Seismic response reduction analysis of large chassis base-isolated structure under long-period ground motions☆

Feiyn Li ,Linjin Wng ,Yingxiong Wu

Keywords:Long-period ground motions Large chassis structure Base isolation Seismic response reduction analysis

ABSTRACT Long-period structures (e.g.Isolated structures) tend to produce pseudo-resonance with low frequency components of long-period ground motions,resulting in the increase in damage.Stiffness mutation occurs due to the setback in the upper body of the large chassis structure.In the parts with stiffness mutation,the torsion effect caused by the tower is far greater than that of the chassis itself.In this study,a total of 273 ground motions are collected and then filtered into four types,including the near-field ordinary,near-field pulse,far-field ordinary,and farfield harmonic.An 8-degree (0.2 g) fortified large chassis base-isolated structure is established.Furthermore,ETABS program software is used to conduct nonlinear time history analysis on the isolation and seismic model under bi-directional earthquake ground motions.The comparison results show that the seismic isolation effect of the base-isolated structure under long-period ground motions is worse than that associated with ordinary ground motions when the seismic response reduction rate of the large base floor significantly decreases compared with that of the tower.When the inter-story displacement angle and the displacement of isolation layer of the chassis exceeds the limit of Code for Seismic Design of Buildings(GB 50011-2010),it is recommended to adopt composite seismic isolation technology or add limit devices.Under the condition of long-period ground motions,the baseisolated structure reduces the lateral-torsional coupling effect of the large chassis structure,while the torsion response of large chassis’top layer increases.Under long-period ground motions with the same acceleration peak,the response of the base-isolated structure increases much more than that of the seismic structure and the consideration of this impact is suggested to be added to the Code.

1.Introduction

The base-isolated structure can effectively extend the natural vibration period of the structure,utilize the lead rubber bearing (LRB) to consume seismic energy,and reduce the seismic actions of the input superstructure(Zhou,1997;Guo et al.,2018;Pan et al.,2019).Research on ground motions shows that long-period ground motions include near-field pulse ground motions and far-field harmonic ground motions(Xu et al.,2008).In particular,near-field pulse ground motions are characterized by large amplitude,simple waveform and short duration(Somerville Paul,2003),while multiple pulse circulations similar to harmonic vibrations will occur in the late stage of far-field harmonic ground motions(Kazuki and Hiroe,2008;Chung et al.,2010).Previous investigations on seismic isolation theory are mostly based on the ordinary ground motions.The seismic design response spectrum in China's Code for Seismic Design of Buildings(GB 50011-2010)(State Standard of the Peo,2016)(hereinafter referred to as“Design Code”)is mainly based on the ordinary ground motions with short-period components,which ignores the influence of long-period ground motions.The post-disaster investigation and analysis of the Wenchuan earthquake and the great earthquake in east Japan show that long-period structure tends to produce a pseudo-resonance effect with the long-period component of ground motions,thus increasing the displacement response of the structure(Liu,2018).

Some researchers have studied the dynamic response and seismic response reduction effect of isolated structures under long-period ground motions.Heaton et al.(1995)suggest that under the effect of near-fault pulse ground motion,the base-isolated structure will produce large deformation in the isolation layer,and the instantaneous high-energy pulse may lead to unstable overturning of the structure.Li et al.(2012)indicate that the energy released by near-field pulse ground motions is large and harmful to the base-isolated structure.Du Y F(Du et al.,2014)and Wang Ya'nan et al.(Wang et al.,2017) show that the response of base-isolated structure under long-period far-field ground motions is greater than that with the effect of ordinary ground motions.Therefore,ignoring the influence of long-period ground motions in calculating isolated structures will lead to severe consequences.

As the frameworks of modern buildings become more complex,large chassis structures are applied to large public buildings.Due to the setback of the tower,the large chassis structure has an abrupt change in stiffness.In addition,due to the different layout of the tower,the lateraltorsional coupling effect of the structure is apparent.Seismic isolation technology can better improve the complex internal force distribution caused by the vertical irregularity of the large chassis structure (Wang,2014),and reduce the torsion effect of the structure.Du Yongfeng (Du and Jia,2012) and Ma Xiaoming et al.(Ma et al.,2017) investigate the seismic performance of the multi-tower base-isolated structure,and analyze the corresponding parameter variations under ground motions,such as the inter-story displacement,shear force,displacement angle.The results show that the base-isolated structure has a good seismic response reduction effect and can effectively restrain the torsion of the structure.Wu Yingxiong et al.(Wu et al.,2017) conduct a shaking table test for simulating the isolated structure of large chassis foundation,suggesting that the isolation effect of large chassis base works well.

The seismic response and reduction effect of large chassis baseisolated structure under ordinary ground motions have been well understood;however,studies regarding the effect associated with long period ground motions are limited.In this study,a total of 273 seismic events are collected and filtered into four types:near-field ordinary(NFO),near-field pulse (NFP),far-field ordinary (FFO),and far-field harmonic (FFH).Then,an 8-degree (0.2g) fortified large chassis baseisolated structure is established.The ETABS program software is used to conduct nonlinear time history analysis of the isolation and seismic model under bi-directional ground motions.By comparing the models,top floor acceleration,story shear,story acceleration,story displacement,inter-story displacement angle,and story displacement ratio,we probe the seismic response performance of large chassis base-isolated structure under long-period ground motions and analyze the lateral-torsional coupling effect of complex isolated structure.

2.Selection of ground motions

A total of 273 ground motions records are obtained from PEER strong earthquake database,including the Chi-Chi earthquake,Landers earthquake,Northridge earthquake,and Kobe earthquake.According to the definition of long-period ground motions in literature(Li et al.,2018),we select near-field ordinary ground motions (CHY028E,ELC180,TCU053E),near-field pulse ground motions (TCU068E,TCU052E,TCU102E),far-field ordinary ground motions (H05000,ILA007N,PLC000),and far-field harmonic ground motions (ILA004N,ILA055N,ILA056N),respectively.Considering that the peak acceleration of near-field ground motions is high,but the acceleration for far-field ground motions is low and stable,the two values are uniformly adjusted to 200 and 100 gal,respectively.

3.Dynamic analysis model of large chassis base-isolated structure

The inter-story series rigid plate model is adopted to simulate a large chassis base-isolated structure under the ground motions,as shown in Fig.1.Each floor of the structure is considered as rigid.Under the effect of bi-directional horizontal ground motions,there are three types of degree of freedom in each floor:two displacements inx-andy-direction and one horizontal angle.The motion equation of the structure can be expressed as:

whereKxx,Kyyare lateral stiffness inx-andy-direction,KxθandKyθare lateral-torsional stiffness inx-andy-direction.The eccentricity between centroid and stiffness center as well as that between centroids should be considered.

Fig.1.Eccentric foundation analysis model.

Kθx=Kθy=Kθθis the torsional stiffness matrix of th structure.

whereC0is the damping matrix of the superstructure,Cdis the additional damping of the isolation layer.

4.Isolated structure model and its rationality verification

4.1.Isolated structure model

A typical large chassis structure with offset single-tower is selected in this study.The large chassis is 6 span in the long direction and 4 span in the short direction;meanwhile,it has four floors with a layer height of 4.9 m.The tower possesses a long span of four spans and a short span of two spans and has eight floors with a layer height of 3.5 m.The dimensions of the column grid are shown in Fig.2 with a total height of 47.6 m.The main design parameters include the fortification intensity of eight degrees,the design seismic acceleration of 0.2g,the site condition of type II,and the characteristic period of 0.35 s.The load on each floor of the structure is the same with a constant load of 3 kN/m2and a live load of 2.5 kN/m2on the sections of the floors.The dimensions of the major frame column are 700 mm × 700 mm and 500 mm × 500 mm for the chassis and the tower,respectively.The size of the frame beam is 300 mm×700 mm.Concrete with a strength grade of C35 is used in this study.The thickness of the concrete slab for isolation layer is 160 mm,while that for the other slab is 120 mm.

In order to continue the research on the large chassis isolated structure,we conduct a shaking table test in the later stage.Limited by the size of the shaking table,the prototype structure is simplified into a reduced structure,and the scale design is performed with a length similarity ratio of 1:7.The final model size is three long spans in the long direction (xdirection) of the chassis,two spans in the short direction (y-direction),two floors,with a height of 0.7 m.The tower has two spans in the long direction(x-direction),and one span in the short direction(y-direction),four floors,with a height of 0.50 m.A steel frame model is adopted,and the configuration is cast-in-place with the floor slab.The thickness of the cast-in-place concrete floor slab is 200 mm.The base-isolated structure scale model is shown in Fig.3.The scale model shown in Fig.3a is divided into six layers to represent the actual number of floors of the model,while in Fig.3b,it is divided into eight layers to represent the number of floors based on the test results for convenience.After preliminary trial calculations,four lead rubber bearings (LRB) and eight liquid natural rubbers (LNR) are used,and the LRBs are distributed in four corner posts to ensure the minimum distance between the center of the isolation layer and the center of mass of the superstructure.The arrangement of isolation bearing is shown in Fig.4.The mechanical properties of the seismic isolation support have been tested through experiments,and its design parameters are shown in Table 1.

Fig.2.Planar graph of the column grid of the typical structure (unit:mm).

ETABS is used to establish the isolation and seismic models.In the modeling process,the concrete slab is simulated by layered shell elements,the beam and column are simulated by space bar elements,and the isolation bearing is simulated by Isolator 1 connecting elements.Only the elastic deformation of the shock-isolating rubber bearing is considered.Because the seismic excitation input to the model in this study has only horizontal components,the strength loss and stiffness hardening caused by horizontal shear deformation are ignored.The horizontal stress-strain characteristic is not affected by the vertical stress-strain.A linear elastic model is used for LNR,and the equivalent stiffness calculated from Table 1 is used to describe the horizontal control parameters.A spatial bi-directional simplified Bouc-Wen model is used for LRB,and the horizontal control parameters include pre-and post-yielding stiffnesses and yield strength.The vertical tensile and compressive stiffnesses are equal for the two bearings.In order to correctly simulate the stress–strain relationship of seismic isolation rubber bearings,the above assumptions are proposed.The double-fold line model is used for constructing the constitutive relationship of steel,and the post-yielding stiffness ratio of the steel is 0.01.The yield strength is 400 Mpa.This model can accurately describe the stress–strain relationship of steel and accurately simulate the mechanical properties of steel.Before tseismic excitation,the inter-story stiffness of the calculated model is shown in Table 2.The finite element model is shown in Fig.5.

Table 1 Parameters of the isolation bearing.

Table 2 Inter-story stiffness of the model.

4.2.Verification for the rationality of the model

The natural vibration period of the structure is examined by the shaking table test,and then compared with the results of the finite element analysis.The results show that the natural vibration period test value of the seismic model is 0.255 s,the finite element value is 0.276 s,and the error is 7.6%.The natural vibration period test value of the baseisolated model under moderate earthquakes is 0.683s,the finite element value is 0.706 s,and the error is 3.3%.Such results indicate that the two models have a good agreement,authenticating the rationality of the numerical model for subsequent analyses.

5.Nonlinear response analysis of the structure

Since the peak acceleration of the far-field ground motions is generally small,the peak values are set to 0.1gand 0.2gin finite element analysis,and the values of near-field ground motions is set to 0.2gand 0.4g.The seismic wave is input bi-directionally,and the peak value ratio of the accelerations inx-andy-directions are adjusted with the ratio of 0.85:1.Due to the limited space and the similar nonlinear response of the structure inx-andy-directions,we only list the results of the structure's nonlinear response to the peak acceleration of 0.2gin they-direction.In the Figs,“IS”means isolated structure,“SS”means seismic structure,“O′′means ordinary ground motions,“P′′means near-field pulse ground motions,“H′′means far-field harmonic ground motions.

5.1.Top floor acceleration response

Fig.6 shows the top floor acceleration in they-direction of the baseisolated structure and the seismic structure under the influence of nearfield ordinary ground motion ELC180,near-field pulse ground motion.

Fig.3.Scale model for the shaking table test (unit:mm).(a) Front view of the model;(b) Side view of the model (c) Upper tower plan;(d) Chassis plan.

Fig.4.Isolation bearing arrangement.

As shown in Fig.6,the base-isolated structure has a good seismicreduction performance under the ordinary ground motions with significantly decreasing responses to the top floor acceleration.Under the nearfield pulse ground motions,the top floor acceleration of the isolated structure is reduced in the early stage,but the same as that of the seismic structure in the later stage with an increasing pulse.Under the far-field harmonic ground motions,the top floor acceleration is also reduced in the early stage but increased much more than that of the seismic structure in the later stage,indicating that under long-period ground motions,the isolated structure generates a significant resonant response under a long period and high component,increasing the acceleration responses and reducing the effect of seismic reduction.

5.2.Story shear response

Fig.7 is the comparisons of the story shear response under the nearand far-field ground motions.The floor of all the following Figs can be expressed in Fig.3b,in which a total of eight layers have been set.For the floor numbers,0 represents the basic solid end (the shaking table),1 represents the top surface of the isolation bearing,2 represents the first floor,3–7 represent Floors 2–6,respectively,and 8 represents the top floor.

Fig.5.Finite element analysis model.

As shown in Fig.7 and Table 3,regardless of the near-field pulse or far-field harmonic ground motions,both the bottom-layer shears of the isolated structure and the seismic structure are around two times larger than those under ordinary ground motions.Under the near-and far-field ordinary ground motions,the isolated structure exhibits a good seismicreduction performance,and the seismic reduction rate is 55%–70%.However,under the near-field pulse and far-field harmonic ground motions,its seismic-reduction performance is reduced.Particularly,on the floors of the large chassis,the seismic reduction rate is merely about 30%.

Table 3 Seismic reduction rate of the story shear.

5.3. Story acceleration response

Fig.8 is the comparison of story acceleration under the near-and farfield ground motions.

It can be seen from Fig.8 that the overall story acceleration of the seismic structure increases with the rise of the number of floors,and the chassis acceleration response is not that different.However,the acceleration rate of the tower under long-period ground motions is greater than that of ordinary ground motions,indicating that the long-period ground motions is more sensitive to the structure of stiffness change.Furthermore,the energy generated by long-period ground motions has a greater impact on the structure.The overall story acceleration of the base-isolated structure does not change much with the number of floors,and is basically translational.The story acceleration under near-field pulse and far-field harmonic ground motions is greater than that under ordinary ground motions.Under ordinary ground motions,the story acceleration of the base-isolated structure is obviously smaller than that of the seismic structure,indicating that the seismic-reduction effect is obvious.However,under the near-field pulse and far-field harmonic ground motions,the story acceleration of the base-isolated structure in the chassis and the seismic structure is not that different,indicating that the damping effect of the chassis is poor under long-period ground motions.

5.4. Story displacement response

Fig.9 is the comparison of story displacement in they-direction under near-field (0.4g) and far-field ground motions (0.2g).

Fig.6.Comparison of top floor accelerations.

Fig.7.Comparison of the story shear.

Fig.9 indicates that the story displacement of the seismic structure rises slowly with the increase of the floor,exhibiting a large increase at the junction between the chassis and the tower.Under the ordinary ground motions,the base-isolated structure shows a good seismic reduction performance.In detail,the story displacement is mainly concentrated in the isolation layer,and the superstructure is almost translational.Regardless of near-field pulse or far-field harmonic ground motions,the story displacement of the isolated structure is larger than that generated under the ordinary ground motions.Under far-field harmonic ground motions (0.2g),the displacement of the isolation layer in they-direction is approximately seven times than that under ordinary ground motions.Under the near-field pulse ground motions (0.4g),they-direction displacement of the isolation layer is transfinite,which is about six times than that under the normal ground motions,much larger than the near-field influence coefficient of 1.5 in the Code for Seismic Design of Buildings.The results show that long-period ground motions exert a great impact on the isolation layer,while it has not been taken into consideration in the existing design code.

In order to present the influence of long-period ground motions on the structural response,we compare they-direction displacement in the condition of 8-degree fortification pulse ground motions (peak acceleration of 0.2g) and 8-degree rare ordinary ground motions (peak acceleration of 0.4g).Likewise,the two types of conditions with a peak acceleration of 0.1 g and 0.2gare also compared.The results are shown in Fig.10.

Fig.10 indicates that the displacement responses of the seismic structure are similar under 8-degree fortification pulse ground motions and 8-degree rare ordinary ground motions.The displacement response of the base-isolated structure under 8-degree fortification pulse ground motions is about 3.4 times than that under 8-degree rare ordinary ground motions.The displacement responses of the seismic structure are similar under 8-degree frequent harmonic ground motions and 8-degree fortification ordinary ground motions.The displacement response of the base-isolated structure under 8-degree frequent harmonic ground motions is about 2.5 times than that under 8-degree fortification ordinary ground motions.The results show that the energy generated by long-period ground motions is huge and thus unfavorable to structural safety.The classification of seismic intensity is not suitable for long-period ground motions,especially for the base-isolated structure.The structure designed for isolation according to the traditional design method may cause serious consequences such as transfinite isolation layer and the overall collapse of the isolated structure under long-period ground motions.

5.5.Inter-story displacement angle response

Fig.11 is the comparison of the inter-story displacement angle responses between the near-and far-field ground motions.When we consider that the displacement of the isolation layer is large,the height of the isolation layer is small and the inter-story displacement angle between the bottom layers of the isolated structure is large,there is no practical comparison significance.Therefore,the comparison is started on the second floor.

As shown in Fig.11,the inter-story displacement angle under the near-field pulse and far-field harmonic ground motions is larger than that under the ordinary ground motions regardless of the seismic structure or the isolated structure.Under the ordinary ground motions,the baseisolated structure shows a good isolation effect,which can effectively reduce the inter-story displacement angle,making it smaller than the limit set by the Code for Seismic Design of Buildings.However,under the near-field pulse ground motions and the far-field harmonic ground motions,the inter-story displacement angle of the seismic structures is overlimit,while the seismic response reduction effect of the isolated structure is reduced.The inter-story displacement angle is also over-limit,especially for that between the layers of the large chassis floor,leading to possible security risks.

5.6.Floor torque analysis

Fig.12 is the comparison of the floor torque under near-and far-field ground motions.

As shown in Fig.12,the structural torque is gradually reduced from the bottom to the upper structure.Under the ordinary ground motions,the base-isolated structure can better reduce the structural torque,while under the near-field pulse or far-field harmonic ground motions,the structural torque is greater than the ordinary ground motions,indicating that the long chassis torque is reduced under long-period ground motions.

5.7.Story displacement ratio

Controlling the story displacement ratio can limit the structural torsion.According to Technical Specifications for Concrete Structures of Tall Buildings(JGJ3-2010)(State Standard of the People's Republic of China,2011),the displacement ratio of high-rise buildings should not be 1.2 times greater than the average of the floor displacements and cannot be 1.5 times greater than the average of the floor displacements.Fig.13 is the comparison of story displacement ratios under near-and far-field ground motions.Since the seismic structure has no isolation layer,only the upper structure floor is taken for comparison.

It can be seen from Fig.13 that due to the vertical set-back of the large chassis structure,the seismic center of the seismic structure tower and the mass center of the large chassis are eccentric,similar to the mass center of the base-isolated structure and the stiffness center of the isolation layer.Therefore,an obvious torsional effect exists at the bottom of the large chassis structure.Under the ordinary ground motions,the base-isolated structure shows good seismic response reduction effect,which can reduce the lateral-torsional coupling effect of the large chassis,and the floor displacement ratio is about 1.2.However,both the results of near-field pulse or the far-field harmonic ground motions indicate that the seismic response reduction effect of the isolated structure is reduced and thus the bottom torsion effect is enlarged.The large chassis story displacement ratio is about 1.5,indicating a significant torsion effect.

Fig.8.Comparison of story acceleration.

Fig.9.Comparison of story displacement.

Fig.10.Comparison of story displacement of different acceleration.

Fig.11.Comparison of inter-story displacement angle.

Fig.12.Comparison of floor torque.

6.Conclusions

(1) The seismic response reduction effect of the base-isolated structure under long-period ground motions is worse than that under ordinary ground motions.The seismic response reduction effect of the floors with large chassis is significantly lower than that of the tower.

(2) Under long-period ground motions,the inter-story displacement angle of the chassis under fortification intensity exceeds the limit of the Design Code,and so does the displacement of isolation layer under rare earthquake intensity.Therefore,it is recommended to adopt composite seismic isolation technology or add limit devices.

(3) The base-isolated structure can reduce the translational-torsional coupling effect of the large chassis structure.The long-period ground motions increase the torsional response to a greater extent compared with ordinary ground motions.The large chassis has a greater torsional response than the tower,and the greatest torsional response is at the top of the large chassis.

(4) Under long-period ground motions with the same acceleration peak,the response of the base-isolated structure and the seismic structure both increases.However,due to the resonance effect,the response of the base-isolated structure increases larger than that of the seismic structure.Therefore,the method which divides the ground motion level according to the peak acceleration is not suitable for the long-period ground motions.In this case,the consideration of this impact is suggested to be added to the Code

Fig.13.Story displacement ratio.

Acknowledgement

This project is jointly sponsored by Yunnan Youth Earthquake Science Foundation (2020K06),the National Natural Science Foundation of China (51778149) and Xiamen University Tan Kah College School-Enterprise Cooperation Foundation (JGH2020034).