Cross-Passage Blockage Probability in Railway Tunnels: A Geometric-Probabilistic Contribution to Collective Risk Assessment

This study examines whether a train fire near an evacuation interface in a railway tunnel can create an adverse configuration relevant to evacuation design and collective risk assessment. It focuses on twin single-track tunnels, in which the parallel tunnel serves as a safe area, and evacuation is carried out through cross-passages and boundary portals. If a fire impairs such an interface, evacuees may be forced to continue to a more distant exit. The problem is formulated as a geometric-probabilistic screening task. The model calculates the probability that, after the train has stopped, the fire lies within a tolerance zone around an evacuation interface. The probability is derived analytically using deterministic convolution and verified via Monte Carlo simulation for trains with lengths of 200 m and 400 m. This verification concerns mathematical calculation only, not the physical, smoke, operational, or evacuation assumptions. The geometric probability is linked to collective risk through representative train fire frequencies, external consequence indicators, and selected F/N criteria. With ε = 37 m and portals included as boundary evacuation interfaces of the finite tunnel domain, the adverse-configuration probabilities are similar: approximately 14.0% for the 200 m train and 14.6% for the 400 m train. The difference becomes decisive only after considering the magnitude of the consequences and the traffic intensity. Under the reference assumptions, the 400 m high-occupancy case reaches the selected Dutch criterion at about four train passages per day. A fire near an evacuation interface, therefore, cannot be treated as marginal solely because the tunnel meets the 500 m cross-passage spacing requirement. Acceptability depends on geometry, occupancy, fire frequency, the definition of consequences, traffic intensity, and the selected risk framework. The homogeneous fire-origin distribution is used only as a neutral first-order assumption; more refined spatial fire-origin models and broader comparisons across safety criteria are needed.