Coarse grain inverted filter design method for synergistically exerting soil filtering and drainage pressure reduction performance

Abstract

The invention discloses a coarse-grained inverted filter design method for synergistically exerting soil filtering and drainage pressure reduction performance. The coarse-grained inverted filter design method comprises the following steps: judging the soil filtering performance of a coarse-grained inverted filter material and judging the drainage pressure reduction performance of the coarse-grained inverted filter material on the basis of a probability statistics principle; when the coarse-grain inverted filter layer is designed, the soil filtering and drainage pressure reducing performance is synergistically exerted. According to the invention, based on the theory of particle mechanics, the particle size of protected soil and the control aperture of an inverted filter material are taken as random variables, the method for discriminating the filter soil performance of the soil-inverted filter material system based on the failure probability p (ir) is provided, and the influence of factors such as particle gradation distribution, aperture distribution, relative compactness and inverted filter layer thickness is comprehensively considered. On the basis of a hydrodynamic theory and in combination with a soil filtering performance failure probability limit p (ir) being less than 0.5 and a drainage performance failure probability limit p (ihc) being less than 0.0095, a set of inverted filter layer design method capable of synergistically exerting the soil filtering performance and the drainage pressure reduction performance of a coarse-grained inverted filter material is provided. And combined judgment and synergistic exertion of the soil filtering performance and the drainage pressure reduction performance of the inverted filter layer can be realized.

Description

Technical Field

[0001] The present invention relates to the technical field of water conservancy and hydropower engineering, and particularly relates to a design method of a coarse-grained filter layer based on the probability of performance failure, and more particularly to a design method of a coarse-grained filter layer that synergistically exerts the functions of soil filtration and drainage pressure relief. Background Art

[0002] Seepage erosion is one of the main factors affecting the safety and service life of earth-rock dams. So-called seepage erosion refers to the erosion inside the soil caused by the seepage of water in the soil skeleton, which gradually enlarges its pores and induces the occurrence of seepage failure in the soil mass inside the earth-rock dam and its foundation. The filter layer is one of the effective measures to prevent the induced damage of hydraulic structures such as earth-rock dams due to seepage erosion. The function of the filter layer is to retain fine particles from being carried away by seepage and ensure the smoothness of the seepage process, mainly including the functions of soil filtration and drainage pressure relief. These two functions of the filter material are significantly mutually restrictive. Therefore, it is necessary to develop a design method for the filter layer that synergistically exerts these two functions, which is not only the need for the evaluation and prevention and control of the hydraulic disaster mechanism of engineering disasters, but also the urgent need for the safe service of water conservancy project infrastructure in complex environments.

[0003] The existing design methods for filter layers mainly use characteristic particle sizes to distinguish the soil filtration and drainage pressure relief functions of filter materials. However, the method for distinguishing the performance of filter materials considering the particle size distribution needs to be further studied.

[0004] For example, Terzaghi proposed a method for distinguishing the soil filtration performance for uniformly graded coarse-grained filter materials in his monograph "Theoretical soil mechanics": d 15(f) ≤5d 85(s) where d x represents the particle size (mm) with a sieve passing percentage of x%; the subscripts (f) and (s) represent the filter material and the protected soil respectively, and an excessive ratio is not conducive to the seepage stability of the system. However, this discrimination method does not consider the influence of particle size distribution.

[0005] For example, the International Commission on Large Dams (ICOLD) proposed a method for distinguishing the soil filtration performance of coarse-grained filter materials (hereinafter referred to as the ICOLD method) in the monograph "Embankment dams–filters and drains, bulletin No 95": d 15(f) ≤12d 85(s). The discrimination steps of this method are based on the Terzaghi filter soil performance discrimination method, and improvements are made to soils with wide gradation, discontinuous gradation and upward concave gradation distribution. However, the filtration phenomenon mainly depends on the particle size distribution of the protected soil and the pore size distribution of the filter material, and the particle size and pore size are essentially random variables rather than given characteristic parameters. Therefore, when judging the performance of coarse-grained filter materials, the probability statistical method should be combined with the hydrodynamic equation, and the particle gradation distribution of the protected soil and the pore size distribution of the filter material should be further introduced into the study of the filtration soil and drainage pressure reduction performance discrimination method.

[0006] For example, the Natural Resources Conservation Service (NRCS) proposed a method for judging the filtration performance of coarse-grained filter media in its monograph "Soil engineering: national engineering handbook" (hereinafter referred to as the NRCS method): 15(f) ≤9d 85(s) . This method adjusts the particle grading curves of wide-graded soil and discontinuous-graded soil by the percentage passing the 4.75 mm sieve and the minimum discontinuity size, respectively, and then divides the soil into four categories based on the percentage passing the 0.075 mm sieve on the adjusted curve. In the discrimination step, the particle grading distribution of the soil is adjusted to take into account the fine particle content that enters the filter layer due to the internal instability of the soil. The filter material d corresponding to each soil type 15(f) The minimum value is determined by an empirical formula based on test data. 15(f) The minimum value should exceed the protected soil d 15(s) The value is 4 times and does not exceed 0.1 mm. However, the permeability stability of the coarse-grained filter material needs to meet the requirements of soil filtration and drainage pressure reduction at the same time. This method does not take into account and synergize the soil filtration and drainage pressure reduction performance of the coarse-grained filter material.

[0007] Chinese patent CN 116384072 A discloses a filter layer design method for protecting internal unstable soil. The method evaluates the internal stability of the core wall material according to the particle grading curve of the core wall material; determines the boundary particle size of the coarse and fine particles of the core wall material; and determines the d of the core wall material according to the boundary particle size and the particle grading curve of the core wall material. 85(s) d 15(s) ; The characteristic particle size d of the filter layer is calculated according to the formula 15(f) According to d 15(f) Determine the gradation of the filter layer. However, this method neither considers the pore size distribution of the filter material when designing the filter layer, nor considers how to synergistically exert the soil filtration and drainage pressure reduction performance of the coarse-grained filter material. Summary of the invention

[0008] The object of the present invention is to overcome the deficiencies of the above-mentioned prior art and provide a design method for a coarse-grained filter layer that synergistically exerts the soil filtration and drainage pressure relief performance based on probability statistics, aiming to achieve the joint discrimination and synergistic exertion of the soil filtration and drainage pressure relief performance of the filter layer.

[0009] To achieve the above object, the present invention adopts the following technical solutions:

[0010] A design method for a coarse-grained filter layer that synergistically exerts the soil filtration and drainage pressure relief performance is implemented according to the following steps:

[0011] Step 1: Based on the principle of probability statistics, discriminate the soil filtration performance of the coarse-grained filter material.

[0012] Step 1.1: Estimate the pore size distribution of the coarse-grained filter material.

[0013] Since the aggregate composed of four particles is relatively loose, in order to consider the most unfavorable conditions in the discrimination of soil filtration performance, the present invention selects the aggregate of four particles to simulate the coarse-grained filter material, and calculates parameters such as the pore size and pore area of the aggregate.

[0014] Step 1.2: Construct a safety margin limit state function for non-uniform particle size soil particles facing soil filtration requirements.

[0015] When discriminating the soil filtration performance of the filter material, the safety margin limit state function facing soil filtration requirements is extended to non-uniform particle size soil particles:

[0016] M s (G, V) = G i - V j (1)

[0017] Where: G i and V j are samples taken from the particle size distribution and pore size distribution respectively. When M s ≥0, the filter material is effective; when M s <0, the filter material fails. Since G i and V j are random variables, there is a probability corresponding to each variable value.

[0018] Step 1.3: Calculate the failure probability of soil filtration performance.

[0019] The failure probability p (ir) of soil filtration performance can be defined either as the probability that the pore size is larger than the particle size or as the proportion of the content of soil particles that cannot be retained by the filter material (the subscript (ir) represents soil filtration failure, and the subscripts shown below are the same). p (ir) can be calculated by Monte Carlo simulation of the following formula, and its calculation result will converge as the sample number N increases:

[0020]

[0021] Step 1.4, divide the boundary of the failure probability of the soil filtration performance

[0022] The soil-inverse filter column test results carried out on the present invention and existing literature verify the effectiveness of the soil filtration performance discrimination method proposed by the present invention, and then these data are discriminated to determine the failure probability p (ir) of the soil filtration performance.

[0023] Step two, discriminate the drainage and decompression performance of the coarse-grained inverse filter material

[0024] Step 2.1, construct a performance function for drainage and decompression requirements based on the permeability coefficient

[0025] The hydraulic gradient of most geotechnical structures generally does not exceed 25. In order to consider the most unfavorable conditions in the design of the inverse filter layer in the present invention, the relationship between the permeability coefficients of the protected soil and the inverse filter material is taken as K (f) ≥25K (s) (the subscripts (f) and (s) represent the inverse filter material and the protected soil respectively, and the subscripts shown below are the same), aiming to strictly meet the drainage and decompression requirements. Thus, the performance function for drainage and decompression requirements can be expressed as:

[0026] ω(K (f) ,K (s) )=K (f) / K (s) (3)

[0027] When ω≥25, the performance of the soil-inverse filter material system is effective; when ω<25, its performance fails.

[0028] Step 2.2, calculate the failure probability of the drainage and decompression performance

[0029] The variability of the permeability coefficient K of the soil-inverse filter material system can be described by the logarithmic form of the permeability coefficient ratio K (f) / K (s) (i.e., the permeability coefficient performance function) and the coefficient of variation COV. Thus, the probability p (ihc) of the drainage and decompression performance failure is expressed as:

[0030] p (ihc) =φ(x)(4a)

[0031]

[0032] In the formula: φ is the standard normal distribution function; the subscript (ihc) represents the drainage and decompression failure, and the subscripts shown below are the same.

[0033] Step 2.3, divide the boundary of the drainage and decompression performance

[0034] Since the mean value can be obtained through actual measurement or prediction, p (ihc) is essentially a function of COV. To meet the strict requirements of K (f) ≥25K (s) for drainage and pressure relief, let COV = 100% correspond to the most unfavorable conditions considered in the design of the filter layer. Then, the drainage and pressure relief performance p (ihc) of the boundary value can be calculated using equations (4a), (4b), and (4c).

[0035] Step 3: When designing the coarse-grained filter layer, give full play to its soil filtration and drainage and pressure relief performance

[0036] Step 3.1: Reclassify the particle size distribution curve of the protected soil

[0037] For gravelly soil, well-graded soil with a particle size greater than 2 mm, and discontinuously graded soil, their particle size distribution curves need to be reclassified. In the semi-logarithmic coordinate system, using the effective particle size d 10 , d 30 and the control particle size d 60 corresponding data points for linear interpolation, the particle size distribution curve formula for any particle size d F with respect to the corresponding sieve passing rate F can be deduced:

[0038]

[0039] The boundary of the filter layer is determined by selecting the range of d 10 values that meet the requirements of soil filtration and drainage and pressure relief. The minimum and maximum values of d 10 depend on the minimum and maximum particle sizes of the filter material. The minimum value of d 10 should not be less than 0.1 mm, and its maximum value should not be greater than 2.5 mm.

[0040] Step 3.2: Determine the effective performance zone of the coarse-grained filter layer by combining the failure probability boundaries of soil filtration and drainage and pressure relief

[0041] The fine-grained boundary of the filter layer is determined based on the drainage and pressure relief requirement of p (ihc) < 0.0095. When other properties of the soil are known, p (ihc) depends only on d 10 . During the process of d 10 increasing from the minimum value to the maximum value, p (ihc) gradually decreases. If the p 10 value when d (ihc) takes the minimum value is greater than 0.1, the iterative value of d 10 should be increased to the design value of d 10 at the fine-grained boundary of the filter material to meet the boundary of p (ihc) < 0.0095; if d10 The p when taking the minimum value (ihc) If the value is less than 0.0095, then d 10 The minimum value is the d of the fine-grained boundary of the filter material 10 Design value. Adopt the d of the fine-grained boundary 10 Design value, coefficient of uniformity C u And coefficient of curvature C c The particle size distribution curve of the fine-grained boundary of the filter material can be determined

[0042] According to p (ir) <0.5 soil filtration requirements, the coarse-grained boundary of the filter material can be determined. When other properties of the soil are known, p (ir) Depends on d 10 And the thickness of the filter layer. The thickness of the filter layer is determined according to its application range and standards. At d 10 During the process of increasing the iteration value to its maximum value, p (ir) Gradually increases. If the d of the fine-grained boundary of the filter material 10 The corresponding p of the value (ihc) Is less than 0.5, then the iteration value of d 10 Should be reduced to the d of the coarse-grained boundary of the filter material 10 Design value, so as to meet p (ir) <0.5 boundary; If d 10 The p when taking the maximum value (ir) Is less than 0.5, then d 10 The maximum value is the d of the coarse-grained boundary of the filter material 10 Design value. Adopt the d of the coarse-grained boundary 10 Design value, coefficient of uniformity C u And coefficient of curvature C c The particle size distribution curve of the coarse-grained boundary of the filter material can be determined

[0043] The particle size distribution curve of the filter layer is generally flexibly selected within the performance effective band, and this effective band is composed of the drainage and decompression boundary corresponding to the fine-grained boundary and the soil filtration boundary corresponding to the coarse-grained boundary

[0044] Compared with the existing filter layer design method, the beneficial effects of the present invention are reflected in:

[0045] 1. Based on the theory of particle mechanics, taking the particle size of the protected soil and the control aperture of the filter material as random variables, a method for judging the soil filtration performance of the soil-filter material system based on the failure probability p (ir) Is proposed, comprehensively considering the influence of factors such as particle size distribution, aperture distribution, relative density and filter layer thickness

[0046] 2. Based on the theory of hydrodynamics, and combined with the soil filtration performance failure probability limit p (ir) <0.5 and the drainage performance failure probability limit p(ihc) <0.0095, a set of filter layer design methods that can synergistically exert the soil filtration and drainage and decompression performance of coarse-grained filter materials is proposed. Description of the Drawings

[0047] Figure 1 is the flowchart of the filter layer design method;

[0048] Figure 2 is the definition diagram of the pore size composed of four-particle aggregates;

[0049] Figure 3 is the structural diagram of the maximum and minimum pore areas and the maximum and minimum interior angles α composed of four-particle aggregates;

[0050] Figure 4 is the discretization diagram of the particle size distribution curve represented by mass, surface area, and quantity;

[0051] Figure 5 is the schematic diagram of generating samples from the particle size distribution curve and the pore size distribution curve;

[0052] Figure 6 is an example to illustrate the estimation of p (ir) The particle size distribution curve and pore size distribution curve diagrams of the soil and filter material used in the estimation steps;

[0053] Figure 7 is the calculation flowchart of the failure probability of the soil filtration performance;

[0054] Figure 8 is the Monte Carlo simulation flowchart of the soil filtration process;

[0055] Figure 9 is the particle size distribution curve diagram of the silty sand No. 1-2 and the filter material at the coarse-grained boundary before and after the test;

[0056] Figure 10 is the diagram of the permeability test device for discriminating the soil filtration performance of the soil-filter column;

[0057] Figure 11 is the change curve diagram of the permeability coefficient of two soil-filter columns with time;

[0058] Figure 12 is the diagram for determining the boundary of the soil filtration performance and comparing the method of the present invention with the Terzaghi method;

[0059] Figure 13 is the comparison diagram of the soil filtration performance discrimination method of the present invention with the ICOLD method;

[0060] Figure 14 is the comparison diagram of the soil filtration performance discrimination method of the present invention with the NRCS method;

[0061] Figure 15 is the influence diagram of the coefficient of variation COV on the failure probability p of the drainage and decompression performance (ihc) ;

[0062] Figure 16 is the particle size distribution curve described by two straight lines in the semi-logarithmic coordinate system;

[0063] Figure 17 is the effective zone diagram of the filter material performance designed for the silty sand example listed in the NRCS method;

[0064] Figure 18 is the effective zone diagram of the filter material performance designed for the silty sandy gravel example listed in the NRCS method;

[0065] Figure 19 is the effective zone diagram of the filter material performance designed for the silty gravel example listed in the NRCS method. Specific implementation manners

[0066] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0067] The structures, ratios, sizes, etc. shown in the drawings of this specification are only used to cooperate with the content disclosed in the specification for those skilled in this technology to understand and read, and are not used to limit the limited conditions under which the present invention can be implemented. Therefore, they do not have technical substance significance. Any modification of the structure, change of the proportional relationship or adjustment of the size, without affecting the effects that the present invention can produce and the purposes that can be achieved, should still fall within the scope covered by the technical content disclosed in the present invention. At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" cited in this specification are only for the convenience of clear description and are not used to limit the scope under which the present invention can be implemented. The change or adjustment of their relative relationships, without substantial change in the technical content, should also be regarded as the scope under which the present invention can be implemented.

[0068] A design method for a coarse-grained filter layer that synergistically exerts the soil filtration and drainage and decompression performances, as Figure 1 shown, is implemented according to the following steps:

[0069] Step 1, based on the probability and statistics principle, determine the soil filtration performance of the coarse-grained filter material,

[0070] Existing experience and analytical methods for soil filtration requirements regard the characteristic particle sizes and pore sizes of soil and filter material as determined variables. However, during the filtration process, soil particles with random particle sizes will penetrate into pores with random diameters. It can be seen that the particle sizes and pore sizes are not determined variables but random variables that follow a specific distribution. Therefore, the particle sizes and pore sizes are essentially uncertain physical quantities. Therefore, when determining the soil filtration performance of the filter material, random phenomena and the probability and statistics principle should be considered. The specific steps are as follows:

[0071] Step 1.1, estimate the pore size distribution curve of the coarse-grained filter material,

[0072] Since the aggregate composed of four particles is relatively loose, in order to consider the most unfavorable conditions in the discrimination of the soil filtration performance, the present invention selects the aggregate of four particles to simulate the coarse-grained filter material, and the pore size formed by this aggregate can be expressed as:

[0073] d v = 4A v / C v (1)

[0074] Where: A v and C v are respectively the area and perimeter of the pores formed by four spherical particles, and are related to the interior angles of the quadrilateral formed by the connecting lines of the centers of the four particles, as shown in Figure 2 Shown. The interior angle of the corresponding quadrilateral for a given relative density D r can be obtained by linear interpolation

[0075] α(D r ) = α v(max) - D r (α v(max) - α v(min) ) (2)

[0076] Where: α v(max) and α v(min) are respectively the interior angles of the quadrilateral when the maximum and minimum pore areas are formed by the aggregate of four particles, as shown in Figure 2 Shown. The other interior angles β, γ and δ can be determined with respect to the α angle through plane geometric analysis:

[0077]

[0078] Where: A = d k + d l , B = d i + d l , C = d i + d j , D = d j + d k .

[0079] The pore area is calculated according to the following formula:

[0080]

[0081] The maximum and minimum pore areas can be obtained by repeatedly trial calculations by changing the α value within the range of α min ~α max , where α max and α minThey are the maximum and minimum possible values of α when the spherical particles are all in point contact, as Figure 3 shown, and can be calculated based on trigonometric functions.

[0082]

[0083]

[0084] The particle size distribution curve measured by the sieving method is essentially a particle size distribution curve expressed in terms of mass. According to the literature, the pore size distribution curve estimated using such a particle size distribution curve reflects a relatively high content of coarse particles, while the pore size distribution curve estimated from the particle size distribution curve expressed in terms of quantity reflects a relatively high content of fine particles. Therefore, the particle size distribution curve expressed in terms of surface area is the optimal choice for estimating the pore size distribution curve. The particle size distribution curves expressed in terms of mass, surface area, and quantity are as Figure 4 shown. Discretize the particle size distribution curve expressed in terms of mass into n segments of particle sizes (d1, d2... d n ), then the probabilities of the corresponding particle sizes appearing are p m1 , p m2 ... p mn . Thus, the probability p sa of the particles in the particle size distribution curve expressed in terms of surface area can be expressed as follows:

[0085]

[0086] In the formula: The probability p v of the pore size d v appearing is related to the number of times of contact with the same four particles, and this number is in turn related to the probability of each particle appearing. Therefore, p v can be calculated according to the multinomial distribution as follows:

[0087]

[0088] In the formula: r i , r j , r k and r l are the numbers of times of d i , d j , d k and d l appearing in the four-particle aggregate respectively; p i , p j , p k and p l are the probabilities of d i , d j , d k and d l appearing respectively.

[0089] Step 1.2, construct the safety margin limit state function of non-uniform particle size soil particles for soil filtration requirements.

[0090] The process of uniform particle size soil particles infiltrating into pores with a uniform diameter is similar to sieving. When the pore diameter is smaller than the particle size, the soil filtration performance of the filter material is effective; when the pore diameter is larger than the particle size, the soil filtration performance of the filter material fails. This similar relationship can be extended to non-uniform particle size soil particles by introducing the safety margin limit state function for soil filtration requirements:

[0091] M s (G, V) = G i - V j (9)

[0092] Where: G i and V j are samples taken from the particle size distribution and pore diameter distribution respectively. When M s ≥0, the filter material is effective; when M s <0, the filter material fails. Since G i and V j are random variables, there is a probability corresponding to each variable value. Therefore, the result of the failure of the soil filtration performance is composed of the set of all pore diameters larger than the particle size. To generate samples of the particle size distribution curve and pore diameter distribution curve, uniform random numbers (u i ) can be generated first in the interval of 0 to 1, and then the abscissa of the intersection points of the horizontal line passing through this random number and the particle size distribution curve and pore diameter distribution curve are the required samples, as Figure 5 shown;

[0093] Step 1.3, calculate the failure probability of soil filtration performance.

[0094] The failure probability p (ir) of the soil filtration performance can be defined either as the probability that the pore diameter is larger than the particle size or as the proportion of the soil particles that the filter material cannot retain. p (ir) can be calculated by Monte Carlo simulation of the following formula, and its calculation result will converge as the number of samples N increases:

[0095]

[0096] Estimate the failure probability p (ir) of the soil filtration performance. The required data includes the particle size distribution curve, relative density D r and the thickness of the filter layer. Taking the soil-filter material system shown in Figure 6 as an example (the D r of the protected soil and the filter material are taken as 0.5 and 0.8 respectively), the estimation of p (ir) can be achieved from the following 3 steps according to the process shown in Figure 7 :

[0097] (1) Discretize the particle size distribution curve of the filter material expressed in mass into n segments (for this example, the particle size distribution curve of the filter material can be discretized into 10 segments). At the same time, use Equation (7) to obtain the particle size distribution curve expressed in surface area. Based on C n,4 Determine the number of four-particle aggregates (for this example, C 10,4 is equal to 715 four-particle aggregates). In each aggregate, use Equations (2) and (1) combined with the relative density D of the filter material r to calculate the pore size of the aggregate, and then use Equation (8) to calculate the probability of each pore size occurring. Cumulating the probabilities of the pore sizes of all four-particle aggregates gives the pore size distribution curve of the filter material (the pore size distribution curve of the filter material obtained in this example is also as Figure 6 shown).

[0098] (2) When the particle size distribution of the protected soil is extremely good or discontinuous, it is necessary to correct the particle size distribution curve expressed in mass, aiming to consider the fine particles that may infiltrate from the coarse particle aggregates in the soil to the soil-filter material interface. For this purpose, introduce the separation particle size d of the fine particles and the coarse particles * reclassify the protected soil, divide the sieve passing rate of the soil particles smaller than d * by the sieve passing rate corresponding to d * to obtain the corrected particle size distribution curve. Regarding the selection of d * , the particle size group smaller than 2 mm in the soil is more likely to infiltrate to the soil-filter material interface than the coarse particle group of gravel. Therefore, in this paper, the extremely well-graded soil is reclassified at the 2 mm sieve hole diameter, and the discontinuous graded soil is reclassified at the inflection point. In this example, d * is 2 mm, and the corresponding sieve passing rate is 72%.

[0099] (3) Extract samples from the particle size distribution curve of the protected soil and the pore size distribution curve of the filter material, conduct Monte Carlo simulation, use Equation (9) to obtain the values of different safety margin limit state functions, and then substitute them into Equation (10) to calculate the corresponding probability p of filter soil performance failure (ir) value (including the probability value at the filter layer thickness). In this example, using Equation (10), the p at the soil-filter material interface can be calculated (ir) = 0.32. To consider the influence of the filter layer thickness, 1055 samples corresponding to the contraction layers along the filtration path were examined. The number of contraction layers was calculated by dividing the filter layer thickness (100 mm) by the thickness of each contraction layer (0.095 mm). The thickness of each contraction layer can be regarded as the average contraction size obtained from the average value of the pore size distribution curve samples. By excluding the samples of the protected soil that were not retained by the 1055 contraction layers but had infiltrated to the filter material interface, the p (ir) = 0.098 can be calculated.

[0100] Example 1

[0101] According to the particle size distribution curve data of the soil to be protected and the pore size distribution curve data of the filter material, Monte Carlo simulation is carried out. The simulation process is as Figure 8 shown. At the same time, Table 1 gives two typical examples of effective soil filtration and soil filtration failure during the soil filtration process.

[0102] The particle size distribution curves of the filter material and the silty sand No. 1 and No. 2 are discretized, and a set is randomly selected from the samples to obtain the examples in Table 1. The particle size distribution samples of the silty sand No. 1 and No. 2 and the pore size samples of the filter material are both 10 6 , the number of failures of the silty sand No. 1 is 604,070 times, and the failure probability p (ir) is 0.604. The number of failures of the silty sand No. 2 is 367,940 times, and the failure probability p (ir) is 0.368.

[0103] Table 1 Two typical examples in Monte Carlo simulation

[0104]

[0105] Step 1.4, divide the boundary of the failure probability of the soil filtration performance,

[0106] Based on the results of the soil-filter column test carried out according to the present invention and the existing literature, determine the boundary of the failure probability p (ir) of the soil filtration performance calculated by the present invention, and verify the effectiveness of the soil filtration performance discrimination method proposed by the present invention.

[0107] (1) The soil-filter column test carried out by the present invention:

[0108] Select two typical coarse-grained soils and the filter material to form a system, analyze the results of the permeability test under constant head conditions, and discriminate the soil filtration performance of these two soil-filter material systems from the experimental perspective. As Figure 9 shown, the particle size distribution curves of the silty sand No. 1 and No. 2 selected in the test are in the shapes of concave up and concave down respectively, and the d 15 and d 85 of these two soils are the same. Figure 9 Also given is the particle size distribution curve of the filter material at the coarse-grained boundary, and d 15(f) / d 85(s) <4, which basically meets the NRCS and ICOLD discrimination methods. Since d 15 and d 85 are the same, the silty sand No. 1 and No. 2 share this filter material at the coarse-grained boundary. The basic physical property parameters of these two soils and the filter material are shown in Table 2, where the maximum and minimum void ratios (e max and e minMeasured according to the relative density test method for coarse-grained soils described in the Geotechnical Test Methods Standard "GB / T 50123-2019".

[0109] Adopt Figure 10 The test device shown in the figure is used to carry out the permeability test on the cylindrical system composed of No. 1-2 silty sand and the filter material at the coarse-grained boundary, aiming to judge the soil filtration performance of this filter material. The diameter of the soil-filter column is 150 mm, and the height of the soil and the filter material is 100 mm each. During the sample preparation process, the soil and the filter material are respectively compacted to the relative density D r = 0.5 and 0.8. Constant head conditions are maintained at both the inlet and outlet of the soil-filter column, and then the downward seepage process with a hydraulic gradient of 5 is adopted to simulate the adverse working conditions. During the test, an image acquisition system based on a high-pixel digital camera is used to observe the starting, migration of fine particles and the expansion process of erosion cracks at the interface between the protected soil and the filter material, and the particle size distribution curve of the filter material is measured after the test to comprehensively judge the soil filtration performance of the filter material.

[0110] The particle size distribution curves of the No. 1 soil-filter column or the No. 2 soil-filter column after the permeability test are also as Figure 9 shown. There are significant differences in the filtration characteristics of No. 1 silty sand and No. 2 silty sand. The curves of the permeability coefficient of these two soil-filter columns changing with time are as Figure 11 shown. When the permeability coefficient of the soil-filter column gradually decreases over time, it indicates that a skeleton structure is gradually formed inside the soil-filter column; when the permeability coefficient of the soil-filter column gradually increases over time, it indicates that erosion begins to occur inside the soil-filter column. Observing the No. 1 soil-filter column, it can be found that erosion occurs inside it at the initial stage of the test, and then it gradually enters a stable state; observing the No. 2 soil-filter column, it can be found that its permeability coefficient gradually decreases until it enters a stable state( Figure 11 ). From the particle size distribution curve of the soil-filter column after the test( Figure 9 ), it can be seen that the loss of fine particles in the No. 1 soil-filter column is higher than that in the No. 2 soil-filter column. It can be seen that for the filter material at the coarse-grained boundary designed according to d 15(f) / d 85(s) < 4, the No. 1 soil-filter column belongs to the transitional state between performance failure and effectiveness, and the No. 2 soil-filter column belongs to effective performance.

[0111] Table 2 Basic physical properties of the silty sand and filter material used in the test

[0112] Parameter Name Silty Sand No. 1 Silty Sand No. 2 Filter Material at Coarse-Grain Limit <![CDATA[d 15 (mm)]]> 0.075 0.075 4.75 <![CDATA[d 85 (mm)]]> 1.18 1.18 0.85 <![CDATA[C u > 6.73 20 4.1 <![CDATA[C c > 1.18 4.15 0.87 <![CDATA[e max > 0.57 0.54 0.81 <![CDATA[e min > 0.31 0.27 0.54 <![CDATA[D r K (cm / s) when = 0.5]]> <![CDATA[4.3×10 –3 > <![CDATA[2.7×10 –3 > ––

[0113] (2) Soil-filter column tests in existing literature:

[0114] Lafleur et al. conducted a large number of permeability tests on well-graded till as dam material. Indraratna et al. carried out filter tests on homogeneous red clay and three kinds of homogeneous graded sand filter materials. Indraratna et al. proposed an analytical model for filter, and then carried out verification tests on medium-graded soil and sand filter materials. Indraratna et al. conducted verification tests on the filter discrimination method based on shrinkage pore size. Nguyen et al. judged the performance of the soil-filter material system during the filter test according to the change of particle size distribution and flow velocity at different depths of the filter layer: the flow velocity measured in the system with effective performance is stable, while the flow velocity measured in the system with ineffective performance is unstable. The above literature can provide 56 groups of test data of the soil-filter material system, among which 31 groups of data have effective performance and 25 groups of data have ineffective performance, which are used to divide the failure probability p (ir) of the filter performance. The particle size distribution parameters, relative density and test discrimination results of the 56 groups of soil-filter material systems in the above literature are shown in Table 3. In the tests described in the literature, the hydraulic gradient was taken as 3 - 10, and the thickness of the filter layer was taken as 100 - 200 mm, aiming to simulate the typical working conditions of the filter layer of rock-fill dams. All tests were carried out under the most unfavorable condition of downward flow.

[0115] Table 3 Particle size distribution parameters, relative density and test discrimination results of soil-filter material systems in existing literature

[0116]

[0117] Continued Table 3

[0118]

[0119] (3) Divide the failure probability p (ir) of the filter performance based on the test results

[0120] The failure probability p (ir) of the filter performance calculated for the 56 groups of soil-filter material system tests in the above literature is as Figure 12 shown. Each data point represents a group of tests for discriminating the soil-filter material system, and the data points are divided into two categories: effective and ineffective filter performance. The purpose of discriminating these data is to determine the boundary of p (ir) so as to provide important reference suggestions for the design of the filter layer. Three regions of the filter performance can be divided from Figure 12 , namely the effective region (p (ir) < 0.5), the transition region (p (ir) = 0.5 - 0.75) and the failure region (p (ir) > 0.75). The boundary division results show that when p (ir)When it is less than 0.5, the soil filtration performance remains effective, and a stable skeleton structure is formed in the soil-inverted filter system. d 15(f) / 5d 85(s) The vertical dividing line shown in Figure 1 describes the Terzaghi discrimination method, which is used to divide the effective and ineffective soil-inverted filter systems in terms of performance. The left area of the dividing line is the effective area, and the right area is the ineffective area, as Figure 12 shown.

[0121] Moreover,[[]] Figure 12 also lists the filtration performance discrimination results of the Terzaghi discrimination method for these 56 soil-inverted filter systems, and compares them with the effectiveness of the discrimination method of the present invention. The effectiveness of the soil filtration discrimination method depends on the number of ineffective soil-inverted filter data points in the effective performance area. As can be seen from Figure 12 it, all ineffective data points are above the dividing line shown in p (ir) = 0.5. In contrast, 9 ineffective data points are on the left side of the vertical dividing line shown in d 15(f) / 5d 85(s) = 1, and at the same time, 4 effective data points are classified into the ineffective area, which is contrary to the Terzaghi method.

[0122] In addition, the effectiveness of the discrimination method of the present invention and the ICOLD method and the NRCS method in discriminating soil filtration performance can also be compared and analyzed, as Figures 13 - 14 shown. The horizontal axis is d 15(f) / 12d 85(s) and d 15(f) / 9d 85(s) . The ICOLD method and the NRCS method divide the effective area and the ineffective area of soil filtration performance by the vertical dividing lines shown in d 15(f) / 12d 85(s) = 1 and d 15(f) / 9d 85(s) = 1, as Figures 13 - 14 shown. These two figures respectively have 6 and 5 ineffective data points on the left side of the vertical dividing lines shown in d 15(f) / 12d 85(s) = 1 and d 15(f) / 9d 85(s) = 1, and a large number of effective data points are on the right side of the vertical dividing lines shown in d 15(f) / 12d 85(s) = 1 and d 15(f) / 9d 85(s) = 1, and these data points violate the ICOLD method and the NRCS method.

[0123] The discrimination method proposed by the present invention also demonstrates its effectiveness in discriminating the soil filtration performance of Soil-Inverted Filter Columns 1 and 2. As can be seen from Example 1, in the verification example, p of the Soil-Inverted Filter System No. 1(ir) = 0.604, while for the soil - filter material system No. 2, p (ir) = 0.368. Based on p (ir) the discrimination results are consistent with the seepage test discrimination results of the soil - filter columns No. 1 and No. 2. However, according to the Terzaghi method, the ICOLD method, and the NRCS method, the performance of the soil - filter columns No. 1 and No. 2 is judged to be effective. Thus, this shows that the discrimination method based on the failure probability p (ir) proposed by the present invention has made improvements in terms of applicability and accuracy when discriminating the soil - retaining performance of the soil - filter material system compared with the existing discrimination methods.

[0124] Step two, discriminate the drainage and pressure - relief performance of the coarse - grained filter material,

[0125] Step 2.1, construct a performance function for drainage and pressure - relief requirements based on the permeability coefficient,

[0126] The hydraulic gradient of most geotechnical structures generally does not exceed 25. In order to consider the most unfavorable conditions in the design of the filter layer in the present invention, the relationship between the permeability coefficients of the protected soil and the filter material is taken as K (f) ≥ 25K (s) (the subscripts (f) and (s) represent the filter material and the protected soil respectively), aiming to strictly meet the drainage and pressure - relief requirements. Thus, the performance function for drainage and pressure - relief requirements can be expressed as:

[0127] ω(K (f) , K (s) ) = K (f) / K (s) (11)

[0128] When ω ≥ 25, the performance of the soil - filter material system is effective; when ω < 25, the performance fails.

[0129] Step 2.2, calculate the failure probability of the drainage and pressure - relief performance,

[0130] The variability of the permeability coefficient K of the soil - filter material system can be described by the logarithmic form of the permeability coefficient ratio K (f) ≥ 25K (s) (i.e., the permeability coefficient performance function) and the coefficient of variation COV. Thus, the probability p (ihc) of the failure of the drainage and pressure - relief performance is expressed as:

[0131] p (ihc) = φ(x)(12a)

[0132]

[0133]

[0134] In the formula: φ is the standard normal distribution function.

[0135] Step 2.3, dividing the drainage and decompression performance limit,

[0136] Since the mean value can be obtained through actual measurement or prediction, p (ihc) is essentially a function of COV. According to existing literature, the COV of K varies in the range of 68% - 90%, and as Figure 15 shown, p (ihc) increases with the increase of COV. Therefore, to meet the strict drainage and decompression requirement of K (f) ≥ 25K (s) by setting COV = 100% corresponding to the most unfavorable condition considered in the design of the filter layer, the limit value of p (ihc) can be calculated as 0.0095 using Equation (12), also as Figure 15 shown.

[0137] Step Three, giving full play to the soil filtration and drainage and decompression performance of the coarse-grained filter layer during design,

[0138] Step 3.1, reclassifying the particle size distribution curve of the protected soil,

[0139] The performance of the filter layer needs to meet two requirements: soil filtration and drainage and decompression. When the failure probability p (ir) of soil filtration is less than 0.5 and the failure probability p (ihc) of drainage and decompression is less than 0.0095, the performance of the filter layer is effective. The design content of the filter layer mainly includes the selection of the particle size distribution curve, relative density, and thickness of the filter material.

[0140] Moreover, the design of the filter layer also requires the particle size distribution curve and relative density data of the protected soil. For gravelly soil, well-graded soil with particle size greater than 2 mm, and discontinuously graded soil, their particle size distribution curves need to be reclassified. Therefore, it is necessary to derive the particle size distribution curve formula of any particle size d F with respect to the corresponding sieve passing rate F, and the specific derivation process is as follows:

[0141] A complete particle size distribution curve can be described by two straight lines connected by three control points - G1(d 10 , 10%), G2(d 30 , 30%), G3(d 60 , 60%) in the semi-logarithmic coordinate system, as Figure 16 shown. The equation of the straight line G1G2 can be expressed as

[0142]

[0143] where: the intercept C1 can be expressed as

[0144]

[0145] Let d F =d 30 Available

[0146]

[0147] Then, substituting equation (15) into equation (13), it can be rearranged as

[0148]

[0149] Similarly, by Figure 16 The equation of the line segment G2G3 is

[0150]

[0151] Where: The intercept C2 can be expressed as

[0152]

[0153] Let d F =d 30 Available

[0154]

[0155] Then, substituting equation (19) into equation (17), it can be rearranged as

[0156]

[0157] The complete particle size distribution curve can be composed of the straight line G1G2 in the range of F = 0-30% and the straight line G2G3 in the range of F = 30%-100%. Therefore, the arbitrary particle size d can be obtained by combining equations (16) and (20): F The particle grading curve formula corresponding to the screening rate F is:

[0158]

[0159] The limit of the filter layer is determined by selecting a d that meets the requirements of soil filtration and drainage pressure reduction. 10 The value range is determined. 10 The minimum and maximum values ​​of the filter media depend on the minimum and maximum particle sizes of the filter media. 10 The minimum value should not be less than 0.1mm, and the maximum value should not be greater than 2.5mm.

[0160] Step 3.2, determine the effective performance zone of the coarse-grained filter layer by combining the failure probability limit of the filter soil and drainage pressure relief performance.

[0161] The fine particle limit of the filter layer is based on p (ihc)Determined by the drainage and decompression requirement of < 0.0095. When other properties of the soil are known, p (ihc) depends only on d 10 . During the process of d 10 increasing from the minimum value to the maximum value, p (ihc) gradually decreases. If the p 10 value when d takes the minimum value (ihc) is greater than 0.1, then the iterative value of d 10 should be increased to the design value of d at the fine-grained limit of the filter material, so as to meet the limit of p 10 < 0.0095; if the p (ihc) value when d takes the minimum value 10 is less than 0.0095, then the minimum value of d (ihc) is the design value of d at the fine-grained limit of the filter material 10 . Using the design value of d at the fine-grained limit, the coefficient of uniformity C 10 and the coefficient of curvature C 10 can determine the particle size distribution curve of the fine-grained limit of the filter material u . c

[0162] According to the requirement of filtering soil with p (ir) < 0.5, the coarse-grained limit of the filter material can be determined. When other properties of the soil are known, p (ir) depends on d 10 and the thickness of the filter layer. The thickness of the filter layer is determined according to its application scope and standards. During the process of the iterative value of d 10 increasing to its maximum value, p (ir) gradually increases. If the p 10 value corresponding to the d (ihc) value at the fine-grained limit of the filter material 10 is less than 0.5, then the iterative value of d 10 should be reduced to the design value of d at the coarse-grained limit of the filter material, so as to meet the limit of p (ir) < 0.5; if the p 10 value when d takes the maximum value (ir) is less than 0.5, then the maximum value of d 10 is the design value of d at the coarse-grained limit of the filter material 10 . Using the design value of d at the coarse-grained limit, the coefficient of uniformity C 10 and the coefficient of curvature C u can determine the particle size distribution curve of the coarse-grained limit of the filter material c .

[0163] ​The performance effective zone of the filter material is composed of the drainage and decompression limit corresponding to the fine-grained boundary and the soil filtration limit corresponding to the coarse-grained boundary. Generally, the particle size distribution curve of the filter layer required in a specific project is flexibly selected within the performance effective zone. The performance effective zone of the filter material should be as narrow as possible to minimize the segregation phenomenon during construction. By adjusting the fine-grained boundary or the coarse-grained boundary of the filter material through the minimum allowable diameter ratio or the difference in sieve passing rate, the width of the performance effective zone of the filter material can be reduced.

[0164] Analyze and discriminate the examples given by the NRCS method to discuss the applicability of the design results of the method of the present invention. According to the NRCS method, soil can be classified into four categories according to the percentage of soil particles smaller than the sieve hole diameter of No. 200. Here, one example is selected from each of the three types of coarse-grained soils to compare and analyze the design results of the NRCS method and the method of the present invention. Let the relative densities of the protected soil and the filter material be 0.5 and 0.8 respectively, and the thickness of the filter layer is 300 mm. Figures 17 - 19 The performance effective zones of the filter materials designed by the NRCS method and the method of the present invention are given. By comparison, it is found that:

[0165] On the one hand, as Figure 17 shown, for the silty sand example listed in the NRCS method, the concavity degree of the particle size distribution curve shape gradually increases, and its curvature coefficient C c value is 1.54; the performance effective zone of the filter material designed by the method of the present invention is smaller than that of the NRCS method and is closer to the fine-grained boundary designed by the NRCS method. As Figure 18 shown, for the silty gravel example listed in the NRCS method, the convexity degree of the particle size distribution curve shape gradually increases, and its curvature coefficient C c value is 0.87; the performance effective zone of the filter material designed by the method of the present invention is still smaller than that of the NRCS method and is closer to the coarse-grained boundary designed by the NRCS method. From these two examples, it can be seen that the shape of the particle size distribution curve has a significant impact on the position and width of the performance effective zone of the filter material, which is consistent with the conclusion drawn by Lafleur et al. that the particle size distribution curve should be considered during the soil filtration process.

[0166] On the other hand, as Figure 19 shown, for the sandy gravel example listed in the NRCS method, the fine-grained boundary designed by the method of the present invention is finer than that designed by the NRCS method. The NRCS method stipulates that only the d 15 value is used to describe the drainage and decompression requirements, without considering the shape of the particle size distribution curve and the relative density. In contrast, the permeability coefficient in the method of the present invention is calculated from the pore size distribution estimated by the particle size distribution curve and the relative density. From Figure 19 it can also be seen that the concavity degree of the particle size distribution curve shape of this example gradually increases, and its curvature coefficient C cThe value is 5.4, belonging to the discontinuous gradation soil. It can be seen that when calculating the permeability coefficient of this kind of discontinuous gradation soil on the premise of meeting the requirements of drainage and pressure relief, the concavity and convexity of the particle size distribution curve and the relative density should be considered.

[0167] Although the specific implementation manners of the present invention have been described above in conjunction with the accompanying drawings, it is not a limitation to the protection scope of the present invention. Those skilled in the art should understand that based on the technical solutions of the present invention, various modifications or deformations that can be made by those skilled in the art without creative efforts are still within the protection scope of the present invention.

Claims

1. A method for designing a coarse-grained filter layer that synergistically exerts soil filtration and drainage pressure reduction performance, characterized in that: The following steps are involved: Step 1: Determine the filtration performance of coarse-grained filter media based on the principle of probability statistics. Step 1.1, estimate the pore size distribution of the coarse-grained filter media; Step 1.2, constructing the safety margin limit state function of uneven particle size soil particles oriented to soil filtration requirements; Step 1.3, calculate the probability of soil filter failure p (ir) ; Step 1.4, dividing the limit of the probability of failure of soil filtration performance; Step 2, determining the drainage and pressure reduction performance of the coarse-grained filter material; Step 2.1, constructing a performance function for drainage pressure reduction requirements based on the permeability coefficient; Step 2.2, calculate the failure probability p of drainage pressure relief performance (ihc) ; Step 2.3, dividing the drainage pressure relief performance limit; Step 3: When designing the coarse-grained filter layer, its soil filtration and drainage pressure relief performance are synergistically utilized; Step 3.1, reclassifying the particle grading curve of the protected soil; For gravel soil, well-graded soil with particle size greater than 2 mm, and discontinuously graded soil, the particle grading curve needs to be reclassified. In the semi-logarithmic coordinate system, the particle grading curve is used. 10 ,d 30 and d 60 Corresponding data points can be linearly interpolated to deduce any particle size d F The particle grading curve formula corresponding to the screening rate F is: The limit of the filter layer is determined by selecting a d that meets the requirements of soil filtration and drainage pressure reduction. 10 The value range is determined, d 10 The minimum and maximum values ​​of the filter media depend on their particle size. 10 The minimum value should not be less than 0.1mm, and the maximum value should not be greater than 2.5mm; Step 3.2, determine the effective performance zone of the coarse-grained filter layer by combining the failure probability limits of the filter soil and drainage pressure relief performance; The fine particle limit of the filter layer is based on p (ihc) Determined by the drainage pressure reduction requirement of <0.0095; According to p (ir) Filter soil with a particle size of less than 0.5 requires the determination of the coarse particle limit of the filter material.

2. The method for designing a coarse-grained filter layer that synergistically exerts soil filtration and drainage pressure relief performance as claimed in claim 1, characterized in that: The function of step 1.2 is: M s (G,V)=G i -V j (2) Where: G i and V j are samples taken from particle size distribution and pore size distribution respectively; when M s ≥0, the filter material is effective; when M s When G is less than 0, the filter material fails. i and V j is a random variable, then there is a probability corresponding to each value of the variable.

3. The method for designing a coarse-grained filter layer for synergistically exerting soil filtration and drainage pressure reduction performance as claimed in claim 1, characterized in that: The probability of failure of soil filtration performance in step 1.3 is p (ir) It can be defined as the probability that the pore size is larger than the particle size, or as the proportion of soil particles that cannot be retained by the filter material; p (ir) By performing Monte Carlo simulation calculations on the following formula, the calculation results will converge as the number of samples N increases:

4. The method for designing a coarse-grained filter layer for synergistically exerting soil filtration and drainage pressure reduction performance as claimed in claim 1, characterized in that: In step 2.1, the hydraulic gradient of most geotechnical structures does not exceed 25, and the permeability coefficient relationship between the protected soil and the filter material is K (f) ≥25K (s) , subscripts (f) and (s) represent the filter material and the protected soil, respectively. The performance function for drainage and pressure reduction requirements is expressed as: ω(K (f) ,K (s) )=K (f) / K (s) (4) When ω≥25, the performance of the soil-filter material system is effective; when ω<25, the performance is ineffective.

5. The method for designing a coarse-grained filter layer that synergistically exerts soil filtration and drainage pressure reduction performance as claimed in claim 1, characterized in that: In step 2.2, the variability of the permeability coefficient K of the soil-filter material system is measured using the permeability coefficient ratio K (f) / K (s) and the logarithmic form of the coefficient of variation COV; thus, the failure probability of drainage and decompression performance p (ihc) It is expressed as: p (ihc) =φ(x)(5a) Where: φ is the standard normal distribution function.

6. The method for designing a coarse-grained filter layer for synergistically exerting soil filtration and drainage pressure reduction performance as claimed in claim 5, characterized in that: In step 2.3, since the mean value can be obtained through actual measurement or prediction, p (ihc) It is essentially a function of COV; to satisfy K (f) ≥25K (s) Strict drainage pressure reduction requirements, let COV = 100% corresponding to the most unfavorable conditions considered in the design of the filter layer, then use formula (5a), (5b), (5c) to calculate the drainage pressure reduction performance p (ihc) The limit value of .

7. The method for designing a coarse-grained filter layer that synergistically exerts soil filtration and drainage pressure reduction performance as claimed in claim 5, characterized in that: In step 3.2, when other properties of the soil are known, p (ihc) Depends only on d 10 ; in d 10 In the process of increasing from the minimum value to the maximum value, p (ihc) is gradually decreasing; if d 10 The minimum value of p (ihc) If the value is greater than 0.1, d 10 The iteration value should be increased to the fine particle limit of the filter material. 10 Design value to satisfy p (ihc) <0.0095 limit; if d 10 The minimum value of p (ihc) If the value is less than 0.0095, then d 10 The minimum value is the fine particle limit of the filter material d 10 Design value; using fine grain limit d 10 Design value, non-uniformity coefficient C u and the curvature coefficient C c That is, the particle grading curve that can determine the fine particle boundary of the filter material.

8. The method for designing a coarse-grained filter layer that synergistically exerts soil filtration and drainage pressure reduction performance as claimed in claim 5, characterized in that: In step 3.2, when other properties of the soil are known, p (ir) Depends on 10 and the thickness of the filter layer; the thickness of the filter layer is determined according to its application scope and standards; in d 10 As the iteration value increases to its maximum value, p (ir) is gradually increasing; if the fine particle boundary of the filter material is 10 The value corresponding to p (ihc) If it is less than 0.5, then d 10 The iteration value should be reduced to the coarse particle limit of the filter material d 10 Design value to satisfy p (ir) <0.5 limit; if d 10 The maximum value of p (ir) If the value is less than 0.5, d 10 The maximum value is the coarse particle limit of the filter material. 10 Design value; using the coarse-grained limit d 10 Design value, non-uniformity coefficient C u and the curvature coefficient C c That is, the particle grading curve of the coarse particle boundary of the filter material can be determined.

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