# Durability Investigation of Fiber-Reinforced Functionally Graded Concretes in Cold Regions
## 2 Test Methods and Proportioning Model
### Shrinkage Performance Tests
#### 2.1.2 Self-Drying Shrinkage  
Concrete self-drying shrinkage is defined as the shrinkage deformation under sealed conditions due to the reduction in relative humidity inside the cementitious material system. Generally, the limit value of ordinary concrete shrinkage strain is only 100 \(\times\) 10\({}^{-6}\) microstrain, the impact of which can be ignored from a practical point of view. However, the influence of drying shrinkage needs to be considered. The high-strength concrete exhibits earlier, faster, and more pronounced self-drying shrinkage because of the large amount of cementitious materials and low water-to-cement ratio. These observations confirm that the drying shrinkage of high-strength concrete is much more less than the self-drying shrinkage (about 3:7). On the other hand, the self-drying shrinkage of high-strength concrete increases sharply in the initial stage and then increases slowly over time, and more than 90% of the self-drying shrinkage occurs in the first 28 days. Therefore, self-drying and drying shrinkage must be considered for high-strength concrete under dry conditions. The self-drying shrinkage test was conducted by the non-contact method in this study, and an integrated concrete shrinkage deformation tester was used to measure the concrete shrinkage deformation. The concrete surface was covered with film after forming, demolded after two days of curing, put into a standard curing room for three days, and then kept at a temperature of 20 \({}^{\circ}\)C and humidity of 60% for the self-drying shrinkage test. The drying shrinkage of concrete was used to evaluate the self-drying shrinkage characteristics, and the self-drying shrinkage was calculated by Formula (2):  
Figure 3: Trend of drying shrinkage with age for benchmark concretes of different strength grades and parts. \[\varepsilon_{st}=\frac{(L_{10}-L_{1t})+(L_{20}-L_{2t})}{L_{0}} \tag{2}\]  
where \(\varepsilon_{st}\) is the autogenous shrinkage of concrete for a test period of \(t\) days, \(t\) is the time of measuring the initial length, \(L_{10}\) is the initial reading of the left non-contact displacement transducer (mm), \(L_{1t}\) is the reading of the left non-contact displacement transducer for the test period \(t\) (mm), \(L_{20}\) is the initial reading of the right non-contact displacement transducer (mm), \(L_{2t}\) is the reading of the right non-contact displacement transducer for the test period \(t\) (mm), and \(L_{0}\) is the measurement distance of the specimen (mm), which can be defined as the specimen length minus the sum of the length between the two reflective targets buried along the specimen's length. Figure 4 shows the test results of self-drying shrinkage from the #1 to #6 concrete specimens. It can be seen that the self-drying shrinkage of the internal concrete of the bearing (C35) of proportion #2 and the external concrete of the bearing (C35) of proportion #3 was significantly lower than that of the regular C35 concrete of proportion #1. Similarly, the self-drying shrinkage rates of the internal pier (C40) concrete of mix ratio #5 and the external pier concrete of mix ratio #6 were also much lower than that of the ordinary C40 concrete of mix ratio #4. Moreover, the normal concrete with ratio #4 had the most considerable self-drying shrinkage, because its cement component is significant. The exothermic heat of hydration was mainly concentrated in the early stage. The total self-drying shrinkage was reduced, and slowed down the shrinkage rate of the concrete, because of the inclusion of fly ash and mineral powder at the location of the bearing and pier. Figure 4 shows that the growth rate of self-drying shrinkage was significantly reduced with the increase in fly ash and mineral powder, and the shrinkage curve becomes gentle when comparing #2 and #3 with the other mix ratios. This can be explained by the micro-aggregate effect of fly ash. The fine particles of fly ash are uniformly dispersed in the cement paste, and become the core of many hydrate deposits.