A method for determining the critical hydraulic gradient of erosion failure

Abstract

This invention provides a method for determining the critical hydraulic gradient of burrowing failure, belonging to the field of hydraulic engineering technology. The method includes: taking in-situ samples and measuring their particle size distribution and porosity; determining the fine particle content, overall representative particle size, and fine particle representative particle size based on the particle size distribution; calculating the hydraulic amplification factor of the fine particles based on the porosity, fine particle representative particle size, overall representative particle size, and the hydraulic gradient to be applied; calculating the fine particle stress reduction factor based on the porosity and fine particle content, and then combining this with the fine particle hydraulic amplification factor to calculate the critical hydraulic gradient of burrowing failure. This invention can rapidly predict the critical hydraulic gradient of burrowing failure in soil samples in actual environments and can be directly applied to practical scenarios, increasing the accuracy of burrowing failure assessment under various working conditions, such as actual engineering site operations.

Description

Technical Field

[0001] This invention belongs to the field of water conservancy engineering technology, and in particular relates to a method for determining the critical hydraulic gradient of erosion failure. Background Technology

[0002] Pitting erosion is a common seepage failure phenomenon in structures such as dams and landslide dams, or on their foundations. The hydraulic gradient corresponding to the occurrence of pitting erosion in a material is called the critical hydraulic gradient. Accurately determining the critical hydraulic gradient of a material in its actual operating environment is of great engineering significance for dam engineering design, seepage safety assessment of dams and landslide dams, and emergency response.

[0003] Current experimental research indicates that the occurrence of burrowing is influenced by material physical conditions, stress conditions, and hydraulic conditions. Material physical conditions mainly include fine particle content and porosity; stress conditions primarily concern the stress state of the material and its impact on fine particle stress; and hydraulic conditions mainly involve the hydraulic loading method and flow velocity. Existing formulas for predicting the critical hydraulic gradient of burrowing are mostly based on Terzaghi's theory of soil erosion and the physical properties of burrowing materials, such as particle size distribution and porosity. They use stress reduction to account for changes in fine particle stress and determine the critical state of the fine particles. However, this stress reduction prediction method does not consider the influence of the physical properties of the burrowing material on the fluid drag force. This results in insufficient consideration of influencing factors in the prediction formulas established solely based on stress reduction, affecting the prediction results. Summary of the Invention

[0004] To address the aforementioned shortcomings in existing technologies, this invention provides a method for determining the critical hydraulic gradient of erosion failure. This method can rapidly predict the critical hydraulic gradient of erosion failure in soil samples under actual environmental conditions and can be directly applied to real-world scenarios, increasing the accuracy of erosion failure assessment under various working conditions, such as actual operation at engineering sites.

[0005] To achieve the above objectives, the technical solution adopted by this invention is as follows: a method for determining the critical hydraulic gradient of erosion failure, comprising the following steps:

[0006] S1. Take in-situ samples and measure the particle size distribution and porosity of the in-situ samples respectively.

[0007] S2. Based on the particle size distribution, determine the fine particle content, overall representative particle size, and fine particle representative particle size respectively;

[0008] S3. Calculate the hydraulic amplification factor of the fine particles based on the porosity, the representative particle size of the fine particles and the overall representative particle size, as well as the hydraulic gradient to be applied.

[0009] S4. Based on the porosity and fine particle content, calculate the fine particle stress reduction factor, and then combine it with the fine particle hydraulic amplification factor to calculate the critical hydraulic gradient of the undercut failure, thus completing the determination of the critical hydraulic gradient of the undercut failure.

[0010] Furthermore, S2 specifically refers to:

[0011] The overall representative particle size is calculated based on the particle size distribution and fine particle content.

[0012] Based on the particle size distribution, the fine particles are selected, and the representative particle size of the fine particles is calculated.

[0013] Furthermore, the expression representing the overall particle size is as follows:

[0014]

[0015] Among them, D rep The overall particle size is represented by f. i D represents the particle fraction between two sieve sizes. li and D si They represent the f i Maximum and minimum particle size within the range, P f Indicates fine particle content, d min and d max D represents the minimum and maximum particle sizes of the fine particles, respectively. min and D max These represent the minimum and maximum particle sizes of the coarse particles, respectively.

[0016] Furthermore, the expression for the particle size represented by the fine particles is as follows:

[0017]

[0018] Where, d rep Fine particles represent particle size, f fi d represents the fraction of fine particles between two sieve sizes. li and d si They represent the f fi The maximum and minimum particle size within the range.

[0019] Furthermore, S3 specifically refers to:

[0020] Calculate the overall flow velocity under the applied hydraulic gradient based on porosity, overall representative particle size, and fluid density.

[0021] The actual fluid velocity within the material pores is calculated based on the overall flow velocity and porosity.

[0022] The fine-particle Reynolds number is calculated based on the representative particle size of the fine particles and the actual fluid velocity.

[0023] The fine-grained drag coefficient is calculated based on the fine-grained Reynolds number.

[0024] Calculate the fine particle drag force under the applied hydraulic gradient based on the representative particle size, actual fluid velocity, and fine particle drag force coefficient.

[0025] The fine-grained gradient force under the applied hydraulic gradient was calculated.

[0026] The hydraulic amplification factor of the fine particles is calculated based on the drag force and gradient force of the fine particles under the applied hydraulic gradient.

[0027] Furthermore, the expression for the hydraulic amplification factor of the fine particles is as follows:

[0028]

[0029] Where β represents the hydraulic amplification factor for fine particles, F press F represents the fine-grained gradient force under the applied hydraulic gradient i. drag d represents the fine-particle drag force under the applied hydraulic gradient i. rep Fine particles represent particle size, ρ f Let C represent the fluid density, g represent the acceleration due to gravity, and C represent the acceleration due to gravity. d ν represents the fine-particle drag coefficient. s R represents the actual fluid velocity within the pores of the material. ep ν represents the fine-grained Reynolds number, μ represents the hydrodynamic viscosity coefficient, n represents the porosity, ν represents the overall flow velocity, and i represents the applied hydraulic gradient.

[0030] Furthermore, S4 specifically refers to:

[0031] The fine-particle stress reduction factor is calculated based on the porosity and fine-particle content.

[0032] The gradient reduction factor is calculated based on the hydraulic amplification factor and the stress reduction factor of fine particles.

[0033] Based on the gradient reduction factor and the unit weight of the material, the critical hydraulic gradient for burrowing failure is calculated, thus completing the determination of the critical hydraulic gradient for burrowing failure.

[0034] Furthermore, the expression for the critical hydraulic gradient of the erosion failure is as follows:

[0035]

[0036] Among them, i c γ' represents the critical hydraulic gradient for burrowing failure, ρ represents the material's unit weight, and γ' represents the material's density. fLet g represent fluid density, ζ represent gravitational acceleration, α represent the gradient reduction factor, β represent the fine-particle stress reduction factor, β represent the hydraulic amplification factor of the fine particles, and n represent porosity. f This indicates the content of fine particles.

[0037] The beneficial effects of this invention are:

[0038] This invention calculates the hydraulic amplification factor of fine particles by determining the overall representative particle size and the fine representative particle size, and calculates the critical hydraulic gradient for seepage failure by combining porosity and fine particle content. This invention has a wide range of applications and can be applied to landslide dams, dam foundations with loose overburden, earth-rock dam bodies, embankment foundations, etc. At the same time, this invention can consider the nonlinear influence of stress conditions and hydraulic conditions on the critical hydraulic gradient, increasing the accuracy of the assessment of seepage failure in engineering sites. Attached Figure Description

[0039] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0040] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0041] Example

[0042] like Figure 1 As shown, this invention provides a method for determining the critical hydraulic gradient of erosion failure, the implementation of which is as follows:

[0043] S1. Take in-situ samples and measure the particle size distribution and porosity of the in-situ samples respectively.

[0044] S2. Based on the particle size distribution, determine the fine particle content, overall representative particle size, and fine particle representative particle size, as follows:

[0045] The overall representative particle size is calculated based on the particle size distribution and fine particle content.

[0046] Based on the particle size distribution, the fine particles are selected, and the representative particle size of the fine particles is calculated.

[0047] In this embodiment, the expression representing the overall particle size is as follows:

[0048]

[0049] Among them, D rep The overall particle size is represented by f.i D represents the particle fraction between two sieve sizes. li and D si They represent the f i Maximum and minimum particle size within the range, P f Indicates fine particle content, d min and d max D represents the minimum and maximum particle sizes of the fine particles, respectively. min and D max These represent the minimum and maximum particle sizes of the coarse particles, respectively.

[0050] In this embodiment, the expression for particle size representing fine particles is as follows:

[0051]

[0052] Where, d rep Fine particles represent particle size, f fi d represents the fraction of fine particles between two sieve sizes. li and d si They represent the f fi The maximum and minimum particle size within the range.

[0053] S3. Based on the porosity, representative particle size of fine particles, representative particle size of the whole, and the hydraulic gradient to be applied, calculate the hydraulic amplification factor of the fine particles, specifically as follows:

[0054] Calculate the overall flow velocity under the applied hydraulic gradient based on porosity, overall representative particle size, and fluid density.

[0055] The actual fluid velocity within the material pores is calculated based on the overall flow velocity and porosity.

[0056] The fine-particle Reynolds number is calculated based on the representative particle size of the fine particles and the actual fluid velocity.

[0057] The fine-grained drag coefficient is calculated based on the fine-grained Reynolds number.

[0058] Calculate the fine particle drag force under the applied hydraulic gradient based on the representative particle size, actual fluid velocity, and fine particle drag force coefficient.

[0059] The fine-grained gradient force under the applied hydraulic gradient was calculated.

[0060] The hydraulic amplification factor of the fine particles is calculated based on the drag force and gradient force of the fine particles under the applied hydraulic gradient.

[0061] In this embodiment, the expression for the hydraulic amplification factor of fine particles is as follows:

[0062]

[0063]

[0064] Where β represents the hydraulic amplification factor for fine particles, F press F represents the fine-grained gradient force under the applied hydraulic gradient i. drag d represents the fine-particle drag force under the applied hydraulic gradient i. rep Fine particles represent particle size, ρ f Let C represent the fluid density, g represent the acceleration due to gravity, and C represent the acceleration due to gravity. d ν represents the fine-particle drag coefficient. s R represents the actual fluid velocity within the pores of the material. ep ν represents the fine-grained Reynolds number, μ represents the hydrodynamic viscosity coefficient, n represents the porosity, ν represents the overall flow velocity, and i represents the applied hydraulic gradient.

[0065] S4. Based on the porosity and fine particle content, calculate the fine particle stress reduction factor, and then combine it with the fine particle hydraulic amplification factor to calculate the critical hydraulic gradient for undercutting failure, thus completing the determination of the critical hydraulic gradient for undercutting failure. Specifically:

[0066] The fine-particle stress reduction factor is calculated based on the porosity and fine-particle content.

[0067] The gradient reduction factor is calculated based on the hydraulic amplification factor and the stress reduction factor of fine particles.

[0068] Based on the gradient reduction factor and the unit weight of the material, the critical hydraulic gradient for burrowing failure is calculated, thus completing the determination of the critical hydraulic gradient for burrowing failure.

[0069] In this embodiment, the expression for the critical hydraulic gradient of the erosion failure is as follows:

[0070]

[0071] Among them, i c γ' represents the critical hydraulic gradient for burrowing failure, ρ represents the material's unit weight, and γ' represents the material's density. f Let g represent fluid density, ζ represent gravitational acceleration, α represent the gradient reduction factor, β represent the fine-particle stress reduction factor, β represent the hydraulic amplification factor of the fine particles, and n represent porosity. f This indicates the content of fine particles.

[0072] In summary, this invention calculates the hydraulic amplification factor of fine particles by determining the overall representative particle size and the fine representative particle size, and calculates the critical hydraulic gradient for seepage failure by combining porosity and fine particle content. It has a wide range of applications and can be used for landslide dams, dam foundations with loose overburden, earth-rock dam bodies, embankment foundations, etc. At the same time, this invention can consider the nonlinear influence of stress conditions and hydraulic conditions on the critical hydraulic gradient, increasing the accuracy of the assessment of seepage failure in engineering sites.

Claims

1. A method for determining a critical hydraulic gradient of a pitting damage, characterized by, The method comprises the following steps: S1, taking in-situ samples, and measuring the particle size distribution and porosity of the in-situ samples respectively; S2, determining the fine particle content, the overall representative particle size and the fine particle representative particle size according to the particle size distribution; S3, calculating the hydraulic amplification factor of the fine particles according to the porosity, the fine particle representative particle size, the overall representative particle size, and the hydraulic gradient to be applied; the S3 is specifically as follows: calculating the overall flow velocity under the action of the applied hydraulic gradient according to the porosity, the overall representative particle size, the fluid dynamic viscosity coefficient and the fluid density; and calculating the actual fluid velocity in the material pores according to the overall flow velocity and the porosity: calculating the fine particle Reynolds number according to the fine particle representative particle size, the fluid density, the fluid dynamic viscosity coefficient and the actual fluid velocity in the material pores; calculating the fine particle drag coefficient according to the fine particle Reynolds number; calculating the fine particle drag force under the action of the applied hydraulic gradient according to the fine particle representative particle size, the actual fluid velocity, the fluid density and the fine particle drag coefficient; calculating the fine particle gradient force under the action of the applied hydraulic gradient according to the fine particle representative particle size and the fluid density; calculating the hydraulic amplification factor of the fine particles according to the fine particle drag force under the action of the applied hydraulic gradient and the fine particle gradient force; the expression of the hydraulic amplification factor of the fine particles is as follows: ； wherein, represents the hydraulic amplification factor of the fine particles, represents the gradient force of the fine particles under the applied hydraulic gradient represents the gradient force of the fine particles under the applied hydraulic gradient represents the gradient force of the fine particles under the applied hydraulic gradient represents the drag force of the fine particles under the applied hydraulic gradient S4, calculating the fine particle stress reduction factor according to the porosity and the fine particle content, and then combining the hydraulic amplification factor of the fine particles to calculate the critical hydraulic slope of the hidden erosion damage, so as to determine the critical hydraulic slope of the hidden erosion damage; the S4 is specifically as follows: calculating the fine particle stress reduction factor according to the porosity and the fine particle content; calculating the gradient reduction factor according to the hydraulic amplification factor of the fine particles and the fine particle stress reduction factor; the expression of the gradient reduction factor is as follows: ； calculating the critical hydraulic slope of the hidden erosion damage according to the gradient reduction factor and the bulk density of the material, so as to determine the critical hydraulic slope of the hidden erosion damage; the expression of the critical hydraulic slope of the hidden erosion damage is as follows: ； wherein, represents the critical hydraulic slope of incipient erosion failure, represents the unit weight of the material, represents the gradient reduction factor, represents the stress reduction factor of fine particles, represents the hydraulic amplification factor of fine particles, represents the fluid density, represents the gravitational acceleration.

2. The method of determining a pitting corrosion failure threshold hydraulic gradient according to claim 1, wherein, The S2 is specifically as follows: calculating the overall representative particle size according to the particle size distribution and the fine particle content; calculating the fine particle representative particle size by selecting the fine particle part according to the particle size distribution.

3. The method of determining the critical hydraulic gradient for incipient corrosion failure according to claim 2, wherein, The expression of the overall representative particle size is as follows: wherein, D50 represents the overall representative particle size, D10 and D90 represent the particle fraction between the two sieve sizes, and Dmax and Dmin represent the maximum and minimum particle size, respectively, in the range, D10 and D90 represent the particle fraction between the two sieve sizes, Df represents the fine particle content, and Dmin and Dmax represent the minimum and maximum particle size, respectively, of the fine particles, and Dmin and Dmax represent the minimum and maximum particle size, respectively, of the coarse particles.

4. The method of determining the incipient failure critical hydraulic gradient according to claim 2, wherein, The expression of the fine particle representative particle size is as follows: wherein, Dp represents the fine particle mean diameter, Dp represents the fine particle mean diameter, and respectively represent the maximum particle size and the minimum particle size within the range of Dp represents the fine particle mean diameter.

5. The method of determining a pitting corrosion failure threshold hydraulic gradient according to claim 1, wherein, The expressions of the fine particle drag force under the action of the applied hydraulic gradient and the fine particle gradient force under the action of the applied hydraulic gradient are as follows: ； ； ； ； ； ； wherein, represents the fine particle representative diameter, represents the fluid density, represents the fine particle drag coefficient, represents the actual fluid velocity within the material porosity, represents the fluid dynamic viscosity coefficient, represents the porosity, represents the bulk flow rate, represents the applied hydraulic gradient, represents the gravitational acceleration, represents the fine particle Reynolds number, represents the bulk representative diameter.

6. The method of determining a pitting corrosion failure threshold hydraulic gradient according to claim 1, wherein, The expression of the fine particle stress reduction factor is as follows: wherein, represents the fine particle content, represents the porosity.

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