## 3 Evaluation of Service Life Using Different Design Approaches
### Service Life Variation with Random Variables (Probabilistic Methods)  
#### 3.4.1 Service Life from the Different Methods Considering Temperature Effect  
The random variables were defined as cover depth, diffusion coefficient, mixture conditions (Al\({}_{2}\)O\({}_{3}\) content), and exterior sulfate concentration. Their probability patterns were assumed to be normal distributions, and the measured results (mean and COV) were adopted for the simulation. For seed generation, 10,000 simulations were performed for each case. A flowchart for MCS (Monte Carlo Simulation) is shown in Figure 11. The PDF (probability of durability failure) with increasing temperature and the comparison of service life from different methods are shown in Figures 12 and 13, respectively. Figure 11: Flowchart for random generation and calculation of failure probability. Figure 10: Reduced service life with increasing exterior temperature. The results in Figure 13 show a consistent trend, showing a gradual reduction in service life with temperature, and the results from the deterministic method provide more conservative results of 1-3 years. In the previous research, more conservative results (reduced service life) were evaluated for carbonation and chloride attack [12; 22]; however, more conservative service life was observed in the deterministic method since the outer steel diameter (13.0 mm) was additionally excluded from cover depth in this simulation. Regarding the temperature effect on service life, the service life decreased to 30.0% for the deterministic method and 31.8% for the probabilistic method, which showed a similar reduction in the results since design parameters have a reasonable level of COV without the time effect. The critical condition (maximum allowable PDF) was set to 10.0% in this study, which is the same as the case of chloride attack. So far, the international codes and specifications (EN, ACI, JSCE, and KCI) have provided a generalized design process without critical PDF since the critical condition for service life judgement can be changed for the importance and maintenance difficulty of the target structures. Regarding the design process, the deterministic method has a strong point with simple load and reduction factor; however, the probabilistic method has further engineering merit, like the consideration of the uncertainty of design parameters, such as the detailed quality condition of cover depth and material properties. Figure 12: PDF with increasing temperature. Figure 13: Temperature effect on service life from different evaluation methods. The analysis results in Figures 14-17 are those of PDF and service life with increasing COV from 0.1 to 0.3 and the multiplied design parameters from 0.5- to 2.0-times under the control condition in Table 4, where the exterior sulfate condition of 200 ppm was considered. Regarding cover thickness, the service life significantly decreased with increasing COV. For 75 mm and 100 mm of cover depth, the difference between COV 0.1 and 0.3 was 11 years and 14 years, respectively, which showed more than 10 years with increasing COV. It is very important to ensure reasonable variation for cover depth, which directly explains detailed construction skills since its COV greatly affects the service life. In the case of Al\({}_{2}\)O\({}_{3}\) content, 37 years, 35 years, and 33 years of service life were evaluated with increasing COV to 0.3 for 0.05% of Al\({}_{2}\)O\({}_{3}\). There was no significant difference compared to a COV of 0.1, and the service life decreased up to 89.2% with the largest COV (0.3). The effect of sulfate concentration and diffusion coefficient on service life also had a similar tendency to Al\({}_{2}\)O\({}_{3}\) since the adopted governing equation used linearly proportional design parameters to the deteriorated depth. For the control condition of 200 ppm, 40 years, 37 years, and 34 years were evaluated with increasing COV, respectively, showing over 10.0% of the service life reduction ratio.