**1. Introduction**

Underwater tunnels, especially undersea tunnels, are usually considered as essential components in urban traffic engineering due to their heavy traffic volumes, complex vehicle composition, obvious slope, and consequent high fire risk with complicated heat transfer [1] and, hence, mostly have larger scales as well; thus, the shield method is widely used in their construction. Moreover, fewer installations of transverse passages and escape shafts in undersea tunnels [2] are harmful to fire evacuation safety because of the limitations of the structure and internal space. Therefore, reasonable design alternatives for ventilation and evacuation are promising steps to reduce initial and operational costs and to improve the long-term operational performance for undersea tunnels [3].

The high construction cost of evacuation passages and smoke vents for an undersea tunnel is attributed to the complex geological environment; thus, full jet longitudinal ventilation and longitudinal evacuation with bottom passage are adopted in a large proportion of undersea tunnels. Unlike the transverse evacuation method using cross passages or using a parallel escape tunnel between two tunnels, longitudinal evacuation is possible with simple construction and low cost. One only needs to install evacuation slides or stairs at a reasonable spacing inside the tunnel to connect the upper space and the bottom passage, avoiding adding auxiliary facilities outside. Related simulation work [4] found that the evacuation spacing of longitudinal evacuation was 150~200 m shorter than that of

**Citation:** Na, W.; Chen, C. A Study on the Evacuation Spacing of Undersea Tunnels in Different Ventilation Velocity Conditions. *Fire* **2022**, *5*, 48. https://doi.org/ 10.3390/fire5020048

Academic Editors: Chuangang Fan and Dahai Qi

Received: 10 March 2022 Accepted: 4 April 2022 Published: 7 April 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). *fire*

transverse evacuation on the conditions of equivalent evacuation capacity and satisfying evacuation safety. The denser evacuation spacing means that more evacuation slides (stairs) need to be built, which requires a balance between engineering economy and evacuation safety. A basic principle for ensuring life safety in tunnel fires is that the available safe escape time (ASET) is greater than the required safe escape time (RSET) by an adequate safety margin [5]. Too large a spacing may mean that the RSET does not satisfy evacuation safety, while too small a spacing leads to an excessive safety margin and a high engineering cost. Thus, reasonable evacuation spacing designs are crucial to balance economy and safety.

A lack of consistent standards is a threat to reasonable fire evacuation design for undersea tunnels. Fire smoke is the biggest threat to the people trapped [6], and longitudinal ventilation velocity can significantly affect the hazard level of the smoke environment and then affect the ASET. The high-velocity mode is recommended by the Chinese design standard for ventilation of highway tunnels [7] for the operation of fire ventilation in tunnels with one-way traffic; i.e., the longitudinal ventilation velocity is equal to or greater than the critical velocity (vc) to eliminate the smoke back-layering occurring in the tunnel. The related design standards of Germany, France, Switzerland, Austria [8,9] and the Permanent International Association of Road Congress (PIARC) [10] proposed that the low-velocity mode could be adopted in the self-evacuation phase after fire, which requires the longitudinal velocity to be far lower than v<sup>c</sup> in order to maintain the stability of smoke stratification downstream of the fire source. In the meanwhile, various perspectives have been presented by other authors, including Xue et al. [11], who recommended that the ventilation velocity should be lower than or close to vc. Hu [12] and Guo et al. [13] suggested using stratified velocity and constrained velocity, respectively. Liu [14] suggested that the velocity should be regulated below 1.0 m/s. Chen et al. [2] posited that mechanical ventilation should be turned off during evacuation. Jan et al. [15] and Espinosa et al. [16] believed that using two-stage ventilation (low velocity to high velocity) is more conducive to smoke control and evacuation in undersea tunnel fires. In other words, during the ventilation control stage of a tunnel fire, the decision makers or control system may use any velocity modes based on the judgment of fire scenes to achieve different requirements, such as ensuring no smoke in upstream rescue routes, or maintaining the downstream smoke stratification as much as possible, or using a combination of these methods. Fully considering the possible ventilation conditions is very meaningful for evacuation spacing design. Yin et al. [17] considered the ineffective and effective situations of exhaust, then proposed a safety spacing of 50 m and 75 m accordingly, by calculating the ASET distributions of two conditions. In most previous studies of evacuation spacing design, however, empirical fixed values of ASET were usually used to simplify the calculation, ignoring the influence of the possible conditions of ventilation velocity on the distribution of ASET. Yuan et al. [18] experimented and calculated the evacuation process of an undersea tunnel with longitudinal bottom evacuation, referring to the empirical value 360 s of ASET, and proposed that the reasonable value of evacuation interval was 64.3 m. Zhang et al. [19] and Shen et al. [20] put forward a reasonable slide spacing of 80 m for different undersea tunnels in Chittagong and Hangzhou by using ASET values of 900 s and 600 s, respectively, according to engineering experiences. Hui et al. [21] used an ASET value of 480 s and recommended a slide spacing of 45 m. The conclusions of the above studies were not comprehensive, which indicates the limitations of using empirical fixed values. Reasonable evacuation spacing designs need to rely more on accurate analyses of ASET distributions. Thus, it is necessary to take into account the dynamic distribution of ASET in different ventilation velocity conditions of tunnel fire and make corresponding design suggestions.

The present study concentrated on the reasonable evacuation spacings of undersea tunnels in possible longitudinal ventilation conditions. The ventilation and smoke diffusion of tunnel fire were dynamically simulated by FDS(V6). The effects of five typical ventilation velocities of four velocity modes ranging from 0 m/s to satisfying v<sup>c</sup> on ASET distributions were investigated, and the RSET distributions were calculated through the simulations of evacuation processes in six spacings by Pathfinder software. Ultimately, design suggestions

of reasonable spacings in different ventilation velocities that satisfy evacuation safety requirements were put forward through the comparative analysis of ASET with RSET, thereby providing a design method reference for calculations of evacuation spacing in undersea tunnels. **2. Numerical Modeling**  *2.1. Tunnel Descriptions*  2.1.1. Tunnel Configuration

sion of tunnel fire were dynamically simulated by FDS(V6). The effects of five typical ventilation velocities of four velocity modes ranging from 0 m/s to satisfying vc on ASET distributions were investigated, and the RSET distributions were calculated through the simulations of evacuation processes in six spacings by Pathfinder software. Ultimately, design suggestions of reasonable spacings in different ventilation velocities that satisfy evacuation safety requirements were put forward through the comparative analysis of ASET with RSET, thereby providing a design method reference for calculations of evacuation

## **2. Numerical Modeling** A medium-length, double-hole undersea tunnel, built using tunneling shields in the

spacing in undersea tunnels.

## *2.1. Tunnel Descriptions* city of Macao, was selected in this study. The tunnel is a one-way, two-lane tunnel with a
