Seismic Vulnerability Analysis of Steel Clarification Tank

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Introduction
Te probability of a certain degree of damage to a steel clarifcation tank under diferent ground shaking responses, i.e., fragility, is a probabilistic event.Fragility can not only predict the components and location of structural damage of steel clarifcation tank but also prevent disasters induced by structural damage due to fragile components.Terefore, many scholars have studied fragility to determine the location of structural damage under earthquake conditions, which has become a method to determine the damage of structures under earthquakes in many studies, is widely used to identify the reliability of steel clarifcation tank under earthquakes, and is also used to determine the seismic resistance of steel clarifcation tank.
Kong et al. [1] obtained the susceptibility curves under each performance parameter through a large number of nonlinear fnite element simulations and analyzed the probability of dam damage under seismic efects of diferent intensities.Based on the energy density and maximum plastic strain criterion, Zhao et al. [2] established the limit state equations for the damage failure of chemical storage tanks under the coupled action of explosion shock wave and debris.Chen et al. [3,4] established the limit state equation for the target liquid storage tank under the coupled action of temperature load and explosive fragment impact load and analyzed the infuence law of explosive fragment mass, impact velocity, and impact angle on the vulnerability of the target liquid storage tank under diferent tank wall temperatures.Ye et al. [5] calculated the various susceptibility parameters of the tank to derive the damage curve to analyze the low failure probability values.Aliche et al. [6] used the concept of natural hazard vulnerability based on the vulnerability index (I-V) assessment to predict the possible degradation and aging of the tank structure.Wei et al. [7] analyzed the form of the relationship between seismic acceleration and the degree of damage to the storage tank by using probabilistic estimation.Qi [8] plotted the vulnerability curves of vaulted tanks under explosive fragments by the fnite element method for large vertical liquid storage tanks sampled and calculated.Sun et al. [9] introduced a probability model of random variables and a failure probability calculation method based on susceptibility theory and concluded that multiple failure modes for seismic susceptibility study of liquid storage tanks are more scientifc than susceptibility study from a single failure mode.Li [10] studied the seismic damage characteristics of liquid storage tanks and determined the failure mode and damage criterion of liquid storage tanks accordingly.Rong et al. [11] performed an incremental dynamic analysis of the containment structure by establishing a refned fnite element model.Vamvatsikos and Cornell [12] analyzed the seismic capacity of the structure statistically by amplitude modulation of selected multiple seismic waves and by many dynamic responses using incremental dynamic analysis to make the structure go through from elastic to inelastic phase.Lu et al. [13] did dynamic elastoplastic time analysis to calculate and analyze the whole process of the structure under the action of diferent ground shaking intensities in going through elastic and elastoplastic phases and fnally to collapse thus deriving the vulnerability results.Zhang [14] used the damage state of a liquid storage tank to calculate the failure mode of the structure and to study the susceptibility and failure probability of the structure.Te methods that can be used to perform structural susceptibility analysis include the expert discrimination method, empirical analysis method, analytical method, and hybrid method, among which Razzaghi and Eshghi [15] evaluated the susceptibility of steel storage tanks by using analytical and empirical analysis methods to analyze the safety of the structure and studied that the height-to-diameter ratio and liquid storage volume are the main indicators afecting the susceptibility of the storage tanks.Phan et al. [16] analyzed the seismic susceptibility of a high-level steel storage tank supported by reinforced concrete frame columns and fnally concluded that PGA is the most efective seismic strength indicator.Zhang et al. [17] studied the dynamic properties of the structure by numerical simulation and further analyzed the damage mechanism of the structure, concluding that the tank wall was compressed along the annulus and tensioned along the axial direction during the dynamic response.
In summary, seismic performance analysis can efectively estimate the hazard of a structure under earthquake action, and many scholars have studied the susceptibility to damage to determine the location of structural damage under earthquake conditions.In order to study the susceptibility of steel clarifcation tank under seismic waves, this study analyzes the seismic capacity of steel clarifcation tank by using near-feld impulse seismic waves, near-feld noimpulse seismic waves, and far-feld seismic waves for dynamic response analysis, analyzes the seismic capacity of steel clarifcation tank by IDA curve clusters, and studies the susceptibility of steel clarifcation tank based on the susceptibility method, which has guiding signifcance for the structure in terms of higher stress and member destabilization damage.

Analytical Model and Parameter Setting
In this paper, the fnite element method is used to analyze the clarifcation tank.Te schematic diagram is shown Figure 1.Te parameters are selected in Table 1.Te body of the clarifcation tank is a steel structure.Te diameter of the outer tank is 11.50m, the diameter of the inner tank is 3.65m, and the height is 10.50m.Te main components include the guide plate, reaction barrel, water collection tank, fender, and other components for the steel plate.Te fnite element software ADINA is used.Te wall, inner barrel, cone, and bottom of the clarifcation tank are divided into shell elements.In order to make the numerical simulation results more accurate, the cell mesh size is less than 1/10∼1/8 wave length, and the three-dimensional fnite element analysis model is obtained, as shown in Figure 2.

Failure Criterion of Steel Clarification Tank
Steel clarifcation tank as a special structure, the peak of liquid shaking will be too large to cause the outfow of liquid, which will lead to disaster, considering the special characteristics of the clarifcation tank, using the following failure criterion [18].

Liquid Shake Height Limit (H limit ).
Te liquid in the clarifcation tank will sway under the excitation of the seismic wave.If the reserved dry chord height does not exceed the maximum height of the liquid sloshing peak, the liquid will overfow from the clarifcation tank, causing secondary disasters and certain economic losses.Terefore, it is very important to set the liquid sloshing peak as the failure criterion.Te failure criterion is as follows: where H is the liquid sloshing height and H limit is the distance from the static liquid level to the top of the panel, which is the dry chord height.

Structural Displacement Limit (S limit ).
Te structure of clarifcation tank will produce a large horizontal displacement S under the action of an earthquake.When a rare earthquake is encountered, the structural displacement S will be larger.Selecting the displacement limit S limit of the clarifcation tank as the failure criterion not only has a guiding efect on the damage of the structure but also has important judgment signifcance for the outfow rate of liquid under the cracking of the structure.
2 Shock and Vibration where S is the structural displacement and S limit is the maximum structural displacement [18].

Vulnerability Analysis Method.
Vulnerability refers to the probability that the structure reaches or exceeds a certain limit state under diferent intensity earthquakes, or the possibility of some degree of damage to the structure due to the occurrence of earthquakes.At present, the methods that can be used for structural vulnerability analysis mainly include expert discrimination method, empirical analysis method, analytical method, and mixed method.Te main steps of structural vulnerability analysis based on the analytical method are as follows: (a) Select a certain number of seismic records, gradually increase the seismic intensity, and perform incremental dynamic analysis on the structure in turn.(b) Determine the index PI that can refect the structural failure (failure) state, and defne a reasonable value PI i .(c) Te probability P of structural damage DM exceeding the damage index PI i under earthquakes with diferent intensities IM i is calculated.Te existing research shows that the probability distribution of structural damage DM conforms to the lognormal distribution.Te advantage of this assumption is that it can provide mathematical convenience for the uncertainty and randomness of   Shock and Vibration 3 structural seismic capacity and seismic demand.Te details can be expressed as follows: where μ ln DM|IM�IM i and μ ln DM|IM�IM i are the log mean and log standard deviation of the structural damage DM when IM � IM i .Φ(•) is the standard normal cumulative distribution function.(d) Taking the ground motion intensity index IM as the abscissa and the exceedance probability P as the ordinate, the seismic vulnerability curve of the structure can be obtained by ftting the data points with statistical methods.

Critical Amplitude.
Regarding the sloshing wave height of the fuid in the liquid storage structure, the "Standard for seismic design of petrochemical steel equipments" (GB50761-2012) [19] stipulates where k is the long-period response spectrum coefcient, T is the basic period of fuid sloshing, and a is the seismic infuence coefcient.

Ground Motion Information
In order to study the incremental dynamic analysis and vulnerability of steel clarifcation tank, a certain number of seismic waves are selected under diferent types of near-feld pulse, near-feld nonpulse, and far-feld seismic waves.In order to reduce the infuence of seismic wave uncertainty on IDA (increment dynamic analysis) analysis of clarifcation tank, 10 seismic waves are randomly selected under diferent types of seismic waves for analysis and research to obtain relatively accurate and reliable evaluation and judgment results.

IDA Curve Cluster of Clearing Tank under Near-Field Pulseless Seismic
Wave.In order to analyze the clarifcation tank structure and liquid under near-feld no-pulse, 10 seismic waves are selected from the near-feld database, as shown in Table 2.In order to analyze the vulnerability and incremental dynamic analysis more accurately, PGA (peak acceleration of earthquake) is used to indicate the intensity index, and then, the amplitude of the seismic waves is adjusted, so that the PGAs are gradually adjusted from 0.1 g to 1.0 g, and each adjustment increases by 0.1 g for a total of 10 times, and then, the fnite element software is applied in near-feld no-pulse seismic action on the clarifcation tank in the full water state, the maximum stress, maximum displacement, and the maximum peak of liquid shaking are recorded, and then, the data are organized, respectively, and IDA curve clusters of structural stress, IDA curve clusters of structural displacement, IDA curve clusters of wave height, and IDA curve clusters under near-feld no-pulse seismic waves are shown in Figure 3.
It can be seen from Figure 3 that the IDA curve shows a diferentiation trend after the maximum structural stress of the clarifcation tank is PGA 0.4 g; after the liquid sloshing wave height is PGA >0.1 g, the IDA curve diferentiation phenomenon appears, and the diferentiation is more uniform, refecting that the selection of near-feld nonpulse seismic waves is random, and the evaluation results will be more accurate.

IDA Curve Cluster of Clearing Pond Structure under Near-Field Impulse
Earthquake.In order to analyze the structure and liquid of the clarifcation tank under near-feld pulsed, 10 seismic waves are selected from the near-feld pulsed database, as shown in Table 3, and the intensity index is expressed by PGA, and then, the amplitude of the seismic waves is adjusted, so that the PGAs are gradually adjusted from 0.1 g to 1.0 g, and each adjustment increases by 0.1 g, for a total of 10 times, and the fnite element software is applied to the clarifcation tank flled with water under near-feld pulsed seismic action.By the calculation, the IDA curve clusters of structural forces, structural displacements and wave height under near-feld pulse seismic wave are shown in Figure 4.
As can be seen from Figure 4, the structural maximum stress of the clarifcation tank is basically similar to the structural interlayer displacement response at PGA <0.1 g; the structural displacement of the clarifcation tank shows IDA curve divergence after PGA >0.2 g; the shaking wave height of the liquid shows IDA curve divergence after PGA >0.1 g, and the divergence is basically uniform except for the rest at the beginning, refecting the selection of near-feld with pulsed seismic waves with randomness, and the assessment results will be more accurate.

IDA Curve Cluster of Clearing Pond
Structure under Far-Field Earthquake.In order to analyze the structure and liquid under the action of the far-feld earthquake, 10 seismic waves are selected from the far-feld database, as shown in Table 4.In order to analyze the susceptibility and incremental dynamic analysis more accurately, PGA is used to indicate the intensity index, and equal steps of amplitude response is the largest category under the three diferent types of waves, and the exceedance probability of steel clarifcation under near-feld unpulsed seismic action is the smallest.In the near-feld pulsed and far-feld seismic waves, the transcendence probability of steel clarifcation under these two types of seismic waves is very close; among the three types of seismic waves selected, the transcendence probability of damage occurs when the PGA reaches and exceeds 1.0 g.From this aspect, it is inferred that the probability of damage to the clarifcation tank under particularly large seismic waves is very high, and in order to prevent the clarifcation tank from breaking the ring due to the earthquake, it is very important to prevent the damage of the clarifcation tank by some strengthening measures.It is very necessary to prevent the damage to the clarifcation tank by some strengthening measures.Compared with the research results [18], the results are consistent with the research results, which prove the reliability of the research results.

Conclusions
(1) Under the near-feld pulse ground motion response, the stress of the clarifcation tank structure is basically similar when PGA <0.1 g.After PGA >0.4 g, the IDA curve of the structural displacement of the clarifcation tank showed a diferentiation trend.After the sloshing wave height of the liquid in the clarifcation tank is PGA >0.1 g, the IDA curve diferentiation occurs, and the diferentiation is more uniform.(2) Under the near-feld ground motion without a pulse, the interstory displacement response of the structure is similar when PGA <0.1 g.After PGA >0.2 g, the IDA curve diferentiation phenomenon appeared in the structural displacement of clarifcation tank.After PGA >0.1 g, the IDA curve diferentiation phenomenon appears in the sloshing wave height of the clear tank liquid.
(3) Under the far-feld seismic response, the structural displacement response of the clarifcation tank is basically similar when PGA <0.1 g; after PGA >0.2 g, the IDA curve diferentiation phenomenon appeared in the structural displacement of clarifcation tank.When PGA >0.1 g, the IDA curve diferentiation phenomenon appears in the liquid sloshing wave height of the clarifying tank.(4) Te failure probability of the clarifcation tank is diferent under diferent ground motion intensities, and the exceeding probability of the liquid wave height of the clarifcation tank under the far-feld earthquake is the largest, the exceeding probability of the liquid wave height of the clarifcation tank under the near-feld pulse earthquake is the second, and the exceeding probability of the liquid wave height of the clarifcation tank under the near-feld nonpulse earthquake is the smallest.Te exceeding probability of near-feld pulse and far-feld earthquake is similar.