**5.1. Application of microsimulation to bridge loading**

An application of traffic microsimulation to long-span bridge loading is presented for a stretch of a two-lane same-direction 8000 m long highway, based on [60]. The microsimulation is carried out using the car-following IDM (Section 2.4.1) and the lane-changing model MOBIL (Section 2.4.2). In order to highlight the influence of several traffic features on bridge loading, a simplified vehicle stream made up of two classes of vehicle, cars and trucks, is used with the parameters shown in **Table 4**. Real sites are likely to have a more complex traffic stream, but site-specific traffic data could be equally introduced [87].

The car-following parameters are based on those calibrated and used in [36], who used only identical vehicles to successfully replicate obseved congestion patterns, as described in Section 2.4.1. Trucks are introduced here and assigned greater length and weight and slower desired speed [88, 89]. Other truck parameters are kept the same as the parameter set in [36], as consideration of different parameters is not strictly necessary to reproduce congested patterns [36, 58].

The desired speeds, *v*0, of both vehicle classes are uniformly randomly distributed. Although the desired speed governs the free traffic behaviour in the IDM, it is necessary to introduce speed randomness in order to correctly model lane-changing manoeuvres [59]. Trucks are assigned mean Gross Vehicle Weight (GVW) equal to the European minimum legal limit of 44 t [90, 91] and the GVW is considered normally distributed with a Coefficient of Variation (CoV: standard deviation divided by the mean) of 10%. Those two assumptions can be easily adapted to a specific site, as truck GVWs and speed histograms can be computed from WIM.

Cars and trucks are assigned the same MOBIL parameters, as calibrated in [15]. However, the assigned difference in the IDM desired speed, *v*0, has also the desirable effect of making trucks less prone to undertake a lane-changing manoeuvre. Notably, bridge loading is not found to be significantly sensitive to the lane-changing parameters [15].

Two long-span bridges (200 and 1000 m long) are centred at 5000 m. The dynamic capacity Qout is 3070 veh/h for a flow with 20% trucks. A range of bottleneck strengths Δ*Q* is generated downstream of the bridge by locally increasing the safe time headway *T* from 1.6 s to the values of 1.9, 2.2, 2.8, 4.0 and 6.4 s, thereby inducing the following traffic states: SGW, OCT, HCT/OCT, HCT(1) and HCT(2). HCT(1) and HCT(2) differ for the average speed of traffic (approximately 8.7 and 5.0 km/h). The full-stop condition (FS) is also simulated, for which Δ*Q*= *Q*'out.

It is assumed that congestion occurs for one hour during every working day (i.e. 250 times per year). One-year equivalent of traffic is simulated for each bottleneck strength. The hourly/daily maxima of total load are captured for subsequent statistical extrapolation with the Block Maxima approach, as described in Section 3.1. Note that load effects, such as shear or bending moment, may be equally output. However, this requires the choice of a structural form for the bridges. Since such forms may be quite different for long spans, the total load is used here to maintain generality.
