Study on Mechanical Properties and Mesoscopic Numerical Simulation of Recycled Concrete

: To obtain the mechanical properties of recycled concrete (RC) under different replacement rates (RRs) of recycled coarse aggregate (RCA), a quasi-static uniaxial compression test, a uniaxial splitting tension test and a uniaxial dynamic compression test of RC with replacement rates (RRs) of 0%, 20%, 40%, 60%, 80% and 100% were carried out. ABAQUS was used to investigate the cracking and failure of RC. The results showed that, when the RR was less than 60%, the uniaxial compressive and tensile strengths of RC decreased with the increase in RR, but slightly increased when RR was greater than 80%. Under impact load, the dynamic compressive strength of RC increased linearly with the increase in the strain rate, showing an obvious strain rate effect. With the increase in RR, the strain rate sensitivity of RC gradually decreased. The concrete damage plastic (CDP) model can describe the mechanical behavior of RC well. The damage and failure of RC occurred ﬁrst at the old interface transition zone (ITZ) and old mortar. As the strain rate increases, the damage and failure rate of the specimens is intensiﬁed. Research on the mechanical properties of RC can provide a basis for the application and promotion of RC technology.


Introduction
Concrete, as the most widely used building material, is used very widely. Additionally, its demand for resources and environmental hazards are also increasing [1]. Reasonable application of recycled aggregate (RC) can solve the problems of environmental hazards and resource shortage. However, reliable technology is needed to improve the utilization rate of RC [2]. The application of and research into, RC has made great advances in environmental pollution prevention and control and in the development of green ecology [3].
RC is also known as recycled aggregate concrete (RCA). It forms new concrete through a special process by demolishing old buildings and selecting coarse aggregates instead of natural aggregates (NAs) [4]. Compared with NA, the surface of RCA is covered with an old mortar of indeterminate thickness. Due to the large void and loose and uneven distribution of these mortars, the apparent density and bulk density of RCA are smaller than that of NA.
Compared with plain concrete (PC), RC has great differences in performance, reflected in low strength, poor durability and large dispersion [5]. A layer of old mortar remains on the surface of the RCA. Moreover, there are many micro-cracks in the mortar and also appears in the aggregate when it is crushed and affected by mechanical crushing. This makes the water absorption rate of the RCA much higher than that of the NA [6]. Meanwhile, the cohesiveness between hardened cement and aggregate interface on the surface of RCA is poor. The porosity between interfaces is large and part of the mortar will enter into the pores [7]. Due to the uneven distribution of RAC surface and different shapes of the hardened mortar, the strength of hardened mortar is much lower than that of NA. In the production process of RCA, the collision and friction among aggregates produce tiny cracks inside it. Additionally, it makes the crushing index of RCA much larger than that of NA [8].
Most of the research on the mechanical properties of RC focuses on its quasi-static mechanical properties. Sagoe-crentsil et al. [9] discussed the effect of RCA on concrete strength and found that the compressive and tensile strengths of RC were 5% lower than that of PC. Xiao et al. [10] tested the mechanical properties of RC with different RRs of RCA and declared that RR has an obviously significant effect on the strength of RC. Casucio et al. [11] used NA and RCA from two different sources to prepare concrete and pointed out that the compressive strength of RC was reduced by 1-15% and the elastic modulus was reduced by 13-18%. Zhou et al. [12] used different kinds of RCA to make RC, pointing out that the compressive failure mode of RC had nothing to do with the RR of RCA and the failure of specimens mainly occurred at the ITZ. Job et al. [13] pointed out that, when the RR of RCA was less than 25%, it had no significant effect on the strength of RC.
In terms of numerical simulation, Wang et al. [14] established the ITZ model of RC and studied the influence of the thickness of ITZ on the strength, peak strain and crack behavior of RC. Based on the Monte Carlo method and digital image technology, the numerical mesoscopic model of RC was established. The effects of the old mortar and new mortar with different RRs of RCA on its mechanical properties and failure modes were studied [15]. Ying et al. [16] proposed the basis element method for the dynamic damage problem and discussed the dynamic mechanical behavior of RC. The softening and dynamic strengthening of stress-strain curves under different loading conditions were researched. In the aspect of concrete structure reinforcement, Rodrigues et al. have conducted much valuable research [17,18].
Based on the above research background, this paper took RC as the research object and carried out a systematic study on its mechanical properties. The quasi-static uniaxial compression test, uniaxial splitting tensile test and uniaxial dynamic compression test were carried out for RC with different RRs at different curing ages. ABAQUS and CDP models were used to simulate the loading process of RC and the damage and failure characteristics of the meso-structure during the loading process were studied.

Specimen Preparation
The RC used in the test was an abandoned concrete structure from the construction site and the RCA particles were obtained after crushing and processing, as shown in Figure 1. will enter into the pores [7]. Due to the uneven distribution of RAC surface and different shapes of the hardened mortar, the strength of hardened mortar is much lower than that of NA. In the production process of RCA, the collision and friction among aggregates produce tiny cracks inside it. Additionally, it makes the crushing index of RCA much larger than that of NA [8].
Most of the research on the mechanical properties of RC focuses on its quasi-static mechanical properties. Sagoe-crentsil et al. [9] discussed the effect of RCA on concrete strength and found that the compressive and tensile strengths of RC were 5% lower than that of PC. Xiao et al. [10] tested the mechanical properties of RC with different RRs of RCA and declared that RR has an obviously significant effect on the strength of RC. Casucio et al. [11] used NA and RCA from two different sources to prepare concrete and pointed out that the compressive strength of RC was reduced by 1-15% and the elastic modulus was reduced by 13-18%. Zhou et al. [12] used different kinds of RCA to make RC, pointing out that the compressive failure mode of RC had nothing to do with the RR of RCA and the failure of specimens mainly occurred at the ITZ. Job et al. [13] pointed out that, when the RR of RCA was less than 25%, it had no significant effect on the strength of RC.
In terms of numerical simulation, Wang et al. [14] established the ITZ model of RC and studied the influence of the thickness of ITZ on the strength, peak strain and crack behavior of RC. Based on the Monte Carlo method and digital image technology, the numerical mesoscopic model of RC was established. The effects of the old mortar and new mortar with different RRs of RCA on its mechanical properties and failure modes were studied [15]. Ying et al. [16] proposed the basis element method for the dynamic damage problem and discussed the dynamic mechanical behavior of RC. The softening and dynamic strengthening of stress-strain curves under different loading conditions were researched. In the aspect of concrete structure reinforcement, Rodrigues et al. have conducted much valuable research [17,18].
Based on the above research background, this paper took RC as the research object and carried out a systematic study on its mechanical properties. The quasi-static uniaxial compression test, uniaxial splitting tensile test and uniaxial dynamic compression test were carried out for RC with different RRs at different curing ages. ABAQUS and CDP models were used to simulate the loading process of RC and the damage and failure characteristics of the meso-structure during the loading process were studied.

Specimen Preparation
The RC used in the test was an abandoned concrete structure from the construction site and the RCA particles were obtained after crushing and processing, as shown in  The water absorption rate (WAR) of RCA can be measured by mass method: The water absorption rate (WAR) of RCA can be measured by mass method: where ω is the WAR in different time periods, m 1t is the total aggregate mass, m 2t is the total mass of the saturated aggregate and t is the different time periods, which were 10 min, 1 h, 6 h, 12 h and 24 h. Figure 2 shows the WAR of natural and recycled coarse aggregates measured in the test.
Sustainability 2022, 14, x FOR PEER REVIEW 3 of 17 where ω is the WAR in different time periods, 1t m is the total aggregate mass, 2t m is the total mass of the saturated aggregate and t is the different time periods, which were 10 min, 1 h, 6 h, 12 h and 24 h. Figure 2 shows the WAR of natural and recycled coarse aggregates measured in the test. In Figure 2, the WAR of RCA was significantly greater than that of NCA and the final WAR of RCA was 8.23 times higher than that of NA. The difference in the absorbance of recycled aggregate was an important factor that affects the performance of RC. Combined with Figure 1, it can be seen that the RCA produced by discarded concrete test blocks was coated with a large amount of old mortar, which has the characteristics of a porous and loose internal structure due to its own defects. Therefore, RCA has high water absorption performance when immersed in water [15].
Considering the influence of the RR of RCA on mechanical properties of RC, the RRs of RCA were designated as 0%, 20%, 40%, 60%, 80% and 100% in the test. The corresponding concrete mix ratio is listed in Table 1. Distilled water, river sand and ordinary Portland cement were used. Among these, medium sand was used in the test and the fineness modulus was 2.62. The coarse aggregate was continuously graded from 5 mm to 31.5 mm; the grading curves are shown in Figure 3. In Figure 2, the WAR of RCA was significantly greater than that of NCA and the final WAR of RCA was 8.23 times higher than that of NA. The difference in the absorbance of recycled aggregate was an important factor that affects the performance of RC. Combined with Figure 1, it can be seen that the RCA produced by discarded concrete test blocks was coated with a large amount of old mortar, which has the characteristics of a porous and loose internal structure due to its own defects. Therefore, RCA has high water absorption performance when immersed in water [15].
Considering the influence of the RR of RCA on mechanical properties of RC, the RRs of RCA were designated as 0%, 20%, 40%, 60%, 80% and 100% in the test. The corresponding concrete mix ratio is listed in Table 1. Distilled water, river sand and ordinary Portland cement were used. Among these, medium sand was used in the test and the fineness modulus was 2.62. The coarse aggregate was continuously graded from 5 mm to 31.5 mm; the grading curves are shown in Figure 3. Concrete specimens were prepared and poured according to the above mix ratio and the aggregate, cement, sand and water were added to the mixer in turn. After mixing evenly, the concrete was poured. The template size was 100 × 100 × 100 mm cube mold and 75 mm PVC pipe inner diameter. After pouring, it was placed on the shaking table for 2 min. The mold was removed after 24 h, the concrete was maintained to the specified Sustainability 2022, 14, 12125 4 of 16 age by water curing and the water temperature was controlled at 20 ± 3 • C. The cylinder specimens were cut, polished and prepared as standard specimens according to ISRM standards after curing for 28 days. The cube specimen with a side length of 100 mm was used in the quasi-static tests, while a cylinder specimen with a length of 50 mm and a diameter of 75 mm was used in the dynamic tests. Considering the dispersion of the specimen, 3 to 5 repetitions were performed for each set of tests. In this research, a total of 36 cube and 72 cylindrical specimens were used.  Concrete specimens were prepared and poured according to the above mix ratio and the aggregate, cement, sand and water were added to the mixer in turn. After mixing evenly, the concrete was poured. The template size was 100 × 100 × 100 mm cube mold and 75 mm PVC pipe inner diameter. After pouring, it was placed on the shaking tabl for 2 min. The mold was removed after 24 h, the concrete was maintained to the specified age by water curing and the water temperature was controlled at 20 ± 3 °C. The cylinde specimens were cut, polished and prepared as standard specimens according to ISRM standards after curing for 28 days. The cube specimen with a side length of 100 mm wa used in the quasi-static tests, while a cylinder specimen with a length of 50 mm and a diameter of 75 mm was used in the dynamic tests. Considering the dispersion of the spec imen, 3 to 5 repetitions were performed for each set of tests. In this research, a total of 36 cube and 72 cylindrical specimens were used.
The specimens used in the experiment are shown in Figure 4.  The specimens used in the experiment are shown in Figure 4.  Concrete specimens were prepared and poured according to the above mix ratio and the aggregate, cement, sand and water were added to the mixer in turn. After mixing evenly, the concrete was poured. The template size was 100 × 100 × 100 mm cube mold and 75 mm PVC pipe inner diameter. After pouring, it was placed on the shaking table for 2 min. The mold was removed after 24 h, the concrete was maintained to the specified age by water curing and the water temperature was controlled at 20 ± 3 °C. The cylinder specimens were cut, polished and prepared as standard specimens according to ISRM standards after curing for 28 days. The cube specimen with a side length of 100 mm was used in the quasi-static tests, while a cylinder specimen with a length of 50 mm and a diameter of 75 mm was used in the dynamic tests. Considering the dispersion of the specimen, 3 to 5 repetitions were performed for each set of tests. In this research, a total of 36 cube and 72 cylindrical specimens were used.
The specimens used in the experiment are shown in Figure 4.

Quasi-Static Compressive Strength
The displacement loading method was adopted in the test loading process and the displacement rate was 0.005 mm/s.
The curing age has a considerable influence on the strength of RC. Therefore, the quasi-static tests at a curing age of 7 d, 14 d and 28 d were measured and its variation trends are shown in Figure 5. Figure 5 shows that, when RR was less than 80%, the compressive strength of RC decreases with the increase in RR at any stage of the curing age. The reason is that the surface defects of RCA were caused by hammering and crushing in the production and crushing process. Additionally, the greater the recycled aggregate content, the more likely it was to crack and break under the external force.

Quasi-Static Compressive Strength
The displacement loading method was adopted in the test loading process and the displacement rate was 0.005 mm/s.
The curing age has a considerable influence on the strength of RC. Therefore, the quasi-static tests at a curing age of 7 d, 14 d and 28 d were measured and its variation trends are shown in Figure 5.  Figure 5 shows that, when RR was less than 80%, the compressive strength of RC decreases with the increase in RR at any stage of the curing age. The reason is that the surface defects of RCA were caused by hammering and crushing in the production and crushing process. Additionally, the greater the recycled aggregate content, the more likely it was to crack and break under the external force.
When the RR was 20% and the curing ages were 14 d and 28 d, the compressive strength of RC specimens were about 26 MPa and 34 MPa, respectively, which were 17% and 12% lower than that of PC specimens at 14 d and 28 d. When the RR was 60%, the compressive strength of RC decreases the most at different curing ages. When the RR was larger than 60%, the strength of RC was less affected by RR, which is mostly caused by the old mortar. Due to its large porosity, there were enough weak surfaces to crack, expand and break under the action of load [19].
When the RR was 60% or 80%, the strength of RC was the lowest. The strength variation was not obvious and only slightly increased when the RR was 100%. The reason was that the RCA has large porosity and small cracks and the new mortar fills these cracks in the mixing process. The hydration products in the later stage can make the old and new mortar more closely combined with the aggregate.

Quasi-Static Splitting Tensile Strength
The quasi-static tensile strength of RC at different curing ages and RRs are shown in Figure 6. When the RR was 20% and the curing ages were 14 d and 28 d, the compressive strength of RC specimens were about 26 MPa and 34 MPa, respectively, which were 17% and 12% lower than that of PC specimens at 14 d and 28 d. When the RR was 60%, the compressive strength of RC decreases the most at different curing ages. When the RR was larger than 60%, the strength of RC was less affected by RR, which is mostly caused by the old mortar. Due to its large porosity, there were enough weak surfaces to crack, expand and break under the action of load [19].
When the RR was 60% or 80%, the strength of RC was the lowest. The strength variation was not obvious and only slightly increased when the RR was 100%. The reason was that the RCA has large porosity and small cracks and the new mortar fills these cracks in the mixing process. The hydration products in the later stage can make the old and new mortar more closely combined with the aggregate.

Quasi-Static Splitting Tensile Strength
The quasi-static tensile strength of RC at different curing ages and RRs are shown in Figure 6. At the same curing age, the tensile strength of RC decreases first and then increases with the increase in RR as seen in Figure 6. Under the different curing ages, the splitting tensile strength changed from decreasing to increasing in RC with an RR of 80%. When the RR was less than 80%, the splitting tensile strength decreases with the increase in RR. When the RR was larger than 80%, the splitting tensile strength of concrete shows an opposite trend. There are two reasons for this change. Firstly, the old mortar of RCA reduces the overall aggregate strength and thus reduces the tensile strength of concrete. However, compared with the NA, the surface of RCA was rougher, which can effectively increase At the same curing age, the tensile strength of RC decreases first and then increases with the increase in RR as seen in Figure 6. Under the different curing ages, the splitting tensile strength changed from decreasing to increasing in RC with an RR of 80%. When the RR was less than 80%, the splitting tensile strength decreases with the increase in RR. When the RR was larger than 80%, the splitting tensile strength of concrete shows an opposite trend. There are two reasons for this change. Firstly, the old mortar of RCA reduces the overall aggregate strength and thus reduces the tensile strength of concrete. However, compared with the NA, the surface of RCA was rougher, which can effectively increase the bonding force between aggregates and mortar. With the increase in RR, the influence of the bonding force of rough surface on the tensile strength gradually appears. When the influence degree exceeds the threshold, it turns from degradation to enhancement. Secondly, the PC only has the bonding interface of aggregate and new mortar, while the RC has bonding interfaces between old mortar and aggregate and new mortar.
In concrete materials, the bonding interface is the weakest. There are many pores on the surface of RA and the WAR of RA is significantly higher than that of NA. It absorbs more water during hydration, which plays a role in weakening the ITZ structure. As the thickness and area of the ITZ increases, the internal defects increase, resulting in a decrease in the completeness of the specimen. Thus, as RR increases, the tensile strength of the specimen decreases [20,21].

Dynamic Compressive Strength
The SHPB test system was used to conduct uniaxial dynamic compression tests on RC specimens and the relationships between the uniaxial dynamic compressive strength and strain rate were obtained, as illustrated in Figure 7. In Figure 7, with the increase in strain rate, the RC shows an obvious strain rate effect. That is, the uniaxial dynamic compressive strength of RC increases with the increase in strain rate, which is the result of the joint action of the end friction effect, lateral inertia effect, crack evolution effect and water viscosity effect [22]. Under the impact load, the pore water in the specimen has a viscous effect on the crack and the higher the content of pore water is, the more significant the effect is. There is a certain friction between the end face of the specimen and the bar, which will increase the strength of the specimen. Additionally, the lateral inertia effect of the specimen also causes the passive confining pressure around the specimen. It is noticeable that with the increase in RR, the dynamic compressive strength of RC decreases first and then increases. When the substitution rate was 60% or 80%, the values were at a minimum and they were similar to each other. When RR was 100%, the dynamic compressive strength of the specimen was improved to a certain extent, but less than the dynamic compressive strength when the RR was 40%.
According to the fitting equations of curves in Figure 5, the relationship between dynamic compressive strength and strain rate of RC was linear. Among them, the slope of the line represents the strain rate sensitivity of specimen. The strain rate sensitivity of PC was the highest. With the increase in RR, the strain rate sensitivity decreases gradually, but increases slightly when the RR was 100%. In Figure 7, with the increase in strain rate, the RC shows an obvious strain rate effect. That is, the uniaxial dynamic compressive strength of RC increases with the increase in strain rate, which is the result of the joint action of the end friction effect, lateral inertia effect, crack evolution effect and water viscosity effect [22]. Under the impact load, the pore water in the specimen has a viscous effect on the crack and the higher the content of pore water is, the more significant the effect is. There is a certain friction between the end face of the specimen and the bar, which will increase the strength of the specimen. Additionally, the lateral inertia effect of the specimen also causes the passive confining pressure around the specimen. It is noticeable that with the increase in RR, the dynamic compressive strength of RC decreases first and then increases. When the substitution rate was 60% or 80%, the values were at a minimum and they were similar to each other. When RR was 100%, the dynamic compressive strength of the specimen was improved to a certain extent, but less than the dynamic compressive strength when the RR was 40%.

CDP Model
According to the fitting equations of curves in Figure 5, the relationship between dynamic compressive strength and strain rate of RC was linear. Among them, the slope of the line represents the strain rate sensitivity of specimen. The strain rate sensitivity of PC was the highest. With the increase in RR, the strain rate sensitivity decreases gradually, but increases slightly when the RR was 100%.

CDP Model
From the stress-strain curves of RC obtained from uniaxial tensile and compression tests, it can be seen that the material enters the strain-hardening stage after reaching the yield strength under compression state and enters the strain-softening stage after reaching the ultimate stress. Under the uniaxial tensile state, the RC directly reaches the ultimate tensile stress after the elastic stage and then the material enters the strain softening stage. According to relevant studies on RC [23], stiffness degradation occurs after yield stress is reached, which is consistent with the mechanical characteristics of PC. Therefore, the CDP model was used to characterize the constitutive relationship of RC.
The CDP model in ABAQUS introduces the influence of damage on material stiffness and can better simulate the characteristics that unloading stiffness decreases continuously due to the increase in damage in the strain hardening and strain softening stages [6,24]. The stress-strain relationships of concrete under uniaxial tension and compression are depicted in Figure 8. In the CDP model, the effective stress of concrete considering damage is expressed as: where d is the damage variable, 0 1 d < < ; σ is the effective stress.  In the CDP model, the effective stress of concrete considering damage is expressed as: where d is the damage variable, 0 < d < 1; σ is the effective stress. The effective stress can be expressed below: where D el 0 is the initial stiffness of the material; ε pl is the plastic strain of the material. In combination with Equations (2) and (3), there are: Among them, the stiffness degradation is represented by tensile damage and compression damage. Under uniaxial stress, it can be expressed as: According to Figure 6, Equations (5) and (6), the stiffness of concrete degrades from E 0 to (1 − d t )E 0 and (1 − d c )E 0 in the process of tension and compression.
According to the energy equivalence principle [25,26], the elastic residual energy of undamaged materials can be obtained by following Equation (7).
The equivalent elastic residual energy of damaged material can be obtained by following Equation (8).
Combined with Equations (2), (7) and (8), the elastic modulus of damaged material can be expressed below: According to Lamitre's equivalent strain principle [26], there is: The calculation equation of damage factor under uniaxial compression is as follows: The calculation equation of damage factor under uniaxial tension is as follows: where Considering that the concrete has an obvious strain rate effect under dynamic load, the CEB model [27] is introduced to describe the rate behavior of concrete, where the dynamic growth factor (DIF c ) under uniaxial compression is expressed as: where f cs and f cd are the quasi-static compressive strength and dynamic compressive strength of concrete under uniaxial conditions, respectively; α s = 1/(5 + 9 f cs / f c0 ); γ s = 10 (6.15α s −2) ; . ε s = 30 × 10 −6 s −1 ; f c0 = 10MPa. The dynamic growth factor under uniaxial tension is expressed as: where f ts and f td are the quasi-static tensile strength and dynamic tensile strength of concrete under uniaxial conditions, respectively; .

Recycled Concrete Parameters
At the mesoscopic level, RC can be seen as a composite material composed of fivephase heterogeneous materials, divided into old mortar, new mortar, old ITZ, new ITZ and aggregate.
It is assumed that the shape of NCA and RCA is round, residual mortar is attached to the surface of RCA and the new ITZ is generated during the preparation of RC. The structural composition of RC is shown in Figure 9.

Recycled Concrete Parameters
At the mesoscopic level, RC can be seen as a composite material composed of fivephase heterogeneous materials, divided into old mortar, new mortar, old ITZ, new ITZ and aggregate.
It is assumed that the shape of NCA and RCA is round, residual mortar is attached to the surface of RCA and the new ITZ is generated during the preparation of RC. The structural composition of RC is shown in Figure 9.  The thickness of the old mortar is set as 0.3 times of the radius of the RCA and the thickness of the ITZ is about 50 µm, but this thickness is too small to cause convergence difficulties, so it is set as 0.5 mm. Continuous gradation was used for the particle size and range distribution of recycled aggregate and the particle size distribution ranged from 5 to 31.5 mm. Fuller's curve was used to calculate the particle size distribution of RCA in mesoscopic simulation.
The equation of Fuller's curve is: where P(d) is the mass percentage of aggregate passing through the sieve with diameter of d; d max is the maximum size of aggregate; n is the exponential of the equation and 0.5 is used in this paper. In this paper, PYTHON is used to generate a meso-model of RC, the Monte Carlo method is used to place RCA and contact judgment is set to ensure the independence of RCA. The generation process of the RC meso-model is shown in Figure 10.
The equation of Fuller's curve is: where ( ) P d is the mass percentage of aggregate passing through the sieve with diameter of d ; max d is the maximum size of aggregate; n is the exponential of the equation and 0.5 is used in this paper.
In this paper, PYTHON is used to generate a meso-model of RC, the Monte Carlo method is used to place RCA and contact judgment is set to ensure the independence of RCA. The generation process of the RC meso-model is shown in Figure 10. Combined with the research in this paper and the literature studies [28], the mechanical parameters of each material phase are calculated, as listed in Table 2.  Combined with the research in this paper and the literature studies [28], the mechanical parameters of each material phase are calculated, as listed in Table 2.

Meshing Size
After the RC modeling was completed, grids of 1 mm, 2 mm, 3 mm and 5 mm were used to divide the meso-model. The quasi-static compressive test results are illustrated in Figure 11. Figure 11 shows that the stress-strain curves with different mesh sizes have little difference and the simulated curves have a high fitting degree with the test curves. Considering that smaller grid size would significantly increase the calculation time, a 2 mm grid was adopted for further calculation.

Quasi-Static Uniaxial Compression Test
The loading method of the quasi-static uniaxial compression test was displacementcontrolled. The bottom of the specimen was in fixed-hinged mode and uniform vertical downward load was applied on the top. The damage cloud diagrams of RC in the loading process are shown in Figure 12

Meshing Size
After the RC modeling was completed, grids of 1 mm, 2 mm, 3 mm and 5 mm were used to divide the meso-model. The quasi-static compressive test results are illustrated in Figure 11.  Figure 11 shows that the stress-strain curves with different mesh sizes have little difference and the simulated curves have a high fitting degree with the test curves. Considering that smaller grid size would significantly increase the calculation time, a 2 mm grid was adopted for further calculation.

Quasi-Static Uniaxial Compression Test
The loading method of the quasi-static uniaxial compression test was displacementcontrolled. The bottom of the specimen was in fixed-hinged mode and uniform vertical downward load was applied on the top. The damage cloud diagrams of RC in the loading process are shown in Figure 12. In Figure 12, there were no visible cracks on the surface of the specimen at the early loading stage. The force between the components inside the specimen is enough to resist the load force; that is, the external force does not reach the allowable range of the concrete. This is the elastic stage and the process belongs to the reversible deformation stage. With the increase in the load, the old ITZ and the old mortar inside the RC first appear damaged and destroyed and some small cracks appear. The external load force exceeds the   Figure 11 shows that the stress-strain curves with different mesh sizes have little difference and the simulated curves have a high fitting degree with the test curves. Considering that smaller grid size would significantly increase the calculation time, a 2 mm grid was adopted for further calculation.

Quasi-Static Uniaxial Compression Test
The loading method of the quasi-static uniaxial compression test was displacementcontrolled. The bottom of the specimen was in fixed-hinged mode and uniform vertical downward load was applied on the top. The damage cloud diagrams of RC in the loading process are shown in Figure 12. In Figure 12, there were no visible cracks on the surface of the specimen at the early loading stage. The force between the components inside the specimen is enough to resist the load force; that is, the external force does not reach the allowable range of the concrete. This is the elastic stage and the process belongs to the reversible deformation stage. With the increase in the load, the old ITZ and the old mortar inside the RC first appear damaged and destroyed and some small cracks appear. The external load force exceeds the In Figure 12, there were no visible cracks on the surface of the specimen at the early loading stage. The force between the components inside the specimen is enough to resist the load force; that is, the external force does not reach the allowable range of the concrete. This is the elastic stage and the process belongs to the reversible deformation stage. With the increase in the load, the old ITZ and the old mortar inside the RC first appear damaged and destroyed and some small cracks appear. The external load force exceeds the maximum allowable range of specimens; this is the crack initiation and expansion stage. As the loading continues, the microcracks continue to expand, from both sides to the inside and the cracks grow exponentially. This stage is the rapid development stage of cracks. With the continuous increase in the number and length of cracks, both vertical and transverse cracks were formed. The cracks develop in any direction and the specimen loses its bearing capacity and fails.
As shown in the compressive damage figures of RC, under the action of load, the RC will first appear damaged and failing on the surface of RCA. As the weakest part of the specimen, the old ITZ is rapidly damaged and cracked, while the aggregate always keeps its elasticity due to its high compressive strength limit. The failure of the specimen mainly extends along the vertical crack in the direction of load, accompanied by part of the mortar and aggregate falling off. With the increase in the RR of RCA, RC has more weak positions and more cracks under the action of load; thus, the compressive strength decreases gradually.

Quasi-Static Uniaxial Splitting Tensile Test
To accurately simulate the splitting tensile test of RC, the loading method was to set the semicircular rigid body at the contact position between the specimen and steel plate and to control the loading through displacement. The obtained tensile stress curves are shown in Figure 13. The numerical simulation result was in good agreement with the experimental curve and the calculation accuracy meets the analysis requirements. and more cracks under the action of load; thus, the compressive strength decreases gradually.

Quasi-Static Uniaxial Splitting Tensile Test
To accurately simulate the splitting tensile test of RC, the loading method was to set the semicircular rigid body at the contact position between the specimen and steel plate and to control the loading through displacement. The obtained tensile stress curves are shown in Figure 13. The numerical simulation result was in good agreement with the experimental curve and the calculation accuracy meets the analysis requirements. The damage cloud diagrams of RC in the loading process are shown in Figure 14.

Quasi-Static Uniaxial Splitting Tensile Test
To accurately simulate the splitting tensile test of RC, the loading method was to set the semicircular rigid body at the contact position between the specimen and steel plate and to control the loading through displacement. The obtained tensile stress curves are shown in Figure 13. The numerical simulation result was in good agreement with the experimental curve and the calculation accuracy meets the analysis requirements. The damage cloud diagrams of RC in the loading process are shown in Figure 14.   Figure 14 shows that under concentrated load, the RC specimen reaches its ultimate tensile strength and fails. The damage mainly occurs along the internal weak surface of the RC, that is, the ITZ and the old mortar. The cracking mainly occurred along the surface of RCA, which leads to the poor smoothness of the cracking surface of the concrete. Furthermore, several long cracks appear near the loading end due to stress concentration. With the increase in the RR of RCA, the parts in the specimen that reach the ultimate tensile strength gradually increase under the same load and the failure degree of the specimen increases. The failed part was mostly the surface of RCA, that is, the damage to weak area. This shows that the cohesiveness of the ITZ is poor and the failure mainly occurs along the interface of aggregate and mortar.

Dynamic Uniaxial Compression Test
According to the dynamic uniaxial compression test of RC, a numerical calculation model of the SHPB test system was established. The length of incident bar and transmission bar was 2500 mm with a Young's modulus of 210 GPa and Poisson ration of 0.3. The specimen was loaded by means of loading waveform input. Taking strain rates of 60 s −1 and 150 s −1 as examples, the input pressure curves at the end of the incident bar are shown in Figure 15 and the damage cloud diagrams of the specimens in the loading process are shown in Figure 16

Dynamic Uniaxial Compression Test
According to the dynamic uniaxial compression test of RC, a numerical calculation model of the SHPB test system was established. The length of incident bar and transmission bar was 2500 mm with a Young's modulus of 210 GPa and Poisson ration of 0.3. The specimen was loaded by means of loading waveform input. Taking strain rates of 60 s −1 and 150 s −1 as examples, the input pressure curves at the end of the incident bar are shown in Figure 15 and the damage cloud diagrams of the specimens in the loading process are shown in Figure 16. In Figure 16, when the strain rate was 60 s −1 , the damage degree of RC was low and only a few main cracks were propagated and linked up. The specimen was mainly damaged by compression and the fragmentation was large after failure. At t = 108 μs, the specimen underwent an elastic deformation stage and then entered a strain-hardening stage and a few microcracks appeared inside the specimen. At t = 168 μs, the main crack extends to transfixion and the damage develops from two sides to the middle. At t = 270 μs, the secondary cracks gradually spread and coalesced and the specimen failed. When the strain rate was 150 s −1 , the damage degree of RC was high and the cracks spread and coalesced along the surface of RCA. The specimen was seriously damaged by shear mode and the fragmentation degree of the specimen was small. The compressive damage was the main damage form, while the tensile damage was obvious outside the specimen. At t = 72 μs, a few partially penetrating oblique cracks appeared outside the specimen. At t = 96 μs, the main cracks outside the specimen rapidly extended to transfixion. At t = 156 μs, the number of main cracks increases obviously, accompanied by the expansion of secondary cracks in all directions and the specimen was seriously damaged. It shows that with the increase in impact load, the damage degree of RC was significantly aggravated and the integrity of specimen was reduced. The increase in the RR means the more initial damage of RC. Under loading, more cracks and damage appear in the old and new ITZ and  In Figure 16, when the strain rate was 60 s −1 , the damage degree of RC was low and only a few main cracks were propagated and linked up. The specimen was mainly damaged by compression and the fragmentation was large after failure. At t = 108 µs, the specimen underwent an elastic deformation stage and then entered a strain-hardening stage and a few microcracks appeared inside the specimen. At t = 168 µs, the main crack extends to transfixion and the damage develops from two sides to the middle. At t = 270 µs, the secondary cracks gradually spread and coalesced and the specimen failed. When the strain rate was 150 s −1 , the damage degree of RC was high and the cracks spread and coalesced along the surface of RCA. The specimen was seriously damaged by shear mode and the fragmentation degree of the specimen was small. The compressive damage was the main damage form, while the tensile damage was obvious outside the specimen. At t = 72 µs, a few partially penetrating oblique cracks appeared outside the specimen. At t = 96 µs, the main cracks outside the specimen rapidly extended to transfixion. At t = 156 µs, the number of main cracks increases obviously, accompanied by the expansion of secondary cracks in all directions and the specimen was seriously damaged. It shows that with the increase in impact load, the damage degree of RC was significantly aggravated and the integrity of specimen was reduced. The increase in the RR means the more initial damage of RC. Under loading, more cracks and damage appear in the old and new ITZ and the old mortar, which intensifies the damage and failure of the specimen and thus the strength decreases significantly.

Conclusions
In this paper, the mechanical properties of RC with different RRs of RCA were studied experimentally and numerically. The uniaxial compressive strength, uniaxial splitting tensile strength and dynamic compressive strength of RC were obtained and the failure processes were simulated by ABAQUS. The following conclusions can be drawn: (1) With the increase in curing age, the uniaxial compressive strength and splitting tensile strength of RC increase continuously. The compressive strength and splitting strength of RC show a decreasing trend with the increase in the RR of RCA. The reason was that the increase in the proportion of RCA increases the number of initial micro-cracks and damages in concrete. (2) Under impact load, the dynamic compressive strength of RC increases linearly with the increase in strain rate, showing an obvious strain rate enhancement effect. With the increase in the RR of RCA, the strain rate sensitivity of RC decreases gradually, but slightly increases when the RR is 100%. (3) The CDP model can also describe the mechanical behavior of RC. The numerical simulation results show that the damage and failure of RC first occur at the old ITZ and old mortar under loading. With the increase in strain rate, the damage and failure degree of the specimen were intensified.
The research on RC is of great significance to the development and application of green building. Macroscopically, there have been many research results on the mechanical properties of RC. The subsequent research should start from the microscopic view to study the internal structure characteristics and hydration products. Ways to improve the utilization rate of RC and the research on RC of other strength grades will also be the focus of future studies.

Conflicts of Interest:
The authors declare that there are no conflicts of interest regarding the publication of this paper.