PSI - Issue 78

Amirmahmoud Behzadi et al. / Procedia Structural Integrity 78 (2026) 513–520

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1. Introduction Bridge design codes often rely on deterministic models to estimate braking forces. These models use simplified assumptions about vehicle types, numbers, and deceleration, potentially leading to conservative or non-conservative estimates depending on the scenario. With the advancement of Weigh-In-Motion (WIM) technologies, it is now feasible to derive braking force models grounded in actual traffic behavior. This work introduces a methodology that integrates WIM traffic data and stochastic simulations to estimate braking forces in a probabilistic framework, enhancing design and assessment accuracy for both existing and new bridges. Various standards (e.g., Eurocode EC1-2, Italian standards, BS 5400) propose different deterministic models for braking force. Fig. 1 compares the characteristic value of braking force computed according to EC1-2, Italian standards, SIA 160, and BS 5400. The Eurocode, for instance, assumes a set of five 40-ton vehicles braking simultaneously, resulting in a maximum braking force of 900 kN. The SIA models evolved from assuming a constant braking force to adopting more dynamic representations. British standards tend to be more conservative due to tighter vehicle spacing assumptions. These discrepancies highlight the limitations of deterministic approaches, particularly in their failure to reflect actual traffic variations. Recent developments in traffic modeling have focused on estimating braking forces through probabilistic methods that account for variability in vehicle characteristics, traffic dynamics, and driver behavior, providing a more realistic representation by using distributions derived from real-world traffic data. Martins et al. (2015) introduced a stochastic approach using traffic microsimulation based on Swiss motorway data and driver behavior, showing that braking forces estimated probabilistically are lower than those prescribed by design standards while still satisfying safety levels associated with a 1000-year return period. They also compared deterministic and probabilistic models Martins et al. (2016), demonstrating that the latter align better with the return periods used for vertical loads by accounting for the likelihood of braking events on bridges. Building on this, Breveglieri and Feltrin (2023) developed a model that integrates real traffic data, stochastic variables, and bridge specific characteristics, highlighting the influence of span length, vehicle clustering, and braking frequency on the magnitude of braking forces. Currently, Behzadi et al. (2025) proposed a methodology for deriving a Probabilistic Braking Force Model (PBFM), based on traffic data collected from WIM sensors. The results of the latest reference are presented in this conference paper.

Fig. 1. Braking force models comparison.