# Durability Investigation of Fiber-Reinforced Functionally Graded Concretes in Cold Regions
## 2 Test Methods and Proportioning Model
### Shrinkage Performance Tests
#### 2.1.1 Drying Shrinkage  
The drying shrinkage is irreversible after the concrete stops curing and loses the adsorbed water in the internal capillaries and gel pores to unsaturated air. Drying shrinkage may occur on one surface of the concrete member or all surfaces of the concrete member, and has a relatively long development process compared to autogenous shrinkage. The test was carried out using a vertical concrete shrinkage apparatus, and the prism specimen size was 100 mm in depth by 100 mm in width by 515 mm in length. Six concrete categories from Group 1 to Group 6 were selected with proportions as shown in Table 1, and three identical specimens were produced for each category. The surface of the concrete specimen was covered with film after forming during the test, and the mold was demolded after curing for two days, then put into the standard curing room for three days, and then moved to a constant temperature of 20 \({}^{\circ}\)C and humidity of 60% for the drying shrinkage test. After determining the specimen's initial length, the deformation readings of the specimen were measured at intervals of 1 d, 3 d, 7 d, 14 d, 28 d, 45 d, and 60 d. The arithmetic mean of the test results of each ratio is the early shrinkage determination value of the concrete specimens of that ratio. Formula (1) calculates the drying shrinkage \(S_{t}\):  
\[S_{t}=\frac{L_{0}-L_{t}}{L_{b}} \tag{1}\]  
where \(S_{t}\) is the drying shrinkage of concrete for a test period of \(t\) days, \(t\) is the time of measuring the initial length, \(L_{0}\) is the initial reading of the specimen length, \(L_{t}\) is the measured length of the specimen at test period \(t\), and \(L_{b}\) is the vertical concrete shrinkage meter to measure the distance.  
Figure 2: Shrinkage test.  
The drying shrinkage test results are shown in Figure 3. Concrete #4 with the maximum cement amount has the most extensive drying shrinkage, with 321.7 \(\times\) 10\({}^{-6}\) for 28 d and 345.1 \(\times\) 10\({}^{-6}\) for 60 d. The drying shrinkage value decreases with the increase in mineral admixtures such as fly ash and mineral powder when the total amount of cement material is the same. It can be explained that the addition of fly ash slows down the degree and speed of hydration of cementitious materials in the concrete [10]. Moreover, its micro-aggregate effect fills the capillary channels in cementie, blocking some of the C-H-S gel pores and compacting the internal structure of the concrete. This makes the evaporable concrete channels more curved, making it difficult for water to evaporate, reducing the dry shrinkage value of concrete under exposure to atmospheric conditions. By comparing the drying shrinkage of the six group specimens' mix ratios, it can be seen that the composite anti-freezing and shrinkage-reducing polycarboxylic acid water reducer has a noticeable shrinkage-reducing effect. Therefore, the drying shrinkage value of the concrete used for the exterior of the bearing and pier is much lower than that of the ordinary concrete of the same strength grade.