Abstract
The reliability of engineering structures and infrastructure is a critical requirement to ensure a continuous functionality throughout their expected service life. The lifespan extension of concrete structures—especially those belonging to critical infrastructure—is vital to the sustainability and resilience of the whole built environment. This investigation explores the potential to extend the service lifetime of concrete structures by considering the role of modern design codes and conformity standards on concrete production in combination with reliability-based safety concepts applied to the resistance side. The study demonstrates how evaluation criteria derived from empirical concrete samples influence the service life of structures and, in consequence, the safety format established in international codes. The results suggest that by considering measures of concrete variability—as the coefficients of variation—and integrating them into a quality control system, hidden safety margins can be identified and, ultimately, activated to extend the service lifetime of structures. Therefore, this investigation contributes to the sustainable development of infrastructure ensuring that future demands on infrastructure can be met while maintaining high safety standards.
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All data generated and analysed during the current study are available from the corresponding author upon reasonable request.
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Acknowledgements
The Authors are very thankful to ASFINAG and to ÖBB-Infrastructure AG.The sole responsibility for the content of this publication lies with the Authors and it does not necessarily reflect the opinion of ÖBB-Infrastructure AG. The Authors would like to express their gratitude to Dr. W. Pichler (Matcon), Dr. C. Saywald (ÖBB-Infrastructure AG) and to o.Univ.Prof. Dipl.-Ing. Dr.phil. Dr.techn. K. Bergmeister, MSc. PhD. (BOKU) for the valuable contribution throughout this investigation. The support of Mr. T. Lux, MSc. (TU Dortmund University) with the edition of the graphics presented in this manuscript is warmly thanked.
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Saeideh Faghfouri: Data curation, Formal analysis, Investigation, Methodology, Analysis, Software, Validation, Visualization, Writing—Original Draft, Writing—Review & Editing. Tânia Feiri: Formal analysis, Investigation, Validation, Visualization, Writing—Original Draft, Writing—Review & Editing. Marcus Ricker: Formal analysis, Supervision, Validation, Visualization, Writing—Review & Editing. Alfred Strauss: Conceptualization, Formal analysis, Funding acquisition, Methodology, Resources, Project administration, Supervision, Validation, Writing—Review & Editing.
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Appendix 1: Iterative procedure to determine the statistical parameters of the lognormal distribution
Appendix 1: Iterative procedure to determine the statistical parameters of the lognormal distribution
To determine the coefficient of variation (COV) and the standard deviation \(\sigma\) of the lognormal distribution from given mean value and a 5 \(\%\) fractile (quantile), an iterative procedure was considered. Let’s assume that the mean value \({f}_{cm}\) is known, for example, \({f}_{cm}\) = 38 MPa for concrete class C25/30 under water curing conditions (Table 8). The 5 \(\%\) fractile is taken as \({f}_{ck}\) = 30 MPa for this concrete class. The objective is to find parameters of the lognormal distribution that reproduce these two statistical properties. For a Lognormally-distributed variable \({f}\), the relationship between the mean \({f}_{cm}\), the standard deviation \(\sigma\) and the parameters for the underlying normal distribution—\(\lambda\) (mean of the logarithmic variable) and \(\xi\) (standard deviation of the logarithmic variable)16—is given as:
with the parameter \(\lambda\) and \(\xi\) being determined as:
Note that the parameters \(\lambda\) and \(\xi\) fully define the lognormal distribution. To identify a consistent pair of COV and \(\sigma\), an iterative loop is performed:
- 1.
Start with an initial estimate of the COV.
- 2.
Compute the corresponding standard deviation \(\sigma \, = \text {COV} \cdot {f}_{cm}\).
- 3.
- 4.
Determine the 5 \(\%\) quantile \({f}_{ck.calc}\) of the resulting lognormal distribution, using the inverse transformation of the normal distribution: \({f}_{ck.calc}\) = \(\text {exp}\) ( \(\sigma\) + \({z}_{0.05}\) · \(\zeta\)) with \({z}_{0.05}\) = – 1.645 being the 5 \(\%\) quantile of the standard normal distribution.
- 5.
Compare the calculated \({f}_{ck.calc}\) with the target value \({f}_{ck}\) = 30 MPa.
- 6.
Adjust the COV and repeat the process until the calculated quantile matches the target value within an acceptable tolerance.
Once convergence is achieved, the resulting values of COV and \(\sigma\) are consistent with the specified mean strength \({f}_{cm}\) and 5 \(\%\) characteristic strength \({f}_{ck}\).
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Faghfouri, S., Feiri, T., Ricker, M. et al. Probabilistic modelling of material properties based on structural design and testing standards and its impact on the assessment of structural service life. Sci Rep (2026). https://doi.org/10.1038/s41598-026-42352-y
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DOI: https://doi.org/10.1038/s41598-026-42352-y
