The cement selected was P.O42.5 Portland cement produced by Yatai (Group) limited company. The initial setting time of P.O42.5 cement was 2h 45 min, and the final setting time was 3h and 45 min. Table 1 demonstrates the test results of cement samples.

The particle size of the coarse aggregate included was 5~20mm. The bulk density of coarse aggregate was 2620kg/m3, and the content of mudstone was less than 0.5%.

Longitudinal steel bars of HRB500 and HRB600 were used. Table 2 shows the mechanical properties of the selected longitudinal bars. The stress-strain curves of HRB500 and HRB600 steel bars are shown in Fig. (1). For example: in HRB600, HRB is a hot-rolled ribbed steel bar, and 600 means that the yield strength of this kind of reinforcement is 600MPa.

Fig. (1). The stress-strain curves of HRB500 and HRB600 steel bars.

In order to make the slump of concrete with higher strength grade and reach the specified index, superplasticizer polycarboxylate (SP) was added when making concrete specimens. SP is a new generation of environmental protection and high-performance superplasticizer based on new synthetic technology. Its main component is polycarboxylate, and its apparent physical characteristic is dark yellow transparent liquid, solid content is 20%, the water reduction rate is 25%, and the quality of the content is 0.2%~5%.

The test specimen design was divided into two groups. The concrete in the test specimen was ordinary concrete, the concrete strength grade was C30, C40, C50 and C60, and the size was 150mm×150mm×450mm (b ×h×H). Table 3 shows the mixed proportion of concrete.

Section and reinforcement of 150mm×150mm×450mm test specimen are shown in Fig. (2) and Table 4. The numbers in Table 4 consist of four parts: concrete strength grade, total reinforcement ratio of longitudinal compression reinforcement, and steel grades. Considering C30-1.40%-HRB600 as an example, it is a test specimen with a concrete strength grade of C30. The total reinforcement ratio of longitudinal compression reinforcement is 1.40%, and the grade of the longitudinal compression steel bar is HRB600. Three shrinkage contrast test specimens were prepared for each strength grade. Shrinkage values were tested from day 62 to day 270.

Fig. (2). 150mm×150mm×450mm test specimen.

Fig. (3). Time history curve of temperature and relative humidity.

Fig. (4). Experimental instruments and test specimen.

The temperature and relative humidity changes in all test specimens during the test are shown in Fig. (3). During the test specimen test, the temperature and humidity controller was introduced into the laboratory. The temperature and humidity were relatively stable; the temperature was 15±1 °C, and the average relative humidity of the environment was 42%.

The shrinkage test was carried out according to GB/T 50082-2009 “Standard of test method for long-term performance and durability of ordinary concrete” [16]. Two sets of strain collection devices were placed on the opposite sides of concrete prisms, the distance between the two measuring points in the strain collection device was 200mm, three concrete prisms in each strength grade were tested for shrinkage, and the mean shrinkage of the three concrete prisms was recorded as the shrinkage value of the group of concrete specimens (Fig. (4).

Fig. (5) shows the shrinkage time history curve of the reinforced concrete specimen from the beginning of the experiment. ρs in Fig. (5) is the total reinforcement ratio of longitudinal reinforcement. The shrinkage strain of reinforced concrete specimens decreased with an increase in the longitudinal reinforcement ratio. At the end of the shrinkage test, the contraction strain of the 1.40% specimen with longitudinal reinforcement ratio was reported to be 76%~89% of that of plain concrete, and the contraction strain of the 2.01% specimen with longitudinal reinforcement ratio was 52%~76% of that of plain concrete. It can be concluded that longitudinal reinforcement inhibited the development of free shrinkage, and the higher the reinforcement ratio, the more pronounced the inhibition effect.

On the other hand, according to Fig. (5), with the improvement in concrete grade, the shrinkage of the reinforced concrete specimen gradually decreased, due to which the structure of the reinforced concrete specimen became dense. The dense structure made the water in the reinforced concrete short specimen difficult to evaporate, thus reducing the shrinkage of the reinforced concrete specimen.

Currently, there are few research works on reinforced concrete specimen shrinkage. Based on the CEB-FIP model, Yuan Gao [15] introduced the influence coefficient of reinforced concrete and proposed a reinforced concrete shrinkage model. The calculation formula of its shrinkage model is as follows:

(1)

(2)

(3)

In the formula, the value of β_sc is determined by the type of cement; β_RH is determined by the relative humidity of the environment; β(t-t_s) is the coefficient of shrinkage strain change. t is the age of concrete; t_s is the age when the concrete begins to shrink. ƒ_s is the compressive strength of concrete; α_e = E_s/E_c; ρ is the ratio of reinforcement.

Fig. (5). Shrinkage time history curve of the reinforced concrete specimen from 62d.

Fig. (6). The fitting of the existing reinforced concrete specimen shrinkage model and modified reinforced concrete specimen shrinkage model with actual data.

The comparison between the existing reinforced concrete specimen shrinkage model and the test values is shown in Fig. (6). It can be seen that the prediction accuracy of the existing reinforced concrete specimen shrinkage model is high when the strength is higher, but the prediction effect is worse when the strength is lower. Taking the longitudinal reinforcement ratio of 1.40% as an example, when the shrinkage test time is 210d, the ratio fractions of calculated values and test values of C30, C40, C50 and C60 reinforced concrete specimens are 83.8%, 81.7%, 116.4% and 95.80%, respectively.

Based on the test results and CEB-FIP shrinkage model, the regression-modified calculation model of reinforced concrete specimen shrinkage is fitted considering the effects of longitudinal reinforcement ratio and concrete strength, as shown in Formula 4. The values of the modified reinforced concrete specimen contraction model were compared with the existing model using the contraction test, as shown in Fig. (6). It can be seen that the modified reinforced concrete specimen contraction model was in good agreement with the test value, and the prediction accuracy was higher than the existing reinforced concrete specimen contraction model (ƒ_c is the design value of the axial compressive strength of concrete).

(4)

In order to evaluate the precision of the shrinkage prediction model for reinforced concrete specimens, four indexes, R (correlation coefficient), MSE (mean square error), MAPE (mean absolute percentage error) and IAE (integral absolute error), were used to evaluate the prediction results. R reflects the correlation between independent variables and dependent variables, MSE reflects the average error, MAPE reflects the degree of data dispersion, and IAE reflects the accuracy of prediction results. The calculation formulas of each index are shown in Eqs 5-8 [17, 18].

(5)

(6)

(7)

(8)

Where O_i is the actual value of the contraction strain of the reinforced concrete specimen, O_i is the predicted value of the contraction strain of the reinforced concrete specimen, Ō_s is the average value of the actual value of the contraction strain of the reinforced concrete specimen, C̄_i is the average value of the predicted value of the contraction strain of the reinforced concrete specimen, and n is the number of data points.

Table 5 shows the specific comparison of prediction accuracy between existing and modified reinforced concrete specimen shrinkage models. It can be seen that the R-value predicted by the revised RC specimen shrinkage model is higher than the existing reinforced concrete specimen shrinkage model, while the MSE, MAPE and IAE are smaller than the existing reinforced concrete specimen shrinkage model. Fig. (7) compares the predicted value of the existing reinforced concrete specimen shrinkage model and the modified reinforced concrete specimen model with the experimental value. It can be seen that for the existing reinforced concrete specimen shrinkage model, most of the experimental data points fall at the lower side of the Y=X line, indicating that the existing reinforced concrete specimen shrinkage model underestimates the reinforced concrete specimen shrinkage on the whole. For the modified reinforced concrete specimen shrinkage model, the data points are evenly distributed on both sides of Y=X, indicating that the modified model can accurately predict the reinforced concrete specimen shrinkage.

Fig. (7). Comparison of actual and simulated shrinkage values.