DOI: 10.3303/CET2290073 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 30 December 2021; Revised: 17 March 2022; Accepted: 6 May 2022 
Please cite this article as: Luan X., Huo J., Zhao S., Zhang B., 2022, Risk control of overtopping phenomenon after a catastrophic tank failure 
through optimized bund design, Chemical Engineering Transactions, 90, 433-438  DOI:10.3303/CET2290073 
  

 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 90, 2022 

A publication of 

 
The Italian Association 

of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Aleš Bernatík, Bruno Fabiano 
Copyright © 2022, AIDIC Servizi S.r.l. 
ISBN 978-88-95608-88-4; ISSN 2283-9216 

Risk Control of Overtopping Phenomenon after a 
Catastrophic Tank Failure Through Optimized Bund Design 

Xiaoyang Luan, Jiali Huo, Shuaiyu Zhao, Bin Zhang* 
College of Safety Science and Engineering, Nanjing Tech University, Nanjing 211816, China 
bzhang@njtech.edu.cn 

Liquid fuels are stored in the large tanks, e.g., LNG (Liquefied Natural Gas). A catastrophic tank failure can 
suddenly release a huge volume of flammable materials, and cause severe incidents. The Cleveland Natural 
Gas Explosion resulted in more than 130 fatalities, which was caused by LNG tank failures. Currently, bunds 
are required by regulations to control the risk of tank failures, e.g., NFPA 59 A; however, there is no specific 
guideline to design effective bund systems, and overtopping can still occur to undermine the risk control 
effectiveness of bund systems. This study aims to optimize the bund design for a better risk control of a 
catastrophic tank failure incident. An experimental apparatus was constructed to simulate the catastrophic tank 
failure incident, and key parameters of bund design were investigated for their effect to control the overtopping 
risk, i.e., bund shape, height/radius, inclination angle of bund wall, and breakwater. The experimental data were 
analyzed to propose a predictive model of bund overtopping fraction. Also, CFD (Computational Fluid Dynamic) 
models were developed using RNG k-ε and LES (Large Eddy Simulation) methods, which were validated 
against experimental data. The study reveals key parameters of bund design for the overtopping risk control, 
and contributes to providing a scientific guideline for optimizing the bund design based on both experimental 
findings and CFD models.  

1. Introduction 
Bunds are essential for the process safety of Liquefied Natural Gas (LNG) storage tanks. It can effectively 
control the diffusion of the liquid pool and limit the vaporization caused by the accidental leakage of the LNG 
storage tank (Davies et al., 1996). But some accidents such as the one in Buncefield (Johnson, 2009) in 2005 
indicate that the catastrophic failure of tanks can lead the liquid overtop from the bund wall to result in serious 
consequences (Thyer et al., 2009). Actually, experiments and some theoretical model studies have shown that 
bund overtopping is not rare (Thyer et al., 2002a; Trainor, 2011). Therefore the evaluation of the effectiveness 
of the bund is very important. Overtopping fraction is a key parameter for determining the extent of liquid leakage 
and the effectiveness of the bund design in a tank failure incident, it is defined as the fraction of the mass of the 
leaked liquid in the original liquid mass in the storage tank. Previous work has demonstrated that the design of 
a bund can have a significant impact on the liquid flow behavior and overtopping fraction. 
The previous experimental work on the catastrophic failure of storage tanks was mainly simulated by the free 
fall of a liquid column by lifting a storage tank instantaneously. Greenspan and Johansson (1981) studied the 
effect of circular vertical and inclined bund configurations on the overtopping fraction for catastrophic tank 
failures. Atherton (2005) studied the effects of circular, square, rectangular, and diamond vertical bunds on the 
overtopping fraction after catastrophic storage tank failures. He conducted a series of experiments to compare 
the overtopping process for different shapes bunds. 
Daish (1998), SreeRaJ (2008), and Webber (2009,2010) respectively developed CFD models based on the 
shallow water equation to describe the interaction between released liquids and bund. The shallow water 
equation is considered accurate for describing inviscid fluids but is not applicable to complex turbulent 
processes, Liu et al. (2017), Ramajo et al. (2018) developed CFD models by Reynolds Averaged Navier Stokes 
(RANS) model to calculate turbulence effects during bund overtopping. 

433



Some scholars have developed predictive models of overtopping fraction based on the experimental results 
from the studies of catastrophic tank failure. Greenspan and Johansson (1981) summarized their experiments 
and found that the overtopping fraction Q mainly depends on the design of storage tanks and bund. Based on 
Greenspan's (1981) research, Clark et al. (2001) and Hirst (Thyer et al., 2002b) developed predictive models 
using Greenspan's data respectively, Hirst (Thyer et al., 2002b) believes that overtopping fraction is mainly 
determined by ratio of bund height and radius to liquid height as shown in Eq. (1). 

𝑄𝑄 = 𝐴𝐴 + 𝐵𝐵 ∗ 𝑙𝑙𝑙𝑙(
ℎ
𝐻𝐻

) + 𝐶𝐶 ∗ 𝑙𝑙𝑙𝑙(
𝑟𝑟
𝐻𝐻

) (1) 

Where h is the bund height; r is the bund radius; R is the tank radius, H is the liquid height in the tank. When θ 
= 90°, A = 0.044, B = −0.264, C = −0.116; when θ = 60°, A = 0.287, B = −0.229, C = −0191; when θ = 30°, 
A = 0.155, B = −0.360, C = −0.069. Atherton (2005) developed a new predictive model based on his own 
experimental results. These models have high accuracy in predicting the overtopping fraction, but the models 
were developed from a certain series still have limitations. 
As described earlier, most previous experimental works were conducted using laboratory-scale setups without 
setting up field-scale experiments. Also, previous works studied the overtopping phenomena of water but not 
cryogenic liquids, such as liquid nitrogen and LNG, which are widely used in industry. Due to the lack of 
experimental data for other bund shapes, all existing mathematical predictive models were developed to predict 
the overtopping fraction of circular bunds. Therefore, the existing models have a small range of applicability. In 
addition, no work has been done to screen the suitability of turbulence models for the bund overtopping process. 
In conclusion, the bund overtopping of tank catastrophic failure still requires more research. A series of 
experiments, simulations, and predictive models were conducted to make up for the lack of bund overtopping 
study. These works have deepened the understanding of the physical process of fluid capsizing under various 
complex bund conditions and provided scientific recommendations for the bund design of the storage tanks. 

2. Experimental studies 
As shown in Figure 1 a, the experiment was designed as a laboratory-scale and a field-scale to investigate the 
effect of the experimental scale on bund overtopping. The laboratory-scale tests were used two tanks with 
diameters of 0.05m and 1m. The laboratory-scale tests were used a tank with a diameter of 0.229m. The circular 
storage tanks are located in the middle of the circular or square bunds. The power of the cylinder is provided by 
compressed air to lift the tank rapidly. The liquid in the tank will be leaked into the bund. Then the liquid will 
overtop the bund. The overtopping liquid is accepted by the receiving container and weighed by the balance. 
The bunds were designed with different shapes and curvatures for control experiments. The experiments are 
the first to use liquid nitrogen and LNG as the overtopping liquid. In addition, in recent experiments, the pressure 
on the bund was measured by pressure sensors as shown in Figure 1b, the liquid overtopping process in the 
square and circular bund was collected by a high-speed camera, and the data was transmitted to a computer. 

 

Figure 1. Experimental setups for overtopping (a) (Zhang et al., 2017) and bund with pressure sensors (b) 

Previous experiments systematically studied the prevention effects of the bund (Zhang et al., 2017), including 
the scale of the experiment, the ratio of h/r, the design of the bund wall (curved bund and linear bund), the 
material of the bund, and the type of liquid (water, LN2, and LNG). The results show that the scaling up of the 
experimental scale and the materials of the bunds show high similarity on the overtopping fraction. Bunds with 
high h/r have lower overtopping fraction. Compared to curved bunds, straight bunds can contain liquids more 
effectively, especially at high filling ratio. As for the type of liquids (water, LN2, and LNG), the results for the 
overtopping fraction were similar. These studies provide scientific recommendations for the bund design. 

434



However, in actual production, the design of bunds is usually complex, so we further investigated the 
overtopping fraction and dynamic pressure of complex bund including shape, inclination, and breakwater 
structure. Compared with the square bund, the overtopping fraction and the maximum pressure on the wall of 
the circular bund are slightly lower. In addition, the greater the inclination angle of the bund, the lower the 
overtopping fraction, and the greater the maximum pressure on the bund wall. Breakwaters are effective in 
reducing the bund overtopping, and the overtopping fraction of horizontal breakwaters is slightly lower than that 
of inclined breakwaters. These experiments enriched the experimental data of bund overtopping. It provided 
data support for the practical application and theoretical analysis of bund overtopping research. 

3. Predictive model 
3.1 Model development 

Previous studies have provided the theoretical basis for the development of the overtopping fraction predictive 
model. Finding the key variables is the most important part of the model development. Clark et al. (2001) 
considered the overtopping fraction as the function of tank height H and bund height h. The dimensionless 
variable h/H was used in the predictive model. Clark's model ignored key parameters such as the bund radius r 
and tank radius R, so only a rough estimate of the trend in overtopping fraction can be made. Based on Clark's 
work, Hirst (Thyer et al., 2002b) introduced new equation variables to improve the accuracy of the prediction 
model, and the bund radius r was considered as an important parameter in the predictive model. Later, Atherton 
(2005) developed a complex model to predict the overtopping fraction of circular straight bunds and validated it 
using their experimental data. The model has good accuracy but a complex form because nearly all the 
dimensionless variables are considered. Too many variables make it more difficult to apply the model to practical 
calculate. Therefore, simple equation form and efficient prediction performance are the main needs for 
developing new models. For the accuracy of the equations, h/H, r/H, R/H, and θ are considered into the new 
model. In addition, for the simplicity of the equations, a multiple linear regression model is chosen after trying 
numerous equation forms, and the model form has good predictive performance after being verified by 
experimental data. Three series of experimental data (Greenspan and Johansson, 1981; Atherton, 2005; Zhang 
et al., 2017) were used to develop new models to increase the reliability of the models. Equation 2 (Luan et al., 
2020) is obtained by fitting all the data of the circular bund. However, the predictive model developed based on 
circular bund does not apply to the square bund. Square bunds are common in industrial tank farms, so it is 
necessary to develop a corresponding square bund model. The model developed by square bund data is shown 
in Equation 3 (Luan et al., 2020). In practical applications, due to terrain limitations and actual needs, the bund 
may have irregular shapes and arbitrary inclination angles. It is very practical for industrial production to use all 
experimental data to establish a general predictive model, the function as shown in Equation 4 (Luan et al., 
2020). 

𝑄𝑄 = −0.3195 ∗ 𝑙𝑙𝑙𝑙�
ℎ
𝐻𝐻
� − 0.3031 ∗ 𝑙𝑙𝑙𝑙�

𝑟𝑟
𝐻𝐻
� + 0.2782 ∗ 𝑙𝑙𝑙𝑙�

𝑅𝑅
𝐻𝐻
� + 0.1174 + 0.4200 ∗ 𝑐𝑐𝑐𝑐𝑐𝑐𝜃𝜃 (2) 

𝑄𝑄 = −0.2283 ∗ 𝑙𝑙𝑙𝑙�
ℎ
𝐻𝐻
� − 0.2688 ∗ 𝑙𝑙𝑙𝑙�

𝑟𝑟
𝐻𝐻
� + 0.1665 ∗ 𝑙𝑙𝑙𝑙�

𝑅𝑅
𝐻𝐻
� + 0.1564 (3) 

𝑄𝑄 = −0.2180 ∗ 𝑙𝑙𝑙𝑙�
ℎ
𝐻𝐻
� − 0.1534 ∗ 𝑙𝑙𝑙𝑙�

𝑟𝑟
𝐻𝐻
� + 0.0861 ∗ 𝑙𝑙𝑙𝑙�

𝑅𝑅
𝐻𝐻
� + 0.1479 + 0.3018 ∗ 𝑐𝑐𝑐𝑐𝑐𝑐𝜃𝜃 (4) 

3.2 Model validation 

The accuracy of the model is verified by comparing the model prediction results with experimental 
measurements. The models show a good performance in predicting the overtopping fraction of different bund 
shapes. Taking the general model as an example, three different shapes of bund overtopping experiments were 
carried out to validate the applicability of the general model, the experimental setup is shown in Table 1. The 
predicted results of the general model are as shown in Figure 2. The points on the diagonal in the figure indicate 
a perfect prediction; the data points that are plotted below the diagonal indicate underprediction. Otherwise, the 
predicted value is higher than the measurements. The dotted lines represent ± 50% error. The general model 
was developed for irregular bunds that are difficult to evaluate the overtopping fraction, and the accuracy was 
sacrificed to ensure the generality of the model so if accurate predictions are desired. Despite various shapes, 
the general model has a good enough prediction of overtopping fraction. 
Overall, the development of the square bund model and the general model compensates for the existing 
predictive models that can only predict the overtopping fraction of circular bunds. These models provide a 
scientific and convenient tool for the engineering design of tank and bund system. 

435



Table 1: Design parameters of the tank and bunds 

Bund Shape Inclination h(mm) re(mm) H(mm) R(mm) Q 

Circular 

90° 100 272 386 135 0.333 
90° 100 272 363 135 0.310 
90° 100 272 337 135 0.277 
90° 100 272 306 135 0.237 
90° 100 272 245 135 0.180 
90° 100 272 183 135 0.098 

Square 

90° 100 272 357 135 0.377 
90° 100 272 332 135 0.373 
90° 100 272 305 135 0.292 
90° 100 272 244 135 0.262 
90° 100 272 182 135 0.110 

Rectangle 

90° 100 272 360 135 0.371 
90° 100 272 333 135 0.333 
90° 100 272 309 135 0.290 
90° 100 272 275 135 0.249 
90° 100 272 183 135 0.103 

0.0 0.1 0.2 0.3 0.4 0.5
0.0

0.1

0.2

0.3

0.4

0.5

Pr
ed

ic
tio

n 
by

 Z
ha

ng
's 

m
od

el

Measurement

 Vertical circular
 Vertical square
 Vertical rectangle

0.0 0.1 0.2 0.3 0.4 0.5
0.0

0.1

0.2

0.3

0.4

0.5

Pr
ed

ic
tio

n 
by

 Z
ha

ng
's 

m
od

el

Measurement

 Vertical circular
 Vertical square
 Vertical rectangle

 
Figure 2. Overtopping fraction prediction using the general model. 

4. CFD Simulation 
4.1 Model setup 

Computational fluid dynamics (CFD) is an effective tool for simulating bund overtopping phenomena, and CFD 
models are developed in ANSYS Fluent. In this work, several common turbulence models: LES, RNG k-ε, 
Realizable k-ε, Reynolds stress, Shear-Stress Transport (SST) k-ω and Standard k-ε are compared. RNG k-ε 
and LES model are more suitable for bund overtopping studies. Because these two models can calculate the 
laminar, turbulent and transition flow processes of liquid. The model is essentially isothermal and uses the VOF 
method to simulate the liquid overtopping process. The 2D model is an axisymmetric model, the 3D model is 
chosen to simulate a quarter of the geometry and computational domain to reduce computational resources. In 
this study, a mesh with an element size of 0.005m was chosen to develop the model. The boundary conditions 
are shown in Figure 3. The bund and the ground inside the bund are set as walls. The computational domain is 
initialized using the standard initialization, and the initial turbulent kinetic energy and turbulent energy dissipation 
rate are set to zero because the initial state of the liquid is laminar. 

 
Figure 3. Quarter of the geometric for square bund with test L3 (Huo et al., 2022) 

436



4.2 Model validation 

The comparison between the simulation results of the overtopping fraction based on the RNG k-ε model and 
the experimental data is shown in Figure 4. It is found that the simulation results of the overtopping fraction are 
within an acceptable range, and most of the simulated overtopping fraction tends to be over-predict, which puts 
forward higher requirements for bund design and helps to minimize liquid overtopping. 
The liquid dynamic process of L1 with a filling ratio of 87.8% is shown in Figure 5. The behavior of the liquid 
during catastrophic failure of the storage tank is divided into the following six stages: initial column (a), collapse 
(b), surge and impact (c), hydraulic bore (d, e), overtopping (f), reflux and center spike (g), as shown in Figure 
5a. As for Figure 5b, the six stages of the experiment and 3D models can be well matched. The simulated height 
of the center spike (h) of the 2D model (H2D=0.076m) is slightly higher than that of the 3D model (H3D=0.048m) 
and the experimental image (HExp=0.044m). In addition, the secondary overtopping process can be effectively 
observed in the 3D model and experimental images, but only one overtopping process can be observed in the 
2D model. In general, the dynamic process of the 3D model can more reliably show the interaction between 
liquids and bunds wall. These models can be used to further study the flow behavior and turbulence effects in 
the overtopping process of bund under complex conditions. 

 
Figure 4. Simulation results of 3-D on RNG k-ε model (Huo et al., 2022) 

 
(a) (b)
Figure 5. Dynamic Process of liquid of catastrophic tank failure: (a) experiment (Zhang et al., 2017), (b) 3D 
simulation of L1 (Huo et al., 2022) 

5. Conclusion 
Despite the low frequency of catastrophic failure of storage tanks, this is still one of many possible failure modes. 
Storage tanks show a trend of large-scale, centralized as the development of tank technology. Therefore, the 
potential hazards of catastrophic failure of storage tanks need to be taken more seriously. The serious 
consequences of this form of failure are not affordable. The study of bund overtopping can be used by interested 
parties to understand the bund overtopping hazard and take effective protective measures. This paper 
systematically investigated the catastrophic failure of storage tanks through experimental, simulation, and 
predictive modeling methods. The main conclusions are as follows. 
(1) The configuration of the bund has a large impact on the overtopping fraction. For the same filing ratio, tests 

with high h/r and R/r values tended to give smaller overtopping fractions. Circular bund is considered better 

0.0 0.2 0.4 0.6 0.8 1.0
0.0

0.2

0.4

0.6

0.8

1.0
 L1
 L2
 L3
 L4
 L5
 L7
 L8
 L11

Si
m

ul
at

io
n

Experiment

437



than the rectangle bund. Breakwaters can effectively control the liquid overtopping. In addition, the reliability 
of the results of laboratory scale experiments applied to field experiments was verified. 

(2) Three predictive models for circular, square and general bund shapes were developed using richer 
experimental data. These predicative models have more accurate prediction accuracy and a wider 
application range. Predictive models have been developed to estimate liquid overtopping fraction rapidly 
and help interested parties to assess the hazard of the tank farm. 

(3) The reliability of the CFD models has been systematically verified by experimental results, and the 
overtopping fraction and flow behavior are in accordance with the experimental results. The LES and RNG 
k-e turbulence models have proven to be suitable for bund overtopping study. 

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	Risk Control of Overtopping Phenomenon after a Catastrophic Tank Failure Through Optimized Bund Design