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

Abstract

The invention discloses a method for determining the optimal gradation of mixed recycled aggregate based on fractal dimension, and belongs to the technical field of building material testing, and the method comprises the following steps: 1, determining the optimal gradation of the mixed recycled aggregate; step 2, carrying out optimal gradation inspection; 3, drawing an optimal grading curve, and determining the recycled aggregate substitution rate of the coarse aggregate and the fine aggregate; according to the method, on the basis of the idea that stacking and crushing of brittle granular materials are inverse to each other, according to fractal dimension definition and the change rule of the 4.75 mm screen residue volume content in the loading process, the fractal dimension of the mixed recycled aggregate is determined through experimental testing and theory combination, and then the optimal grading of the mixed recycled aggregate is determined; a corresponding fractal dimension inspection method is provided; according to the method, the optimal grading of the recycled mixed aggregate can be effectively determined, the workload is small, and the labor intensity is low.

Description

Technical Field

[0001] The invention belongs to the technical field of building material testing, and in particular relates to a method for determining the optimal gradation of mixed recycled aggregate based on fractal dimension. Background Art

[0002] Civil engineering and construction consume 60% of the raw materials extracted from the lithosphere. Natural aggregates are generally used as concrete aggregates, accounting for 60% to 75% of the total volume. To address the shortage of natural materials and eliminate the environmental pressure caused by construction waste, recycled aggregates are being used in place of natural aggregates in recycled concrete. However, recycled aggregates generally have a lower specific gravity and lower strength than natural aggregates, are more porous and absorbent, and have relatively high variability in aggregate quality. Therefore, how to blend natural and recycled aggregates and determine the optimal gradation of the mixed recycled aggregates is an urgent challenge, and a scientific and standardized method has yet to be established.

[0003] Fuller believed that if solid particles of different sizes were regularly mixed in a certain proportion, theoretically, the aggregate composition with the highest density and the smallest voids could be obtained. To facilitate the calculation of aggregate gradation, after research and improvement, it was believed that when the gradation curve is a parabola, the aggregate can achieve the maximum density, which is expressed as Formula 9;

[0004] Formula 9: ;

[0005] Where: P i is the passing rate of the sieve holes in the i-th layer; d i is the aperture of the sieve hole in the i-th layer; d max is the maximum particle size of the gradation.

[0006] Talbol et al. believed that Formula 9 is an overly idealized curve. In practice, there is a certain range of fluctuations in order to obtain the maximum density. The value of the index should not be a constant, but a variable β. β is the experimental index, with a value of 0.3~0.5, and its expression is Formula 10.

[0007] Formula 10: ;

[0008] Through further research, Tyler linked aggregate gradation with fractals, and thus established the aggregate gradation design formula 11. Assuming that the maximum particle size of the aggregate sample is d max , the aperture of the sieve hole in the i-th layer is d i The total mass of aggregate passing through the sieve hole is M(d i ), the total mass of the aggregate sample is M0. Then it is greater than a certain characteristic particle size d i (d i >d i+1) decreases with the increase of i value, and its expression is formula 11;

[0009] Formula 11: ;

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

[0011] According to Mandelbrot's monograph "The Fractal Geometry of Nature," the fractal dimension of solid aggregate in three-dimensional space is between 2 and 3. However, for aggregate gradation, the range of the fractal dimension D is too wide. For example, when calculating the sand content passing a 4.75mm sieve (using Formula 10), fractal dimensions between 2 and 3 correspond to sand content exceeding 17.9% and approaching 100%, respectively. This wide range of variation clearly makes it unusable in practical engineering. According to Talbol's research, when the slope k is 0.3-0.5, the fractal dimension is 2.5-2.7, corresponding to sand content of 42.3%-59.7%. Although the sand content range is reduced, this formula is primarily for natural aggregates, using an empirical range obtained from limited material testing. It does not consider the impact of material properties on the fractal dimension. This is especially true for recycled aggregates mixed with solid waste, where the effects of different material mixing ratios and crushed particle morphology on aggregate gradation need to be considered. In addition, Formula 11 uses the relationship between mass ratio and diameter ratio to characterize the fractal dimension. For natural materials, the effect of particle size on apparent density can be ignored. However, for solid waste mixed materials, particle size affects the number of defects, and apparent density is related to particle size. Changes in the mixing ratio and particle size will affect the apparent density of the mixed material, causing changes in the gradation curve, which further affects the fractal dimension. Therefore, determining the fractal dimension range of solid waste mixed recycled aggregate and how to apply the fractal dimension to conveniently design and optimize the gradation of mixed recycled aggregates are engineering problems that need to be solved. Summary of the Invention

[0012] The present invention overcomes the shortcomings of the prior art and proposes a method for determining the optimal gradation of mixed recycled aggregate based on fractal dimension, which can conveniently use fractal dimension to design the gradation of mixed recycled aggregate. The present invention is achieved through the following technical solutions:

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

[0014] The first step is to determine the optimal gradation of mixed recycled aggregate:

[0015] 1.1, According to the maximum particle size d of the gradation max , prepare natural aggregate and recycled aggregate of a single particle size that is the same as the maximum particle size of the gradation, dry and preserve them, and measure the apparent density of the prepared natural aggregate and recycled aggregate respectively;

[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 crushed mixed recycled aggregate gradation under

[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 , find the value that is equal to max{V 4.75，m The corresponding coarse gradation fractal dimension D max ;

[0023] 1.9. Fractal dimension D of full gradation and coarse gradation a，m and D c，m As the vertical axis, the loading level pressure F m As the horizontal axis, plot F m ~D curve, find the fractal dimension D corresponding to the vertical coordinate of the intersection of the two curves j ; Obtain 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 mixed recycled aggregate, and the full gradation that matches the coarse gradation is the optimal full gradation of mixed recycled aggregate;

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

[0025] The third step is to draw the optimal gradation curve after completing the first and second steps to determine the replacement rate of recycled aggregate for coarse aggregate with a particle size of not less than 4.75 mm and fine aggregate with a particle size of less than 4.75 mm.

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

[0027] Furthermore, F max It is 1.0~1.2 times the saturated compressive strength of the rock sample corresponding to natural aggregate.

[0028] Furthermore, in step 1.6, the volume gradation of the mixed recycled coarse aggregate is calculated based on the mass gradation, wherein the volume of the recycled aggregate is calculated based on the apparent density of the recycled aggregate of the graded particle size or based on the average apparent density of the recycled coarse aggregate with a particle size of not less than 4.75 mm.

[0029] Furthermore, in step 1.7, the full gradation curve and the coarse gradation curve after crushing are drawn in the double logarithmic coordinate system, and the corresponding curve slopes k are obtained by linear fitting method. a，m and k c，m And the correlation coefficient R a，m and R c，m , and then use the formula D=3-k to calculate the fractal dimension D of the full gradation and the coarse gradation respectively a，m and D c，m .

[0030] Furthermore, in step 1.8, V 4.75，m In line with formula 1;

[0031] Formula 1: ;

[0032] Where: M n，m and M r，m They represent the mass of the 4.75 mm standard square hole sieve residue of natural aggregate and recycled aggregate after pressure crushing at the mth loading level, that is, the mass of particles with a size of 4.75 to 9.5 mm, and ρ n represents the apparent density of natural aggregate, ρ r，4.75 It represents the apparent density of recycled aggregate with a particle size of 4.75~9.5mm, and the subscript n represents natural aggregate.

[0033] Furthermore, in the second step, the curvature coefficient C c and the non-uniformity coefficient C u The joint test is to calculate D opt Curvature coefficient C corresponding to full gradation c and the non-uniformity coefficient C u , determine whether the judgment standard is met; the judgment standard is: when C u ≥15, and 1≤C c When ≤3, the gradation is good; the unevenness coefficient C u According to formula 2, the curvature coefficient C c Calculate according to formula 3;

[0034] Formula 2: ;

[0035] Formula 3: ;

[0036] 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 10Indicates the particle size corresponding to 10% cumulative mass percentage.

[0037] Furthermore, in the second step, the fractal dimension discrimination criterion test includes the following steps:

[0038] S1: curvature coefficient C c The fractal dimension is expressed by formula 4, and the non-uniformity coefficient C u The fractal dimension is expressed by formula 5;

[0039] Formula 4: ;

[0040] Formula 5: ;

[0041] Combined with condition C u ≥15, and 1≤C c ≤3, the upper and lower boundaries of the fractal dimension can be expressed as formula 6;

[0042] Formula 6: 2.34≤D≤2.63;

[0043] S2: Determine the maximum particle size d max and minimum particle size d min After that, the volume sand rate P s The upper and lower limits of the fractal dimension D are determined as 35% and 50% respectively. 35 and D 50 , calculated using formula seven;

[0044] Formula 7: ;

[0045] From formula 7, we can know that the fractal dimension D corresponding to the volume sand ratio of 35% and 50% is 35 and D 50 ;

[0046] S3: Combining Formula 6 and Formula 7, the boundary of the fractal dimension is obtained as Formula 8;

[0047] Formula 8: max{2.34,D 35}≤D≤min{2.63,D 50};

[0048] Use formula 8 to judge D opt Whether it is satisfied or not, if it is satisfied then it is reasonable, otherwise it is unreasonable.

[0049] Furthermore, in the second step, the correlation coefficient test is to draw the full gradation curve and the coarse gradation curve after crushing respectively, and use the linear fitting method to calculate the correlation coefficient R of the slope of the gradation curve. a，m and R c，m The closer it is to 1, the better the corresponding fractal dimension.

[0050] The beneficial effects of the present invention compared to the prior art are:

[0051] Based on the concept that the accumulation and crushing of brittle granular materials are inverse processes, and building on previous research, this paper proposes a design method for determining the fractal dimension of mixed recycled aggregate using a combination of experimental testing and theoretical analysis, thereby determining the optimal gradation of mixed recycled aggregate. The method also proposes a corresponding fractal dimension verification method. This method effectively determines the optimal gradation of mixed recycled aggregate with minimal workload and low labor intensity. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

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

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

[0056] Figure 5 Graph showing the content of the optimally graded recycled gangue brick aggregate and natural limestone aggregate in the embodiment. DETAILED DESCRIPTION

[0057] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention more clearly understood, the present invention is further described in detail with reference to the embodiments and the accompanying drawings. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention. The technical solutions of the present invention will be described in detail below with reference to the embodiments and the accompanying drawings, but the scope of protection is not limited thereto.

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

[0059] The first step is to determine the optimal gradation of mixed recycled aggregate:

[0060] 1.1. Collect natural limestone aggregate and recycled gangue brick aggregate.

[0061] 1.2. Select the maximum particle size d of the research gradation max=26.5mm; natural limestone aggregate and recycled gangue brick aggregate were collected, crushed separately by crusher, sieved with 19-26.5mm standard square hole sieve, and the initial samples of 19-26.5mm natural limestone aggregate and recycled gangue brick aggregate were prepared. The initial samples were dried and preserved; the apparent density of natural limestone aggregate was measured to be 2.690g / cm 3 The apparent density of recycled gangue brick aggregate is 2.240g / cm 3 .

[0062] 1.3. The sample cylinder should be φ150mm×150mm×10mm in size, with a bottom thickness of 8mm and a top loading plate thickness of 25mm.

[0063] 1.4. Determine the maximum loading pressure F max =60MPa.

[0064] 1.5. Select the minimum particle size d for research gradation min =0.075mm; take a portion of the 19~26.5mm recycled gangue brick aggregate initial sample prepared in step 1.2, perform a confined crushing test under a pressure of 5MPa, sieve the crushed sample, and measure the apparent density of the crushed recycled gangue brick aggregate at each level of sieve residue, which is recorded as ρ r，i ; i = 0.075mm, 0.15mm, ..., 19mm; the apparent density of recycled gangue brick aggregate is shown in Table 1:

[0065]

[0066] 1.6. Weigh the initial sample of natural limestone aggregate and the initial sample of recycled gangue brick aggregate prepared in step 1.2, mix them evenly in a mass mixing ratio of 60% and 40% to obtain a mixed recycled aggregate sample, and then divide the prepared mixed recycled aggregate sample into 7 parts.

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

[0068] Weigh one portion of the mixed recycled aggregate sample prepared in step 1.6 and divide it into three equal portions. Take one portion and place it into the sample tube. Apply static loading to the mixed recycled aggregate sample, and select the first loading level pressure value F1 = 3MPa. After the static loading reaches the predetermined pressure value of 3MPa, stand still for 5s and then unload. Perform parallel tests on the remaining two mixed recycled aggregate samples at this pressure to obtain the crushed mixed recycled aggregate samples under this loading level pressure.

[0069] 1.8. The crushed mixed recycled aggregate samples after three parallel tests were mixed evenly and then sieved to obtain the mass gradation of mixed recycled full aggregate with a particle size of not less than 0.075 mm corresponding to the loading grade pressure (hereinafter referred to as full gradation). The sieved mixed recycled aggregate samples with a particle size of not less than 4.75 mm were manually sorted to obtain mixed recycled coarse aggregate. The masses of natural limestone aggregate and recycled gangue brick aggregate in the mixed recycled coarse aggregate were weighed respectively. The volume gradation of coarse aggregate was calculated based on the mass gradation. The volume of recycled gangue brick aggregate was calculated according to the apparent density of recycled gangue brick aggregate measured in Table 1, or according to the average apparent density of recycled gangue brick coarse aggregate with a particle size of not less than 4.75 mm, to obtain the volume gradation of mixed recycled coarse aggregate with a particle size of not less than 4.75 mm (hereinafter referred to as coarse gradation). The calculation results are shown in Table 2.

[0070] 1.9. Draw the full gradation and coarse gradation curves after crushing in the double logarithmic coordinate system, and use the linear fitting method to obtain the corresponding slope k a，1 = 0.72 and k c，1 =1.14 and the correlation coefficient R a，1 =0.9587 and R c，1 =0.9687, and then use the formula D=3-k to calculate the fractal dimension D of the full gradation and the coarse gradation respectively a，1 =2.28 and D c，1 =1.86, see Figure 1 and Figure 2 .

[0071] 1.10. Select all loading levels F2 = 6MPa, F3 = 12MPa, ..., F7 = 60MPa in turn, repeat steps 1.7 to 1.9 to complete the test of mixed recycled aggregate under all loading levels. Draw the full gradation and coarse gradation curves after crushing in a double logarithmic coordinate system, and use the linear fitting method to calculate the pressure F of each loading level. m The corresponding curve slope k a，m and k c，m And the correlation coefficient R a，m and R c，m , and then use the formula D=3-k to calculate the fractal dimension D of the full gradation and the coarse gradation respectively a，m and Dc，m (Calculation results are shown in Table 2), m and loading level pressure F m The angle code number is the same.

[0072] Table 2 Confined crushing gradation for each loading level pressure

[0073]

[0074] Note: The symbol k before the “ / ” in the lower three rows of the first column of Table 2 a，m 、D a，m and R 2 a，m Corresponding to the mass gradation of all aggregates, the symbol k after “ / ” c，m 、D c，m and R 2 c，m Corresponding to the volume gradation of coarse aggregate.

[0075] 1.11. Calculate the pressure F at each level of loading from Table 2 m Corresponding 4.75mm sieve residue volume content V 4.75，m , find the value that is equal to max{V 4.75,m The corresponding coarse gradation fractal dimension D max =2.53, the calculation 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. Fractal dimension D of full gradation and coarse gradation a，m and D c，m As the vertical axis, the pressure F of each loading level m As the horizontal axis, plot F m ~D curve (loading grade pressure-fractal dimension curve), that is, full grade D a，m Curve and coarse gradation D c，m Curve, get the full grade D a，m Curve and coarse gradation D c，m The fractal dimension D corresponding to the vertical coordinate of the intersection of the curve j =2.45, see Figure 3 .

[0079] 1.13. From steps 1.11 and 1.12, we know that: D max =2.53 and D j =2.45, then:

[0080] 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 soil. In the present invention, the characteristic particle size of soil corresponds to the characteristic particle size of the corresponding aggregate; d 60 d 30 and d 10 It can be directly obtained by interpolation from Table 2.

[0088] 2.2. Fractal dimension judgment standard test:

[0089] S1: curvature coefficient C c The fractal dimension is expressed by formula 4, and the non-uniformity coefficient C u The fractal dimension is expressed by formula 5;

[0090] Formula 4: ;

[0091] Formula 5: ;

[0092] Combined with condition C u ≥15, and 1≤C c ≤3, the upper and lower boundaries of the fractal dimension can be expressed as formula 6;

[0093] Formula 6: 2.34≤D≤2.63;

[0094] S2: Determine the maximum particle size d max and minimum particle size d min After that, the volume sand rate P s The upper and lower limits of the fractal dimension D are determined as 35% and 50% respectively. 35 and D 50 , calculated using formula seven;

[0095] Formula 7: ;

[0096] From formula 7, we can know that the fractal dimension D corresponding to the volume sand ratio of 35% and 50% is 35 and D 50 ;

[0097] In this embodiment, the maximum particle size d max =26.5mm and minimum particle size d min =0.075mm, according to formula 7, the corresponding fractal dimensions of the volume sand ratio of 35% and 50% are D 35 =2.43 and D 50 =2.68.

[0098] S3: Combine Formula 6 and Formula 7, according to Formula 8;

[0099] Formula 8: max{2.34,D 35 =2.43}≤D≤ min{ 2.63,D50 =2.68};

[0100] The boundary range of the fractal dimension can be determined as: 2.43≤D≤2.63.

[0101] From step 1.13, we know that D opt =2.53, use formula 8 to determine D opt =2.53∈[2.43,2.63] meets the requirements of fractal dimension.

[0102] 2.3. Correlation coefficient test:

[0103] Draw the full gradation and coarse gradation curves after crushing respectively, and calculate the fractal dimension D of the full gradation and coarse gradation a，m and D c，m , and the corresponding correlation coefficient 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, it can be seen from Table 2 that the correlation coefficient R of the full gradation and coarse gradation fitting curves is a，4 and R c，4 The values are 0.9990 and 0.9972 respectively, which are the maximum values of all correlation coefficients of full gradation and coarse gradation, and the corresponding curves are the crushing gradation curves when the loading pressure is 24 MPa. The fitting correlation is the best, and the optimal fractal dimension D is opt =2.53.

[0104] Optimal fractal dimension D opt =2.53 corresponds to the full gradation that satisfies the combined test of curvature coefficient and unevenness coefficient, the fractal dimension judgment standard test and the correlation coefficient test. This gradation is the optimal gradation curve that meets the test.

[0105] The third step is to determine the optimal gradation curve and recycled aggregate replacement rate:

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

[0107] The above content is a further detailed description of the present invention in combination with a specific preferred embodiment. It cannot be considered that the specific embodiments of the present invention are limited to this. For ordinary technicians in the technical field to which the present invention belongs, they can make several simple deductions or substitutions without departing from the present invention, which should be regarded as falling within the scope of patent protection determined by the claims submitted by the present invention.

Claims

1. A method for determining the optimal gradation of mixed recycled aggregate based on fractal dimension, characterized in that: The following steps are involved: The first step is to determine the optimal gradation of mixed recycled aggregate: 1.1, According to the maximum particle size d of the gradation max , prepare natural aggregate and recycled aggregate of a single particle size that is the same as the maximum particle size of the gradation, dry and preserve them, and measure the apparent density of the prepared natural aggregate and recycled aggregate respectively; 1.

2. Determine the maximum loading 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. 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. 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 crushed mixed recycled aggregate gradation under 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 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 ; 1.

8. Calculate the pressure F at each level of loading m Corresponding 4.75mm sieve residue volume content V 4.75，m , find the value that is equal to max{V 4.75，m The corresponding coarse gradation fractal dimension D max ; 1.

9. Fractal dimension D of full gradation and coarse gradation a，m and D c，m As the vertical axis, the loading level pressure F m As the horizontal axis, plot F m ~D curve, find the fractal dimension D corresponding to the vertical coordinate of the intersection of the two curves j ; Obtain 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 mixed recycled aggregate, and the full gradation that matches the coarse gradation is the optimal full gradation of mixed recycled aggregate; The second step is to test the optimal gradation: D opt The corresponding full gradation also satisfies the curvature coefficient C c and the non-uniformity coefficient C u The gradation is the optimal gradation curve that meets the test of joint test, fractal dimension discrimination standard test and correlation coefficient test; The third step is to draw the optimal gradation curve after completing the first and second steps to determine the replacement rate of recycled aggregate for coarse aggregate with a particle size of not less than 4.75 mm and fine aggregate with a particle size of less than 4.75 mm.

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

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

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

5. The method for determining the optimal gradation of mixed recycled aggregate based on fractal dimension according to claim 1, characterized in that: In step 1.7, the full gradation curve and the coarse gradation curve after crushing are drawn in the double logarithmic coordinate system, and the corresponding curve slope k is obtained by linear fitting method. a，m and k c，m And the correlation coefficient R a，m and R c，m , and then use the formula D=3-k to calculate the fractal dimension D of the full gradation and the coarse gradation respectively a，m and D c，m .

6. The method for determining the optimal gradation of mixed recycled aggregate based on fractal dimension according to claim 1, characterized in that: In step 1.8, V 4.75，m In line with formula 1; Formula 1: ; Where: M n，m and M r，m They represent the mass of the 4.75 mm standard square hole sieve residue of natural aggregate and recycled aggregate after pressure crushing at the mth loading level, that is, the mass of particles with a size of 4.75 to 9.5 mm, and ρ n represents the apparent density of natural aggregate, ρ r，4.75 It represents the apparent density of recycled aggregate with a particle size of 4.75~9.5mm, and the subscript n represents natural aggregate.

7. The method for determining the optimal gradation of mixed recycled aggregate based on fractal dimension according to claim 1, characterized in that: In the second step, the curvature coefficient C c and the non-uniformity coefficient C u The joint test is to calculate D opt Curvature coefficient C corresponding to full gradation c and the non-uniformity coefficient C u , determine whether the judgment standard is met; the judgment standard is: when C u ≥15, and 1≤C c When ≤3, the gradation is good; the unevenness coefficient C u According to formula 2, the curvature coefficient C c Calculate according to formula 3; Formula 2: ; Formula 3: ; 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.

8. The method for determining the optimal gradation of mixed recycled aggregate based on fractal dimension according to claim 7, characterized in that: In the second step, the fractal dimension discrimination criterion test includes the following steps: S1: curvature coefficient C c The fractal dimension is expressed by formula 4, and the non-uniformity coefficient C u It is expressed as the fractal dimension by formula 5; Formula 4: ; Formula 5: ; Combined with condition C u ≥15, and 1≤C c ≤3, the upper and lower boundaries of the fractal dimension can be expressed as formula 6; Formula 6: 2.34≤D≤2.63; S2: Determine the maximum particle size d max and minimum particle size d min After that, the volume sand rate P s The upper and lower limits of the fractal dimension D are determined as 35% and 50% respectively. 35 and D 50 , calculated using formula seven; Formula 7: ; From formula 7, we can know that the fractal dimension D corresponding to the volume sand ratio of 35% and 50% is 35 and D 50 ; S3: Combining Formula 6 and Formula 7, the boundary of the fractal dimension is obtained as Formula 8; Formula 8: max{2.34,D 35 }≤D≤ min{ 2.63,D 50 }; Use formula 8 to judge D opt Whether it is satisfied or not, if it is satisfied then it is reasonable, otherwise it is unreasonable.

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

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