Numerical Simulation Method for the Evolution of Disaster Chain from Debris Flow Blocking a River to Landslide Dam Breach and Flood

Abstract

This invention discloses a numerical simulation method for the disaster chain of debris flow blocking a river – landslide dam failure flood evolution, including: obtaining the data required for the numerical simulation method based on a continuous medium fluid dynamics model coupling water, coarse particles, and fine particles. This application combines continuous medium mechanics theory, couples water, coarse particles, and fine particles into a continuous medium fluid dynamics model, and uses the finite difference method to achieve numerical simulation of the disaster chain of debris flow blocking a river – landslide dam failure flood evolution. This application considers the sediment transport effect of the main river flow when the debris flow flows into the main river and the influence of the main river channel sediment transport process on the landslide dam failure process and the evolution of the failure flood. It can simultaneously simulate whether the debris flow blocks the river, how the landslide dam fails after blocking the river, and the evolution of the failure flood, achieving a complete coupling of the physical processes of the debris flow blocking a river – landslide dam failure flood evolution disaster chain.

Description

Technical Field

[0001] This invention belongs to the field of mountain disaster simulation technology, and in particular relates to a numerical simulation method for the evolution of a disaster chain from debris flow blocking a river to a landslide dam failure and flood. Background Technology

[0002] Debris flow damming, landslide dam failure, and flood evolution constitute a typical mountain disaster chain, posing a significant threat to human life, property, and the ecological environment. Accurate simulation of these processes is crucial for early warning, disaster prevention and mitigation, and risk management. Among related technologies, debris flow damming assessment methods are mainly divided into two categories: statistical empirical models based on disaster history data and models based on physical mechanisms. Physical mechanism-based models, compared to statistical empirical models based on disaster history data, can better describe the development process of debris flow damming, landslide dam failure, and flood evolution.

[0003] In recent years, with the deepening research on the dynamic mechanism of debris flow, people have gradually realized that the relative ratio of debris flow flow to main river flow has an important impact on the debris flow blocking process. The existing physical mechanism-based model—numerical simulation of debris flow blocking the river—first simulates the debris flow and then uses a landslide dam failure model for further simulation. It does not achieve a complete coupling of physical processes, nor does it consider the impact of sediment transport in the main river when the debris flow flows into the main river and the sediment transport process in the main river channel on the landslide dam failure and the evolution of the flood, resulting in a large deviation between the simulation results and the actual situation. Summary of the Invention

[0004] The purpose of this invention is to provide a numerical simulation method for the evolution of the disaster chain of debris flow blocking a river - landslide dam failure flood, so as to solve the problem that the current numerical simulation results of debris flow blocking a river have a large deviation from the actual situation.

[0005] The embodiments of this application are implemented as follows: a numerical simulation method for the evolution disaster chain of debris flow blocking a river-dam failure flood includes: a continuous medium fluid dynamics model based on coupled water, coarse particles and fine particles three-phase medium, and obtaining the data required for the numerical simulation method. The data includes at least one of the following: topographic data, debris flow volume, debris flow initiation location, debris flow particle size distribution, gully soil size distribution, main river flow, and main river roughness coefficient.

[0006] In some embodiments, the governing equations of the continuous medium hydrodynamic model are:

[0007] ;

[0008] ;

[0009] ;

[0010] In the formula, Depth of mudslide or breach flood, unit: ;

[0011] For mudslides or breach floods along Flow rate per unit width in each direction, unit: ;

[0012] For mudslides or breach floods along Flow rate per unit width in each direction, unit: ;

[0013] For mudslides or breach floods along Directional flow velocity, unit: ;

[0014] For mudslides or breach floods along Flow velocity in direction, unit: ;

[0015] Density of debris flow or outburst flood, unit: ;

[0016] It is the volume concentration of water in debris flows or floods, in dimensionless units.

[0017] It is the volume concentration of coarse particles in debris flows or floods caused by breaches, in dimensionless quantities.

[0018] It is the volume concentration of fine particles in debris flows or floods caused by landslides or breaches, in dimensionless quantities.

[0019] Density of particulate matter in debris flows or outburst floods, unit: ;

[0020] The density of pure water, unit: ;

[0021] For mudslides or breach floods along Subgrade resistance in the direction of movement, unit: ;

[0022] For mudslides or breach floods along Subgrade resistance in the direction of movement, unit: ;

[0023] Elevation of the terrain required for numerical simulation, in units: ;

[0024] , where is the acceleration due to gravity, unit: ;

[0025] Total erosion rate from debris flow or outburst flood, unit: ;

[0026] Total particulate matter deposition rate in debris flow or outburst floods, unit: ;

[0027] For time, in units: .

[0028] In some embodiments, the transport equations for water, fine particles, and coarse particles during the movement of debris flows or outburst floods are as follows:

[0029] ;

[0030] ;

[0031] ;

[0032] In the formula, Depth of mudslide or breach flood, unit: ;

[0033] For mudslides or breach floods along Directional flow velocity, unit: ;

[0034] For mudslides or breach floods along Flow velocity in direction, unit: ;

[0035] It is the volume concentration of water in debris flows or floods, in dimensionless units.

[0036] It is the volume concentration of coarse particles in debris flows or floods caused by breaches, in dimensionless quantities.

[0037] It is the volume concentration of fine particles in debris flows or floods caused by landslides or breaches, in dimensionless quantities.

[0038] Erosion rate in debris flows or outburst floods, unit: ;

[0039] The percentage of water volume in a gully during the erosion process by debris flow or outburst flood, in dimensionless form.

[0040] The percentage of fine particles of material in the gully during debris flow or outburst flood erosion, in dimensionless units.

[0041] The percentage of coarse particles in the gully material during debris flow or outburst flood erosion, in dimensionless units.

[0042] Deposition rate of fine particulate matter in debris flows or outburst floods, unit: ;

[0043] The deposition rate of coarse-grained material in debris flows or outburst floods, in units of: ;

[0044] The diffusion coefficient of fine particulate matter in debris flows or outburst floods, in units of: ;

[0045] For time, in units: .

[0046] In some embodiments, the evolution equation of the terrain is:

[0047] ;

[0048] In the formula, Porosity of the trench bed, unit: dimensionless;

[0049] Elevation of the terrain, unit: ;

[0050] It is the total deposition rate of debris flows or outburst floods, in units of: ;

[0051] Total erosion rate of debris flow or outburst flood, unit: ;

[0052] The sediment transport rate per unit width along the x-direction, in units of: ;

[0053] The sediment transport rate per unit width along the y-direction, in units of: ;

[0054] For time, in units: .

[0055] Furthermore, the diffusion coefficient of fine particles in the transport equation of fine particles The calculation formula is as follows:

[0056] ;

[0057] In the formula, The diffusion coefficient of fine particles in debris flows or outburst floods, in units of: ;

[0058] κ = 0.4 represents the von Kármán constant, in dimensionless form;

[0059] The surface friction velocity of a debris flow or flood breach, in units of: ;

[0060] The resultant resistance of the bedbed in debris flow or outburst floods, in units of: ;

[0061] For mudslides or breach floods along Subgrade resistance in the direction of movement, unit: ;

[0062] For mudslides or breach floods along Subgrade resistance in the direction of movement, unit: ;

[0063] Density of debris flow or outburst flood, unit: ;

[0064] h This refers to the depth of a mudslide or breach flood, in units of: .

[0065] Furthermore, in the governing equations, the erosion rate of debris flow or outburst floods... The calculation method is as follows:

[0066] ;

[0067] In the formula, It is the total erosion rate of the gully bed sediment caused by the outflow flood, in units of: ;

[0068] This is the total erosion rate of debris flow, in units of: ;

[0069] Γ is the transition factor from outburst flood to debris flow, in dimensionless form. It represents the critical volume concentration of total sediment material that distinguishes between outburst floods and debris flows, and is calculated using the following formula:

[0070] ;

[0071] In the formula, α is the decay exponent, in dimensionless form, with a value of 13.8;

[0072] It is the volume concentration of coarse particles in debris flows or floods caused by breaches, in dimensionless quantities.

[0073] It is the volume concentration of fine particles in debris flows or floods caused by landslides or breaches, in dimensionless quantities.

[0074] It is the critical total particulate matter concentration at the boundary between outburst floods and debris flows, in dimensionless form, with a value of 0.18.

[0075] Furthermore, In China, the total erosion rate of debris flows The calculation equation is as follows:

[0076] ;

[0077] In the formula, The resultant resistance of the bedbed in debris flow or outburst floods, in units of: ;

[0078] For mudslides or breach floods along Subgrade resistance in the direction of movement, unit: ;

[0079] For mudslides or breach floods along Subgrade resistance in the direction of movement, unit: ;

[0080] For mudslides or breach floods along Directional flow velocity, unit: ;

[0081] For mudslides or breach floods along Directional flow velocity, unit: ;

[0082] Density of debris flow or outburst flood, unit: ;

[0083] For the calculated depth of debris flow or outburst flood, the unit is: ;

[0084] The pore water pressure coefficient in the gully bed material during debris flow erosion of the gully channel, unit: dimensionless;

[0085] The slope of the ditch, in degrees (°).

[0086] The friction angle of particulate matter in a gully during debris flow erosion, in degrees.

[0087] The cohesion of particulate matter in a gully during debris flow erosion, unit: ;

[0088] Acceleration due to gravity, unit: .

[0089] Understandable. The slope of the ditch is expressed in degrees (°) and is calculated from the terrain.

[0090] Furthermore, In the middle, the total erosion rate of the gully bed sediment by the outflow flood The calculation method is as follows

[0091] ;

[0092] In the formula, The total erosion rate of the gully bed sediment caused by the outburst flood, in units of: ;

[0093] The combined resistance of the bedbed during a breach flood, in units of: ;

[0094] To breach the floodwaters along Subgrade resistance in the direction of movement, unit: ;

[0095] To breach the floodwaters along Subgrade resistance in the direction of movement, unit: ;

[0096] The erosion resistance of the gully bed material during the erosion process of a breach flood, unit: ;

[0097] Empirical coefficient for erosion caused by outburst floods, unit: .

[0098] Understandable. for and Take the larger of the two numbers.

[0099] It is understandable that, since the debris flow is highly integrated due to the thorough mixing of sediment particles during its movement, the settling of sediment particles is negligible, and only the settling of fine and coarse sediment particles during the movement of the flood is considered.

[0100] Furthermore, in the transport equations for fine and coarse particles and The calculation method is as follows:

[0101] ;

[0102] ;

[0103] In the formula, The deposition rate of fine particles during the outburst flood movement, in units of: ;

[0104] The deposition rate of coarse particles during the outburst flood movement, in units of: ;

[0105] It is the volume concentration of coarse particles in debris flows or floods caused by breaches, in dimensionless quantities.

[0106] It is the volume concentration of fine particles in debris flows or floods caused by landslides or breaches, in dimensionless quantities.

[0107] This is an empirical parameter, ranging from 2.0 to 5.0, in dimensionless units.

[0108] Γ is the transition factor from outburst flood to debris flow, in dimensionless form.

[0109] Settling velocity of fine particles during the movement of a breach flood, unit: The calculation formula is:

[0110] ;

[0111] In the formula, The kinematic viscosity of clear water, unit: ;

[0112] Representative particle size of fine particles during the movement of a flood caused by a breach; unit: ;

[0113] Density of fine particulate matter in debris flows or outburst floods, unit: ;

[0114] The density of pure water, unit: ;

[0115] Acceleration due to gravity, unit: ;

[0116] Settlement rate of coarse particles during the movement of a breach flood, unit: The calculation formula is:

[0117] ;

[0118] In the formula, The kinematic viscosity of clear water, unit: ;

[0119] Representative particle size of coarse particles during the movement of a flood breach, unit: ;

[0120] Density of coarse-grained material in debris flows or outburst floods, unit: ;

[0121] The density of pure water, unit: ;

[0122] Acceleration due to gravity, unit: .

[0123] Furthermore, Medium coarse grain unit width sediment transport rate along the x-direction and the unit width sediment transport rate of coarse particles along the y-direction The calculation methods are as follows:

[0124] ;

[0125] ;

[0126] In the formula, For mudslides or breach floods along Flow rate per unit width in each direction, unit: ;

[0127] For mudslides or breach floods along Flow rate per unit width in each direction, unit: ;

[0128] The unit width sediment transport rate for coarse particles, in units of: The calculation formula is:

[0129] ;

[0130] In the formula, It is the Froude number of the fluid, with the unit being dimensionless;

[0131] Depth of mudslide or breach flood, unit: ;

[0132] For mudslides or breach floods along Directional flow velocity, unit: ;

[0133] For mudslides or breach floods along Flow velocity in direction, unit: ;

[0134] This is the dimensionless bed shear stress, i.e., the Shields number;

[0135] For mudslides or breach floods along Subgrade resistance in the direction of movement, unit: ;

[0136] For mudslides or breach floods along Subgrade resistance in the direction of movement, unit: ;

[0137] Density of coarse-grained material in debris flows or outburst floods, unit: ;

[0138] The density of pure water, unit: ;

[0139] Representative particle size of coarse particles during the movement of a flood breach, unit: ;

[0140] Acceleration due to gravity, unit: ;

[0141] The critical Shield number, in dimensionless form, is calculated as follows:

[0142] ;

[0143] In the formula, Empirical coefficients, unit: dimensionless;

[0144] The slope of the ditch, in degrees (°).

[0145] The friction angle between particles in a gully when a breached flood erodes the gully, measured in degrees (°).

[0146] Furthermore, and Debris flow or flood breach along the middle of the river directional bed resistance And mudslides or breach floods along directional bed resistance The calculation formula is:

[0147] ;

[0148] ;

[0149] In the formula, Density of debris flow or outburst flood, unit: ;

[0150] It is the volume concentration of water in debris flows or floods, in dimensionless units.

[0151] It is the volume concentration of coarse particles in debris flows or floods caused by breaches, in dimensionless quantities.

[0152] It is the volume concentration of fine particles in debris flows or floods caused by landslides or breaches, in dimensionless quantities.

[0153] Density of particulate matter in debris flows or outburst floods, unit: ;

[0154] The density of pure water, unit: ;

[0155] The roughness coefficient during the movement of a breach flood, in units of: ;

[0156] Depth of mudslide or breach flood, unit: ;

[0157] For mudslides or breach floods along Flow rate per unit width in each direction, unit: ;

[0158] For mudslides or breach floods along Flow rate per unit width in each direction, unit: ;

[0159] For mudslides or breach floods along Directional flow velocity, unit: ;

[0160] For mudslides or breach floods along Flow velocity in direction, unit: ;

[0161] Γ is the transition factor from outburst flood to debris flow, in dimensionless form.

[0162] and These are either debris flows or outburst floods, where the liquid phase slurry flows along... direction and Subgrade resistance in the direction of movement, unit: ;

[0163] and These are either debris flows or outburst floods with coarse particles along the way. direction and Subgrade resistance in the direction of movement, unit: ;

[0164] Acceleration due to gravity, unit: .

[0165] Furthermore, the liquid phase slurry of mudslides or outburst floods... directional bed resistance and directional bed resistance The calculation formulas are as follows:

[0166] ;

[0167] ;

[0168] In the formula, Depth of mudslide or breach flood, unit: ;

[0169] For mudslides or breach floods along Directional flow velocity, unit: ;

[0170] For mudslides or breach floods along Flow velocity in direction, unit: ;

[0171] The dynamic viscosity of pure water, measured in Pa·s;

[0172] Represents the volume concentration of fine particulate matter in liquid mud, unit: dimensionless;

[0173] It is the maximum permissible volume concentration of fine-grained sediments in liquid mud, in dimensionless form, and is calculated as follows:

[0174] ;

[0175] In the formula, and They represent the first in fine-grained sediment. i Diameter and mass percentage of each particle size class, in dimensionless form;

[0176] S v0 It is the critical volume concentration at which a fluid transforms from a Newtonian fluid to a Bingham fluid, measured in dimensionless quantities. The calculation formula is:

[0177] ;

[0178] k 0 is a correction factor, unit: dimensionless, expression:

[0179] .

[0180] Understandable. It is the maximum permissible volume concentration of fine-grained sediments in liquid mud, in dimensionless form. This parameter is usually related to the specific surface area of ​​the particles.

[0181] Furthermore, coarse-grained material from mudslides or breach floods travels along... directional bed resistance and directional bed resistance The calculation formulas are as follows:

[0182] ;

[0183] ;

[0184] In the formula, For coarse particles in debris flows or outburst floods Resistance to motion in the direction of motion, unit: ;

[0185] For coarse particles in debris flows or outburst floods Resistance to motion in the direction of motion, unit: ;

[0186] Density of debris flow or outburst flood, unit: ;

[0187] Density of a liquid slurry composed of fine particles and water, in units of: ;

[0188] It is the volume concentration of water in debris flows or floods, in dimensionless units.

[0189] It is the volume concentration of coarse particles in debris flows or floods caused by breaches, in dimensionless quantities.

[0190] It is the volume concentration of fine particles in debris flows or floods caused by landslides or breaches, in dimensionless quantities.

[0191] Density of particulate matter in debris flows or outburst floods, unit: ;

[0192] The density of pure water, unit: ;

[0193] For mudslides or breach floods along Flow rate per unit width in each direction, unit: ;

[0194] For mudslides or breach floods along Flow rate per unit width in each direction, unit: ;

[0195] For mudslides or breach floods along Directional flow velocity, unit: ;

[0196] For mudslides or breach floods along Flow velocity in direction, unit: ;

[0197] Depth of mudslide or breach flood, unit: ;

[0198] For mudslides or breach floodbed edges Slope of direction, unit: °;

[0199] For the bed edge of debris flow Slope of direction, unit: °;

[0200] The friction angle between coarse-grained material and the bedrock in debris flow, in degrees;

[0201] The turbulence coefficient of coarse-grained material in debris flow, unit: ;

[0202] , where is the acceleration due to gravity, unit: .

[0203] Understandable. and All were calculated based on the terrain.

[0204] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0205] This application combines continuum mechanics theory with a continuum fluid dynamics model coupling water, coarse particles, and fine particles into a three-phase medium. It employs the finite difference method to achieve numerical simulation of the debris flow blocking a river – landslide dam failure flood evolution chain. This application considers the sediment transport effect of the main river flow when the debris flow enters the main river, and the impact of the main river's sediment transport process on the landslide dam failure process and the evolution of the failure flood. It can simultaneously simulate whether a debris flow blocks the river, how the landslide dam fails after blocking the river, and the evolution of the failure flood, achieving a fully coupled physical process of the debris flow blocking a river – landslide dam failure flood evolution chain. Attached Figure Description

[0206] Figure 1 This is the particle size distribution curve for debris flow in this invention;

[0207] Figure 2 Numerical simulation diagram of the evolution of debris flow movement - river blockage - landslide dam failure - breach flood. Detailed Implementation

[0208] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0209] The technical solution of this application is as follows:

[0210] This application provides a numerical simulation method for the evolution of a debris flow-dammed river flood disaster chain, including: a continuous medium fluid dynamics model based on coupled water, coarse particles, and fine particles, and obtaining the data required for the numerical simulation method. The data includes at least one of the following: topographic data, debris flow volume, debris flow initiation location, debris flow particle size distribution, gully soil size distribution, main river flow, and main river roughness coefficient.

[0211] This application combines continuum mechanics theory with a continuum fluid dynamics model coupling water, coarse particles, and fine particles into a three-phase medium. It employs the finite difference method to achieve numerical simulation of the debris flow blocking a river – landslide dam failure flood evolution chain. This application considers the sediment transport effect of the main river flow when the debris flow enters the main river, and the impact of the main river's sediment transport process on the landslide dam failure process and the evolution of the failure flood. It can simultaneously simulate whether a debris flow blocks the river, how the landslide dam fails after blocking the river, and the evolution of the failure flood, achieving a fully coupled physical process of the debris flow blocking a river – landslide dam failure flood evolution chain.

[0212] The numerical simulation method for the evolution disaster chain of debris flow blocking a river-landlock dam failure flood proposed in this application first selects a cross-section in the upper reaches of the main river and sets a main river flow rate. Volume concentration of coarse-grained sediment transport in the main river Main River fine-particle sediment transport volume concentration Volume fraction of the main river water And satisfy Further settings include the initial initiation location, volume, and initial fine particle volume concentration in the debris flow. Initial coarse particle volume concentration and the initial water content in the mud and rock fluid Then, the numerical simulation method for the evolution of the debris flow-dammed river-landlocked dam-break flood disaster chain is used to simulate the main river's flow process. When the main river flows to a specific downstream section, the debris flow movement in the simulated debris flow channel is calculated based on this method. After the debris flow merges into the main river, the concentration of coarse and fine particles in the debris flow changes due to the influence of the main river flow, thus altering the flow resistance and state. Finally, the numerical simulation method automatically calculates whether the debris flow will block the river and how the flood will move after the blockage.

[0213] In some embodiments, the governing equations of the continuous medium hydrodynamic model are:

[0214] ;

[0215] ;

[0216] ;

[0217] In the formula, Depth of mudslide or breach flood, unit: ;

[0218] For mudslides or breach floods along Flow rate per unit width in each direction, unit: ;

[0219] For mudslides or breach floods along Flow rate per unit width in each direction, unit: ;

[0220] For mudslides or breach floods along Directional flow velocity, unit: ;

[0221] For mudslides or breach floods along Flow velocity in direction, unit: ;

[0222] Density of debris flow or outburst flood, unit: ;

[0223] It is the volume concentration of water in debris flows or floods, in dimensionless units.

[0224] It is the volume concentration of coarse particles in debris flows or floods caused by breaches, in dimensionless quantities.

[0225] It is the volume concentration of fine particles in debris flows or floods caused by landslides or breaches, in dimensionless quantities.

[0226] Density of particulate matter in debris flows or outburst floods, unit: ;

[0227] The density of pure water, unit: ;

[0228] For mudslides or breach floods along Subgrade resistance in the direction of movement, unit: ;

[0229] For mudslides or breach floods along Subgrade resistance in the direction of movement, unit: ;

[0230] Elevation of the terrain required for numerical simulation, in units: ;

[0231] , where is the acceleration due to gravity, unit: ;

[0232] Total erosion rate from debris flow or outburst flood, unit: ;

[0233] Total particulate matter deposition rate in debris flow or outburst floods, unit: ;

[0234] For time, in units: .

[0235] In some embodiments, the transport equations for water, fine particles, and coarse particles during the movement of debris flows or outburst floods are as follows:

[0236] ;

[0237] ;

[0238] ;

[0239] In the formula, Depth of mudslide or breach flood, unit: ;

[0240] For mudslides or breach floods along Directional flow velocity, unit: ;

[0241] For mudslides or breach floods along Flow velocity in direction, unit: ;

[0242] It is the volume concentration of water in debris flows or floods, in dimensionless units.

[0243] It is the volume concentration of coarse particles in debris flows or floods caused by breaches, in dimensionless quantities.

[0244] It is the volume concentration of fine particles in debris flows or floods caused by landslides or breaches, in dimensionless quantities.

[0245] Erosion rate in debris flows or outburst floods, unit: ;

[0246] The percentage of water volume in a gully during the erosion process by debris flow or outburst flood, in dimensionless form.

[0247] The percentage of fine particles of material in the gully during debris flow or outburst flood erosion, in dimensionless units.

[0248] The percentage of coarse particles in the gully material during debris flow or outburst flood erosion, in dimensionless units.

[0249] Deposition rate of fine particulate matter in debris flows or outburst floods, unit: ;

[0250] The deposition rate of coarse-grained material in debris flows or outburst floods, in units of: ;

[0251] The diffusion coefficient of fine particulate matter in debris flows or outburst floods, in units of: ;

[0252] For time, in units: .

[0253] In some embodiments, the evolution equation of the terrain is:

[0254] ;

[0255] In the formula, Porosity of the trench bed, unit: dimensionless;

[0256] Elevation of the terrain, unit: ;

[0257] It is the total deposition rate of debris flows or outburst floods, in units of: ;

[0258] Total erosion rate of debris flow or outburst flood, unit: ;

[0259] The sediment transport rate per unit width along the x-direction, in units of: ;

[0260] The sediment transport rate per unit width along the y-direction, in units of: ;

[0261] For time, in units: .

[0262] Furthermore, the diffusion coefficient of fine particles in the transport equation of fine particles The calculation formula is as follows:

[0263] ;

[0264] In the formula, The diffusion coefficient of fine particles in debris flows or outburst floods, in units of: ;

[0265] κ = 0.4 represents the von Kármán constant, in dimensionless form;

[0266] The surface friction velocity of a debris flow or flood breach, in units of: ;

[0267] The resultant resistance of the bedbed in debris flow or outburst floods, in units of: ;

[0268] For mudslides or breach floods along Subgrade resistance in the direction of movement, unit: ;

[0269] For mudslides or breach floods along Subgrade resistance in the direction of movement, unit: ;

[0270] Density of debris flow or outburst flood, unit: ;

[0271] h This refers to the depth of a mudslide or breach flood, in units of: .

[0272] Furthermore, in the governing equations, the erosion rate of debris flow or outburst floods... The calculation method is as follows:

[0273] ;

[0274] In the formula, It is the total erosion rate of the gully bed sediment caused by the outflow flood, in units of: ;

[0275] This is the total erosion rate of debris flow, in units of: ;

[0276] Γ is the transition factor from outburst flood to debris flow, in dimensionless form. It represents the critical volume concentration of total sediment material that distinguishes between outburst floods and debris flows, and is calculated using the following formula:

[0277] ;

[0278] In the formula, α is the decay exponent, in dimensionless form, with a value of 13.8;

[0279] It is the volume concentration of coarse particles in debris flows or floods caused by breaches, in dimensionless quantities.

[0280] It is the volume concentration of fine particles in debris flows or floods caused by landslides or breaches, in dimensionless quantities.

[0281] It is the critical total particulate matter concentration at the boundary between outburst floods and debris flows, in dimensionless form, with a value of 0.18.

[0282] Furthermore, In China, the total erosion rate of debris flows The calculation equation is as follows:

[0283] ;

[0284] In the formula, The resultant resistance of the bedbed in debris flow or outburst floods, in units of: ;

[0285] For mudslides or breach floods along Subgrade resistance in the direction of movement, unit: ;

[0286] For mudslides or breach floods along Subgrade resistance in the direction of movement, unit: ;

[0287] For mudslides or breach floods along Directional flow velocity, unit: ;

[0288] For mudslides or breach floods along Directional flow velocity, unit: ;

[0289] Density of debris flow or outburst flood, unit: ;

[0290] For the calculated depth of debris flow or outburst flood, the unit is: ;

[0291] The pore water pressure coefficient in the gully bed material during debris flow erosion of the gully channel, unit: dimensionless;

[0292] The slope of the ditch, in degrees (°).

[0293] The friction angle of particulate matter in a gully during debris flow erosion, in degrees.

[0294] The cohesion of particulate matter in a gully during debris flow erosion, unit: ;

[0295] Acceleration due to gravity, unit: .

[0296] Understandable. The slope of the ditch is expressed in degrees (°) and is calculated from the terrain.

[0297] Furthermore, In the middle, the total erosion rate of the gully bed sediment by the outflow flood The calculation method is as follows

[0298] ;

[0299] In the formula, The total erosion rate of the gully bed sediment caused by the outburst flood, in units of: ;

[0300] The combined resistance of the bedbed during a breach flood, in units of: ;

[0301] To breach the floodwaters along Subgrade resistance in the direction of movement, unit: ;

[0302] To breach the floodwaters along Subgrade resistance in the direction of movement, unit: ;

[0303] The erosion resistance of the gully bed material during the erosion process of a breach flood, unit: ;

[0304] Empirical coefficient for erosion caused by outburst floods, unit: .

[0305] Understandable. for and Take the larger of the two numbers.

[0306] It is understandable that, since the debris flow is highly integrated due to the thorough mixing of sediment particles during its movement, the settling of sediment particles is negligible, and only the settling of fine and coarse sediment particles during the movement of the flood is considered.

[0307] Furthermore, in the transport equations for fine and coarse particles and The calculation method is as follows:

[0308] ;

[0309] ;

[0310] In the formula, The deposition rate of fine particles during the outburst flood movement, in units of: ;

[0311] The deposition rate of coarse particles during the outburst flood movement, in units of: ;

[0312] It is the volume concentration of coarse particles in debris flows or floods caused by breaches, in dimensionless quantities.

[0313] It is the volume concentration of fine particles in debris flows or floods caused by landslides or breaches, in dimensionless quantities.

[0314] This is an empirical parameter, ranging from 2.0 to 5.0, in dimensionless units.

[0315] Γ is the transition factor from outburst flood to debris flow, in dimensionless form.

[0316] Settling velocity of fine particles during the movement of a breach flood, unit: The calculation formula is:

[0317] ;

[0318] In the formula, The kinematic viscosity of clear water, unit: ;

[0319] Representative particle size of fine particles during the movement of a flood caused by a breach; unit: ;

[0320] Density of fine particulate matter in debris flows or outburst floods, unit: ;

[0321] The density of pure water, unit: ;

[0322] Acceleration due to gravity, unit: ;

[0323] Settlement rate of coarse particles during the movement of a breach flood, unit: The calculation formula is:

[0324] ;

[0325] In the formula, The kinematic viscosity of clear water, unit: ;

[0326] Representative particle size of coarse particles during the movement of a flood breach, unit: ;

[0327] Density of coarse-grained material in debris flows or outburst floods, unit: ;

[0328] The density of pure water, unit: ;

[0329] Acceleration due to gravity, unit: .

[0330] Furthermore, Medium coarse grain unit width sediment transport rate along the x-direction and the unit width sediment transport rate of coarse particles along the y-direction The calculation methods are as follows:

[0331] ;

[0332] ;

[0333] In the formula, For mudslides or breach floods along Flow rate per unit width in each direction, unit: ;

[0334] For mudslides or breach floods along Flow rate per unit width in each direction, unit: ;

[0335] The unit width sediment transport rate for coarse particles, in units of: The calculation formula is:

[0336] ;

[0337] In the formula, It is the Froude number of the fluid, with the unit being dimensionless;

[0338] Depth of mudslide or breach flood, unit: ;

[0339] For mudslides or breach floods along Directional flow velocity, unit: ;

[0340] For mudslides or breach floods along Flow velocity in direction, unit: ;

[0341] This is the dimensionless bed shear stress, i.e., the Shields number;

[0342] For mudslides or breach floods along Subgrade resistance in the direction of movement, unit: ;

[0343] For mudslides or breach floods along Subgrade resistance in the direction of movement, unit: ;

[0344] Density of coarse-grained material in debris flows or outburst floods, unit: ;

[0345] The density of pure water, unit: ;

[0346] Representative particle size of coarse particles during the movement of a flood breach, unit: ;

[0347] Acceleration due to gravity, unit: ;

[0348] The critical Shield number, in dimensionless form, is calculated as follows:

[0349] ;

[0350] In the formula, Empirical coefficients, unit: dimensionless;

[0351] The slope of the ditch, in degrees (°).

[0352] The friction angle between particles in a gully when a breached flood erodes the gully, measured in degrees (°).

[0353] Furthermore, and Debris flow or flood breach along the middle of the river directional bed resistance And mudslides or breach floods along directional bed resistance The calculation formula is:

[0354] ;

[0355] ;

[0356] In the formula, Density of debris flow or outburst flood, unit: ;

[0357] It is the volume concentration of water in debris flows or floods, in dimensionless units.

[0358] It is the volume concentration of coarse particles in debris flows or floods caused by breaches, in dimensionless quantities.

[0359] It is the volume concentration of fine particles in debris flows or floods caused by landslides or breaches, in dimensionless quantities.

[0360] Density of particulate matter in debris flows or outburst floods, unit: ;

[0361] The density of pure water, unit: ;

[0362] The roughness coefficient during the movement of a breach flood, in units of: ;

[0363] Depth of mudslide or breach flood, unit: ;

[0364] For mudslides or breach floods along Flow rate per unit width in each direction, unit: ;

[0365] For mudslides or breach floods along Flow rate per unit width in each direction, unit: ;

[0366] For mudslides or breach floods along Directional flow velocity, unit: ;

[0367] For mudslides or breach floods along Flow velocity in direction, unit: ;

[0368] Γ is the transition factor from outburst flood to debris flow, in dimensionless form.

[0369] and These are either debris flows or outburst floods, where the liquid phase slurry flows along... direction and Subgrade resistance in the direction of movement, unit: ;

[0370] and These are either debris flows or outburst floods with coarse particles along the way. direction and Subgrade resistance in the direction of movement, unit: ;

[0371] Acceleration due to gravity, unit: .

[0372] Furthermore, the liquid phase slurry of mudslides or outburst floods... directional bed resistance and directional bed resistance The calculation formulas are as follows:

[0373] ;

[0374] ;

[0375] In the formula, Depth of mudslide or breach flood, unit: ;

[0376] For mudslides or breach floods along Directional flow velocity, unit: ;

[0377] For mudslides or breach floods along Flow velocity in direction, unit: ;

[0378] The dynamic viscosity of pure water, measured in Pa·s;

[0379] Represents the volume concentration of fine particulate matter in liquid mud, unit: dimensionless;

[0380] It is the maximum permissible volume concentration of fine-grained sediments in liquid mud, in dimensionless form, and is calculated as follows:

[0381] ;

[0382] In the formula, and They represent the first in fine-grained sediment. i Diameter and mass percentage of each particle size class, in dimensionless form;

[0383] S v0It is the critical volume concentration at which a fluid transforms from a Newtonian fluid to a Bingham fluid, measured in dimensionless quantities. The calculation formula is:

[0384] ;

[0385] k 0 is a correction factor, unit: dimensionless, expression:

[0386] .

[0387] Understandable. It is the maximum permissible volume concentration of fine-grained sediments in liquid mud, in dimensionless form. This parameter is usually related to the specific surface area of ​​the particles.

[0388] Furthermore, coarse-grained material from mudslides or breach floods travels along... directional bed resistance and directional bed resistance The calculation formulas are as follows:

[0389] ;

[0390] ;

[0391] In the formula, For coarse particles in debris flows or outburst floods Resistance to motion in the direction of motion, unit: ;

[0392] For coarse particles in debris flows or outburst floods Resistance to motion in the direction of motion, unit: ;

[0393] Density of debris flow or outburst flood, unit: ;

[0394] Density of a liquid slurry composed of fine particles and water, in units of: ;

[0395] It is the volume concentration of water in debris flows or floods, in dimensionless units.

[0396] It is the volume concentration of coarse particles in debris flows or floods caused by breaches, in dimensionless quantities.

[0397] It is the volume concentration of fine particles in debris flows or floods caused by landslides or breaches, in dimensionless quantities.

[0398] Density of particulate matter in debris flows or outburst floods, unit: ;

[0399] The density of pure water, unit: ;

[0400] For mudslides or breach floods along Flow rate per unit width in each direction, unit: ;

[0401] For mudslides or breach floods along Flow rate per unit width in each direction, unit: ;

[0402] For mudslides or breach floods along Directional flow velocity, unit: ;

[0403] For mudslides or breach floods along Flow velocity in direction, unit: ;

[0404] Depth of mudslide or breach flood, unit: ;

[0405] For mudslides or breach floodbed edges Slope of direction, unit: °;

[0406] For the bed edge of debris flow Slope of direction, unit: °;

[0407] The friction angle between coarse-grained material and the bedrock in debris flow, in degrees;

[0408] The turbulence coefficient of coarse-grained material in debris flow, unit: ;

[0409] , where is the acceleration due to gravity, unit: .

[0410] Understandable. and All were calculated based on the terrain.

[0411] Experimental Example

[0412] A simulation calculation was conducted using a ditch in Sichuan as an example. The constant flow of the main river downstream of the ditch is... 150 m 3 / s (average flow rate), volume concentration of coarse sediment transported in the main river upstream. The volume concentration of fine-particle sediment transported in the main river is 0.01 (unit: dimensionless). The volume fraction of the main river water is 0.03 (unit: dimensionless). The value is 0.96 (unit: dimensionless), and the riverbed roughness coefficient is taken as 0.035. The total volume of the debris flow in the gully was 98,300 cubic meters. 3 Initial fine particle volume concentration in mudflow The initial coarse particle volume concentration is 0.25 (unit: dimensionless). The initial water content in the mudflow is 0.35 (unit: dimensionless). 0.40 (unit: dimensionless). Percentage of water by volume in a gully during erosion by debris flow or outburst flood. The volume percentage of coarse particles in the channel material is 0.35 (unit: dimensionless). The volume percentage of fine particles in the channel material is 0.38 (unit: dimensionless). The porosity of the trench bed is 0.27 (unit: dimensionless). The value is 0.35 (unit: dimensionless). Empirical parameter for particle sedimentation during the movement of a breach flood. The value is 3.0 (unit: dimensionless). Density of particulate matter in debris flows or floods. The density of clear water The friction angle between coarse particles and the bedrock in debris flows. The turbulence coefficient of coarse-grained debris flow material is 28°. It is 25.5 Representative particle size of coarse particles during the movement of a flood burst. The value is 0.01 , The representative particle size for fine particles during the movement of the flood burst is taken as 0.0005. Friction angle between particles in the channel when calculating the sediment transport rate per unit width for coarse particles in a breach flood. The angle is 30°. The erosion resistance of the gully bed material during the erosion process of a breach flood. 30 , The empirical coefficient for erosion from a breach flood is 0.00059 (unit: The particle size distribution curve of debris flow is as follows: Figure 1As shown. A digital elevation model (DEM) of the debris flow gully's watershed was established based on a 1:10000 topographic map of the gully. The parameters mentioned above were input into the numerical model to obtain the process of debris flow movement, river blockage, and outburst flood evolution, as shown below. Figure 2 As shown in the figure. The results indicate that under the above parameter conditions, debris flow can block the downstream main river, with the maximum height of the debris flow dam being 9.84 m. With continuous inflow from the upstream main river, the water level of the landslide dammed lake rises, its backwater length is approximately 362 m, and the total reservoir capacity of the landslide dammed lake is approximately 18.43 × 10⁻⁶ m. 4 m 3 The debris flow dam subsequently collapsed rapidly, with a peak flow rate of 952.2 m³ / s. 3 / s.

[0413] Figure 2 (a) Simulation of debris flow movement; (b) Simulation of debris flow blocking the river process; (c) Simulation of debris flow dam failure process; (d) Simulation of debris flow dam failure flood evolution.

[0414] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A numerical simulation method for a debris flow blocking river - dam-break flood evolution disaster chain, characterized in that, The method comprises the following steps: Obtaining data required by a numerical simulation method based on a continuous medium hydrodynamic model of three-phase medium of coupled water, coarse particles and fine particles, the data comprising at least one of the following: terrain data, debris flow volume, debris flow starting position, debris flow particle size distribution, gully soil size distribution, main river flow, and main river channel roughness coefficient; The transport equations of water, fine particles and coarse particles during the movement of the debris flow or the breaching flood are as follows: ； ； ； In the formula, Depth of debris flow or bursting flood flow, unit: ; debris flow or a breached dam along directional velocity, units: ; flow velocity of the debris flow or the burst flood along the direction, unit: ; is the volume concentration of water in a debris flow or a burst flood, dimensionless; is the volume concentration of coarse particles in a debris flow or a burst flood, dimensionless; is the volume concentration of fine particles in a debris flow or a burst flood, dimensionless; For erosion rate in debris flow or bursting flood, unit: ; Volume fraction of water in the gully during the process of debris flow or bursting flood erosion gully, unit: dimensionless; Percentage of fine fraction of channel material during debris flow or flood erosion process, unit: dimensionless; Vp = volume percentage of coarse fraction of channel material during debris flow or flood erosion process, dimensionless; deposition rate of fine-grained material in a debris flow or a break flood, unit: ; deposited volume, unit: ; Df = diffusion coefficient for fine-grained material in a debris flow or a break flood, unit: ; Time, units: ; Diffusion coefficient of fine particles in transport equation of fine particles The formula for calculating the diffusion coefficient is as follows: ； wherein Dp is the diffusion coefficient of fine particles in a debris flow or a burst flood, unit: ; The control equation of the continuous medium hydrodynamic model is as follows: = 0.4 represents the von Karman constant, dimensionless; bed friction velocity of a debris flow or a breached flood, unit: ; cohesion of debris flow or burst flood bed, unit: ; bed resistance of debris flow or burst flood along direction, unit: ; bed resistance of debris flow or burst flood along direction, unit: ; Density of debris flow or burst flood, unit: ; h is the flow depth of the debris flow or the burst flood flow, .

2. The numerical simulation method of debris flow dam-break-flood routing disaster chain according to claim 1, characterized in that, The evolution equation of the terrain is as follows: ； ； ； In the formula, is the flow depth of the debris flow or the burst flood, unit: ; , the single width flow of debris flow or burst flood along direction, unit: ; , the single width flow of debris flow or burst flood along direction, unit: ; debris flow or a break flood along directional velocity, unit: ; flow rate of the debris flow or the burst flood along the direction, unit: ; Density of debris flow or burst flood, unit: ; is the volume concentration of water in a debris flow or a burst flood, dimensionless; is the volume concentration of coarse particles in a debris flow or a burst flood, dimensionless; is the volume concentration of fine particles in a debris flow or a burst flood, dimensionless; D is the density of the granular material in the debris flow or the burst flood, in kg / m3; ; Density of clear water, units: ; bed resistance of debris flow or burst flood along direction, unit: ; bed resistance of debris flow or burst flood along direction, unit: ; ELEVATION, units, for terrain required for numerical simulation ; g is the gravitational acceleration, unit: ; Total erosion rate for debris flow or break flood, unit: ; Total sediment yield of debris flow or flood, unit: ; Time, units: .

3. The numerical simulation method of debris flow dam-break-flood routing disaster chain according to claim 1, characterized in that, Γ is a transition factor of the breaching flood to the debris flow, unit: dimensionless, representing a critical volume concentration of total sediment material for distinguishing the breaching flood and the debris flow, and the calculation formula is ； wherein is the ditch bed porosity, dimensionless; ELEVATION, unit: ; is the total deposition rate of the debris flow or the burst flood, in units of: ; Total erosion rate for a debris flow or a break flood, unit: ; To move the sediment discharge per unit width along the x direction, the unit is: ; To move the sediment discharge per unit width along the y direction, the unit is: ; Time, units: .

4. The numerical simulation method of debris flow dam-break-flood routing disaster chain according to claim 2, characterized in that, In the governing equations, the erosion rate of debris flow or outburst floods The calculation method is as follows: ； wherein is the total rate of erosion of the channel bed sediment by the flood, in units of: ; is the total erosion rate of debris flow, unit: ; In the formula, α is an attenuation index, unit: dimensionless, and the value is 13.8; ； Γ is a transition factor of the breaching flood to the debris flow, unit: dimensionless; is the volume concentration of coarse particles in a debris flow or a burst flood, dimensionless; is the volume concentration of fine particles in a debris flow or a burst flood, dimensionless; is the critical total sediment concentration that separates debris flow from hyperconcentrated flow, dimensionless, and is taken as 0.

18.

5. The numerical simulation method of debris flow dam-break-flood routing disaster chain according to claim 4, characterized in that, Total erosion rate of debris flow The calculation equation is: ； wherein Cm is the frictional resistance of the debris flow or the collapsed flood bed, unit: ; bed resistance of the debris flow or the burst flood along the direction, unit: ; bed resistance of debris flow or burst flood along direction, unit: ; debris flow or a breached dam along directional velocity, units: ; debris flow or a break flood along directional velocity, unit: ; Density of debris flow or burst flood, unit: ; For computed debris flow or break flood depth, units: ; Kp is the pore water pressure coefficient of the material in the gully bed when the debris flow invades the gully, unit: dimensionless; Channel slope, unit: °; the friction angle of the channel material when eroded by a debris flow, in °; The cohesion of the channel granular material when the debris flow erodes the channel is: ; g is the gravitational acceleration, units: ; and / or Method for calculating the total erosion rate of channel bed sediment by a breaching flood is ； wherein is the total erosion rate of the channel bed sediment by the breaking flood, in units of: ; For the resistance of the flood bottom, unit: ; bottom shear for a breach flood along the direction of flow, units: ; bed resistance in the direction of the flood flow, units: ;​ To the erosion resistance of the channel bed material during the process of the breach flood, unit: ; For the coefficient of experience of the flood erosion, unit: .

6. The numerical simulation method of debris flow dam-break-flood routing disaster chain according to claim 1, characterized in that, The transport equation for fine and coarse particles and The calculation method is: ； ； wherein is the settling velocity of the fine particles in the flood flow, in units of: ; To the deposition rate of coarse particles in the movement of a breach flood, unit: ; is the volume concentration of coarse particles in a debris flow or a burst flood, dimensionless; is the volume concentration of fine particles in a debris flow or a burst flood, dimensionless; is an empirical parameter having a value of 2.0-5.0, dimensionless; Γ is a transition factor of the breaching flood to the debris flow, unit: dimensionless; The settling velocity of fine particles in the movement of a breach flood is: The calculation formula is: ； wherein is the kinematic viscosity of the water, in units of ; Representative particle size of fine particles during the movement of a flood caused by a breach; unit: ; D is the density of the fine-grained material of a debris flow or a break flood, in kg / m3 ; Density of clear water, units: ; g is the gravitational acceleration, unit: ; The settling velocity of coarse particles in the movement of a breach flood is: The calculation formula is: ； wherein is the kinematic viscosity of the water, in units of ; D50 is the median diameter of the coarse fraction of the sediment, in meters. ; Dd density of coarse-grained material of a debris flow or a break flood, unit: ; For the density of the clear water, units: ; g is the gravitational acceleration, unit: .

7. The numerical simulation method of debris flow dam-break-flood routing disaster chain according to claim 3, characterized in that, Medium grain single-width sediment transport rate along x direction and along y direction The calculation methods are respectively: ； ； In the formula, For mudslides or breach floods along Flow rate per unit width in each direction, unit: ; Direction of flow of debris flow or burst flood along Unit: m3 / s / m ; For the coarse fraction, the single-width sediment discharge rate is given by: The formula is: ； wherein is the Froude number of the fluid, dimensionless; Depth of debris flow or burst flood flow, unit: ; debris flow or a flood along directional velocity, unit: ; flow velocity of the debris flow or the burst flood in the direction of the flow, unit: flow velocity of the debris flow or the burst flood in the direction of the flow, unit: flow velocity of the debris flow or the burst flood in the direction of the flow, unit: is the dimensionless bed shear stress, i.e. the Shields number; bed resistance of debris flow or burst flood along direction, unit: ; bed resistance of a debris flow or a burst flood in the direction of flow, unit: bed resistance of a debris flow or a burst flood in the direction of flow, unit: bed resistance of a debris flow or a burst flood in the direction of flow, unit: D the density of the coarse-grained material of a debris flow or a break flood, unit: ; Density of clear water, units: ; D50 is the median diameter of the coarse fraction of the sediment, in meters. ; g is the gravitational acceleration, unit: ; Hill number of criticality, dimensionless, calculated as ； wherein is an empirical coefficient, dimensionless; Channel slope, unit: °; Fb is the friction angle between the channel materials when the channel is being eroded by a flood, in degrees.

8. The numerical simulation method of debris flow dam-break-flood routing disaster chain according to claim 2, characterized in that, and the bed resistance of a mudflow or a break flood along the direction of the bed resistance of a mudflow or a break flood along the direction of the calculation formula is: ； ； In the formula, Density of debris flow or bursting flood: ; is the volume concentration of water in a debris flow or a burst flood, dimensionless; is the volume concentration of coarse particles in a debris flow or a burst flood, dimensionless; is the volume concentration of fine particles in a debris flow or a burst flood, dimensionless; D is the density of the granular material in the debris flow or the burst flood, in kg / m3; ; Density of clear water, units: ; For the roughness coefficient in the process of flood routing, unit: ; Depth of debris flow or burst flood flow, unit: ; For mudslides or breach floods along Flow rate per unit width in each direction, unit: ; , the single width flow of debris flow or burst flood along direction, unit: ; to flow along directional velocity, units: ; flow velocity of the debris flow or the burst flood along the direction, unit: ; Γ is a transition factor of the breaching flood to the debris flow, unit: dimensionless; and are the bed resistance of the debris flow or the flood flow slurry along the direction and direction, respectively, in units of: ; and are the bed resistance of the coarse particles of a debris flow or a breaching flood along the direction and direction, respectively, in units of: ; g is the gravitational acceleration, unit: ; Debris flow or outburst flood liquid phase slurry along directional bed resistance and directional bed resistance The calculation formulas are as follows: ； ； In the formula, is the flow depth of the debris flow or the burst flood, unit: ; debris flow or a break flood along directional velocity, unit: ; flow rate of the debris flow or the burst flood along the direction, unit: ; Power viscosity of the clear water, unit: Pa-s; Vp represents the volume concentration of fine particulate matter in the liquid slurry, dimensionless; is the maximum allowable volume concentration of fine-grained sediments in the liquid slurry, dimensionless, calculated as: ； wherein, and Dp and Mp represent the diameter and the mass percentage of the i-th size class of fine sediment, respectively, dimensionless units. i Dp and Mp represent the diameter and the mass percentage of the i-th size class of fine sediment, respectively, dimensionless units. S v0 is the critical volume fraction at which the fluid transitions from a Newtonian fluid to a Bingham fluid, dimensionless, calculated as ； k 0 is a correction factor of one, dimensionless, expressed as: ； Debris flow or flood outburst: coarse particles along directional bed resistance and directional bed resistance The calculation formulas are as follows: ； ； In the formula, For coarse particles in debris flows or outburst floods Resistance to motion in the direction of motion, unit: ; for the movement of coarse particles in a debris flow or a burst flood in the direction of the flow, unit: ;​ Density of debris flow or burst flood, unit: ; Density of the liquid phase slurry consisting of fine particles and water, units: ; is the volume concentration of water in a debris flow or a burst flood, dimensionless; is the volume concentration of coarse particles in a debris flow or a burst flood, dimensionless; is the volume concentration of fine particles in a debris flow or a burst flood, dimensionless; D is the density of the granular material in the debris flow or the burst flood, in kg / m3; ; For the density of the clear water, units: ; Direction of debris flow or flood along Unit: m / s ; Direction of debris flow or flood along Unit: m / s ; debris flow or a break flood along directional velocity, unit: ; flow velocity of the debris flow or the burst flood in the direction of the flow, unit: flow velocity of the debris flow or the burst flood in the direction of the flow, unit: flow velocity of the debris flow or the burst flood in the direction of the flow, unit: Depth of debris flow or burst flood flow, unit: ; for debris flow or breached flood bed along slope of direction, unit: °; for a debris flow bed along slope of the direction, unit: °; is the friction angle of the bed material, in °; is the turbulent coefficient of the coarse-grained material of the debris flow, unit: ; g is the gravitational acceleration, unit: .

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