A 1:4 scale seismic simulation shaking table experiment was designed and performed to study the sloshing wave height response of a storage tank under displacement due to seismic excitation, wherein a 1000 m 3 vertical storage tank was used to compare the sloshing wave height for different tanks with different foundations. Under different foundation forms, the tank motion includes sway and roll. Meanwhile, the design code and finite element method were used to compare with the experiment for mutual verification. The results show that the peak value of the sloshing wave height is at its minimum at the center, and the maximum is near the tank wall when the model tank was excited to the ground motion with the predominant frequency range from 0.29 and 0.32 Hz, and the floating roof can significantly reduce the sloshing wave height. For different input conditions with equivalent seismic magnitude, the wave heights were notably different, so the design should use multiple seismic waves as inputs. The acceleration values were different when different foundations were used, but there was little effect on the sloshing wave height. Besides, the sloshing wave heights measured in the experiment were close to those calculated using standard equations and finite element results, which proves that the three can verify each other.

The causes of roof damage found on a large-scale water storage tank were investigated using hydrodynamic analysis. All operation and weather data, such as temperature inside and outside of the storage tank, atmospheric pressure, water level according to time, condensed water check inside pipelines, snowfall, and wind speed, were precisely reviewed. Four potential scenarios were postulated to estimate the vacuum pressure, presumed to be a direct cause of the roof damage to the storage tank. In the scenarios, an energy equation with a friction loss for pipelines and fittings was adopted to compute the pressure differences between the inlet and outlet of the ventilation and overflow pipes. A timewise pressure drop for the condition of fully clogged connected lines during a discharge operation was also carried out. A sequence solution for the unsteady Bernoulli equation to represent the dynamic motion of a water column inside a loop seal was successfully derived. This can predict the vacuum pressure limit inside the storage tank required to drain out the water from the loop seal. The predicted vacuum pressure was compared with the vacuum pressure required to cause the buckling phenomena at the roof support structures. In-depth analysis of each scenario showed that the roof damage of the storage tank developed when the vacuum pressure reached over the estimated vacuum pressure limit. To prevent further roof damage, including the storage tank of the same design at other plant, change of the layout of the air ventilation line was recommended.

The behavior of aboveground storage tanks subjected to seismic excitation was investigated using numerical methods by taking flexibility of foundation into account. The hydrostatic load due to stored liquid has an axisymmetric distribution on the tank shell and base. However, during seismic events, the hydrodynamic load originating from the seismic acceleration of liquid in the tank starts to act in the direction of the earthquake motion. This leads to a nonaxisymmetric loading distribution, which may result in buckling and uplifting of the tank structure. Finite element models were created having nonlinear material properties and large deformation capabilities. Three different tank geometries with liquid height to tank radius aspect ratios of 0.67, 1.0, and 3.0 were selected representing broad, nominal, and slender tanks. These tanks were subjected to two different hydrodynamic loading based on Housner's and Jacobsen–Veletsos' pressure distributions, which forms the basis of design provisions used in American Petroleum Institute API 650 and Eurocode 8, respectively. These pressure distributions were formulated under the assumption of rigid tank wall and base. Furthermore, each tank for a given geometry was subjected to two different foundations: (1) representing a rigid foundation and (2) representing a flexible foundation. The flexible foundation was created using a series of compression-only elastic springs attached to tank base having equivalent soil stiffness. Static analysis corresponding to maximum dynamic force was performed. The finite element results for circumferential and longitudinal stress in the shell were compared with the provisions of API 650. It was found that the effect of foundation flexibility from the practical design point of view may be neglected for broad tanks, but should be considered for nominal and slender tanks.

Seismic hazard represents one of the possible triggering causes for NaTech accidents in refineries and production plants. The vulnerability of steel storage tanks was evaluated within the framework of a rapid risk assessment. Tanks dataset is composed of 70 refinery items in located in various parts of Italy and the seismic calculations are performed in accordance to API 650 Annex E Standard. The paper summarizes the results of the investigation through two normalized parameters related to the masses and to the seismic load. Some trends in the solution are highlighted. The empirical fragility curve obtained from the analysis is compared with similar curves found in the literature and the resulting similarities (and dissimilarities) are critically discussed.

Catastrophic failure of the above ground steel storage tanks was observed during past earthquakes, which caused serious economic and environmental consequences. Many of the existing tanks were designed in the past with outdated analysis methods and with underestimated seismic loads. Therefore, the evaluation of the seismic vulnerability of these tanks, especially ones located in seismic prone areas, is extremely important. Seismic fragility functions are useful tools to quantify the seismic vulnerability of structures in the framework of probabilistic seismic risk assessment. These functions give the probability that a seismic demand on a given structural component meets or exceeds its capacity. The objective of this study is to examine the seismic vulnerability of an unanchored steel storage tank, considering the uncertainty of modeling parameters that are related to material and geometric properties of the tank. The significance of uncertain modeling parameters is first investigated with a screening study, which is based on nonlinear static pushover analyses of the tank using the abaqus software. In this respect, a fractional factorial design and an analysis of variance (ANOVA) have been adopted. The results indicate that the considered modeling parameters have significant effects on the uplift behavior of the tank. The fragility curves of two critical failure modes, i.e., the buckling of the shell plate and the plastic rotation of the shell-to-bottom plate joint, are then developed based on a simplified model of the tank, where the uplift behavior is correctly modeled from the static pushover analysis. The uncertainty associated with the significant parameters previously identified are considered in the fragility analysis using a sampling procedure to generate statistically significant samples of the model. The relative importance of different treatment levels of the uncertainty on the fragility curves of the tank is assessed and discussed in detail.

A simplified approach is presented for the seismic performance assessment of liquid storage tanks. The proposed methodology relies on a nonlinear static analysis, in conjunction with suitable “strength ratio-ductility-period” relationships, to derive the associated structural demand for the desired range of seismic intensities. In the absence of available relationships that are deemed fit to represent the nonlinear-elastic response of liquid storage tanks, several incremental dynamic analyses are performed for variable post-yield hardening ratios and periods in order to form a set of data that enables the fitting of the response. Following the identification of common modes of failure such as elephant's foot buckling (EFB), base plate plastic rotation, and sloshing wave damage, the aforementioned relationships are employed to derive the 16%, 50%, and 84% percentiles for each of the respective response parameters. Fragility curves are extracted for the considered failure modes, taking special care to appropriately quantify both the median and the dispersion of capacity and demand. A comparison with the corresponding results of incremental dynamic analysis (IDA) reveals that the pushover approach offers a reasonable agreement for the majority of failure modes and limit states considered.

Earthquakes represent a class of natural-technical (NaTech) hazards which in the past have been responsible of major accidents and significant losses in many industrial sites. However, while codes and standards are issued to design specific structures and equipment in both the civil and industrial domain, established procedures for seismic quantitative risk assessment (QRA) of process plants are not yet available. In this paper, a critical review of seismic QRA methods applicable to process plants is carried out. Their limitations are highlighted and areas where further research is needed are identified. This will allow to refine modeling tools in order to increase the capabilities of risk analysis in process plants subjected to earthquakes.

Aboveground vertical steel storage tanks use stiffener rings to prevent their shell wall from buckling under wind loading. The existing stiffener rings design rules from API 650 standard is known to be overly conservative. This study investigates the possibility of modifying the design rules by reducing the required size of the top stiffener ring to the same size as the intermediate stiffener ring. In this study, we used finite element analysis (FEA) to perform linear bifurcation analysis (LBA) and geometrically nonlinear analysis including imperfections (GNIA) to obtain failure load of modeled tanks. The buckling pressure load was obtained to ensure it is larger than the design pressure. Moreover, the effects of higher strength materials, different buckling modes, and various wind profiles were also studied to ensure the design suggested by this study is practical and universal to different situations. The results show that for cylindrical storage tanks, which only needs one intermediate stiffener ring, the size of the top stiffener ring can be set to the same size as the intermediate stiffener ring.

In this paper, performance criteria for the seismic design of industrial liquid storage tanks and piping systems are proposed, aimed at introducing those industrial components into a performance-based design (PBD) framework. Considering “loss of containment” as the ultimate damage state, the proposed limit states are quantified in terms of local quantities obtained from a simple and efficient earthquake analysis. Liquid storage tanks and the corresponding principal failure modes (elephant's foot buckling, roof damage, base plate failure, anchorage failure, and nozzle damage) are examined first. Subsequently, limit states for piping systems are presented in terms of local strain at specific piping components (elbows, Tees, and nozzles) against ultimate strain capacity (tensile and compressive) and low-cycle fatigue. Modeling issues for liquid storage tanks and piping systems are also discussed, compared successfully with available experimental data, and simple and efficient analysis tools are proposed, toward reliable estimates of local strain demand. Using the above reliable numerical models, the proposed damage states are examined in two case studies: (a) a liquid storage tank and (b) a piping system, both located in areas of high seismicity.

In this study, two failure modes, yield buckling of the compression ring section and strength failure in the roof-to-shell of the tank, have been proposed for a vertical vaulted tank. The failure criteria of the two failure modes in the roof-to-shell of vault tanks are established via finite element analysis of three tanks of 640 m 3 , 3200 m 3 , and 6800 m 3 in volume. The finite element models are built with axisymmetric elements and spatial multi-elements. Based on the strength failure criterion, the failure pressure formula in the vaulted tank roof-to-shell is derived. The maximum relative error between the theoretical calculation and numerical simulation is 9.7%. Finally, we verify the strength failure criterion through a tank failure test; the maximum relative error between the test and theoretical calculation is 9.6%. The failure pressure of both failure modes has been compared and analyzed. The failure pressure of the yield buckling in the compression ring section is about 1.65 times that of the strength failure in the roof-to-shell of the tank.

Design of the top wind stiffeners of aboveground storage tanks designed to the requirements of API 650 is investigated. The current design methodology is based on intuition and experience without a sound technical justification. This paper investigates a diameter limit to be used in the design of the top stiffener ring by using finite-element analysis (FEA) in a parametric study. Linear bifurcation analysis (LBA) and geometrically nonlinear analysis including imperfections (GNIA) were performed on cylindrical storage tanks. By modeling tanks with different diameters and limiting the design of top stiffener ring for a diameter of 170-ft (52-m), the buckling loads are investigated. It was found that the 170-ft (52-m) diameter is a suitable upper limit to design the top stiffener rings for larger diameters.

A series of numerical modeling and simulations were conducted for dynamic responses of a fluid-filled storage tank subjected to impact loading resulting from a high-velocity projectile. The focus of the study was placed on two phases. The first phase examined the structural response during the impact period without penetration while the second phase investigated the period of a projectile traveling through a fluid medium inside the storage tank. Some parametric studies were conducted to understand the dynamic responses of the structure. The parameters considered were the fluid filling level in the storage tank, fluid density, tank material properties, and projectile mass and velocity. Understanding what parameters would result in most severe damage to the structure can lead to improved design of storage tanks and proper protection against any potential incident.

Sloshing response of a cylindrical liquid storage tank with the double deck type floating roof (DDFR) subjected to seismic excitation is considered in this paper. The aim of the paper is to clarify the significant parameters that should be considered in the seismic design of a DDFR and proposing a practical seismic design procedure for evaluating the dynamic stresses inside a DDFR. A numerical method including fluid–structure interaction and the geometry details of a DDFR tank are established. The geometric nonlinear effects on the seismic behavior of the DDFR as well as the accuracy of common analytical solution suggested in the literature are examined by the numerical model. The numerical results show that the geometric nonlinear effects can considerably reduce the seismic stress in DDFR, but have no significant effect on the liquid hydrodynamic pressure exerted on the DDFR and the roof's vertical displacement. It is also revealed that not only the general displacement of DDFR but also the local effects of liquid hydrodynamic pressure on the bottom plate should be considered for seismic design of a DDFR. Finally, a design procedure for the evaluation of dynamic stress in the DDFR due to the seismic loads is proposed and discussed.

Liquid-roof interaction imposes a complicated distribution of out-of-plane deformation on the single-deck type floating roof (SDRF), which is the main source of considerable seismic stresses in floating roof. In this paper, an analytical solution for evaluating the dynamic interaction between the liquid and the floating roof is developed. Main physical and geometrical parameters are involved by the proposed analytical solution (PAS) for evaluating the seismic stresses of a single deck floating roof tanks (SDFR). The results of PAS are compared with the results of existing empirical formulas for various dimensions of SDRF tanks. In order to assess the validity of PAS for various sloshing wave height, a numerical model based on finite element method is established and the PAS results are compared with the finite element method (FEM) analysis results. The PAS predictions are in very good agreement with both the available empirical formula and the numerical model results.

Using extended Hamiltonian variational principle, the governing equations for sloshing response of floating roofed storage tanks are derived. The response of the floating roofed storage tanks is evaluated for different types of ground motions, including near-source and long-period far-field records. Besides comparing the response of the roofed and unroofed tanks, the effect of different ground motions on the wave elevation, lateral forces, and overturning moments induced on the tank is investigated. It is concluded that the dimensionless sloshing heights for the roofed tanks are solely a function of their first natural period. Also it is shown that while long-period far-field ground motions control the free board height, near-source records give higher values for lateral forces and overturning moments induced on the tank. This means that same design spectrum could not be used to evaluate the free board and lateral forces in the seismic design of storage tanks. Finally, two cases are studied to reveal the stress patterns caused by different earthquakes.

Storage tanks are widely used in the industry to store hydrocarbon products. Corrosion damage is considered to be a serious threat to the structural integrity of the industrial storage tanks if it occurs on the primary pressure containment boundary. Therefore, fitness-for-service (FFS) assessment of these structures is performed periodically in order to ensure the operational safety and structural integrity. In this paper, evaluation methods are proposed for FFS assessment of storage tanks undergoing corrosion damage. The proposed methods are shown to give reasonably accurate and conservative assessment of the remaining strength factor. The methods are demonstrated through an example and the results are verified by inelastic finite element analysis.

The dynamic response of a floating roof in a cylindrical liquid storage tank under wind loads is investigated analytically. Wind tunnel test in a turbulent flow is carried out to measure the wind pressure distributing over the roof surface. The measured data for the wind pressure is then utilized to predict the dynamic response of the floating roof, which is idealized herein as an isotropic elastic plate of uniform stiffness and mass. The dynamic interaction between the liquid and the floating roof is taken into account exactly in numerical sense within the framework of linear potential theory. The numerical results are presented, which illustrate the significant effect of wind loads on the dynamic response of liquid-floating-roof system in a storage tank.

An explicit analytical solution is derived for sloshing in a cylindrical liquid storage tank with a single-deck type floating roof under seismic excitation. The floating roof is composed of an inner deck, which may be idealized as an isotropic elastic plate with uniform thickness and mass, and connected to an outer pontoon, which can be modeled as an elastic curved beam. The contained liquid is assumed to be inviscid, incompressible, and irrotational. By expanding the response of the floating roof into free-vibration modes in air and applying the Fourier–Bessel expansion technique in cylindrical coordinates, the solution is obtained in an explicit form, which is exact within the framework of linear potential theory. Numerical results are presented to investigate the effect of the type (single-deck or double-deck) and stiffness of the floating roof on the sloshing response.

A finite element method (FEM)-based formulation is developed for an effective computation of the eigenmode frequencies, the decomposition of total liquid mass into impulsive and convective parts, and the distribution of wall pressures due to sloshing in liquid storage tanks of arbitrary shape and fill height. The fluid motion is considered to be inviscid (slip wall condition) and linear (small free-surface steepness). The natural modal frequencies and shapes of the sloshing modes are computed, as a function of the tank fill height, on the basis of a conventional FEM modeling. These results form the basis for a convective-impulsive decomposition of the total liquid mass, at any fill height, for the first few (two or three at most) sloshing modes, which are by far the most important ones in comparison to all other higher modes. This results into a simple yet accurate and robust model of discrete masses and springs for the sloshing behavior. The methodology is validated through comparison studies involving vertical cylindrical tanks. Additionally, the application of the proposed methodology to conical tanks and to the seismic analysis of spherical tanks on a rigid or flexible supporting system is demonstrated and the results are compared to those obtained by rigorous FEM analyses.