PSI - Issue 84

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

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The load models in Eurocode 1 part 2, hereinafter EC1-2, were calibrated on a heavily trafficked route (Bruls et al., 1996), but most bridges are unlikely to experience such high levels of traffic loading over their lifetime. Besides, the load to be used in structural verifications has not generally received as much attention as the resistance. Using site-specific traffic data to assess existing structures allows for structural verifications with realistic load effects, yet in line with the safety levels required by standards and guidelines. Suitable traffic data is typically collected from Weigh-in-Motion (WiM) systems, usually paired with loop detectors. The data typically collected are the Gross Vehicle Weight (GVW), axle load, axle spacing, speed and time headways. The data to be analysed mainly depend on the bridge span: GVWs generally suffice for longer spans, but axle loads are very much relevant for shorter spans, which are governed by free traffic conditions with a dynamic allowance. Data mostly comes from free traffic conditions, since congested events are rarer and some WiM technologies are not able to collect data at low or very low speeds. Congested conditions govern long-span bridges (roughly longer than 40 m), but dynamic effects are not relevant as extreme loading scenarios occur at low speeds. To replicate congested conditions, a queue of vehicles has been traditionally used, whereas more recently some authors have used traffic micro-simulation – see for instance Lipari et al. (2012) or OBrien et al. (2015). It is generally accepted that lower load effects can be used for the structural verification of existing structures, grounded in a reduced remaining service life and in available site-specific data from testing and monitoring, which effectively reduce uncertainties (Caspeele et al., 2013). Typically, partial safety factors are reduced compared to the design case and sometimes are the actions too. For instance, the Italian guidelines on existing bridges allow for verifications with reduced partial safety factors and, in certain cases, for reduced load models (Ministero delle Infrastrutture e dei Trasporti, 2022). In the UK, the Design Manual for Roads and Bridges provides an Assessment Live Loading for highway bridges, but partial safety factors are not reduced (National Highways, 2022). 2. Concepts on reliability analysis and statistics The safety level of a structure is expressed as its probability of failure , P f , for a reference period , t ref , which is typically taken as the design service life for new structures or the residual service life for existing structures. P f is the probability that the safety margin Z = R – S becomes less than or equal to 0, that is R ≤ S (Ghosn et al., 2003), in which R is the resistance and S the load effect. P f is often expressed as a reliability index β . The determination of P f or β is not straightforward, except for particular cases. For instance, when using Gaussian variables, β is given by the ratio of the mean to the standard deviation of Z (i.e., the inverse of the Coefficient of Variation): = = − √ 2 + 2 (1) P f is then related to β through the relation = (− ) , in which Φ is the normal Cumulative Distribution Function (CDF). Reliability analyses are applied to derive the partial safety factors commonly found in codes of practice. The target reliability indices used in the Eurocodes are 3.3, 3.8 and 4.3 for Consequence Classes CC1, CC2 and CC3, respectively, in the 50-year reference period (European Committee for Standardization, 2023b). For existing structures, partial safety factors are generally reduced according to two main methods (Fédération internationale du béton, 2016): the Design Value Method (DVM) and the Adjusted Partial Factor Method (APFM). In short, the DVM computes partial safety factors from the actual distribution of the variables based on site- or structure-specific data, whereas the APFM reduces the partial safety factors used for design by an adjustment factor , thereby implicitly assuming the same statistical distributions considered for design. The APFM is generally more conservative than the DVM (Gino et al., 2020). The characteristic value of an action is the value chosen to correspond to a prescribed probability of not being exceeded unfavourably during a specified reference period (European Committee for Standardization, 2023b), i.e., the probability of non-exceedance F , which can also be expressed as a return period T , defined as the average number of years (or other time unit) in which an action is exceeded once (European Committee for Standardization, 2023b). For a generic reference period n, which may be taken equal to t ref , the two variables are linked through the relation: