## 4 Bridge Deck Waterproof Cohesive Layer Interlayer Design Method
### Design Example  
Taking the cement concrete bridge around the southern city of Ulanchabu in Inner Mongolia as an example, the bridge is a two-way, four-lane road with a bridge deck thickness of 10 cm and a design life of 12 years. The average annual growth rate of traffic volume is 6%. According to the fatigue equivalent principle of the bonding material, \(N_{1}\) is 4690 repetitions/day, and \(N_{e}\) is 1.44 million repetitions. Air temperature was provided by the National Meteorological Information Center of China Meteorological Administration ([[http://data.cma.cn/](http://data.cma.cn/)]([http://data.cma.cn/](http://data.cma.cn/))), and frequency data for the air temperature distribution was determined statistically, as shown in Table 13.  
To determine the effect of temperature on shear fatigue failure, the relationship between the temperature field and the temperature at different depths into the bridge deck pavement was obtained based on research results from [PERSON] and [PERSON] [36], as shown in Equation (13):  
\[T_{d}=0.91T_{a}-0.21d+4.84 \tag{13}\]  
where \(T_{d}\) is the temperature of deck pavement structure (\({}^{\circ}\)C) at an arbitrary depth \(d\), \(T_{a}\) is the atmospheric temperature (\({}^{\circ}\)C), and \(d\) is the distance from any position on the bridge deck pavement structure to the road surface (cm). The temperature distribution at the interlayer position of the bridge deck was calculated using the prediction model for the temperature field and atmospheric temperature distribution. To simplify the calculation, 10 \({}^{\circ}\)C was taken as the representative temperature when the atmospheric temperature was lower than 10 \({}^{\circ}\)C. In other temperature ranges, the intermediate temperature within the temperature range was used as the representative value. The representative values were used in Equation (13) to calculate the temperature and frequency at the interlayer position of the bridge deck. The calculation results are shown in Table 14. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Temperature Range (\({}^{\circ}\)C)** & \(-\)30 to \(-\)20 & \(-\)20 to \(-\)10 & \(-\)10 to 0 & 0 to 10 & 10 to 20 & 20 to 25 & 25 to 30 & 30 to 35 \\ \hline
**Distribution Frequency** & 0.04 & 0.14 & 0.21 & 0.25 & 0.19 & 0.09 & 0.06 & 0.02 \\ \hline \end{tabular}
\end{table} 
Table 13: Frequency data for air temperature distribution in Ulanchabu. The correction coefficient \(Z_{N}\) for the shear fatigue temperature for different waterproof cohesive layer materials and the data in Table 14 were substituted into Equation (5) in order to calculate the equivalent interlaminar shear fatigue temperature. The equivalent temperatures of different waterproof cohesive layer materials were calculated and are shown in Table 15.  
Table 15 shows that the equivalent temperatures calculated for different waterproof cohesive layer materials are different, but they are all near 15 \({}^{\circ}\)C. This is because the shear fatigue lives of different waterproof cohesive layer materials have different sensitivities to temperature, but the equivalent temperature depends more on the local temperature distribution frequency and has little correlation with material. Considering that the indoor fatigue test is continuous loading, the shear deformation is not constrained, but the actual situation is that the pavement layers are constrained, and the driving load is intermittent. Therefore, considering the influence factors such as load intermittence time, crack propagation time, transverse distribution of wheel load, refer to [PERSON]'s research [37; 38], according to the indoor shear fatigue equation for different materials obtained in Table 11, the actual shear fatigue equation is expanded by 100 repetitions [39], as shown in Table 16.  
One can see that the interlaminar shear fatigue check of 90 ordinary hot asphalt does not meet the design requirements, while the interlayer fatigue of SBS-modified emulsified asphalt and SBS-modified asphalt meet the design requirements.