# Durability Investigation of Fiber-Reinforced Functionally Graded Concretes in Cold Regions
## 2 Test Methods and Proportioning Model
### Early Crack Resistance Test  
The difference between the internal and external temperature of the mass concrete and the drop in external temperature cause temperature shrinkage, and restraint is inevitable in the actual project, which inevitably leads to tensile stresses within the concrete. Moreover, the tensile strength of concrete in the early stages is generally low. Early cracking occurs when the internal tensile stress caused by shrinkage exceeds the tensile strength of concrete, and the appearance of cracks accelerates the deterioration of concrete and seriously affects the safety and durability of the structure. Therefore, it is essential to study the early cracking resistance of concrete [28]. The early crack resistance test was conducted using the flat-plate method with a test temperature of 20 \({}^{\circ}\)C and relative humidity of 60%, subject to 24 h crack data after pouring. The test results are shown in Table 3.  
According to the evaluation method stipulated in the Concrete Durability Inspection and Evaluation Standard (JGJ/T 193-2009), it can be seen that the early crack resistance grades of concretes #2, #4, and #5 all reach level IV, as shown in Table 3. However, with excellent crack resistance performance, concretes #3 and #6 had significantly improved crack resistance due to the incorporation of imitation steel fibers, with their crack resistance grade reaching level V. On the other hand, the early crack resistance grade of the #1 specimen of ordinary concrete was III, which is relatively poor. Figure 5 shows the results of the concrete cracking characteristics for the six different ratio groups. As shown in Figure 5, by comparing the crack characteristics of #3 and #6 with #1, #2, #4, and #5, whether with the mix ratio of C35 or C40, the cracks of #3 and #6 with increased fibers were both few and without obvious directionality, showing excellent crack resistance. On the other hand, the average cracking area and quantity of concrete cracks in ratios #2 and #4 did not increase much, because the polypropylene imitation steel fibers incorporated in #3 and #6 have excellent crack-arresting and matrix-strengthening functions. In addition, the cracked fiber grid system forms a whole with the cement stone when microcracks occur in the cement stone structure under external forces, thus dispersing the fracture stress to other parts. Figure 6 shows the concretes' early cracking resistance analysis results. The different contents of fly ash and mineral powder play an essential role in the early cracking resistance of concrete in terms of the initial cracking time, as shown in Figure 6a. The initial cracking time was significantly delayed for C35 and C40 concrete mixed with higher amounts of fly ash and mineral powder. The trend of initial cracking time was similar between C35 and C40, and slightly similar between #2, #3, #5, and #6. The greater the mineral admixture content, the longer its initial cracking time, and the early cracking resistance of #2, #3, #5, and #6 is good. This is because polycarboxylic acid water reducer is an efficient surfactant, which can effectively reduce the internal capillary tension of concrete. Furthermore, the slow-setting component makes the setting time of the concrete longer. The early hydration of cement is relatively reduced, the volume reduction of the cementie is low, and the deformation ability of the concrete before setting reduces the shrinkage stress due to early shrinkage. The creep performance of this concrete shows enhanced creep ability, effectively reducing the risk of concrete cracking. Figure 6b shows the number of cracks per unit