PSI - Issue 84

Sebastian Thöns et al. / Procedia Structural Integrity 84 (2026) 1310–1317

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2.1. Environmental impact analysis The environmental impact is characterised in terms of carbon dioxide equivalent emissions associated with the life cycle phases of material production em,prod E , construction em,const E , operation em,op E , and decommissioning em,dec E . Emissions from material production, construction, and portions of the operational phase have already occurred and are therefore irreversible. As a result, the absolute emissions from the material production and construction phases may appear substantial. However, these emissions should be assessed in relation to the service life of the system through the temporal emission intensity I,em E : ( ) I,em em,prod em,const em,op em,dec SL E E E E E / t = + + + (12) To enable aggregation with expected costs, consequences, and benefits (see previous Sections), emissions are monetised. This monetisation is based on projected damages to human health, ecosystems, and social assets, with impacts on human health accounting for approximately 70–97% of the total damage (Dong, Hauschild et al. (2019)). The monetary value of emission consequences ( ) em I ,em SL C E ,t is calculated and transferred to present values with expected damage cost of 150.00 US$ (2017) per tCO₂eq, as derived from the range of studies synthesised in Dong, Hauschild et al. (2019). 3. System performance quantification: expected benefits, costs, consequences and emissions A high bridge failure of the Øresund Fixed Link is considered and the risks, expected benefits and expected emissions are quantified for the original service life of 100 years and envisaged service life of 200 years. The bridge failure scenario is calculated with fatigue in relation to the highly utilised orthotropic plate and the stay cables. The structural reliability for steel fatigue is determined using a SN damage accumulation according to the design documentation. For the case of a monotonically increasing damage and constant damage, the maximum probability of fatigue damage in a time period equals the actual probability of fatigue damage, i.e.: ( ) ( ) ( ) ( ) ( ) 1 0 t T max P F t P g t T t D   = = = = −     (13) In Equ. (13),  is the fatigue damage capacity, D is the yearly fatigue damage caused the fatigue stress ranges,  is the annual number of stress cycles, and t is time in years. For the two-parameter Weibull distribution of fatigue loads, the expected value of the stress ranges m E      can be calculated with scale parameter k and shape parameter  and a two-slopes SN curve with parameters K , 1 m , 2 m (EN 1993-1-1 (2005)) and constant amplitude fatigue limit (Ayala-Uraga and Moan (2007)). The random variable M represents the model uncertainty: ( ) 1 2 m CAFL E WBL ,k,K,m ,m , ,M         (14) The probabilistic model documented in Table 2 is adopted here based on values provided in the scientific literature. The annual number of stress cycles  , the accumulated damage ( ) d D T at the end of the design life d T , and the partial safety factors for loading and resistance are modelled according to the design documentation.

Table 2: Probabilistic model for fatigue reliability analysis Parameter Dim. Dist.

Exp. value

Stand. dev.

Reference

MPa Det.

Calibr.

Scale parameter k

Weibull shape parameter 

-

Det.

1.6

Imam Boulent, Righiniotis Timothy and Chryssanthopoulos Marios (2008) for railway fatigue loads

Loading model and nominal stress uncertainty M

Norm. 0.80

0.14 Imam,

Chryssanthopoulos

and

Frangopol (2012)