# Life Cycle Assessment of Bridges Using Bayesian Networks and Fuzzy Mathematics
## 4 Case and Results
### Operation and Maintenance  
According to the design codes for bridges and culverts in China (JTJ)021-89, 024-85, 023-85, 004-89), the service life of a cable-stayed bridge is 100 years. To ensure the safety and normal use of the bridge during the design reference period, the maintenance department should carry out regular maintenance and repair. The maintenance cycle is shown in Table 3.  
The existing carbonization models are basically divided into four categories: theoretical models [59], empirical models [60], semi-theoretical and semi-empirical models [61], and random models [62]. The theoretical model of carbonization depth can be simplified as:  
\[\text{X}=\text{k}\sqrt{\text{t}} \tag{8}\]  
where X is the carbonization depth; t is the carbonation reaction time; and k is the carbonation coefficient (A comprehensive parameter reflecting the rate of carbonization). The China promulgated GB/T51355-2019 in 2019 stipulates that the calculation formula of C carbonization coefficient is [63]:  
\[\text{k}=3\text{K}_{\text{CO}_{2}}\text{K}_{\text{k1}}\text{K}_{\text{kt}} \text{K}_{\text{gs}}\text{K}_{\text{F}}\text{T}^{0.25}\text{RH}^{1.5}(1-\text {RH})\bigg{(}\frac{58}{\text{f}_{\text{cu,e}}}-0.76\bigg{)} \tag{9}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Duration of** & **Total** & **Main Tower** & **Working** & **Equipment** & **Managed** & **Construction** \\
**Bridge** & **the Hanging** & **Basket** & **Period** & **Lifting** & **Power** & **Weight** & **Personnel** & **Worker** \\
**Name** & **(Days)** & **(Days)** & **Equipment** & **(kwh)** & **(Tonnes)** & **(Persons)** & **(Persons)** & **(Persons)** \\ \hline SQ & 255 & 729 & Tower crane & 90 & 78.54 & 24 & 260–320 \\ EH & 495 & 601 & Tower crane & 82.4 & 72.15 & 28 & 280–340 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Data summary table for construction. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **SQ, EH Maintenance and Repair Cycle** & \\ \hline
**Material** & **Damage Mechanism** & **Cycle** \\ \hline Steel & Aging; carbonization; rust; chloride salt corrosion; & Maintenance/1 Year \\  & freeze-thaw environment; sulfate corrosion; alkali & Inspection and repair/2 Years \\  & aggregation reaction & Maintenance and repair/70 Years \\ \hline Expansion joint; Waterproof & Wear; aging; chloride salt corrosion; freeze–thaw & Maintenance/1 Year \\ level; Bridge deck pavement & environment; sulfate corrosion; destruction & Inspection and repair/2 Years \\ Main beam; Anti-collision & Shock; vibration; overload; uneven settlement; & Replacement/10 years \\ guardrail; Bridge deck & chloride salt corrosion; freeze–thaw environment; & Maintenance/1 Year \\ drainage; Lighting & sulfate corrosion; alkaline material reaction & Replacement/50 Years \\ Paint for caps; Piers and beams & Chemical attack; abrasion; erosion; aging; chloride & Maintenance/1 Year \\ salt attack; freeze–thaw environment; sulfate attack & Replacement/55 Years \\  & Maintenance/1 Year \\  & Chemical attack; wear; impact; aging & Inspection and repair/5 Years \\  & Replacement,255/ears \\ Main Galasso & Chemical corrosion; vehicle overload and & Maintenance/1 Year \\  & insufficient maintenance & Inspection and repair/5 Years \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Maintenance and repair data.