CN110232165B - A Calculation Method of Maximum Deposition Thickness of Viscous Debris Flow - Google Patents

Abstract

The invention discloses a method for calculating the maximum deposition thickness of a viscous debris flow, which belongs to the technical field of debris flow prevention and control engineering, and is characterized in that it comprises the following steps: a, calculating the yield stress τ of the debris flow, b, analyzing the particle composition of the debris flow, Calculate the equivalent clay mineral percentage content P; c, calculate the volume concentration C ₀ of debris flow; d, calculate the yield stress τ of debris flow at different frequencies or adjacent watersheds. Calculate the maximum deposition thickness H of debris flow at different frequencies or in adjacent watersheds. Aiming at the problem that the debris flow yield stress of intermediate particles and the maximum deposition thickness of debris flow calculated therefrom are not considered in the existing calculation method, the present invention studies the influence of fine-grained clay minerals, coarse particles and intermediate particles, and can accurately calculate the yield stress , the maximum deposition thickness, thus providing an accurate basis for the design of debris flow prevention and control projects.

Description

A method for calculating the maximum sedimentation thickness of viscous debris flow

Technical Field

The invention relates to the technical field of debris flow prevention and control engineering, and in particular to a method for calculating the maximum siltation thickness of viscous debris flow.

Background Art

Most of the settlements such as towns and villages located in the alpine valley area are built on debris flow or mountain torrent accumulation fans, and most of the mountain roads and railways pass through debris flow accumulation fans. When the debris flow passes through the debris flow flow area and flows out of the mountain pass into the accumulation area, the speed of the debris flow gradually slows down due to the gentle slope and widening of the ditch, and siltation is formed in the accumulation area, causing damage. For example, after the Wenchuan earthquake, a large-scale debris flow broke out in Xishanpogou near the old county town of Beichuan on September 24, 2008. After the debris flow entered the old county town of Beichuan, it accumulated with a maximum thickness of 12m; on August 13, 2010, a huge debris flow disaster broke out in Wenjiagou, Qingping Township, Mianzhu City, Sichuan Province. The maximum siltation thickness of the debris flow in the Mianyuan River exceeded 15m, and more than 300 acres of farmland were destroyed. It can be seen that siltation is one of the main forms of debris flow disasters. The siltation thickness of debris flow is one of the most important parameters of debris flow, and it is also one of the most important parameters for debris flow disaster assessment and prevention.

The thickness of debris flow is determined by the nature of debris flow and the slope of the sedimentation area. A specific debris flow has a certain maximum sedimentation thickness at a specific slope. In addition to the specific factors of the sedimentation area, the key factors that determine the maximum sedimentation thickness of debris flow are the debris flow properties: the bulk density of debris flow and the yield stress of debris flow. At present, there are two main methods for calculating the yield stress of debris flow at home and abroad: 1) Research based on fine particles, taking into account the characteristics of different clay minerals, and giving a calculation formula for debris flow, but this method has not considered the role of coarse particles, and there are errors in the calculation of the yield stress of debris flow containing coarse particles, and there is an undetermined coefficient; 2) The role of coarse particles is considered, but the role of clay minerals of fine particles is not considered, and there are 3 undetermined coefficients; 3) The role of fine and coarse particles is considered, but the role of intermediate particles between coarse particles and fine particles is not considered. The particle size of the intermediate particles is between 0.005mm-0.20mm.

The yield stress of debris flow is determined by the nature of the debris flow itself. The volume concentration of sediment, clay mineral composition and content, size of coarse particles, and gradation distribution in the debris flow will affect the yield stress of the debris flow. The equivalent clay mineral percentage P in the debris flow is related to the content of clay minerals such as montmorillonite, illite, kaolin, chlorite, and bentolite contained in the debris flow. Most of them contain two or more clay mineral components in nature, which is also related to the origin, weathering degree, geological background, etc. of these clay minerals. However, the existing technology cannot determine the exact content of various clay minerals, let alone distinguish the differences between the same types of clay minerals in different regions, so it is impossible to determine the equivalent clay mineral percentage P in the debris flow. Therefore, it is impossible to accurately calculate the yield stress of debris flow at different frequencies, and then calculate the maximum siltation thickness of the debris flow.

A Chinese patent document with publication number CN 104809345A and publication date July 29, 2015 discloses a method for calculating the yield stress and maximum siltation thickness of a debris flow, which is characterized in that it includes the following steps: determining the equivalent clay mineral percentage P in the debris flow according to existing debris flow surveys, setting the equivalent clay mineral percentage P of the debris flow in the basin unchanged; calculating the debris flow volume concentration _C0 value according to the debris flow bulk density value of the debris flow at different frequencies, or the debris flow bulk density value of the adjacent basin; and then calculating the debris flow yield stress τ and the maximum siltation thickness H at different frequencies or in adjacent basins according to the Cc value and dv value of the particle grading and the equivalent clay mineral percentage P calculated above.

The calculation method for the yield stress and maximum siltation thickness of debris flow disclosed in this patent document takes into account the influence of coarse particles, but does not take into account the role of intermediate particles between coarse particles and fine particles in the yield stress of debris flow. The calculated yield stress is too small, and the maximum siltation thickness is also too small, which cannot provide an accurate basis for the design of debris flow prevention and control projects.

Summary of the invention

In order to overcome the defects of the above-mentioned prior art, the present invention provides a method for calculating the maximum siltation thickness of viscous debris flow. The present invention aims at the problem that the debris flow yield stress of intermediate particles and the maximum siltation thickness of the debris flow calculated thereby are not considered in the existing calculation method, and the influence of fine-grained clay minerals, coarse particles and intermediate particles is studied. The yield stress and the maximum siltation thickness can be accurately calculated, thereby providing an accurate basis for the design of debris flow prevention and control projects.

The present invention is achieved through the following technical solutions:

A method for calculating the maximum siltation thickness of a viscous debris flow, characterized in that it comprises the following steps:

a. Investigate the maximum sedimentation thickness H of the existing debris flow, the bottom slope of the debris flow θ, and the bulk density ρ of the debris flow, and calculate the yield stress τ of the debris flow according to formula 1.

τ＝ρgH sinθ Formula 1

H——maximum sediment thickness of debris flow, m;

τ——debris flow yield stress, Pa;

ρ——debris flow bulk density, kg/m ³ ;

g——acceleration due to gravity, g=9.81m/ ^s2 ;

θ——slope of the bottom slope of debris flow deposition, degrees;

b. Analyze the particle composition of the debris flow, and obtain the percentage X of intermediate particles, the percentage Y of coarse particles, Cd value, S value, Cc value and dv value, _d30 , _d10 , _d50 and _d60 values corresponding to coarse particles and intermediate particles, and volume concentration _C0 value, which are calculated by formula 8, the C value is calculated by formula 3, formula 4 and formula 6, and the equivalent clay mineral percentage content P is calculated by formula 2;

τ＝τ ₀ C ² e ^22CP Formula 2

C＝C ₀ (Xa+Yb) Formula 3

b＝1.14C _d ^0.14 (S/6.61) ^-0.012 Equation 6

S＝πd ₅₀ ² /ψ Formula 7

in:

τ——debris flow yield stress, Pa;

τ ₀ ——empirical coefficient, Pa;

C——equivalent sediment volume concentration, calculated by formula 3;

P——equivalent clay mineral percentage;

a——Correction coefficient 1, calculated by formula 4;

b——Correction coefficient 2, calculated by formula 6;

C ₀ —— sediment volume concentration;

Cc is the curvature coefficient of coarse-grained sediment, which is calculated by formula 5, where d ₃₀ , d ₁₀ and d ₆₀ are the values of coarse particles, respectively;

C _c '——coarse-grained effective sediment curvature coefficient;

_Ce ——curvature coefficient of sediment of intermediate particles, calculated by formula 5, where _d30 , _d10 and _d60 are the values of intermediate particles respectively;

C _d ——effective sediment curvature coefficient of intermediate particles;

d _v ——volume average particle size of coarse sediment particles, mm;

C _c0 ——constant 1, C _c0 = 0.523;

d _v0 ——constant 2, d _v0 =1.23mm;

d ₃₀ —— particle size of sediment particles that account for less than 30% of the coarse sediment, mm;

d ₁₀ —— particle size of sediment particles that account for less than 10% of the coarse sediment, mm;

_d50 ——the particle size of sediment particles that is less than 50% in coarse sediment, mm;

_d60 ——the particle size of sediment particles that is less than 60% in coarse sediment, mm;

S——average surface area of intermediate particles, mm ² ; calculated by formula 7;

π——pi, the value is 3.1416;

ψ——sphericity value of intermediate particles, ψ＝0.72;

C ₁ ——constant three, C ₁ = 0.18;

C ₂ ——Constant 4, C ₂ =-0.01;

X——the percentage of intermediate particles in particles other than clay particles;

Y——the percentage of coarse particles in particles other than clay particles;

c. According to the bulk density of the debris flow at different frequencies or the bulk density of the debris flow in the adjacent basin, the debris flow volume concentration _C0 value is calculated by formula 8;

in:

ρ ₀ ——Specific gravity of water, ρ ₀ = 1000kg/m ³ ;

ρ _S ——bulk density of solid particles in debris flow, ρ _S = 2700kg/m ³ ;

d. Then, according to the X value, Y value, Cd value, S value, Cc value and dv value of the intermediate and coarse particle grading and the _d30 , _d10 , _d50 and _d60 values corresponding to the coarse and intermediate particles, the equivalent clay mineral percentage P is calculated, and the debris flow yield stress τ at different frequencies or in adjacent basins is calculated by formula 2. Then, according to formula 1 and the debris flow yield stress τ, the debris flow siltation bottom slope θ at the location, and the debris flow bulk density ρ at different frequencies or in adjacent basins, the maximum debris flow siltation thickness H at different frequencies or in adjacent basins is calculated.

In the step b, when 0.59≥C＞0.47, τ ₀ is 30e ^5(C-0.47) Pa; when C＞0.59, τ ₀ is 30e ^{5(C -0.47)} e ^8(C-0.59) Pa.

In the step b, when Cc≤1, Cc'=Cc; when Cc＞1, Cc'=1/Cc.

In the step b, when Ce≤1, Cd=Ce; when Ce＞1, Cd=1/Ce.

In the step c, the adjacent basins specifically refer to basins having the same geological background and assuming that the equivalent clay mineral percentage P in the debris fluid is the same.

The fine particles refer to particles with a particle size less than 0.005 mm, the intermediate particles refer to particles with a particle size between 0.005 mm and 0.2 mm, and the coarse particles refer to particles with a particle size greater than 0.2 mm.

The basic principles of the present invention are as follows:

The equivalent clay mineral percentage P in debris flow needs to be determined first based on the existing debris flow survey, and the equivalent clay mineral percentage P of the debris flow in the basin is set unchanged, and then the new yield stress and maximum sedimentation thickness are calculated based on the change in bulk density of the debris flow, or the debris flow yield stress and maximum sedimentation thickness of the adjacent basin are calculated.

The beneficial effects of the present invention are mainly manifested in the following aspects:

1. The present invention, "a. Investigate the maximum siltation thickness H of the existing debris flow, the slope of the debris flow bottom slope θ, and the bulk density ρ of the debris flow, and calculate the yield stress τ of the debris flow according to Formula 1; b. Analyze the particle composition of the debris flow, and respectively obtain the percentage X of intermediate particles, the percentage Y of coarse particles, the Cd value, the S value, the Cc value and the dv value, the _d30 , _d10 , _d50 and _d60 values corresponding to the coarse particles and the intermediate particles, and the volume concentration _C0 value, which are calculated by Formula 8, and the C value is calculated by Formula 3, Formula 4 and Formula 6, and the equivalent clay mineral percentage P is calculated by Formula 2; c. According to the bulk density of the debris flow at different frequencies of the debris flow or the bulk density of the debris flow in the adjacent basin, the volume concentration C of the debris flow is calculated by Formula 8 ₀ value; d, then according to the X value, Y value, Cd value, S value, Cc value and dv value of the intermediate and coarse particle grading and the d ₃₀ , d ₁₀ , d ₅₀ , d ₆₀ values corresponding to the coarse particles and the intermediate particles, the equivalent clay mineral percentage P is calculated, and the debris flow yield stress τ at different frequencies or in adjacent basins is calculated by formula 2. Then, by formula 1 and the debris flow yield stress τ, the debris flow siltation bottom slope θ at the location, and the debris flow bulk density ρ at different frequencies or in adjacent basins, the maximum siltation thickness H" of the debris flow at different frequencies or in adjacent basins is calculated. Compared with the existing technology, through a large number of innovative studies, the intermediate particle sediment curvature coefficient Ce and the coarse particle sediment median particle size d ₅₀ and the yield stress of debris flow; Debris flow slurry is mainly clay, and viscosity is also provided by it; The particle size of coarse particles also has an important influence on yield stress; The better the structure of debris flow, the greater the shear strength, and the greater its yield stress; If the particle size of coarse particles is large, it will be difficult for the coarse particles to form a network structure because the viscosity is less than their own gravity; In addition, the larger the particle size, the smaller the specific surface area, and the smaller the adhesion of the coarse particles. These factors will have a certain impact on the yield stress. Therefore, the larger the particle size of the coarse particles, the smaller the yield stress of the debris flow; In view of the problem that the debris flow yield stress of the intermediate particles and the maximum sedimentation thickness of the debris flow calculated by the existing calculation method are not considered, the influence of fine clay minerals, coarse particles and intermediate particles is studied, and the yield stress and maximum sedimentation thickness can be accurately calculated, thereby providing an accurate basis for the design of debris flow prevention and control projects.

2. In the present invention, the intermediate particles in the debris flow have similar effects to the coarse particles, but because the intermediate particles are much smaller than the coarse particles, only using the characteristics of the coarse particles to represent the characteristics of all particles other than the fine particles underestimates the role of the intermediate particles, and also underestimates the yield stress and maximum sedimentation thickness of the debris flow. By introducing the role of the intermediate particles, the important role of the intermediate particles in the structural properties and network structure of the debris flow is reflected, making the calculation of the maximum sedimentation thickness of the debris flow more accurate. The expressions of Formula 6 and Formula 7 are the embodiment of this relationship.

3. The present invention further solves the defects of the existing formulas and methods for calculating the yield stress and maximum siltation thickness of debris flows, while taking into account the influence of fine particles and coarse particles in the debris flow, especially the important influence of intermediate particles, and can more accurately calculate the maximum siltation thickness of debris flows occurring at different frequencies or in adjacent basins, providing effective technical support for the assessment and prevention of debris flow disasters.

DETAILED DESCRIPTION

Example 1

A method for calculating the maximum siltation thickness of a viscous debris flow comprises the following steps:

a. Investigate the maximum sedimentation thickness H of the existing debris flow, the bottom slope of the debris flow θ, and the bulk density ρ of the debris flow, and calculate the yield stress τ of the debris flow according to formula 1.

τ＝ρgH sinθ Formula 1

H——maximum sediment thickness of debris flow, m;

τ——debris flow yield stress, Pa;

ρ——debris flow bulk density, kg/m ³ ;

g——acceleration due to gravity, g=9.81m/ ^s2 ;

θ——slope of the bottom slope of debris flow deposition, degrees;

b. Analyze the particle composition of the debris flow, and obtain the percentage X of intermediate particles, the percentage Y of coarse particles, Cd value, S value, Cc value and dv value, _d30 , _d10 , _d50 and _d60 values corresponding to coarse particles and intermediate particles, and volume concentration _C0 value, which are calculated by formula 8, the C value is calculated by formula 3, formula 4 and formula 6, and the equivalent clay mineral percentage content P is calculated by formula 2;

τ＝τ ₀ C ² e ^22CP Formula 2

C＝C ₀ (Xa+Yb) Formula 3

b＝1.14C _d ^0.14 (S/6.61) ^-0.012 Equation 6

S＝πd ₅₀ ² /ψ Formula 7

in:

τ——debris flow yield stress, Pa;

τ ₀ ——empirical coefficient, Pa;

C——equivalent sediment volume concentration, calculated by formula 3;

P——equivalent clay mineral percentage;

a——Correction coefficient 1, calculated by formula 4;

b——Correction coefficient 2, calculated by formula 6;

C ₀ —— sediment volume concentration;

Cc is the curvature coefficient of coarse-grained sediment, which is calculated by formula 5, where d ₃₀ , d ₁₀ and d ₆₀ are the values of coarse particles, respectively;

C _c '——coarse-grained effective sediment curvature coefficient;

_Ce ——curvature coefficient of sediment of intermediate particles, calculated by formula 5, where _d30 , _d10 and _d60 are the values of intermediate particles respectively;

C _d ——effective sediment curvature coefficient of intermediate particles;

d _v ——volume average particle size of coarse sediment particles, mm;

C _c0 ——constant 1, C _c0 = 0.523;

d _v0 ——constant 2, d _v0 =1.23mm;

_d30 ——the particle size of sediment particles that accounts for less than 30% of the coarse sediment, mm;

d ₁₀ —— particle size of sediment particles that account for less than 10% of the coarse sediment, mm;

_d50 ——the particle size of sediment particles that is less than 50% in coarse sediment, mm;

_d60 ——the particle size of sediment particles that is less than 60% in coarse sediment, mm;

S——average surface area of intermediate particles, mm ² ; calculated by formula 7;

π——pi, the value is 3.1416;

ψ——sphericity value of intermediate particles, ψ＝0.72;

C ₁ ——constant three, C ₁ = 0.18;

C ₂ ——Constant 4, C ₂ =-0.01;

X——the percentage of intermediate particles in particles other than clay particles;

Y——the percentage of coarse particles in particles other than clay particles;

c. According to the bulk density of the debris flow at different frequencies or the bulk density of the debris flow in the adjacent basin, the debris flow volume concentration _C0 value is calculated by formula 8;

in:

ρ ₀ ——Specific gravity of water, ρ ₀ = 1000kg/m ³ ;

ρ _S ——bulk density of solid particles in debris flow, ρ _S = 2700kg/m ³ ;

d. Then, according to the X value, Y value, Cd value, S value, Cc value and dv value of the intermediate and coarse particle grading and the _d30 , _d10 , _d50 and _d60 values corresponding to the coarse and intermediate particles, the equivalent clay mineral percentage P is calculated, and the debris flow yield stress τ at different frequencies or in adjacent basins is calculated by formula 2. Then, according to formula 1 and the debris flow yield stress τ, the debris flow siltation bottom slope θ at the location, and the debris flow bulk density ρ at different frequencies or in adjacent basins, the maximum debris flow siltation thickness H at different frequencies or in adjacent basins is calculated.

"a. Investigate the maximum siltation thickness H of the existing debris flow, the slope of the debris flow bottom slope θ, and the bulk density ρ of the debris flow, and calculate the yield stress τ of the debris flow according to Formula 1. b. Analyze the particle composition of the debris flow, and obtain the percentage X of intermediate particles, the percentage Y of coarse particles, Cd value, S value, Cc value and dv value of particles other than fine particles, the _d30 , _d10 , _d50 and _d60 values corresponding to coarse particles and intermediate particles, and the volume concentration _C0 value, which are calculated by Formula 8. The C value is calculated by Formula 3, Formula 4 and Formula 6, and the equivalent clay mineral percentage P is calculated by Formula 2; c. According to the bulk density of the debris flow at different frequencies of this debris flow or the bulk density of the debris flow in the adjacent basin, the volume concentration C of the debris flow is calculated by Formula 8 ₀ value; d, then according to the X value, Y value, Cd value, S value, Cc value and dv value of the intermediate and coarse particle grading and the d ₃₀ , d ₁₀ , d ₅₀ , d ₆₀ values corresponding to the coarse particles and the intermediate particles, the equivalent clay mineral percentage P is calculated, and the debris flow yield stress τ at different frequencies or in adjacent basins is calculated by formula 2. Then, by formula 1 and the debris flow yield stress τ, the debris flow siltation bottom slope θ at the location, and the debris flow bulk density ρ at different frequencies or in adjacent basins, the maximum siltation thickness H" of the debris flow at different frequencies or in adjacent basins is calculated. Compared with the existing technology, through a large number of innovative studies, the intermediate particle sediment curvature coefficient Ce and the coarse particle sediment median particle size d ₅₀ and the yield stress of debris flow; the debris flow slurry is mainly clay, and the viscosity is also provided by it; the particle size of coarse particles also has an important influence on the yield stress; the better the structure of the debris flow, the greater the shear strength, and the greater its yield stress; if the coarse particle size is large, it will be difficult for the coarse particles to form a network structure because the viscosity is less than their own gravity; in addition, the larger the particle size, the smaller the specific surface area, and the smaller the adhesion of the coarse particles. These factors will have a certain impact on the yield stress. Therefore, the larger the coarse particle size, the smaller the yield stress of the debris flow; in view of the problem that the debris flow yield stress of the intermediate particles and the maximum sedimentation thickness of the debris flow calculated by the existing calculation method are not considered, the influence of fine clay minerals, coarse particles and intermediate particles is studied, and the yield stress and maximum sedimentation thickness can be accurately calculated, thereby providing an accurate basis for the design of debris flow prevention and control projects.

Example 2

A method for calculating the maximum siltation thickness of a viscous debris flow comprises the following steps:

a. Investigate the maximum sedimentation thickness H of the existing debris flow, the bottom slope of the debris flow θ, and the bulk density ρ of the debris flow, and calculate the yield stress τ of the debris flow according to formula 1.

τ＝ρgH sinθ Formula 1

H——maximum sediment thickness of debris flow, m;

τ——debris flow yield stress, Pa;

ρ——debris flow bulk density, kg/m ³ ;

g——acceleration due to gravity, g=9.81m/ ^s2 ;

θ——slope of the bottom slope of debris flow deposition, degrees;

b. Analyze the particle composition of the debris flow, and obtain the percentage X of intermediate particles, the percentage Y of coarse particles, Cd value, S value, Cc value and dv value, _d30 , _d10 , _d50 and _d60 values corresponding to coarse particles and intermediate particles, and volume concentration _C0 value, which are calculated by formula 8, the C value is calculated by formula 3, formula 4 and formula 6, and the equivalent clay mineral percentage content P is calculated by formula 2;

τ＝τ ₀ C ² e ^22CP Formula 2

C＝C ₀ (Xa+Yb) Formula 3

b＝1.14C _d ^0.14 (S/6.61) ^-0.012 Equation 6

S＝πd ₅₀ ² /ψ Formula 7

in:

τ——debris flow yield stress, Pa;

τ ₀ ——empirical coefficient, Pa;

C——equivalent sediment volume concentration, calculated by formula 3;

P——equivalent clay mineral percentage;

a——Correction coefficient 1, calculated by formula 4;

b——Correction coefficient 2, calculated by formula 6;

C ₀ —— sediment volume concentration;

Cc is the curvature coefficient of coarse-grained sediment, which is calculated by formula 5, where d ₃₀ , d ₁₀ and d ₆₀ are the values of coarse particles, respectively;

C _c '——coarse-grained effective sediment curvature coefficient;

_Ce ——curvature coefficient of sediment of intermediate particles, calculated by formula 5, where _d30 , _d10 and _d60 are the values of intermediate particles respectively;

C _d ——effective sediment curvature coefficient of intermediate particles;

d _v ——volume average particle size of coarse sediment particles, mm;

C _c0 ——constant 1, C _c0 = 0.523;

d _v0 ——constant 2, d _v0 =1.23mm;

d ₃₀ —— particle size of sediment particles that account for less than 30% of the coarse sediment, mm;

d ₁₀ —— particle size of sediment particles that account for less than 10% of the coarse sediment, mm;

_d50 ——the particle size of sediment particles that is less than 50% in coarse sediment, mm;

_d60 ——the particle size of sediment particles that is less than 60% in coarse sediment, mm;

S——average surface area of intermediate particles, mm ² ; calculated by formula 7;

π——pi, the value is 3.1416;

ψ——sphericity value of intermediate particles, ψ＝0.72;

C ₁ ——constant three, C ₁ = 0.18;

C ₂ ——Constant 4, C ₂ =-0.01;

X——the percentage of intermediate particles in particles other than clay particles;

Y——the percentage of coarse particles in particles other than clay particles;

c. According to the bulk density of the debris flow at different frequencies or the bulk density of the debris flow in the adjacent basin, the debris flow volume concentration _C0 value is calculated by formula 8;

in:

ρ ₀ ——Specific gravity of water, ρ ₀ = 1000kg/m ³ ;

ρ _S ——bulk density of solid particles in debris flow, ρ _S = 2700kg/m ³ ;

d. Then, according to the X value, Y value, Cd value, S value, Cc value and dv value of the intermediate and coarse particle grading and the _d30 , _d10 , _d50 and _d60 values corresponding to the coarse and intermediate particles, the equivalent clay mineral percentage P is calculated, and the debris flow yield stress τ at different frequencies or in adjacent basins is calculated by formula 2. Then, according to formula 1 and the debris flow yield stress τ, the debris flow siltation bottom slope θ at the location, and the debris flow bulk density ρ at different frequencies or in adjacent basins, the maximum debris flow siltation thickness H at different frequencies or in adjacent basins is calculated.

In the step b, when 0.59≥C＞0.47, τ ₀ is 30e ^5(C-0.47) Pa; when C＞0.59, τ ₀ is 30e ^{5(C -0.47)} e ^8(C-0.59) Pa.

In the step b, when Cc≤1, Cc'=Cc; when Cc＞1, Cc'=1/Cc.

In the step b, when Ce≤1, Cd=Ce; when Ce＞1, Cd=1/Ce.

The intermediate particles in debris flow have similar effects as coarse particles, but because the intermediate particles are much smaller than the coarse particles, using only the characteristics of coarse particles to represent the characteristics of all particles other than fine particles underestimates the role of the intermediate particles and the yield stress and maximum deposition thickness of debris flow. By introducing the role of intermediate particles, the important role of intermediate particles in the structural and network structure of debris flow is reflected, making the calculation of the maximum deposition thickness of debris flow more accurate. The expressions of Equations 6 and 7 are the embodiment of this relationship.

Example 3

A method for calculating the maximum siltation thickness of a viscous debris flow comprises the following steps:

a. Investigate the maximum sedimentation thickness H of the existing debris flow, the bottom slope of the debris flow θ, and the bulk density ρ of the debris flow, and calculate the yield stress τ of the debris flow according to formula 1.

τ＝ρgH sinθ Formula 1

H——maximum sediment thickness of debris flow, m;

τ——debris flow yield stress, Pa;

ρ——debris flow bulk density, kg/m ³ ;

g——acceleration due to gravity, g=9.81m/ ^s2 ;

θ——slope of the bottom slope of debris flow deposition, degrees;

b. Analyze the particle composition of the debris flow, and obtain the percentage X of intermediate particles, the percentage Y of coarse particles, Cd value, S value, Cc value and dv value, _d30 , _d10 , _d50 and _d60 values corresponding to coarse particles and intermediate particles, and volume concentration _C0 value, which are calculated by formula 8, the C value is calculated by formula 3, formula 4 and formula 6, and the equivalent clay mineral percentage content P is calculated by formula 2;

τ＝τ ₀ C ² e ^22CP Formula 2

C＝C ₀ (Xa+Yb) Formula 3

b＝1.14C _d ^0.14 (S/6.61) ^-0.012 Equation 6

S＝πd ₅₀ ² /ψ Formula 7

in:

τ——debris flow yield stress, Pa;

τ ₀ ——empirical coefficient, Pa;

C——equivalent sediment volume concentration, calculated by formula 3;

P——equivalent clay mineral percentage;

a——Correction coefficient 1, calculated by formula 4;

b——Correction coefficient 2, calculated by formula 6;

C ₀ —— sediment volume concentration;

Cc is the curvature coefficient of coarse-grained sediment, which is calculated by formula 5, where d ₃₀ , d ₁₀ and d ₆₀ are the values of coarse particles, respectively;

C _c '——coarse-grained effective sediment curvature coefficient;

_Ce ——curvature coefficient of sediment of intermediate particles, calculated by formula 5, where _d30 , _d10 and _d60 are the values of intermediate particles respectively;

C _d ——effective sediment curvature coefficient of intermediate particles;

d _v ——volume average particle size of coarse sediment particles, mm;

C _c0 ——constant 1, C _c0 = 0.523;

d _v0 ——constant 2, d _v0 =1.23mm;

_d30 ——the particle size of sediment particles that accounts for less than 30% of the coarse sediment, mm;

d ₁₀ —— particle size of sediment particles that account for less than 10% of the coarse sediment, mm;

_d50 ——the particle size of sediment particles that is less than 50% in coarse sediment, mm;

_d60 ——the particle size of sediment particles that is less than 60% in coarse sediment, mm;

S——average surface area of intermediate particles, mm ² ; calculated by formula 7;

π——pi, the value is 3.1416;

ψ——sphericity value of intermediate particles, ψ＝0.72;

C ₁ ——constant three, C ₁ = 0.18;

C ₂ ——Constant 4, C ₂ =-0.01;

X——the percentage of intermediate particles in particles other than clay particles;

Y——the percentage of coarse particles in particles other than clay particles;

c. According to the bulk density of the debris flow at different frequencies or the bulk density of the debris flow in the adjacent basin, the debris flow volume concentration _C0 value is calculated by formula 8;

in:

ρ ₀ ——Specific gravity of water, ρ ₀ = 1000kg/m ³ ;

ρ _S ——bulk density of solid particles in debris flow, ρ _S = 2700kg/m ³ ;

d. Then, according to the X value, Y value, Cd value, S value, Cc value and dv value of the intermediate and coarse particle grading and the _d30 , _d10 , _d50 and _d60 values corresponding to the coarse and intermediate particles, the equivalent clay mineral percentage P is calculated, and the debris flow yield stress τ at different frequencies or in adjacent basins is calculated by formula 2. Then, according to formula 1 and the debris flow yield stress τ, the debris flow siltation bottom slope θ at the location, and the debris flow bulk density ρ at different frequencies or in adjacent basins, the maximum debris flow siltation thickness H at different frequencies or in adjacent basins is calculated.

In the step b, when 0.59≥C＞0.47, τ ₀ is 30e ^5(C-0.47) Pa; when C＞0.59, τ ₀ is 30e ^{5(C -0.47)} e ^8(C-0.59) Pa.

In the step b, when Cc≤1, Cc'=Cc; when Cc＞1, Cc'=1/Cc.

In the step b, when Ce≤1, Cd=Ce; when Ce＞1, Cd=1/Ce.

In the step c, the adjacent basins specifically refer to basins having the same geological background and assuming that the equivalent clay mineral percentage P in the debris fluid is the same.

The fine particles refer to particles with a particle size less than 0.005 mm, the intermediate particles refer to particles with a particle size between 0.005 mm and 0.2 mm, and the coarse particles refer to particles with a particle size greater than 0.2 mm.

It solves the defects of the existing formulas and methods for calculating the yield stress and maximum sedimentation thickness of debris flows, and takes into account the influence of fine and coarse particles in debris flows, especially the important influence of intermediate particles. It can more accurately calculate the maximum sedimentation thickness of debris flows occurring at different frequencies or in adjacent basins, and provide effective technical support for the assessment and prevention of debris flow disasters.

The following describes the embodiments of the present invention in detail with reference to specific examples:

From June 2015 to December 2018, a field survey was conducted on debris flow gullies in Li County, Wenchuan County, Sichuan Province, and Linzhi District, Tibet, and some basic parameters and siltation thickness data of debris flow basins were obtained (see Table 1).

19 debris flow gullies were investigated in Linzhi, Tibet. The field survey of Tianmogou in Basu County showed that the thickness of debris flow siltation was 2.7m, the siltation slope was 4.5°, the bulk density was calculated to be 2.12g/ ^cm3 , the yield stress was calculated to be 4380pa, and the equivalent clay content value P was 0.125. 15 debris flow gullies were investigated in Xuecheng Town, Li County, Sichuan Province. The field survey of Sunjiagou showed that the thickness of debris flow siltation was 2.6m, the siltation slope was 5.6°, the bulk density was calculated to be 2.16g/ ^cm3 , the yield stress was calculated to be 5371pa, and the equivalent clay content P0 was 0.132. 5 debris flow gullies were investigated in Wenchuan County, Sichuan Province. The field survey of Mozigou in Yingxiu Town showed that the thickness of debris flow siltation was 2.5m, the siltation slope was 6°, and the bulk density was calculated to be 2.15g/ ^cm3 , the yield stress is calculated to be 5506pa, and the equivalent clay content P is 0.127. According to the P values obtained in each region, the maximum sedimentation thickness of other debris flows in each region can be calculated respectively, including 18 ditches in Linzhi, Tibet, 14 ditches in Xuecheng Town, Li County, Sichuan, and 4 ditches in Wenchuan County, Sichuan. Table 1 shows the main parameters of debris flows and the calculation and field investigation of the maximum sedimentation thickness.

Table 1

In Table 1: τ _c (Pa) is the debris flow yield stress calculated by Formula 2; τ _m (Pa) is the debris flow yield stress calculated by actual measurement; Hc (m) is the maximum sedimentation thickness of the debris flow calculated by Formula 1; Hm (m) is the maximum sedimentation thickness of the debris flow measured.

The calculation results in Table 1 show that the calculated maximum sedimentation thickness of debris flow in 36 debris flow ditches is within 10% of the measured value in 16 ditches, accounting for 44.4%; the error is between 10% and 20%, accounting for 50%; and the error is greater than 20% in only 2 ditches, accounting for 5.6%. In general, the error is small, which is consistent with the actual situation, indicating that the maximum sedimentation thickness calculation of viscous debris flow by the present invention is more accurate.

Claims (4)

1. A method for calculating the maximum siltation thickness of a viscous debris flow, characterized in that it comprises the following steps: a. Investigate the maximum sedimentation thickness H of the existing debris flow, the bottom slope of the debris flow θ, and the bulk density ρ of the debris flow, and calculate the yield stress τ of the debris flow according to formula 1. τ＝ρgHsinθ Formula 1 H——maximum sediment thickness of debris flow, m; τ——debris flow yield stress, Pa; ρ——debris flow bulk density, kg/m ³ ; g——acceleration due to gravity, g=9.81m/ ^s2 ; θ——slope of the bottom slope of debris flow deposition, degrees; b. Analyze the particle composition of the debris flow, and obtain the percentage X of intermediate particles, the percentage Y of coarse particles, Cd value, S value, Cc value and dv value, _d30 , _d10 , _d50 and _d60 values corresponding to coarse particles and intermediate particles, and the volume concentration _C0 value, which are calculated by formula 8, and the C value is calculated by formula 3, formula 4 and formula 6. The debris flow yield stress τ is calculated by formula 2; τ＝τ ₀ C ² e ^22CP Formula 2 C＝C ₀ (Xb+Ya) Formula 3

b＝1.14C _d ^0.14 (S/6.61) ^-0.012 Equation 6 S＝πd ₅₀ ² /ψ Formula 7 in: τ——debris flow yield stress, Pa; τ ₀ ——empirical coefficient, Pa; C——equivalent sediment volume concentration, calculated by formula 3; P——equivalent clay mineral percentage; a——Correction coefficient 1, calculated by formula 4; b——Correction coefficient 2, calculated by formula 6; C ₀ —— sediment volume concentration; Cc is the curvature coefficient of coarse-grained sediment, which is calculated by formula 5, where d ₃₀ , d ₁₀ and d ₆₀ are the values of coarse particles, respectively; C _c '——coarse-grained effective sediment curvature coefficient; _Ce ——curvature coefficient of sediment of intermediate particles, calculated by formula 5, where _d30 , _d10 and _d60 are the values of intermediate particles respectively; C _d ——effective sediment curvature coefficient of intermediate particles; d _v ——volume average particle size of coarse sediment particles, mm; C _c0 ——constant 1, C _c0 = 0.523; d _v0 ——constant 2, d _v0 =1.23mm; _d30 ——the particle size of sediment particles that accounts for less than 30% of the coarse sediment, mm; d ₁₀ —— particle size of sediment particles that account for less than 10% of the coarse sediment, mm; _d50 ——the particle size of sediment particles that is less than 50% in coarse sediment, mm; _d60 ——the particle size of sediment particles that is less than 60% in coarse sediment, mm; S——average surface area of intermediate particles, mm ² ; calculated by formula 7; π——pi, the value is 3.1416; ψ——sphericity value of intermediate particles, ψ＝0.72; C ₁ ——constant three, C ₁ = 0.18; C ₂ ——Constant 4, C ₂ =-0.01; X——the percentage of intermediate particles in particles other than clay particles; Y——the percentage of coarse particles in particles other than clay particles; c. According to the bulk density of the debris flow at different frequencies or the bulk density of the debris flow in the adjacent basin, the debris flow volume concentration _C0 value is calculated by formula 8;

in: ρ ₀ ——Specific gravity of water, ρ ₀ = 1000kg/m ³ ; ρ _S ——bulk density of solid particles in debris flow, ρ _S = 2700kg/m ³ ; d. Then, according to the X value, Y value, Cd value, S value, Cc value and dv value of the intermediate and coarse particle grading and the _d30 , _d10 , _d50 and _d60 values corresponding to the coarse and intermediate particles, the equivalent clay mineral percentage P is used to calculate the debris flow yield stress τ at different frequencies or in adjacent basins through formula 2. Then, according to formula 1 and the debris flow yield stress τ, the slope of the debris flow deposition bottom slope θ at the location, and the debris flow bulk density ρ at different frequencies or in adjacent basins, the maximum deposition thickness H of the debris flow at different frequencies or in adjacent basins is calculated. In the step b, when Cc≤1, Cc'=Cc; when Cc＞1, Cc'=1/Cc; In the step b, when Ce≤1, Cd=Ce; when Ce＞1, Cd=1/Ce. 2. A method for calculating the maximum siltation thickness of viscous debris flow according to claim 1, characterized in that: in the step b, when 0.59≥C＞0.47, τ ₀ is 30e ^5(C-0.47) Pa; when C＞0.59, τ ₀ is 30e ^5(C-0.47) e ^8(C-0.59) Pa. 3. A method for calculating the maximum siltation thickness of a viscous debris flow according to claim 1, characterized in that: in the step c, adjacent basins specifically refer to basins having the same geological background and setting the equivalent clay mineral percentage P in the debris flow to be the same. 4. A method for calculating the maximum siltation thickness of a viscous debris flow according to claim 1, characterized in that: the fine particles refer to particles with a particle size less than 0.005 mm, the intermediate particles refer to particles with a particle size between 0.005 mm and 0.2 mm, and the coarse particles refer to particles with a particle size greater than 0.2 mm.