deformation in the direction parallel to the cross-section. In the field of waste dump site failure, in gravity-driven flows such as debris flows or debris flows, the inertial effect dominates, and the influence of viscous force accounts for a relatively small proportion. The traditional shear stress formula based on Newtonian fluid may not have good accuracy. Therefore, in this embodiment, gravity is taken as the main consideration factor for fluid shear stress.

[0027] Regarding the explanation of fluid shear stress, the gravity of the waste dump fluid on the slope can be decomposed into two components in different directions: the normal component perpendicular to the slope surface, which generates static pressure ; The tangential component parallel to the slope direction drives the movement of the waste slag fluid, and the driving force per unit area is... Since the fluid is set as a uniform laminar flow in this embodiment, and the influence of viscous force and turbulence is reduced to mainly consider the shear effect driven by gravity, the shear stress of the waste slag fluid is directly provided by the component of gravity along the slope at this time, and the tangential component is set as the fluid shear stress. The average slope value controls the shear force of the fluid on the slope. The steeper the slope, the greater the shear stress. In the calculation formula, the fluid shear stress τ1 is affected by the depth, density, and slope of the fluid. When the fluid is deeper, denser, and the slope is steeper, the shear force of the fluid on the ground surface is enhanced, and it is easier to cause erosion or collapse in the downstream area. If the fluid shear stress τ1 is too large, it indicates that the fluid scouring ability is strong, and erosion or collapse may occur in the downstream plot.

[0028] As a feasible application, in a specific implementation, preferably, without considering the expansion and contraction of voids and assuming that solid particles are uniformly suspended in the fluid without stratification or aggregation effects, to improve the accuracy of fluid shear stress, the waste slag fluid is split and statistically analyzed into fluid density ρf, solid particle density ρs, and solid volume concentration C v For multi-phase flow density correction; the acquisition process of the waste slag fluid density ρ1 is expressed by the calculation formula as: ... The density ρ1 of the mixed waste slag fluid increases with the increase of the solid concentration, directly increasing the shear stress. When the solid volume concentration C v is equal to 0, there are no solid particles in the fluid, and the equivalent density is equal to the pure fluid density; when the solid volume concentration C v is equal to 1, the fluid is theoretically completely composed of solid particles; when the solid volume concentration C v is between 0 and 1, the density of the mixed waste slag fluid at this time is between the fluid density ρf and the solid particle density ρs. In a specific implementation, the fluid density ρf, solid particle density ρs, and solid volume concentration C v can be obtained by data sampling through a rock density meter, a laser particle size analyzer, and on-site sampling and screening methods.

[0029] In the critical shear stress calculation formula, is set in line with the Mohr-Coulomb yield criterion, which is used to measure that when the ratio of the shear stress to the normal stress on the shear plane reaches the maximum, the material yields or fails. Since in most cases the density of soil solid particles is greater than the density of water or mud mixture, the specific gravity difference mainly includes and two cases. If , it means that the soil particles are heavier than the fluid, are more difficult to be scoured, and have stronger erosion resistance. If , the buoyancy effect of the fluid on the soil particles is enhanced, making the soil more easily scoured and eroded. The larger the median particle size d of the soil, such as gravelly soil, crushed stones, etc., means stronger particle stability and less likely to be carried away by the fluid, so τ2 will be larger; the smaller the median particle size d of the soil, such as components like silt and clay, means it is easier to be scoured by the fluid, so τ2 will be smaller. The larger the internal friction angle θ of the soil, the stronger the friction between particles, the increase in tanθ means it is more difficult to be washed away by the fluid, and the critical shear stress τ2 will be larger; the weaker the friction between particles, the easier it is for the fluid to scour, so the critical shear stress τ2 will be smaller. The adjustment coefficient K is based on experimental fitting and is used to correct the response of different soil types to scouring. It should be noted that the units corresponding to the multiplication of each term on the right side of the critical shear stress calculation formula are expressed as: , is consistent with the unit of Pascal of the critical shear stress on the left side of the formula.

[0030] Furthermore, as a feasible implementation method, let the critical sliding depth representing the critical state in the limit equilibrium method in each downstream plot be denoted as hc, and the calculation content of the critical sliding depth includes: Let the calculation formula of the critical sliding depth hc be expressed as: .

[0031] The critical state of the limit equilibrium method is the balance of the anti-sliding force and the sliding force. That is, in this embodiment, the equilibrium equation reflecting the critical state is to construct the anti-sliding force and the sliding force calculations on both sides of the equation. The critical sliding depth hc represents the vertical thickness of the damaged ground surface assuming a shallow sliding failure occurs. In this embodiment, as a feasible implementation method, the acquisition method of the critical sliding depth hc through calculation relationship is: Let the amount of collapsed land in the critical sliding depth be denoted as W, and the calculation formula of the amount of collapsed land is expressed as: .

[0032] Set: , .

[0033] The meaning of the amount of collapsed land W is the weight of the collapsed land. The units corresponding to the multiplication of each term on the right side of the calculation formula of the amount of collapsed land are expressed as: , that is, the final unit of the amount of collapsed land W is Newton, representing the total weight of the collapsed land. In this embodiment, through the calculation relationship between the soil particle unit weight value γ2 and the amount of collapsed land and the balance relationship between the constructed anti-sliding force and the sliding force, the critical sliding depth hc is calculated. The anti-sliding force is composed of the inherent shear strength of the soil and the frictional force caused by the soil self-weight. The anti-sliding force provided for the shear resistance of the soil itself, which means that when there is no external load, the total shear force that can be resisted only by the strength of the soil itself (determined by particle size, unit weight, and internal friction angle). It represents the anti-sliding force provided by the self-weight of the soil mass through friction, and is used to measure the ability of the land to resist sliding through friction. The normal force on the sliding surface is , and the product of it and the friction coefficient tanθ is the frictional force, which reflects the ability of the soil self-weight to resist sliding through friction. Among them, cosφ represents the component coefficient of decomposing the soil self-weight in the direction perpendicular to the slope surface.

[0034] The physical meaning of the sliding force is the superposition of the downward component force of the soil self-weight along the slope and the fluid shear force. It represents the downward sliding force of the soil self-weight along the slope direction. The component of the gravity in the slope direction is the main driving force for triggering sliding. The larger φ is and the steeper the slope is, the stronger the sliding force is. It represents the total shear force exerted by the waste residue fluid on the downstream ground surface. The fluid generates a shear effect on the ground surface during the movement process, further promoting the sliding of the soil mass. Especially in the initial stage of collapse or during heavy rainfall, the fluid impact force significantly enhances the sliding force. The sliding force is the resultant force of the gravity-driven downward sliding force and the fluid impact force, which determines the magnitude of the driving force for soil mass instability.

[0035] The equilibrium equation in the limit equilibrium method is: anti-sliding force = sliding force, Derive Equation 1: , substitute into the equilibrium equation, Derive Equation 2: , After eliminating A and moving the remaining variables to the other side of the equation, the calculation formula for the critical sliding depth hc can be solved. When performing detailed calculations, substituting the calculation formulas of the fluid shear stress and the critical shear stress into the calculation can obtain: . Embodiment

[0036] Calculate the potential collapse volume of each risk plot, and update the collapse volume as auxiliary data to the digital elevation model; set the size of the collapse volume as the product of the critical sliding depth and the sliding area; assume that the process of obtaining the sliding area includes: Mark the size data of the grid cells in the digital elevation model, calculate the slope area of each grid cell on the downstream ground surface of the waste dump site, and sum all the grid cells for each downstream plot and set the result as the sliding area.

[0037] The update process of the modified elevation model includes: Convert the calculated critical sliding depth into terrain elevation changes, update it to the initial elevation data points in the digital elevation model, and correct it to the elevation modification data points in the modified elevation model; perform Gaussian filtering on the modified elevation model to eliminate the jagged edges caused by discrete distribution; add a Boolean field to the attribute table of the digital elevation model to mark the elevation modification data points; the process of converting the critical sliding depth into terrain elevation changes is as follows: use the vertical projection method to convert the critical sliding depth.

[0038] The process of converting the critical sliding depth into terrain elevation changes refers to converting the potential failure depth of the soil mass obtained from mechanical calculations into an elevation adjustment amount that can be quantitatively operated in the digital terrain model. The critical sliding depth directly affects the height of the ground surface, and the area where the collapse occurs will drop a certain height. As a feasible application method, the conversion process using the vertical projection method specifically includes: setting the elevation amount in the modified elevation model to be represented as Z, then , this equation converts the sliding depth hc in the slope direction into the elevation change ΔZ in the vertical direction to update the elevation data in the digital elevation model; in real terrain, collapses often occur along the slope direction, and its sliding depth hc is the distance along the slope. However, the elevation in the digital elevation model DEM is the elevation perpendicular to the horizontal plane, and the critical sliding depth hc is the failure depth perpendicular to the slope, while the elevation value on the digital elevation model is in the absolute vertical direction, that is, the Z-axis direction in the three-dimensional coordinate axis. Therefore, projecting the sliding body from the slope to the vertical direction can more accurately update the digital elevation model to reflect the new geomorphic structure. The grid cell size is the size of the set grid cells in the digital elevation model, usually a certain ground area. For example, a grid cell may represent the surface data within each rectangular or square area. The actual slope area of the surface slope represented by each grid cell will be calculated based on the slope and terrain data at its location. The steeper the slope, the larger the slope area may be because the actual area of the slope is larger than the planar area. Summing up the slope areas of each grid cell according to its boundary, the sliding area of each downstream plot is finally obtained. The collapse volume of each risk plot is calculated using the critical sliding depth and the sliding area, and the collapse volume is updated to the digital elevation model as auxiliary data. As a specific application example, in addition to updating the elevation change of the digital elevation model, the collapse volume as auxiliary data can also be reflected as follows: the collapse volume can be distributed to all grid cells of each downstream plot according to the fluid direction to generate a thickness distribution field; the unit weight value and the internal friction angle value of the downstream plot are corrected according to the material composition of the collapse volume; the slope curvature of the corrected elevation model is updated, and the downstream plots with too fast curvature changes are screened out. Updating the terrain elevation change brought by the critical sliding depth to the digital elevation model, specifically to the corresponding elevation data points, and smoothing the corrected elevation data through Gaussian filtering to remove the jagged edges caused by irregular terrain changes or discrete data distributions. By converting the critical sliding depth into an elevation change, the digital elevation model can be dynamically corrected, making the prediction and simulation closer to the actual terrain; Gaussian filtering effectively eliminates the discrete discontinuity points in the correction process, improving the smoothness and stability of the model.

[0039] Further, when using boolean fields to mark elevation modification data points within each downstream plot, the corrected elevation model is marked with boolean fields according to the quadtree structure, and the process includes: Take all the elevation modification data points of the entire corrected elevation model as the root nodes of the quadtree structure, with the coverage range being the entire geographical range of the corrected elevation model, and recursively divide all the root nodes of the corrected elevation model; set the marker screening conditions, mark the child nodes that meet the marker screening conditions after division with boolean fields, and continue to recursively divide the remaining child nodes until convergence. For each grid cell with elevation modification data points having boolean field marks in each downstream plot, perform hydrodynamic calculations to complete the process of re-solving the prediction of the movement of waste slag fluid; estimate the energy contributions of the root nodes and child nodes after subdivision before each division, set an energy threshold, and stop dividing if the energy contributions of each root node and child node are lower than the energy threshold.

[0040] In this embodiment, the quadtree structure is used to mark the Boolean field data points in the corrected elevation model. Through quadtree recursive partitioning, a large range of elevation data can be effectively managed and processed, and refined partitioning is performed according to the energy contribution to ensure the prediction accuracy. A quadtree is a spatial partitioning data structure, especially suitable for processing two-dimensional spatial data. The basic idea of a quadtree is to recursively partition a rectangular area into four sub-areas until specific conditions are met. This structure is applicable to scenarios such as geographical data and image processing. A quadtree generally includes: a root node, which represents the entire area or data set; and child nodes, which are the four sub-areas formed by further partitioning the root node. The root node refers to all elevation modification data points in the entire corrected elevation model as the root node of the quadtree, and the coverage range of the root node is the entire geographical area of the corrected elevation model. The recursive partitioning refers to starting from the root node and recursively partitioning the area into four child nodes according to the quadtree structure. Each partitioning will further refine the data processing area. To ensure the validity of the data and the accuracy of the prediction, marking and screening conditions need to be set after each partitioning. The screening conditions are set according to factors such as the attributes of the elevation modification data points and terrain features, determining which child nodes will be marked; the child nodes that meet the screening conditions will have a Boolean field mark added in the corrected elevation model, indicating that there are valid elevation modification data points in this area. The energy contribution estimation means that before each partitioning, the energy contributions of the root node and child nodes will be estimated. The energy contribution represents the degree of influence of each node on the fluid motion prediction. The energy threshold setting means that if the energy contribution of a root node or child node is lower than a predetermined energy threshold, it indicates that the elevation change of this node has a relatively small impact on the fluid motion prediction, and the partitioning can be stopped. In this way, unnecessary subdivisions are avoided, and the calculation efficiency is improved. After identifying the grid cells with Boolean field marks, hydrodynamic calculations of the corrected elevation model are performed on these cells to further solve the corrected motion prediction of the waste fluid. In this embodiment, the quadtree structure is used to decompose complex geographical data into multiple small areas through recursive partitioning, facilitating efficient processing. In the case of large-scale waste dumps or complex terrains, elevation modification data points can be accurately marked and managed. In the fluid motion prediction of complex terrains such as waste dumps, mine exploitation, and accumulations, the quadtree structure can effectively process and simulate different slopes and changing areas. Through accurate marking and simulation, when instability and collapse occur, the impact force and range of the fluid can be predicted in a timely manner, providing a basis for disaster warning and emergency handling, being able to efficiently utilize computing resources, avoiding excessive calculation of unimportant areas, and achieving a balance between real-time performance and accuracy.

[0041] Preferably, as a feasible embodiment, the process of the energy contribution estimation is set as: The energy contribution is expressed as a kinetic energy perturbation value, and the kinetic energy perturbation value is predicted based on the flow velocity gradient perturbation; after constructing the initial digital elevation model (DEM), the shallow water equations are used to solve for the initial flow velocity field representing the slag discharge fluid velocity distribution unaffected by terrain perturbations; the collapse volume is updated into the digital elevation model (DEM) to obtain a corrected elevation model, and fluid prediction is performed again to obtain a corrected flow velocity field representing the correction of the initial flow velocity field. Then, the velocity perturbation amount is calculated for each grid cell, and the velocity perturbation amount represents the average value of the local velocity change of the fluid caused by terrain changes; then, the velocity perturbation amount is used as the velocity value and substituted into the kinetic energy calculation formula to calculate the kinetic energy value of each node and represent the kinetic energy value as the kinetic energy perturbation value.

[0042] Among them, the calculation formula for the velocity perturbation amount is set as: , where represents the area of the i-th plot, represents the flow velocity field under the original terrain, represents the flow velocity field under the corrected terrain, represents the flow velocity change amount at the i-th node after terrain changes; represents the double integral over the area of this plot, integrating the perturbation amplitude at each point on this plot to obtain the total perturbation intensity of each space within this plot; represents taking the mean value, dividing the total perturbation intensity of this plot by the area to obtain the average perturbation flow velocity. When the terrain changes, some areas may accelerate or decelerate originally, and the meaning of the calculation formula for the velocity perturbation amount is: how much the overall average value of the velocity changes in the entire plot.

[0043] The specific embodiments described above further elaborate on the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only the specific embodiments of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A fluid boundary prediction method for the instability and collapse of waste dumps, characterized in that The method includes: Step S1: Construct a digital elevation model for the target waste dump and the downstream area, conduct an initial prediction of the waste fluid movement for the target waste dump, and mark the initial boundary lines of all predicted waste fluids on the digital elevation model; Step S2: Collect the waste parameters of all waste deposits in the target waste dump, obtain the geological parameters of the downstream area of the target waste dump from the digital elevation model, and divide the downstream area into a certain number of downstream plots containing several grid cells; Step S3: Screen out the downstream plots with potential collapses based on the waste parameters and geological parameters and label them as risk plots, and use the limit equilibrium method to calculate the critical sliding depth representing potential soil collapse in all risk plots; Step S4: Update all the critical sliding depths to the digital elevation model and mark it as the corrected elevation model, and use the corrected elevation model to re-solve the waste fluid movement prediction and mark the corrected boundary lines representing the updated waste fluid.

2. The fluid boundary prediction method for the instability and collapse of a waste dump according to claim 1, wherein The process of screening out risk plots includes: calculating the fluid shear stress and critical shear stress of each downstream plot based on the waste parameters and geological parameters, where the fluid shear stress represents the shear force exerted by the breach of the waste fluid on the surface of the downstream area of the target waste dump, and the critical shear stress represents the minimum shear stress threshold for the surface of the downstream area of the target waste dump to resist erosion; when the fluid shear stress of the downstream plot is greater than the critical shear stress, label the downstream plot as a risk plot.

3. A method for predicting the fluid boundary of the instability and collapse of a waste dump, according to claim 2, characterized in that The waste parameters collected in each downstream plot of the target waste dump include the following values taken as averages: The unit weight value of the waste fluid, which represents the gravity value of the solid particles and pore water contained in the waste fluid per unit volume; The density of the waste fluid, which represents the overall mass of the waste fluid per unit volume; The depth of the waste fluid, which represents the vertical height perpendicular to the ground surface in the flow direction of the waste fluid; The geological parameters collected in each downstream plot of the target waste dump include: The average slope angle, which represents the slope angle of the average slope of the surface downstream of the waste dump; The unit weight value of soil particles, which represents the gravity value of the soil solid particles themselves per unit volume; The median particle size of the soil, which represents the median value of the particle size distribution of the soil particles; The internal friction angle of the soil, which represents the amplitude of the internal friction characteristics between the particles in the soil.

4. A method for predicting the fluid boundary of the instability and collapse of a waste dump according to claim 3, characterized in that, let The waste fluid is a uniform laminar flow; let the unit weight value of the waste fluid be denoted as γ1, the density of the waste fluid be denoted as ρ1, the depth of the waste fluid be denoted as h; the unit weight value of soil particles be denoted as γ2, the median particle size of the soil be denoted as d, and the internal friction angle of the soil be denoted as θ; let the average slope angle be denoted as φ; let the fluid shear stress and critical shear stress be denoted as τ1 and τ2 respectively, The calculation formula of the fluid shear stress is expressed as: , The calculation formula of the critical shear stress is expressed as: , where sinφ represents the average slope value of the downstream area, and K represents the adjustment coefficient of the soil particles in the downstream area of the target waste dump.

5. A method for predicting the fluid boundary of the instability and collapse of a waste dump, according to claim 4, wherein Let the critical sliding depth representing the critical state in the limit equilibrium method in each downstream plot be denoted as hc, and the calculation content of the critical sliding depth includes: Let the calculation formula of the critical sliding depth hc be expressed as: 。 6. A method for predicting the fluid boundary of the instability and collapse of a waste dump, according to claim 1, wherein Calculate the potential collapse volume of each risk plot and update the collapse volume as auxiliary data to the digital elevation model; Set the size of the collapse volume to the product of the critical sliding depth and the sliding area; Let the process of obtaining the sliding area include: Mark the size data of grid cells in the digital elevation model, calculate the slope area of the surface of each grid cell downstream of the waste dump site, and sum all grid cells for each downstream plot and set the result as the sliding area.

7. A method for predicting the fluid boundary of the instability and collapse of a waste dump, according to claim 1, wherein The update process of the corrected elevation model includes: Convert the calculated critical sliding depth into a topographic elevation change, update it to the initial elevation data points in the digital elevation model, and correct it to the elevation modification data points in the corrected elevation model; perform Gaussian filtering on the corrected elevation model to eliminate the jagged edges caused by discrete distribution; add a Boolean field to the attribute table of the digital elevation model to mark the elevation modification data points.

8. A method for predicting the fluid boundary of the instability and collapse of a waste dump, according to claim 7, wherein The process of converting the critical sliding depth into a topographic elevation change is: use the vertical projection method to convert the critical sliding depth.

9. A method for predicting the fluid boundary of the instability and collapse of a waste dump, according to claim 8, wherein When using the Boolean field to mark the elevation modification data points within each downstream plot, mark the Boolean field of the corrected elevation model according to the quadtree structure. The process includes: Take all the elevation modification data points of the entire corrected elevation model as the root node of the quadtree structure, with the coverage range being the entire geographical range of the corrected elevation model, and recursively divide all the root nodes of the corrected elevation model; set the marking screening conditions, mark the child nodes that meet the marking screening conditions after division with the Boolean field, and continue to recursively divide the remaining child nodes until convergence. Perform hydrodynamic calculations on the grid cells with marked elevation modification data points with the Boolean field in each downstream plot to complete the process of re-solving the waste fluid motion prediction.

10. A method for predicting the fluid boundary of the instability and collapse of a waste dump, according to claim 9, wherein Estimate the energy contribution after subdivision of the root node and child nodes before each division, set an energy threshold, and stop the division if the energy contribution of each root node and child node is lower than the energy threshold.

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