A fluid boundary prediction method for the instability and collapse of waste dumps

Abstract

The present invention discloses a fluid boundary prediction method for the instability and collapse of a waste dump, which relates to the field of disaster monitoring. The method comprises: step S1: implementing an initial waste dump fluid movement prediction and marking the initial boundary line of all waste dump fluids; step S2: collecting waste dump parameters, obtaining geological parameters, and dividing the downstream area into downstream plots; step S3: screening out risk plots with potential collapse, and using the limit equilibrium method to calculate the critical sliding depth; step S4: updating all critical sliding depths to a digital elevation model to re-solve the waste dump fluid movement prediction and mark the revised boundary line. The present invention updates the digital elevation model by calculating the volume of the potential collapse area, so that the prediction result is continuously adjusted as the collapse process occurs, avoiding the problem of low prediction accuracy of the waste dump fluid coverage range due to the fixed terrain assumption, and has the advantages of dynamically correcting the boundary of the waste dump collapse fluid trajectory and improving the disaster prevention capability of the collapse.

Description

Technical Field

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

[0002] A waste dump is a special artificial landform formed by loose accumulations of waste soil, gravel, and other materials generated during activities such as mining, tunnel construction, and water conservancy projects. Due to its loose structure, complex material composition, and lack of natural geological stability, it is very easy to become unstable and collapse under the influence of external factors such as heavy rainfall, earthquakes, or human disturbances, forming high-speed mudslides or debris flows, posing a serious threat to downstream residential areas, infrastructure, and the ecological environment. The deposits 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 gradual erosion of natural soil and water loss, the collapse of the waste dump is more of a sudden instability. Most waste dumps are located in artificially modified terrain, such as gully fill areas and slope foot accumulations. After the collapse, they are affected by both artificial roads or building structures and the natural terrain.

[0003] Existing methods for assessing the static stability of waste dumps often use computational fluid dynamics models to simulate the flow process of debris flows. When a waste dump becomes unstable and collapses, soil-based waste dumps are prone to progressive damage to the land as they flow downstream after a collapse. During the progressive collapse, the fluid erodes the base or accumulates coarse particles, dynamically changing the terrain. Currently, in the process of disaster early warning assessment of waste dump instability and collapse, existing conventional fluid dynamics waste dump prediction methods usually calculate fixed terrain boundaries, but fail to consider the changes in fluid coverage boundaries caused by terrain changes during fluid flow. The use of fixed terrain boundaries makes it difficult for existing models to simulate the problem of fluid displacement caused by fluid erosion forming new terrain. This may cause the predicted fluid coverage size of the waste dump debris flow fluid to be lower than the actual peak flow velocity, which in turn leads to insufficient estimation of the impact kinetic energy of the collapsing fluid, and ultimately makes it easy for the predicted destructiveness of the waste dump instability and collapse accident to be lower than the actual extent of the occurrence. Summary of the Invention

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

[0005] The present invention is achieved through the following technical solutions:

[0006] A fluid boundary prediction method for waste dump instability and collapse, the method comprising:

[0007] Step S1: constructing a digital elevation model at the target spoil site and the downstream area, performing an initial spoil fluid movement prediction for the target spoil site, and marking the initial boundary lines of all predicted spoil fluids on the digital elevation model;

[0008] Step S2: collecting spoil parameters of all spoil deposits in the target spoil site, obtaining geological parameters of the downstream area of the target spoil site from the digital elevation model, and dividing the downstream area into a certain number of downstream plots containing a certain number of grid cells;

[0009] Step S3: Based on the spoil parameters and geological parameters, downstream plots with potential collapse are screened out and marked as risk plots. The critical sliding depth indicating potential soil collapse in all risk plots is calculated using the limit equilibrium method.

[0010] Step S4: After updating all critical sliding depths to the digital elevation model, the model is marked as a revised elevation model, and the spoil fluid movement prediction is re-solved using the revised elevation model, and a revised boundary line representing the spoil fluid update is marked.

[0011] At present, in the process of disaster early warning and assessment of the instability and collapse of waste dumps, the existing fluid mechanics models usually fix the terrain boundaries. The boundary predictions made by conventional fluid mechanics models can predict the fluid boundaries based on the fixed terrain, but usually lack consideration of the changes in the fluid coverage boundaries caused by the changes in the terrain when the fluid flows. The use of fixed terrain boundaries causes the existing models to have difficulty in simulating the potential impact energy generated after the fluid scours to form new terrain. This may cause the downstream flow velocity peak value and the size of the fluid coverage of the waste dump debris flow fluid to be lower than the actual flow velocity peak value, thereby resulting in insufficient estimation of the impact kinetic energy of the collapsing fluid, and ultimately making it easy to make the prediction of the destructiveness of the waste dump instability and collapse lower than the actual degree of occurrence. Based on this, the present invention provides a fluid boundary prediction method for the instability and collapse of waste dumps, which solves the problem that the existing fluid prediction process lacks correction of the waste dump fluid trajectory boundary due to terrain changes when the waste dump collapses, resulting in poor prediction results.

[0012] Furthermore, the process of screening out risky plots includes: calculating the fluid shear stress and critical shear stress of each downstream plot based on the spoil parameters and geological parameters, the fluid shear stress represents the shear force exerted by the spoil fluid burst on the surface of the downstream area of the target spoil site, and the critical shear stress represents the minimum shear stress threshold for the surface of the downstream area of the target spoil site to resist erosion; when the fluid shear stress of the downstream plot is greater than the critical shear stress, the downstream plot is marked as a risky plot.

[0013] Furthermore, the waste parameters collected in each downstream plot of the target waste dump include the average values of:

[0014] The bulk density of the waste fluid indicates the gravity of the waste fluid per unit volume, including solid particles and pore water;

[0015] The density of the spoil fluid indicates the mass of the spoil fluid per unit volume;

[0016] The spoil fluid depth represents the vertical height of the spoil fluid perpendicular to the ground surface in the direction of flow;

[0017] The geological parameters collected in each downstream plot of the target spoil site include:

[0018] Average slope angle, which represents the slope angle of the average surface slope downstream of the spoil dump;

[0019] Soil particle bulk density value indicates the gravity value of soil solid particles per unit volume;

[0020] Soil median particle size represents the middle value of the soil particle size distribution;

[0021] The internal friction angle of soil indicates the amplitude of internal friction characteristics between particles inside the soil.

[0022] Furthermore, the waste fluid is assumed to be a uniform laminar flow; the bulk density of the waste fluid is represented by γ1, the density of the waste fluid is represented by ρ1, and the depth of the waste fluid is represented by h; the bulk density of the soil particles is represented by γ2, the median particle size of the soil is represented by d, and the internal friction angle of the soil is represented by θ; the average slope angle is represented by φ; the fluid shear stress and critical shear stress are represented by τ1 and τ2 respectively,

[0023] The calculation formula of fluid shear stress is expressed as: ,

[0024] The calculation formula of critical shear stress is expressed as: ,

[0025] 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.

[0026] Furthermore, the critical sliding depth of the critical state in the limit equilibrium method in each downstream block is represented as hc. The calculation content of the critical sliding depth includes:

[0027] Assume that the calculation formula of critical sliding depth hc is expressed as: .

[0028] Furthermore, the potential collapse volume of each risk plot is calculated and the collapse volume is used as auxiliary data to update the digital elevation model; the size of the collapse volume is set as the product of the critical sliding depth and the sliding area; the process of obtaining the sliding area includes:

[0029] The size data of the grid cells are marked in the digital elevation model, and the slope area of each grid cell on the surface downstream of the waste dump is calculated. For each downstream plot, the sum of all grid cells is set as the sliding area.

[0030] Furthermore, the updating process of the modified elevation model includes:

[0031] The calculated critical sliding depth is converted into terrain elevation change, updated to the initial elevation data point in the digital elevation model, and corrected to the elevation modification data point in the modified elevation model; Gaussian filtering is performed on the modified elevation model to eliminate jagged edges caused by discrete allocation; a Boolean field is added to the attribute table of the digital elevation model to mark the elevation modification data point; the process of converting the critical sliding depth into terrain elevation change is: using the vertical projection method to convert the critical sliding depth.

[0032] Furthermore, when using Boolean fields to mark elevation modification data points in each downstream plot, the modified elevation model is marked with Boolean fields according to a quadtree structure. The process includes:

[0033] All elevation modification data points of the entire modified elevation model are used as the root nodes of the quadtree structure, covering the entire geographical range of the modified elevation model, and all root nodes of the modified elevation model are recursively split; mark filtering conditions are set, and the child nodes that meet the mark filtering conditions after segmentation are marked with Boolean fields. The remaining child nodes are recursively split until convergence, and fluid dynamics calculations are performed on the grid cells with elevation modification data points marked with Boolean fields in each downstream plot to complete the process of resolving the spoil fluid movement prediction.

[0034] Furthermore, before each segmentation, the energy contribution of the root node and child nodes after segmentation is estimated, and an energy threshold is set. If the energy contribution of each root node and child node is lower than the energy threshold, the segmentation is stopped.

[0035] Compared with the existing technology, 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 spoil dump to correct the digital elevation model, so that the prediction results are continuously adjusted as the collapse process progresses, avoiding the problem of low prediction accuracy of the spoil fluid coverage range due to the fixed terrain assumption, realizing real-time interaction between fluid movement and terrain erosion, and having the advantages of dynamically correcting the boundaries of the spoil collapse fluid trajectory and the beneficial effect of improving the collapse disaster prevention capability. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings:

[0037] Figure 1 It is a flowchart of the present invention. DETAILED DESCRIPTION

[0038] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with examples and drawings. The exemplary embodiments of the present invention and their descriptions are only used to explain the present invention and are not intended to limit the present invention. Example

[0039] like Figure 1 As shown, this embodiment is a fluid boundary prediction method for the instability and collapse of a waste dump, the method comprising:

[0040] Step S1: constructing a digital elevation model at the target spoil site and the downstream area, performing an initial spoil fluid movement prediction for the target spoil site, and marking the initial boundary lines of all predicted spoil fluids on the digital elevation model;

[0041] Step S2: collecting spoil parameters of all spoil deposits in the target spoil site, obtaining geological parameters of the downstream area of the target spoil site from the digital elevation model, and dividing the downstream area into a certain number of downstream plots containing a certain number of grid cells;

[0042] Step S3: Based on the spoil parameters and geological parameters, downstream plots with potential collapse are screened out and marked as risk plots. The critical sliding depth indicating potential soil collapse in all risk plots is calculated using the limit equilibrium method.

[0043] Step S4: After updating all critical sliding depths to the digital elevation model, the model is marked as a revised elevation model, and the spoil fluid movement prediction is re-solved using the revised elevation model, and a revised boundary line representing the spoil fluid update is marked.

[0044] The target waste dump refers to a specific area of waste soil and gravel accumulation formed during mining, tunnel construction, water conservancy projects and other activities. Its accumulation mainly includes soil, gravel, clay, sand, etc., which are usually loose materials that have not been naturally consolidated. The waste accumulation generally has the characteristics of large particle size span, high porosity, low density, etc., and is easily unstable and collapsed under the influence of external forces. Due to the lack of natural consolidation process, the waste accumulation is prone to secondary disasters such as landslides and mudslides under conditions such as heavy rainfall, earthquakes, and artificial disturbances; the erosion of waste fluid causes the bottom to weaken, gradually causing local or overall collapse. The digital elevation model is a three-dimensional terrain model constructed based on ground height data. It can accurately describe the terrain undulations, including slopes, valleys, ridges, etc. It is usually stored and calculated in the form of a regular grid or triangulated network, providing a digital way to describe the terrain undulations. It is widely used in terrain analysis, watershed modeling, landslide prediction, fluid simulation, disaster warning and other fields. In the prior art, digital elevation models are mainly collected and constructed through satellite remote sensing data, lidar or drone photogrammetry. The spoil fluid movement prediction is completed using a conventional fluid calculation model. The initial spoil fluid movement prediction means using a conventional model calculation method to complete a conventional prediction of the fluid movement of the spoil deposit in the target spoil field "without considering the impact of terrain changes on the spoil fluid". Preferably, the conventional fluid dynamics model or prediction method selected in the specific implementation 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 evaluation of debris fluid dynamic simulation. The initial boundary line refers to the area that the fluid is initially expected to cover after it starts to move in the early stage of the spoil field collapse, which is used to indicate the initial range of the potential impact area of the fluid. The spoil parameters of the spoil deposit refer to the acquisition of various physical and engineering property parameters related to the spoil deposit, which are used to describe the basic characteristics of the spoil deposit. The spoil parameter collection process can be carried out by surveying the on-site terrain and deposit characteristics, collecting spoil samples, and performing physical and chemical analysis. The geological parameters of the downstream area refer to the use of terrain information in the digital elevation model to extract geological parameters such as soil, rock, groundwater, etc. related to the downstream area of the waste dump, wherein the terrain information can be automatically extracted from the digital elevation model using the geographic information system GIS software. The downstream area refers to the range to which the fluid may expand and flow after the waste dump collapses; it is divided into multiple grid units of equal or unequal sizes according to the terrain size and prediction accuracy requirements of the downstream area. In each gridded unit, the flow velocity, erosion, impact energy and other parameters 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, thereby improving the prediction accuracy of the overall fluid trajectory.

[0045] The risk plots refer to downstream plots that are at risk of potential soil collapse or other geological instability during the collapse of the waste dump. Once the waste fluid collapses, its impact will have an impact on the downstream area, especially the area prone to erosion. If buildings, roads, bridges and other infrastructure are located on the risk plots, they may be impacted by the waste fluid, resulting in damage to the infrastructure. The critical sliding depth represents the thickness of the damaged surface perpendicular to the surface when shallow sliding damage is assumed to occur. Identifying the risk plots and their potential critical sliding depths can identify 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 assess the risk of landslide, collapse or collapse of soil or rock masses. The calculated critical sliding depth is updated to the digital elevation model as part of the correction content of the revised elevation model to reflect potential terrain changes that may occur. By calculating the potential critical sliding depth and dynamically correcting the terrain, the expansion range, flow rate and impact energy of the waste fluid can be more accurately predicted, avoiding underestimation of the impact of the collapse on the downstream area. Resolving the spoil fluid movement prediction using a revised elevation model involves re-simulating and predicting fluid movement based on updated elevation data, taking into account potential terrain changes. This real-time simulation of dynamic terrain changes enables more accurate predictions of fluid flow paths, velocities, and impact ranges during a collapse, thereby improving disaster warning and prevention capabilities. The revised boundary represents an updated and adjusted fluid movement boundary based on the initial boundary of the initial prediction, taking into account the impact of potential collapse areas on spoil fluids.

[0046] Furthermore, the process of screening out risky plots includes: calculating the fluid shear stress and critical shear stress of each downstream plot based on the spoil parameters and geological parameters, the fluid shear stress represents the shear force exerted by the spoil fluid burst on the surface of the downstream area of the target spoil site, and the critical shear stress represents the minimum shear stress threshold for the surface of the downstream area of the target spoil site to resist erosion; when the fluid shear stress of the downstream plot is greater than the critical shear stress, the downstream plot is marked as a risky plot.

[0047] The fluid shear stress refers to the shear force exerted by the fluid on the solid surface it contacts during the flow process; during the instability and collapse of the waste dump, the waste fluid will cause scouring effect on the surface of the downstream area. The critical shear stress refers to the minimum shear stress value required to cause the soil or rock surface to slide, collapse or erode. In the process of screening risk plots, the role of fluid shear stress is to measure the scouring and erosion ability of the waste fluid on the downstream surface; fluid shear stress refers to the tangential force exerted by the waste fluid on the surface, which represents 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 at which the surface soil of the plot can resist external shear without being eroded or washed away, and is used to measure the erosion resistance of the downstream plot. When the fluid shear stress of the downstream plot is greater than the critical shear stress, it means that the surface of the plot cannot resist fluid erosion, and erosion or collapse may occur, and it is marked as a risk plot; when the fluid shear stress of the downstream plot is less than the critical shear stress, it means that the surface of the plot is still stable enough and will not be marked as a risk plot. Example

[0048] Furthermore, the waste parameters collected in each downstream plot of the target waste dump include the average values of:

[0049] The bulk density of the waste fluid indicates the gravity of the waste fluid per unit volume, including solid particles and pore water;

[0050] The density of the spoil fluid indicates the mass of the spoil fluid per unit volume;

[0051] The spoil fluid depth represents the vertical height of the spoil fluid perpendicular to the ground surface in the direction of flow;

[0052] The geological parameters collected in each downstream plot of the target spoil site include:

[0053] Average slope angle, which represents the slope angle of the average surface slope downstream of the spoil dump;

[0054] Soil particle bulk density value indicates the gravity value of soil solid particles per unit volume;

[0055] Soil median particle size represents the middle value of the soil particle size distribution;

[0056] The internal friction angle of soil indicates the amplitude of internal friction characteristics between particles inside the soil.

[0057] As a feasible implementation method, the waste fluid is assumed to be a uniform laminar flow; the bulk density of the waste fluid is represented by γ1, the density of the waste fluid is represented by ρ1, and the depth of the waste fluid is represented by h; the bulk density of the soil particles is represented by γ2, the median particle size of the soil is represented by d, and the internal friction angle of the soil is represented by θ; the average slope angle is represented by φ; the fluid shear stress and the critical shear stress are represented by τ1 and τ2 respectively,

[0058] The calculation formula of fluid shear stress is expressed as: ,

[0059] The calculation formula of critical shear stress is expressed as: ,

[0060] 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.

[0061] The bulk density of the waste fluid refers to the weight of a unit volume of waste fluid (i.e., a mixture of waste and water) under the action of gravity. It is a physical quantity used to describe the density and fluid properties of the waste fluid, that is, the relationship between the mass of a unit volume of waste fluid and gravity. The density of the waste fluid refers to the mass of a unit volume of the waste fluid. The depth of the waste fluid refers to the vertical height of the waste fluid relative to the ground surface in the direction of flow in the waste field. The slope angle refers to the angle between the ground surface and the horizontal plane, which measures the degree of inclination of the terrain; 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 bulk density of the soil particles refers to the mass of soil particles per unit volume, reflecting the weight of the solid particles in the soil. The median particle size of the soil refers to the particle size at the median position in the particle size distribution of the soil particles. 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, and can usually be measured through a shear test.

[0062] The fluid shear stress is the interaction force that appears on both sides of any cross section of an object when it is deformed due to external factors, which is called internal force; the concentration of 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 pressure and shear stress both describe the average value of force on a surface, and their dimensional forms are consistent. 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, causing a certain cross section to produce pressure deformation in a direction perpendicular to the cross section; shear stress is a tangential effect, causing the cross section to produce dislocation deformation in a direction parallel to the cross section. With regard to the field of waste dump collapse, in gravity-driven flows such as mudslides or debris flows, inertia plays a dominant role, and the influence of viscous force accounts for a relatively small proportion. The traditional shear stress formula based on Newtonian fluid may not be accurate, so in this embodiment, gravity is used as the main consideration for fluid shear stress.

[0063] Regarding the explanation of fluid shear stress, the gravity of the spoil fluid on the slope can be decomposed into two components: the normal component perpendicular to the slope, which produces static pressure. ; The tangential component parallel to the slope direction drives the movement of the waste fluid, and its driving force per unit area is. Since the fluid is set to uniform laminar flow in this embodiment, and the influence of viscosity and turbulence is reduced, the shear effect driven by gravity is mainly considered. Therefore, the shear stress of the waste fluid is set to be directly provided by the component of gravity along the slope, and the tangential component is set to 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, the density is greater, and the slope is steeper, the shear force of the fluid on the surface is enhanced, which is more likely to cause erosion or collapse in the downstream area. If the fluid shear stress τ1 is too large, it indicates that the fluid has a strong scouring ability, and the downstream land may be eroded or collapsed.

[0064] As a feasible application, in the specific implementation, preferably, without considering the expansion and contraction of the voids and assuming that the solid particles are uniformly suspended in the fluid without stratification or aggregation effect, in order to improve the accuracy of the fluid shear stress, the waste fluid is decomposed into the fluid density ρf, the solid particle density ρs and the solid volume concentration C v To perform multiphase flow density correction; the acquisition process of the waste fluid density ρ1 is expressed by the calculation formula: The density ρ1 of the mixed waste fluid increases with the increase of solid concentration, which directly increases the shear stress. v When it is equal to 0, there are no solid particles in the fluid and the equivalent density is equal to the density of the pure fluid; when the solid volume concentration C v When the solid volume concentration C is equal to 1, the fluid is theoretically composed entirely of solid particles; when the solid volume concentration C is equal to 1, the fluid is theoretically composed entirely of solid particles.v Between 0 and 1, the density of the mixed waste fluid is between the fluid density ρf and the solid particle density ρs. In specific implementation, the fluid density ρf, the solid particle density ρs and the solid volume concentration C v Data sampling can be obtained through rock density meters, laser particle size analyzers and on-site sampling and screening methods.

[0065] In the critical shear stress calculation formula, The setting is in accordance with the Mohr-Coulomb yield criterion, which is used to measure the yield or failure of the material when the ratio of shear stress to normal stress on the shear surface reaches the maximum. Since the density of soil solid particles is greater than that of water or mud mixture in most cases, the specific gravity difference Mainly includes and There are two situations. If , indicating that soil particles are heavier than fluids, are more difficult to be washed away, and have stronger erosion resistance. , the buoyancy effect of the fluid on the soil particles is enhanced, making the soil more susceptible to erosion. The larger the median particle size d of the soil, such as gravel soil, crushed stone, etc., means that the particles are more stable and not easily carried away by the fluid, so τ2 will be larger; the smaller the median particle size d of the soil, such as silt, clay and other components, means that it is easy to be washed away by the fluid, so τ2 will be smaller. The larger the internal friction angle θ of the soil, the stronger the friction between the particles, and the larger tanθ, which means that it is more difficult to be washed away by the fluid, and the larger the critical shear stress τ2 will be; the weaker the friction between the particles, the easier it is for the fluid to wash away, so the smaller the critical shear stress τ2 will be. The adjustment coefficient K is based on experimental fitting and is used to correct the response of different soil types to erosion. It should be noted that the units corresponding to the multiplication of the terms on the right side of the formula for the critical shear stress calculation formula are expressed as: , which is consistent with the critical shear stress unit of Pascal on the left side of the formula.

[0066] Furthermore, as a feasible implementation method, let the critical sliding depth of the critical state in the limit equilibrium method in each downstream block be expressed as hc, and the calculation content of the critical sliding depth includes:

[0067] Assume that the calculation formula of critical sliding depth hc is expressed as: .

[0068] The critical state of the limit equilibrium method is the balance between the anti-slip force and the sliding force. That is, in this embodiment, the equilibrium equation reflecting the critical state is the equation that constructs the anti-slip force and sliding force calculations on the left and right sides respectively. The critical sliding depth hc represents the vertical thickness of the damaged surface when shallow sliding failure occurs. In this embodiment, as a feasible implementation method, the critical sliding depth hc is obtained by converting the calculation relationship as follows:

[0069] Assume that the amount of collapsed land in the critical sliding depth is expressed as W, and the calculation formula of the collapsed land amount is expressed as: .

[0070] set up: , .

[0071] The collapsed land volume W means the weight of the collapsed land. The units after multiplying the items on the right side of the collapsed land volume calculation formula are expressed as: , i.e., the final unit of the collapsed land mass W is Newton, representing the total weight of the collapsed land. In this embodiment, the critical sliding depth hc is calculated by calculating the relationship between the soil particle bulk density value γ2 and the collapsed land mass, and establishing a balance between the anti-sliding force and the sliding force. The anti-sliding force is composed of the inherent shear strength of the soil and the friction caused by the soil's own weight. It means the anti-sliding force provided by the soil's own shear resistance, which means the total amount of shear force that can be resisted by the soil's own strength (determined by particle size, bulk density, and internal friction angle) when there is no external load. It represents the anti-sliding force provided by the soil's own weight 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 The product of this and the friction coefficient tanθ is the friction force, which reflects the ability of the soil's own weight to resist sliding through friction. Where cosφ represents the coefficient that decomposes the soil's own weight into components perpendicular to the slope.

[0072] The physical meaning of the sliding force is the superposition of the sliding component of the soil's own weight along the slope and the fluid shear force. It represents the downward force of the soil's own weight along the slope. The component of gravity in the slope direction is the main driving force causing sliding. The larger φ is, the steeper the slope is, and the stronger the downward force is. This represents the total shear force exerted by the spoil fluid on the downstream surface. The fluid shears the surface during its movement, further driving soil sliding. This is particularly true in the early stages of a breach or during heavy rainfall, where the fluid impact force significantly enhances the sliding force. The sliding force is the combined force of the gravity-driven downward force and the fluid impact force, and it determines the magnitude of the driving force for soil instability.

[0073] The equilibrium equation in the limit equilibrium method is: anti-sliding force = sliding force,

[0074] Formula 1 is obtained: ,Will Substituting into the balanced equation,

[0075] Formula 2 is obtained: ,

[0076] Eliminating A and moving the remaining variables to the other side of the equation yields the formula for the critical slip depth hc. Substituting the formulas for fluid shear stress and critical shear stress into the equations for detailed calculations yields: . Example

[0077] Calculate the potential collapse volume of each risk plot and update the collapse volume as auxiliary data to the digital elevation model; set the collapse volume to be the product of the critical sliding depth and the sliding area; suppose the process of obtaining the sliding area includes:

[0078] The size data of the grid cells are marked in the digital elevation model, and the slope area of each grid cell on the surface downstream of the waste dump is calculated. For each downstream plot, the sum of all grid cells is set as the sliding area.

[0079] The updating process of the modified elevation model includes:

[0080] The calculated critical sliding depth is converted into terrain elevation change, updated to the initial elevation data point in the digital elevation model, and corrected to the elevation modification data point in the modified elevation model; Gaussian filtering is performed on the modified elevation model to eliminate jagged edges caused by discrete allocation; a Boolean field is added to the attribute table of the digital elevation model to mark the elevation modification data point; the process of converting the critical sliding depth into terrain elevation change is: using the vertical projection method to convert the critical sliding depth.

[0081] The process of converting the critical sliding depth into terrain elevation change refers to converting the potential failure depth of the soil obtained by mechanical calculation into an elevation adjustment that can be quantified 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 in the modified elevation model to Z, then This equation converts the sliding depth hc along the slope into a vertical elevation change ΔZ, allowing for updating the elevation data in the digital elevation model. In real terrain, collapses often occur along the slope surface, and the sliding depth hc is the distance along the slope surface. However, the elevation in the digital elevation model (DEM) is measured perpendicular to the horizontal plane, and the critical sliding depth hc is the failure depth perpendicular to the slope surface. Elevation in the digital elevation model (DEM) is measured in the absolute vertical direction, i.e., the Z-axis in the three-dimensional coordinate system. Therefore, projecting the sliding body from the slope surface to the vertical direction allows for a more accurate update of the digital elevation model to reflect the new topographic structure. The grid cell size is the size of the grid cell in the digital elevation model, typically a certain ground area. For example, a grid cell may represent the surface data within each rectangular or square area. The actual slope area represented by each grid cell is calculated based on the slope and terrain data at its location. Steeper slopes may increase the slope area because the actual area of a slope is larger than that of a flat surface. The slope area of each grid unit is summed up according to its boundary, and 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 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 units of each downstream plot according to the flow direction to generate a thickness distribution field; the bulk density value and 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 to screen out downstream plots with too fast curvature changes. The terrain elevation changes brought about by the critical sliding depth are updated to the digital elevation model, specifically to the corresponding elevation data points, and the corrected elevation data is smoothed by Gaussian filtering to remove jagged edges caused by irregular terrain changes or discrete data distribution. By converting the critical sliding depth into elevation changes, the digital elevation model can be dynamically corrected, making the prediction and simulation closer to the actual terrain; Gaussian filtering effectively eliminates discrete discontinuities in the correction process, improving the smoothness and stability of the model.

[0082] Furthermore, when using Boolean fields to mark elevation modification data points in each downstream plot, the modified elevation model is marked with Boolean fields according to a quadtree structure. The process includes:

[0083] All elevation modification data points of the entire modified elevation model are used as the root nodes of the quadtree structure, covering the entire geographical range of the modified elevation model, and all root nodes of the modified elevation model are recursively split; mark filtering conditions are set, and the child nodes that meet the mark filtering conditions after splitting are marked with Boolean fields. The remaining child nodes are recursively split until convergence, and fluid dynamics calculations are performed on the grid cells with elevation modification data points marked with Boolean fields in each downstream plot to complete the process of resolving the spoil fluid motion prediction; before each splitting, the energy contribution of the root node and child node after subdivision is estimated, and an energy threshold is set. If the energy contribution of each root node and child node is lower than the energy threshold, the splitting is stopped.

[0084] The quadtree structure described in this embodiment is used to mark Boolean field data points in the modified elevation model. Through recursive quadtree segmentation, large-scale elevation data can be effectively managed and processed, and refined segmentation can be performed based on energy contribution to ensure prediction accuracy. A quadtree is a spatial segmentation data structure that is particularly 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 suitable for scenarios such as geographic data and image processing. A quadtree typically includes: a root node, which is the entire area or data set; and child nodes, which are four sub-areas formed by further partitioning of the root node. The root node refers to all elevation-modified data points in the entire modified elevation model as the root node of the quadtree, and the root node covers the entire geographic area of the modified elevation model. The recursive segmentation refers to recursively partitioning the area into four child nodes, starting from the root node, according to the quadtree structure. Each partition further refines the data processing area. To ensure data validity and prediction accuracy, label filtering conditions need to be set after each partition. The screening conditions are set according to factors such as the attributes of the elevation modification data points and the terrain characteristics to determine which child nodes will be marked; the child nodes that meet the screening conditions will have a Boolean field mark added to the modified elevation model, indicating that there are valid elevation modification data points in the area. The energy contribution estimation means that before each segmentation, the energy contribution of the root node and the child node 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 a child node is lower than the predetermined energy threshold, it means that the elevation change of the node has little influence on the fluid motion prediction, and the segmentation can be stopped. In this way, unnecessary subdivision is avoided and computational efficiency is improved. After identifying the grid cells with Boolean field marks, the fluid mechanics calculation of the modified elevation model is performed on these cells to further solve the motion prediction of the waste fluid after correction. In this embodiment, the quadtree structure is used to decompose complex geographic data into multiple small areas through recursive segmentation to facilitate efficient processing. In the case of large-scale waste dumps or complex terrain, elevation modification data points can be accurately marked and managed. When predicting fluid movement in complex terrains such as waste dumps, mining operations, and accumulations, the quadtree structure effectively processes and simulates areas of varying slopes and variations. Through precise labeling and simulation, it can promptly predict the impact force and range of fluids in the event of an instability or failure, providing a basis for disaster warning and emergency response. This approach efficiently utilizes computing resources, avoids overcalculation in unimportant areas, and achieves a balance between real-time performance and accuracy.

[0085] Preferably, as a feasible implementation method, the process of energy contribution estimation is set as follows:

[0086] The energy contribution is expressed as a kinetic energy disturbance value, and the kinetic energy disturbance value is predicted based on the velocity gradient disturbance; after constructing the initial digital elevation model (DEM), the shallow water equation is used to solve the initial velocity field representing the velocity distribution of the spoil fluid that is not affected by the terrain disturbance; the collapse volume is updated into the digital elevation model (DEM) to obtain a revised elevation model, and the fluid prediction is re-performed to obtain a revised velocity field representing the correction of the initial velocity field. Then, the velocity disturbance amount is calculated for each grid cell, and the velocity disturbance amount represents the mean value of the local velocity change of the fluid caused by the terrain change; then, the velocity disturbance amount is substituted into the kinetic energy calculation formula as the velocity value, the kinetic energy value of each node is calculated, and the kinetic energy value is expressed as the kinetic energy disturbance value.

[0087] Among them, the calculation formula of the velocity disturbance is expressed as: ,

[0088] in represents the area of the i-th plot, represents the velocity field under the original terrain, represents the velocity field under the corrected terrain, represents the change in flow velocity at the i-th node after the terrain changes; It represents the double integral over the area of the plot, integrating the disturbance amplitude at each point on the plot to find the total disturbance intensity at each space in the plot; This represents a mean value, dividing the total disturbance intensity by the area of the plot to obtain the average disturbance velocity. When the terrain changes, some areas may experience acceleration or deceleration. The velocity disturbance calculation formula means: how much the overall average velocity changes across the entire plot.

[0089] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A fluid boundary prediction method for the instability and collapse of a waste dump, characterized by: The method includes: Step S1: constructing a digital elevation model at the target spoil site and the downstream area, performing an initial spoil fluid movement prediction for the target spoil site, and marking the initial boundary lines of all predicted spoil fluids on the digital elevation model; Step S2: collecting spoil parameters of all spoil deposits in the target spoil site, obtaining geological parameters of the downstream area of the target spoil site from the digital elevation model, and dividing the downstream area into a certain number of downstream plots containing a certain number of grid cells; Step S3: Based on the spoil parameters and geological parameters, downstream plots with potential collapse are screened out and marked as risk plots. The critical sliding depth indicating potential soil collapse in all risk plots is calculated using the limit equilibrium method. Step S4: updating all critical sliding depths to the digital elevation model and marking it as a revised elevation model, using the revised elevation model to re-solve the spoil fluid movement prediction, and marking the revised boundary line representing the spoil fluid update; The process of screening out risky plots includes: calculating the fluid shear stress and critical shear stress of each downstream plot based on spoil parameters and geological parameters, wherein the fluid shear stress represents the shear force exerted on the surface of the downstream area of the target spoil site by the spoil fluid outburst, and the critical shear stress represents the minimum shear stress threshold for the surface of the downstream area of the target spoil site to resist erosion; when the fluid shear stress of the downstream plot is greater than the critical shear stress, the downstream plot is marked as a risky plot; The spoil parameters collected in each downstream plot of the target spoil site include the average values of: The bulk density of the waste fluid indicates the gravity of the waste fluid per unit volume, including solid particles and pore water; The density of the spoil fluid indicates the mass of the spoil fluid per unit volume; The spoil fluid depth represents the vertical height of the spoil fluid perpendicular to the ground surface in the direction of flow; The geological parameters collected in each downstream plot of the target spoil site include: Average slope angle, which represents the slope angle of the average surface slope downstream of the spoil dump; Soil particle bulk density value indicates the gravity value of soil solid particles per unit volume; Soil median particle size represents the middle value of the soil particle size distribution; The internal friction angle of soil indicates the amplitude of internal friction characteristics between particles inside the soil; Assume that the spoil fluid is a uniform laminar flow; the bulk density of the spoil fluid is represented by γ1, the density of the spoil fluid is represented by ρ1, and the depth of the spoil fluid is represented by h; the bulk density of the soil particles is represented by γ2, the median particle size of the soil is represented by d, and the internal friction angle of the soil is represented by θ; the average slope angle is represented by φ; the fluid shear stress and critical shear stress are represented by τ1 and τ2 respectively, The calculation formula of fluid shear stress is expressed as: , The calculation formula of 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; Assume that the critical sliding depth of the critical state in the limit equilibrium method in each downstream block is expressed as hc. The calculation content of the critical sliding depth includes: Assume that the calculation formula of critical sliding depth hc is expressed as: .

2. The method for predicting fluid boundaries for instability and collapse of a waste dump according to claim 1, characterized in that: Calculate the potential collapse volume of each risk plot and update the digital elevation model with the collapse volume as auxiliary data; The size of the collapse volume is set as the product of the critical sliding depth and the sliding area; Assume that the process of obtaining the sliding area includes: The size data of the grid cells are marked in the digital elevation model, and the slope area of each grid cell on the surface downstream of the waste dump is calculated. For each downstream plot, the sum of all grid cells is set as the sliding area.

3. The method for predicting fluid boundaries for instability and collapse of a waste dump according to claim 1, characterized in that: The updating process of the modified elevation model includes: The calculated critical sliding depth is converted into terrain elevation change, updated to the initial elevation data point in the digital elevation model, and corrected to the elevation modification data point in the revised elevation model; Gaussian filtering is performed on the revised elevation model to eliminate jagged edges caused by discrete allocation; and a Boolean field is added to the attribute table of the digital elevation model to mark the elevation modification data point.

4. The method for predicting fluid boundaries for instability and collapse of a waste dump according to claim 3, characterized in that: The process of converting the critical sliding depth into the terrain elevation change is: converting the critical sliding depth using a vertical projection method.

5. The method for predicting fluid boundaries for instability and collapse of a waste dump according to claim 4, characterized in that: When using Boolean fields to mark elevation modification data points in each downstream plot, the modified elevation model is marked with Boolean fields according to the quadtree structure. The process includes: All elevation modification data points of the entire modified elevation model are used as the root nodes of the quadtree structure, covering the entire geographical range of the modified elevation model, and all root nodes of the modified elevation model are recursively split; mark filtering conditions are set, and the child nodes that meet the mark filtering conditions after segmentation are marked with Boolean fields. The remaining child nodes are recursively split until convergence, and fluid dynamics calculations are performed on the grid cells with elevation modification data points marked with Boolean fields in each downstream plot to complete the process of resolving the spoil fluid movement prediction.

6. The method for predicting fluid boundaries for instability and collapse of a waste dump according to claim 5, characterized in that: Before each split, the energy contribution of the root node and child nodes after subdivision is estimated, and an energy threshold is set. If the energy contribution of each root node and child node is lower than the energy threshold, the splitting is stopped.

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