When cylindrical tanks installed on the ground, such as oil tanks and liquid storage tanks, receive strong seismic waves, including the long-period component, motion of the free liquid surface inside the tank called sloshing may occur. If high-amplitude sloshing occurs and the waves collide with the tank roof, it may lead to accidents such as damage to the tank roof or outflow of internal liquid. Therefore, it is important to predict the wave height of sloshing generated by an earthquake input. Sloshing is vibration of the free liquid surface, and when the sloshing wave height is small, it can be approximated with a linear vibration model. In that case, the velocity-response-spectrum method using velocity potential can estimate the sloshing wave height under an earthquake input. However, when the sloshing wave height increases and the sloshing becomes nonlinear, it is necessary to evaluate the wave height using other methods such as numerical analysis. Taking into consideration that design earthquake levels tend to increase and the use of seismic isolation mechanisms has continued to spread in recent years, the amplitude of the long-period components of an earthquake input which act on cylindrical tanks may also increase. Therefore, although the evaluation of nonlinear sloshing wave height is important, there are few examples which quantitatively evaluate the wave height of nonlinear sloshing. The purpose of this study is to construct a simple evaluation technique of a nonlinear sloshing wave height of cylindrical tanks. In this study, the simple evaluation technique of the nonlinear sloshing wave height was proposed based on the study result shown by the 1st report (PVP2018-84416). Moreover, in order to verify the applicability of the proposed evaluation technique, the shaking table test and flow analysis which used the small cylindrical tank were carried out. As a result, the applicability of the proposed evaluation technique has been verified.

Buckling behavior of tanks with a conical roof under harmonic settlement has been researched in this paper. A real tank in engineering is taken into account and the harmonic settlement is applied to the bottom of the tank to simulate its buckling behavior. Results show that the tank wall will be subjected to a deformation mutation when the settlement reaches a critical value. It means that compared to the conical roof, the tank wall is more vulnerable to buckling. Because of the complexity added by the grid of rafters and rings on the roof, two different simplified models are presented. For the first model, the tank’s roof is modified to an equivalent thickness based on the smeared method; for the other one, the roof is completely eliminated and its influence is represented by simply supported boundary conditions at the top of the tank wall. Analysis shows that the tank model without a roof can’t reflect buckling behavior of the real tank in engineering very well. While the model with an equivalent thickness roof can avoid this deficiency and achieve high efficiency and accuracy. It’s recommended to be applied to buckling analysis of tanks under settlement. Based on that, effects of wave numbers on the critical settlement for the three models are researched and compared. Result shows that the simplified tank model with an equivalent thickness roof presented in this paper is efficient and useful for buckling analysis of tanks with a conical roof under settlement.

When cylindrical tanks installed on the ground, such as oil tanks and liquid storage tanks, receive strong seismic waves, including the long-period component, motion of the free liquid surface inside the tank called sloshing may occur. If high-amplitude sloshing occurs and the waves collide with the tank roof, it may lead to accidents such as damage to the tank roof or outflow of internal liquid. Therefore, it is important to predict the wave height of sloshing generated by an earthquake input. Sloshing is vibration of the free liquid surface, and when the sloshing wave height is small, it can be approximated with a linear vibration model. In that case, the velocity-response-spectrum method using velocity potential can estimate the sloshing wave height under an earthquake input. However, when the sloshing wave height increases and the sloshing becomes nonlinear, it is necessary to evaluate the wave height using other methods such as numerical analysis. Taking into consideration that design earthquake levels tend to increase and the use of seismic isolation mechanisms has continued to spread in recent years, the amplitude of the long-period components of an earthquake input which act on cylindrical tanks may also increase. Therefore, although the evaluation of nonlinear sloshing wave height is important, there are few examples which quantitatively evaluate the wave height of nonlinear sloshing. The purpose of this study is to construct a simple evaluation technique of a nonlinear sloshing wave height of cylindrical tanks. In this study, the shaking table test using the small cylindrical tank for studying the behavior of nonlinear sloshing was carried out. Furthermore, verification of the flow-analysis technique described by previous report (PVP2017-65313) was carried out by comparing with test results. As a result, the data for constructing an evaluation technique has been acquired. Moreover, the validity of the flow-analysis technique was has been verified.

In order to study the structural fatigue safety of in-service fixed roof storage tanks after uneven settlement, an exponential curve method of settlement prediction has been constructed. A finite element model based on the contact condition between the elastic ring beam foundation and the tank base was also proposed. On the basis of above, a fatigue life prediction method of in-service storage tanks based on the settlement prediction model has been established. Combined with the engineering example of an in-service tank, the structural fatigue safety under the actual uneven settlement was analyzed. The results indicate that the trend of foundation settlement with time could be predicted accurately and the contact condition between base and foundation could be simulated simultaneously. Subsequently, the in-service tank’s structural fatigue life under the uneven settlement could be predicted.

Pressure release tank is a key component of nuclear power plant safeguard. Evaluating the fluid thrust force against nearby structures from high pressure and high temperature flow jet under postulated accidents is an essential task for nuclear system design and safety estimation. In this work, flow jet impingement from pressure release tank to nearby building roof is computed via a two-stage strategy. First, the 1-dimensional RELAP5 code is applied to estimate thermal-hydraulic conditions at pressure release tank outlet. The thermal-hydraulic computational model includes key components of pressure release tank and its connection to the pressurizer. Based upon the thermal-hydraulic estimation at the pressure release tank outlet, detailed computational fluid dynamics (CFD) simulation is performed with full considerations of how flow thrust is applied on nearby structures. The two-stage computational strategy provides a practical paradigm of fluid thrust force estimation for industrial applications.

Floating roofs are commonly used worldwide on top of cylindrical oil storage tanks as a primary means to prevent formation of vapor above stored products into the storage tanks and should provide a safe and efficient storage of products with minimal risk for the environment. However, aboveground storage reservoirs built in seismic zones are prone to earthquake damage. Extensive research has been done to enhance performance of the floating roof tanks against damage to ground foundations, fixed and floating roof, tank shells as well as adjacent piping. Indeed, the stored oil sloshing in a cylindrical storage tank is known to have caused damage to the tank shell, tank roof and as well to anti-rotation columns. One of the possible dangers of liquid sloshing is the resultant damage to in-situ roof drain systems within external floating roof tanks. Indeed, roof drain systems are designed for continuous withdrawal of rainwater from external floating roofs, and if damaged, would result in dysfunction of the systems and irreversible discharge of oil products into the containment dyke. In this regard, a reliable roof drain system should have the capability to withstand liquid sloshing effects, and to a certain degree, ensure resistance in events of displacement of the floating roof. The aim of this document is to use knowledge of flexible pipe technology and industry recognized dynamic analysis software to analyze the effects of earthquakes on the integrity of a flexible drain pipe system. Analysis of liquid sloshing effects on flexible drain pipe systems using dynamic analysis software will be presented and the effects of structural damages such as loss of anti-rotation columns on the integrity of flexible drain pipe systems will be assessed. In the end, the document will propose recommendations on how industry can further enhance roof drain systems within external floating roof tanks to ensure performance and functionality after occurrence of earthquakes.

When cylindrical tanks installed in the ground, such as oil tanks and liquid storage tanks, receive strong seismic waves, including the long-period component, motion of the free liquid surface inside the tank called sloshing may occur. If high-amplitude sloshing occurs and the waves collide with the tank roof, it may lead to accidents such as damage to the tank roof or outflow of internal liquid. Therefore, it is important to predict the wave height of sloshing generated by an earthquake input. Sloshing is vibration of the free liquid surface, and when the sloshing wave height is small, it can be approximated with a linear vibration model. In that case, the velocity-response-spectrum method using velocity potential can estimate the sloshing wave height under an earthquake input. However, when the sloshing wave height increases and the sloshing becomes nonlinear, it is necessary to evaluate the wave height using other methods such as numerical analysis. Taking into consideration that design earthquake levels tend to increase and the use of seismic isolation mechanisms has continued to spread in recent years, it is possible that the long-period components of an earthquake input which act on cylindrical tanks will also increase. Therefore, although it is thought that the evaluation of nonlinear sloshing wave height is important, there are few examples which quantitatively evaluate the wave height of nonlinear sloshing. In this study, as a simple evaluation technique of a nonlinear sloshing wave height, the applicability of the correction coefficient proposed by Shimada et al. was examined based on the flow analysis which used Volume of Fluid (VOF) method. Moreover, it was studied that the VOF method can be used to evaluate nonlinear sloshing wave height and sloshing wave crest impact pressure acting on the fixed roof of a tank. Shaking table tests will continue to be carried out in order to verify the applicability of the simple evaluation technique of nonlinear sloshing wave height. Results from flow analysis code will also be validated against these test results.

Liquid steel storage tanks are strategic structures for industrial facilities and have been widely used both in nuclear and non-nuclear power plants. Typical damage to tanks occurred during past earthquakes such as cracking at the bottom plate, elastic or elastoplastic buckling of the tank wall, failure of the ground anchorage system, and sloshing damage around the roof, etc. Due to their potential and substantial economic losses as well as environmental hazards, implementations of seismic isolation and energy dissipation systems have been recently extended to liquid storage tanks. Although the benefits of seismic isolation systems have been well known in reducing seismic demands of tanks; however, these benefits have been rarely investigated in literature in terms of reduction in the probability of failure. In this paper, A vulnerability-based design approach of a sliding concave bearing system for an existing elevated liquid steel storage tank is presented by evaluating the probability of exceeding specific limit states. Firstly, nonlinear time history analyses of a three-dimensional stick model for the examined case study are performed using a set of ground motion records. Fragility curves of different failure modes of the tank are then obtained by the well-known cloud method. In the following, a seismic isolation system based on concave sliding bearings is proposed. The effectiveness of the isolation system in mitigating the seismic response of the tank is investigated by means of fragility curves. Finally, an optimization of design parameters for sliding concave bearings is determined based on the reduction of the tank vulnerability or the probability of failure.

Catastrophic failure of above ground storage tanks was observed due to past earthquakes causing serious economic and environmental consequences. Therefore, the evaluation of the seismic vulnerability of existing liquid storage tanks located in seismic prone areas is an important task. Seismic fragility functions are useful tools in order to quantify the seismic vulnerability of structures. These functions give a probability that a seismic demand on a structural component meets or exceeds its capacity, and are generally derived by a variety of approaches, e.g., field observations of damage, static structural analyses, judgment, or analytical fragility functions. Unlike the other methods, the analytical fragility functions are developed from a coupling of the structural response analysis and a probabilistic seismic demand model. The objective of this study is to investigate the seismic vulnerability of above ground steel storage tanks using different analytical methods of the fragility function. A comparison of the well-known cloud method and the incremental dynamic analysis is performed at different limit states for two existing cylindrical steel storage tanks. The first tank represents a slender geometry with a fixed-roof and the second one is a broad tank, unanchored, and provided with a floating roof.

Double-deck floating roof has gained more and more popularity in large oil storage tanks. Wind load is one of the main factors that cause failure of the floating roofs. Because of complexity of structure and difficulty in theoretical calculation, wind load on double-deck floating roof has not been considered into the general design standards. An engineering calculation method based on finite element method for the strength and stability of double-deck floating roof under wind load is established. The relation between pressure distribution on floating roof and liquid height is studied when the double-deck floating roof locates at different levels. Results show that pressure difference on the roof reaches maximum when the liquid height is 100%. The finite element model of double-deck floating roof is established based on large deformation theory, the overall displacement, deformation and stress are obtained by applying pressure distribution on the roof. The first anti-sinking criterion and axial compression stability criterion of long bar are selected to verify the strength and stability of floating roofs under wind load. Results show that the engineering calculation method presented can be effectively used to analyze the strength and stability of double-deck floating roof under wind load.

In this paper, performance criteria for the seismic design of industrial liquid storage tanks and piping systems are proposed, aimed at defining a performance-based design framework towards reliable development of fragility curves and assessment of seismic risk. Considering “loss of containment” as the ultimate damage state, the proposed performance limits 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, performance limits 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, for an efficient analysis that provides reliable estimates of local strain demand. These models are compared successfully with available experimental data. Using those reliable numerical models, the proposed performance limits are applied in two case studies: (a) a liquid storage tank and (b) a piping system, both located in areas of high seismicity.

Floating roofs are widely used to prevent evaporation of content in large cylindrical aboveground oil storage tanks. The 2003 Hokkaido Earthquake caused severe damages to the floating roofs due to sloshing. These accidents became a cause to establish structural integrity of the floating roof tanks in sloshing. However, many designers do not have a solution for the sloshing of floating roof tanks except for three-dimensional FEA computer codes. The three-dimensional FEA requires a long computational time and expenses. The sloshing of floating roof tanks is a coupling vibration problem with fluid and structure. The simplified and convenient method has been desired for this solution. This paper presents a simplified development method of a FEA code in the axisymmetric linear problem. It is performed to modify an existing structural analysis code. The fluid behavior is formulated in terms of displacement as the Lagrangian approach.

Severe damages in aboveground storage tanks (AST) have been often experienced due to earthquakes in Japan and Taiwan. In this paper, earthquake damages of ASTs which occurred for the last several decades are reviewed. These are damages in the 1964 Niigata Earthquake, the 1978 Miyagi Earthquake, the 1983 Sea of Japan Earthquake, the 1995 Kobe Earthquake, the 2003 Hokkaido Earthquake and the 2011 Great East Japan Earthquake in Japan. Damages of ASTs in the 921 Earthquake in Taiwan are also included in this paper. The damages of ASTs can be classified into 3 types in accordance with the causes. These are the impulsive motion due to a high frequency earthquake, the sloshing motion due to a low frequency earthquake and the tsunami attack. In the impulsive motion, buckling of sidewall plates and uplift of sidewall-to-bottom joints occurred. In the sloshing motion, sinking of floating roofs into liquid and buckling of sidewall-to-roof joints occurred. In the tsunami attack, ASTs moved and overturned to leak oil.

A series of seismic table tests about the large steel cylindrical liquid storage tank models with floating roof were taken in this study. Different direction seismic excitations were input to the experimental structure system under different working conditions to test and analyze the seismic response behavior. The effects of various factors, such as the liquid surface height, the floating roof, the different wave amplitudes and frequencies, as well as their combined effects to the seismic dynamic response were taken into account. Dynamic fluid pressure data was got by the tests, and a new method that rain flow counting method was used in this study, in order to consider mean pressure throughout the vibration process, the pressure amplitude and the effective amplitude of the cumulative number of cycles factors together. Through this method, the strength of the dynamic fluid pressure could be described more reasonably. In addition, the relationship between the test results and the tank uplift responses which were studied in our former work were discussed. A reliable basis could be provided for theoretical analysis, structural design and computer numerical simulation research through this investigation.

In this paper, two finite element models are established for a super-large storage tank with or without a floating roof on the medium level. Time-history analysis with consideration of fluid-solid coupling for the deformation of tank wall and medium sloshing during or after an earthquake is performed with the emphasis on the effects of the floating roof. It is found that the upper part of tank is more sensitive to the earthquake action than the lower part. The wind girders and the reinforcing rings play a big role in limiting the radial deformation of the upper part of the tank wall. The floating roof has little effect on the tank wall deformation, but it is effective in suppressing the medium sloshing during the earthquake. After the earthquake, the radial deformation of the tank wall attenuates quickly, but the sloshing attenuation of the medium presents a slow progress and the floating roof inhibits the sloshing attenuation of the medium.

In practical engineering, local settlement is a typical differential settlement under structures. It has drawn the attention of many researchers. This is because this kind of settlement has an important effect on tank structure. From research, the buckling behavior caused by local settlement has been reported. In most research, the local settlement is usually considered alone and the influence of hydrostatic pressure has not been reported. This work studies the effect of hydrostatic pressure on the buckling strength of conical roof tanks under local settlement. The results show that the pressure has a stiffening effect on buckling strength, preventing the shell from buckling. In addition, for small uplift half angles, buckling may not occur for liquid heights larger than the critical liquid height; while for large uplift half angles buckling may occur with full tanks. It is also shown that the critical local settlement for a small uplift half angle is more sensitive to the liquid height and hydrostatic pressure than the critical load for large uplift half angles. Finally, the relationship between the critical liquid height and uplift half angle is reported.

A multi dynamic absorber for suppressing liquid sloshing in a floating roof tank is presented. As well known, many seismic damages on floating roof tanks by the sloshing of their contained liquid due to long periodic components of earthquake motion were reported. Since the natural period of sloshing varies according to the height of liquid surface, robustness for parameters such as natural period is required for the sloshing suppression device to obtain a good suppression performance. From this point of view, we developed a multi dynamic absorber instead of the single dynamic absorber which is sensitive to the parameter variance. A multi degree of freedom mechanical model for sloshing of the contained liquid and the presented multi dynamic absorber which sets up on the floating roof of the tank is derived to design the optimal tuning for parameters of the multi dynamic absorber and to evaluate the sloshing suppression performance. Numerical simulations for an actual size floating roof tank were conducted to examine the performance of the present device. As the result the effect of the presented multi dynamic absorber was effective to suppress the sloshing response of the floating roof and to be robust for the natural period variance.

The dynamic stability of a flexible plate subjected to a parallel flow is investigated when it moves in a flowing fluid. As the flexible flat plates, the papers in a high speed printing machine, the papers discharged by a paper machine, and the thin plastic and metal films, the fluttering flag and the oscillating doom roof caused by wind are enumerated. The fluid is assumed to be treated as an ideal fluid in a subsonic domain, and the fluid pressure is calculated using the velocity potential theory. The fluid-structure coupled equation of motion of a flexible flat plate supported simply at the both ends is derived into consideration with the added mass, added damping and added stiffness of a fluid, respectively. In addition, the effect of tension acting on a flexible plate, the influence of velocity of a moving plate and that of a fluid velocity, are also included into the coupled equation of motion respectively. The eigenvalue analysis is performed for the dynamic stability analysis. Changing the velocities of a plate and a fluid, and the specifications of a plate as parameter studies, the influences of these parameters on the dynamic stability of a plate are clarified. It is made clear that the plate moving in a still fluid becomes unstable at slightly lower velocity than the stationary plate subjected to a parallel flow. Moreover, it is found that the present solution shows a good agreement with the already reported experiments in which the flexible flat plate was a paper.

The deck plates of a single-deck-type floating roof for large oil storage tanks are joined by single-welded full-fillet lap joints. In areas with frequent strong winds, fatigue cracks sometimes occur in the welds of the deck plates. The aim of the present study is to investigate the effect of the gap imperfection of the lap joint on the fatigue life. Generally, weld imperfections significantly reduce the fatigue crack propagation life of the welded joints. A stress analysis using the finite element method was performed to provide the basic data for the fatigue crack growth analysis.

The deck plates of single-deck-type floating roofs for large oil storage tanks are joined by single-welded Full-fillet lap joints. In areas with frequent strong winds, fatigue cracks sometimes occur in the welds of the deck plate. The aim of the present study is to investigate the effect of the gap imperfection of the lap joints on the fatigue life. In the case that tensile load acted on Full-fillet lap joints, the stress at the crack face becomes larger by gap imperfection of the lap joint. The authors have developed a software system called “SCANP (Surface Crack Analysis Program)”, a software system to evaluate the stress intensity factor, K , and to simulate fatigue crack propagation for surface cracks for arbitrarily distributed surface stresses. The fatigue life of a lap joint was predicted by the “SCANP” using the calculated stresses at the root crack face and the toe crack face. The number of loading cycles to penetration for arbitrary bending load amplitudes and tensile load amplitudes are obtained.