# Safety Concept for Textile-Reinforced Concrete Structures with Bending Load
## 5 Reliability Calculation Results
### Influence of the Reinforcement Type  
The influence of the reinforcement type on the reliability index was investigated using specimens reinforced with AR-glass and a carbon textile reinforcement. In the calculations, the type of reinforcement was taken into account by different parameters for the tensile strength \(f_{\mathrm{t}}\) and the Young's modulus \(E_{\mathrm{t}}\). The results are shown in Figure 10.  
According to Figure 10, the shapes of the reliability index curves are similar, independently of the reinforcement type. Only the transition from state A to B occurs for the AR-glass textile reinforcement at a higher reinforcement ratio, which is due to the different tensile strengths. In comparison to AR-glass textile reinforcement, carbon textile reinforcement can withstand significantly larger tensile force \(F_{\mathrm{t}}\) with the same reinforcement ratios \(\rho_{\mathrm{1}}\) presupposed. Thus, to fulfil the equilibrium of forces with the same reinforcement ratio, a greater concrete pressure zone force \(F_{\mathrm{c}}\) is required for carbon textile reinforcement than for AR-glass textile reinforcement. Since the same concrete compressive strength\(f_{\mathrm{c}}\) is assumed for both types of reinforcement, concrete failure occurs in specimens with carbon reinforcement at a lower reinforcement ratio. Figure 9: Reliability indices calculated according to FORM considering an effective depth of \(d=60\) mm: (a) linear \(\sigma\)–\(\varepsilon\) diagram; (b) rectangular \(\sigma\)–\(\varepsilon\) diagram. In state A, a partial safety factor \(\gamma_{\rm T}\) equal to 1.3 for both types of reinforcement and a partial safety factor \(\gamma_{\rm C}\) equal to 1.5 for the concrete are sufficient to achieve the desired safety level of \(\beta_{\rm target}\) equal to 3.8. For a reinforcement ratio of \(\rho_{\rm I}\approx 3.5\%\), the reliability index calculated goes below the threshold of 3.8 by about \(\Delta\beta=0.1\). Due to the governing concrete failure, the safety level can then no longer be significantly increased by applying a larger partial safety factor \(\gamma_{\rm T}\) for the textile reinforcement. From the authors' point of view, the undercutting of the target index of 0.1 is still acceptable. In state C, the reliability index is initially slightly below the target value of \(\beta\) equal to 3.8; however, the value increases for a higher reinforcement ratio. As a result, the calculated reliability indices rapidly reach the threshold value of 3.8. The assumed partial safety factor for the textile reinforcement (\(1.0\leq\gamma_{\rm T}\leq 1.5\)) has no influence on the reliability indices calculated, as the different curves in state C have the same value due to the governing concrete failure. The sensitivity factors for each parameter depending on the reinforcement ratio \(\rho_{\rm I}\) are shown in Figure 11. These factors describe the influence of the different parameters on the reliability index \(\beta\). The sensitivity factors are similar for both types of textiles. In all the three states, it is noticeable that the live load \(q\) has the greatest influence on the reliability index due to its wide scattering. At the same time, it can be observed that the textile tensile strength \(f_{\rm t}\) is a governing factor in state A, while the most influential factor in state C is the concrete compressive strength \(f_{\rm c}\). In total, the sensitivity factor of the impact side \(\alpha_{\rm E}\), which is composed by the sensitivity factor for the model uncertainty of the loading models \(\theta_{\rm E}\) and the sensitivity factors for the dead load \(g\) and the live load \(q\), has a value of approximately 0.9 in state A and approximately 0.8 in state C. Hence, these values exceed the recommendation in EN 1990 (EC0) [21], where \(\alpha_{\rm E,EC0}\) is equal to 0.7. This value is proposed in the code for semi-probabilistic calculations, in which the resistance side can be considered decoupled from the impact side by specifying corresponding constant weighting factors.