Pounding responses of a base-isolated liquid storage tank under bidirectional earthquakes

ABSTRACT The probability of seismic pounding of sliding isolation liquid storage tank (LST) is high. Considering normal impact force and tangential friction force at the location of pounding under bidirectional earthquake, a 3D calculation model of sliding isolation LST is established based on a finite element method. Pounding dynamic responses under unidirectional and bidirectional earthquakes are comparatively investigated, and frequency domain analysis is also conducted. Finally, mitigation measure for adverse effect caused by the pounding is proposed. Results show that the influence of concrete nonlinearity on the pounding is very significant. Dynamic responses are significantly increased due to the pounding, and the maximum tensile stress of tank wall reaches 2.510 MPa under ChiChi earthquake, which exceeds the concrete tensile strength. Besides, pounding causes a high-frequency response. A reasonable rubber cushion design can ensure that the maximum displacement of the sliding isolation LST is limited by the moat wall, and the failure probability caused by the pounding is decreased.


Introduction
As the lifeline of engineering facilities, liquid storage tanks (LSTs) play irreplaceable roles in the development of national economy.However, there are many cases of damage of LSTs in previous earthquakes.Due to the special characteristics of this kind of structure, the failure will cause several disasters, such as liquid leakage, and fire and environment pollution, so research on dynamic responses of LST is a hot topic.Li et al. (2015) investigated the dynamic responses of LST under different seismic excitations by ABAQUS and concluded that the peak displacement and stress of the tank appeared behind the peak ground acceleration.Park, Bae, and Oh (2016) conducted a dynamic test of LST under horizontal earthquake and concluded that the combination of beam-type and oval-type vibration modes governed the tank vibration.Farajian, Khodakarami, and Kontoni (2017) studied the dynamic responses of LST considering the fluid-structure interaction and the soil-structure interaction (SSI) and concluded that the SSI decreased the impulsive displacement, overturning moment and base shear force.Compagnoni and Curadelli (2018) pointed out that a finite element model (FEM) could obtain good approximation for all responses, while a simplified mechanical model underestimated sloshing height and overestimated base shear force and overturning moment.Moslemi, Farzin, and Kianoush (2019) conducted a parametric study using a rigorous finite element technique considering the nonlinear fluid-structure interaction and concluded that the sloshing nonlinearity had a significant effect on the seismic performance of LST.Miladi and Razzaghi (2019) performed a numerical analysis using FEM and concluded that a numerical model was capable of estimating the tank's actual performance.
Rubber isolation can reduce the dynamic responses of LSTs, such as base shear force, overturning moment and wall internal force, but its reduction effect on liquid sloshing wave height is very limited or even causes opposite effect (Alhan, Gazi, and Guler 2018).On the contrary, some kinds of friction sliding isolation can reduce the dynamic responses of LST itself and liquid sloshing wave height (Cheng, Jing, and Gong 2017;Jing, Cheng, and Shi 2018), namely, the sliding isolation was better than the rubber isolation for the LST (Shrimali and Jangid 2011).Bagheri and Farajian (2018) investigated the effects of peak ground acceleration (PGA) and the pulse-like characteristics of earthquake on seismic behavior of the LST isolated by the friction pendulum system (FPS) and concluded that the tank responses were significantly reduced.Compagnoni, Curadelli, and Ambrosini (2018) carried out shaking table tests of tanks isolated by the sliding concave bearings (SCBs) and concluded that the SCB reduced the base shear force without significantly CONTACT Wei Jing jingwei3276@163.comWestern Engineering Research Center of Disaster Mitigation in Civil Engineering of Ministry of Education, Lanzhou University of Technology, Lanzhou 730050, PR China affecting the sloshing height.Uckan et al. (2018) investigated the seismic responses of the base-isolated LST subjected to the real and the simulated near-fault ground motions and concluded that the real earthquakes could be replaced by equivalent pulses especially for isolation periods larger than 3 s.Dampers can enhance the seismic performance of the isolated LSTs.Güler and Alhan (2021) studied the seismic responses of LSTs with different characteristics of isolation bearings and viscous dampers and suggested the performance limits of the benchmark LST with different baseisolation systems with/without supplemental dampers.Waghmare, Madhekar, and Matsagar (2022) studied the effect of the semi-active pseudo-negative stiffness dampers on the seismic responses of LSTs and concluded that installing the semi-active pseudo-negative stiffness dampers significantly reduced the seismic input energy.Zhang et al. (2022) combined the traditional FPS with an inertial system to improve the performance of base-isolated LSTs.Zhu, Tang, and Luo (2023) achieved simultaneous reduction on the isolator displacement and sloshing response of a base-isolated LST by using the negative stiffness dampers (NSDs) and concluded that the NSD improved the seismic performance of the base-isolated LST with different height-diameter ratios.From this, it can be concluded that adding dampers to the base-isolated LST can significantly improve the seismic performance.
Although sliding isolation can significantly reduce the dynamic responses, the defect is that the large horizontal displacement will be caused.As a result, pounding will be easily caused and has a significant effect on the structure dynamic responses (Kazemi 2020;Komodromos 2008) found that the pounding dynamic responses were increased with increases in the impact stiffness and the isolation stiffness.Masroor and Mosqueda (2013) considered a moat wall flexibility in the pounding model of an isolated structure and concluded that the moat wall characteristics had a significant influence on the dynamic response amplification and damage degree.Fan, Long, and Zhao (2014) studied the vulnerability of an isolation structure with a moat wall and concluded that the structure mass and the mechanical parameters of the isolation bearing had significant influence on the maximum base displacement.Masroor and Mosqueda (2015) obtained that model flexibility and ductility were helpful for the superstructure to absorb energy caused by pounding.Cheng et al. (2017) studied the pounding of sliding isolation liquid storage structure under unidirectional earthquake and concluded that the structure acceleration and the liquid sloshing height were amplified because of pounding.Maniatakis et al. (2017) focused on pounding effects on masonry structure and concluded that pounding significantly affected the dynamic responses.Mavronicola, Polycarpou, and Komodromos (2020) found that pounding incidences had detrimental consequences on the anticipated seismic behavior and performance of the base-isolated structures.Jing, Feng, and Cheng (2021) investigated the influence of different types of earthquake on pounding probability of sliding isolation LST and concluded that the pounding probability was the largest under the action of the near-field pulse-like earthquake.Hubballi and Jangid (2023) studied the pounding responses of the adjacent base-isolated buildings and the effect of cushioning materials on the pounding responses and concluded that the mitigating material is more efficient for the nearer frequency combinations than for the different frequency frame combinations.
The above researches on the pounding problem are mainly carried out under unidirectional earthquake, but many literatures have shown that the effect of bidirectional earthquake on the dynamic responses is significant.Wei et al. (2012) analyzed the seismic responses of sliding isolation frame considering pounding and concluded that the maximum base displacement under the bidirectional earthquake excitations was larger than that of under the unidirectional earthquake excitation.Pant and Wijeyewickrema (2014) investigated the effects of earthquake pounding on responses of base-isolated buildings under bidirectional excitations and pointed out that considering unidirectional excitations instead of bidirectional excitation provided highly un-conservative estimation of superstructure demands.Mavronicola, Polycarpou, and Komodromos (2017) parametrically investigated the pounding effect on the peak responses of the baseisolated structures in a 3D domain and concluded that the peak inter-story drift ratio was significantly influenced by the directionality of ground motion.Li, Chen, and Shi (2017) proposed a multi-scale FEM and concluded that the bidirectional earthquakes would induce eccentric poundings to the girders and different failure modes to the adjacent piers.Li et al. (2019) fabricated a scale curved bridge model and concluded that the peak pounding force under the bidirectional excitations is significantly greater than those under the unidirectional excitations.Zheng et al. (2019) compared the seismic capacities of the reinforced concrete containment under the unidirectional and bidirectional earthquakes and concluded that the seismic capacity under the unidirectional earthquakes would be overestimated by 30%.Wen, Han, and Du (2019) pointed out that the bidirectional earthquake affected bridge dynamic responses; if bidirectional earthquake was ignored, deck displacement would be underestimated.Although some researches have been carried out on the structure dynamic responses under the bidirectional earthquake actions, the researches considering pounding are very limited.
In summary, pounding has a significant influence on the structure dynamic responses.At present, research on the dynamic responses of LST considering pounding is very limited, and there is no literature on the dynamic responses of the base-isolated LST considering bidirectional earthquake.Fluid-structure interaction, normal pounding and tangential friction effect under bidirectional earthquake actions are considered, and a 3D nonlinear calculation model of the sliding isolation LST with a moat wall is established.Effects of concrete nonlinearity and pounding on the dynamic responses are investigated under unidirectional and bidirectional earthquake actions.Lastly, in order to improve the seismic capacity of the sliding isolation LST, the pounding mitigation measure is investigated.Mouzakis and Papadrakakis (2004) studied the two adjacent fixed-base buildings considering the 3D contact and friction effect and observed up to a twofold increase in the displacements of the flexible building when the friction coefficient was 0.1.Jankowski (2009) and Polycarpou, Papaloizou, and Komodromos (2014) used the finite element software to investigate the 3D pounding of a fixed building considering friction and concluded that the friction effect played an important role in the overall structure responses.Guo, Li, and Li (2011) studied the point-tosurface pounding under bidirectional earthquake actions by using a modified contact-friction element and concluded that the point-to-surface pounding should be considered in the structure design to lighten the pounding damage under the strong earthquake excitation.Under the bidirectional earthquake, the location where structure impacts with the moat wall includes the normal impact force and the tangential friction force, as shown in Figure 1 (Pant and Wijeyewickrema 2014).

Simulation of pounding under bidirectional earthquake actions
Under the bidirectional earthquake actions, the total pounding force F p is divided into the normal impact force F pn and the tangential impact force F pt .A contact element method is an effective technique to simulate the normal pounding (Jankowski 2005), and the normal impact force F pn can be expressed as where u sy is the LST displacement in the y direction, g p is the gap between tank and moat wall, _ u sy is the tank velocity, F pn-k is the normal impact force related to stiffness and F pn-c is the normal impact force related to damping.
The tangential impact force F pt can be obtained by the combination of the normal impact force F pn and the Kulun friction law (Cho and Barber 1999): where F pt-k is the tangential friction force related to stiffness, F pt-c is the tangential friction force related to damping and μ is the friction coefficient, and Wriggers (2006) obtained that contact friction coefficient between concrete and concrete was 0.5-1.0 in the pounding research of concrete structure.

Solution of dynamic equation
where u s , _ u s and € u s are the tank displacement, velocity and acceleration under earthquake, respectively, € u g is the earthquake acceleration, F f is the friction force, F p is the impact force and M s , C s and K s are the tank mass matrix, stiffness matrix and damping matrix, respectively.
where B is the strain matrix, D is the elastic matrix, N is the shape function matrix, ρ s is the tank material density, α and β are the mass and stiffness damping coefficients, respectively, ξ s is the structure damping ratio and is taken as 0.05, and ω i and ω j are the ithorder and jth-order circular frequencies of the tank, respectively.Newmark-β method is adopted to solve the matrix differential equation, namely where τ and ς are the constants.
Motion differential equation at time t + Δt is With regard to basic parameters of Newmark-β, it is absolutely stable when τ = 0.5, ς = 0.25 andΔt � T max 100 (T max is the maximum natural vibration period), and the results can meet the accuracy requirements.
Substituting Equation 4and Equation 5 into Equation 6: From Equation 5, it can be obtained: Substituting Equation 8 into Equation 7: where � K eff and � F eff are the effective stiffness and effective load, respectively, and � u s;tþΔt is obtained by Equation 9, and € u s;tþΔt and _ u s;tþΔt are obtained by Equation 8 and Equation 5, respectively.
Because the calculation model includes strong nonlinearities, in order to improve convergence and calculation accuracy, automatic-time-stepping method is used (Bathe et al., 1999).

Case study
The size of LST is 6 m × 6 m × 4.8 m (Cheng, Jing, and Gong 2017), and the wall thickness is 0.3 m.Referring to the American engineering standards (American Petroleum Institute 2007), when the uneven deformation occurs between the LST and the supporting pipelines, the attached pipelines will be damaged, and the limit of deformation difference should be less than 150 mm.Therefore, to avoid excessive isolation layer displacement that can cause pipeline destruction and liquid leakage, the limit of isolation layer displacement of the sliding base-isolated LST with subsidiary pipelines should also be less than 150 mm, so the g p is defined as 0.15 m.The friction coefficient between the tank and the moat wall is 0.5 (Wriggers 2006).Material parameters of nonlinear concrete are shown in Table 1, and nonlinear constitutive model is shown in Figure 2 (Saenz 1964); this kind of material model can be unloaded and reloaded, namely, which can bear cyclic load, after the failure of concrete material, and there are three behaviors: tensile cracking, crushing and strain softening.3D solid element is used to simulate concrete, which is an eight-node and iso- parametric displacement-based finite element; besides, special mixed-interpolation is also available, and the displacement and pressure are interpolated.In general, the element is suitable for the analysis in which 3D state of stress is required (ADINA 2012).The liquid depth is 3.6 m, assuming that the liquid is irrotational, inviscid and incompressible, the density is 1000 kg/m 3 , and the bulk modulus is 2.3 × 10 9 Pa.Based on the subsonic potential flow theory, 3D fluid element with eight nodes is used to simulate the liquid.The potential-based fluid element can simulate fluid-structure interaction and free surface, respectively.In order to reflect the real sloshing behavior of liquid, potential interface boundary condition is set on the liquid-free surface.The fluid-structure interaction boundary is used for the contact interface between the fluid and the structure.When the potential fluid theory is used, ADINA User Interface can automatically generate fluid-structure interface boundary between the fluid and the structure, so it is not artificially needed to define fluid-structure potential interfaces.
The diameter and spacing of rebar are 12 mm and 200 mm, the rebar material parameters are shown in Table 2, and the bilinear constitutive model is used to simulate the rebar.
Concrete tensile strength is taken as the limit state, seven earthquake waves are selected to conduct time history analysis and the seven near-field earthquake waves are selected from the SeismoSignal software, which have different characteristics and can comprehensively evaluate the influence of pounding on baseisolated liquid storage structures.Details of earthquake waves are shown in Table 3, and acceleration response spectra are shown in Figure 3.In order to improve calculation efficiency and capture more real pounding results, the finite time step is set as 0.005 s.The same seismic wave is input in both horizontal directions, and the acceleration ratio in both directions is adjusted to 1:0.85.
The sliding isolation layer is simulated by setting contact surface between the structure bottom and the base, and the friction coefficient of sliding isolation is 0.04.The omnidirectional degree of freedom constraint is defined for the base, namely, three translational and three rotational degrees of freedom are fixed, respectively.A contact between the moat wall and the tank is set, which is modeled using contact groups, one contact group is composed of tank contact surfaces, the other contact group is composed of moat wall contact surfaces and contact pairs are then defined.3D contact is defined, the contact surfaces are defined as regions that are anticipated to come into contact during the solution and coulomb-type friction model is used to reflect tangential mechanical properties.Constraintfunction algorithm is used to calculate the normal contact condition.A regularized friction model is used for the conditions of possible contact forces along the tangential direction, which can improve convergence difficulty of iteration in numerical calculation caused by sudden change and reflect actual friction phenomenon in physics and relative sliding accompanied by tangential friction (Guo, Zhang, and Li 2012).The calculation model of the sliding isolation LST with the moat wall established by ADINA is shown in Figure 4.

Effect of concrete nonlinearity on dynamic responses considering pounding
At the moment of pounding, LST will show nonlinearity, so it is necessary to investigate the concrete nonlinearity effect on the pounding dynamic responses.
For the case of linear concrete, the elastic modulus is 3 × 10 10 Pa, the density is 2500 kg/m 3 and the Poisson's ratio is 0.2.ChiChi wave is a typically near-field and stiff-soil record; ChiChi wave is taken as an example, and calculation results corresponding to linear and nonlinear concrete are shown in Table 4.
As shown in Table 4, after the concrete nonlinearity being considered, tensile stress and acceleration of LST are increased significantly, and the influence of concrete nonlinearity on wall tensile stress and acceleration is greater than that of liquid sloshing wave height.After concrete nonlinearity being considered, stress-XX is increased from 1.377 MPa to 1.480 MPa, and stress-YY is increased from 1.553 MPa to 1.611 MPa under unidirectional earthquake; stress-XX is increased from 1.887 MPa to 2.226 MPa and stress-YY is increased from 2.032 MPa to 2.510 MPa under bidirectional   earthquake, which makes tensile stress exceed concrete tensile strength and the tank wall be cracked.The reason is that after concrete nonlinearity being considered, with the increase in strain, the material damage is aggravated, so the nonlinear characteristic of the concrete has a significant influence on the stress value and distribution of the tank wall.On the whole, the effect of concrete nonlinearity on the dynamic responses caused by pounding under bidirectional earthquake actions is greater than that of unidirectional earthquake action.Material nonlinearity should be taken into account in the research of the base-isolated concrete LSTs when the pounding is considered.

Effect of pounding on dynamic responses
From the above analysis, it is obtained that the concrete nonlinearity has a significant effect on the pounding dynamic responses of LST; besides, concrete will show strong nonlinearity under pounding, so concrete nonlinearity is considered in the following study.In order to study pounding effect on the dynamic responses, the sliding isolation LSTs with or without moat wall are used as the objects to be analyzed.The two most common failure modes of the concrete LST are wall cracking and liquid overflow, so pounding effects on wall tensile stress and liquid sloshing height are investigated.Earthquake wave is input unidirectionally (Y axis) and bidirectionally (X and Y axes), respectively.PGA is adjusted to 0.60 g, when the seismic wave is input only in the Y axis direction.According to Chinese code (GB 50011-2010), when calculating the dynamic responses under bidirectional earthquake, the ratio of PGA of the main axis to its vertical axis is 1:0.85,so PGAs corresponding to the X and Y axes are adjusted to 0.51 g and 0.60 g when the seismic wave is input in the X and Y axes directions.
Taking the dynamic responses under ChiChi earthquake as an example, wall stresses in the X axis direction are shown in Figures 5 and 6, wall stresses in the Y axis direction are shown in Figures 7 and 8 and liquid sloshing wave heights are shown in Figures 9 and 10.

Wall stress in X axis direction
As shown in Figures 5 and 6, under unidirectional earthquake, the maximum wall tensile stresses in the X axis direction corresponding to no pounding and pounding are 0.847 MPa and 1.480 MPa, respectively; under bidirectional earthquake, the maximum wall tensile stresses in the X axis direction corresponding to no pounding and pounding are 0.903 MPa and 2.226 MPa, respectively.
Whether considering pounding or not, it is obtained that wall tensile stresses in the X axis direction corresponding to bidirectional earthquake are greater than that of unidirectional earthquake.Pounding will increase wall tensile stress in the X axis direction, and the increased effect on wall tensile stress caused by pounding is more significant under bidirectional seismic action, which makes tensile stress exceed concrete tensile strength.When pounding occurs, it can be obtained that the tank wall will be easily cracked and reduction effect of sliding isolation will be even lost.

Wall stress in Y axis direction
As shown in Figures 7 and 8, under unidirectional earthquake, wall tensile stresses in the Y axis direction corresponding to no pounding and pounding are 0.895 MPa and 1.661 MPa, respectively; under bidirectional earthquake, wall tensile stresses in the Y axis direction corresponding to no pounding and pounding are 0.903 MPa and 2.510 MPa, respectively.
Whether considering pounding or not, it is obtained that the wall tensile stresses in the Y axis direction corresponding to bidirectional earthquake are greater than that of unidirectional earthquake.Pounding causes an increase in wall tensile stress in the Y axis direction, and the increased effect on the wall tensile stress caused by pounding is more significant under bidirectional earthquake, which makes the wall tensile stress exceed concrete tensile strength (2.01 MPa); as a result, the tank safety is seriously threatened.
Under the unidirectional earthquake, because the X axis is perpendicular to earthquake action direction, in this case, liquid hydrodynamic pressure is perpendicular to the X axis, and the tank wall in the X axis will be in a bending state under the action of liquid hydrodynamic pressure.As a result, the results of the X axis under the unidirectional earthquake are almost similar to that in the Y axis.

Liquid sloshing wave height
As shown in Figures 9 and 10, under unidirectional earthquake, liquid sloshing heights corresponding to no pounding and pounding are 0.147 m and 0.166 m, respectively; under bidirectional earthquake, liquid sloshing heights corresponding to no pounding and pounding are 0.343 m and 0.482 m, respectively.
Whether considering pounding or not, it is obtained that liquid sloshing heights corresponding to bidirectional earthquake are greater than that of unidirectional earthquake.Pounding will cause an increase in liquid sloshing height, and the increased effect on liquid sloshing height caused by pounding is more obvious under bidirectional earthquake.As a result, if the freeboard is insufficient, liquid overflow will be easily caused.

Tank acceleration
The reason why the dynamic responses of LST are amplified is that the instantaneous pounding will produce large impact force, the tank acceleration will be directly affected after the impact force being introduced into Equation 10 and the other dynamic responses will also be affected, so effect of pounding on the tank acceleration is necessary to be investigated.Considering pounding or not, acceleration distributions along the tank height in the Y axis are shown in Figure 11.
As shown in Figure 11, under unidirectional and bidirectional earthquake actions, when pounding is not considered, the maximum acceleration appears in the middle position of tank height because of liquid pulse effect, and the change of acceleration along tank  height is very small.When the pounding occurs, the maximum acceleration appears at the tank bottom, and acceleration under bidirectional earthquake is obviously larger than that of under unidirectional earthquake.
From the above analysis about pounding effect on the wall tensile stress, liquid sloshing height and tank acceleration, it is obtained that the dynamic responses considering pounding under bidirectional earthquake are greater than those of under unidirectional earthquake, and the pounding effect on the dynamic responses under bidirectional earthquake is obviously larger than that of unidirectional earthquake.Therefore, in order to ensure the safety of sliding isolation LST, it is necessary to consider the effect of bidirectional earthquake in a reasonable way.
In order to further study the pounding effect on the dynamic responses of sliding isolation LST, frequency domain analysis is conducted, and the Fourier spectrum and power spectrum are shown in Figures 12-14.
As shown in Figures 12-14, under unidirectional and bidirectional seismic actions, the Fourier spectrum and power spectrum are mainly concentrated in the low-frequency domain when pounding is not considered.On the contrary, the Fourier spectrum and power spectrum are mainly concentrated in high-frequency domain when pounding is considered.Therefore, it can be obtained that pounding induces the highfrequency response of sliding isolation LST, and the tank failure probability will be increased.
In order to comprehensively investigate adverse effects of the pounding on base-isolated LSTs, the maximum dynamic responses under seven earthquake actions are summarized in Table 5.
As shown in Table 5, under unidirectional and bidirectional earthquakes, pounding significantly increases the dynamic responses of LST.Especially under the action of bidirectional earthquake, pounding will easily make tank wall be cracked and destroyed.Impact forces under bidirectional earthquake actions are significantly larger than those of under unidirectional   earthquake action, and in most cases, the magnification is 2-3 times larger.

measure for pounding
From the above analysis, when concrete LST collides with moat wall, the wall tensile stress and liquid sloshing height are increased.Especially under the action of bidirectional earthquake, the pounding will make the wall tensile stress close to or exceed concrete tensile strength, so failure mode caused by wall cracking will occur.Therefore, in order to improve the effectiveness of the sliding isolation LST, it is necessary to study the mitigation measure for the pounding.A simple and inexpensive method is to add a rubber cushion at the bottom of LST, as shown in Figure 15.The thickness and height of buffer cushion are 0.1 m and 0.3 m.Similar to structure, 3D solid is also used for the rubber.Hyperelastic Mooney-Rivlin material model is used to simulate rubber cushion (Major and Major 2015), which is effective and can be preferred in the analysis of incompressible media and inelastic materials (specifically for materials in which Poisson's ratio is close to 0.5, for rubber-like materials and for elastoplastic materials).The strain energy density function W that is described by the invariant of the deformation tensor is where C ij is the material constants, which is generally determined by experiment, and I is the deformation tensor invariant.Mooney-Rivlin material constants are shown in Table 6, and bulk modulus is used to model the compressibility of the material (Yuan 1993).
In order to investigate the effectiveness of rubber cushion, ChiChi and Hollister earthquakes are chosen to conduct time history analysis; wall tensile stress and liquid sloshing wave height corresponding to pounding and pounding with rubber cushion are shown in Figures 16-21, and the effects of rubber cushion on the pounding dynamic responses are summarized in Table 7.
As shown in Figures 16-21 and Table 7, under ChiChi and Hollister earthquakes, the wall tensile  stresses are all decreased.For example, under bidirectional ChiChi earthquake, Stress-YY is decreased from 2.510 MPa to 1.743 MPa; under bidirectional Hollister earthquake actions, Stress-YY is decreased from 1.918 MPa to 1.281 MPa.Liquid sloshing is a very problem.Previous research on base-isolated LST with rubber bearings has shown that the rubber isolation does not always reduce the liquid sloshing wave height, and in some cases, it may even produce amplification effects, and rubber cushion here may have similar reasons.
Besides, rubber cushion is more important for the control of the dynamic responses caused by pounding under bidirectional earthquake, and the probability that the wall tensile stress exceeds the concrete tensile strength is significantly decreased.After rubber cushion being added, the moat wall can not only limit the tank horizontal displacement but also reduce the amplification effect of pounding on the dynamic responses.As a result, the effectiveness of sliding isolation will be significantly improved.responses of base-isolated LSTs.In addition, pounding belongs to complex seismic responses, and it is necessary to conduct parameter analysis, such as gap size, height-width ratio and liquid level height.

Figure 1 .
Figure 1.Illustration of pounding under bidirectional earthquake actions.

Figure 14 .
Figure 14.Frequency domain analysis of dynamic responses in Y axis direction under bidirectional ChiChi earthquake.(a) Fourier spectrum.(b) Power spectrum.

Figure 12 .
Figure 12.Frequency domain analysis of dynamic responses in Y axis direction under unidirectional ChiChi earthquake.(a) Fourier spectrum.(b) Power spectrum.

Figure 16 .
Figure 16.Wall stress in X axis direction after mitigation measure being taken under ChiChi earthquake (unit: Pa).(a) Unidirectional excitation.(b) Bidirectional excitation.

Figure 17 .
Figure 17.Wall stress in Y axis direction after mitigation measure being taken under ChiChi earthquake (unit: Pa).(a) Unidirectional excitation.(b) Bidirectional excitation.

Figure 19 .
Figure 19.Wall stress in X axis direction after mitigation measure being taken under Hollister earthquake (unit: Pa).(a) Unidirectional excitation.(b) Bidirectional excitation.

Figure 20 .
Figure 20.Wall stress in Y axis direction after mitigation measure being taken under Hollister earthquake (unit: Pa).(a) Unidirectional excitation.(b) Bidirectional excitation.

Table 2 .
Material parameters of rebar.

Table 3 .
Earthquakes used to conduct time history analysis.

Table 4 .
Effect of concrete nonlinearity on pounding dynamic responses.

Table 6 .
Material parameters of Mooney-Rivlin model.

Table 5 .
Effects of pounding on base-isolated LST.
Figure 15.Mitigation measure for pounding.