A method for optimizing sand and gravel aggregate gradation based on Bailey method

Abstract

The invention discloses a sand and gravel aggregate gradation optimization method based on Bailey method, which considers gradation solution from the perspective of reverse solution (assuming that the obtained gradation is the optimal gradation), and finally draws an image of gradation parameter values ​​and optimal gradation by solving the values ​​of characteristic parameters under the optimal gradation for multiple times, and obtains a table of all optimal characteristic parameters of the designed gradation, which is stored in an aggregate gradation library. In this way, in the subsequent gradation solution process, it is only necessary to query the optimal gradation characteristic parameter value of the corresponding type to constrain the designed gradation to obtain the optimal gradation of aggregate, thereby obtaining a more accurate aggregate gradation.

Description

Technical Field

[0001] The invention relates to the technical field of aggregate gradation, and more particularly to a sandstone aggregate gradation optimization method based on the Bailey method. Background Art

[0002] The traditional aggregate gradation design methods for asphalt mixtures and cement concrete have gradually exposed their defects and deficiencies in the long-term use process, and are not suitable for the aggregate gradation design of asphalt mixtures and concrete. Poor aggregate gradation will lead to different degrees of crushing of aggregate particles, affecting the quality of engineering construction. At present, most domestic scholars use Excel planning and solving to complete the gradation design work, which is complicated and prone to errors. Some scholars also use VBA to compile programs to solve this problem, but they cannot interact with third-party software, which reduces work efficiency. In order to improve the density of aggregates, some scholars also use the Bailey gradation method to constrain in the planning and solving process to obtain the optimal aggregate dosage, but the specific process of parameter constraints is not considered, that is, the constraint does not work effectively. Different regions have different application environments for mixture engineering, and the requirements for aggregate gradation in mixture design are also different. It is necessary to design an aggregate gradation with excellent coarse and fine matching according to specific conditions. Through the relationship between volume rate and area, a corresponding number of random graphics are placed on a cross-section of a specified size to simulate the microstructure of the mixture, further explaining the distribution of aggregate particles, but the optimal aggregate gradation cannot be directly obtained.

[0003] Therefore, how to provide a sand and gravel aggregate grading optimization method based on the Bailey method that can obtain the optimal aggregate grading is a problem that technical personnel in this field urgently need to solve. Summary of the invention

[0004] In view of this, the present invention provides a sand and gravel aggregate grading optimization method based on the Bailey method, which considers the grading solution from the perspective of inverse solution, and stores all optimal characteristic parameters under the optimal grading into the aggregate grading database. In the subsequent grading solution process, the optimal grading characteristic parameters of the corresponding type can be directly queried to obtain the optimal grading of aggregate.

[0005] In order to achieve the above object, the present invention adopts the following technical solution:

[0006] A method for optimizing the gradation of sandstone aggregates based on the Bailey method comprises the following steps:

[0007] Step 1, the aggregates to be optimized are screened using standard sieves with different sieve sizes to obtain aggregate gradation;

[0008] Step 2: Consider the gradation solution from the perspective of reverse solution. Assuming that the gradation obtained in step 1 is the optimal gradation, the characteristic parameters of coarse aggregate ratio CA and fine aggregate ratio FAC and FAF are used to evaluate the excellence of Bailey gradation method.

[0009] Step 3, dividing the characteristic parameter range into a coarse aggregate range and a fine aggregate range with the median as the boundary;

[0010] Step 4: Construct the solution equation;

[0011] Step 5, using the solution equation to solve the aggregates in the coarse aggregate range and the fine aggregate range obtained in step 3 for multiple times, with a large step of 0.5 and a small step of 0.1, to obtain the change of the synthetic gradation with the characteristic parameter value, and determine the characteristic parameter range and the corresponding optimal aggregate gradation range;

[0012] Step 6: Continue to cyclically solve the characteristic parameter range obtained in step 5 to obtain the value of each characteristic parameter under the optimal gradation, and store it in the aggregate gradation database for subsequent use.

[0013] Furthermore, in step 1, the mass percentage of aggregates in different particle size ranges is calculated according to the following formula:

[0014] Formula 1: Among them, m i is the mass of aggregate remaining on a certain sieve i, m is the total mass of the mixed aggregate after drying; i is numbered in ascending order of particle size;

[0015] Formula 2: A i =a 1 +a 2 +...+a i , where a 1 、a 2 , ..., a i is the percentage of the graded residue of each sieve;

[0016] Formula 3: p i =100-A i , where A i is the cumulative percentage of residues on each sieve; p i is the residual ratio of graded aggregate of the ith grade.

[0017] Furthermore, in step 2, the Bailey grading method is used to dynamically divide the aggregate particle size to control the particle size to constrain the change in the aggregate particle size. The specific sizes are as follows:

[0018] d k =0.22×d n ;

[0019] d 1 =0.22×d k ;

[0020] d 2 =0.22×d 1;

[0021] Among them, d k is the controlled particle size of aggregate, mm; d 1 is the first dividing size of fine aggregate, mm; d 2 It is the second dividing size of fine aggregate;

[0022] The calculation formulas for each characteristic parameter are as follows:

[0023]

[0024]

[0025]

[0026] Among them, CA is the coarse aggregate ratio; D is the maximum aggregate particle size, mm; FAC and FAF are the fine aggregate ratios; P d1 , P dk , P d2 They are the percentage of mixed aggregate passing through sieve i corresponding to the screening size.

[0027] Furthermore, in step 3, according to the characteristics of the optimal gradation, the following mathematical modeling is performed on each characteristic parameter:

[0028] Assume that the percentage of aggregate passing through a certain sieve hole is p j(i) The mass percentage of aggregate in the mixed aggregate is x j(i) , the percentage of mixed aggregate passing through the sieve hole i is p m(i) , then the following formula holds:

[0029] j is 1, 2, ..., n;

[0030] Among them, i is the sieve size number, j represents the jth type of aggregate;

[0031] Assuming that the aggregate gradation meets the requirements of the optimal multi-stage embedded gradation, the optimal gradation characteristic parameters CA, FAC, and FAF are within the engineering experience range, as shown below:

[0032]

[0033]

[0034]

[0035] Rewrite CA, FAC, and FAF in the above formula as x j(i) Matrix inequality for :

[0036]

[0037] Furthermore, step 4 includes:

[0038] Step 41, supplementing the conditional function to make the mass percentage of aggregate in the mixture as close as possible to the median value of the standard gradation;

[0039] Step 42, solving the optimal mass percentage of aggregate in the mixture, the percentage of mixed aggregate passing through a certain sieve hole and the corresponding characteristic parameter values;

[0040] Step 43: If the characteristic parameters calculated in step 42 are within the recommended range of Bailey grading parameters, the result is consistent with the assumption and the assumption is valid.

[0041] Furthermore, the conditional function in step 41 is as follows:

[0042]

[0043]

[0044] Among them, L m(i) , U m(i) are the mass percentage of aggregate in the mixture x j(i) The upper and lower specification limits of

[0045] The mass percentage of aggregate in the mixture is x according to the following formula: j(i) As close as possible to the median value of the specification gradation:

[0046]

[0047] Among them, m j(i) is the median value of the standard gradation; x is the mass percentage of the aggregate to be solved; x 0 is the optimal mass percentage of aggregate; δ is the neighborhood radius, which reflects the proximity of x to x 0 The degree of p is taken as an arbitrarily small positive number; ε is an arbitrarily given positive number, reflecting p m(i) Close to m j(i) The degree of is any given positive number;

[0048] Rewrite the above formula as follows:

[0049]

[0050] Make f(x) take the minimum value.

[0051] Further, step 42 includes:

[0052] Taking the derivative of f(x) we get:

[0053] p j(i) × j(i) =mj(i)

[0054] Will be related to x j(i) The linear equations are rearranged to obtain:

[0055]

[0056] make lb=0、ub=1、

[0057] Call fmincon function to plan the above formula, x = fmincon (fun, x 0 ,A,b,Aeq,beq,lb,ub); where x 0 is the mass percentage of aggregate in the mineral mixture x j(i) The initial value of; fun is the above objective function f(x);

[0058] Solve the above equation to get the optimal mass percentage x of aggregate in the mixture. j(i) ;pass Calculate the percentage p of mixed aggregate passing through a certain sieve hole m(i) .

[0059] Further, in step 42, the recommended range of Bailey grading parameters is:

[0060] The coarse aggregate ratio CA is 0.4-0.8; the fine aggregate ratios FAC and FAF are 0.2-0.5.

[0061] Furthermore, in step 5, the characteristic parameter ranges are: the coarse aggregate ratio CA is 0.4-0.55; the fine aggregate ratio FAC is 0.4-0.5; and the fine aggregate ratio FAF is 0.37-0.5.

[0062] It can be seen from the above technical solution that, compared with the prior art, the present invention discloses a sand and gravel aggregate grading optimization method based on the Bailey method, which considers the grading solution from the perspective of inverse solution (assuming that the obtained grading is the optimal grading), and finally draws an image of the grading parameter value and the optimal grading by repeatedly solving the characteristic parameter under the optimal grading, and obtains a table of all the optimal characteristic parameters of the designed gradation, which is stored in the aggregate grading library. In this way, in the subsequent grading solution process, it is only necessary to query the optimal grading characteristic parameter value of the corresponding type to constrain the designed gradation to obtain the optimal grading of aggregate, thereby obtaining a more accurate aggregate grading. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0064] Figure 1 A flow chart of the sand and gravel aggregate grading optimization method based on Bailey method provided by the present invention;

[0065] Figure 2 A curve showing the change of the synthetic gradation with CA in step 5 provided by the present invention;

[0066] Figure 3 The curve of characteristic parameters FAF and FAC changing with CA in step 5 provided by the present invention;

[0067] Figure 4 A curve showing the change of the synthetic gradation with FAC in step 5 provided by the present invention;

[0068] Figure 5 The curve of characteristic parameters CA and FAF changing with FAC in step 5 provided by the present invention;

[0069] Figure 6 A curve showing the change of the synthetic gradation with FAF in step 5 provided by the present invention;

[0070] Figure 7 The curve of characteristic parameters CA and FAC changing with FAF in step 5 provided by the present invention;

[0071] Figure 8 The grading curves under different CA values ​​provided by the present invention;

[0072] Fig. 9 This is the optimal grading curve provided by the present invention. DETAILED DESCRIPTION

[0073] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0074] like Figure 1 As shown, the embodiment of the present invention discloses a method for optimizing the gradation of sandstone aggregates based on the Bailey method, comprising the following steps:

[0075] Step 1, the aggregates to be optimized are screened using standard sieves with different sieve sizes to obtain aggregate gradation;

[0076] Step 2: Consider the gradation solution from the perspective of reverse solution. Assuming that the gradation obtained in step 1 is the optimal gradation, the characteristic parameters of coarse aggregate ratio CA and fine aggregate ratio FAC and FAF are used to evaluate the excellence of Bailey gradation method.

[0077] Step 3, dividing the characteristic parameter range into a coarse aggregate range and a fine aggregate range with the median as the boundary;

[0078] Step 4: Construct the solution equation;

[0079] Step 5, using the solution equation to solve the aggregates in the coarse aggregate range and the fine aggregate range obtained in step 3 for multiple times, with a large step of 0.5 and a small step of 0.1, to obtain the change of the synthetic gradation with the characteristic parameter value, and determine the characteristic parameter range and the corresponding optimal aggregate gradation range;

[0080] Step 6: Continue to cyclically solve the characteristic parameter range obtained in step 5 to obtain the value of each characteristic parameter under the optimal gradation, and store it in the aggregate gradation database for subsequent use.

[0081] The above steps are further explained below.

[0082] Step 1: For aggregates with a particle size of 0.075 to 25 mm, the aggregates to be optimized are screened using standard sieves with sieve hole side lengths of 26.5 mm, 19 mm, 16 mm, 13.2 mm, 9.5 mm, 4.75 mm, 2.36 mm, 1.18 mm, 0.6 mm, 0.3 mm, 0.15 mm, and 0.075 mm (the standard set of sieves refers to a series of sample sieves whose shape and size specifications meet the requirements, and the standard sieve is a square hole sieve). In the above screening experiment, the sieve residue mass of the aggregate is weighed, and the sub-sieve residue percentage, cumulative sieve residue percentage, and pass percentage of the graded aggregates (12 grades) in different particle size ranges are calculated according to formulas 1, 2, and 3. The sub-sieve residue ratio of the i-th grade graded aggregate is a i , the corresponding sieve hole side length is d i , and i is numbered sequentially in increasing order of particle size.

[0083] The mass percentage of aggregates in different particle size ranges is calculated according to the following formula:

[0084] Formula 1: Among them, m i is the mass of aggregate remaining on a certain sieve i, m is the total mass of the mixed aggregate after drying; i is numbered in ascending order of particle size;

[0085] Formula 2: A i =a1 +a 2 +...+a i , where a 1 、a 2 , ..., a i is the percentage of the graded residue of each sieve;

[0086] Formula 3: p i =100-A i , where A i is the cumulative percentage of residues on each sieve; p i is the residual ratio of graded aggregate of the ith grade.

[0087] The specific screening results are shown in Table 1;

[0088] Table 1 Screening results

[0089]

[0090] In step 2, the Bailey grading method is used to dynamically divide the aggregate particle size, that is, coarse and fine aggregate is only a relative concept, and the particle size change of the aggregate is constrained by controlling the particle size (a function of the nominal maximum particle size of the aggregate). The specific sizes are as follows:

[0091] d k =0.22×d n ;

[0092] d 1 =0.22×d k ;

[0093] d 2 =0.22×d 1 ;

[0094] Among them, d k is the controlled particle size of aggregate, mm; d 1 is the first dividing size of fine aggregate, mm; d 2 It is the second dividing size of fine aggregate;

[0095] The particle size D / 2 of the Bailey method will be larger than the controlled particle size d k The coarse aggregate is further divided into finer and coarser parts, and the coarse aggregate ratio CA is obtained by the following formula:

[0096]

[0097] Where D is the maximum particle size of aggregate, mm. Since changing the coarse-fine ratio of aggregate can change the porosity of aggregate and thus affect the skeleton structure, that is, when the finer part of the coarse aggregate is less, the aggregate is easy to segregate, and when it is more, it will have excessive interference with the coarse aggregate, making it difficult to compact and having greater slippage. According to engineering experience, the coarse aggregate ratio CA is more suitable to be 0.4-0.8.

[0098] Fine aggregate is used to fill coarse aggregate, so its volume needs to be limited. The fine aggregate ratio FAC and FAF are calculated by the following formulas:

[0099]

[0100]

[0101] Where P d1 , P dk , P d2 They are the percentage of mixed aggregates corresponding to their screening sizes passing through sieve i; the fine aggregate ratios FAC and FAF are more appropriately taken as 0.2-0.5 based on engineering experience.

[0102] Since the present invention assumes that the obtained gradation is the optimal gradation, the values ​​of the above-mentioned characteristic parameters should be within the scope of engineering experience, and the composite gradation must also meet the requirements of road engineering specifications, that is, the aggregate composite gradation is greater than the lower limit of the specification, less than the upper limit, and as close to the median as possible.

[0103] In step 3, according to the characteristics of the optimal gradation, the following mathematical modeling is performed on each characteristic parameter:

[0104] Assume that the percentage of aggregate passing through a certain sieve hole is p j(i) The mass percentage of aggregate in the mixed aggregate is x j(i) , the percentage of mixed aggregate passing through the sieve hole i is p m(i) , then the following formula holds:

[0105] j is 1, 2, ..., n;

[0106] Among them, i is the sieve size number, j represents the jth type of aggregate;

[0107] Assuming that the aggregate gradation meets the requirements of the optimal multi-stage embedded gradation, the optimal gradation characteristic parameters CA, FAC, and FAF are within the engineering experience value range (Bailey method parameter range), as shown below:

[0108]

[0109]

[0110]

[0111] Rewrite CA, FAC, and FAF in the above formula as x j(i) Matrix inequality for :

[0112]

[0113] Since the above characteristic parameters are all within a certain range, there are multiple solutions for aggregate gradation when the above conditions are met (see Figure 3 ), but the general linear programming procedure can only solve a series of aggregate mass percentages x in the mixture. j(i) Therefore, the present invention divides the characteristic parameter range into a coarse aggregate range and a fine aggregate range with the median as the boundary, and then obtains the optimal mass percentage x of the aggregate in the mixture through a cyclic solution. j(i) , the range is shown in Table 2:

[0114] Table 2

[0115] Grading parameters CA <![CDATA[FA c ]]> <![CDATA[FA f ]]> Range Average 0.6 0.35 0.35 Fine range 0.6～0.8 0.35～0.5 0.35～0.5 Coarse range 0.4～0.6 0.2～0.35 0.2～0.35

[0116] In a specific embodiment, step 4 includes:

[0117] Step 41, supplement the conditional function to make the mass percentage of aggregate in the mixture as close as possible to the median value of the standard gradation; the conditional function is as follows:

[0118]

[0119]

[0120] Among them, L m(i) , U m(i) are the percentage p of mixed aggregate passing through sieve hole i m(i) The upper and lower specification limits of

[0121] According to the following formula, the passing percentage p of the mixed aggregate on the sieve hole i is m(i) As close as possible to the median value of the specification gradation:

[0122]

[0123] The formula is the limit definition of the function. To ensure that when the mass percentage of aggregate in the mineral mixture is x→x 0 (x 0 is the optimal mass percentage of aggregate), the corresponding function value (the percentage of mixed aggregate passing through the sieve hole i is p m(i) or composite gradation) is infinitely close to the median value m of the standard gradation j(i) . m j(i)is the median value of the standard gradation; x is the mass percentage of the aggregate to be solved; x 0 is the optimal mass percentage of aggregate; δ is the neighborhood radius, which reflects the proximity of x to x 0 The degree of p is taken as an arbitrarily small positive number; ε is an arbitrarily given positive number, reflecting p m(i) Close to m j(i) The degree of is any given positive number;

[0124] Rewrite the above formula as follows:

[0125]

[0126] Make f(x) take the minimum value.

[0127] Step 42, solving the optimal mass percentage of aggregate in the mixture, the percentage of mixed aggregate passing through a certain sieve hole and the corresponding characteristic parameter values; specifically including:

[0128] Taking the derivative of f(x) we get:

[0129] p j(i) × j(i) =m j(i)

[0130] Will be related to x j(i) The linear equations are rearranged to obtain:

[0131]

[0132] make lb=0、ub=1、

[0133] Call the fmincon function in MATLAB to plan the above formula, that is,

[0134] x=fmincon(fun,x 0 ,A,b,Aeq,beq,lb,ub); where x 0 is the mass percentage of aggregate in the mineral mixture x j(i) The initial value of is determined according to the specific engineering plan and can be set to 0 if there is no requirement; fun is the above objective function f(x). By solving it, the optimal mass percentage x of aggregate in the mixture can be obtained. j(i) ;pass Further solve the percentage p of mixed aggregate passing through a certain sieve hole m(i) .

[0135] It should be noted that the above method of the present invention is also applicable to engineering mineral mixtures that have weight requirements on the amount of coarse aggregate or fine aggregate, and it is only necessary to add the corresponding weights in the above augmented matrix [A b].

[0136] Step 43: If the characteristic parameters calculated in step 42 are within the recommended range of Bailey grading parameters, the result is consistent with the assumption and the assumption is valid.

[0137] In a specific embodiment, in step 5, the aggregate within the coarse and fine range described in step 3 is accurately solved, the large step is 0.5, the small step is 0.1, and the initial value x 01 Take 0.015 (i.e. the mass percentage of the aggregate in the maximum particle size range is not less than 1.5%, the actual value is much greater than 1.5%, determined according to the specific engineering plan, if there is no requirement, the value can be 0), and further observe and select the gradation corresponding to the characteristic parameters under the optimal gradation of aggregate. Repeat the above formula to solve the characteristic parameters, and the synthetic gradation changes with CA, FAC, and FAF as shown in Table 3-6 and Figure 2-7 As shown:

[0138] Table 3

[0139]

[0140] Table 4 Solution results when CA is between 0.55 and 0.6

[0141]

[0142]

[0143] Table 5 Synthetic gradation changes with FCA

[0144]

[0145] Table 6 Synthetic gradation changes with FAF

[0146]

[0147]

[0148] From the above data in Table 3-6 and Figure 2-7 It can be seen that the gradation meets the specification conditions only when the CA value is between 0.4 and 0.55, the FAC is between 0.3 and 0.5, and the FAF is between 0.37 and 0.5. This conclusion verifies the effectiveness of the recommended value range of Bailey gradation parameters as test indicators, and indicates that the aggregate composite gradation corresponding to the above characteristic parameters CA, FAC, and FAF ranges is the optimal aggregate gradation range.

[0149] In a specific embodiment, in step 6, the optimal gradation range of aggregate CA, FAC, and FAF in step 5 is still solved cyclically, and there are 4 value points represented by CA. The obtained CA, FAC, FAF values ​​and gradation data are shown in Tables 7-8 and Figure 8 As shown:

[0150] Table 7 Characteristic parameter values

[0151] CA FAC FAF 0.55 0.49 0.47 0.50 0.45 0.46 0.45 0.44 0.46 0.40 0.43 0.46

[0152] Table 8 CA value corresponding gradation

[0153]

[0154]

[0155] From the above, it can be seen that the composite gradation curve has a high degree of coincidence when the gradation size is 0.4, so the optimal gradation is the composite gradation when the characteristic parameters are CA = 0.40, FAC = 0.43, and FAF = 0.46. See Tables 9-10 and Fig. 9 .

[0156] Table 9

[0157]

[0158] Table 10 Mass percentage passing the following sieve holes (mm) / % (optimal gradation)

[0159]

[0160] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0161] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for optimizing the gradation of sandstone aggregates based on the Bailey method, characterized in that: The following steps are involved: Step 1, the aggregates to be optimized are screened using standard sieves with different sieve sizes to obtain aggregate gradation; Step 2: Consider the gradation solution from the perspective of reverse solution. Assuming that the gradation obtained in step 1 is the optimal gradation, the characteristic parameters of coarse aggregate ratio CA and fine aggregate ratio FAC and FAF are used to evaluate the excellence of Bailey gradation method. Step 3, dividing the characteristic parameter range into a coarse aggregate range and a fine aggregate range with the median as the boundary; Step 4: Construct the solution equation; Step 4 Includes: Step 41, supplementing the conditional function to make the mass percentage of aggregate in the mixture as close as possible to the median value of the standard gradation; Step 42, solving the optimal mass percentage of aggregate in the mixture, the percentage of mixed aggregate passing through a certain sieve hole and the corresponding characteristic parameter values; Step 43: If the characteristic parameters calculated in step 42 are within the recommended range of Bailey gradation parameters, the result is consistent with the assumption and the assumption is valid; Step 5, using the solution equation to solve the aggregates in the coarse aggregate range and the fine aggregate range obtained in step 3 for multiple times, with a large step of 0.5 and a small step of 0.1, to obtain the change of the synthetic gradation with the characteristic parameter value, and determine the characteristic parameter range and the corresponding optimal aggregate gradation range; Step 6: Continue to cyclically solve the characteristic parameter range obtained in step 5 to obtain the value of each characteristic parameter under the optimal gradation, and store it in the aggregate gradation database for subsequent use.

2. The method for optimizing the gradation of sandstone aggregates based on the Bailey method according to claim 1, characterized in that: In step 1, the mass percentage of aggregates in different particle size ranges is calculated according to the following formula: Formula 1: Among them, m i is the mass of aggregate remaining on a certain sieve i, m is the total mass of the mixed aggregate after drying; i is numbered in ascending order of particle size; Formula 2: A i =a1+a2+...+a i , where a1, a2, ..., a i is the percentage of the graded residue of each sieve; Formula 3: pi = 100-A i , where A i is the cumulative percentage of residues on each sieve; p i is the residual ratio of graded aggregate of the ith grade.

3. The method for optimizing the gradation of sandstone aggregates based on the Bailey method according to claim 1, characterized in that: In step 2, the Bailey grading method is used to dynamically divide the aggregate particle size to control the particle size to constrain the change of the aggregate particle size. The specific sizes are as follows: d k =0.22×d n ; d1=0.22×d k ; d2 = 0.22 × d1; Among them, d k is the controlled particle size of aggregate, mm; d1 is the first boundary size of fine aggregate, mm; d2 is the second boundary size of fine aggregate; The calculation formulas for each characteristic parameter are as follows: Among them, CA is the coarse aggregate ratio; D is the maximum aggregate particle size, mm; FAC and FAF are the fine aggregate ratios; P d1 , P dk , P d2 They are the percentage of mixed aggregate passing through sieve i corresponding to the screening size.

4. The method for optimizing the gradation of sandstone aggregates based on the Bailey method according to claim 1, characterized in that: In step 3, according to the characteristics of the optimal gradation, the following mathematical modeling is performed on each characteristic parameter: Assume that the percentage of aggregate passing through a certain sieve hole is p j(i) The mass percentage of aggregate in the mixed aggregate is x j(i) , the percentage of mixed aggregate passing through the sieve hole i is p m(i) , then the following formula holds: j is 1, 2, ..., n; Among them, i is the sieve size number, j represents the jth type of aggregate; Assuming that the aggregate gradation meets the requirements of the optimal multi-stage embedded gradation, the optimal gradation characteristic parameters CA, FAC, and FAF are within the engineering experience range, as shown below: Rewrite CA, FAC, and FAF in the above formula as x j(i) Matrix inequality for :

5. The method for optimizing the gradation of sandstone aggregates based on the Bailey method according to claim 1, characterized in that: The conditional function in step 41 is as follows: Among them, L m(i) , U m(i) are the mass percentage of aggregate in the mixture x j(i) The upper and lower specification limits of The mass percentage of aggregate in the mixture is xj according to the following formula: (i) As close as possible to the median value of the specification gradation: Among them, m j(i) is the median of the standard gradation; x is the mass percentage of the aggregate to be solved; x0 is the optimal mass percentage of the aggregate; δ is the neighborhood radius, which reflects the degree to which x is close to x0 and can be any small positive number; ε is any given positive number, which reflects that pm(i) is close to m j(i) The degree of is any given positive number; Rewrite the above formula as follows: Make f(x) take the minimum value.

6. The method for optimizing the gradation of sandstone aggregates based on the Bailey method according to claim 5, characterized in that: Step 42 includes: Taking the derivative of f(x) we get: p j( i ) ×x j( i ) =m j( i ) Will be related to x j(i) The linear equations are rearranged to obtain: make lb=0、ub=1、 Call the fmincon function to plan the above formula, x = fmincon (fun, x0, A, b, Aeq, beq, lb, ub); where x0 is the mass percentage of aggregate in the mineral mixture x j(i) The initial value of; fun is the above objective function f(x); Solve the above equation to get the optimal mass percentage x of aggregate in the mixture. j(i) ;pass Calculate the percentage p of mixed aggregate passing through a certain sieve hole m(i) .

7. The method for optimizing the gradation of sandstone aggregates based on the Bailey method according to claim 1, characterized in that: In step 42, the recommended range of Bailey grading parameters is: The coarse aggregate ratio CA is 0.4-0.8; the fine aggregate ratios FAC and FAF are 0.2-0.

5.

8. The method for optimizing the gradation of sandstone aggregates based on the Bailey method according to claim 1, characterized in that: In step 5, the characteristic parameter ranges are: coarse aggregate ratio CA is 0.4-0.55; fine aggregate ratio FAC is 0.4-0.5; fine aggregate ratio FAF is 0.37-0.5.

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