# Damage Characteristics of Uniaxial Compressed Concrete Embedded Different Aging Rubber by 3D Mesoscale Model

Authors: Shuo Yu; Miaofeng Cao; Changbao Liu; Hao Jin
Journal: Advances in Civil Engineering
 (2022)

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## Abstract

Rapid development of the automobile industry has brought the disposal problem of waste rubber tires. Mixing waste rubber tires into concrete can not only solve environmental problems but also improve the mechanical properties of concrete. Rubber aging is one of the main factors to affect the mechanical properties of rubberized concrete. Therefore, an FEM model of rubberized concrete in mesoscale is established in this paper. The influence of rubber aging on the uniaxial compression damage of rubberized concrete is u;studied. The results show that (1) the elastic modulus and compressive strength of rubberized concrete are negatively correlated with the aging level and content of rubber and positively correlated with the particle size of rubber. (2) After uniaxial compression of concrete enters the softening section, the crack resistance of concrete is positively correlated with the aging level and content of rubber and negatively correlated with the particle size of rubber. (3) Compared with the elastic modulus, the compressive strength of rubberized concrete is more sensitive to the change of parameters of rubber, that is, the change range of the compressive strength of rubberized concrete is always greater than the change range of its elastic modulus, when the aging level, content, and particle size of rubber change.


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## Body

## 1. Introduction

With the rapid development of economy and technology, the development of the automobile industry is getting faster and faster, and the output of automobile is getting bigger and bigger. Rubber tires, as an indispensable part of automobiles, have huge output and scrap. A large number of waste rubber tires are produced and piled up every year in the world. It is estimated that about 1.5 billion tires are produced every year in the world. About 1 billion tires are scrapped every year, and more than 50% tires are directly discarded without any treatment [1–3]. The generation of a large number of waste rubber tires has brought great environmental problems. Rubber is a polymer material, which is not easy to degrade. Rubber accumulation may also lead to fire and endanger people’s property and life safety. The concept of rubberized concrete was put forward to improve the disposal of waste rubber tires. On the one hand, rubberized concrete can consume a lot of waste rubber tires, on the other hand, it can change the performance of concrete. Concrete is a composite material composed of aggregate and mortar, and rubberized concrete uses rubber particles to replace fine aggregate in concrete drawing, so as to achieve the functions of waste utilization and performance improvement.A large number of researchers have invested in the direction of rubberized concrete and studied the static performance, durability, and dynamic performance of rubberized concrete [4–8]. Such as Hamdi et al. [4] assessed the feasibility of utilizing shredded tire in concrete for structures and pavements through critical review of its rheological, static/dynamic mechanical, and durability properties. Qaidi et al. [5] highlight the impact in terms of aggregate substitution content, form, size, and waste treatment on the fresh and mechanical properties of crumb rubber concrete (CRC). Strukar et al. [6] discussed the potential use of rubber as aggregate in structural reinforced concrete element and point out rubber in structure not only subjected to earthquake actions but also exposed to fire and explosion. A large number of studies show that replacing part of aggregate with rubber particles will lead to the decline of mechanical properties of concrete [9–12]. Improve the interfacial adhesion between rubber particles and cement matrix can improve the macroscopic mechanical properties of concrete [13]. The performance of concrete varies with rubber particle size. The larger the rubber particle size, the greater the decrease of compressive strength and tensile strength of concrete [14]. Sabir et al. [15] show that the compressive strength and splitting tensile strength will decrease when the rubber is added. And splitting tensile strength is more sensitive to rubber content than compressive strength. Zhu et al. [16] studied the influence of rubber particle size and content on the freeze-thaw resistance of rubberized concrete. Zhu et al. [17] analyzed the influence of temperature on chloride ion corrosion resistance of rubberized concrete and carried out four-point compression test on corroded rubberized concrete beams. The results show that, when the ambient temperature is lower than 20°C, the rubber aggregate concrete has better resistance to chloride ion corrosion. The research of Tahir et al. [18] shows that the addition of rubber particles improves the freeze-thaw resistance and impact resistance of concrete, and the higher the particle size and content of rubber, the better the impact resistance of concrete. Gupta et al. [19] studied the durability of rubberized concrete in adverse environment with fibrous and granular rubber aggregate shapes. Rubberized concrete has good acid resistance and chloride ion diffusion resistance, but improper adhesion between rubber and concrete matrix leads to corrosion of steel bars due to oxygen inflow. According to the research results of Khalid [20], the incorporation of rubber particles reduces the mechanical strength of concrete, but improves the strain capacity, and rubberized concrete has good vibration damping property. A large number of researches have studied the influence of rubber particles on the mechanical properties and durability of rubberized concrete from the aspects of rubber content, particle size, and shape.Waste rubber tires are the main source of rubber aggregate, and the tires are aged to varying levels due to wear, temperature, and moisture. The aging of rubber will change its mechanical properties such as hardness, tensile strength, elongation at break, modulus stress, and so on. Wu et al. [21] showed that the hardness of silicone rubber increased with the aging of rubber. Aging leads to the degradation of rubber sealing performance. Jie et al. [22] studied the changes of mechanical properties of rubber during aging, and the results showed that the tensile strength of rubber first increased and then decreased with the increase of crosslinking density during aging. The research of Zhao et al. [23] shows that aging changes the constitutive parameters of rubber. Rubber is one of the three-phase components of rubberized concrete; the change of its constitutive parameters will definitely affect the mechanical properties of rubberized concrete.From the perspective of rubber aging, this study studies the influence of rubber aging on the failure of rubberized concrete under uniaxial compression. The meso-model of rubber aggregate concrete with different aging levels is established by using geometric intrinsic concrete meso-model [24]. Based on the study of aging level, the effects of aging rubber content and aging rubber particle size on uniaxial compression stress-strain curve of rubber aggregate concrete were studied.


## 2. 3D Mesoscale Model of Rubberized Concrete for Uniaxial Compressive Test

### 2.1. Geometry Sizes

Test block size of rubberized concrete for research is 50 mm × 50 mm × 50 mm [25], as shown in Figure 1. Rubberized concrete is a three-phase composite material composed of aggregate, mortar, and rubber at mesoscale.Figure 1
Test block of rubberized concrete.


### 2.2. Material Properties

The calculation model is composed of three materials: aggregate, rubber, and mortar. In the model, the aggregate adopts linear elastic constitutive model with elastic modulus of 80000 MPa and Poisson’s ratio of 0.16 [26]. The rubber adopts linear elastic constitutive model, with elastic modulus of 5 MPa and Poisson’s ratio of 0.49. During the bearing process of concrete, the destruction of mortar is the main reason for the decline of mechanical properties of concrete. Therefore, the mortar adopts the concrete damaged plasticity model [27–29], the mortar parameters used in the model as shown in Table 1. In Table 1, Ec is the Young’s modulus ν is the Poisson’s ratio, ψ is the dilatancy angle, κ is the eccentricity, fb0/fc0 is the compression strength ratio, Kc is the yield constant, and μ is the viscosity coefficient.Table 1
Mortar parameters used in the model [26].
Ec/GPaνψκfb0/fc0Kcμ260.2230°0.11.160.66670.0001After concrete is damaged, its stiffness decreases and its elastic modulus decreases. At this time, its compressive and tensile stress expressions are as follows:(1)σc=1−dcE0εc−εcpl,σt=1−dtE0εt−εtpl,εcpl=εcin−dc1−dcσcE0,εtpl=εtck−dt1−dtσtE0,where E0 is the initial elastic modulus, σc is the compressive stress, σt is the tensile stress, εcpl is the equivalent plastic compressive strain, εtpl is the equivalent plastic tensile strain, εcin is a compressive inelastic strain, and εtck is the tensile cracking strain.Abaqus passed the definitionσc−εcin, σt−εtck to describe the characteristic of strain softening after cracking of concrete, and define at the same time dc−εcin, dt−εtck to describe the stiffness degradation characteristics of concrete caused by damage. The calculation expressions of εcin、 εtck are as follows:(2)εcin=εc−ε0cel=εcpl+dc1−dcσcE0,εtck=εt−ε0tel=εtpl+dt1−dtσtE0,ε0cel=σcE0,ε0tel=σtE0,where ε0cel is the elastic recovery strain under compression and ε0tel is the elastic recovery strain under tension.


### 2.3. Load and Boundary Conditions

The compression test diagram is shown in Figure2, the upper part of the cube test block is loaded, and the bottom part is not restrained. Accordingly, the face 1234 is constrained in the y direction, the midpoints of edges 12 and 34 constrain the x direction, and the midpoints of edges 23 and 14 constrain the z direction. The face 5678 applies a load in the -Y direction, as shown in Figure 1.Figure 2
Schematic diagram of compression test.


### 2.4. Finite Element Model

Due to the irregular shape and complex boundary of aggregate and mortar, the tetrahedron element is used to divide the aggregate and mortar into grids, as shown in Figure3(a) and 3(c). Rubber adopts 8-node hexahedron unit, as shown in Figure 3(b).Figure 3
Finite element model of rubberized concrete. (a) Typical aggregate, (b) rubber, (c) motar.
(a)(b)(c)


## 2.1. Geometry Sizes

Test block size of rubberized concrete for research is 50 mm × 50 mm × 50 mm [25], as shown in Figure 1. Rubberized concrete is a three-phase composite material composed of aggregate, mortar, and rubber at mesoscale.Figure 1
Test block of rubberized concrete.


## 2.2. Material Properties

The calculation model is composed of three materials: aggregate, rubber, and mortar. In the model, the aggregate adopts linear elastic constitutive model with elastic modulus of 80000 MPa and Poisson’s ratio of 0.16 [26]. The rubber adopts linear elastic constitutive model, with elastic modulus of 5 MPa and Poisson’s ratio of 0.49. During the bearing process of concrete, the destruction of mortar is the main reason for the decline of mechanical properties of concrete. Therefore, the mortar adopts the concrete damaged plasticity model [27–29], the mortar parameters used in the model as shown in Table 1. In Table 1, Ec is the Young’s modulus ν is the Poisson’s ratio, ψ is the dilatancy angle, κ is the eccentricity, fb0/fc0 is the compression strength ratio, Kc is the yield constant, and μ is the viscosity coefficient.Table 1
Mortar parameters used in the model [26].
Ec/GPaνψκfb0/fc0Kcμ260.2230°0.11.160.66670.0001After concrete is damaged, its stiffness decreases and its elastic modulus decreases. At this time, its compressive and tensile stress expressions are as follows:(1)σc=1−dcE0εc−εcpl,σt=1−dtE0εt−εtpl,εcpl=εcin−dc1−dcσcE0,εtpl=εtck−dt1−dtσtE0,where E0 is the initial elastic modulus, σc is the compressive stress, σt is the tensile stress, εcpl is the equivalent plastic compressive strain, εtpl is the equivalent plastic tensile strain, εcin is a compressive inelastic strain, and εtck is the tensile cracking strain.Abaqus passed the definitionσc−εcin, σt−εtck to describe the characteristic of strain softening after cracking of concrete, and define at the same time dc−εcin, dt−εtck to describe the stiffness degradation characteristics of concrete caused by damage. The calculation expressions of εcin、 εtck are as follows:(2)εcin=εc−ε0cel=εcpl+dc1−dcσcE0,εtck=εt−ε0tel=εtpl+dt1−dtσtE0,ε0cel=σcE0,ε0tel=σtE0,where ε0cel is the elastic recovery strain under compression and ε0tel is the elastic recovery strain under tension.


## 2.3. Load and Boundary Conditions

The compression test diagram is shown in Figure2, the upper part of the cube test block is loaded, and the bottom part is not restrained. Accordingly, the face 1234 is constrained in the y direction, the midpoints of edges 12 and 34 constrain the x direction, and the midpoints of edges 23 and 14 constrain the z direction. The face 5678 applies a load in the -Y direction, as shown in Figure 1.Figure 2
Schematic diagram of compression test.


## 2.4. Finite Element Model

Due to the irregular shape and complex boundary of aggregate and mortar, the tetrahedron element is used to divide the aggregate and mortar into grids, as shown in Figure3(a) and 3(c). Rubber adopts 8-node hexahedron unit, as shown in Figure 3(b).Figure 3
Finite element model of rubberized concrete. (a) Typical aggregate, (b) rubber, (c) motar.
(a)(b)(c)


## 3. Effect of Aging Rubber

### 3.1. Different Aging Rates of Rubber

In order to verify the accuracy of the model, it is compared with the concrete compression test [30] with irregular rubber. The distribution location of aggregate and rubber in the test are as shown in Figure 4. Figure 5 shows the damage cloud diagram obtained from the test and numerical calculation. It can be seen that the crack trend is basically the same, the result shows that the model is reasonable and feasible to calculate damage of rubber concrete, and local difference is caused by the different shape and location of rubber.Figure 4
Aggregate and rubber distribution in the test [30].Figure 5
Comparison of test [30] and calculated result.Rubber aging will lead to the increase of hardness and elastic modulus. Therefore, this study simulates rubber aggregate aging by increasing the elastic modulus of rubber and defines the ratio of elastic modulus of rubber after aging to elastic modulus of rubber before aging as rubber elastic modulus aging ratio, assuming that Poisson’s ratio does not change during aging. Rubber aging is considered in five cases, as shown in Table2. In the model, the aggregate size is 5–16 mm, the rubber content is 5%, and the rubber size is 3.0 mm, so as to study the aging.Table 2
Different aging ratios of elastic modulus of rubber [31].
Case①②③④⑤Elastic modulus/MPa53550100150Aging ratio of elastic modulus17102030


### 3.2. Compressive Stress-Strain Relationship

Figures6(a)–6(c) are stress-strain curves, compressive strength, and elastic modulus of rubberized concrete under different aging ratios of elastic modulus. It can be seen from the figure that the aging level of rubber will affect the stress-strain curve, compressive strength, and elastic modulus of rubberized concrete.Figure 6
Compressive properties of rubberized concrete with different aging levels. (a) Stress-strain relation, (b) compressive strength, (c) elastic modulus.
(a)(b)(c)Table3 shows the uniaxial compressive elastic modulus and compressive strength of rubber aggregate concrete under different aging elastic modulus ratios. When the rubber aging elastic modulus ratio is 1, that is, when the rubber is not aging, the elastic modulus and compressive strength of rubber aggregate concrete are 20.29 GPa and 27.68 MPa, respectively. The elastic modulus and compressive strength of rubber aggregate concrete are 20.27 GPa and 27.49 MPa, respectively, compared with nonaging rubberized concrete, it is reduced by 0.09% and 0.69%, respectively; When the elastic modulus ratio of rubber aging is 10, the elastic modulus and compressive strength of rubber aggregate concrete are 20.26 GPa and 27.41 MPa, respectively, which are 0.16% and 0.98% lower than those of unaged rubberized concrete. The elastic modulus and compressive strength of rubber aggregate concrete are 20.21 GPa and 27.16 MPa, respectively, compared with nonaging rubberized concrete, and it is reduced by 0.39% and 1.88%, respectively; When the elastic modulus ratio of rubber aging is 30, the elastic modulus and compressive strength of rubber aggregate concrete are 20.16 GPa and 26.94 MPa, respectively, which are 0.64% and 2.67% lower than those of nonaging rubberized concrete.Table 3
Table of elastic modulus and compressive strength of concrete with different aging elastic modulus ratio.
Mechanical propertyAging ratio of elastic modulus17102030Elastic modulus/GPa20.2920.2720.2620.2120.16Decrease of elastic modulus—0.09%0.16%0.39%0.64%Compressive strength/MPa27.6827.4927.4127.1626.94Decrease in compressive strength—0.69%0.98%1.88%2.67%Rubber aging leads to the decrease of elastic modulus and compressive strength of rubber aggregate concrete. Different aging levels have different levels of decrease, which shows that the greater the elastic modulus of rubber, the lower the elastic modulus and compressive strength of rubber aggregate concrete, and the decrease of compressive strength is greater than that of elastic modulus.The peak strength of concrete with different aging elastic modulus ratios all appeared near strain 0.00183, and the strain continued to increase, and the rubber aggregate concrete began to fail, entering the softening stage, and the stress-strain curve began to decline. It can be seen from the figure that the stress-strain curves of rubber aggregate concrete with different aging levels have different decline rates in the softening section, and each stress-strain curve has a strain of 0. There is an intersection near 0024. The modulus of rubber aggregate concrete with aging elastic modulus ratio of 1, 7, 10, 20, and 30 in the descending section is 14.47 GPa, 13.31 GPa, 12.99 GPa, and 11.72 GPa, respectively, which is 0%, 8.02%, 10.23%, 18.12%, and 19.02 GPA higher than that of nonaging rubber, respectively The higher the modulus of concrete in softening section, the faster the performance degradation, whereas the lower the modulus, the slower the performance degradation. That is, the greater the aging level of rubber, the slower the performance degradation of rubber aggregate concrete in the descending section, the better the crack resistance.


### 3.3. Damage Characteristics

In order to explain the above phenomenon and analyze the influence of aging on the stress-strain curve of rubber aggregate concrete, from the microscopic point of view, slices were made in the concrete alongX and Y axes, and the slices were located at 20 mm and 40 mm in X and Y axes, respectively. A total of four rubber units are selected on the damaged strip at the cutting position of rubber aggregate concrete, concrete internal damage strip and rubber selected from the strip, select mortar units around the selected rubber, and analyze the curve of tensile damage factor of mortar units with strain, as shown in Figure 7.Figure 7
Tensile damage strip of concrete and selected rubber. (a) Front view, (b) back view, (c) left side view, (d) right side view.
(a)(b)(c)(d)It can be seen from Figure8 that with the increase of strain of rubber aggregate concrete in various aging levels, the tensile damage factor of mortar units around rubber also increases, and the growth rate of damage factor increases first and then decreases, and the maximum growth rate is about 0.00183, which corresponds to the peak strain of macro stress-strain curve of rubber aggregate concrete. The aging level of rubber increases, the tensile damage factor of mortar unit around rubber is produced in advance, and the greater the aging level, the earlier the tensile damage factor appears.Figure 8
Variation curve of tensile damage factor with strain of selected mortar unit. (a) #1 mortar unit, (b) #2 mortar unit, (c) #3 mortar unit, (d) #4 mortar unit.
(a)(b)(c)(d)Among that four selected mortar units, Figures8(a) and 8(b) and Figures 8(c) and 8(d), respectively, represent mortar with less damage and mortar with greater damage, but in the process of concrete compression, the mechanical properties of concrete are mainly controlled by mortar units with larger damage factors. The damage numerical change of mortar element with large damage factor is analyzed. In the stage of small strain, the greater the aging level of rubber, the greater the tensile damage factor of surrounding mortar; in the stage of greater strain, the greater the aging level of rubber, the smaller the tensile damage factor of surrounding mortar. The larger the damage factor, the more serious the concrete damage is, that is, the aging of rubber leads to the more serious damage of concrete in the early stage, and the lower the damage level in the later stage.The aging of rubber affects the variation of damage factor of mortar unit around rubber with macro strain of concrete, the differences of macroscopic stress-strain curves of rubber aggregate concrete under different aging levels are explained in Figure6, that is, the greater the aging level of rubber, the greater the elastic modulus of rubber, and the lower the elastic modulus and compressive strength of rubber aggregate concrete, but the rubber aggregate concrete with higher aging level in softening stage has smaller degradation rate and stronger crack resistance. Combined with the performance of the ascending and descending sections of concrete, rubber aggregate with a certain level of aging can reduce the elastic modulus and compressive strength of concrete in the early stage of uniaxial compression, but it can improve the crack resistance in the later stage of uniaxial compression to a certain extent. In the follow-up study, rubber with an aging modulus ratio of 7 is used, and its elastic modulus and compressive strength are reduced by 0.09%, 0.69%, and the later performance is improved and the crack resistance is improved by 8.02%.


## 3.1. Different Aging Rates of Rubber

In order to verify the accuracy of the model, it is compared with the concrete compression test [30] with irregular rubber. The distribution location of aggregate and rubber in the test are as shown in Figure 4. Figure 5 shows the damage cloud diagram obtained from the test and numerical calculation. It can be seen that the crack trend is basically the same, the result shows that the model is reasonable and feasible to calculate damage of rubber concrete, and local difference is caused by the different shape and location of rubber.Figure 4
Aggregate and rubber distribution in the test [30].Figure 5
Comparison of test [30] and calculated result.Rubber aging will lead to the increase of hardness and elastic modulus. Therefore, this study simulates rubber aggregate aging by increasing the elastic modulus of rubber and defines the ratio of elastic modulus of rubber after aging to elastic modulus of rubber before aging as rubber elastic modulus aging ratio, assuming that Poisson’s ratio does not change during aging. Rubber aging is considered in five cases, as shown in Table2. In the model, the aggregate size is 5–16 mm, the rubber content is 5%, and the rubber size is 3.0 mm, so as to study the aging.Table 2
Different aging ratios of elastic modulus of rubber [31].
Case①②③④⑤Elastic modulus/MPa53550100150Aging ratio of elastic modulus17102030


## 3.2. Compressive Stress-Strain Relationship

Figures6(a)–6(c) are stress-strain curves, compressive strength, and elastic modulus of rubberized concrete under different aging ratios of elastic modulus. It can be seen from the figure that the aging level of rubber will affect the stress-strain curve, compressive strength, and elastic modulus of rubberized concrete.Figure 6
Compressive properties of rubberized concrete with different aging levels. (a) Stress-strain relation, (b) compressive strength, (c) elastic modulus.
(a)(b)(c)Table3 shows the uniaxial compressive elastic modulus and compressive strength of rubber aggregate concrete under different aging elastic modulus ratios. When the rubber aging elastic modulus ratio is 1, that is, when the rubber is not aging, the elastic modulus and compressive strength of rubber aggregate concrete are 20.29 GPa and 27.68 MPa, respectively. The elastic modulus and compressive strength of rubber aggregate concrete are 20.27 GPa and 27.49 MPa, respectively, compared with nonaging rubberized concrete, it is reduced by 0.09% and 0.69%, respectively; When the elastic modulus ratio of rubber aging is 10, the elastic modulus and compressive strength of rubber aggregate concrete are 20.26 GPa and 27.41 MPa, respectively, which are 0.16% and 0.98% lower than those of unaged rubberized concrete. The elastic modulus and compressive strength of rubber aggregate concrete are 20.21 GPa and 27.16 MPa, respectively, compared with nonaging rubberized concrete, and it is reduced by 0.39% and 1.88%, respectively; When the elastic modulus ratio of rubber aging is 30, the elastic modulus and compressive strength of rubber aggregate concrete are 20.16 GPa and 26.94 MPa, respectively, which are 0.64% and 2.67% lower than those of nonaging rubberized concrete.Table 3
Table of elastic modulus and compressive strength of concrete with different aging elastic modulus ratio.
Mechanical propertyAging ratio of elastic modulus17102030Elastic modulus/GPa20.2920.2720.2620.2120.16Decrease of elastic modulus—0.09%0.16%0.39%0.64%Compressive strength/MPa27.6827.4927.4127.1626.94Decrease in compressive strength—0.69%0.98%1.88%2.67%Rubber aging leads to the decrease of elastic modulus and compressive strength of rubber aggregate concrete. Different aging levels have different levels of decrease, which shows that the greater the elastic modulus of rubber, the lower the elastic modulus and compressive strength of rubber aggregate concrete, and the decrease of compressive strength is greater than that of elastic modulus.The peak strength of concrete with different aging elastic modulus ratios all appeared near strain 0.00183, and the strain continued to increase, and the rubber aggregate concrete began to fail, entering the softening stage, and the stress-strain curve began to decline. It can be seen from the figure that the stress-strain curves of rubber aggregate concrete with different aging levels have different decline rates in the softening section, and each stress-strain curve has a strain of 0. There is an intersection near 0024. The modulus of rubber aggregate concrete with aging elastic modulus ratio of 1, 7, 10, 20, and 30 in the descending section is 14.47 GPa, 13.31 GPa, 12.99 GPa, and 11.72 GPa, respectively, which is 0%, 8.02%, 10.23%, 18.12%, and 19.02 GPA higher than that of nonaging rubber, respectively The higher the modulus of concrete in softening section, the faster the performance degradation, whereas the lower the modulus, the slower the performance degradation. That is, the greater the aging level of rubber, the slower the performance degradation of rubber aggregate concrete in the descending section, the better the crack resistance.


## 3.3. Damage Characteristics

In order to explain the above phenomenon and analyze the influence of aging on the stress-strain curve of rubber aggregate concrete, from the microscopic point of view, slices were made in the concrete alongX and Y axes, and the slices were located at 20 mm and 40 mm in X and Y axes, respectively. A total of four rubber units are selected on the damaged strip at the cutting position of rubber aggregate concrete, concrete internal damage strip and rubber selected from the strip, select mortar units around the selected rubber, and analyze the curve of tensile damage factor of mortar units with strain, as shown in Figure 7.Figure 7
Tensile damage strip of concrete and selected rubber. (a) Front view, (b) back view, (c) left side view, (d) right side view.
(a)(b)(c)(d)It can be seen from Figure8 that with the increase of strain of rubber aggregate concrete in various aging levels, the tensile damage factor of mortar units around rubber also increases, and the growth rate of damage factor increases first and then decreases, and the maximum growth rate is about 0.00183, which corresponds to the peak strain of macro stress-strain curve of rubber aggregate concrete. The aging level of rubber increases, the tensile damage factor of mortar unit around rubber is produced in advance, and the greater the aging level, the earlier the tensile damage factor appears.Figure 8
Variation curve of tensile damage factor with strain of selected mortar unit. (a) #1 mortar unit, (b) #2 mortar unit, (c) #3 mortar unit, (d) #4 mortar unit.
(a)(b)(c)(d)Among that four selected mortar units, Figures8(a) and 8(b) and Figures 8(c) and 8(d), respectively, represent mortar with less damage and mortar with greater damage, but in the process of concrete compression, the mechanical properties of concrete are mainly controlled by mortar units with larger damage factors. The damage numerical change of mortar element with large damage factor is analyzed. In the stage of small strain, the greater the aging level of rubber, the greater the tensile damage factor of surrounding mortar; in the stage of greater strain, the greater the aging level of rubber, the smaller the tensile damage factor of surrounding mortar. The larger the damage factor, the more serious the concrete damage is, that is, the aging of rubber leads to the more serious damage of concrete in the early stage, and the lower the damage level in the later stage.The aging of rubber affects the variation of damage factor of mortar unit around rubber with macro strain of concrete, the differences of macroscopic stress-strain curves of rubber aggregate concrete under different aging levels are explained in Figure6, that is, the greater the aging level of rubber, the greater the elastic modulus of rubber, and the lower the elastic modulus and compressive strength of rubber aggregate concrete, but the rubber aggregate concrete with higher aging level in softening stage has smaller degradation rate and stronger crack resistance. Combined with the performance of the ascending and descending sections of concrete, rubber aggregate with a certain level of aging can reduce the elastic modulus and compressive strength of concrete in the early stage of uniaxial compression, but it can improve the crack resistance in the later stage of uniaxial compression to a certain extent. In the follow-up study, rubber with an aging modulus ratio of 7 is used, and its elastic modulus and compressive strength are reduced by 0.09%, 0.69%, and the later performance is improved and the crack resistance is improved by 8.02%.


## 4. Effect of Content of Aging Rubber

### 4.1. Different Contents

Based on the study of rubber aging, the influence of rubber aggregate content on the compressive mechanical properties of rubber aggregate concrete was studied, and the rubber aggregate concrete models with different rubber aggregate content under the same aging level, the same rubber particle size were established. The content of rubber aggregate is 3%, 5%, and 8%, the aging elastic modulus ratio of rubber is 7, and the particle size of rubber aggregate is 3.0 mm.


### 4.2. Compressed Stress-Strain Relationship

According to the analysis of the aging level of rubber, rubber with aging elastic modulus ratio of 7 was selected for content research. The uniaxial compressive properties of concrete with different rubber aggregate contents are shown in Figures9(a)–9(c). It can be seen from Figure 9 that the addition of rubber aggregate reduces the elastic modulus and compressive strength of concrete to varying levels. The greater the content of rubber aggregate, the greater the decrease of elastic modulus and compressive strength of concrete, and the uniaxial compressive peak strain appears near 0.00183.Figure 9
Compressive properties of rubberized concrete with different contents. (a) Stress-strain relation, (b) compressive strength, (c) elastic modulus.
(a)(b)(c)Table4 is the elastic modulus and compressive strength of concrete with different rubber aggregate content under uniaxial compression are 20.74 GPa and 28.25 MPa, respectively, when the rubber aggregate content is 3%. The elastic modulus and compressive strength of concrete with 5% rubber aggregate content are 20.27 GPa and 27.49 MPa, respectively, which are 2.27% and 2.69% lower than those of concrete with 3% rubber aggregate content. The elastic modulus and compressive strength of concrete with 8% rubber aggregate content are 19.70 GPa and 26.36 MPa, respectively, which are 5.01% and 6.69% lower than those without rubber.Table 4
Elastic modulus and compressive strength of concrete with different contents of rubber.
Mechanical propertyRubber aggregate content3%5%8%Elastic modulus/GPa20.7420.2719.70Decrease of elastic modulus—2.27%5.01%Compressive strength/MPa28.2527.4926.36Decrease in compressive strength—2.69%6.69%On the basis of rubber aging elastic modulus ratio of 7 and rubber particle size of 3.0 mm, the increase of rubber aggregate content will lead to the decrease of elastic modulus and compressive strength of concrete, and with the increase of rubber content, the decrease of compressive strength of rubber aggregate concrete is always greater than that of elastic modulus. That is, compressive strength is more sensitive to rubber content.


### 4.3. Damage Characteristics

In concrete, the damage level of concrete can be judged by the number of damaged mortar units. The larger the unit damage factor and the more damaged mortar units, the worse the mechanical state of concrete will be. Figure10 is that the number of mortar units with different rubber aggregate content and pull-down damage factor greater than 0.7 changes with concrete strain.Figure 10
Number of mortar units with damage factor greater than 0.7 under different rubber content. (a) Overall stage, (b) rising stage, (c) falling stage.
(a)(b)(c)It can be seen from Figure10(a) that with the increase of concrete strain, the number of damaged mortar units increases continuously, after the peak strain is 0.00183, the number of damaged mortar units increases sharply. It can be seen from Figure 9(a) that when the strain is near 0.00183, the stress-strain curve of concrete begins to enter the descending section, that is, after the stress-strain curve of concrete enters the descending section, the number of damaged mortar units in concrete suddenly increases, the concrete begins to destroy, and the mechanical properties decrease greatly. Accordingly, Figure 10(a) can be divided into two strain stages in Figures 10(b) and 10(c), which, respectively, represent the rising and falling stage of concrete stress-strain.It can be seen from Figure10(b) that the rubber content affects the number of damaged mortar units in the ascending section of concrete. The greater the rubber content, the more damaged mortar units will be. After the strain exceeds 0.00183, the concrete will enter the descending section and the curves will start to cross. It can be seen from Figure 10(c) that with the continuous increase of concrete strain, the number curves of damage units with 3%, 5%, and 8% of rubber content begin to cross, which shows that the more rubber content, the less damage mortar units. In rubberized concrete, in the rising section of uniaxial compression stress-strain curve of concrete, the greater the content of rubber aggregate, the more the number of damaged mortar units. However, in the descending section, the rubber content is larger and the number of damaged mortar units is smaller.The change of the number of damaged mortar units-strain curve with rubber content can well explain the change of stress-strain curve of concrete with rubber content. The analysis shows that the increase of rubber content will reduce the elastic modulus and compressive strength of concrete, and the increase of rubber content is manifested in the whole strain process of concrete. Before the peak strain of concrete, the greater the rubber content, the lower the elastic modulus and compressive strength, and the worse its performance. After the concrete enters the softening section, the greater the rubber content, the better its performance.In the process of concrete strain, the damage nephogram of concrete under each aging rubber aggregate content is as shown in Figure11. It can be seen from the figure that when the concrete reaches the final state under uniaxial compression, that is, when the concrete strain is 0.003, a large number of damages are produced on the surface of rubberized concrete under various contents, and obvious damage strips are formed, and the content has little influence on the path of damage strips. However, with the increase of rubber content, the single-point damage position of concrete surface increases, this is caused by the increase of rubber content. Mortar around rubber and aggregate is easy to be damaged. The increase of rubber content will inevitably lead to the increase of single-point damage of concrete.Figure 11
Tensile damage nephogram of concrete with different contents of rubber. (a) Rubber contents is 3%, (b) rubber contents is 5%, (c) rubber contents is 8%.
(a)(b)(c)


## 4.1. Different Contents

Based on the study of rubber aging, the influence of rubber aggregate content on the compressive mechanical properties of rubber aggregate concrete was studied, and the rubber aggregate concrete models with different rubber aggregate content under the same aging level, the same rubber particle size were established. The content of rubber aggregate is 3%, 5%, and 8%, the aging elastic modulus ratio of rubber is 7, and the particle size of rubber aggregate is 3.0 mm.


## 4.2. Compressed Stress-Strain Relationship

According to the analysis of the aging level of rubber, rubber with aging elastic modulus ratio of 7 was selected for content research. The uniaxial compressive properties of concrete with different rubber aggregate contents are shown in Figures9(a)–9(c). It can be seen from Figure 9 that the addition of rubber aggregate reduces the elastic modulus and compressive strength of concrete to varying levels. The greater the content of rubber aggregate, the greater the decrease of elastic modulus and compressive strength of concrete, and the uniaxial compressive peak strain appears near 0.00183.Figure 9
Compressive properties of rubberized concrete with different contents. (a) Stress-strain relation, (b) compressive strength, (c) elastic modulus.
(a)(b)(c)Table4 is the elastic modulus and compressive strength of concrete with different rubber aggregate content under uniaxial compression are 20.74 GPa and 28.25 MPa, respectively, when the rubber aggregate content is 3%. The elastic modulus and compressive strength of concrete with 5% rubber aggregate content are 20.27 GPa and 27.49 MPa, respectively, which are 2.27% and 2.69% lower than those of concrete with 3% rubber aggregate content. The elastic modulus and compressive strength of concrete with 8% rubber aggregate content are 19.70 GPa and 26.36 MPa, respectively, which are 5.01% and 6.69% lower than those without rubber.Table 4
Elastic modulus and compressive strength of concrete with different contents of rubber.
Mechanical propertyRubber aggregate content3%5%8%Elastic modulus/GPa20.7420.2719.70Decrease of elastic modulus—2.27%5.01%Compressive strength/MPa28.2527.4926.36Decrease in compressive strength—2.69%6.69%On the basis of rubber aging elastic modulus ratio of 7 and rubber particle size of 3.0 mm, the increase of rubber aggregate content will lead to the decrease of elastic modulus and compressive strength of concrete, and with the increase of rubber content, the decrease of compressive strength of rubber aggregate concrete is always greater than that of elastic modulus. That is, compressive strength is more sensitive to rubber content.


## 4.3. Damage Characteristics

In concrete, the damage level of concrete can be judged by the number of damaged mortar units. The larger the unit damage factor and the more damaged mortar units, the worse the mechanical state of concrete will be. Figure10 is that the number of mortar units with different rubber aggregate content and pull-down damage factor greater than 0.7 changes with concrete strain.Figure 10
Number of mortar units with damage factor greater than 0.7 under different rubber content. (a) Overall stage, (b) rising stage, (c) falling stage.
(a)(b)(c)It can be seen from Figure10(a) that with the increase of concrete strain, the number of damaged mortar units increases continuously, after the peak strain is 0.00183, the number of damaged mortar units increases sharply. It can be seen from Figure 9(a) that when the strain is near 0.00183, the stress-strain curve of concrete begins to enter the descending section, that is, after the stress-strain curve of concrete enters the descending section, the number of damaged mortar units in concrete suddenly increases, the concrete begins to destroy, and the mechanical properties decrease greatly. Accordingly, Figure 10(a) can be divided into two strain stages in Figures 10(b) and 10(c), which, respectively, represent the rising and falling stage of concrete stress-strain.It can be seen from Figure10(b) that the rubber content affects the number of damaged mortar units in the ascending section of concrete. The greater the rubber content, the more damaged mortar units will be. After the strain exceeds 0.00183, the concrete will enter the descending section and the curves will start to cross. It can be seen from Figure 10(c) that with the continuous increase of concrete strain, the number curves of damage units with 3%, 5%, and 8% of rubber content begin to cross, which shows that the more rubber content, the less damage mortar units. In rubberized concrete, in the rising section of uniaxial compression stress-strain curve of concrete, the greater the content of rubber aggregate, the more the number of damaged mortar units. However, in the descending section, the rubber content is larger and the number of damaged mortar units is smaller.The change of the number of damaged mortar units-strain curve with rubber content can well explain the change of stress-strain curve of concrete with rubber content. The analysis shows that the increase of rubber content will reduce the elastic modulus and compressive strength of concrete, and the increase of rubber content is manifested in the whole strain process of concrete. Before the peak strain of concrete, the greater the rubber content, the lower the elastic modulus and compressive strength, and the worse its performance. After the concrete enters the softening section, the greater the rubber content, the better its performance.In the process of concrete strain, the damage nephogram of concrete under each aging rubber aggregate content is as shown in Figure11. It can be seen from the figure that when the concrete reaches the final state under uniaxial compression, that is, when the concrete strain is 0.003, a large number of damages are produced on the surface of rubberized concrete under various contents, and obvious damage strips are formed, and the content has little influence on the path of damage strips. However, with the increase of rubber content, the single-point damage position of concrete surface increases, this is caused by the increase of rubber content. Mortar around rubber and aggregate is easy to be damaged. The increase of rubber content will inevitably lead to the increase of single-point damage of concrete.Figure 11
Tensile damage nephogram of concrete with different contents of rubber. (a) Rubber contents is 3%, (b) rubber contents is 5%, (c) rubber contents is 8%.
(a)(b)(c)


## 5. Effect of Size of Aging Rubber Particle

### 5.1. Different Sizes

In addition to the influence of rubber aggregate content on the mechanical properties of rubber aggregate concrete, the influence of rubber aggregate particle size has also attracted researchers’ attention. In this study, rubber aggregate is represented by cubic blocks, and the particle size of rubber aggregate is controlled by the side length of cubic blocks. In order to study the influence of particle size of aged rubber aggregate on compressive mechanical properties of concrete, in this paper, a three-dimensional meso-model of concrete with the same content and aging level and different particle sizes of rubber aggregate is established. Under the same rubber aggregate content, the larger the rubber particle size, the less the number of rubber in concrete. In this study, the rubber content is 5%, and the aging elastic modulus ratio of rubber aggregate is 7, that is, the elastic modulus is 35 MPa and Poisson’s ratio is 0.49. In the model with 5% rubber content, the total number of rubber aggregates with particle size of 2.5 mm, 3 mm, and 3.5 mm in concrete is 374, 189, and 83, respectively.


### 5.2. Compressed Stress-Strain Relationship

The effect of rubber particle size on the stress-strain curve of concrete under uniaxial compression was studied under the aging level of rubber aging elastic modulus ratio of 7; Figure12 is the stress-strain curve of rubber aggregate concrete with rubber aggregate content of 5% and particle size of 2.5 mm, 3.0 mm, and 3.5 mm, respectively.Figure 12
Compressive properties of rubberized concrete with different particle sizes. (a) Stress-strain relation, (b) compressive strength, (c) elastic modulus.
(a)(b)(c)It can be seen from the figure that under the same conditions, the larger the particle size of rubber aggregate, the greater the elastic modulus and compressive strength of rubber aggregate concrete. However, the stress-strain curves of rubberized concrete with different rubber particle sizes intersect in the descending section. It can be seen from Table5 that the elastic modulus and compressive strength of concrete with rubber particle size of 2.5 mm are 20.08 GPa and 27.12 MPa, respectively, while those with rubber particle size of 3.0 mm are 20.29 GPa and 27.49 MPa, respectively, which are 0.95% and 1.36% higher than those with rubber particle size of 2.5 mm, respectively. When the rubber particle size is 3.5 mm, the elastic modulus and compressive strength of concrete are 20.68 GPa and 28.24 MPa, respectively, which are 2.99% and 4.13% higher than those of concrete with particle size of 2.5 mm. That is, the particle size of rubber aggregate will affect the stress-strain curve of rubber aggregate concrete under uniaxial compression. The larger the particle size of rubber, the higher the elastic modulus and compressive strength of rubber aggregate concrete. The variation range of compressive strength is greater than that of elastic modulus, that is, the compressive strength of concrete is more sensitive to rubber particle size.Table 5
Elastic modulus and compressive strength of concrete with different particle sizes of rubber.
Mechanical propertyParticle size of rubber aggregate2.5 mm3.0 mm3.5 mmElastic modulus/GPa20.0820.2720.68Elastic modulus increase—0.95%2.99%Compressive strength/MPa27.1227.4928.24Compressive strength increase—1.36%4.13%It can be seen from Table5 that when the strain exceeds 0.00183, the stress-strain curve of concrete begins to decline, and the concrete enters the performance degradation stage. The uniaxial compression stress-strain curves of concrete with different rubber aggregate particle sizes cross, that is, the different rubber aggregate particle sizes will have an impact on the mechanical properties of concrete softening section. The modulus of the three curves in the falling section is calculated. When the strain is near 0.0025, the particle size is 2. The moduli of 5 mm, 3.0 mm, and 3.5 mm are 11.95 GPa, 13.87 GPa, and 14.22 GPa, respectively. The larger the modulus of uniaxial compressive stress-strain curve of concrete in the descending section, the faster the loss of bearing capacity and crack resistance in the descending section, that is, the smaller the particle size of rubber aggregate, the slower the loss of compressive and crack resistance of concrete in the softening section.


### 5.3. Damage Characteristics

In concrete, the damage level of concrete can be judged by the number of damaged mortar units. The larger the unit damage factor and the more damaged mortar units, the worse the mechanical state of concrete will be. Counting the number of mortar units with damage factor greater than 0.7. Under the same aging level and content, the number of mortar units with tensile damage factor greater than 0.7 in concrete with different particle sizes varies with concrete strain, as shown in Figure13.Figure 13
Number of units with tensile damage factor greater than 0.7. (a) Overall stage, (b) rising stage, (c) falling stage.
(a)(b)(c)It can be seen from Figure13(a) that with the constant increase of concrete strain, the number of tensile damage units in concrete increases continuously, and the number of damage units increases slowly before the concrete strain is 0.00183, and increases sharply after exceeding 0.00183. By comparing the stress-strain curve of concrete in Figure 12(a), it can be seen that 0.00183 is the peak strain of concrete under uniaxial compression. When the strain exceeds this value, the concrete enters the softening section, at which time the concrete begins to damage and its performance begins to decline, that is, the rapid increase in the number of damage units leads to the destruction and decline of concrete performance. Figure 13(a) is divided into two strain processes, as shown in Figures 13(b) and 13(c). Figures 13(b) and 13(c), respectively, represent the changes in the number of damage units of concrete before and after softening. It can be seen from Figures 13(b) and 13(c) that the larger the diameter of rubber aggregate before softening of concrete, the smaller the number of damage units of mortar. After softening, the larger the particle size of the rubber aggregate, the fewer the number of damaged units in the mortar.The damage level of concrete can be judged by the number of damage units. Under the same concrete strain, the more damage mortar units, the worse the performance of concrete. On the contrary, the better the concrete performance, that is, before concrete softening, the larger the particle size of rubber aggregate, the better the mechanical properties of rubber aggregate concrete; after softening, the smaller the particle size of rubber aggregate is, the better the mechanical properties of corresponding rubber aggregate concrete. The change of microscopic damage in concrete leads to the change of macroscopic stress-strain curve of concrete under uniaxial compression.In the process of concrete strain, the damage nephogram of concrete under different aging rubber particle sizes is as follows. It can be seen from Figure14 that when the concrete reaches the final state under uniaxial compression, that is, when the concrete strain is 0.003, a large number of damages are produced on the surface of rubberized concrete under various grain sizes, and obvious damage strips are formed, and the grain size has little influence on the development path of damage strips. Rubber with different particle sizes is randomly distributed in concrete. But in the end, the paths of damage strips formed by concrete are basically the same, which indicates that aggregate mainly controls the generation of large cracks in concrete, and the size of rubber particle size only affects the mortar damage near the area.Figure 14
Tensile damage nephogram of concrete with different particle size of rubber. (a) Rubber side length is 2.5 mm, (b) rubber side length is 3 mm, (c) rubber side length is 3.5 mm.
(a)(b)(c)


## 5.1. Different Sizes

In addition to the influence of rubber aggregate content on the mechanical properties of rubber aggregate concrete, the influence of rubber aggregate particle size has also attracted researchers’ attention. In this study, rubber aggregate is represented by cubic blocks, and the particle size of rubber aggregate is controlled by the side length of cubic blocks. In order to study the influence of particle size of aged rubber aggregate on compressive mechanical properties of concrete, in this paper, a three-dimensional meso-model of concrete with the same content and aging level and different particle sizes of rubber aggregate is established. Under the same rubber aggregate content, the larger the rubber particle size, the less the number of rubber in concrete. In this study, the rubber content is 5%, and the aging elastic modulus ratio of rubber aggregate is 7, that is, the elastic modulus is 35 MPa and Poisson’s ratio is 0.49. In the model with 5% rubber content, the total number of rubber aggregates with particle size of 2.5 mm, 3 mm, and 3.5 mm in concrete is 374, 189, and 83, respectively.


## 5.2. Compressed Stress-Strain Relationship

The effect of rubber particle size on the stress-strain curve of concrete under uniaxial compression was studied under the aging level of rubber aging elastic modulus ratio of 7; Figure12 is the stress-strain curve of rubber aggregate concrete with rubber aggregate content of 5% and particle size of 2.5 mm, 3.0 mm, and 3.5 mm, respectively.Figure 12
Compressive properties of rubberized concrete with different particle sizes. (a) Stress-strain relation, (b) compressive strength, (c) elastic modulus.
(a)(b)(c)It can be seen from the figure that under the same conditions, the larger the particle size of rubber aggregate, the greater the elastic modulus and compressive strength of rubber aggregate concrete. However, the stress-strain curves of rubberized concrete with different rubber particle sizes intersect in the descending section. It can be seen from Table5 that the elastic modulus and compressive strength of concrete with rubber particle size of 2.5 mm are 20.08 GPa and 27.12 MPa, respectively, while those with rubber particle size of 3.0 mm are 20.29 GPa and 27.49 MPa, respectively, which are 0.95% and 1.36% higher than those with rubber particle size of 2.5 mm, respectively. When the rubber particle size is 3.5 mm, the elastic modulus and compressive strength of concrete are 20.68 GPa and 28.24 MPa, respectively, which are 2.99% and 4.13% higher than those of concrete with particle size of 2.5 mm. That is, the particle size of rubber aggregate will affect the stress-strain curve of rubber aggregate concrete under uniaxial compression. The larger the particle size of rubber, the higher the elastic modulus and compressive strength of rubber aggregate concrete. The variation range of compressive strength is greater than that of elastic modulus, that is, the compressive strength of concrete is more sensitive to rubber particle size.Table 5
Elastic modulus and compressive strength of concrete with different particle sizes of rubber.
Mechanical propertyParticle size of rubber aggregate2.5 mm3.0 mm3.5 mmElastic modulus/GPa20.0820.2720.68Elastic modulus increase—0.95%2.99%Compressive strength/MPa27.1227.4928.24Compressive strength increase—1.36%4.13%It can be seen from Table5 that when the strain exceeds 0.00183, the stress-strain curve of concrete begins to decline, and the concrete enters the performance degradation stage. The uniaxial compression stress-strain curves of concrete with different rubber aggregate particle sizes cross, that is, the different rubber aggregate particle sizes will have an impact on the mechanical properties of concrete softening section. The modulus of the three curves in the falling section is calculated. When the strain is near 0.0025, the particle size is 2. The moduli of 5 mm, 3.0 mm, and 3.5 mm are 11.95 GPa, 13.87 GPa, and 14.22 GPa, respectively. The larger the modulus of uniaxial compressive stress-strain curve of concrete in the descending section, the faster the loss of bearing capacity and crack resistance in the descending section, that is, the smaller the particle size of rubber aggregate, the slower the loss of compressive and crack resistance of concrete in the softening section.


## 5.3. Damage Characteristics

In concrete, the damage level of concrete can be judged by the number of damaged mortar units. The larger the unit damage factor and the more damaged mortar units, the worse the mechanical state of concrete will be. Counting the number of mortar units with damage factor greater than 0.7. Under the same aging level and content, the number of mortar units with tensile damage factor greater than 0.7 in concrete with different particle sizes varies with concrete strain, as shown in Figure13.Figure 13
Number of units with tensile damage factor greater than 0.7. (a) Overall stage, (b) rising stage, (c) falling stage.
(a)(b)(c)It can be seen from Figure13(a) that with the constant increase of concrete strain, the number of tensile damage units in concrete increases continuously, and the number of damage units increases slowly before the concrete strain is 0.00183, and increases sharply after exceeding 0.00183. By comparing the stress-strain curve of concrete in Figure 12(a), it can be seen that 0.00183 is the peak strain of concrete under uniaxial compression. When the strain exceeds this value, the concrete enters the softening section, at which time the concrete begins to damage and its performance begins to decline, that is, the rapid increase in the number of damage units leads to the destruction and decline of concrete performance. Figure 13(a) is divided into two strain processes, as shown in Figures 13(b) and 13(c). Figures 13(b) and 13(c), respectively, represent the changes in the number of damage units of concrete before and after softening. It can be seen from Figures 13(b) and 13(c) that the larger the diameter of rubber aggregate before softening of concrete, the smaller the number of damage units of mortar. After softening, the larger the particle size of the rubber aggregate, the fewer the number of damaged units in the mortar.The damage level of concrete can be judged by the number of damage units. Under the same concrete strain, the more damage mortar units, the worse the performance of concrete. On the contrary, the better the concrete performance, that is, before concrete softening, the larger the particle size of rubber aggregate, the better the mechanical properties of rubber aggregate concrete; after softening, the smaller the particle size of rubber aggregate is, the better the mechanical properties of corresponding rubber aggregate concrete. The change of microscopic damage in concrete leads to the change of macroscopic stress-strain curve of concrete under uniaxial compression.In the process of concrete strain, the damage nephogram of concrete under different aging rubber particle sizes is as follows. It can be seen from Figure14 that when the concrete reaches the final state under uniaxial compression, that is, when the concrete strain is 0.003, a large number of damages are produced on the surface of rubberized concrete under various grain sizes, and obvious damage strips are formed, and the grain size has little influence on the development path of damage strips. Rubber with different particle sizes is randomly distributed in concrete. But in the end, the paths of damage strips formed by concrete are basically the same, which indicates that aggregate mainly controls the generation of large cracks in concrete, and the size of rubber particle size only affects the mortar damage near the area.Figure 14
Tensile damage nephogram of concrete with different particle size of rubber. (a) Rubber side length is 2.5 mm, (b) rubber side length is 3 mm, (c) rubber side length is 3.5 mm.
(a)(b)(c)


## 6. Conclusions

Based on the two-dimensional meso-model, a three-dimensional meso-model considering the real aggregate shape is established in this paper. Considering the heterogeneity of rubberized concrete, rubberized concrete is regarded as a three-phase composite material composed of aggregate, rubber, and mortar. This study mainly studies the influence of rubber aging on the mechanical properties of concrete under uniaxial compression. Through the stress-strain curve and the number-strain curve of concrete damage units, the differences of rubber aging level, the content of aging rubber, and the particle size of aging rubber are analyzed, and the following conclusions are drawn:(1)
When the aging level of rubber is higher, the elastic modulus and compressive strength of rubberized concrete are lower. The sensitivity of compressive strength to rubber aging is stronger than that of elastic modulus. Rubber aging will improve the performance of concrete in the softening section and reduce the degradation rate of concrete in the softening section, such as compression resistance and crack resistance.(2)
When the content of rubber increases, the elastic modulus and compressive strength of concrete will decrease accordingly. The sensitivity of compressive strength to rubberized content is stronger than that of elastic modulus. Before concrete enters the softening section, the larger the content of rubber is, the worse the mechanical properties are. After concrete enters the softening section, the rule is opposite.(3)
The larger the rubberized particle size is, the higher the elastic modulus and compressive strength of rubberized concrete are. With the increase of rubber particle size, the increase of compressive strength is greater than that of elastic modulus. When concrete enters the softening section, the smaller the rubber particle size is, the slower the degradation of concrete mechanical properties will be.



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*Source: 9533618-2022-06-08.xml*