## 3 Results and Discussion
### Crack Propagation Life Analysis
#### 3.4.4 Calculated Crack Propagation Life  
The fatigue crack propagation life of the cable-girder anchorage zone of Heilongjiang Bridge was obtained through integration of the Paris formula as described in Equation (4), from initial crack size \(a_{0}\) to critical crack size \(a_{c}\).  
The calculated results of crack propagation life in an anchorage structure under different service conditions are listed in Table 4. The critical crack size of the upper crack tip \(a_{c,upper}\) is smaller than that of the lower crack tip, so the crack propagation life of the upper crack tip \(N_{upper}\) is thus conservatively taken as the \(N\) of the cable-girder anchorage zone.  
As shown in Table 4, when we compare operating cases I and II both serviced under room temperature, we can see that the higher the stress level is, the shorter the fatigue crack propagation life becomes. When the low-temperature effect is taken into account for the cable force range, the stress range increases by 19% and the fatigue crack propagation life of the structural detail is reduced by 27% accordingly. A comparison of operating cases II and III in Table 4, which are serviced under the same load magnitude, reveals that low temperature is beneficial in terms of the fatigue crack growth rate, and the fatigue crack propagation life of the structural detail increases to 2.1 times that at room temperature. Considering the effect of low temperature on both load response and fatigue resistance, the fatigue crack propagation life of the anchorage structure at low temperature is about 1.6 times that in normal operating conditions. Low temperature shows no adverse effect on crack propagation life, and operating case II corresponding to the fatigue test yields the most unfavorable results.  
It is worth emphasizing that steel tends to become brittle at low temperatures, and the above conclusion might seem counterintuitive. Fracture toughness at low temperatures is smaller than at room temperature, as shown in Tables 2 and 3. However, bridge steel toughness is high even at low temperatures, and brittle fracture potential is small (Section 3.4.2). Fracture toughness mainly determines the crack size \(a_{\mathit{cf}}\), considering fracture instability. The critical crack size \(a_{\mathit{c}}\) is controlled by geometry boundaries and plays little role in fatigue propagation life (discussed further in Section 3.4.5).  
On the contrary, the crack grows much slower at lower temperatures, as shown in Tables 2 and 4. Even with a slightly larger initial crack size of \(a_{0}\), the calculated fatigue crack propagation life is longer. Therefore, low temperature has a beneficial effect on crack propagation life as opposed to room temperature. Nevertheless, the conclusion is only valid for the structure and loading considered; cautions must be exercised beyond the scope of the conducted work.  
When dividing \(N\) by the yearly stress cycles of the anchor box, its fatigue crack propagation life can be expressed in years. As the standard cable distance of the Heilongjiang Bridge is 12 m, only one stress cycle is caused by the passing of one fatigue vehicle [28]. Based on Chinese technical standards [29], the number of stress cycles experienced by a single lane in 100 years of service is 100 \(\times\) 365 \(\times\) 15,000/2 = 2.74 \(\times\) 10\({}^{8}\). When computed according to the predicted traffic volume in engineering drawings of the bridge, the number of stress cycles becomes 100 \(\times\) 365 \(\times\) 3738/2 = 6.9 \(\times\) 10\({}^{7}\). Fatigue crack propagation life in years is listed in the last column of Table 4, with data before and after \"/\" being calculations from stipulated and forecasted traffic volume, respectively. For all three cases, the remaining fatigue life is in the order of 1-10 years.