Dam coarse-grained soil grading design method and system based on two-parameter grading equation

Abstract

The application discloses a dam coarse-grained soil grading design method and system based on a two-parameter grading equation, which comprises the following steps: designing the grading of coarse-grained soil with different grading parameters and maximum particle sizes based on the two-parameter grading equation; performing compaction density tests on each grading to obtain the compaction density of coarse-grained soil under different grading conditions; analyzing the relationship between the grading parameters, the maximum particle size and the compaction density based on the test data, and constructing a corresponding mathematical equation set; solving the equation set to obtain the grading parameters of coarse-grained soil with compaction characteristics under different maximum particle sizes, thereby obtaining the design grading of dam coarse-grained soil. The application establishes a quantitative correlation between the grading of coarse-grained soil and the compaction characteristics by constructing a mathematical relationship model between the grading parameters, the maximum particle size and the compaction density. The quantitative relationship considers the influence of the maximum particle size on the compaction characteristics of coarse-grained soil, and breaks through the limitation that the traditional grading design mainly relies on empirical judgment and specification limit control.

Description

Technical Field

[0001] This invention relates to the field of water conservancy and hydropower technology, and more specifically, to a method and system for designing the gradation of coarse-grained soil for dam construction based on a two-parameter gradation equation. Background Technology

[0002] Earth-rock dams have become the preferred dam type for water retention in hydropower resource development, and their engineering performance largely depends on the particle size distribution characteristics of the coarse-grained soil used for filling.

[0003] Currently, the design of coarse-grained soil gradation is mainly controlled based on relevant specifications and engineering experience. Specifications typically only set limits on the content of fine particles; for example, the content of particles smaller than 5 mm should not exceed 20%, and the content of particles smaller than 0.075 mm should not exceed 5%. In terms of gradation evaluation, the coefficient of uniformity and the coefficient of curvature are usually used as evaluation indicators. Generally, a gradation is considered good when the coefficient of uniformity is greater than 5 and the coefficient of curvature is in the range of 1 to 3.

[0004] However, the above-mentioned gradation design method has the following shortcomings: First, the engineering properties of various gradations that meet the specifications still vary greatly, and it is difficult to accurately control the filling quality by relying solely on empirical indicators; second, the existing methods mainly rely on engineering experience and lack quantitative design basis; third, as the construction height of earth-rock dams continues to exceed 200m or even 300m, the maximum particle size of coarse-grained soil for dam construction has increased significantly, with some reaching the 1000mm level. The impact of gradation on compaction performance is more significant, but the existing methods have not fully considered the influence of the maximum particle size on compaction characteristics.

[0005] Therefore, it is necessary to propose a gradation design method that can take into account gradation characteristics and maximum particle size, so as to provide a theoretical basis for the gradation optimization of coarse-grained soil for on-site dam construction. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method and system for designing the gradation of coarse-grained soil for dam construction based on a two-parameter gradation equation.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A method for designing the gradation of coarse-grained soil for dam construction based on a two-parameter gradation equation includes the following steps:

[0009] Step S1: Design coarse-grained soil gradations with different gradation parameters and maximum particle size based on the two-parameter gradation equation. The maximum particle size covers large particles with a diameter of not less than 60 mm.

[0010] Step S2: Conduct compaction density tests on each grade of gradation to obtain the compaction density of coarse-grained soil under different gradation conditions;

[0011] Step S3: Analyze the relationship between gradation parameters, maximum particle size and compaction density based on experimental data, and construct a set of mathematical equations including the maximum particle size variable;

[0012] Step S4: Solve the system of equations to obtain the coarse-grained soil gradation parameters with optimal compaction characteristics under different maximum particle sizes, thereby obtaining the design gradation of coarse-grained soil for dam construction.

[0013] Furthermore, in step S1, the two-parameter gradation equation is defined as:

[0014]

[0015] In the formula, Particle size; Maximum particle size; The content of particles smaller than a certain particle size; and These are the gradation parameters.

[0016] Furthermore, in step S1, the number of coarse-grained soil gradation tests shall not be less than 10 groups, and different gradations shall be designed by changing the combination of gradation parameters and the maximum particle size, wherein the maximum particle size shall not be less than 3.

[0017] Furthermore, in step S2, the compaction density test is performed using the surface vibration compaction method or the shaking table method.

[0018] Furthermore, in step S3, the construction of the system of mathematical equations includes:

[0019] Constructing the area of ​​gradation curves to characterize the gradation structure The calculation formula is as follows:

[0020]

[0021]

[0022] Establish compaction density Area of ​​gradation curve The quadratic function relationship between them:

[0023]

[0024] In the formula, , and It is a constant; and These are the gradation parameters.

[0025] Furthermore, in step S3, the construction of the system of mathematical equations also includes:

[0026] Constructing comprehensive parameters to characterize gradation features The calculation formula is as follows:

[0027]

[0028]

[0029] Establish compaction density With comprehensive parameters The quadratic function relationship between them:

[0030]

[0031] In the formula, , and It is a constant; Maximum particle size; It is a constant.

[0032] Furthermore, in step S4, the area of ​​the gradation curve is set... and comprehensive parameters Take the compaction density respectively By solving a system of mathematical equations, we can obtain different maximum particle sizes when a specific value is reached at its maximum. Optimal gradation parameters and .

[0033] Furthermore, the area of ​​the gradation curve and comprehensive parameters The specific value is obtained through extreme value analysis of the experimental data.

[0034] This invention also provides a dam construction coarse-grained soil gradation design system based on a two-parameter gradation equation, comprising:

[0035] Memory, used to store computer programs and data;

[0036] A processor is used to execute computer programs to implement the steps of the coarse-grained soil gradation design method for dam construction based on the two-parameter gradation equation, as described above.

[0037] The beneficial effects of this invention are:

[0038] This invention establishes a quantitative correlation between coarse-grained soil gradation and compaction characteristics by constructing a mathematical relationship model between gradation parameters, maximum particle size, and compaction density. This quantitative relationship considers the influence of maximum particle size on the compaction characteristics of coarse-grained soil, overcoming the limitations of traditional gradation design which mainly relies on empirical judgment and specification limit control. Based on the above quantitative relationship, gradation parameters with better compaction characteristics under different maximum particle size conditions can be obtained, which can meet the design requirements for coarse-grained soil gradation in earth-rock dam engineering and realize the inverse optimization design of coarse-grained soil gradation for dam construction. Attached Figure Description

[0039] Figure 1 This is a flowchart of a coarse-grained soil gradation design method for dam construction based on a two-parameter gradation equation in this embodiment;

[0040] Figure 2a This is a gradation curve diagram of different gradation parameters in this embodiment at a maximum particle size of 60 mm;

[0041] Figure 2b This is a gradation curve diagram of different gradation parameters in this embodiment at maximum particle sizes of 40mm, 20mm, and 10mm.

[0042] Figure 3 This is a schematic diagram of the area of ​​the gradation curve in this embodiment;

[0043] Figure 4 This is a graph showing the relationship between compaction density and gradation characteristic parameters in this embodiment;

[0044] Figure 5 This is a gradation curve diagram designed for earth-rock dams in this embodiment. Detailed Implementation

[0045] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] Example: A method for designing the gradation of coarse-grained soil for dam construction based on a two-parameter gradation equation, such as... Figure 1 As shown, it includes the following steps:

[0047] Step S1, Design experimental gradation based on two-parameter gradation equation: Design coarse-grained soil gradation with different gradation parameters and maximum particle size based on two-parameter gradation equation. The number of coarse-grained soil gradation tests shall not be less than 10 groups. Different gradations shall be designed by changing the combination of gradation parameters and maximum particle size, among which the maximum particle size shall not be less than 3.

[0048] This step aims to generate a series of representative coarse-grained soil gradations through theoretical equations, providing a basis for subsequent experiments.

[0049] The two-parameter gradation equation used is as follows:

[0050] (1)

[0051] In equation (1), Particle size; Maximum particle size; The content of particles smaller than a certain particle size; and Here are the gradation parameters, where the gradation parameters are... The main factors affecting the shape of the gradation curve are the gradation parameters. The main influence is on the steepness of the gradation curve, and the two together determine the morphological characteristics of the gradation curve.

[0052] In this embodiment, a total of 15 different coarse-grained soil test gradations with different gradation parameters and maximum particle size were designed, such as... Figure 2a and Figure 2b As shown, the maximum particle size Four different values ​​were selected: 60mm, 40mm, 20mm, and 10mm; gradation parameters Three different values ​​were selected: 1.0, 0.7, and 0.4; gradation parameters Three different values ​​were selected: -1.0, 0.1, and 0.6. Through the above parameter combinations, 15 experimental gradations covering different gradation forms were obtained, which can effectively reflect the influence of gradation characteristics on compaction density.

[0053] Step S2, conduct compaction density test: Conduct compaction density test on each grade of the soil mix from step S1 to obtain the compaction density of coarse-grained soil under different gradation conditions. The compaction density test adopts the surface vibration compaction method or the shaking table method.

[0054] In this embodiment, the test material was taken from the coarse-grained soil of a dam under construction. It was prepared according to the 15 gradations designed above, and then the surface vibration compaction test was carried out on each grade of soil material (refer to the "Standard for Geotechnical Testing Methods" GB / T 50123-2019) to obtain the compaction density of each grade of soil material, as shown in Table 1.

[0055] Table 1. 15 Design Gradients and Their Compacted Densities

[0056]

[0057] Step S3: Establish a set of mathematical equations: Analyze the relationship between gradation parameters, maximum particle size and compaction density based on experimental data, and construct the corresponding set of mathematical equations.

[0058] This step aims to establish a quantitative relationship between compaction density and gradation characteristics through data analysis.

[0059] Analysis of the data in Table 1 shows that coarse-grained soils with different gradations have different compaction densities. These differences stem from two aspects: firstly, the maximum particle size differs, and secondly, the gradation structure differs. The gradation structure is determined by the gradation parameters. and gradation parameters The compaction density is jointly determined, but varies with the gradation parameters. and gradation parameters Individual variations exhibit complex patterns, making it difficult to directly establish functional relationships. Therefore, this method constructs two parameters that comprehensively reflect the gradation characteristics. Specifically:

[0060] Step S31, construct the area of ​​the gradation curve

[0061] like Figure 3 As shown, the area of ​​the gradation curve Defined as the area enclosed by the gradation curve and the coordinate axes, its physical meaning is to characterize the degree of concentration of particle distribution, and its calculation formula is:

[0062] (2)

[0063] Based on the two-parameter gradation equation in step S1, the following relationship can be derived:

[0064] (3)

[0065] Substituting equation (3) into equation (2), and after transformation, we get:

[0066] (4)

[0067] in, The smallest particle size is 0.075 in this embodiment; The content of particles smaller than the minimum particle size is expressed as follows:

[0068] (5)

[0069] It should be noted that "60" in formula (5) is the maximum particle size reference value used in this embodiment, and can be adjusted according to specific circumstances in actual applications.

[0070] The relationship between the area of ​​the gradation curves and the compaction density for gradations 1 to 11 was analyzed, such as... Figure 4 As shown, a good quadratic function relationship can be observed between the two, expressed as:

[0071] (6)

[0072] In the formula, , and The constant is obtained by fitting experimental data; in this embodiment, =-0.652, =1.18, =2.42.

[0073] From equation (6), it can be seen that when the area of ​​the gradation curve... When the density reaches 1.18, the compacted density reaches its maximum value of 2.42 g / cm³. 3 At this point, the filling relationship between the graded particles is optimal; that is, from the perspective of the graded structure, =1.18 is the optimal value.

[0074] Step S32, construct comprehensive parameters

[0075] Although equation (6) reveals the area of ​​the gradation curve With compaction density The relationship exists, but this formula alone cannot be used to deduce the optimal gradation parameters. and gradation parameters The value of . Therefore, this method further constructs a comprehensive parameter. This parameter takes into account both the gradation structure and the maximum particle size, and its calculation formula is as follows:

[0076] (7)

[0077] in, (8)

[0078] Content of particles with a diameter of 5 mm; =1mm, which is a constant.

[0079] The physical meaning of Equation (7) is that the first term reflects the contribution of the gradation structure, the second term reflects the contribution of the maximum particle size, and the third term reflects the contribution of the fine particle content. The product of the three factors comprehensively characterizes the influence of gradation on compaction density.

[0080] Compaction density and comprehensive parameters of 15 gradations Analyze the relationships between them, such as Figure 4 As shown, the two also exhibit a good quadratic function relationship, expressed as:

[0081] (9)

[0082] In the formula, , and The constant is obtained by fitting experimental data; in this embodiment, =-0.0894, =2.31, =2.38.

[0083] From equation (9), it can be seen that when the comprehensive parameter When the density reaches 2.31, the compacted density reaches its maximum value of 2.38 g / cm³. 3 .

[0084] Thus, this method establishes two mathematical equations: Equation (6) describes the relationship between compaction density and the area of ​​the gradation curve, and Equation (9) describes the relationship between compaction density and comprehensive parameters. These two equations together form the basis for the solution in step S4.

[0085] Step S4, Solve to obtain the design gradation: Solve the system of equations to obtain the gradation parameters of coarse-grained soil with compaction characteristics under different maximum particle sizes, thereby obtaining the design gradation of coarse-grained soil for dam construction.

[0086] When solving the system of mathematical equations consisting of equations (6) and (9), let the area of ​​the gradation curve be... and comprehensive parameters Take the compaction density respectively By solving a system of mathematical equations to determine the specific value at which the maximum particle size is reached, we can obtain the maximum particle size for different values. Optimal gradation parameters and Area of ​​gradation curve and comprehensive parameters The specific value is obtained through extreme value analysis of experimental data; specifically, it is based on the relationship between compaction density and the area of ​​the gradation curve. The quadratic function relationship determines the area of ​​the gradation curve. The specific value is 1.18, based on the compaction density and comprehensive parameters. Determining the comprehensive parameters from the quadratic function relationship The value is 2.31.

[0087] Will =1.18, =2.31, substituting into equations (4) and (7), we obtain the gradation parameters. and gradation parameters The system of equations:

[0088]

[0089] For different maximum particle sizes Solving the above system of equations will yield the corresponding optimal gradation parameters. and In this embodiment, respectively take Solve for 60mm, 40mm, 20mm, and 10mm to obtain the corresponding gradation parameter combinations.

[0090] Based on the solution results, gradation curves with better compaction characteristics under different maximum particle sizes were plotted, such as... Figure 5As shown, these gradation curves represent the design gradation of coarse-grained soil for this earth-rock dam project.

[0091] This embodiment also provides a dam coarse-grained soil gradation design system based on a two-parameter gradation equation. The system includes a memory and a processor. The memory is used to store computer programs and data. The processor is used to execute the computer program to implement the steps of the dam coarse-grained soil gradation design method based on the two-parameter gradation equation.

[0092] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for designing the gradation of coarse-grained soil for dam construction based on a two-parameter gradation equation, characterized in that, Includes the following steps: Step S1: Design coarse-grained soil gradations with different gradation parameters and maximum particle size based on the two-parameter gradation equation. The maximum particle size covers large particles with a diameter of not less than 60 mm. Step S2: Conduct compaction density tests on each grade of gradation to obtain the compaction density of coarse-grained soil under different gradation conditions; Step S3: Analyze the relationship between gradation parameters, maximum particle size and compaction density based on experimental data, and construct a set of mathematical equations including the maximum particle size variable; Step S4: Solve the system of equations to obtain the coarse-grained soil gradation parameters with optimal compaction characteristics under different maximum particle sizes, thereby obtaining the design gradation of coarse-grained soil for dam construction.

2. The method for designing the gradation of coarse-grained soil for dam construction based on a two-parameter gradation equation as described in claim 1, characterized in that, In step S1, the two-parameter gradation equation is defined as: In the formula, Particle size; Maximum particle size; The content of particles smaller than a certain particle size; and These are the gradation parameters.

3. The method for designing the gradation of coarse-grained soil for dam construction based on a two-parameter gradation equation as described in claim 1, characterized in that, In step S1, the number of coarse-grained soil gradation tests shall not be less than 10 groups. Different gradations shall be designed by changing the combination of gradation parameters and the maximum particle size, among which the maximum particle size shall not be less than 3.

4. The method for designing the gradation of coarse-grained soil for dam construction based on a two-parameter gradation equation as described in claim 1, characterized in that, In step S2, the compaction density test is performed using the surface vibration compaction method or the shaking table method.

5. The method for designing the gradation of coarse-grained soil for dam construction based on a two-parameter gradation equation as described in claim 1, characterized in that, In step S3, the construction of the system of mathematical equations includes: Constructing the area of ​​gradation curves to characterize the gradation structure The calculation formula is as follows: Establish compaction density Area of ​​gradation curve The quadratic function relationship between them: In the formula, , and It is a constant; and These are the gradation parameters.

6. The method for designing the gradation of coarse-grained soil for dam construction based on a two-parameter gradation equation as described in claim 5, characterized in that, In step S3, the construction of the system of mathematical equations also includes: Constructing comprehensive parameters to characterize gradation features The calculation formula is as follows: Establish compaction density With comprehensive parameters The quadratic function relationship between them: In the formula, , and It is a constant; Maximum particle size; It is a constant.

7. The method for designing the gradation of coarse-grained soil for dam construction based on a two-parameter gradation equation according to claim 6, characterized in that, In step S4, let the area of ​​the gradation curve be... and comprehensive parameters Take the compaction density respectively By solving a system of mathematical equations, we can obtain different maximum particle sizes when a specific value is reached at its maximum. Optimal gradation parameters and .

8. The method for designing the gradation of coarse-grained soil for dam construction based on a two-parameter gradation equation according to claim 7, characterized in that, Area of ​​gradation curve and comprehensive parameters The specific value is obtained through extreme value analysis of the experimental data.

9. A dam-building coarse-grained soil gradation design system based on a two-parameter gradation equation, characterized in that, include: Memory, used to store computer programs and data; A processor for executing a computer program to implement the steps of the dam coarse-grained soil gradation design method based on a two-parameter gradation equation as described in any one of claims 1-8.

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