Method for determining optimal gradation of mixed recycled aggregate based on fractal dimension

Abstract

The application discloses a method for determining optimal gradation of mixed recycled aggregate based on fractal dimension, and belongs to the technical field of building material testing, which comprises the following steps: first step, determining optimal gradation of mixed recycled aggregate; second step, testing the optimal gradation; and third step, drawing an optimal gradation curve to determine the recycled aggregate replacement rate of coarse aggregate and fine aggregate; the application is based on the idea that the accumulation and crushing of brittle granular materials are reciprocal processes, and the fractal dimension of the mixed recycled aggregate is determined by combining experimental testing and theory according to the definition of fractal dimension and the change rule of the volume content of 4.75mm sieve residue in the loading process, so as to determine the optimal gradation of the mixed recycled aggregate, and the corresponding fractal dimension testing method is provided; the application can effectively determine the optimal gradation of the mixed recycled aggregate, and has the advantages of less workload and low labor intensity.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of building material testing, and particularly relates to a method for determining optimal grading of mixed recycled aggregate based on fractal dimension. BACKGROUND

[0002] Civil engineering and construction consumes 60% of raw materials extracted from the lithosphere. Natural aggregate is generally used for concrete aggregate, and aggregate accounts for 60% to 75% of the total volume. In order to cope with the shortage of natural materials and eliminate environmental pressure caused by construction waste, recycled aggregate is used to replace natural aggregate for recycled concrete. However, the specific gravity of recycled aggregate is smaller than that of natural aggregate, the strength is weak, the porosity is large, the water absorption is large, and the quality discreteness of the aggregate is relatively large. How to mix natural aggregate and recycled aggregate and determine the optimal grading of mixed recycled aggregate is a difficult problem that needs to be solved, and there is no scientific and standardized method so far.

[0003] Fuller believed that if solid particles of different particle sizes are regularly mixed according to a certain proportion, theoretically, the aggregate composition with the maximum density and the minimum void can be obtained. In order to facilitate the calculation of aggregate grading, it is believed that when the grading curve is a parabola, the aggregate can reach the maximum density, and the expression is formula nine.

[0004] Formula nine: ;

[0005] In the formula, P i is the passing rate of the i-th layer sieve; d i is the i-th layer sieve aperture; and d max is the maximum particle size of grading.

[0006] Talbol et al. believed that formula nine is an idealized curve, and there is a certain range of fluctuations in obtaining the maximum density in practice. The value of the index should not be a constant, but a variable β. β is a test index, and the value is 0.3 to 0.5. The expression is formula ten.

[0007] Formula ten: ;

[0008] Through further research, Tyler linked aggregate grading to fractals, and established aggregate grading design formula eleven. Let the maximum particle size of the aggregate sample be d max , the i-th layer sieve aperture be d i , the cumulative total mass of the aggregate passing through the sieve be M(d i ), and the total mass of the aggregate sample be M0. Then, greater than a certain characteristic particle size d i (d i >d i+1The aggregate number of the formula (11) is reduced with the increase of the i value, and the expression is formula (11);

[0009] Formula (11): ;

[0010] In the formula, D is the fractal dimension, D=3-k, k is the slope of the fitting straight line of the aggregate gradation curve in the double logarithmic coordinates.

[0011] According to the monograph of Mandelbrot, "Fractal Geometry of Nature", the fractal dimension of the three-dimensional solid aggregate is between 2 and 3. However, for the aggregate gradation, the range of the fractal dimension D is too wide. For example, the sand rate passing through a 4.75 mm sieve is calculated (using formula 10), when the fractal dimension is between 2 and 3, the corresponding sand rate is greater than 17.9% and close to 100%, respectively. The range of change is so large that it is obviously impossible to use in practical engineering. According to Talbol's research, the slope k is 0.3-0.5, and the fractal dimension is 2.5-2.7, and the corresponding sand rate is 42.3%-59.7%. Although the sand rate range is reduced, this formula is mainly for natural aggregate, and the experience range is obtained by using limited material tests, and the influence of material properties on the fractal dimension is not considered, especially for solid waste mixed recycled aggregate, the influence of different material mixing ratio and broken particle morphology on the aggregate gradation needs to be considered. In addition, formula (11) uses the relationship between the mass ratio and the diameter ratio to represent the fractal dimension. For natural materials, the influence of particle size on apparent density can be ignored, but for solid waste mixed materials, the particle size will affect the number of defects. The apparent density is related to the particle size, and the change of the mixing ratio and the particle size will affect the apparent density of the mixed material, causing the change of the gradation curve, and further affecting the change of the fractal dimension. Therefore, it is an engineering problem to determine the fractal dimension range of the solid waste mixed recycled aggregate and how to apply the fractal dimension to conveniently design and optimize the gradation of the mixed recycled aggregate. SUMMARY

[0012] The present application overcomes the shortcomings of the prior art and provides a method for determining the optimal gradation of mixed recycled aggregate based on fractal dimension, which can conveniently design the gradation of mixed recycled aggregate using fractal dimension. The present application is realized by the following technical solutions:

[0013] A method for determining the optimal gradation of mixed recycled aggregate based on fractal dimension, comprising the following steps:

[0014] Step 1, determination of the optimal gradation of mixed recycled aggregate:

[0015] 1.1, according to the maximum particle size d max of the gradation, prepare natural aggregate and recycled aggregate with the same single particle size as the maximum particle size of the gradation and dry storage, and respectively measure the apparent density of the prepared natural aggregate and recycled aggregate;

[0016] 1.2. Determine the maximum loading pressure F max ;

[0017] 1.3. Select the minimum particle size d for research gradation min , and take the recycled aggregate prepared in step 1.1, and max The crushed recycled aggregate is crushed under a certain pressure, and the crushed recycled aggregate is sieved to measure the apparent density of the crushed recycled aggregate at each level of sieve residue. The apparent density of the recycled aggregate at each level of sieve residue is recorded as ρ r，i ; r represents recycled aggregate, i represents the maximum particle size d max To the minimum particle size d min The number of the standard square hole sieve between max Numerically equal to the maximum standard square hole sieve diameter, d min Numerically equal to the minimum standard square hole sieve diameter;

[0018] 1.4. Determine the mixing ratio of the mixed recycled aggregate. Weigh the natural aggregate and recycled aggregate prepared in step 1.1 again according to the mixing ratio, mix them according to the mixing ratio, and then divide the prepared mixed recycled aggregate into several portions.

[0019] 1.5. Set the maximum loading pressure F max It is divided into multiple loading levels in sequence, and the pressure of each loading level is recorded as F m , the subscript m represents the loading sequence number; static loading is performed on the mixed recycled aggregate prepared in step 1.4; the pressure F of different loading levels is obtained m The gradation of crushed mixed recycled aggregate under the following conditions;

[0020] 1.6、For different loading levels of pressure F m The crushed mixed recycled aggregate grading is screened and sorted separately, and the pressure F of each loading level is weighed separately. m Under the mass of natural aggregate and recycled aggregate, the loading grade pressure F is obtained m The corresponding value is not less than d min The mass gradation of mixed recycled whole aggregate with a particle size of not less than 4.75 mm is the full gradation, and the volume gradation of mixed recycled coarse aggregate with a particle size of not less than 4.75 mm is the coarse gradation;

[0021] 1.7. Draw the full gradation curve and coarse gradation curve after crushing respectively, and calculate the pressure F of each level of loading m The fractal dimension D corresponding to full gradation and coarse gradation a，m and D c，m ;

[0022] 1.8. Calculate the pressure F at each level of loading m Corresponding 4.75mm sieve residue volume content V4.75，m , the coarse gradation fractal dimension D 4.75，m corresponding to max{V max} is obtained.

[0023] 1.9, the fractal dimension D a，m and D c，m of the full gradation and the coarse gradation are taken as the ordinate, the loading level pressure F m is taken as the abscissa, the F m ~D curve is drawn, the fractal dimension D j corresponding to the intersection point of the two curves is obtained; the optimal fractal dimension D opt is obtained, D opt =max{D j , D max}, and the coarse gradation corresponding to D opt is the optimal coarse gradation of the mixed recycled aggregate, and the full gradation matched with the coarse gradation is the optimal full gradation of the mixed recycled aggregate;

[0024] Second step, optimal gradation test: the full gradation corresponding to D opt simultaneously satisfies the curvature coefficient C c and the non-uniformity coefficient C u joint test, fractal dimension discrimination standard test and correlation coefficient test, and the gradation is the optimal gradation curve that meets the test;

[0025] Third step, after completing the first step and the second step, the optimal gradation curve is drawn, and the recycled aggregate replacement rate of the coarse aggregate with a particle size not less than 4.75 mm and the fine aggregate with a particle size less than 4.75 mm is determined.

[0026] Further, in step 1.5, the static loading is performed by loading the mixed recycled aggregate into a steel sample cylinder; the inner diameter and height of the sample cylinder are 5-10 times the maximum particle size d max of the gradation, the thickness of the wall of the sample cylinder is not less than 10 mm, the thickness of the bottom of the sample cylinder is not less than 5 mm, and the thickness of the top loading plate of the sample cylinder is not less than 25 mm.

[0027] Further, F max is 1.0-1.2 times the saturated compressive strength of the rock sample block corresponding to the natural aggregate.

[0028] Further, in step 1.6, the volume gradation of the mixed recycled coarse aggregate is calculated by the mass gradation, wherein the volume of the recycled aggregate is calculated according to the apparent density of the recycled aggregate with a classified particle size or according to the average apparent density of the recycled coarse aggregate with a particle size not less than 4.75 mm.

[0029] Further, in step 1.7, the broken full-graded curve and the broken coarse-graded curve are respectively plotted in a double logarithmic coordinate system, and the corresponding curve slopes k a，m and k c，m and the correlation coefficients R a，m and R c，m are respectively obtained by using a linear fitting method, and then the fractal dimensions D a，m and D c，m of the full-graded and coarse-graded are respectively calculated by using the formula D=3-k 4.75，m .

[0030] Further, in step 1.8, V 4.75，m meets the formula one.

[0031] Formula one: ;

[0032] In the formula, M n，m and M r，m represent the 4.75mm standard square hole screen residue mass of the natural aggregate and the recycled aggregate 4.75~9.5mm particle size mass after the mth loading level pressure crushing, respectively, ρ n represents the apparent density of the natural aggregate, ρ r，4.75 represents the apparent density of the 4.75~9.5mm particle size recycled aggregate, and the subscript n represents the natural aggregate.

[0033] Further, in the second step, the curvature coefficient C c and the uneven coefficient C u are jointly tested, that is, the curvature coefficient C opt and the uneven coefficient C c of D u corresponding to the full-graded are calculated, and whether the judgment standard is met is determined; the judgment standard is that when C u ≥15 and 1≤C c ≤3, the gradation is good; the uneven coefficient C u is calculated according to the formula two, and the curvature coefficient C c is calculated according to the formula three.

[0034] Formula two: ;

[0035] Formula three: ;

[0036] In the formula, d 60 , d 30 and d 10 are all characteristic particle sizes of soil, and the unit is mm; on the particle size distribution curve of soil, d 60 represents the particle size corresponding to 60% cumulative mass percentage, d 30 represents the particle size corresponding to 30% cumulative mass percentage, and d 10Particle size corresponding to 10% cumulative mass percentage.

[0037] Further, in the second step, the fractal dimension discriminant criterion test comprises the following steps:

[0038] S1: curvature coefficient C c Fractal dimension is represented by formula four, non-uniformity coefficient C u Fractal dimension is represented by formula five;

[0039] Formula four: ;

[0040] Formula five: ;

[0041] Combined condition C u ≥ 15, and 1 ≤ C c ≤ 3, the upper and lower boundaries of fractal dimension are formula six;

[0042] Formula six: 2.34 ≤ D ≤ 2.63;

[0043] S2: determine the maximum particle size d max And the minimum particle size d min After that, the volume sand rate P s 35% and 50% respectively determine the upper and lower limits of fractal dimension D 35 And D 50 , calculated by formula seven;

[0044] Formula seven: ;

[0045] According to formula seven, the corresponding fractal dimensions D 35 And D 50 When the volume sand rate is 35% and 50% respectively;

[0046] S3: combined with formula six and formula seven, the boundary of fractal dimension is formula eight;

[0047] Formula eight: max{2.34, D 35} ≤ D ≤ min{2.63, D 50};

[0048] Use formula eight to judge whether D opt Satisfies, if yes, it is reasonable, otherwise it is unreasonable.

[0049] Further, in the second step, the correlation coefficient test is to draw the full gradation curve and the coarse gradation curve after crushing respectively, and the correlation coefficient R a，m And R c，m The closer to 1, the better the corresponding fractal dimension.

[0050] The beneficial effects of the present application relative to the prior art are:

[0051] The present application is based on the idea that the accumulation and crushing of brittle granular materials are inverse processes, and on the basis of previous research, a design method for determining the fractal dimension of mixed recycled aggregate and the optimal grading of mixed recycled aggregate by combining experimental testing and theory is proposed according to the definition of fractal dimension and the change rule of the volume content of 4.75mm sieve residue during loading, and a corresponding fractal dimension test method is proposed. The present application can effectively determine the optimal grading of mixed recycled aggregate, with less workload and low labor intensity. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1 Figure 3 is the mass grading curve of 3MPa mixed recycled full aggregate in the embodiment;

[0053] Figure 2 Figure 4 is the volume grading curve of 3MPa mixed recycled coarse aggregate in the embodiment;

[0054] Figure 3 Figure 5 is the loading level pressure-fractal dimension curve graph in the embodiment;

[0055] Figure 4 Figure 6 is the optimal grading curve in the embodiment;

[0056] Figure 5 Figure 7 is the optimal grading recycled coal gangue brick aggregate and natural limestone aggregate content curve graph in the embodiment. DETAILED DESCRIPTION

[0057] In order to make the technical problems to be solved by the present application, the technical solutions and beneficial effects more clear and explicit, the present application is further described in detail in combination with the embodiments and drawings. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application. The technical solutions of the present application are described in detail below in combination with the embodiments and drawings, but the protection scope is not limited by this.

[0058] The present embodiment provides a method for determining the optimal grading of mixed recycled aggregate based on fractal dimension, specifically a method for determining the optimal grading of mixed aggregate of natural limestone aggregate and recycled coal gangue brick:

[0059] Step 1, determine the optimal grading of mixed recycled aggregate:

[0060] 1.1, collect natural limestone aggregate and recycled coal gangue brick aggregate.

[0061] 1.2, select the maximum particle size d max= 26.5 mm; the natural limestone aggregate and the recycled coal gangue brick aggregate were collected and then crushed by a crusher, and were sieved by a 19-26.5 mm standard square hole sieve to prepare 19-26.5 mm natural limestone aggregate and recycled coal gangue brick aggregate initial samples, and the initial samples were dried and stored; the apparent density of the natural limestone aggregate was measured as 2.690 g / cm 3 , and the apparent density of the recycled coal gangue brick aggregate was measured as 2.240 g / cm 3 .

[0062] 1.3, the size of the sample cylinder was selected as φ150 mm x 150 mm x 10 mm, the bottom thickness was 8 mm, and the top loading plate thickness was 25 mm.

[0063] 1.4, the maximum loading pressure F max was determined as 60 MPa.

[0064] 1.5, the minimum particle size d min of the research gradation was selected as 0.075 mm; one part of the 19-26.5 mm recycled coal gangue brick aggregate initial sample prepared in step 1.2 was taken and subjected to a side limit crushing test under a pressure of 5 MPa, the crushed sample was sieved, and the apparent density of each size sieve residue of the crushed recycled coal gangue brick aggregate was measured and recorded as p r，i ; i = 0.075 mm, 0.15 mm, …, 19 mm; the apparent density of the recycled coal gangue brick aggregate is shown in Table 1:

[0065]

[0066] 1.6, the natural limestone aggregate initial sample and the recycled coal gangue brick aggregate initial sample prepared in step 1.2 were weighed, and were mixed uniformly according to a quality mixing ratio of 60% and 40% to obtain a mixed recycled aggregate sample, and the prepared mixed recycled aggregate sample was divided into 7 parts.

[0067] 1.7, the maximum loading pressure F max was divided into seven loading levels (F1 = 3 MPa, F2 = 6 MPa, F3 = 12 MPa, F4 = 24 MPa, F5 = 36 MPa, F6 = 48 MPa, F7 = 60 MPa) in sequence; the pressure of each level of loading was recorded as F m (m is 1, 2, 3, 4, 5, 6, 7);

[0068] A portion of the mixed recycled aggregate sample prepared in step 1.6 is weighed, and the mixed recycled aggregate sample is evenly divided into three portions. One portion is loaded into a sample cylinder, and static loading is applied to the mixed recycled aggregate sample. The first loading level is F1=3 MPa. After the static loading reaches the predetermined pressure value of 3 MPa, the system is static for 5 s, and then the loading is unloaded. The remaining two portions of the mixed recycled aggregate sample are subjected to parallel tests at the same pressure, and the broken mixed recycled aggregate sample at the loading level is obtained.

[0069] 1.8. After the three parallel tests, the broken mixed recycled aggregate samples are mixed evenly, and then sieved to obtain the mixed recycled full aggregate mass grading (hereinafter referred to as full grading) corresponding to the loading level pressure, which is not less than 0.075 mm in size. The mixed recycled aggregate sample not less than 4.75 mm in size after sieving is manually sorted to obtain mixed recycled coarse aggregate. The mass of the natural limestone aggregate and the recycled coal gangue brick aggregate in the mixed recycled coarse aggregate is weighed, respectively. The coarse aggregate volume grading is calculated from the mass grading, wherein the volume of the recycled coal gangue brick aggregate is calculated according to the apparent density of the recycled coal gangue brick aggregate determined in Table 1, or according to the average apparent density of the recycled coal gangue brick coarse aggregate not less than 4.75 mm in size. The mixed recycled coarse aggregate volume grading (hereinafter referred to as coarse grading) not less than 4.75 mm in size is obtained, and the calculation results are shown in Table 2.

[0070] 1.9. The full grading and coarse grading curves after breaking are plotted in a double logarithmic coordinate system, respectively. The linear fitting method is used to obtain the corresponding slopes k a，1 =0.72 and k c，1 =1.14 and the correlation coefficients R a，1 =0.9587 and R c，1 =0.9687, respectively. Then, the fractal dimensions D a，1 =2.28 and D c，1 =1.86 of the full grading and coarse grading are calculated using the formula D=3-k, respectively, as shown in Figure 1 and Figure 2 .

[0071] 1.10. All loading levels F2=6 MPa, F3=12 MPa, …, and F7=60 MPa are selected in turn, and steps 1.7-1.9 are repeated to complete the mixed recycled aggregate test at all loading levels. The full grading and coarse grading curves after breaking are plotted in a double logarithmic coordinate system, respectively. The linear fitting method is used to obtain the corresponding curve slopes k m and k a，m and the correlation coefficients R c，m and R a，m at each loading level F c，m , respectively. Then, the fractal dimensions D a，m and Dc，m The results are shown in Table 2, m is the same as the angle code number of the loading level pressure F m .

[0072] Table 2 Side limit crushing gradation of each loading level pressure

[0073]

[0074] Note: In the first column of Table 2, the symbol k before " / " in the lower three lines a，m , D a，m and R 2 a，m correspond to the mass gradation of the total aggregate, the symbol k after " / " c，m , D c，m and R 2 c，m correspond to the volume gradation of the coarse aggregate.

[0075] 1.11, the loading level pressure F m corresponding to the volume content V 4.75，m of the 4.75 mm sieve residue is calculated, and the fractal dimension D 4.75,m corresponding to max{V max} is obtained, which is D a，m =2.53, and the results are shown in Table 3.

[0076] Table 3 Volume content of 4.75 mm sieve residue and corresponding fractal dimension

[0077]

[0078] 1.12, the fractal dimension D a，m and D c，m of the total gradation and the coarse gradation are taken as the ordinate, and the loading level pressure F m is taken as the abscissa, to draw the F m ~D curve (loading level pressure-fractal dimension curve), i.e. the total gradation D a，m curve and the coarse gradation D c，m curve, and the intersection ordinate of the total gradation D a，m curve and the coarse gradation D c，m curve corresponds to the fractal dimension D j =2.45, which is shown in Figure 3 .

[0079] 1.13, from steps 1.11 and 1.12, D max =2.53 and D j =2.45, so:

[0080] The optimal fractal dimension D opt =max{D j ,D max}=max{2.45,2.53}=2.53; D opt The corresponding coarse gradation is the optimal coarse gradation of mixed recycled aggregate, and the full gradation matching the coarse gradation is the optimal full gradation of mixed recycled aggregate.

[0081] The second step is the optimal gradation test:

[0082] 2.1 Curvature coefficient C c and the non-uniformity coefficient C u Joint inspection:

[0083] According to Article 5.2.10, Paragraph 3 of the Railway Roadbed Design Code (TB10001-2016), when C u ≥15, and 1≤C c When ≤3, the gradation is good. opt Curvature coefficient C corresponding to full gradation c and the non-uniformity coefficient C u , determine whether the judgment criteria are met. As shown in Table 1, the optimal fractal dimension D opt = 2.53 The matching full gradation is the gradation obtained by loading the grade pressure of 24MPa, and d 60 =9.2mm, d 30 =2.44mm, d 10 =0.32mm, then the curvature coefficient C is calculated by formula 3 c is 2.01, and the unevenness coefficient C is calculated by formula 2 u It is 28.63, which also meets the "good" standard requirements of the specification gradation.

[0084] Among them, formula 2: ;

[0085] Formula 3: ;

[0086] Where: d 60 d 30 and d 10 are the characteristic particle size of soil, in mm; on the particle size distribution curve of soil, d 60 Indicates the particle size corresponding to 60% cumulative mass percentage, d 30 Indicates the particle size corresponding to 30% cumulative mass percentage, d 10 Indicates the particle size corresponding to 10% cumulative mass percentage.

[0087] It should be noted that the curvature coefficient C c and the non-uniformity coefficient C u It is a parameter used in soil mechanics to evaluate the continuity of soil particle gradation, where d 60 d 30 and d10 are the characteristic particle sizes of the soil, in the present application the characteristic particle sizes of the soil correspond to the characteristic particle sizes of the corresponding aggregate; d 60 , d 30 , and d 10 may be directly obtained from Table 2 by interpolation.

[0088] 2.2, fractal dimension criterion test:

[0089] S1: curvature coefficient C c The fractal dimension is represented by formula four, the non-uniformity coefficient C u The fractal dimension is represented by formula five;

[0090] Formula four: ;

[0091] Formula five: ;

[0092] Combined condition C u ≥ 15, and 1 ≤ C c ≤ 3, the upper and lower boundaries of the fractal dimension are formula six;

[0093] Formula six: 2.34 ≤ D ≤ 2.63;

[0094] S2: determine the maximum particle size d max and the minimum particle size d min , then the volume sand rate P s is 35% and 50% respectively to determine the upper and lower limits of the fractal dimension D 35 and D 50 , calculated by formula seven;

[0095] Formula seven: ;

[0096] According to formula seven, the corresponding fractal dimensions D 35 and D 50 when the volume sand rate is 35% and 50% respectively;

[0097] In this embodiment, the maximum particle size d max = 26.5 mm and the minimum particle size d min = 0.075 mm, according to formula seven, the corresponding fractal dimensions when the volume sand rate is 35% and 50% are D 35 = 2.43 and D 50 = 2.68 respectively.

[0098] S3: combined with formula six and formula seven, according to formula eight;

[0099] Formula eight: max{2.34, D 35 = 2.43} ≤ D ≤ min{2.63, D50 =2.68};

[0100] The boundary range of the fractal dimension is: 2.43≤D≤2.63.

[0101] From step 1.13, D opt =2.53, and using formula eight, D opt =2.53∈[2.43,2.63] meets the requirements of the fractal dimension.

[0102] 2.3, correlation coefficient test:

[0103] Draw the full-graded and coarse-graded curves after crushing, respectively, and calculate the fractal dimensions D a，m and D c，m of the full-graded and coarse-graded, and the corresponding correlation coefficients R a，m and R c，m . The closer the correlation coefficient is to 1, the better the corresponding fractal dimension is. In this embodiment, from Table 2, the correlation coefficients R a，4 and R c，4 of the full-graded and coarse-graded fitting curves are 0.9990 and 0.9972, respectively, which are the maximum values among all the correlation coefficients of the full-graded and coarse-graded, and the corresponding curves are the crushing graded curves under the loading level pressure of 24 MPa, which have the best fitting correlation. The optimal fractal dimension D opt =2.53 at this time.

[0104] The optimal fractal dimension D opt =2.53 corresponds to the full-graded that meets the joint test of the curvature coefficient and the non-uniformity coefficient, the fractal dimension discrimination standard test, and the correlation coefficient test. This graded is the optimal graded curve that meets the test.

[0105] Third step, determine the optimal graded curve and the replacement rate of the recycled aggregate:

[0106] After completing the first and second steps, draw the optimal full-graded curve, see Figure 4 , and determine the content of the recycled coal gangue brick aggregate and the natural limestone aggregate in the coarse aggregate and the fine aggregate, see Figure 5 . Among them, the replacement rate of the recycled coal gangue brick aggregate in the coarse aggregate with a particle size not less than 4.75 mm is 12.66%, and the replacement rate of the recycled coal gangue brick aggregate in the fine aggregate with a particle size less than 4.75 mm is 27.34%.

[0107] The above is further detailed description of the present application in combination with specific preferred embodiments, and cannot be deemed as limitation of the specific embodiments of the present application. For those skilled in the art of the present application, without departing from the present application, a number of simple deductions or substitutions can be made, which shall be deemed as falling within the scope of the patent protection determined by the claims of the present application.

Claims

1. A method for determining the optimum gradation of mixed recycled aggregates based on fractal dimension, characterized by, The method comprises the following steps: The first step is to determine the optimal grading of the mixed recycled aggregate: 1.1, The apparent density of the natural aggregate and the recycled aggregate with the same maximum particle size d max , was measured respectively, which were prepared with the same maximum particle size d 1.

2. Determining the maximum test load pressure F max ; 1.

3. Select the minimum particle size d for research gradation min , and take the recycled aggregate prepared in step 1.1, and max The crushed recycled aggregate is crushed under a certain pressure, and the crushed recycled aggregate is sieved to measure the apparent density of the crushed recycled aggregate at each level of sieve residue. The apparent density of the recycled aggregate at each level of sieve residue is recorded as ρ r，i ; r represents recycled aggregate, i represents the maximum particle size d max To the minimum particle size d min The number of the standard square hole sieve between max Numerically equal to the maximum standard square hole sieve diameter, d min Numerically equal to the minimum standard square hole sieve diameter; 1.

4. Determine the mixing ratio of the mixed recycled aggregate. According to the mixing ratio, the natural aggregate and the recycled aggregate prepared in step 1.1 are weighed again, configured and mixed uniformly according to the mixing ratio, and the configured mixed recycled aggregate is divided into several parts; 1.5、The maximum loading pressure F max is divided into several loading levels in turn, and the pressure of each loading level is denoted as F m , and the subscript m represents the loading sequence number; the mixed recycled aggregate prepared in step 1.4 is subjected to static loading; and the broken mixed recycled aggregate grading under different loading pressures F m is obtained. 1.6、For different loading levels of pressure F m The crushed mixed recycled aggregate grading is screened and sorted separately, and the pressure F of each loading level is weighed separately. m Under the mass of natural aggregate and recycled aggregate, the loading grade pressure F is obtained m The corresponding value is not less than d min The mass gradation of mixed recycled whole aggregate with a particle size of not less than 4.75 mm is the full gradation, and the volume gradation of mixed recycled coarse aggregate with a particle size of not less than 4.75 mm is the coarse gradation; 1.7, draw the full gradation curve and the coarse gradation curve after crushing respectively, calculate the pressure F of each loading level m the fractal dimension D corresponding to the full gradation and the coarse gradation a，m and D c，m ; 1.8, calculate the loading level pressure F of each stage m corresponding 4.75mm sieve residue volume content V 4.75，m , get the coarse gradation fractal dimension D 4.75，m corresponding to max{V max}; 1.9, fractal dimension D of full gradation and coarse gradation a，m and D c，m As the ordinate, load level pressure F m As the abscissa, F m D curve, the intersection point of the two curves corresponds to the fractal dimension D of the ordinate j ; the optimal fractal dimension D opt , D opt =max{D j , D max}, D opt The corresponding coarse gradation is the optimal coarse gradation of the mixed recycled aggregate, and the full gradation matched with the coarse gradation is the optimal full gradation of the mixed recycled aggregate; Second step, the optimal grading test: D opt The corresponding full grading meets the curvature coefficient C c And the non-uniformity coefficient C u The joint test, the fractal dimension discriminant test and the correlation coefficient test, the grading is the optimal grading curve that meets the test; The third step is to draw the optimal grading curve after the first step and the second step, and determine the recycled aggregate replacement rate of the coarse aggregate with a particle size not less than 4.75 mm and the fine aggregate with a particle size less than 4.75 mm.

2. The method for determining the optimal gradation of mixed recycled aggregates based on fractal dimension according to claim 1, characterized in that, In Step 1.5, the static loading is performed by loading the mixed recycled aggregate into a steel sample cylinder; the inner diameter and height of the sample cylinder is 5-10 times the maximum particle size d max of the aggregate, the thickness of the cylinder wall is not less than 10 mm, the thickness of the bottom of the cylinder is not less than 5 mm, and the thickness of the top loading plate of the cylinder is not less than 25 mm.

3. The method for determining the optimal gradation of mixed recycled aggregates based on fractal dimension according to claim 1, characterized in that, F max The saturated compressive strength of the rock sample test block is 1.0-1.2 times the saturated compressive strength of the natural aggregate.

4. The method for determining the optimal gradation of mixed recycled aggregates based on fractal dimension according to claim 1, characterized in that, In step 1.6, the volume grading of the mixed recycled coarse aggregate is calculated from the mass grading, wherein the volume of the recycled aggregate is calculated according to the apparent density of the graded particle size or according to the average apparent density of the recycled coarse aggregate with a particle size not less than 4.75 mm.

5. The method for determining the optimal gradation of mixed recycled aggregates based on fractal dimension according to claim 1, characterized in that, In step 1.7, the broken full-graded curve and the broken coarse-graded curve are respectively plotted in a double logarithmic coordinate system, and the corresponding curve slopes k and k are respectively obtained by using a linear fitting method a，m and k c，m , and the correlation coefficients R a，m and R c，m , and then the fractal dimensions D a，m and D c，m of the full-graded and coarse-graded are respectively calculated by using the formula D=3-k.

6. The method for determining the optimal gradation of mixed recycled aggregates based on fractal dimension according to claim 1, characterized in that, In step 1.8, V 4.75，m Formula One is met. Equation One: ; wherein: M n，m and M r，m represent the mass of the natural aggregate and the recycled aggregate, respectively, retained on a 4.75 mm standard square-hole sieve after the mth loading of the grade compression crushing, i.e., the mass of the 4.75-9.5 mm size fraction, ρ n represents the apparent density of the natural aggregate, ρ r，4.75 represents the apparent density of the 4.75-9.5 mm size fraction of the recycled aggregate, and the subscript n represents the natural aggregate.

7. The method for determining the optimal gradation of mixed recycled aggregates based on fractal dimension according to claim 1, characterized in that, In the second step, the curvature coefficient C c and the unevenness coefficient C u The joint test is to calculate D opt The curvature coefficient C c and the unevenness coefficient C u of the full gradation, and determine whether the judging standard is met; the judging standard is that when C u ≥ 15 and 1 ≤ C c ≤ 3, the gradation is good; the unevenness coefficient C u is calculated according to Formula Two, and the curvature coefficient C c is calculated according to Formula Three; Equation Two: ; Equation Three: ; wherein: d 60 d 30 and d 10 are the characteristic grain sizes of the soil, in mm; on the grain size distribution curve of the soil, d 60 represents the grain size corresponding to 60% of the cumulative mass percentage, d 30 represents the grain size corresponding to 30% of the cumulative mass percentage, d 10 represents the grain size corresponding to 10% of the cumulative mass percentage.

8. The method for determining the optimal gradation of mixed recycled aggregates based on fractal dimension according to claim 7, characterized in that, In the second step, the fractal dimension discriminant criterion test comprises the following steps: S1: the coefficient of curvature C c is expressed as a fractal dimension by Equation Four, the coefficient of unevenness C u is expressed as a fractal dimension by Equation Five; Equation Four: ​ Equation Five: ; Combination condition C u ≥ 15, and 1≤C c ≤ 3, the upper and lower boundaries of the fractal dimension can be obtained as formula six; Formula six: 2.34≤D≤2.63; S2: Determine the maximum particle size d max and the minimum particle size d min After that, the volume sand ratio P s The upper and lower limits of the fractal dimension D 35 and D 50 are determined respectively at 35% and 50%, and the calculation uses Equation Seven; Equation Seven: ​ From Equation 7, the fractal dimension D corresponding to the volume sand ratio of 35% and 50% is 2.45 and 2.32, respectively. 35 and D 50 ; S3: Combined with formula six and formula seven, the boundary of the fractal dimension is formula eight: Equation Eight: max{ 2.34, D 35}≤ D ≤ min{ 2.63, D 50}; Use Equation Eight to determine D opt If satisfied, it is reasonable, otherwise it is unreasonable.

9. The method for determining the optimal gradation of mixed recycled aggregates based on fractal dimension according to claim 5, characterized in that, In the second step, the correlation coefficient test is to draw the full-graded curve and the coarse-graded curve after crushing respectively, and to obtain the correlation coefficient R by linear fitting method a，m and R c，m The closer to 1, the better the fractal dimension.

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