A method for determining particle stress during the collapse process of underwater two-component particles

Abstract

This invention relates to a method for determining particle stress during the collapse process of an underwater two-component particle mass, including the calculation of the collision pressure, friction pressure, collision shear stress, and friction shear stress of the i-th particle component, in order to obtain the i-th particle component. i The pressure and shear stress of each particle component are used to determine the collision and friction pressures during the collapse of the two-component particles. This invention considers the dilatation and shear contraction effects and the influence of interstitial water, reflecting the different levels of resistance from water during the movement of different particle components. By considering the anisotropy between and within each component, as well as the influence of interstitial water, the prediction of the underwater collapse morphology of two-component particles is more accurate. By integrating inter-component particle interactions, anisotropic collisions, and dilatation and shear contraction friction, the invention reflects the particle separation phenomenon of small particles sinking and large particles floating during particle collapse.

Description

Technical Field

[0001] This invention relates to a method for determining particle stress during the collapse process of underwater two-component granular bodies, specifically applied to the determination of collision and frictional stresses of two-component particles in underwater particle flows. This method is used in landslide surge engineering design to determine the particle stress within the landslide body, belonging to the field of hydraulic engineering design techniques in water conservancy and marine engineering. Background Technology

[0002] Underwater slope instability often evolves into particle collapse flow, seriously threatening the safety of hydraulic and marine engineering projects. Its instability flow and sedimentation characteristics are significantly influenced by grain size distribution; however, the underlying mechanical mechanisms remain unclear. For example... Figure 3 The two-component particles on the left collapsed underwater, and each component gradually moved to the right, accompanied by component separation.

[0003] The determination of particle stress widely used in engineering is mainly based on the derivation of rheological and kinetic theories of single-component particles, which does not include the significant differences in the forces experienced by particles of different sizes in the underwater environment, including differences in collision, friction, and interstitial fluid interactions. This leads to a drawback: it cannot accurately reflect the particle collapse process, especially the particle separation phenomenon of small particles sinking and large particles floating. Determining the stress of each component particle is a crucial foundation for determining the underwater collapse process of two-component particles. However, to date, there are no readily available results or methods for comprehensively considering the interactions between particle components, anisotropic collisions, and shear dilatation / shear friction within the stress of each component particle. Summary of the Invention

[0004] This study provides a method for determining particle stress during the collapse of underwater two-component particles. Design calculations using the determined relevant water and sediment parameters can reflect the shear dilatation and shear contraction effects of frictional stress in each particle component and the influence of interstitial water, demonstrating the different levels of resistance from water during the movement of different particle components. The method also reflects the anisotropy between and within each component, as well as the influence of interstitial water, during particle collisions. By integrating the interactions between particle components, anisotropic collisions, and shear dilatation and shear contraction friction, the method reveals the particle separation phenomenon of smaller particles sinking and larger particles floating during particle collapse.

[0005] The objective of this invention is achieved through the following technical solution: The collision and friction effects of underwater two-component particles were obtained using 25 parameters. Specific parameters included: particle size of component 1. Particle size of component 2 Dry particle collision recovery coefficient gravitational acceleration The internal friction angle of component 1 The internal friction angle of component 2 The density of water The density of component 1 The density of component 2 Temperature of component 1 Temperature of component 2 Hydrodynamic viscosity Volume fraction of component 1 Volume fraction of component 2 The dense packing volume fraction of the first component The dense packing volume fraction of the second component Volume fraction of loosely packed particles in two components Component 1, with its additional interstitial fluid, causes viscosity. Component 2, with its additional interstitial fluid, causes viscosity. Three coefficients for particulate materials , , Generalized drag coefficient between particles and fluid The velocity vector of the first component and the velocity vector of the second component .

[0006] Particle stress includes the first The pressure of each particle component ( ) and shear stress ( ), represented as in: and They are the first Collision pressure and friction pressure of individual particle components; and They are the first Impact shear stress and friction shear stress of each particle component.

[0007] No. The collision pressure formula for each particle component is as follows: in, It is the collision recovery coefficient; It is the collision recovery coefficient of dry particles; It is a Stokes number; It is the fluid dynamic viscosity; It is the total radial distribution function value of the two-component particles. It represents the radial distribution function value between different component particles, with subscripts. Indicates different The model more reasonably represents the collision probability of binary particles. It is the first The temperature of each particle component characterizes the magnitude of the particle's turbulent kinetic energy.

[0008] No. The formula for the frictional pressure of each particulate component is as follows: in: ; It is the first Partial pressure coefficient of each particle component , , , It is the percentage of the volume fraction of the first particle component in the total volume fraction of particles. It is the total frictional pressure of the particulate components.

[0009] in, It is the total volume fraction of the particulate component; It is gravitational acceleration; It is the volume fraction of the loosely packed particles in the two-component system; It is the volume fraction of densely packed binary particles; It is the dense packing volume fraction of the first component; It is the dense packing volume fraction of the second component; It is the particle size of component 1; It is the particle size of component 2; , , It is related to the particle material coefficient

[0010] The frictional shear stress of the particle components is described by the continuum assumption and the Mohr-Coulomb friction law. The frictional shear stress of each particle component is: in: It is the first Frictional viscosity of individual particulate components; It is the shear strain rate tensor of the particle components. , It is a unit matrix. It is the first The velocity vectors of each component are considered. The volumetric shear dilation and contraction of particles caused by underwater flow shear, as well as the influence of interstitial water, are taken into account.

[0011] in: ; It is the first The friction angle of the components; The viscosity is caused by the additional interstitial fluid, which reflects the different resistance effects of water on the movement of different particle components;

[0012] Considering anisotropy The formula for the impact shear stress of each particle component is as follows: in, These are the correction factors for anisotropy; It is the first Collision viscosity of individual particle components; It is the volume viscosity coefficient; ; It is pi (π).

[0013] Impact viscosity takes into account both the impact recovery coefficient and the effect of fluid drag, making it suitable for simulating underwater particle collapse processes. The expression is as follows:

[0014] in: , , ; It is the radial distribution function of particles of the same component. It is the generalized drag coefficient between particles and fluid.

[0015] By parameters , , , , , , , , , , , , Substituting into formulas (3), (6), (11), and (12), we obtain the first... Collision pressure of individual particle components ; parameters Substituting into formulas (4), (5), and (6), we get ; parameters Substituting into formulas (9)-(12) yields ; parameters and obtained in step 2 Substituting into formulas (7) and (8), we get ; What will be obtained in the end and Substituting into formula (1), we obtain the pressure of the particulate component. ; The result and Substituting into formula (2) yields the shear stress of the particulate component. ; Complete the calculations of collision and friction between the two-component particles.

[0016] The advantages and beneficial effects of this invention are: due to the adoption of the above technical solutions, see Figure 9 , Figure 15-17 The present invention determines that the collision and friction pressure of the collapse of two-component particles has the following three advantages: 1. The frictional stress of each component particle takes into account the shear dilatation and shear contraction effects and the influence of interstitial water, reflecting the different resistance effects of water on the movement of different particle components.

[0017] 2. The collision stress of each component particle takes into account the anisotropy between and within each component, as well as the influence of interstitial water, making the prediction of the underwater two-component particle collapse morphology more accurate.

[0018] 3. It integrates inter-component particle interactions, anisotropic collisions, and shear dilation and shear contraction friction, demonstrating the particle separation phenomenon of small particles sinking and large particles floating during particle collapse. Attached Figure Description

[0019] Figure 1 It is the temperature of the particulate components. Distribution diagrams (a, b are the distributions of 0.45s particle components 1 and 2; c, d are the distributions of 1.35s particle components 1 and 2).

[0020] Figure 2 It is the collision recovery coefficient. Distribution diagrams (a, b are the distributions of 0.45s particle components 1 and 2; c, d are the distributions of 1.35s particle components 1 and 2).

[0021] Figure 3 It is the particle volume fraction. Distribution diagrams (a, b are the distributions of 0.45s particle components 1 and 2; c, d are the distributions of 1.35s particle components 1 and 2).

[0022] Figure 4 It is the total radial distribution function value of the two-component particles. The distribution plots (a and b are the distributions of 0.45s and 1.35sgis).

[0023] Figure 5 It is collision pressure Distribution diagrams (a, b are the distributions of 0.45s particle components 1 and 2; c, d are the distributions of 1.35s particle components 1 and 2).

[0024] Figure 6 Frictional pressure Distribution diagrams (a, b are the distributions of 0.45s particle components 1 and 2; c, d are the distributions of 1.35s particle components 1 and 2).

[0025] Figure 7 It is the drag coefficient. Distribution diagrams (a, b are the distributions of 0.45s particle components 1 and 2; c, d are the distributions of 1.35s particle components 1 and 2).

[0026] Figure 8 Collision viscosity Distribution diagrams (a, b are the distributions of 0.45s particle components 1 and 2; c, d are the distributions of 1.35s particle components 1 and 2).

[0027] Figure 9 It is speed Distribution diagrams (a, b are the distributions of 0.45s particle components 1 and 2; c, d are the distributions of 1.35s particle components 1 and 2).

[0028] Figure 10 It is velocity divergence Distribution diagrams (a, b are the distributions of 0.45s particle components 1 and 2; c, d are the distributions of 1.35s particle components 1 and 2).

[0029] Figure 11 It is the anisotropy coefficient Distribution diagrams (a, b are the distributions of 0.45s particle components 1 and 2; c, d are the distributions of 1.35s particle components 1 and 2).

[0030] Figure 12 It is collision shear stress Distribution diagram (the diagram shows the equivalent stress) (a, b are the distributions of particle components 1 and 2 at 0.45s; c, d are the distributions of particle components 1 and 2 at 1.35s).

[0031] Figure 13 Friction viscosity Distribution diagrams (a, b are the distributions of 0.45s particle components 1 and 2; c, d are the distributions of 1.35s particle components 1 and 2).

[0032] Figure 14 Frictional shear stress Distribution diagram (the diagram shows the equivalent stress) (a, b are the distributions of particle components 1 and 2 at 0.45s; c, d are the distributions of particle components 1 and 2 at 1.35s).

[0033] Figure 15 It is the pressure of the particulate components. Distribution diagrams (a, b are the distributions of 0.45s particle components 1 and 2; c, d are the distributions of 1.35s particle components 1 and 2).

[0034] Figure 16 It is the shear stress of the particulate components. The distribution map (τi is) Figure 12 and Figure 14 The summation yields a and b, which represent the distributions of particle components 1 and 2 at 0.45 s; and c and d, which represent the distributions of particle components 1 and 2 at 1.35 s.

[0035] Figure 17 It is a comparison of collapse modes (a, b: influence of friction; c, d: influence of collision). Detailed Implementation

[0036] The following detailed description, in conjunction with accompanying diagrams and examples, illustrates how to obtain the... The pressure of each particle component ( ) and shear stress ( The process of ).

[0037] Brief example: The particles are initially fixed and piled up on one side of the wall by the gate. The initial length of the particle column is... The height is After the gate opens, the particles collapse. This is a two-dimensional example. Specific parameters are given in the following procedure, attached. Figures 1-17 The distribution of parameters of particle component 1 and particle component 2 at 0.45s (particle collapse acceleration stage) and 1.35s (particle collapse stabilization stage) is shown, and the results are compared with those of the water tank experiment. Example

[0038] 1. Calculation The provided formulas (3), (6), (11) and (12) are used.

[0039] (1) Given =0.9、 , (include , ), , , The distribution is shown in Figure 1 Substituting into the collision recovery coefficient formula, we obtain... That is, to obtain Figure 2 The result.

[0040] (2) Given , , (include and The distribution of ) is shown in Figure 3 , Substituting the above parameters into equation (6) yields ; will be obtained and , Substituting into formula (12) yields Then and Substituting into formula (11) yields By putting and Substituting into the formula for calculating the total radial distribution function value of the two-component particles, we get That is, to obtain Figure 4 The result.

[0041] (3) , , The above process (1) yields and process (2) obtained Substituting into formula (3) yields That is, to obtain Figure 5 The result.

[0042] 2. Calculation The provided formulas (4)-(6) are used.

[0043] (1) Given , =2、 =5、 , , And the result calculated in step 1 Substituting these parameters into formula (5) yields .

[0044] (2) Through and Calculated ,pass and Calculated ,use and Calculated Then , And obtained from the above process (1) Substituting into formula (4) yields That is, to obtain Figure 6 The result.

[0045] 3. Calculation The provided formulas (9)-(12) are used.

[0046] (1) Given , and Calculations yielded ;pass , , , , (See distribution) Figure 7 ) and the results obtained in step 1 Calculated ;use , And obtained in step 1 Calculated Then , , , And obtained in step 1 Substituting into formula (10) yields That is, to obtain Figure 8 The result.

[0047] (2) Given , , , , And obtained in step 1 Calculations yielded ;use (See distribution) Figure 9 ), (See distribution) Figure 10 )Calculated ;Will (See distribution) Figure 11 ), , Substituting into formula (9) yields (See Figure 12 ).

[0048] 4. Calculation The provided formulas (7) and (8) are used.

[0049] (1) Obtained through step 3 Calculated ; Known (include , ), (include , ), , And the result calculated in step 2 Substituting into formula (8) yields the result. That is, to obtain Figure 13 The result.

[0050] (2) The result obtained in step 3 And obtained from the above process (1) Substituting into formula (7) yields (See Figure 14 ).

[0051] 5. Calculate the first... Pressure of each particle component and shear stress Formulas (1) and (2) are used.

[0052] The parameters obtained in steps 1 and 2 , Substituting into formula (1) yields That is, to obtain Figure 15 The result is the parameters obtained in steps 3 and 4. , Substituting into formula (2) yields That is, to obtain Figure 16 The result.

[0053] Finally, it should be noted that the above is only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention (such as the application of various formulas, the order of steps, etc.) without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for determining particle stress during the collapse process of underwater two-component particles, characterized in that: Includes the following steps: Step 1, the Collision pressure of individual particle components The calculation is performed by using parameters. , , , , , , , , , , , , Substituting into formulas (3), (6), (11), and (12), we obtain the first... Collision pressure of individual particle components ; No. The collision pressure formula for each particle component is as follows: in, It is the collision recovery coefficient; It is the collision recovery coefficient of dry particles; It is a Stokes number; It is the fluid dynamic viscosity; It is the total radial distribution function value of the two-component particles; It represents the radial distribution function value between different component particles, with subscripts. Indicates different The model more reasonably represents the collision probability of binary particles. It is the first The temperature of each particle component characterizes the magnitude of the particle's turbulent kinetic energy; 2. Among them, It is the total volume fraction of the particulate components; It is gravitational acceleration; It is the volume fraction of the loosely packed particles in the two-component system; It is the volume fraction of densely packed binary particles; It is the dense packing volume fraction of the first component; It is the dense packing volume fraction of the second component; It is the particle size of component 1; It is the particle size of component 2; , , It is related to the coefficient of particulate material; in: , , ; It is the radial distribution function of particles of the same component. It is the generalized drag coefficient between particles and fluid; Step 2, the Frictional pressure of individual particle components The calculation will take the parameters Substituting into formulas (4), (5), and (6), we get ; No. The formula for the frictional pressure of each particulate component is as follows: in: ; It is the partial pressure coefficient of the i-th particle component. , , , It is the percentage of the volume fraction of the first particle component in the total particle volume fraction; It is the total frictional pressure of the particulate components; Step 3, the Collision shear stress of individual particle components The calculation will take the parameters Substituting into formulas (9)-(12) yields ; Considering anisotropy The formula for the impact shear stress of each particle component is as follows: in, These are the correction factors for anisotropy; It is the collision viscosity of the i-th particle component; It is the volume viscosity coefficient; ; It is pi. Collision viscosity considers both the impact coefficient of restitution and the effect of fluid drag, and is suitable for simulating underwater particle collapse processes. The expression is as follows: Step 4, the frictional shear stress of the i-th particle component The calculation will take the parameters and obtained in step 2 Substituting into formulas (7) and (8), we get ; The frictional shear stress of the particle components is described by the continuum assumption and the Mohr-Coulomb friction law. The frictional shear stress of the i-th particle component is: in: It is the first Frictional viscosity of each particulate component; It is the shear strain rate tensor of the particle components. , It is a unit matrix. It is the first The velocity vectors of each component are considered. The volumetric shear dilation and contraction of particles caused by underwater flow shear, as well as the influence of interstitial water, are taken into account. in: ; It is the first The friction angle of the components; The viscosity is caused by the additional interstitial fluid, which reflects the different resistance effects of water on the movement of different particle components; Step 5, calculate the first... Pressure of each particle component and shear stress ; The result obtained in step 1 and the result obtained in step 2 Substituting into formula (1), we obtain the pressure of the particulate component. ; The result and Substituting into formula (2) yields the shear stress of the particulate component. ; Particle stress includes the first Pressure of each particle component and shear stress , represented as in: and They are the first Collision pressure and friction pressure of individual particle components; and They are the first Impact shear stress and friction shear stress of each particle component.

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