DOI: 10.3303/CET25116012 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 15 December 2024; Revised: 25 February 2025; Accepted: 29 March 2025 
Please cite this article as: Bai Y., Liu K., Weng W., Wu J., 2025, A Novel QRA Model for Coupling Accidents - A Case Study of Utility Tunnels, 
Chemical Engineering Transactions, 116, 67-72  DOI:10.3303/CET25116012 
  

 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 116, 2025 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Bruno Fabiano, Valerio Cozzani 

Copyright © 2025, AIDIC Servizi S.r.l. 

ISBN 979-12-81206-18-2; ISSN 2283-9216 

A Novel QRA Model for Coupling Accidents - A Case Study of 

Utility Tunnels 

Yiping Baia,*, Kunqi Liub, Wenguo Wenga, Jiansong Wub 

a School of Safety Science, Tsinghua University 
b School of Emergency Management and Safety Engineering, China University of Mining & Technology-Beijing 

baiyiping_1995@163.com; baiyiping@tsinghua.edu.cn  

Since there are more emerging and interacted process installations, the traditional QRA treating risks as 

independent ones may ignore coupling effects and result in risk underestimation. The utility tunnel is a new 

process installation with multiple hazardous pipelines inside a confined space. Existing studies of utility tunnel 

risks focus more on single accidents like cable fire or gas explosion, with limited analysis of the coupling effect. 

In this paper, a novel QRA model for coupling risks is proposed in a new perspective for the coupling risk 

assessment of process installations. The ponding inside utility tunnels coupled with personnel evacuation is 

analysed as a case study. The results show that the current design of utility tunnels is insufficient for preventing 

ponding-triggered drowning in heavy rain like the “7.20” rainstorm. Heightening the water barrier of ground 

ventilation openings to over 0.6 m can effectively reduce the coupling risks. Besides, the proposed model can 

also be further applied to other coupling risks. 

1. Introduction 

Utility tunnels are built for convenient maintenance and efficient use of underground space, containing a variety 

of pipelines like electricity, communications, natural gas, heating, water supply, and drainage. Utility tunnels can 

also significantly strengthen the reliability and service life of underground pipelines in chemical parks or cities. 

However, such integration is prone to trigger coupling accidents like gas leakage, fire, explosion, and ponding, 

which can lead to the paralysis of energy supply systems and corresponding productions. 

The current QRA models of process industries mainly focus on single risks. Zhu et al. (2024) proposed a fire 

risk assessment model for cable fires by integrating FDS and DBN. Since there are various hazardous pipelines 

with corresponding accidents in a utility tunnel, ignoring the coupling effect between different risk factors or 

incomplete consideration of the consequences will lead to deviations in consequence assessment. There are a 

few research implemented so far, Hai et al (2022) applied the N-K model to quantify the coupling relationship 

among human error, equipment failure and management mistakes to quantify the coupling effect, but the 

process relies on expert judgment and lacks measurement of physical effect. Gu et al. (2025) established a 

knowledge base of evolution paths of typical coupling accidents in the case of earthquakes but lacks the 

consequence quantification and detailed decision-making. Therefore, there is still an essential need for dynamic 

coupling risk assessment methods to comprehensively analyze potential coupled risks of utility tunnels and 

similar confined spaces in the process industries. 

Meanwhile, in the case of flooding, the water intrusion into the utility tunnel has a severe impact on the pipeline 

and personnel inside, the ponding inside and corresponding evacuations have a significant coupling effect and 

may result in fatalities. He et al (2024) conducted a risk assessment of the flood disaster in the underground 

space and put forward resilience enhancement measures. Yuan et al (2024) simulated the risk distribution of 

flooding in the underground space. However, the existing research does not take enough consideration on the 

relevance of the coupling effect in the case of flooding of a utility tunnel. 

In this paper, a novel QRA model for coupling risks was proposed to measure the coupling effect systematically. 

The rest of the work is presented as follows: section 2 introduced the methodology, section 3 conducted a case 

study on ponding risks in utility tunnels, and section 4 concluded the whole work. 

67

mailto:baiyiping_1995@163.com
mailto:baiyiping@tsinghua.edu.cn


2. Methodology 

Based on the energy out-of-control theory for risk identification and scenario construction of utility tunnels 

proposed by authors before (Bai et al., 2024). A novel QRA model for coupling risks of hazardous process 

installations is introduced in this work in Figure 1. The proposed model begins with analyzing the out-of-control 

energy and identifying corresponding vulnerable targets associated with the primary event. Subsequently, the 

occurrence of cascading accidents is evaluated based on predefined escalation criteria. If the target remains 

intact, the QRA of the primary event should be performed and the process ends. In the case of one or more 

cascading accidents occurring with multiple energy coexisting and considerable coupling effects, QRA 

considering coupling effect should be conducted. Conversely, if out-of-control energy does not coexist or no 

coupling effect is observed, the effects of each out-of-control energy should be compared. If there is one of the 

energies far greater than others, QRA focusing on the worst accident should be conducted. If not, (i.e. multiple 

out-of-control energies are considerable) the QRA for each accident should be performed and summed up. For 

typical accidents of utility tunnels, the QRA of gas leakage and explosion should be QRA for the worst accidents, 

since the consequence of explosion is far greater than leakage. In case of cascading cable fires, the QRA should 

consider multiple cable damage and sum them up. For the ponding and evacuation inside utility tunnels or other 

confined spaces, there is a considerable coupling effect that should be quantified, which will be elaborated in 

the following. 

 

Figure 1 Flow chart of the proposed QRA model for coupling risks 

3. Case study 

Utility tunnel is an emerging underground infrastructure, and mostly the lowest location of the chemical parks or 

urban areas, therefore, ponding inside the utility tunnel can break in through the escape openings, ventilation 

openings, and other ground openings. Meanwhile, heavy rain or flooding can lead to coupling accidents, which 

will be analysed and measured in this section. 

3.1 Preliminaries 

This section primarily discusses the typical event chain caused by flooding in utility tunnels during heavy rain. 

Ponding entering through ventilation openings (as shown in Figure 2) may not be efficiently drained by the 

internal drainage system to threaten maintenance personnel inside. The event chain with the coupling effect of 

ponding within utility tunnels can be described as follows: rainwater enters through the ventilation opening, 

where gravitational energy is converted into mechanical energy; the water then accumulates inside the tunnel, 

threatening personnel as the mechanical energy shifts back to gravitational energy; and finally, pipeline failure 

occurs when the mechanical energy of the water is transferred to the pipeline’s mechanical system, leading to 

a rupture or malfunction. 

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The rate of water intake from the ventilation opening varies with the depth of depth of the surface water. 

Therefore, in the first stage, when the depth of surface water around the ground ventilation opening is relatively 

low, the water discharges from the ventilation opening in the form of a weir flow, as a result, the ponding of water 

in this stage of the utility tunnel can be calculated by Equation 1-2 (assuming the drainage system fails) (Xia et 

al., 2022): 

𝑄 = 𝐶𝑊𝑃√2𝑔𝐻
1.5 (1) 

𝐻𝑔 = ℎ − ℎ0 + 𝑢2 2𝑔⁄  (2) 

where Q is the inlet flow rate to the vent, m3/s; Cw is the inlet discharge coefficient for the weir flow pattern; g is 

the gravitational acceleration, m/s2; H is the upstream specific energy; h is the water depth over ventilation 

opening, m; u is the corresponding velocities 1 m upstream of the opening, m/s; and P is the perimeter of the 

openings. 

Then, the temporal evolution of water depth (hI) inside the utility tunnel can be calculated by Equation 3 

(assuming the compartment is empty): 

ℎ𝐼 =
(𝑄 − 𝑞𝑤) × 𝑡

𝐿 ×𝑊
 (3) 

where qw is the drainage volume of the utility tunnel drainage system, m3; L and W are the length and width of 

the utility tunnels. 

When the accumulated water reaches a critical depth, people will find it difficult to evacuate inside. So, current 

research has proposed a microscopic model for pedestrian evacuation in underground space under flood, 

according to the experimental results of Zheng et al. (2019), when the depth of the flood water in the utility tunnel 

rises gradually, the change of the maintenance personnel's moving speed can be described by the following 

equations. 

𝑣 = {
𝑣𝑔0，ℎ𝐼 = 0

[𝑣𝑔0× 𝐵 × 𝜔/0.5] × 0.5, ℎ𝐼 > 0
 (4) 

𝐵 = 1 − ℎ𝐼/ℎ′ (5) 

𝜔 = 1.0/(0.982 + exp(1.12𝑡 − 4.0)) (6) 

where vg is the maintenance personnel's velocity, ω is the ratio of speed decrease due to tiredness. h’ is the 

height of a utility tunnel, and hI is the depth of water in a utility tunnel. When maintenance personnel are walking 

on the ground, the maximum speed is vg0, which decreases as the ponding depth rises. 

 

Figure 2 Schematic diagram of the cross-section of a utility tunnel 

3.2 Risk assessment of the typical scenario 

In the era of global climate change, there may occur more flooding and other severe convection weather. The 

underground space may be more vulnerable than the surface for ponding during heavy rain or flood. In the event 

69



of urban flooding, water may enter the utility tunnel from the ventilation openings, threatening the cables, 

pipelines and personnel in the tunnel. The risk assessment of this case focuses on the consequences of the 

actual case. Collecting the time-dependent water depth evolution data of the extremely heavy rainfall in 

Zhengzhou, Henan, China on July 20, 2021 (T16 - T16.8 in Figure 3, because the depth of groundwater in T16 

is 0.5 m, which is equal to the height of the ground ventilation openings), the equation for the time-dependent 

development of the depth of groundwater can be roughly assumed as Equation 7 (only for this case). 

    

Figure 3 The temporal water depth of a typical site in Zhengzhou, China 

h = 2.0924e0.00057t − 1.77507  (7) 

Based on Equation 4-7, in the early stage of ponding without tunnel drainage activation, the inlet flow rate Q 

can be presented in Equation 8. Also, the internal water depth hI can be proposed in Equation 9, where the flow 

rate of inside drainage system qw was set as 20 m3/h in this case based on construction practice. Therefore, the 

temporal evolution of water depth in the cable compartment, natural gas compartment, and comprehensive 

compartment of utility tunnels are shown in Figure 4a. The results indicate that the cable compartment is more 

vulnerable to heavy rain and consequent ponding, so the following research mainly focuses on the cable 

compartment. 

𝑄 = 2.977(2.0924𝑒0.00057𝑥 − 1.77507 + 0.0225 19.6⁄ )1.5  (8) 

ℎ𝐼 =
∫ 2 ∗ {2.977(2.0924e0.00057t − 1.77392)1.5𝑡 − 0.0056𝑡}𝑑𝑡
𝑡

0

200 ×𝑊
 (9) 

    

Figure 4 Temporal evolution of water depth inside utility tunnels and evolution of movement speed 

0 20 40 60 80 100 120

0.0

0.2

0.4

0.6

0.8

1.0

fl
o
w

 s
p
ee

d
/(

m
·s

-1
)

w
at

er
 d

ep
th

 /
 m

time/min

 flow spead

 water depth

0.0

0.1

0.2

0.3

0.4

0.5

a b 

70



𝑣 = [𝑣𝑔0 (1 −
∫ 2 ∗ {2.977(2.0924e0.00057t − 1.77392)1.5𝑡 − 0.0056𝑡}𝑑𝑡
𝑡

0

200 ×𝑊
/3.2)

× (1.0/(0.982 + exp(1.12𝑡 − 4.0)))/0.5] × 0.5 

(10) 

Based on Equation 4-6, the temporal movement speed can be calculated in Equation 10 and illustrated in Figure 

4b based on the above water accumulation equation. The results indicate that in the early stage when the water 

depth is less than 0.5m, its adverse impact on walking of the personnel is limited, while the water depth is higher 

than 0.5m, the moving speed will be greatly reduced with the increase of the water depth. 

3.3 Risk mitigation analysis 

Further, based on the above results and formulas, assume that the maintenance personnel at the center of the 

two ventilation openings in the utility, which is the worst scenario for evacuation. The results are shown in Figure 

5, where the blue line represents the variation in water depth within the cable compartment, while the yellow 

line indicates the evacuation distance affected by the temporal accumulated water. Since the personnel 

evacuation distance inside the utility tunnel is 100 m (the distance from the center of the 200-m fire zone to the 

exits) and the average height of the personnel is assumed as 1.7 m. The red line represents the criteria for the 

successful evacuation of personnel. Based on the results of the typical case study shown in Figure 5, it is evident 

that the current design of the utility tunnel is insufficient to protect inside personnel during extreme rainfall. 

Therefore, further risk mitigation analysis of ponding in utility tunnels is conducted in the following part.  

 

Figure 5 Criteria of evacuation from ponding in utility tunnels 

   

Figure 6 Temporal evolution of water depth and walking distance with different mitigation approaches 

a b 

71



For mitigating ponding risks of utility tunnels, there are mainly two approaches, strengthening drainage system 

capacity and heightening the water barrier. The typical drainage capacity of the pumps in a single fire zone is 

20m³/h. In this section, the drainage capacity is further increased to 40m³/h to compare the evacuation process 

in the case of ponding. As shown in Figure 6, the solid line indicates the original case, and the dashed line 

indicates the improved case. The results in Figure 6a show that increasing the drainage capacity has a positive 

but very limited effect on mitigating ponding risks within the utility tunnel. After the drainage capacity is doubled, 

there is still a drowning possibility since the walking distance is only 98.76 m when the water depth reaches 1.7 

m. Comparing the capacity-doubled scenario and the initial scenario, there is only 0.1 m more walking distance.  

Therefore, the heightening groundwater barrier of the utility tunnel is further analysed. Based on the current 

ventilation height of 0.5 m, more 0.1 m is added, and the results are shown in Figure 6b based on the weir flow 

equations. The results show that the water accumulation in the compartment of the utility tunnel is significantly 

reduced compared to the initial state, and the evacuation possibility of the personnel is also improved. At 203 s, 

the walking distance reaches 100 m, and the water depth is only 1.04 m, which is far lower than the 1.7-m 

drowning criteria, which means even the personnel at the worst position can successfully be evacuated. 

4. Conclusions 

Utility tunnels are emerging process installations for efficient maintenance of pipelines, but also raise concerns 

about the coupling effect among multiple hazardous pipelines, which have not been systematically analyzed in 

previous research. In this paper, a novel QRA model for coupling risks is innovatively proposed to put forward 

a new perspective for the coupling risk assessment of process industries. The ponding of utility tunnels with 

personnel evacuation is selected as a typical accident chain with a coupling effect in the case study. The results 

show that the current 0.5-m height of the ground ventilation opening of the utility tunnel is insufficient for 

mitigating ponding risks in heavy rain like the “7.20” rainstorm and may lead to the drowning of the personnel 

inside the utility tunnels. By comparing risk mitigation approaches such as strengthening drainage system 

capacity and heightening the water barrier, it can be concluded that heightening the water barrier to over 0.6 m 

can effectively and economically improve the risk mitigation ability while strengthening drainage capacity is 

inefficient and impractical to reach the safe criteria. 

Acknowledgements 

This work was supported by the National Key Research and Development Program of China (Grant No. 

2023YFC3807600), the National Natural Science Foundation of China (Grant No. 72034004) 

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