PSI - Issue 84

Alessandro Lipari et al. / Procedia Structural Integrity 84 (2026) 615–622

620

6. A case study In this section, a sample bridge with a single 50-m span is considered. For this span length, congested conditions govern. As described in Lipari et al. (2012), congestion was induced in a micro-simulation tool, based on a recorded traffic dataset, and mid-span bending moments were computed through influence lines. The bridge is assumed to be in the lower class of CC3. 6.1. The dataset The input vehicle stream is made up of about three months of traffic recorded on the A4 motorway (part of the European route E40) near Wroclaw, Poland (Lipari et al., 2012, Caprani et al., 2012). In order to simulate congestions, the original flow was manipulated to increase the inflow Q in up to 1500 veh/h while keeping the original traffic proportions. The injected traffic contained 21.2% of trucks, i.e., vehicles with GVW > 3.5 t. The truck GVWs were mostly low (about 54% below 7.5 t), but there were also 4.6% of overloaded trucks (GVW > 44 t). Two and a half hours of traffic were injected, which resulted in every congestion event lasting about 4 hours. Here, it is conservatively assumed that such a congestion event occurs once every working week. As such, under the assumption of 250 working days (50 working weeks) per year, this corresponds to five years of traffic. 6.2. The traffic simulation The Intelligent Driver Model (IDM) was used to simulate the traffic. The IDM is a car-following model which gives a good match with observed congested traffic, while having relatively few parameters (Treiber et al., 2000). The motion of each vehicle is based on an acceleration function: = [1−( ( ) 0 ) 4 −( ∗ (( ) ) ) 2 ] (7) in which a is the maximum acceleration ; v 0 , the desired speed ; v ( t ), the current speed; s ( t ), the current gap to the vehicle in front; s* ( t ) the minimum desired gap , given by: ∗ ( ) = 0 + ( ) + (2 )√ ( ) (8) in which the term s 0 is the minimum bumper-to-bumper distance ; T , the safe time headway ; Δ v ( t ), the velocity difference between the current vehicle and the vehicle in front; b, the comfortable deceleration . The model parameters were: v 0 = 120 km/h (cars) and 80 km/h (trucks), T = 1.6 s, a = 0.73 m/s 2 , b = 1.67 m/s 2 and s 0 = 2 m. A 5000-m-long road was simulated, containing the sample bridge. Congestion was induced by artificially increasing the safe time headway T downstream of the bridge up to a value T’ = 6.4 s ( inhomogeneity ). This generated a heavily congested pattern, named Homogeneous Congested Traffic (HCT) (Treiber et al., 2000), with an average speed of 7.5 km/h. The maximum midspan bending moments for each weekly congestion event were recorded. The mean of the simulated maxima μ’ was 7133.7 kNm, whereas their standard deviation σ’ was 783.6 kNm. The maximum bending moment in the simulations was 9451.5 kNm. The fitted Gumbel distribution parameters are μ = 6781 and σ = 611.0, whereas the fitted GEV parameters are μ = 6842, σ = 624.9 and ξ = -0.0749, thus resulting in a Weibull distribution (Type III). Despite being μ and σ comparable to those of the Gumbel distribution and ξ close to zero, the two distributions significantly diverge as the SEV and T increase (Fig. 2). Differences between T = 1000 and T = 50 years are in the order of 10%, which accords with other studies (Enright and OBrien, 2013). Table 2 lists the characteristic (unfactored) and design (factored) values of bending moments according to LM1, GEV distribution based on traffic data, and the two heaviest CdS models from the Italian guidelines. 6.3. The load effects