# Determination of Gradation of Recycled Mixed Coarse Aggregates for Pavement Base or Subbase by Crushing Fractals

Authors: Jianjun Li; Yong Pei; Pengcheng Xu; Hui Chang
Journal: Advances in Materials Science and Engineering
 (2019)

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## Abstract

A loading crushing test of recycled mixed coarse aggregates in the same particle diameter range is carried out, and the crushed coarse aggregates are screened, manually sorted, and weighed to study the crushing characteristics of recycled mixed coarse aggregates. The results show that the effect of “reinforcing the strong and discarding the weak” exists between two types of recycled mixed coarse aggregates with different strength in the course of crushing. After crushing, the cumulative mass content under each sieve at all levels and the sieve diameter ratio conform to the geometric fractal characteristics, and the fractal dimension is influenced by the material strength, the initial mixing ratio, and the initial void ratio. On this basis, the fractal dimension of recycled mixed coarse aggregates is determined by the crushing test, and the gradation of recycled mixed coarse aggregates for pavement base or subbase is then determined by fractal dimension. Finally, the mixing amount of recycled clay bricks in recycled mixed coarse aggregates for pavement base or subbase is discussed.


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## Body

## 1. Introduction

Demolition of old buildings in the process of urbanization in China has produced a great deal of construction waste. From 2003 to 2018, approximately 15.64 million tons of construction waste was generated in the urban village reconstruction of Taiyuan City, Shanxi Province (the data are taken from the unpublished data of Taiyuan Urban Renovation Office). The demolished old buildings are mainly of brick-concrete structures. Waste concrete, mortar, and waste clay bricks are the main components of demolition construction wastes. Landfilling is a common practice for treating demolition construction waste, but it takes up a significant amount of land resources and can cause serious environmental problems. The utilization rate of construction waste in China is about 5%∼10% [1]. The reasons for this situation may be related to the lack of relevant policy guidance, and the difficulty and high cost of treating construction waste make it difficult to form high value-added products.Clay bricks are the most widely used building material in the old buildings that were demolished. Over the past 50 years, China has produced at least 20 billion cubic meters of clay bricks, or about 50% of all construction waste [2]. The reuse of recycled clay bricks is limited because of its low strength, high water absorption, and porosity. However, scholars are also trying to explore the reuse of recycled clay bricks. Germany first produced concrete products using crushed clay bricks in 1860, but it was not until the end of the Second World War where crushed bricks were used in large quantities as aggregates to produce fresh concrete [3]. According to the literature, the utilization and research of recycled clay bricks are mainly embodied in the following aspects: (1) the influence of the recycled clay brick aggregates completely or partially replacing the natural aggregates on the mechanical properties and durability of recycled concrete [4–12]; (2) the influence of recycled clay brick powder as part of cement substitute material on the mechanical properties and durability of concrete and mortar [11, 13–16]; and (3) the application of recycled aggregates in subgrade and pavement base or subbase filling [17–24].Infrastructure construction is the engine driving the sustainable development of China’s economy, and it may be a relatively suitable choice to use construction waste to fill the pavement base or subbase of road engineering [17–21, 23–26]. For road engineering, most of the compressive strength generated by pavement load will be transferred to the aggregate of pavement base or subbase. Particle breakage occurs when the stresses imposed on soil particles exceed their strength [27]. The mechanics of particle crushing, or particle breakage, is one of the most intractable problems in geosciences [28]. The amount of particle crushing in a soil element under stress depends on particle size distribution, particle shape, state of effective stress, effective stress path, void ratio, particle hardness, and the presence or absence of water [29]. Mechanical loading (shear or compression) can lead to disaggregation and breakage of particles and thus alter the particle size distribution of granular materials [30].Mandelbrot has observed that several natural phenomena can be accurately described by fractal theory [31]. The fractal dimension, D, is a fraction with a value between 0 and 3.0. The solid phase of many natural porous materials has also been examined for fractal behavior [32]. In many cases, breakage results in a fractal distribution [33, 34]. The particle size distributions of broken and crushed granular materials tend to be self-similar or fractal [32]. Fractal scaling has recently been proposed as a model for soil particle size distribution. A fractal distribution of particle sizes evolves from the compression of an aggregate of uniform grains [34]. Based on the comparative analysis of two models of the cumulative number of soil grains and the cumulative mass distribution, the cumulative number approach used to estimate the fractal dimension is shown to be sensitive to the assumed grain density and characteristic size, while the mass distribution is less sensitive to the assumed grain density and characteristic size and therefore more appropriate for the analysis of field soils [35]. The particle grading can be characterized by defining a fractal dimension, which, remarkably, often tends to be about 2.5 for aggregates subjected to pure crushing [32, 36]. The value of the fractal dimension changes with the failure stress and breakage energy and goes by the name of the quasi-fractal dimension. The quasi-fractal dimension tends to a constant value of 2.60 or so [37].Granular materials such as sand, soil, and rock aggregates are ubiquitous. Particle size distribution of granular materials has great influence on their physicomechanical properties, such as compressibility, yield strength, and permeability [28]. It is important to define the degree to which the particles of an element of soil are crushed or broken during loading. The relative breakage that can be used to estimate the total breakage expected for a given soil subjected to a specified loading is presented, which is defined as the ratio of total breakage to the breakage potential. The relative breakage, Br, is approximately independent of particle size distribution when particle size distribution is the only variable [29]. Einav further developed the concept of breakage based on the existence of an ultimate grain size distribution [28]. Breakage essentially measures the relative proximity of the current grain size distribution to the initial and ultimate distributions. Therefore, the breakage is confined to increase from zero to one with the increase in surface area. The magnitude of fractal crushing dimension reflected the variation of quantity of particle breakage. Large fractal crushing dimension corresponded to large quantities of particle breakage [38, 39]. There was a close relationship between fractal crushing dimension and Hardin index of particle breakage [38].The construction waste recycling mixed aggregate (composed of recycled concrete and recycled clay brick) replaces natural aggregate as pavement base or subbase filling aggregate, which is an effective way to reduce construction waste landfill and realize resource reuse. The aggregate gradation, especially coarse aggregate gradation, plays an important role in the properties of the aggregate skeleton. In research concerning the crushing mechanism of granular materials, natural materials—such as sand [27, 30, 36, 38], soil particles [29], basalt [32], and ice particles [36]—are mostly taken as research objects. Some researchers have experimented with various artificial materials, such as glass beads and plaster, as well as the bottom ash from municipal solid waste incineration [37, 40]. However, few people have attempted to use concrete or clay brick that is commonly used in building materials as crushing materials, and there are no reports of recycled mixed aggregate as crushing materials.In this paper, the lateral confinement crushing tests of recycled mixed aggregates with uniform initial particle size are carried out under given pressure. The particle-size distribution and fractal characteristics of crushed coarse aggregate are studied. The influencing factor of fractal dimension of recycled coarse aggregate after crushing is illustrated. The interaction between recycled concrete and recycled clay brick particles in the crushing process is analyzed. The influence of the ratio of recycled clay brick on the grading curve of coarse aggregate is discussed. In order to shed light on the best usage of recycled clay brick, this paper is expected to provide an effective method for the gradation determination of recycled coarse aggregate used either for pavement base or subbase.


## 2. Test Materials and Methods

### 2.1. Test Equipment

The YE-2000A hydraulic press used in the laterally confined crushing test is shown in Figure1. The maximum load pressure of the press is 2000 kN, and the accuracy of the press is grade I (Figures 1(a) and 1(b)). The sample barrel consists of steel circular cylinder with open ends, bottom plate, and indenter. The steel circular cylinder is 125 mm in height, 150 mm in diameter, and 13.5 mm in wall thickness. Owing to the fact that the wall thickness of the steel circular cylinder is thick enough to restrict the specimen laterally, the radial deformation of the specimen can be ignored. The indenter of the specimen is composed of a solid steel cylinder and a circular plate with a diameter of 149 mm and a thickness of 25 mm (Figure 1(c)). Since the stiffness of the circular plate is large enough, the loading process is equivalent to applying a uniform load on the surface of the specimen. The test method in this paper refers to “Crushing Value Test of Coarse Aggregate” (T 0316-2005) in the current industry standard of China “Test Rules for Aggregate in Highway Engineering” (JTG E42-2005). Article 4.4 of this standard stipulates start the press, apply load evenly, reach the total load of 400 kN in about 10 min, and stabilize the pressure for 5 s [41].Figure 1
Laterally confined crushing test equipment. (a) YE-2000A hydraulic press. (b) Laterally confined crushing test. (c) Sample barrel and indenter.
(a)
(b)
(c)


### 2.2. Test Materials

The materials used in the lateral confinement crushing test are Ordovician limestone, recycled concrete, and recycled clay brick from demolished construction waste. Ordovician limestone comes from the abandoned quarry in Lancun Town, Taiyuan City. The construction waste used in the test was taken from the demolition building of a brick-concrete structure in North University of China in Taiyuan City, Shanxi Province. After removing impurities, the original construction waste is manually classified, and recycled clay bricks and recycled concrete blocks are selected as the test materials. Recycled clay bricks, recycled concrete blocks, and limestone previously prepared are mechanically crushed by a jaw crusher. Recycled aggregates and limestone aggregates obtained by mechanical crushing were screened by vibration, and remove the needle-like and flake particles by means of a profiler. The samples of the recycled concrete aggregates, recycled clay bricks aggregates, and limestone aggregates with particle sizes of 19–26.5 mm and the samples of the recycled concrete aggregates and limestone aggregates with particle sizes of 9.5–13.2 mm were prepared. The samples were prepared as presented in Figure2.Figure 2
Aggregate samples. (a) Recycled concrete aggregates. (b) Recycled clay brick aggregates. (c) Limestone aggregates.
(a)
(b)
(c)


### 2.3. Test Scheme and Process

The recycled mixed aggregates with a particle diameter range of 19 mm to 26.5 mm and 9.5 mm to 13.2 mm in the dry state are selected, and the samples are prepared according to the mass ratio of recycled concrete to recycled clay bricks of 2 : 8, 4 : 6, 5 : 5, 6 : 4, and 8 : 2. At the same time, one batch of recycled concrete (RC), recycled clay bricks (RB), and natural limestone (NL) aggregates of the same particle diameter range are prepared as comparative samples, and three sets of parallel confined crushing tests are carried out for each sample. The test conditions are grouped as shown in Table1.Table 1
Test conditions.
Sample number
Particle diameter range of samples before crushing (mm)
Mass ratio of samples
Vertical pressure (kN)
RB
19∼26.5
100% RB
400
RC2RB8
19∼26.5
20% RC + 80% RB
400
RC4RB6
19∼26.5
40% RC + 60% RB
400
RC5RB5
19∼26.5
50% RC + 50% RB
400
RC6RB4
19∼26.5
60% RC + 40% RB
400
RC8RB2
19∼26.5
80% RC + 20% RB
400
RC
19∼26.5
100% RC
400
NL26.5
19∼26.5
100% natural limestone
400
NL13.2
9.5∼13.2
100% natural limestone
400
RC13.2
9.5∼13.2
100% RC
200Before testing the samples, put them in a drying box for 3-4 h at 100°C for drying so that the aggregates are in a completely dehydrated and dry state. Then, weigh the mass of the sample barrel, and put the samples into the test barrel three times. After each sample was put in, the surface of the sample was smoothed and tamped evenly 25 times with the hemispherical end of the metal rod. Finally, the total mass of the test barrel and the sample is weighed again to obtain the initial massM0 of the samples. Place the prepared samples on the press, then smoothly place the indenter on the surface of the samples, start the press, apply the load evenly, reach a total load of 400 kN in about 10 min, and then unload after stabilizing the pressure for 5 s. The laterally confined crushing test is carried out in accordance with Chinese Standard T0316 [41].The crushed samples are sieved and weighed in order of the aperture of 19 mm, 16 mm, 13.2 mm, 9.5 mm, and 4.75 mm, and fine aggregates (particle diameter <4.75 mm) are sieved and weighed. The mixed aggregates of crushed coarse aggregates (particle diameter ≥4.75 mm) are manually sorted, and recycled concrete and recycled clay brick aggregates in each particle diameter range are weighed separately. In addition, the comparative tests of crushing pressure of 200 kN and 400 kN are carried out for the sample with a particle diameter range of 9.5 mm to 13.2 mm.


## 2.1. Test Equipment

The YE-2000A hydraulic press used in the laterally confined crushing test is shown in Figure1. The maximum load pressure of the press is 2000 kN, and the accuracy of the press is grade I (Figures 1(a) and 1(b)). The sample barrel consists of steel circular cylinder with open ends, bottom plate, and indenter. The steel circular cylinder is 125 mm in height, 150 mm in diameter, and 13.5 mm in wall thickness. Owing to the fact that the wall thickness of the steel circular cylinder is thick enough to restrict the specimen laterally, the radial deformation of the specimen can be ignored. The indenter of the specimen is composed of a solid steel cylinder and a circular plate with a diameter of 149 mm and a thickness of 25 mm (Figure 1(c)). Since the stiffness of the circular plate is large enough, the loading process is equivalent to applying a uniform load on the surface of the specimen. The test method in this paper refers to “Crushing Value Test of Coarse Aggregate” (T 0316-2005) in the current industry standard of China “Test Rules for Aggregate in Highway Engineering” (JTG E42-2005). Article 4.4 of this standard stipulates start the press, apply load evenly, reach the total load of 400 kN in about 10 min, and stabilize the pressure for 5 s [41].Figure 1
Laterally confined crushing test equipment. (a) YE-2000A hydraulic press. (b) Laterally confined crushing test. (c) Sample barrel and indenter.
(a)
(b)
(c)


## 2.2. Test Materials

The materials used in the lateral confinement crushing test are Ordovician limestone, recycled concrete, and recycled clay brick from demolished construction waste. Ordovician limestone comes from the abandoned quarry in Lancun Town, Taiyuan City. The construction waste used in the test was taken from the demolition building of a brick-concrete structure in North University of China in Taiyuan City, Shanxi Province. After removing impurities, the original construction waste is manually classified, and recycled clay bricks and recycled concrete blocks are selected as the test materials. Recycled clay bricks, recycled concrete blocks, and limestone previously prepared are mechanically crushed by a jaw crusher. Recycled aggregates and limestone aggregates obtained by mechanical crushing were screened by vibration, and remove the needle-like and flake particles by means of a profiler. The samples of the recycled concrete aggregates, recycled clay bricks aggregates, and limestone aggregates with particle sizes of 19–26.5 mm and the samples of the recycled concrete aggregates and limestone aggregates with particle sizes of 9.5–13.2 mm were prepared. The samples were prepared as presented in Figure2.Figure 2
Aggregate samples. (a) Recycled concrete aggregates. (b) Recycled clay brick aggregates. (c) Limestone aggregates.
(a)
(b)
(c)


## 2.3. Test Scheme and Process

The recycled mixed aggregates with a particle diameter range of 19 mm to 26.5 mm and 9.5 mm to 13.2 mm in the dry state are selected, and the samples are prepared according to the mass ratio of recycled concrete to recycled clay bricks of 2 : 8, 4 : 6, 5 : 5, 6 : 4, and 8 : 2. At the same time, one batch of recycled concrete (RC), recycled clay bricks (RB), and natural limestone (NL) aggregates of the same particle diameter range are prepared as comparative samples, and three sets of parallel confined crushing tests are carried out for each sample. The test conditions are grouped as shown in Table1.Table 1
Test conditions.
Sample number
Particle diameter range of samples before crushing (mm)
Mass ratio of samples
Vertical pressure (kN)
RB
19∼26.5
100% RB
400
RC2RB8
19∼26.5
20% RC + 80% RB
400
RC4RB6
19∼26.5
40% RC + 60% RB
400
RC5RB5
19∼26.5
50% RC + 50% RB
400
RC6RB4
19∼26.5
60% RC + 40% RB
400
RC8RB2
19∼26.5
80% RC + 20% RB
400
RC
19∼26.5
100% RC
400
NL26.5
19∼26.5
100% natural limestone
400
NL13.2
9.5∼13.2
100% natural limestone
400
RC13.2
9.5∼13.2
100% RC
200Before testing the samples, put them in a drying box for 3-4 h at 100°C for drying so that the aggregates are in a completely dehydrated and dry state. Then, weigh the mass of the sample barrel, and put the samples into the test barrel three times. After each sample was put in, the surface of the sample was smoothed and tamped evenly 25 times with the hemispherical end of the metal rod. Finally, the total mass of the test barrel and the sample is weighed again to obtain the initial massM0 of the samples. Place the prepared samples on the press, then smoothly place the indenter on the surface of the samples, start the press, apply the load evenly, reach a total load of 400 kN in about 10 min, and then unload after stabilizing the pressure for 5 s. The laterally confined crushing test is carried out in accordance with Chinese Standard T0316 [41].The crushed samples are sieved and weighed in order of the aperture of 19 mm, 16 mm, 13.2 mm, 9.5 mm, and 4.75 mm, and fine aggregates (particle diameter <4.75 mm) are sieved and weighed. The mixed aggregates of crushed coarse aggregates (particle diameter ≥4.75 mm) are manually sorted, and recycled concrete and recycled clay brick aggregates in each particle diameter range are weighed separately. In addition, the comparative tests of crushing pressure of 200 kN and 400 kN are carried out for the sample with a particle diameter range of 9.5 mm to 13.2 mm.


## 3. Test Result

### 3.1. Sieve Analysis Results

According to Table1, the crushing test is carried out for each working condition, and then sieving, manual sorting, and weighing are conducted to obtain the crushing and sieving quality of the mixed aggregates at various levels, as shown in Tables 2 and 3.Table 2
Statistical table of crushing and screening of recycled mixed aggregates.
Particle diameter (mm)
Group of aggregates
RB
RC2RB8
RC4RB6
RC5RB5
RC6RB4
RC8RB2
RC
NL26.5
Total mass (g)
RB + RC
1563.28
1645.49
1768.09
1867.24
1938.16
2062.14
2156.85
2551.85
∗19 mm–26.5 mm mass (g)
RC
329.1
707.24
933.62
1162.9
1649.71
2156.85
2551.85
RB
1563.28
1316.39
1060.85
933.62
775.26
412.43
19 mm–26.5 mm mass (g)
RC
94.2
117.72
167.33
205.61
256.08
171.86
179.6
RB
75.07
32.11
21.77
17.12
0
3.49
16 mm–19 mm mass (g)
RC
86.44
126.27
133.93
148.83
158.2
207.82
297.5
RB
87.61
72.75
36.47
41.25
21.91
8.64
13.2 mm–16 mm mass (g)
RC
21
73.38
116.82
131.57
164.13
206.31
269
RB
92.27
66.01
41.59
39.3
25.66
10.74
9.5 mm–13.2 mm mass (g)
RC
30
114.32
129.95
157.63
218.53
282.83
410
RB
151.5
105.56
84.64
68.64
51.06
28.56
4.75 mm–9.5 mm mass (g)
RC
59.2
122.7
165.36
225.16
312.09
472.8
535
RB
275.76
226.04
182.4
141.09
137.36
56.99
<4.75 mm
RB + RC
881.07
852.18
846.83
846.43
833.37
844.68
815.24
860.75
Mass of coarse aggregates (g)
RB
682.21
502.47
366.88
307.41
235.99
108.42
RC
290.84
554.38
713.39
868.8
1109.03
1341.62
1691.1
Mass of fine aggregates (g)
RB + RC
881.07
852.18
846.83
846.43
833.37
844.68
815.24
860.75
Ratio of recycled clay brick (%)
RB
100
63.3
39.8
30.1
21.4
8.9
Loss rate of recycled clay brick in crushed coarse aggregates (%)
RB
56.36
61.83
65.42
67.07
69.56
73.71
Ratio of recycled concrete (%)
RC
36.7
60.2
69.9
78.6
91.1
100
100
Loss rate of recycled concrete in crushed coarse aggregates (%)
RC
11.6
21.6
23.6
25.3
32.8
37.8
33.7
Coarse aggregate content (%)
RB + RC
43.6
48.2
52.1
54.7
57
59
62.2
66.3
Fine aggregate content (%)
RB + RC
56.4
51.8
47.9
45.3
43
41
37.8
33.7
Fractal dimension (D)
2.656
2.614
2.561
2.529
2.502
2.475
2.416
2.338
Correlation coefficient (R2)
0.995
0.995
0.994
0.995
0.996
0.998
0.985
0.983
Note:∗the mass of mixed aggregate before crushing; ratio of recycled clay bricks (%) = the mass of recycled clay bricks in crushed coarse aggregates/the mass of crushed coarse aggregates; ratio of recycled concrete (%) = the mass of recycled concrete in crushed coarse aggregates/the mass of crushed coarse aggregates; loss rate of recycled clay brick coarse aggregates (%) = (the mass of recycled clay bricks before pressurizing−the mass of recycled clay bricks in crushed coarse aggregates)/(the mass of recycled clay bricks before pressurizing) (%); loss rate of recycled concrete coarse aggregates (%) = (the mass of recycled concrete before pressurizing−the mass of recycled concrete in coarse aggregates)/(the mass of recycled concrete before pressurizing) (%); coarse aggregate content (%) = the mass of crushed coarse aggregates/the total mass of aggregates before pressurizing; fine aggregates content (%) = the mass of crushed fine aggregates/the total mass of aggregates before pressurizing.Table 3
Statistical table of crushing and screening of NL13.2 and RC13.2.
Particle diameter (mm)
NL13.2
RC13.2
Total mass (g)
2490.58
2516.7
9.5 mm–13.2 mm mass (g)
602
1000
4.75 mm–9.5 mm mass (g)
850
816.7
2.36 mm–4.75 mm mass (g)
456
366.7
<2.36 mm mass (g)
582.58
333.3
Mass of coarse aggregates (g)
1452
1816.7
Mass of fine aggregates (g)
1038.58
700
Coarse aggregate content (%)
58.3
72.2
Fine aggregate content (%)
41.7
27.8
Fractal dimension (D)
2.153
1.781
Correlation coefficient (R2)
0.999
0.995


### 3.2. Determination of Fractal Dimension of Mixed Coarse Aggregates

Fractals are used to describe the nonsmooth, irregular, and discontinuous phenomena in nature. Since Mandelbrot [31] put forward the main idea of fractal geometry, fractals are widely used in various fields of natural science and social science. The quantitative indicator to describe the degree of irregularity and nonsmoothness in nature is fractal dimension. According to fractal theory, although the physical process of aggregate crushing is very complicated with some randomness and irregularity, its scale is invariable. The kinetic mechanism is the same whether large aggregates are crushed into small aggregates or small aggregates are crushed into smaller aggregates. The distribution of the particle size after crushing is fractal, and the characteristics of the ore materials can be measured by the fractal dimension (D). In 1986, Turcotte [32] made a statistical analysis of the fragmentation distribution of many kinds of geological materials under different crushing modes and concluded that the fragmentation distribution conforms to fractal characteristics. Based on the fractal model of particles in three-dimensional space, Tyler and Wheatcraft [42] deduced that the fractal dimension equation expressed by mass with particle mass replaces volume. Xu and Lin [43] derived the tensile strength formula of the materials according to the fractal dimension of particle crushing and estimated the crushing probability under the given pressure. Zhao et al. [44] quantitatively described the nonlinear dynamic process of disintegration and crushing of red sandstone by using fractal dimension. Wang et al. [45] carried out crushing tests on white marble single particle materials, established the relationship between particle size and deformation during particle crushing, and obtained fractal dimension of particle crushing. Previous studies on the fractal dimension of different particle materials show that the fractal dimension of material crushing is between 2 and 3, and its physical meaning is an entity that is larger than the two-dimensional plane and smaller than the three-dimensional space. Among the construction wastes, the recycled mixed aggregates are used as the coarse aggregates of the pavement base/subbase to replace the natural aggregates. A fractal model is established for the quality and particle diameter of the recycled mixed aggregates after crushing to obtain the fractal dimension (D), which reflects and describes the crushing characteristics of mixed waste aggregates and reveals their inherent law.In accordance with the fractal theory, assume the maximum particle diameter of the aggregate samples asdmax, the sieve diameter of the i−th lay is di, the cumulative aggregate mass passing the sieve diameter di as Mdi, the cumulative aggregate mass retained above the sieve diameter di as Mdi, and the total mass of aggregate samples before pressurizing as M0. The volume Vdi of mixed aggregate corresponding to the particle diameter di larger is(1)Vdi=Cv1−diλi3−D,where D is the fractal dimension and Cv and λi are the constants related to aggregate size and shape.The aggregate density is a fixed value, so the cumulative aggregate mass retained above a certain particle diameterdi is(2)mdi=ρVdi=ρCv1−diλi3−D.The total mass of aggregates before pressurizing may be expressed as(3)M0=ρCv=1−0λi3−D=ρCv.Set the maximum particle diameter of the aggregate sample asdmax, then λi=dmax, and substitute it to formula (2) to obtain(4)MdiM0=M0−mdiM0=didmax3−D.Taking the logarithm on both sides of the formula, the fractal equation is as follows:(5)lgMdiM0=3−Dlgdidmax.According to the test results in Tables2 and 3, calculate the cumulative mass content of the crushed samples under each sieve at all levels and sieve diameter ratio (corresponding to the ratio of the sieve diameter to the maximum sieve pore), and establish a Cartesian coordinate system with lgdi/dmax as the abscissa and lgMdi/M0 as ordinate, indicating the crushing and sieving results of each sample, as shown in Figures 3 and 4. Formula (5) shows that the cumulative mass content and sieve diameter ratio of the crushed samples under each sieve meet the double logarithmic linear relationship, and the linear regression analysis is carried out to obtain the fitting straight line slope k. The corresponding fractal dimension can then be obtained D = 3−k, with the calculation results shown in Tables 2 and 3.Figure 3
Relationship betweenlgdi/dmax and lgMdi/M0 for recycled mixed aggregates with a particle diameter range of 19 mm to 26.5 mm with various mixing ratios (the values are expressed as absolute values).
(a)
(b)Figure 4
Relationship betweenlgdi/dmax and lgMdi/M0 for a particle diameter range of 9.5 mm to 13.2 mm with the crushing pressure of 200 kN and 400 kN (the values are expressed as absolute values).


## 3.1. Sieve Analysis Results

According to Table1, the crushing test is carried out for each working condition, and then sieving, manual sorting, and weighing are conducted to obtain the crushing and sieving quality of the mixed aggregates at various levels, as shown in Tables 2 and 3.Table 2
Statistical table of crushing and screening of recycled mixed aggregates.
Particle diameter (mm)
Group of aggregates
RB
RC2RB8
RC4RB6
RC5RB5
RC6RB4
RC8RB2
RC
NL26.5
Total mass (g)
RB + RC
1563.28
1645.49
1768.09
1867.24
1938.16
2062.14
2156.85
2551.85
∗19 mm–26.5 mm mass (g)
RC
329.1
707.24
933.62
1162.9
1649.71
2156.85
2551.85
RB
1563.28
1316.39
1060.85
933.62
775.26
412.43
19 mm–26.5 mm mass (g)
RC
94.2
117.72
167.33
205.61
256.08
171.86
179.6
RB
75.07
32.11
21.77
17.12
0
3.49
16 mm–19 mm mass (g)
RC
86.44
126.27
133.93
148.83
158.2
207.82
297.5
RB
87.61
72.75
36.47
41.25
21.91
8.64
13.2 mm–16 mm mass (g)
RC
21
73.38
116.82
131.57
164.13
206.31
269
RB
92.27
66.01
41.59
39.3
25.66
10.74
9.5 mm–13.2 mm mass (g)
RC
30
114.32
129.95
157.63
218.53
282.83
410
RB
151.5
105.56
84.64
68.64
51.06
28.56
4.75 mm–9.5 mm mass (g)
RC
59.2
122.7
165.36
225.16
312.09
472.8
535
RB
275.76
226.04
182.4
141.09
137.36
56.99
<4.75 mm
RB + RC
881.07
852.18
846.83
846.43
833.37
844.68
815.24
860.75
Mass of coarse aggregates (g)
RB
682.21
502.47
366.88
307.41
235.99
108.42
RC
290.84
554.38
713.39
868.8
1109.03
1341.62
1691.1
Mass of fine aggregates (g)
RB + RC
881.07
852.18
846.83
846.43
833.37
844.68
815.24
860.75
Ratio of recycled clay brick (%)
RB
100
63.3
39.8
30.1
21.4
8.9
Loss rate of recycled clay brick in crushed coarse aggregates (%)
RB
56.36
61.83
65.42
67.07
69.56
73.71
Ratio of recycled concrete (%)
RC
36.7
60.2
69.9
78.6
91.1
100
100
Loss rate of recycled concrete in crushed coarse aggregates (%)
RC
11.6
21.6
23.6
25.3
32.8
37.8
33.7
Coarse aggregate content (%)
RB + RC
43.6
48.2
52.1
54.7
57
59
62.2
66.3
Fine aggregate content (%)
RB + RC
56.4
51.8
47.9
45.3
43
41
37.8
33.7
Fractal dimension (D)
2.656
2.614
2.561
2.529
2.502
2.475
2.416
2.338
Correlation coefficient (R2)
0.995
0.995
0.994
0.995
0.996
0.998
0.985
0.983
Note:∗the mass of mixed aggregate before crushing; ratio of recycled clay bricks (%) = the mass of recycled clay bricks in crushed coarse aggregates/the mass of crushed coarse aggregates; ratio of recycled concrete (%) = the mass of recycled concrete in crushed coarse aggregates/the mass of crushed coarse aggregates; loss rate of recycled clay brick coarse aggregates (%) = (the mass of recycled clay bricks before pressurizing−the mass of recycled clay bricks in crushed coarse aggregates)/(the mass of recycled clay bricks before pressurizing) (%); loss rate of recycled concrete coarse aggregates (%) = (the mass of recycled concrete before pressurizing−the mass of recycled concrete in coarse aggregates)/(the mass of recycled concrete before pressurizing) (%); coarse aggregate content (%) = the mass of crushed coarse aggregates/the total mass of aggregates before pressurizing; fine aggregates content (%) = the mass of crushed fine aggregates/the total mass of aggregates before pressurizing.Table 3
Statistical table of crushing and screening of NL13.2 and RC13.2.
Particle diameter (mm)
NL13.2
RC13.2
Total mass (g)
2490.58
2516.7
9.5 mm–13.2 mm mass (g)
602
1000
4.75 mm–9.5 mm mass (g)
850
816.7
2.36 mm–4.75 mm mass (g)
456
366.7
<2.36 mm mass (g)
582.58
333.3
Mass of coarse aggregates (g)
1452
1816.7
Mass of fine aggregates (g)
1038.58
700
Coarse aggregate content (%)
58.3
72.2
Fine aggregate content (%)
41.7
27.8
Fractal dimension (D)
2.153
1.781
Correlation coefficient (R2)
0.999
0.995


## 3.2. Determination of Fractal Dimension of Mixed Coarse Aggregates

Fractals are used to describe the nonsmooth, irregular, and discontinuous phenomena in nature. Since Mandelbrot [31] put forward the main idea of fractal geometry, fractals are widely used in various fields of natural science and social science. The quantitative indicator to describe the degree of irregularity and nonsmoothness in nature is fractal dimension. According to fractal theory, although the physical process of aggregate crushing is very complicated with some randomness and irregularity, its scale is invariable. The kinetic mechanism is the same whether large aggregates are crushed into small aggregates or small aggregates are crushed into smaller aggregates. The distribution of the particle size after crushing is fractal, and the characteristics of the ore materials can be measured by the fractal dimension (D). In 1986, Turcotte [32] made a statistical analysis of the fragmentation distribution of many kinds of geological materials under different crushing modes and concluded that the fragmentation distribution conforms to fractal characteristics. Based on the fractal model of particles in three-dimensional space, Tyler and Wheatcraft [42] deduced that the fractal dimension equation expressed by mass with particle mass replaces volume. Xu and Lin [43] derived the tensile strength formula of the materials according to the fractal dimension of particle crushing and estimated the crushing probability under the given pressure. Zhao et al. [44] quantitatively described the nonlinear dynamic process of disintegration and crushing of red sandstone by using fractal dimension. Wang et al. [45] carried out crushing tests on white marble single particle materials, established the relationship between particle size and deformation during particle crushing, and obtained fractal dimension of particle crushing. Previous studies on the fractal dimension of different particle materials show that the fractal dimension of material crushing is between 2 and 3, and its physical meaning is an entity that is larger than the two-dimensional plane and smaller than the three-dimensional space. Among the construction wastes, the recycled mixed aggregates are used as the coarse aggregates of the pavement base/subbase to replace the natural aggregates. A fractal model is established for the quality and particle diameter of the recycled mixed aggregates after crushing to obtain the fractal dimension (D), which reflects and describes the crushing characteristics of mixed waste aggregates and reveals their inherent law.In accordance with the fractal theory, assume the maximum particle diameter of the aggregate samples asdmax, the sieve diameter of the i−th lay is di, the cumulative aggregate mass passing the sieve diameter di as Mdi, the cumulative aggregate mass retained above the sieve diameter di as Mdi, and the total mass of aggregate samples before pressurizing as M0. The volume Vdi of mixed aggregate corresponding to the particle diameter di larger is(1)Vdi=Cv1−diλi3−D,where D is the fractal dimension and Cv and λi are the constants related to aggregate size and shape.The aggregate density is a fixed value, so the cumulative aggregate mass retained above a certain particle diameterdi is(2)mdi=ρVdi=ρCv1−diλi3−D.The total mass of aggregates before pressurizing may be expressed as(3)M0=ρCv=1−0λi3−D=ρCv.Set the maximum particle diameter of the aggregate sample asdmax, then λi=dmax, and substitute it to formula (2) to obtain(4)MdiM0=M0−mdiM0=didmax3−D.Taking the logarithm on both sides of the formula, the fractal equation is as follows:(5)lgMdiM0=3−Dlgdidmax.According to the test results in Tables2 and 3, calculate the cumulative mass content of the crushed samples under each sieve at all levels and sieve diameter ratio (corresponding to the ratio of the sieve diameter to the maximum sieve pore), and establish a Cartesian coordinate system with lgdi/dmax as the abscissa and lgMdi/M0 as ordinate, indicating the crushing and sieving results of each sample, as shown in Figures 3 and 4. Formula (5) shows that the cumulative mass content and sieve diameter ratio of the crushed samples under each sieve meet the double logarithmic linear relationship, and the linear regression analysis is carried out to obtain the fitting straight line slope k. The corresponding fractal dimension can then be obtained D = 3−k, with the calculation results shown in Tables 2 and 3.Figure 3
Relationship betweenlgdi/dmax and lgMdi/M0 for recycled mixed aggregates with a particle diameter range of 19 mm to 26.5 mm with various mixing ratios (the values are expressed as absolute values).
(a)
(b)Figure 4
Relationship betweenlgdi/dmax and lgMdi/M0 for a particle diameter range of 9.5 mm to 13.2 mm with the crushing pressure of 200 kN and 400 kN (the values are expressed as absolute values).


## 4. Discussion

### 4.1. Fractal Dimension of Recycled Coarse Aggregates

Figure3 shows that during the crushing process of the recycled mixed aggregates, the cumulative mass content and particle diameter ratio of recycled mixed aggregates under sieve conform to a double logarithmic linear relationship, the straight line slope k decreases with the increase of recycled clay brick content in the recycled mixed aggregates, and the fractal dimension, D, increases with the increase of recycled clay brick content in recycled mixed aggregates. The strength of the recycled concrete materials is obviously higher than that of the recycled clay brick. With the increase of the recycled concrete content in the recycled mixed aggregates, the whole strength of the mixed aggregates increases, and the aggregate content of each particle diameter range under sieve is relatively reduced after crushing, which is essentially reflected with the decrease of the D value. Accordingly, the D value reflects the strength characteristics of the aggregates.It is further seen from Table2 that the fractal dimension of limestone (NL26.5) is the smallest, that is, 2.338. Recycled concrete (RC) is relatively large, 2.416, and both the NCL26.5 and RC are smaller than the fractal dimension of recycled clay brick aggregates (RB), D = 2.656. It can be seen that the material strength has a significant effect on the fractal dimension, and the larger the aggregate strength is, the smaller the fractal dimension after crushing is. At the same time, the crushing test of limestone (NL13.2) with the initial particle diameter of 9.5 mm∼13.2 mm is conducted. The fractal dimension after crushing is 2.153 (Table 3 and Figure 4). Compared with NL26.5 of limestone samples with the initial particle diameter of 19 mm∼26.5 mm, it is found that the initial particle diameter before crushing has a certain influence on the fractal dimension, and the fractal dimension increases with the increase of the initial particle diameter. When the materials are the same, the bigger the initial particle diameter is, the smaller the void ratio after mixing is. The change of the initial particle diameter essentially changes the void ratio. In other words, the change of the fractal dimension reflects the change of the initial void ratio to some extent. This is the same as the simulation results of single-grain rock fragmentation in the previous literature [46]. In order to further explore the quantitative relationship between fractal dimension and crushing degree of aggregates, the crushing test of limestone (NL13.2) with initial particle diameter of 9.5 mm∼13.2 mm is carried out. The experimental results show that the fractal dimension is 1.781 under vertical pressure 200 kN (Table 3 and Figure 4). It is contrary to the physical meaning that the fractal dimension of coarse aggregates lies in the two-dimensional plane and three-dimensional space, as well as the results of previous studies [35, 43, 47]. It is considered that the aggregates are sufficiently crushed as a prerequisite for the coarse aggregate to satisfy the fractal characteristics, so when the aggregates are crushed, the loading pressure must reach the ultimate compressive strength of the materials to be expressed by fractal geometry. The fractal dimension can satisfy the relation of 2 < D < 3. According to formula (5), the following can be obtained:(6)MdiM0>didmax.The left-hand side of formula (6) is the ratio of the i−th under-sieve aggregates mass to total aggregate mass, which reflects the crushing degree of aggregates. Taking NL13.2 and RC13.2 as an example, the crushing value of fine aggregate content after vertical pressurizing shall meet the following requirement:(7)M4.75M0＞4.7513.2=36.0%.The fine aggregate content of sample RC13.2 is 27.8% (Table3), which is less than 36%, is not in accordance with the requirement of formula 7. Particle-size distribution of sample RC13.2 after crushing is unable to be expressed by fractal geometry. On the contrary, the fine aggregate content of sample NL13.2 is 41.7%, which is greater than 36%, and complies with the requirement of formula 7. Similarly, for samples with an initial grain diameter of 19 mm∼26.5 mm, the fine aggregate content after crushing must be greater than 17.9% according to formula 6. As shown in Table 2, the fine aggregate content of each sample ranges from 33.7% to 56.4%, which meets the requirement of not being less than 17.9%.


### 4.2. Interaction among Recycled Mixed Aggregates in the Crushing Process

According to the crushing test, the content of recycled concrete before crushing (ratio of recycled concrete mass to recycled mixed aggregate mass before crushing) increases from 20% to 80%, and the loss rate of recycled clay bricks in crushed coarse aggregates gradually increases from 61.83% (RC2RB8) to 73.71% (RC8RB2), which is greater than the loss rate (56.36%) of recycled clay bricks of 100% recycled clay brick sample RB. Therefore, as the content of recycled concrete increases before crushing, the ratio of recycled clay bricks in crushed coarse aggregates after crushing decreases from 63.3% (RC2RB8) to 8.9% (RC8RB2). In other words, as the recycled concrete content increases, the crushing resistance of the recycled clay bricks is reduced. The change law of crushing resistance of recycled concrete is just the opposite. As the content of recycled clay bricks before crushing (the ratio of recycled clay bricks mass to recycled mixed aggregate mass before crushing) increases from 20% to 80%, the loss rate of recycled concrete in crushed coarse aggregates after crushing is reduced from 32.8% (RC8RB2) to 11.6% (RC2RB8), and it is greater than the loss rate (37.8%) of recycled concrete of 100% recycled concrete sample RC before crushing. The increase of recycled clay brick content can result in an increase in recycled concrete ratio and an increase in crushing resistance of recycled concrete aggregates. The ratio of recycled concrete in crushed coarse aggregates after crushing increases from 36.7% (RC2RB8) to 91.1% (RC8RB2). In addition, the change rate of the loss rate shows that the content of recycled concrete before crushing increases from 20% to 80%, the loss rate of recycled concrete changes rapidly, increasing from 11.6% to 32.8, up by 21.2%, and the relative change in the loss rate of the bricks is slower, reducing from 73.71% to 61.83%, which is down by 11.88% (Figures5 and 6).Figure 5
Content of recycled concrete before crushing and loss rate of recycled clay brick/concrete in crushed coarse aggregates.Figure 6
Content of recycled concrete before crushing to ratio of RB/RC in crushed coarse aggregates.In the recycled mixed aggregates, compared with the recycled clay bricks, the crushing resistance of the recycled concrete is more sensitive to the amount of the added recycled clay bricks, and the crushing of the recycled concrete in the recycled mixed aggregates is obviously reduced which is caused by the mixing of the recycled clay brick. The recycled clay bricks are broken preferentially, the recycled concrete aggregates in the coarse aggregates are protected, and the content noticeably increases. Adding a certain amount of recycled brick aggregate to recycled concrete aggregate is equivalent to adding a weaker cushion gasket between relatively high-strength aggregate particles, which avoids the direct extrusion and being crushed among relatively high-strength aggregate particles. The particles with low strength are crushed under the action of the surrounding particles with high strength and then crushed when the compressive stress among the particles is higher than the ultimate compressive strength of the high-strength particles with the increase of the applied compressive stress. Therefore, the effect of “reinforcing the strong and discarding the weak” exists between recycled clay bricks and recycled concrete in mixed aggregates, which is basically the same as the results obtained by Ai et al. [48]. After the mixed aggregates are crushed, the residual coarse aggregates are mainly recycled concrete, with a small part being recycled clay bricks, most of which is crushed and filled in the voids between the coarse aggregates as fine aggregates.


## 4.1. Fractal Dimension of Recycled Coarse Aggregates

Figure3 shows that during the crushing process of the recycled mixed aggregates, the cumulative mass content and particle diameter ratio of recycled mixed aggregates under sieve conform to a double logarithmic linear relationship, the straight line slope k decreases with the increase of recycled clay brick content in the recycled mixed aggregates, and the fractal dimension, D, increases with the increase of recycled clay brick content in recycled mixed aggregates. The strength of the recycled concrete materials is obviously higher than that of the recycled clay brick. With the increase of the recycled concrete content in the recycled mixed aggregates, the whole strength of the mixed aggregates increases, and the aggregate content of each particle diameter range under sieve is relatively reduced after crushing, which is essentially reflected with the decrease of the D value. Accordingly, the D value reflects the strength characteristics of the aggregates.It is further seen from Table2 that the fractal dimension of limestone (NL26.5) is the smallest, that is, 2.338. Recycled concrete (RC) is relatively large, 2.416, and both the NCL26.5 and RC are smaller than the fractal dimension of recycled clay brick aggregates (RB), D = 2.656. It can be seen that the material strength has a significant effect on the fractal dimension, and the larger the aggregate strength is, the smaller the fractal dimension after crushing is. At the same time, the crushing test of limestone (NL13.2) with the initial particle diameter of 9.5 mm∼13.2 mm is conducted. The fractal dimension after crushing is 2.153 (Table 3 and Figure 4). Compared with NL26.5 of limestone samples with the initial particle diameter of 19 mm∼26.5 mm, it is found that the initial particle diameter before crushing has a certain influence on the fractal dimension, and the fractal dimension increases with the increase of the initial particle diameter. When the materials are the same, the bigger the initial particle diameter is, the smaller the void ratio after mixing is. The change of the initial particle diameter essentially changes the void ratio. In other words, the change of the fractal dimension reflects the change of the initial void ratio to some extent. This is the same as the simulation results of single-grain rock fragmentation in the previous literature [46]. In order to further explore the quantitative relationship between fractal dimension and crushing degree of aggregates, the crushing test of limestone (NL13.2) with initial particle diameter of 9.5 mm∼13.2 mm is carried out. The experimental results show that the fractal dimension is 1.781 under vertical pressure 200 kN (Table 3 and Figure 4). It is contrary to the physical meaning that the fractal dimension of coarse aggregates lies in the two-dimensional plane and three-dimensional space, as well as the results of previous studies [35, 43, 47]. It is considered that the aggregates are sufficiently crushed as a prerequisite for the coarse aggregate to satisfy the fractal characteristics, so when the aggregates are crushed, the loading pressure must reach the ultimate compressive strength of the materials to be expressed by fractal geometry. The fractal dimension can satisfy the relation of 2 < D < 3. According to formula (5), the following can be obtained:(6)MdiM0>didmax.The left-hand side of formula (6) is the ratio of the i−th under-sieve aggregates mass to total aggregate mass, which reflects the crushing degree of aggregates. Taking NL13.2 and RC13.2 as an example, the crushing value of fine aggregate content after vertical pressurizing shall meet the following requirement:(7)M4.75M0＞4.7513.2=36.0%.The fine aggregate content of sample RC13.2 is 27.8% (Table3), which is less than 36%, is not in accordance with the requirement of formula 7. Particle-size distribution of sample RC13.2 after crushing is unable to be expressed by fractal geometry. On the contrary, the fine aggregate content of sample NL13.2 is 41.7%, which is greater than 36%, and complies with the requirement of formula 7. Similarly, for samples with an initial grain diameter of 19 mm∼26.5 mm, the fine aggregate content after crushing must be greater than 17.9% according to formula 6. As shown in Table 2, the fine aggregate content of each sample ranges from 33.7% to 56.4%, which meets the requirement of not being less than 17.9%.


## 4.2. Interaction among Recycled Mixed Aggregates in the Crushing Process

According to the crushing test, the content of recycled concrete before crushing (ratio of recycled concrete mass to recycled mixed aggregate mass before crushing) increases from 20% to 80%, and the loss rate of recycled clay bricks in crushed coarse aggregates gradually increases from 61.83% (RC2RB8) to 73.71% (RC8RB2), which is greater than the loss rate (56.36%) of recycled clay bricks of 100% recycled clay brick sample RB. Therefore, as the content of recycled concrete increases before crushing, the ratio of recycled clay bricks in crushed coarse aggregates after crushing decreases from 63.3% (RC2RB8) to 8.9% (RC8RB2). In other words, as the recycled concrete content increases, the crushing resistance of the recycled clay bricks is reduced. The change law of crushing resistance of recycled concrete is just the opposite. As the content of recycled clay bricks before crushing (the ratio of recycled clay bricks mass to recycled mixed aggregate mass before crushing) increases from 20% to 80%, the loss rate of recycled concrete in crushed coarse aggregates after crushing is reduced from 32.8% (RC8RB2) to 11.6% (RC2RB8), and it is greater than the loss rate (37.8%) of recycled concrete of 100% recycled concrete sample RC before crushing. The increase of recycled clay brick content can result in an increase in recycled concrete ratio and an increase in crushing resistance of recycled concrete aggregates. The ratio of recycled concrete in crushed coarse aggregates after crushing increases from 36.7% (RC2RB8) to 91.1% (RC8RB2). In addition, the change rate of the loss rate shows that the content of recycled concrete before crushing increases from 20% to 80%, the loss rate of recycled concrete changes rapidly, increasing from 11.6% to 32.8, up by 21.2%, and the relative change in the loss rate of the bricks is slower, reducing from 73.71% to 61.83%, which is down by 11.88% (Figures5 and 6).Figure 5
Content of recycled concrete before crushing and loss rate of recycled clay brick/concrete in crushed coarse aggregates.Figure 6
Content of recycled concrete before crushing to ratio of RB/RC in crushed coarse aggregates.In the recycled mixed aggregates, compared with the recycled clay bricks, the crushing resistance of the recycled concrete is more sensitive to the amount of the added recycled clay bricks, and the crushing of the recycled concrete in the recycled mixed aggregates is obviously reduced which is caused by the mixing of the recycled clay brick. The recycled clay bricks are broken preferentially, the recycled concrete aggregates in the coarse aggregates are protected, and the content noticeably increases. Adding a certain amount of recycled brick aggregate to recycled concrete aggregate is equivalent to adding a weaker cushion gasket between relatively high-strength aggregate particles, which avoids the direct extrusion and being crushed among relatively high-strength aggregate particles. The particles with low strength are crushed under the action of the surrounding particles with high strength and then crushed when the compressive stress among the particles is higher than the ultimate compressive strength of the high-strength particles with the increase of the applied compressive stress. Therefore, the effect of “reinforcing the strong and discarding the weak” exists between recycled clay bricks and recycled concrete in mixed aggregates, which is basically the same as the results obtained by Ai et al. [48]. After the mixed aggregates are crushed, the residual coarse aggregates are mainly recycled concrete, with a small part being recycled clay bricks, most of which is crushed and filled in the voids between the coarse aggregates as fine aggregates.


## 5. Determination of Crushing Fractal Dimension Gradation of Recycled Mixed Aggregates

It can be seen from the literature that the recycled clay bricks in the construction waste are at least equivalent to the amount of recycled concrete [2]. In order to make better use of the recycled clay bricks in the construction waste, it is hoped that there will be more recycled clay brick aggregates in the recycled aggregates. In other words, when conforming to the conditions of engineering strength and deformation, the use of more recycled clay bricks is the key to solving the problem. As such, determining the maximum content of recycled clay bricks in aggregates is a topic that needs further study.The following has been shown in the available literature [49]: the changing law of the shear strength of coarse aggregate soil with the content of coarse aggregates (d ≥ 4.75 mm) is when the content of coarse aggregates is less than 30%, the strength increase is not obvious, and the fine aggregates control the shear strength of the granular materials; when the content of coarse aggregates increases from 30% to 70%, the shear strength continues to increase and peaks; and when the content of coarse aggregates exceeds 70%, the strength index does not increase substantially, but with a decreasing trend.It can be seen from Table2 that the content of recycled concrete before crushing increases from 20% to 100%, and the content of coarse aggregates gradually increases from 48.2% (RC2RB8) to 62.2% (RC8RB2) after crushing, both of which meet the variation of fine aggregate content of 30%∼70%. The strength of recycled concrete aggregates is obviously higher than that of recycled clay bricks. The higher content of recycled concrete in coarse aggregates after crushing is advantageous to the crushing resistance and shear resistance.The Land Transport Authority contains at least 60% recycled concrete aggregates in recycled aggregates for roads [50]. For coarse aggregates, the ratio of recycled concrete of sample RC2RB8 after crushing is 36.7%, which does not meet the requirements. For Sample RC4RB6∼Sample RC8RB2, the ratio of recycled concrete is between 60.2%∼91.1%, which meets the requirements of not being less than 60% recycled concrete aggregates (Table 2).According to the Los Angeles Grind Test Study [18], it was concluded that the recycled clay brick aggregate content in the aggregates used for the road base/subbase should not be higher than 25%. Therefore, the recycled brick aggregate content in coarse aggregates after crushing should not be higher than 25%, which is taken as the limit value, and the particle gradation obtained from the corresponding crushing test is taken as the basis for determining the fractal geometric dimension D. As can be seen from Table 2, the ratio of clay bricks in samples RC6RB4 and RC8RB2 is 21.4% and 8.9%, respectively, satisfying this condition, and Table 2 shows that the fractal dimensions are 2.502 and 2.475, respectively.Li and Deng [51] studied the relationship between fractal characteristics and gradation of aggregates, pointed out that fractal of aggregates is the essential characteristic of gradation, validated in comparison with method m and method k, proved the correctness of determining gradation of aggregates by fractal dimension, and proposed gradation formula determined by the fractal dimension D of the aggregates:(8)Pdi%=di3−D−dmin3−Ddmax3−D−dmin3−D,where di represents the diameter of coarse aggregate (mm), dmax represents the maximum particle diameter (mm), dmin represents the minimum particle diameter (mm), and Pdi represents the throughput rate of screening (%).According to formula (8), there is a one-to-one correspondence between the fractal dimension D value and gradation of coarse aggregates. Given the fractal dimension D value, the aggregate gradation equation can be obtained, and the corresponding gradation curve can be drawn, as presented in Figure 7.Figure 7
Gradation curve (particle diameter from 19 mm to 26.5 mm).In order to verify the rationality of determining the aggregate gradation curve for pavement base or subbase by fractal calculation, the particle content in the corresponding range is sequentially calculated and the gradation curve is drawn according to formula (8), with the fractal dimension D value determined in Table 2. In addition, the recommended gradation curve with a particle diameter of 19 mm∼26.5 mm shall be marked with the specification Technical Guidelines for Construction of Highway Road bases [52] (herein referred to as the “Specifications”). It can be observed from Figure 7 that the gradation curves of the crushed samples RC, RC2RB8, and RC4RB6 obviously fall outside the boundary of the recommended gradation of the Specifications, and the gradation curve of the crushed sample RC5RB5 is near the boundary of the gradation of the Specifications. The gradation curves determined by samples RC6RB4, RC8RB2, and RC fall completely within the gradation range of the Specifications, thus indicating that it is reasonable to mix no more than 25% recycled clay brick aggregates into the coarse aggregates, which has little influence on the engineering properties of coarse aggregates.The fractal dimensions of samples RC6RB4 and RC8RB2 are 2.502 and 2.475, respectively, withdmax=26.5 mm and dmin=0 mm; see Table 4 for the obtained gradation.Table 4
Gradation of recycled mixed aggregates.
Sample number
D value
Particle diameter (mm)
0.075
0.15
0.3
0.6
1.18
2.36
4.75
9.5
13.2
16
19
26.5
RC6RB4
2.502
5
7
10
15
21
29
42
59
70
77
84
100
RC8RB2
2.475
4
6
9
13
19
27
40
58
69
76
83
100As can be seen from Table4, when the D value is 2.502, the nonuniformity coefficient Cu = 31.7 and the curvature coefficient Cc = 1.95. When the D value is 2.475, the nonuniformity coefficient Cu = 29.9 and the curvature coefficient Cc = 2.15. According to the Code for Design on Subgrade of Railway [53], when the coefficient of nonuniformity Cc ≧ 5 and the curvature coefficient Cc = 1∼3, the gradation of mixed aggregates is good. It is found that the gradation determined by the above fractal dimension D is good.From the point of view of fully utilizing recycled clay brick aggregates, it is better to have a higher amount of recycled clay bricks under the premise of meeting the engineering strength and durability. When theD value is 2.502, the recycled clay brick aggregate content in the aggregates used for the road base/subbase could be 21.4%. In this paper, the relevant problems are expounded only from the point of view of determining the gradation of recycled mixed aggregate by the crushing test. The research on the influence of gradation on the strength and durability of recycled mixed aggregates needs to be carried out in the next stage.


## 6. Conclusions

The effect of “reinforcing the strong and discarding the weak” exists in the crushing process of recycled mixed aggregates. Increasing the content of recycled clay bricks is beneficial in improving the crushing resistance of recycled concrete, and increasing the content of recycled concrete will decrease the crushing resistance of recycled clay bricks.After crushing, the cumulative mass content under each sieve at all levels and the sieve diameter ratio conform to the geometric fractal characteristics. The fractal dimension is influenced by the material strength, the initial mixing ratio, and the initial void ratio, which is in the range of 2∼3. The fractal dimension of the mixed aggregates with the initial particle diameter of 19 mm∼26.5 mm is between 2.416∼2.656. Material strength has a significant effect on fractal dimension. The fractal dimension of limestone is the smallest, the recycled concrete aggregates is the second, and the recycled clay bricks is the largest. The fractal dimension of recycled mixed aggregates gradually increases with the increase in the content of recycled clay bricks.The method of determining the fractal dimension of recycled coarse aggregates by the crushing test of recycled mixed aggregates and then determining the gradation of coarse aggregates for pavement base or subbase with the fractal dimension is proposed. It is suggested that it is reasonable to mix no more than 25% recycled clay brick aggregates into the recycled coarse aggregates, which has little influence on the engineering properties of coarse aggregate engineering of pavement base or subbase, meeting the established engineering requirements. At this time, the fractal dimension is 2.502, and the gradation of recycled coarse aggregate can be calculated by formula (8), which is the corresponding gradation of the sample RC6RB4 crushed in Table 4.



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*Source: 7963261-2019-10-07.xml*