Tunnel Ventilation Analysis Using a Probabilistic Approach: Case Study, Fire in Road Tunnels with Longitudinal Ventilation

Abstract

Tunnels are nowadays key elements in transport networks worldwide. To achieve a safe and efficient operation, a proper integration and design of Mechanical, Electrical and Intelligent Transportation Systems is required. Among these systems, tunnel ventilation is one of the most critical ones from the Fire Life Safety perspective, being smoke control to maintain safe conditions during self-evacuation and rescue operations one of its main objectives. Traditionally tunnel ventilation systems are sized following a deterministic approach. Designers, based on requirements and design criteria from Standards and Recommendations, focus on a limited number of fire scenarios and design parameters to reach a solution considered acceptable from a fire safety perspective. This paper proposes the use of a probabilistic approach to assess, in terms of probability of failure, the capacity of a tunnel ventilation system for fire scenarios. The model applied in the proposed process uses a 1D steady state model based on pressure losses, where critical design variables are considered random (unlike with the deterministic approach) to calculate a failure probability associated to an installed ventilation thrust. A case study example is used to analyse results using both, the traditional deterministic approach and the proposed probabilistic one. Results obtained with the deterministic approach show how, under the same design requirements, tunnels with similar characteristics allow different safety margins for the capacity of the ventilation system. These results are confirmed numerically using the probabilistic approach by evaluating failure probabilities. To avoid this, the paper proposes the use of the probabilistic approach to allow a definition of an equivalent uniform safety margin (to achieve a certain probability of failure) which would be of significant help for designers, administrations and tunnel operators. It is not the aim of the study to define the limit for the probability of failure or to characterise the design variables, but to present a useful tool with which important conclusions about the design criteria can be obtained.

Appendix

$$\begin{aligned} {\mathrm{C}}1 & = {\mathrm{L}} + \frac{{{\dot{\mathrm{Q}}}_{\mathrm{a}} {\mathrm{D}}_{\mathrm{H}} }}{{4{\mathrm{h}}_{\mathrm{app}} {\mathrm{ST}}_{0} }} \left( {1 - {\mathrm{e}}^{{\frac{{4{\mathrm{h}}_{\mathrm{app}} }}{{{{\uprho}}_{0} {\mathrm{C}}_{\mathrm{p}} {\mathrm{D}}_{\mathrm{H}} {\mathrm{W}}}}\left( {{\mathrm{x}}_{\mathrm{fire}} - {\mathrm{L}}} \right)}} } \right) \\ {\mathrm{C}}2 & = \frac{{ - {{\uprho}}_{0} {\mathrm{C}}_{\mathrm{p}} {\mathrm{D}}_{\mathrm{H}} {\mathrm{W}}}}{{4{\mathrm{h}}_{\mathrm{app}} }} {\mathrm{Ln}}\left( {\frac{{\frac{{{\dot{\mathrm{Q}}}_{\mathrm{a}} }}{{{{\uprho}}_{0} {\mathrm{C}}_{\mathrm{p}} {\mathrm{SWT}}_{0} }}{\mathrm{e}}^{{\frac{{4{\mathrm{h}}_{\mathrm{app}} }}{{{{\uprho}}_{0} {\mathrm{C}}_{\mathrm{p}} {\mathrm{D}}_{\mathrm{H}} {\mathrm{W}}}}\left( {{\mathrm{x}}_{\mathrm{fire}} - {\mathrm{L}}} \right)}} + 1}}{{\frac{{{\dot{\mathrm{Q}}}_{\mathrm{a}} }}{{{{\uprho}}_{0} {\mathrm{C}}_{\mathrm{p}} {\mathrm{SWT}}_{0} }} + 1}}} \right) \\ {\mathrm{C}}3 & = \left( {\frac{1}{\mathrm{L}}\left( {{\mathrm{L}} + \frac{{{{\uprho}}_{0} {\mathrm{C}}_{\mathrm{p}} {\mathrm{D}}_{\mathrm{H}} {\mathrm{W}}}}{{4{\mathrm{h}}_{\mathrm{app}} }} {\mathrm{Ln}}\left( {\frac{{\frac{{{\dot{\mathrm{Q}}}_{\mathrm{a}} }}{{{{\uprho}}_{0} {\mathrm{C}}_{\mathrm{p}} {\mathrm{SWT}}_{0} }}{\mathrm{e}}^{{\frac{{4{\mathrm{h}}_{\mathrm{app}} }}{{{{\uprho}}_{0} {\mathrm{C}}_{\mathrm{p}} {\mathrm{D}}_{\mathrm{H}} {\mathrm{W}}}}\left( {{\mathrm{x}}_{\mathrm{fire}} - {\mathrm{L}}} \right)}} + 1}}{{\frac{{{\dot{\mathrm{Q}}}_{\mathrm{a}} }}{{{{\uprho}}_{0} {\mathrm{C}}_{\mathrm{p}} {\mathrm{SWT}}_{0} }} + 1}}} \right)} \right) - \frac{\mathrm{W}}{{{\mathrm{W}}_{\mathrm{jet}} }}} \right) \\ {\mathrm{C}}4 & = \left( {1 + \frac{{{\dot{\mathrm{Q}}}_{\mathrm{a}} }}{{{{\uprho}}_{0} {\mathrm{C}}_{\mathrm{p}} {\mathrm{SWT}}_{0} }}{\mathrm{e}}^{{\frac{{ - 4{\mathrm{h}}_{\mathrm{app}} }}{{{{\uprho}}_{0} {\mathrm{C}}_{\mathrm{p}} {\mathrm{D}}_{\mathrm{H}} {\mathrm{W}}}}\left( {{\mathrm{L}} - {\mathrm{x}}_{\mathrm{fire}} } \right)}} } \right) \\ \end{aligned}$$

where ${\dot{\mathrm{Q}}}_{\mathrm{a}}$ the convective HRR (around 2/3 (60-80%) of the total HRR [3, 4]; C_p is the heat capacity; T₀ is the ambient temperature in the tunnel (with no fire); ${\mathrm{h}}_{\mathrm{app}}$ is the coefficient of equivalent thermal exchange that depends on the convective and radiation heat transfers (refer to [4] for detailed description)