Sloshing Wave Height Research Articles

Seismic Response of Foundation Settlement for Liquid Storage Structure in Collapsible Loess Areas

To investigate the impact of foundation settlement in loess areas on the dynamic response of liquid storage structure (LSS) under seismic motion, a finite element analysis model of the liquid–solid coupling of LSS was established using ADINA V9.6 software. By analyzing the dynamic response patterns of LSS under seismic motion with foundation failure, this study examines the effects of foundation failure and the direction of seismic wave incidence on the equivalent stress, maximum shear stress, wall displacement, and liquid sloshing wave height of the structure. The results indicate that among the three foundation failure scenarios, foundation failure at the center of the tank bottom has the least impact on the structural dynamic response. In contrast, foundation failure affecting one-fourth of the tank base has the greatest impact. Furthermore, compared to seismic motion along the X-axis, the dynamic response of the structure is more significantly affected when seismic motion co-occurs along the X-Z-axis.

Seismic performance of base-isolated structures for swimming pool reactors under different foundation conditions.

The swimming pool reactor (SPR) is an innovative and environmentally friendly heating source. An SPR building was selected as the research subject, and a 3D dynamic interaction model incorporating the liquid sloshing effect was created using ANSYS software and the secondary development characteristics of user-programmable features (UPFs). Energy dissipation from scattered waves was accounted for using viscous-spring boundary elements, while the dynamic hydraulic effect was modeled via the Housner equivalent mechanical model. Considering soil-structure interaction (SSI) effects, this study examines the impact of isolation measures on the structure's seismic mitigation performance. It investigates how varying foundation conditions affect the seismic resistance of the isolated structure. Results indicate that seismic isolation ratios for acceleration, floor response spectra, displacement, and base shear diminish as site stiffness decreases. However, regarding sloshing wave height, seismic isolation amplified the height under all conditions but remained within safe limits. These findings offer valuable insights for seismic design across different SPRs.

Failure probability of a liquid storage tank with three-dimensional base-isolation under earthquake action

Liquid storage tanks are widely used in the petrochemical industry, but the fixed-base liquid storage tanks have a high probability of earthquake damage, therefore, the research on isolation and damping control of liquid storage tank has attracted wide attention. Based on the dual control requirements of the seismic response of the liquid storage tank itself and the liquid sloshing wave height, a new type three-dimensional isolation bearing suitable for the liquid storage tank has been obtained. Taking into account the material nonlinearity, the liquid-solid coupling, and the liquid sloshing characteristics, a numerical calculation model of the new type three-dimensional isolated liquid storage tanks is established by ADINA. The seismic vulnerability of the fixed-base and the new type three-dimensional isolated liquid storage tanks are investigated, the failure probability of liquid storage tank under different limit states is discussed, and the annual average failure probability and design life failure probability of the liquid storage tank are finally analyzed. The results show that, the probability of fully damaged wave height and axial stress of fixed-base liquid storage tank is 72.0% and 49.6% respectively, under the 9 degree rare earthquake. Compared to the fixed-base liquid storage tank, the failure probability of the axial compressive stress, hoop stress, and liquid sloshing wave height of the isolated liquid storage tank is significantly reduced, but the displacement of the isolation layer becomes the most easily damaged dynamic response. Besides, the new type three-dimensional isolation can significantly reduce the annual average failure probability and the design life failure probability of the liquid storage tank.

Study on the seismic mitigation effects of inerter isolated storage tanks

Liquefied Natural Gas (LNG) storage tanks can ensure national energy sufficiency, but they are vulnerable to earthquakes. Although ordinary seismic isolation bearings can effectively reduce the base shear force and overturning moment, they tend to amplify the height of the sloshing wave. In this paper, a hybrid vibration control method for LNG storage tanks is proposed, paralleling the series viscous mass damper (SVMD) devices with Lead-core rubber bearings (LRB). The seismic mitigation effects of this parallel seismic isolation scheme were investigated. First, three-dimensional finite element models of fixed base, LRB isolated and SVMD isolated tanks were established, and nonlinear time history analyses were performed for the three types of tanks to compare the seismic responses. It was concluded that SVMD can effectively control the sloshing wave height. In addition, the effects of site types, storage liquid heights, and SVMD's performance parameters on the seismic mitigation effects were also studied. It was found that the softer the site soil, the higher the storage liquid height would make seismic isolation less efficient. The increase of SVMD's additional equivalent mass reduces the sloshing wave height, increases the shear-to-weight ratio, and has little influence on the base displacement. The increase of SVMD's additional equivalent damping reduces the sloshing wave height, base shear force, and base displacement of the tank. The final conclusion is that SVMD can effectively control the sloshing wave height and has a good seismic mitigation effect.

An experimental study on the equivalent nonlinear model for a large-sized tuned liquid damper

A fire-suppression water tank is usually required at the top of a tall building. It would be economical to design a fire-suppression tank as a tuned liquid damper (TLD) during preliminary building design. A TLD has obvious advantages in terms of economy, maintenance, and damping efficiency with small vibrations. The sloshing nonlinearity of a TLD increases design difficulty. The purpose of this study is to investigate the nonlinear dynamic response of a large-scale TLD and provide an equivalent model for the TLD under small excitation suitable for the vibration comfort control of tall buildings. The nonlinear dynamic response was investigated through shaking table experimental results. An experiment was conducted with a TLD with a rectangular tank size of 2500 mm × 1750 mm and a sloshing period of 3.2–6.2 s. A series of TLD tests were performed with different flow-damping devices, water depths, and excitations. The time history of the water sloshing wave height was obtained using a video recognition method; the base shear force of the tank was measured simultaneously. A new nonlinear stiffness and damping model (NSD-h) was proposed that simplified the TLD as a nonlinear tuned mass damper (TMD) to predict the tank base force. In the NSD-h model, the equivalent wave height was introduced to describe the sloshing amplitude of the TLD. The nonlinear frequency and damping ratio of the TLD were calculated using the equivalent wave height. Verified in wind conditions, the NSD-h model demonstrated significantly higher accuracy than the nonlinear stiffness and damping model (NSD) with similar simple equations.

Study on the Influence of Earthquakes with Different Frequency Content on the Peak Liquid Sloshing Wave Height of Liquid Storage Tank

Liquid storage tank is an irreplaceable and extremely important vessel structure used to store liquid medium. In earthquake disaster, the liquid storage tank will not only be seriously damaged directly, but also cause serious secondary disasters, such as fire, explosion, poisoning, nuclear radiation, etc. The peak liquid sloshing wave height is an important reference index to judge whether the seismic design of the liquid storage tank is reasonable or not. The ratio of peak ground acceleration to peak ground velocity of the earthquake records (shown by A/V ratio) can well represent the characteristics of frequency content of earthquake records. In this paper, the finite element numerical simulation method is used to analyze the seismic response of six rectangular concrete tanks with different liquid heights, and their respective peak liquid sloshing wave heights are calculated. Nine seismic records with different A/V ratios are used, which are low frequency category, medium frequency category and high frequency category and there are three records in each category. At the same time, the equation in Eurocode 8 is used to calculate the peak liquid sloshing wave height of each tank for comparative study. The study results show that the peak liquid sloshing wave height calculated by the Eurocode 8 is greater than that calculated by the finite element method under low frequency and medium frequency earthquake records, indicating that Eurocode 8 is conducive to the preliminary design of the seismic performance of the liquid storage tank. However, in the case of high frequency earthquake records, the calculation result of the finite element method is larger than that of the equation in Eurocode 8. The peak liquid sloshing wave height of the liquid storage tank is more sensitive to the earthquakes with high frequency content, and the Eurocode 8 underestimates the impact of high frequency seismic response on the liquid storage tank.

Study on the Predictive Evaluation Method of Nonlinear Sloshing Wave Height and Load of Cylindrical Tanks

Study on the Predictive Evaluation Method of Nonlinear Sloshing Wave Height and Load of Cylindrical Tanks

Study on the Predictive Evaluation Method of Nonlinear Sloshing Wave Height and Load of Cylindrical Tanks

Study on the Predictive Evaluation Method of Nonlinear Sloshing Wave Height and Load of Cylindrical Tanks

Study on the Predictive Evaluation Method of Nonlinear Sloshing Wave Height and Load of Cylindrical Tanks

Study on the Predictive Evaluation Method of Nonlinear Sloshing Wave Height and Load of Cylindrical Tanks

Probabilistic seismic fragility assessment of vertical storage tank with a floating roof

Vertical storage tank is an important facility of oil depot, which may cause catastrophic accidents during strong earthquake, resulting in serious economic and environment consequences. The manuscript studies the seismic fragility of tank with a floating roof. A refined finite element model of the tank with three height-to-diameter ratios is developed. Time-history responses of sloshing wave height, base shear force and base bending moment of tank with and without a floating roof are analyzed. Then, time-history analysis of 55 ground motions is performed to establish seismic demand models for various responses and the most proper intensity measure is determined based on the dispersion and determination coefficient. Appropriate component-level and system-level damage states are defined by identifying possible failure modes during strong earthquake. Seismic fragility curves for different responses are derived for four damage states by cloud analysis. The results indicate that combined spectral acceleration is the most effective and sufficient IM and using only one component fragility to evaluate seismic performance may underestimate the tank system fragility. The results can provide practical advice for seismic risk assessment of individual tank or entire tank farm.

Seismic responses of a liquid storage tank considering structure-soil-structure interaction

Liquid storage tanks play a very important role in the petrochemical industry, in practical applications, they are often arranged in rows with small spacing, as a result, the earthquake responses will be affected by group effect. Considering the liquid–solid-soil coupling, structure-soil-structure interaction, material nonlinearity, and viscoelastic boundary, three-dimensional numerical calculation models of liquid storage tanks with compaction pile composite foundation in loess area under the conditions of single tank and group tanks were established. The seismic responses of a single tank and group tanks were compared, the group effect on the liquid storage tank under earthquake was discussed, and the parameter analysis was conducted. The results show that the group effect had an amplification effect on the effective stress of the tank wall, the liquid sloshing wave height, and the horizontal displacement of the foundation. Under the El-Centro and the Northridge waves, the effective stresses of the tank wall were amplified by 10.07% and 35.54%, respectively. The effects of the foundation deformation parameter (elastic modulus) and strength parameters (cohesion and friction angle) on the dynamic responses of the liquid storage tanks were different, but in most cases, except for axial compressive stress, the influence coefficient of the group effect corresponding to the effective stress, the liquid sloshing wave height, and the foundation horizontal displacement were positive. The influence of the group effect on the dynamic responses of the liquid storage tank under earthquake cannot be ignored.

Dynamic Responses of Liquid Storage Tank Under Near Fault Pulse-Like Earthquakes With Different Focal Mechanisms

A liquid storage tank has a very extensive role in the petrochemical industry, and earthquake damage will cause very serious consequences. Considering the fluid-solid coupling, material nonlinearity and liquid level shaking dynamic behavior, three-dimensional calculation models of non-isolated and isolated liquid storage tanks are established, respectively. 12 earthquake waves are selected from Pacific Earthquake Engineering Research Center (PEER), and there are three earthquake waves of reverse (R), strike slip (SS), reverse oblique (RO) and normal (N) focal mechanisms, respectively. The influence of the focal mechanism on the dynamic responses of the liquid storage tank is investigated. The effectiveness control of sliding isolation on a near fault earthquake is discussed. The influence of the diameter of the limiting device on the shock absorption effect is analyzed. The results show that the order of influence of four types of focal mechanisms on liquid sloshing wave height is as follows: RO$mathrm{>$R$mathrm{>$SS$mathrm{>$N. For the wall displacement, liquid pressure and effective stress of the tank wall, the response under N-type focal mechanism earthquake is generally larger than that of the other three types, and the difference of wall displacement, liquid pressure and wall effective stress under RO, R and SS focal mechanism earthquakes is small. The results show that the dynamic responses of the liquid storage tank under different focal mechanism earthquakes is quite different. Sliding isolation can significantly reduce the dynamic responses of the liquid storage tank under strong near-fault earthquakes, and the diameter of the limiting device will affect the shock absorption effect of sliding isolation.

Sloshing effect analysis of liquid storage tank under seismic excitation

Sloshing wave height is a main parameter in the seismic design of liquid storage tanks, and severe sloshing may lead to the liquid leakage or buckling of the steel tank wall. To accurately evaluate the sloshing wave height of the tank under earthquake action, a total of three shaking table tests were conducted on the liquid storage tanks, and numerical simulation methods based on the direct coupling method as well as the bidirectional coupling method were implemented. The sloshing height results from tests and simulations were compared with the values obtained from the theoretical formula, and the applicability of various calculation methods was analyzed. Thereafter, the theoretical formula of the simplified mechanical model and the bidirectional coupling method were adopted to predict the sloshing wave height of tanks with various dimensions, and the theoretical formula was further modified. Simultaneously, the influence of pulse-like ground motion on sloshing effect and hydrodynamic pressure of large-scale liquefied natural gas (LNG) storage tanks was examined. Additionally, the GB 50341–2014, API 650–2013, and Eurocode 8–2006 were utilized to assess the sloshing wave height of large storage tanks subjected to seismic ground motion, and the applicability of the computed results has been further discussed. Based on the above research, practical design recommendations were proposed in this work, which can provide a guidance for the seismic design of storage tanks.

Hydrodynamic pressure law of ground-rested circular RC tank under bi-directional horizontal seismic action

The research object is the ground-rested circular RC tank. The innovation is to reveal the hydrodynamic pressure law of ground-rested circular RC tanks under bi-directional horizontal seismic action. The relationship between the sloshing wave height and hydrodynamic pressure is determined, the hydrodynamic pressure components and their combination are verified, calculation methods for hydrodynamic pressure are developed, and their distribution laws are presented. The results show that convective hydrodynamic pressure cannot be ignored when the tank is subjected to seismic action. Hydrodynamic pressure under unidirectional horizontal seismic action in X or Y direction is obtained by square root of the sum of impulsive pressure squared and convective pressure squared. Total hydrodynamic pressure under bi-directional horizontal seismic action is obtained by the square root of the sum of X-direction hydrodynamic pressure squared and Y-direction hydrodynamic pressure squared. This method can ensure the accuracy and reliability of hydrodynamic pressure calculation.

Seismic Response considering LSI for Steel Rectangular Water Purification Structures

In this paper, the finite element method (FEM) is used to analyze the dynamic response of steel rectangular water purification structure (SRWPS) considering liquid-solid interaction (LSI) in the water treatment project of the Zhuanglang Water Supply Company in Zhuanglang County. The near-field non-pulse Friuli wave, the near-field pulse Chi-Chi wave, the far-field long-period TOM wave and the Lanzhou wave are inputted along the x-direction of SRWPS, and LSI dynamics of the structure are studied under different earthquakes. The displacement, stress and liquid sloshing laws of SRWPS are obtained. SRWPS exhibits different displacement and stress responses under the action of four different seismic waves. The liquid sloshing wave height is only sensitive to long-field long-period waves. However, the structural deformation and liquid sloshing wave height are more sensitive to the Lanzhou wave. The structural deformation nephogram shows that the structural deformation of SRWPS is located in the middle of the non-hole partition, and the deformation between the open partition and the wallboard is small.

Seismic responses and design recommendations for a plate-shell integrated concrete liquid-storage structure

The seismic capacity of a plate-shell integrated concrete liquid-storage structure (PSICLSS, a new type water treatment structure) is studied under different liquid storage conditions to obtain the most unfavorable liquid storage conditions and provide theoretical guidance for PSICLSS design and construction. In this paper, different liquid storage conditions are analyzed for the maximum displacements, principal stresses, hydraulic pressures and sloshing wave heights of liquids in the structure. The results show that different liquid storage conditions cause significant changes in PSICLSS responses. The principal stress caused by external liquid is larger than that caused by internal liquid and is maximum when both internal and external liquids are stored, close to the tensile strength of concrete. Different liquid storage conditions do not cause significant response changes in the hydraulic pressure and sloshing wave height of the liquid. The hydraulic pressure caused by internal water is higher than that caused by external liquid, but the sloshing wave height of external liquid is higher than that of internal liquid. Further, the structural and hydrodynamic response mechanisms caused by different peak accelerations are similar and only cause peak values to change significantly. Finally, some design and construction recommendations are proposed and applied to an actual project.

Earthquake-induced nonlinear sloshing response of above-ground steel tanks with damped or undamped floating roof

Liquid storage tanks are widely used in the industry and can contain not only harmless substances but also various ones that can be explosive and toxic or pollutant, thus implying that both the structure and the content must remain safe and operational under different types of loading. The same applies to any tank-connected plant system/item. Yet, past earthquakes repeatedly demonstrated that even if structural damage is prevented in the shell, severe occurrences may still be observed due to sloshing phenomena, which drive the tank-fluid system response with high impacts in case of accidental release of chemicals. Therefore, this paper studies an energy dissipation system consisting of floating roof and external dampers that are utilized to control liquid vibration by augmenting the level of damping. In order to evaluate its effectiveness at the design-level earthquakes, a series of explicit nonlinear dynamic analyses have been performed, and comparisons are provided between floating roofed steel cylindrical tanks equipped with supplemental devices and counterparts without them. Changes in seismic performance because of geometrical variations in the tank (i.e. aspect ratio) and seismic input (i.e. far and near field earthquakes) have been quantified by means of experimentally validated numerical models that account for material and geometrical nonlinearities, as well as for fluid-structure interaction in an explicit manner. Shake-table tests available in the literature have been simulated, and the proposed modelling criteria show a good fit with experimental data on two tank specimens. Analysis data sets involving three tank geometries reveal that even if the dissipation system targets mainly large-capacity tanks, it can be effectively used to enhance the performance of any system, reducing the sloshing wave height which can be excessive especially when the tank is subjected to severe near field ground motions.

The sloshing law of liquid surface for ground rested circular RC tank under unidirectional horizontal seismic action

Abstract The dynamic characteristics and liquid sloshing of a circular tank are analysed using ADINA software through seismic response analyses. The maximum sloshing wave height for the circular tank under unidirectional horizontal seismic action is developed. The calculation method involves three parameters such as tank radius, seismic coefficient and dynamic coefficient. The dynamic coefficient of liquid sloshing is determined corresponding to the long-period seismic design β spectrum with a 5% damping ratio using basic sloshing period. The established method can guide the seismic design of liquid-containing structures. The established method of calculating sloshing wave height is compared with those in the American code.

Study on Sloshing Effect of Vertical Storage Tank With Displacement Seismic Excitation

Abstract 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 m3 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.

Shock absorption of concrete liquid storage tank with different kinds of isolation measures

Concrete rectangular liquid storage tanks are widely used, but there are many cases of damage in previous earthquakes. Nonlinear fluid-structure interaction (FSI) is considered, Mooney-Rivlin material is used for rubber bearing, nonlinear contact is used for sliding bearing, numerical calculation models of no-isolation, rubber isolation, sliding isolation and hybrid isolation concrete rectangular liquid storage tanks are established; dynamic responses of different structures are compared to verify the effectiveness of isolation methods; and influences of earthquake amplitude, bidirectional earthquake and far-field long-period earthquake on dynamic responses are investigated. Results show that for liquid sloshing wave height, rubber isolation cause amplification effect, while sliding isolation and hybrid isolation have reduction effect; displacement of rubber isolation structure is much larger than that of sliding isolation with limiting-devices and hybrid isolation structure; when PGA is larger, wall cracking probability of no-isolation structure becomes larger, and probability of liquid sloshing wave height and structure displacement of rubber isolation structure exceeds the limit is also larger; under bidirectional earthquake, occurrence probabilities that liquid sloshing wave height and structure displacement of rubber isolation structure exceed the limit will be increased; besides, far-field long-period earthquake mainly influences structure displacement and liquid sloshing wave height. On the whole, control effect of sliding isolation is the best, followed by hybrid isolation, and rubber isolation is the worst.