*2.3. Specimen Design*

The creep test of RAC was carried out in accordance with "Test Method for Long-term Performance and Durability of Ordinary Concrete" [27]. The creep specimen size was 100 mm × 100 mm × 400 mm, the shrinkage specimen size was 100 mm × 100 mm × 515 mm, cubic specimen size was 150 mm × 150 mm × 150 mm, and prismatic specimen size was 150 mm × 150 mm × 300 mm. The specific number of specimens and uses is shown in Table 3.



#### *2.4. Test Loading Process*

The creep testing of RAC was carried out using a spring-loaded compression creeper that was loaded with a jack. The load was controlled by a pressure sensor and a digital electronic displacement meter, and the constant value of the load was maintained by the spring reaction force. The creep loading device and shrink test device are shown in Figure 1.


**Figure 1.** Site loading schematic.

#### **3. Test Results and Analysis**

#### *3.1. Analysis of Shrinkage Test Results*

The shrinkage of RAC with different substitution rates at 180 days is shown in Figure 2. The shrinkage of RAC is similar to that of normal concrete. At 180 days, the shrinkage of RAC with a 50% and 100% substitution rate in group I increased by 26% and 48%, respectively, compared with that of ordinary concrete, and the shrinkage of RAC with a 50% and 100% substitution rate in group II was increased by 22% % and 47%, respectively, compared with that of ordinary concrete. As the replacement rate of RCA increased, the shrinkage of RAC also increased. In the early stage of shrinkage, the shrinkage of RAC increased faster and shrank faster, and then the rate of shrinkage decreased and slowed down. The shrinkage tended to be gentle until 120 days, and about 95% of the total shrinkage was achieved. It was considered that the shrinkage of RAC tended to be stable at 180 days.

**Figure 2.** Shrinkage deformation curve of RAC with different water–cement ratios. (**a**) *w*/*c* = 0.527; (**b**) *w*/*c* = 0.4. Note: <sup>ε</sup>*sh* indicates shrinkage strain and is dimensionless; *k* indicates the slope and is dimensionless; *ts* indicates the age of the concrete at the start of drying; *t* indicates the age of the concrete.

In the early stage of shrinkage, the shrinkage deformation of normal concrete with *w*/*c* = 0.4 was close to that of normal concrete with *w*/*c* = 0.527, and then the deviation between them gradually increased. Normal concrete shrinkage with *w*/*c* = 0.527 at 180 days was 11% higher than normal concrete shrinkage with *w*/*c* = 0.4. At 180 days, the shrinkage deformation of RAC with *w*/*c* = 0.527 increased by 14% and 12%, respectively, compared with that of RAC with a substitution rate of 50% and 100% with *w*/*c* = 0.4. This shows that the water–cement ratio is not the main factor affecting the shrinkage of RAC. As the age increased, the shrinkage of RAC was not a ffected by the water–cement ratio. In addition, both groups of RAC and ordinary concrete showed an obvious shrinkage development trend in the first 30 days: The average shrinkage slope reached 10.76 and 9.22, respectively; the shrinkage development trend of each group of samples slowed down and contracted from 30 days to 86 days, and the average slope decreased to 2.37 and 2.06, respectively; the shrinkage trend of each group tended to be stable from 90 days to 180 days, and the average shrinkage slopes approached 0.56 and 0.60, respectively. Comparing the changes in the average shrinkage slopes of the two water–cement ratios, it was found that the water–cement ratio had a more obvious influence on the trend of early shrinkage. The average shrinkage slope of the *w*/*c* = 0.527 sample increased by 16.7% in the first stage (≤30 days) compared to the *w*/*c* = 0.4 sample; the second stage of the increase in value accounted for 17.7% of the first stage; the third stage of the average slope slightly decreased to account for 2.3% of the first stage.

Similarly to ordinary concrete, the main cause of the shrinkage of RAC is cement mortar hardening, internal moisture loss, and deformation caused by volume reduction. However, the shrinkage of RAC is higher than that of ordinary concrete, and as the substitution rate increases, the amount of shrinkage also increases. On the one hand, this is because the micro-cracks inside the RCA cause a decrease in the elastic modulus and strength, resulting in a reduced ability to restrain the shrinkage, a smaller volume loss, and a larger shrinkage deformation. On the other hand, compared with ordinary concrete, due to the presence of the old cement mortar, which is not easily peeled o ff on the surface of the RCA, the total amount of mortar of the RAC is larger under the same mix ratio, and the shrinkage is mainly caused by the hardening of the cement mortar. Therefore, the shrinkage of RAC in the same environment is stronger than that of ordinary concrete.

#### *3.2. Analysis of Creep Test Results*

The creep curve of RAC at 180 days is shown in Figure 3. The creep of RAC is similar to that of ordinary concrete. At 180 days, the creep coe fficient of RAC with a 50% and 100% substitution rate in group I increased by 19.6% and 39.6%, respectively, compared with that of ordinary concrete. The creep coe fficient of RAC with a 50% and 100% substitution rate in group II was 23.6% and 44.3% higher than that of ordinary concrete, respectively. At the initial stage of loading, the creep of RAC with a 50% and 100% substitution rate increased faster than that of ordinary concrete, and the creep coe fficient was always higher than ordinary concrete. The creep growth rate decreased with the passage of time, but the decrease rate of the creep growth rate of ordinary concrete that was close to the creep coe fficient of RAC was small. At 120 days, the creep development of all three creeps tended to be flat, and about 90% of the total creep variable was completed, which roughly shows that the creep of the RAC tended to be stable.

**Figure 3.** Creep coe fficient curve of RAC. (**a**) *w*/*c* = 0.527; (**b**) *w*/*c* = 0.4. Note: <sup>ε</sup>*sh* indicates shrinkage strain and is dimensionless; *k* indicates the slope and is dimensionless; *t*0 indicates the loading age of concrete; *t* indicates the age of the concrete.

At the initial stage of loading, the creep of normal concrete with *w*/*c* = 0.4 was faster than that of normal concrete with *w*/*c* = 0.527, and the creep coe fficient was higher than the latter. After that, the creep growth rate of normal concrete with *w*/*c* = 0.4 decreased and that of ordinary concrete with *w*/*c* = 0.527 increased rapidly. When loading to 180 days, the creep coe fficient of normal concrete with *w*/*c* = 0.527 increased by 43.8% compared with that of RAC with *w*/*c* = 0.4. For the RAC with *w*/*c* = 0.4 and a substitution rate of 50% and 100%, the creep development trend was the same. At 180 days, the creep coe fficient of RAC with *w*/*c* = 0.527 increased by 40% and 38.7%, respectively, compared with that of RAC with a substitution rate of 50% and 100% with *w*/*c* = 0.4. This shows that the water–cement ratio is an important factor a ffecting the creep of RAC. The high water–cement ratio and the large amount of recycled mortar have a significant e ffect on creep.

#### **4. Creep and Shrinkage Model of Recycled Aggregate Concrete**

At present, there are many models of shrinkage and creep of ordinary concrete at home and abroad. In this paper, five typical models are selected, which are the CEB-FIP 1990 model [28], ACI209R 1992 model [29], GL2000 model [30], B3 model [31], and GB50010 model [32]. Based on the five models, the recycled aggregate attached mortar is taken as the research object, the increasing coe fficient of the attached mortar is put forward, and the shrinkage creep model of the RAC is established.

#### *4.1. Creep Increasing Coe*ffi*cient of Attached Mortar*

Fathifazl et al. [18] considered that natural aggregate was replaced by mass or volume percentage when RAC was prepared by traditional methods. Compared with ordinary concrete, a certain amount of cement mortar is wrapped on the surface of the recycled aggregate. The content of natural aggregate in the RAC prepared by the conventional method is decreased and the content of the total mortar is increased. The elastic modulus of the component is decreased, and the shrinkage and the amount of creep are increased. It is assumed that the RCA is a two-phase material composed of residual cement mortar and natural aggregate, and the mortar in the RAC consists of residual cement mortar and new cement mortar on the aggregate surface. Based on the creep test results of RAC, the residual cement mortar content of RCA was taken as the research object to establish the creep prediction model of RAC.

$$\mathcal{C}\_{\text{AM}} = \frac{\mathcal{C}\_{\text{RAC}}}{\mathcal{C}\_{\text{NAC}}} = \left(\frac{V\_{\text{NM}}^{\text{RAC}} + V\_{\text{RM}}^{\text{RAC}}}{1 - V\_{\text{RCA}}^{\text{RAC}}}\right)^{1.53},\tag{1}$$

$$V\_{\rm NM}^{\rm BAC} = 1 - V\_{\rm RCA}^{\rm BAC}.\tag{2}$$

Simultaneous equations:

$$\mathbf{C}\_{\rm AM} = \left(\frac{V\_{\rm NM}^{\rm BAC} + V\_{\rm AM}^{\rm BAC}}{1 - V\_{\rm NCA}^{\rm NAC} - V\_{\rm RCA}^{\rm NAC}}\right) \tag{3}$$

According to the composition of RCA, the following equation holds:

$$
\upsilon\_{\rm RCA} = \upsilon\_{\rm AM} + \upsilon\_{\rm OVA}, \quad \upsilon\_{\rm RCA} = \upsilon\_{\rm AM} + m\_{\rm OVA} \tag{4}
$$

$$
\omega\_{\rm RCA} = \upsilon\_{\rm RCA} \times \rho\_{\rm RCA}, \quad \upsilon\_{\rm AM} = \upsilon\_{\rm AM} \times \rho\_{\rm AM}.\tag{5}
$$

$$
\mu\_{\rm OVA} = \upsilon\_{\rm OVA} \times \rho\_{\rm OVA}.\tag{6}
$$

In the equation, *V* is volume (m3); *m* is quality (kg); ρ is apparent density (kg/m3).

The parameter *MAM* is the mass ratio of the attached mortar and the RCA. *MAM* = *mAM*/*mRCA*, and the following equation is derived from the above equation:

$$\rho\_{\rm AM} = \frac{m\_{\rm AM}}{v\_{\rm AM}} = \frac{v\_{\rm RCA} \times \rho\_{\rm RCA} \times M\_{\rm AM}}{v\_{\rm RCA} - \frac{(1 - M\_{\rm AM})v\_{\rm RCA} \times \rho\_{\rm RCA}}{\rho\_{\rm OVA}}} = \frac{M\_{\rm AM}}{\frac{1}{\rho\_{\rm OVA}} - \frac{1 - M\_{\rm AM}}{\rho\_{\rm OVA}}},\tag{7}$$

and *v*AM = *v*RCA × *M*AM × ρRCA ρAM . Simultaneousequations:

$$
\upsilon\_{\rm AM} = \upsilon\_{\rm RCA} \times [1 - (1 - M\_{\rm AM}) \frac{\rho\_{\rm RCA}}{\rho\_{\rm OVA}}]\_{\prime} \tag{8}
$$

$$V\_{\rm AM} = V\_{\rm RCA} \times [1 - (1 - M\_{\rm AM}) \frac{\rho\_{\rm RCA}}{\rho\_{\rm OVA}}].\tag{9}$$

Generally, the replacement rate of RCA is defined as follows:

$$r = \frac{m\_{\rm RCA}^{\rm RAC}}{m\_{\rm RCA}^{\rm RAC} + m\_{\rm NCA}^{\rm RAC}}.\tag{10}$$

The volume ratio of natural coarse aggregate and RCA in RAC is *R*.

$$R = \frac{v\_{\text{NCA}}^{\text{RAC}}}{v\_{\text{RCA}}^{\text{RAC}}} = \frac{V\_{\text{NCA}}^{\text{RAC}}}{V\_{\text{RCA}}^{\text{RAC}}} = \frac{(m\_{\text{RCA}}^{\text{RAC}} + m\_{\text{NCA}}^{\text{RAC}}) \times (1 - r) / \rho\_{\text{NCA}}}{(m\_{\text{RCA}}^{\text{RAC}} + m\_{\text{NCA}}^{\text{RAC}}) \times r / \rho\_{\text{RCA}}} = \frac{1 - r}{r} \times \frac{\rho\_{\text{RCA}}}{\rho\_{\text{NCA}}} \tag{11}$$

Equation (3) can be rewritten as

$$\mathcal{C}\_{\text{AM}} = \left( \frac{1 - V\_{\text{RCA}} \times \left[ \mathcal{R} + (1 - M\_{\text{AM}}) \frac{\rho\_{\text{RCA}}}{\rho\_{\text{OVA}}} \right]}{1 - V\_{\text{RCA}}^{\text{RAC}} \times (1 + R)} \right)^{1.33} \,. \tag{12}$$

In order to simplify the expression, the approximate ρ*RCA* = ρ*OVA* is considered, and the relationship between *CAM* and the RCA replacement rate r is as follows:

$$\mathbf{C\_{AM}} = \left(\frac{1 - V\_{\rm RCA}^{\rm BAC} \times \left[\frac{1 - r}{r} \times \frac{\rho\_{\rm RCA}}{\rho\_{\rm NCA}} + (1 - M\_{\rm AM})\right]}{1 - V\_{\rm RCA}^{\rm BAC} \times \left(1 + \frac{1 - r}{r} \times \frac{\rho\_{\rm RCA}}{\rho\_{\rm NCA}}\right)}\right)^{1.33} \,\tag{13}$$

When *r* = 100%, it is all RAC:

$$C\_{\rm AM} = \left(\frac{1 - V\_{\rm RCA}^{\rm BAC} (1 - M\_{\rm AM})}{1 - V\_{\rm RCA}^{\rm BAC}}\right)^{1.33}.\tag{14}$$

#### *4.2. Shrinkage Increasing Coe*ffi*cient of Attached Mortar*

Concrete is constrained by aggregates, so its dry shrinkage is lower than that of pure grou<sup>t</sup> [33]. The shrinkage of concrete is mainly caused by the hydration of cement mortar. The size of a few coarse aggregates is unstable. However, most of the coarse aggregates have the same size, a large elastic modulus, high crush index, and good restraint on concrete shrinkage. Therefore, the shrinkage of concrete depends on the amount and rigidity of the coarse aggregate in concrete. Considering the combined e ffect of aggregate content and rigidity, the prediction equation of the shrinkage strain of ordinary concrete is as follows:

$$S\_{\rm NAC} = S\_{\rm TP}^{\rm NAC} \left( V\_{\rm TP}^{\rm NAC} \right)^{a}. \tag{15}$$

In the equation, *SNAC*—the shrinkage strain of ordinary concrete; *STP*—the shrinkage strain of cement slurry in common concrete under the same conditions; *VNAC TP* —the volume of the total cement slurry in the ordinary concrete; α—empirical coe fficient. The change range is 1.2–1.7 and the average is 1.45.

Because of the two-phase nature of RCA, the total mortar content in RAC is composed of attached mortar and fresh mortar. The shrinkage strain of RAC can be expressed as the following equation:

$$S\_{\rm BAC} = S\_{\rm TP}^{\rm BAC} \left( V\_{\rm TP}^{\rm BAC} \right)^{\alpha}. \tag{16}$$

It is assumed that the shrinkage characteristics of cement mortar in RAC are the same as those of ordinary concrete, which simultaneously gives the following equation:

$$\frac{S\_{\rm BAC}}{S\_{\rm NAC}} = \left(\frac{V\_{\rm TP}^{\rm BAC}}{V\_{\rm TP}^{\rm NAC}}\right)^a. \tag{17}$$

The definition of SAM is the shrinkage increase coefficient of adhesive mortar, *S*AM = (*V*RAC TP /*V*NAC TP )α. Since the shrinkage of RAC is related to the volume of the total mortar, the volume *V*RAC TP of the total mortar in RAC can be determined according to Equation (9). Then there is the following equation:

$$S\_{\rm AM} = \left(\frac{1 - V\_{\rm RCA}^{\rm BAC} \times \left[\frac{1-r}{r} \times \frac{\rho\_{\rm RCA}}{\rho\_{\rm NCA}} + (1 - M\_{\rm AM})\right]}{1 - V\_{\rm RCA}^{\rm BAC} \times \left(1 + \frac{1-r}{r} \times \frac{\rho\_{\rm RCA}}{\rho\_{\rm NCA}}\right)}\right)^{1.45}.\tag{18}$$

When *r* = 100%, it is all RAC:

$$S\_{\rm AM} = \left(\frac{1 - V\_{\rm RCA}^{\rm BAC} (1 - M\_{\rm AM})}{1 - V\_{\rm RCA}^{\rm BAC}}\right)^{1.45}.\tag{19}$$
