DOI: 10.3303/CET24111028 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 21 February 2024; Revised: 26 February 2024; Accepted: 13 June 2024 
Please cite this article as: Vitale A., Ricci F., Baltzopoulos G., Cozzani V., Iervolino I., 2024, Risk Assessment of Oil Storage Facilities Exposed 
to Tsunami Hazard, Chemical Engineering Transactions, 111, 163-168  DOI:10.3303/CET24111028 
  

 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 111, 2024 

A publication of 

 
The Italian Association 

of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Valerio Cozzani, Bruno Fabiano, Genserik Reniers 
Copyright © 2024, AIDIC Servizi S.r.l. 
ISBN 979-12-81206-11-3; ISSN 2283-9216 

Risk Assessment of Oil Storage Facilities Exposed to 
Tsunami Hazard 

Antonio Vitalea,*, Federica Riccib, Georgios Baltzopoulosa, Valerio Cozzanib, Iunio 
Iervolinoa,c 
aDip.Strutture per l’Ingegneria e l’Architettura, Università di Napoli Federico II, Via Claudio 21, 80125 Naples, Italy. 
bLISES – Laboratory of Industrial Safety and Environmental Sustainability, Department of Civil, Chemical, Environmental 
and Material Engineering, University of Bologna, via Terracini 28, 40131, Bologna, Italy. 
cIUSS Scuola Universitaria Superiore di Pavia, Piazza della Vittoria 15, 27100 Pavia, Italy. 
antonio.vitale5@unina.it 

The term NaTech was coined to describe events where natural hazards trigger technological accidents in 
industrial facilities. Structural damage to the installations, caused by natural events such as earthquakes or 
tsunami, may cause loss of containment, which may in turn lead to fires, blasts, or dispersion of toxic gases. 
Thus, NaTech quantitative risk assessment (QRA) requires a measure of structural risk to provide estimates of 
future losses and a detailed assessment of the consequences arising from such losses. This paper presents an 
industrial risk analysis for anchored atmospheric storage tanks subjected to tsunami hazard, by means of a 
multidisciplinary approach integrating structural analysis and consequence assessment. This is performed for a 
case study consisting of a waterfront tank farm located at a coastal Italian site. The first part of the analysis 
requires calculation of the structural failure rate of storage tanks that suffer content release due to damage 
induced by tsunami inundation, via models of probabilistic hazard for the site of interest and the vulnerability 
(fragility) of the examined structures. Structural failure rates are evaluated for various numbers of simultaneous 
waterfront storage tank failures, using tsunami fragility curves for variable tank geometry and filling level. The 
failure rates and consequence analysis for the tank farm are then used as input parameters for the NaTech 
QRA, leading to the calculation of risk figures for tsunami hazard.  

1. Introduction 
Quantitative assessment of industrial risk due to natural hazards is primarily focused on studying the 
consequences that natural events, such as earthquakes, tsunamis, hurricanes or lightning storms, can provoke. 
These events can induce structural damage to the installation with consequent loss of the containment. 
Therefore, technological accidents triggered by natural events, also called NaTech events, may be the cause of 
other hazardous events such as flash fires, pool fires and vapour cloud explosions involving several industrial 
units in a domino effect (Mesa-Gomez A. et al. 2020; Suarez-Paba M.C. et al. 2019). NaTech risk assessment 
follows a structured outline based on the characterization of the natural hazard at the site of interest, the study 
of the vulnerability of the structures exposed to natural hazard events, the simulation of accidents with escalation 
scenarios, and the estimation of the consequences (Lees, 2012). Traditionally, the crucial point for a quantitative 
risk assessment (QRA) is the evaluation of the vulnerability or, more specifically, of the behaviour of different 
facilities under the natural events. As an example, for atmospheric storage tanks, that are the object of this 
study, technical literature is available for seismic actions, providing vulnerability studies based on observed 
damage from past events, as in Salzano et al. (2003). On the other hand, other vulnerability models are based 
on structural analysis on finite element models as Bakalis et al. (2017). Furthermore, for the tsunami action, 
simplified approaches are developed by Landucci et al. (2012). In the study presented herein, a NaTech QRA 
is discussed, referring to a case-study coastal refinery located in a site in southern Italy (Milazzo, Sicily) featuring 
anchored atmospheric storage tanks exposed to tsunami hazard. The structural damage and the consequences 
due to the loss of contents are discussed considering the examined storage tanks for different levels of oil filling.  

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mailto:antonio.vitale5@unina.it


2. Methodology 
The QRA methodology is split into three main steps: assessment of the hazard at the site of interest, evaluation 
of the vulnerability of the considered structures, and the modelling of consequences. Hazard and the 
vulnerability assessment allow to evaluate the risk in terms of structural failure frequency (rate). The structural 
failure rates are then used for simulating the consequences, in terms of fatalities, that may arise from accidental 
events due to loss of content. 

2.1 Probabilistic tsunami hazard analysis 

Tsunamis are triggered by other natural events, such as earthquakes, volcanic eruptions, submarine landslides, 
atmospheric disturbances, or asteroid impacts. A probabilistic tsunami hazard analysis (PTHA) for the case 
study of Milazzo, was developed by Volpe et al. (2019), considering tsunamis generated by earthquakes. PTHA 
was performed via numerical simulations of inundation scenarios for a grid covering an area including the 
refinery. Figure 1a shows some of the grid points located around the tanks. At each point, a hazard curve is 
obtained by PTHA. This curve depicts the annual rate of tsunamis exceeding different threshold values of 
inundation intensity (𝜆𝜆Φ). The inundation intensity chosen, herein, is the inundation level (Φ), defined as the 
ratio between the maximum inundation depth (ℎ𝑤𝑤), that is the maximum height of the wave measured near the 
structure from the ground level during the simulated inundation, and the maximum filling height �ℎ𝑓𝑓,𝑚𝑚𝑚𝑚𝑚𝑚� of the 
tank. 

 

Figure 1: a) Grid points of interest for the tsunami hazard assessment. b) Schematic representation of an 
anchored storage tank. 

2.2 Tsunami fragility functions 

The vulnerability analysis was carried out for anchored atmospheric storage tanks under tsunami-induced 
actions. Tsunami actions were modelled following a quasi-static approach, where the external pressure acting 
on the vessel can be considered as the sum of a hydrostatic and hydrodynamic component including a buoyant-
force pressure acting from under the base plate. These actions may trigger a series of failure mechanisms that 
govern the tank's response. More specifically, the radially acting hydrostatic pressure can induce shell buckling 
due to the rise of critical compressive circumferential stresses on the thin-walled cylindrical structure. On the 
other hand, the hydrodynamic pressure component, so-called drag force, can cause shear failure in the anchors 
leading to sliding of the tank, when the frictional forces in the steel-concrete foundation interface are exceeded. 
Finally, the combined effects of buoyant and hydrodynamic forces can cause the uplift of the tank, potentially 
leading to anchors’ failure, due to exceeding the steel capacity, or with the concrete cone breakout. This 
behavior was modelled by performing nonlinear static analysis on finite element models of the tanks, while 
varying the internal liquid filling level, the inundation depth and the flow velocity. A detailed description of the 
modelling and analysis can be found in Vitale (2024), while the results are briefly summarized herein.  
The vulnerability analysis resulted in the development of fragility functions expressing the probability of failure 
conditional on a given value of the intensity measure. The tsunami fragility functions express the probability of 
a tank suffering structural damage that leads to loss of containment, given a certain inundation level (Φ) and 
filling level (Ψ), as expressed per Eq. (1): 

𝑃𝑃[𝐹𝐹| Φ,Ψ] = 1 −�𝑒𝑒
−� Φ
𝑚𝑚𝑖𝑖(Ψ)�

𝑏𝑏𝑖𝑖(Ψ)3

𝑖𝑖=1

, (1) 

where Φ = ℎ𝑤𝑤 ℎ𝑓𝑓,𝑚𝑚𝑚𝑚𝑚𝑚⁄  and Ψ = ℎ𝑓𝑓 ℎ𝑓𝑓,𝑚𝑚𝑚𝑚𝑚𝑚⁄  are the normalized inundation depth and filling degree; and ℎ𝑓𝑓 is the 
height of the internal liquid. The subscript 𝑖𝑖 =  1,2,3  indicates the activation of each of the three failure 
mechanisms (shell buckling, shear failure of the anchors, and uplift due to tension failure of the anchors), with 

164



𝑎𝑎𝑖𝑖(Ψ) and 𝑏𝑏𝑖𝑖(Ψ) being the scale and shape parameters of a Weibull distribution, respectively. The value of these 
coefficients is available in Vitale (2024) for different values of tank height-to-radius ratio. 

2.3 Rate of multiple simultaneous structural failures 

The structural failure rate of a storage tank with a given filling level Ψ, is provided by Eq(2): 

𝜆𝜆𝑓𝑓,𝑗𝑗 = 𝜈𝜈 ∙ 𝑃𝑃�𝐹𝐹𝑗𝑗� = ∫ 𝑃𝑃�𝐹𝐹𝑗𝑗|Φ,Ψ� ∙ �𝑑𝑑𝜆𝜆Φ,j�
100%
0 , (2) 

that is, the product of the tsunami occurrence rate (of any intensity) at the site, 𝜈𝜈, and the probability of failure 
given a tsunami event of tank j out of n, 𝑃𝑃�𝐹𝐹𝑗𝑗�, or – equivalently – the integral of the fragility curve times the 
absolute value of the hazard curve’s differential. This rate represents the average annual number of tsunamis 
that trigger the release of contents due to tank structural damage. 
For the consequence analysis, one should consider the simultaneous occurrence of structural failure in more 
than one tank. If failure of various industrial units can be assumed stochastically independent (Cozzani et al. 
2014), for a group consisting of 𝑛𝑛 tanks, the probability to observe exactly 𝑘𝑘 out of 𝑛𝑛 failed tanks is: 

𝑃𝑃[𝐹𝐹 = 𝑘𝑘] = ���1 − 𝑃𝑃�𝐹𝐹𝑗𝑗� + 𝛿𝛿𝑖𝑖𝑗𝑗 ∙ �2 ∙ 𝑃𝑃�𝐹𝐹𝑗𝑗� − 1��
𝑛𝑛

𝑗𝑗=1

�𝑛𝑛𝑘𝑘�

𝑖𝑖=1

 (3) 

where 𝑖𝑖 = 1,2, … , �𝑛𝑛𝑘𝑘� is the number of combinations of k failed tanks out of n, and 𝑗𝑗 = 1,2, … ,𝑛𝑛 is the number 
associated to each individual tank. The symbol 𝛿𝛿𝑖𝑖𝑗𝑗, is an indicator function equaling one if the j-th tank has failed, 
and zero otherwise. Finally, the rate of simultaneous failure of k tanks can be obtained from Eq(4): 

𝜆𝜆𝑓𝑓(𝑘𝑘) = 𝜈𝜈 ∙ 𝑃𝑃[𝐹𝐹 = 𝑘𝑘]. (4) 

2.4 Consequence analysis and risk assessment 

Considering the failure mechanisms described in Section 2.2, the instantaneous release of the complete tank 
content was considered in the consequence analysis. In addition, a worst-case approach was applied to the 
QRA, following Ricci et al. (2024). The method entails including a single representative scenario for each tank 
in the analysis, chosen to be the worst-case in terms of consequences. The quantification of NaTech scenarios 
including the possibility of simultaneous multiple equipment failures was performed following the methodology 
proposed by Cozzani et al. (2014). Individual and societal risk indices can then be calculated, reflecting the 
consequences of the technological scenarios on human life. Specifically, consequences are quantified via (local 
specific) maps of the individual risk (IR). In these maps, the annual death rates of an unprotected individual, 
assumed in a specific location around the area of the plant, continuously exposed to accident scenarios arising 
from all the risk sources considered are reported. The societal risk, on the other hand, is a measure to evaluate 
the risk of multiple fatalities. The outcomes are illustrated by means of F/N plots, in which N is the number of 
deaths and F(N) is the cumulative annual frequency of accidents with N or more deaths (Uijt de Haag, Ale, 
2005). Societal risk can be also expressed using more concise risk indices: the Potential Life Loss (𝑃𝑃𝑃𝑃𝑃𝑃) and 
the Expectation Value (𝐸𝐸𝐸𝐸), calculated according to Eqs (5) and (6) respectively: 

𝑃𝑃𝑃𝑃𝑃𝑃 = � 𝑓𝑓(𝑁𝑁) ∙ 𝑁𝑁 
𝑁𝑁

 (5) 

𝐸𝐸𝐸𝐸 = � 𝑓𝑓(𝑁𝑁) ∙ 𝑁𝑁𝛼𝛼
𝑁𝑁

 (6) 

in which 𝑓𝑓(𝑁𝑁) is the annual frequency of scenarios causing 𝑁𝑁 fatalities, and 𝛼𝛼 is a parameter used to give more 
relevance to the consequences of the accidents leading to multiple fatalities. In the present study, a value of 2 
is attributed to the 𝛼𝛼  parameter (Misuri et al. 2023). A conventional QRA for the industrial site was also 
performed following the approach proposed by Uijt de Haag and Ale (2005) to compare the results of risk figures. 
Specifically, F/N curves were calculated considering only internal failures and including also the scenarios 
triggered by the tsunami (Antonioni et al. 2009). 

3. Case study 
QRA was carried out for the case study of a hypothetical coastal refinery located in Milazzo (ME) in southern 
Italy. The facilities considered are the six atmospheric storage tanks in Figure 1a. All tanks are anchored to the 
base and equipped with a floating roof. The roof moves with the internal liquid up to a height ensuring a freeboard 
to avoid spillage. A typical section of the examined tanks is shown schematically in Figure 1b, while the main 
features are provided in Table 1. Typically, the contents are highly flammable substances, like crude oil and 
gasoline, which are considered in the case study.  

165



Table 1: Geometric properties, storage liquid and basin area of the case study tanks. 

ID item Height [m] Diameter [m] Content Catch basin area [m2] 

𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘1, 𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘2 16 55 Crude oil 7600 
𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘3, 𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘4, 𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘5, 𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘6 13 40 Gasoline 3200 
 
The tsunami QRA is performed considering the tanks with three different degrees of filling: 10%, 50%, and 90%. 
For consequence evaluation, pool fires were considered as the worst-case scenario after a catastrophic failure 
of the tank. The probability of immediate pool fire ignition for tsunamis is assumed 0.013 (Ricci et al. 2021). 
Established literature models were applied for consequence analysis (Van Den Bosh & Weterings, 2005). For 
the sake of simplicity, a single set of meteorological conditions was considered: a uniform wind distribution and 
neutral atmospheric stability (wind speed at 5 m/s, Pasquill class D). For societal risk calculation, a uniform 
population density of 50 inhabitants/hectare was considered, with a presence probability of 60%. 

4. Results and discussion 
Figure 2a presents the hazard curves derived from the PTHA for the grid points identified by the red squares in 
the Figure 1a. The hazard results show that tanks located closer to the coast, as 𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘1 and 𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘3, are generally 
at greater hazard. In addition, for the site of the case study, the inundation levels considered in PTHA never 
reach values larger than half of the height of the tanks, more specifically, slightly more than 40 % for 𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘3, 
about the 37 % for 𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘1  and 𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘4 , about the 30 % for 𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘2 , 𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘5  and 𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘6.All tanks have about the 
same height-radius ratio, thus, the fragility curves of Figure 2b can be representative of all of them. The figure 
shows the fragility curves for the three normalized filling levels considered: 10%, 50%, and 90%. As can be 
seen, an almost empty tank is more vulnerable than a full tank. 

 
Figure 2: a) Hazard curves associated with each tank. b) Fragility functions for three filling levels. 

Table 2: Structural failure rates of each tank for the three filling levels. 

Ψ 𝜆𝜆𝑓𝑓 [1 𝑦𝑦⁄ ] 
[%] 𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘1 𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘2 𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘3 𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘4 𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘5 𝑇𝑇𝑎𝑎𝑛𝑛𝑘𝑘6 
10 3.94E-06 1.03E-06 2.77E-06 1.39E-06 6.14E-07 3.89E-07 
50 4.97E-09 1.07E-09 4.96E-09 1.61E-09 5.68E-10 3.59E-10 
90 6.03E-10 1.37E-10 4.54E-10 2.22E-10 7.24E-11 4.42E-11 

Table 3: Probability of failure of exactly k tanks given the failure at least one for the three filling levels. 

Ψ 𝑃𝑃[𝐹𝐹 = 𝑘𝑘|𝐹𝐹 ≥ 1] 
[%] 𝑘𝑘 = 1 𝑘𝑘 = 2 𝑘𝑘 = 3 𝑘𝑘 = 4 𝑘𝑘 = 5 𝑘𝑘 = 6 
10 0.87 0.12 8.31E-03 3.24E-04 6.64E-06 5.57E-08 
50 0.99 1.51E-04 1.16E-08 4.85E-13 1.04E-17 9.12E-23 
90 0.99 1.79E-05 1.67E-10 8.53E-16 2.27E-21 2.45E-27 

 
The fragility and the hazard curves are integrated to derive the structural failure rate of each tank and the values 
are reported in Table 2. As expected from the fragility models, failure rates in Table 2 are higher for near-empty 
tanks. For the consequence analysis, all rates of 𝑘𝑘 simultaneous tank failures are considered, with 𝑘𝑘 spanning 
all values from 1 to 6. In Table 3 a more parsimonious version of that result is shown, that is the probability of 
observing exactly 𝑘𝑘 failed tanks given that the tsunami event has caused at least one failure, 𝑃𝑃[𝐹𝐹 = 𝑘𝑘|𝐹𝐹 ≥ 1]. 
From the values reported in the table, it appears that the probability of observing the simultaneous failure of 
more units than one, given that the tsunami has caused at least one failure has occurred, ranges from an order 

166



of 10−1 up to 10−8 for 10% filling level, depending on the number of failures.The rates obtained considering the 
simultaneous failures are then used together with the consequences assessment results to provide risk figures. 
Figure 3 illustrates the local specific IR maps considering the tsunami impact on the case-study tank facility. 
The calculation is performed considering all tanks simultaneously found in one of three filling levels: 10% (panel 
a), 50% (panel b), and 90% (panel c). The contour lines indicate that by increasing the filling level, the IR due 
to tsunami hazard decreases. This effect is especially pronounced between filling levels of 10% to 50%, where 
the maximum individual risk decreases by three orders of magnitude. This trend somehow reflects the one 
related to the failure rates of tanks, strongly influenced by the filling level. On the contrary, consequences are 
less affected by the reduction of the content, since the liquid loss covers the entire catch basin even with smaller 
filling levels, leading to similar consequences arising from pool fire. Noteworthy, the duration of the pool fire 
increases considerably as the filling level increases, but in all cases considered it is well above twenty seconds, 
which are considered in the probit function for calculating the death probability (Van Den Bosh CJH, 1992).  

 

Figure 3: Local specific maps of Individual Risk considering different filling levels in the tanks. a) 10%. b) 50%. 
c) 90%. 

 

Figure 4: (a) Risk index calculated for the three filling levels considered in the analysis. (b) Societal risk 
expressed in terms of cumulative frequency vs number of fatalities calculated for conventional activities. 

Figure 4 shows the societal risk outcomes. Panel a) illustrates the values of the risk indices, PLL and EV, for 
the three filling levels considering accident scenarios triggered by tsunami action. The order of magnitude of 
both indices decreases with increasing tank filling levels, confirming the trend discussed previously. Panel b) 
compares the F/N curves considering the conventional risk (red curve) and conventional risk adding the 
contribution of the tsunami risk (blue curve). Conventional risk refers to the potential hazards associated with 
typical activities and internal failures. The calculation of the tsunami risk is carried out considering the tanks with 
a uniform distribution of the three filling levels included in the study. The comparison between the red and blue 
curve reveals that up to twenty fatalities, the tsunami risk has a negligible impact, yet beyond this value, tsunami 
significantly increases the potential for fatalities. In fact, conventional causes of accidents lead to a maximum of 
about thirty-five fatalities, while the addition of tsunami risk may cause a death toll of about one-hundred due to 
the possible multiple simultaneous failures of tanks. 

167



5. Conclusions 
This paper presented a comprehensive QRA analysis for a petrochemical plant of anchored atmospheric 
storage tanks under tsunami action, in southern Italy, examining their behaviour for three filling levels. The key 
results of the analysis are that the tanks are more vulnerable for low filling levels; and that the values of structural 
failure rates are strongly influenced by the hazard at the site. While this case study is based on an actual 
petrochemical facility at that location, a limited number of tanks was considered, to maintain the computational 
burden of QRA manageable. Therefore, these results are useful in a comparative sense, rather than for 
considerations of risk acceptability for the entire facility. In fact, the QRA results show that, for this site, tsunami 
hazard is a non-negligible source of risk if compared to the conventional activities risk.  

Acknowledgments 

The study presented was developed within the RETURN “Multi-risk science for resilient communities under a 
changing climate” (National Recovery and Resilience Plan-NRPP, Mission 4, Component 2, Investment 1.3 – 
D.D. n.341 15/3/2022, PE0000005); PRIN 2017 Assessment of Cascading Events triggered by the Interaction 
of Natural Hazards and Technological Scenarios involving the release of Hazardous Substances funded by the 
Italian Ministry of Universities and Research; and within the activities with ReLUIS-DPC (Rete di Laboratori 
d’Ingegneria Sismica-Dipartimento di Protezione Civile) 2022−2024 research agreement, funded by the Italian 
Department of Civil Protection. 

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