PSI - Issue 84

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

1315

The risks first increase, then this increase approaches zero towards the end of the service life. This behaviour is attributed to the interplay of the failure probability over time (Figure 1) with changing inclinations and the exponential influence of the discounting rate of 2% reflecting the average annual economic growth in Denmark and Sweden. Towards the end of the of the service life, the failure probability increase becomes lower and the discounting leads to zero increasing risks over time. Here, the emissions risks are negligible (Section 2.1). In Figure 3, both the intact and failed states of the bridge are considered with their respective complementary probabilities. The intact system state utility is based on the operation cost and benefits (Øresundsbro Konsortiet I/S (2024) over time with discount rate of 2%. It should be noted that the failure probabilities are relatively small and that the probability of an intact system state is close to 1.0. This results in the dominance of the expected benefits over time. The temporal behaviour of the expected benefit is dominated by discounting and the slowly decreasing probability of an intact system state is negligible.

Total risks and emissions Risks and emissions Direct risks Indirect risks Exp. emmission risks Exp. operational cost, emissions and benefits

DKK 1-900-000-000.00

DKK 1-400-000-000.00

DKK 900-000-000.00

DKK 400-000-000.00

-DKK 100-000-000.00

25

50

75

100

125

150

175

200

Annual risks and emissions in E[DKK]

Service life year

Figure 3: Expected benefits, risks and expected emission for the High Bridge failure state. When only looking at the time span from 100 years to 200 years (Figure 4), the expected benefits still dominate. However, during these years, the relative contribution of the indirect risks increases towards the end of the 200 year service life.

Total risks and emissions

DKK 180-000-000.00

Risks and emissions

DKK 130-000-000.00

Direct risks

Indirect risks

DKK 80-000-000.00

Exp. emmission risks

DKK 30-000-000.00

Exp. operational cost, emissions and benefits

-DKK 20-000-000.00 Annual risks and emissions in E[DKK]

100

125

150

175

200

Service life year

Figure 4: Expected benefits, risks and expected emission for the High Bridge failure state towards the end of the service life.