Subsurface erosion damage critical hydraulic gradient determination method

Abstract

The invention provides a subsurface erosion damage critical hydraulic gradient determination method, which belongs to the technical field of hydraulic engineering, and comprises the following steps: taking an in-situ sample, and respectively measuring the grain composition and porosity of the in-situ sample; according to the grain composition, the fine grain content, the overall representative grain size and the fine grain representative grain size are determined respectively; according to the porosity, the representative particle size of the fine particles, the representative particle size of the whole and the hydraulic gradient to be applied, the hydraulic amplification coefficient of the fine particles is calculated; according to the porosity and the fine particle content, the fine particle stress reduction coefficient is calculated, and then the subsurface erosion damage critical hydraulic gradient is calculated in combination with the fine particle hydraulic amplification coefficient. According to the method, the critical hydraulic gradient of subsurface erosion damage of the soil sample in an actual environment can be rapidly predicted, the method is directly applied to an actual scene, and the accuracy of subsurface erosion damage assessment under various working conditions such as actual operation of an engineering site is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of water conservancy engineering, and particularly relates to a method for determining the critical hydraulic gradient of piping erosion damage. Background Art

[0002] Piping erosion is a relatively common seepage failure phenomenon in structures such as dams and barrier bodies or their foundations. The corresponding hydraulic gradient when the material undergoes piping erosion is the critical hydraulic gradient. Accurately determining the critical hydraulic gradient of the material in the actual operating environment has important engineering significance for dam engineering design, seepage safety assessment and emergency rescue of dams and barrier bodies, etc.

[0003] Current experimental studies show that the occurrence of piping erosion is affected by aspects such as the physical conditions, stress conditions, and hydraulic conditions of the material. Among them, the physical conditions of the material mainly include fine-grain content, porosity, etc., the stress conditions are mainly the stress state in which the material exists and its influence on the stress of fine grains, and the hydraulic conditions are mainly the hydraulic loading method, flow velocity, etc. Existing prediction formulas for the critical hydraulic gradient of piping erosion are mostly based on Terzaghi's quicksand theory formula and the physical properties such as the particle size distribution and porosity of the piping erosion material, and consider the change of the stress of fine grains in the piping erosion material by stress reduction, and determine it through the critical state of fine grains. This stress reduction prediction method does not consider the influence of the physical property conditions of the piping erosion material on the fluid drag force. This results in insufficient consideration of influencing factors in the prediction formula established only by stress reduction, which affects the prediction results. Summary of the Invention

[0004] In view of the above deficiencies in the prior art, the present invention provides a method for determining the critical hydraulic gradient of piping erosion damage, which can quickly predict the critical hydraulic gradient of the piping erosion damage of the soil sample in the actual environment and directly apply it to the actual scenario, increasing the accuracy of the assessment of piping erosion damage under various working conditions such as the actual operation of the engineering site.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is: a method for determining the critical hydraulic gradient of piping erosion damage, 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. Determine the fine-grain content, overall representative particle size, and fine-grain representative particle size respectively according to the particle size distribution;

[0008] S3. Calculate the hydraulic amplification coefficient of fine grains according to the porosity, fine-grain representative particle size, overall representative particle size, and the proposed applied hydraulic gradient;

[0009] S4. Calculate the fine-grained stress reduction coefficient based on the porosity and fine-grained content, and then combine it with the hydraulic amplification coefficient of the fine-grained material to calculate the critical hydraulic gradient for piping failure, thus determining the critical hydraulic gradient for piping failure.

[0010] Further, the specific content of S2 is as follows:

[0011] Calculate the overall representative particle size based on the particle size distribution and fine-grained content;

[0012] Select the fine-grained part according to the particle size distribution and calculate the representative particle size of the fine-grained material.

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

[0014]

[0015] Wherein, D rep represents the overall representative particle size, f i represents the particle fraction between two sieve sizes, D li and D si respectively represent the maximum and minimum particle sizes within the range of this f i , P f represents the fine-grained content, d min and d max respectively represent the minimum and maximum particle sizes of the fine-grained material, D min and D max respectively represent the minimum and maximum particle sizes of the coarse-grained material.

[0016] Furthermore, the expression of the representative particle size of the fine-grained material is as follows:

[0017]

[0018] Wherein, d rep represents the representative particle size of the fine-grained material, f fi represents the fine-grained particle fraction between two sieve sizes, d li and d si respectively represent the maximum and minimum particle sizes within the range of this f fi .

[0019] Furthermore, the specific content of S3 is as follows:

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

[0021] Calculate the actual fluid velocity inside the pores of the material based on the overall flow velocity and porosity;

[0022] Calculate the fine-grained Reynolds number based on the representative particle size of the fine-grained material and the actual fluid velocity;

[0023] Calculate the fine-grained drag coefficient according to the fine-grained Reynolds number;

[0024] Calculate the fine-grained drag force under the action of the applied hydraulic gradient according to the representative fine-grained particle size, the actual fluid velocity, and the fine-grained drag coefficient;

[0025] Calculate the fine-grained gradient force under the action of the applied hydraulic gradient;

[0026] Calculate the hydraulic amplification coefficient of the fine-grained particles according to the fine-grained drag force and the fine-grained gradient force under the action of the applied hydraulic gradient.

[0027] Furthermore, the expression of the hydraulic amplification coefficient of the fine-grained particles is as follows:

[0028]

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

[0030] Furthermore, the specific content of S4 is as follows:

[0031] Calculate the fine-grained stress reduction coefficient according to the porosity and the fine-grained content;

[0032] Calculate the gradient reduction coefficient according to the hydraulic amplification coefficient of the fine-grained particles and the fine-grained stress reduction coefficient;

[0033] Calculate the critical hydraulic gradient for piping failure according to the gradient reduction coefficient and the unit weight of the material, and complete the determination of the critical hydraulic gradient for piping failure.

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

[0035]

[0036] Where i c represents the critical hydraulic gradient for piping failure, γ' represents the unit weight of the material, ρ f\(\rho\) represents the fluid density, \(g\) represents the acceleration due to gravity, \(\zeta\) represents the gradient reduction coefficient, \(\alpha\) represents the fine-grained stress reduction coefficient, \(\beta\) represents the hydraulic amplification coefficient of fine grains, \(n\) represents the porosity, and \(P\) f represents the fine-grained content.

[0037] The beneficial effects of the present invention are as follows:

[0038] By determining the overall representative particle size and the representative particle size of fine grains, calculating the hydraulic amplification coefficient of fine grains, and combining the porosity and the fine-grained content to calculate the critical hydraulic gradient for piping failure, the present invention has a wide range of applications and can be applied to landslide dams, loose overburden dam foundations, earth-rock dam bodies, levee foundations, etc. At the same time, the present invention can consider the non-linear effects of stress conditions and hydraulic conditions on the critical hydraulic gradient, increasing the accuracy of the assessment of seepage failure at the engineering site. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flowchart of the method of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0040] The following describes the specific embodiments of the present invention to facilitate those skilled in the art to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions made using the concept of the present invention are within the scope of protection.

[0041] Embodiment

[0042] As Figure 1 shown, the present invention provides a method for determining the critical hydraulic gradient for piping failure, and the implementation method 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. According to the particle size distribution, determine the fine-grained content, the overall representative particle size and the representative particle size of fine grains respectively. Specifically:

[0045] Calculate the overall representative particle size according to the particle size distribution and the fine-grained content;

[0046] Select the fine-grained part according to the particle size distribution and calculate the representative particle size of fine grains.

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

[0048]

[0049] where \(D\) rep represents the overall representative particle size, and \(f\)i Represents the particle fraction between two sieve sizes, D li and D si respectively represent the maximum particle size and the minimum particle size within the range of this f i , P f represents the fine particle content, d min and d max respectively represent the minimum particle size and the maximum particle size of the fine particles, D min and D max respectively represent the minimum and maximum particle sizes of the coarse particles.

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

[0051]

[0052] Among them, d rep represents the representative particle size of the fine particles, f fi represents the fine particle fraction between two sieve sizes, d li and d si respectively represent the maximum particle size and the minimum particle size within the range of this f fi .

[0053] S3. Calculate the hydraulic amplification coefficient of the fine particles according to the porosity, the representative particle size of the fine particles and the overall representative particle size, and the hydraulic gradient to be applied, specifically:

[0054] Calculate the overall flow velocity under the action of the applied hydraulic gradient according to the porosity, the overall representative particle size and the fluid density;

[0055] Calculate the actual fluid velocity in the pores of the material according to the overall flow velocity and the porosity;

[0056] Calculate the Reynolds number of the fine particles according to the representative particle size of the fine particles and the actual fluid velocity;

[0057] Calculate the drag coefficient of the fine particles according to the Reynolds number of the fine particles;

[0058] Calculate the drag force of the fine particles under the action of the applied hydraulic gradient according to the representative particle size of the fine particles, the actual fluid velocity and the drag coefficient of the fine particles;

[0059] Calculate the gradient force of the fine particles under the action of the applied hydraulic gradient;

[0060] Calculate the hydraulic amplification coefficient of the fine particles according to the drag force of the fine particles and the gradient force of the fine particles under the action of the applied hydraulic gradient.

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

[0062]

[0063]

[0064] Among them, β represents the hydraulic amplification coefficient of fine particles, F press represents the fine particle gradient force under the action of the applied hydraulic gradient i, F drag represents the fine particle drag force under the action of the applied hydraulic gradient i, d rep represents the representative particle size of fine particles, ρ f represents the fluid density, g represents the acceleration due to gravity, C d represents the fine particle drag coefficient, ν s represents the actual fluid velocity within the pores of the material, R ep represents the fine particle Reynolds number, μ represents the dynamic viscosity of the fluid, n represents the porosity, ν represents the overall flow velocity, and i represents the applied hydraulic gradient.

[0065] S4. Calculate the fine particle stress reduction coefficient according to the porosity and the fine particle content, and then combine it with the hydraulic amplification coefficient of the fine particles to calculate the critical hydraulic gradient for piping failure, thereby completing the determination of the critical hydraulic gradient for piping failure. Specifically:

[0066] Calculate the fine particle stress reduction coefficient according to the porosity and the fine particle content;

[0067] Calculate the gradient reduction coefficient according to the hydraulic amplification coefficient of the fine particles and the fine particle stress reduction coefficient;

[0068] Calculate the critical hydraulic gradient for piping failure according to the gradient reduction coefficient and the unit weight of the material, thereby completing the determination of the critical hydraulic gradient for piping failure.

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

[0070]

[0071] Among them, i c represents the critical hydraulic gradient for piping failure, γ' represents the unit weight of the material, ρ f represents the fluid density, g represents the acceleration due to gravity, ζ represents the gradient reduction coefficient, α represents the fine particle stress reduction coefficient, β represents the hydraulic amplification coefficient of the fine particles, n represents the porosity, P f represents the fine particle content.

[0072] In summary, the present invention determines the overall representative particle size and the fine particle representative particle size, calculates the hydraulic amplification coefficient of the fine particles, and calculates the critical hydraulic gradient for piping failure in combination with the porosity and the fine particle content. It has a wide range of applications and can be applied to landslide dams, loose overburden dam foundations, earth-rock dam bodies, levee foundations, etc. At the same time, the present invention can consider the non-linear effects of stress conditions and hydraulic conditions on the critical hydraulic gradient, improving the accuracy of the assessment of seepage failure at the engineering site.

Claims

1. A method for determining the critical hydraulic gradient of erosion damage, characterized in that: The following steps are involved: S1. Take in-situ samples and measure the particle size distribution and porosity of the in-situ samples respectively; S2. According to the particle grading, the fine particle content, the overall representative particle size and the fine particle representative particle size are determined respectively; S3. Calculate the hydraulic amplification factor of the fine particles based on the porosity, the representative particle size of the fine particles and the representative particle size of the whole, and the hydraulic gradient to be applied; S4. Calculate the fine particle stress reduction coefficient based on the porosity and fine particle content, and then calculate the critical hydraulic gradient of erosion damage in combination with the hydraulic amplification coefficient of the fine particles to complete the determination of the critical hydraulic gradient of erosion damage.

2. The method for determining the critical hydraulic gradient of erosion damage according to claim 1, characterized in that: The S2 is specifically: The overall representative particle size is calculated based on the particle grading and fine particle content; According to the particle grading, the fine particles are selected and the representative particle size of the fine particles is calculated.

3. The method for determining the critical hydraulic gradient of erosion damage according to claim 2 is characterized in that: The expression of the overall representative particle size is as follows: Among them, D rep Indicates the overall representative particle size, f i Denotes the particle fraction between two sieve sizes, D li and D si Respectively represent the f i The maximum and minimum particle sizes within the range, P f Indicates the fine particle content, d min and d max Respectively represent the minimum and maximum particle sizes of fine particles, D min and D max Represent the minimum and maximum particle sizes of coarse particles, respectively.

4. The method for determining the critical hydraulic gradient of erosion damage according to claim 2, characterized in that: The expression representing the particle size of the fine particles is as follows: Among them, d rep Indicates that fine particles represent particle size, f fi represents the fine particle fraction between two sieve sizes, d li and d si Respectively represent the f fi The maximum and minimum particle sizes within the range.

5. The method for determining the critical hydraulic gradient of erosion damage according to claim 1, characterized in that: The S3 is specifically: According to the porosity, overall representative particle size and fluid density, the overall flow velocity under the action of hydraulic gradient is calculated; Based on the overall flow velocity and porosity, the actual fluid velocity in the pores of the material is calculated; The fine particle Reynolds number is calculated based on the representative particle size of the fine particles and the actual fluid velocity; According to the fine particle Reynolds number, the fine particle drag coefficient is calculated; According to the representative particle size of fine particles, the actual fluid velocity and the fine particle drag coefficient, the fine particle drag force under the action of hydraulic gradient is calculated; The fine-grained gradient force under the action of hydraulic gradient is calculated; The hydraulic amplification coefficient of fine particles is calculated based on the fine particle drag force and fine particle gradient force under the action of hydraulic gradient.

6. The method for determining the critical hydraulic gradient of erosion damage according to claim 5, characterized in that: The expression of the hydraulic amplification factor of the fine particles is as follows: Where β is the hydraulic amplification factor of fine particles, F press represents the fine-grained gradient force under the action of hydraulic gradient i, F drag represents the drag force of fine particles under the action of hydraulic gradient i, d rep represents the particle size of fine particles, ρ f represents the fluid density, g represents the acceleration due to gravity, C d is the fine particle drag coefficient, ν s Represents the actual fluid velocity in the pores of the material, R ep represents the fine particle Reynolds number, μ represents the fluid dynamic viscosity, n represents the porosity, ν represents the overall flow velocity, and i represents the applied hydraulic gradient.

7. The method for determining the critical hydraulic gradient of erosion damage according to claim 1, characterized in that: The S4 is specifically: According to the porosity and fine particle content, the fine particle stress reduction coefficient is calculated; The gradient reduction factor is calculated based on the hydraulic amplification factor of fine particles and the stress reduction factor of fine particles; According to the gradient reduction coefficient and the bulk density of the material, the critical hydraulic gradient of erosion damage is calculated to complete the determination of the critical hydraulic gradient of erosion damage.

8. The method for determining the critical hydraulic gradient of erosion damage according to claim 7, characterized in that: The expression of the critical hydraulic gradient of erosion damage is as follows: Among them, i c represents the critical hydraulic gradient of erosion damage, γ' represents the bulk density of the material, and ρ f represents fluid density, g represents gravity acceleration, ζ represents gradient reduction coefficient, α represents fine particle stress reduction coefficient, β represents fine particle hydraulic amplification coefficient, n represents porosity, P f Indicates the fine particle content.

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