earthquake engineering & structural dynamics

7/27/2019 Earthquake engineering & Structural dynamics

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EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2005; 34:120

Published online 25 October 2004 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/eqe.398

Earthquake-induced interaction between adjacent reinforcedconcrete structures with non-equal heights

Chris G. Karayannis; and Maria J. Favvata

Reinforced Concrete Lab.; Department of Civil Engineering; Democritus University of Thrace;

Xanthi; 67100 Greece

SUMMARY

The inuence of the structural pounding on the ductility requirements and the seismic behaviour ofreinforced concrete structures designed to EC2 and EC8 with non-equal heights is investigated. Specialpurpose elements of distributed plasticity are employed for the study of the columns. Two distinct typesof the problem are identied: Type A, where collisions may occur only between storey masses; andType B, where the slabs of the rst structure hit the columns of the other (72 Type A and 36 Type Bpounding cases are examined). Type A cases yielded critical ductility requirements for the columns inthe pounding area mainly for the cases where the structures were in contact from the beginning of theexcitation. In both pounding types the ductility requirements of the columns of the taller building aresubstantially increased for the oors above the highest contact storey level probably due to a whiplashbehaviour. The most important issue in the pounding type B is the local response of the column ofthe tall structure that suers the hit of the upper oor slab of the adjacent shorter structure. In all theexamined cases this column was in a critical condition due to shear action and in the cases where thestructures were in contact from the beginning of the excitation, this column was also critical due to highductility demands. It can be summarized that in situations of potential pounding, neglecting its possible

eects leads to non-conservative building design or evaluation that may become critical in some cases.Copyright ? 2004 John Wiley & Sons, Ltd.

KEY WORDS: structural pounding; reinforced concrete structures; ductility requirements; non-linearseismic analysis

1. INTRODUCTION

The interaction of adjacent buildings and the collisions that occur between them during anearthquake have been repeatedly identied as a usual cause of damage. This problem betweenstructural systems that are in contact or in close proximity to each other is commonly referredto as structural pounding.

The literature provides many examples about the seismic hazard that the structural pound-ing poses [13]. Based on the substantial knowledge that has been acquired so far through

Correspondence to: Chris G. Karayannis, Reinforced Concrete Lab., Department of Civil Engineering, DemocritusUniversity of Thrace, Xanthi, 67100 Greece.E-mail: [email protected]

Received 11 June 2003

Revised 28 April 2004Copyright ? 2004 John Wiley & Sons, Ltd. Accepted 29 April 2004

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2 C. G. KARAYANNIS AND M. J. FAVVATA

numerous eld observations after damaging earthquakes it can be concluded that poundingis frequently observed when strong earthquakes strike big cities and densely populated urbanareas. In these events the interaction between adjacent buildings is a usual cause of damageand there are cases reported in the literature where pounding has been identied as a primary

cause for the initiation of collapse. In the earthquake that struck Mexico City in 1985 therst assessment, which subsequently was revised, had attributed to pounding a big part of theobserved damage and identied many cases where pounding led to collapse [2, 4]. Althoughin this respect the earthquake of Mexico City is unique in terms of damage and collapse casesattributed to pounding and the phenomenon has been overstated and exaggerated concerningthe damage, it is a fact that in all major earthquakes of the last decades structural poundingwas always present [1, 3, 5].

The typical measure that modern codes specify against structural pounding is the provisionfor sucient separation between adjacent buildings in order to preclude pounding [68]. Thereare however some factors that make these code provisions not always eective or applicable.First, common code interpretations and code applications lead sometimes to building separa-tions that are inadequate and inconsistent with the philosophy of modern codes that implylarge deformations can occur during major earthquakes due to inelastic response. Further, thehigh cost of land in densely populated metropolitan cities and the small lot sizes make theseismic separation requirements not always easy to apply. In addition, there is the argumentthat weak buildings in contact with stronger ones in city blocks may actually benet fromthat contact, provided that the pounding will not cause any serious local damage from whichfailure could be initiated [3, 9].

As alternatives to seismic separation a few measures against structural pounding have beenproposed. In order to reduce the eects of pounding in the case of existing small separationdistances Anagnostopoulos [10] proposed the lling of the gap between the adjacent build-ings with shock absorbing material. Westermo [11] studied the use of permanent connections

between the adjacent buildings in order to eliminate pounding. The new Hellenic Code for

seismic design of structures and Eurocode 8 propose the use of strong stiening shear wallsin order to prevent pounding.Many analytical works on structural pounding have been reported in the last two decades.

In the beginning these studies were based on the response of pairs or sets of colliding singledegree of freedom systems in earthquake excitations. Anagnostopoulos [10] examined thecase of pounding of several adjacent single degree of freedom systems in a row. In thisstudy elastic and inelastic systems were studied using ve real earthquake motions and many

problem parameters were examined. The results indicated that in the case of alike systemsexterior systems tend to suer more due to the pounding eect than do the interior ones,the latter often experiencing reductions in their response. Further, Athanasiadou et al. [9],working in the same direction, examined the inuence of a constant phase dierence in the

base motion of each system in an attempt to approximate the travelling wave eect.

Anagnostopoulos and Spiliopoulos [12] examined the pounding eect in multi-degree-of-freedom systems. They idealized the buildings as lumped mass, shear beam type, multi-degree-of-freedom systems with bilinear forcedeformation characteristics. They reported theresults of collisions on the response of a 5-storey building in congurations of 2, 3 and 4

buildings in contact. They also examined the pounding eect in several cases of two buildingswith dierent heights. In situations like these, according to the authors, pounding can becatastrophic [12].

Copyright ? 2004 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn.2005; 34:120

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EARTHQUAKE-INDUCED INTERACTION BETWEEN ADJACENT STRUCTURES 3

Numerical formulations for the pounding of two structures focusing primarily on advancedsolution techniques have also been reported during the past decade [1315]. Maison and Kasai[16, 17] proposed the formulation and the solution of the multiple degree of freedom equationsof motion for a type of structural pounding between two buildings and presented the pounding

between a tall 15-storey structure and a shorter 8-storey stier and more massive building.The formulation and results are based on elastic dynamic analysis.

Karayannis and Fotopoulou [18] have examined various cases of structural pounding be-tween multistorey reinforced concrete structures designed according to the Eurocodes 2 [7]and 8 [8]. The work was based on non-linear dynamic step-by-step analysis and its purposewas to present initial results for the inuence of some critical pounding parameters on theductility requirements of the columns and to examine the possibility of taking into account the

pounding eect during the design process according to EC2 to EC8. In the examined casesthe storey levels of the two colliding structures were always the same. The eect of soilexibility on the inelastic seismic response of a particular case of adjacent 12- and 6-storeyreinforced concrete moment-resisting frames has been examined by Rahman et al. [19].

It is emphasized that all the previously mentioned papers examine pounding problems withbuildings that have storeys with equal inter-storey heights and consequently the poundingtakes place always between the oor masses of the colliding structures.

2. SCOPE OF THE STUDY

This study is based on the thoughts that: (a) pounding is an important cause of structuraldamage that under certain conditions can lead to collapse initiation; (b) according to the newdesign codes (Eurocodes 2 and 8) exible frame structures can be designed; (c) adequateseismic separation is not always easy to apply; and (d) most of the existing analytical studieshave yielded conclusions not directly applicable to the design of multistorey buildings po-

tentially under pounding. In this paper an attempt to study and quantify the inuence of thestructural pounding on the ductility requirements and the overall seismic response of rein-forced concrete frame structures with unequal heights designed according to the codes EC2and EC8 is presented.

The study of the pounding of adjacent multistorey reinforced concrete buildings with un-equal total heights and dierent storey heights is also a main objective of this work. Thisis probably the most critical case of interaction between adjacent buildings and although itis a common case in practice it has not been studied before in the literature as far as theauthors are aware. Furthermore, the inuence of the size of the gap distance between adjacentstructures on the eects of the pounding is also investigated. Non-linear dynamic step-by-stepanalysis and special purpose elements are employed for the needs of this study.

3. KEY ASSUMPTIONS

3.1. Model idealization of structural pounding

In this work the interaction of two adjacent structures with dierent total heights is studied.Each structure responds dynamically and vibrates independently. It is considered that one


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3

32

1

2

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1

Figure 1. Actual condition and model idealization of the pounding problem. Structures withunequal total heights and the heights of the storey levels of the two structures are not equal.

Pounding at the columns (inter-storey pounding).

exible multistorey building is in contact or in close proximity to one less-exible shorterstructure. If there is a gap distance between the structures collisions occur when the lateraldisplacements of the structures exceed the pre-dened gap distance (dg). The inuence of thegap size on the pounding eects is parametrically investigated. Two distinct types of structural

pounding are identied:

(a) Pounding case type A. The storey levels of the two structures have the same height so

that collisions may occur between the storey diaphragms and consequently between thestorey masses.(b) Pounding case type B. The heights of the storey levels of the two structures are not equal

(Figure 1). In this very common case the slabs of the diaphragms of each structure hit thecolumns of the other structure at a point within the deformable height. This phenomenonis especially intense at the contact point of the upper storey level of the short stierstructure with the corresponding column of the tall building. The actual condition andthe model idealization of this pounding case are shown in Figure 1. Contact points aretaken into account at the levels of the oor slabs of the short structure. Nevertheless,from the analyses of the examined pounding cases it has been found that the responseof the interacting structures is inuenced only by the position and the characteristics ofthe contact point at the shorter structures top oor. The inuence of the other contact

points on the results proved to be negligible in the examined cases. The same conclusionalso holds, more or less, for the examined cases with zero distance gap. This is mainlyattributed to the signicant height dierence of the interacting structures in the studiedcases. Thus, in the following analyses and results, only the inuence of the poundingeect through the top oor contact point on the whole behaviour of the structures andon the response and ductility requirements of the columns is examined. Analyses have

been performed using time steps of the order of 1=5000 to 1=10000 in order to achieve


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numerical stability and to adequately reproduce higher mode response excited by theshort-duration impacts.

3.2. Contact element

Collisions are simulated using special purpose contact elements that become active whenthe corresponding nodes come into contact. This idealization is consistent with the buildingmodel used and appears adequate for studying the eects of pounding on the overall structuralresponse for the pounding cases under examination. Local eects such as inelastic exuraldeformations, yield of the exural reinforcement and ductility requirements of the columns inthe pounding area are taken into account through the special purpose elements employed forthe modelling of the columns.

The response of the contact elements has three parts. First, the negative direction of theX-axis that represents the condition that the buildings move away from each other. In thepositive direction of the X-axis there are two parts in order to simulate the actual behaviour ofthe structures in case there is a small gap distance (dg) between them. It is possible that the

structures move one towards the other but the displacements are small and the existing gap isnot covered. In this case the contact element remains non-active and the buildings continueto vibrate independently. In the case where the structures move one towards the other andthe displacements bridge the existing gap or the structures are in contact from the beginningthen the contact element responds as a spring with almost innite stiness.

The damage at the contact area is expected to be concentrated from the beginning at thecolumn (pounding case B) that suers the impact. Thus, considering that the damage of the

building materials and the damage of the slabs of the shorter structure are not signicant,an elastic contact element has been used. Moreover, analyses of interaction cases (poundingcases B) using contact elements that can account for damping have been performed as well.From comparisons between the results of these analyses with the results of the analyses usingelastic contact elements, it can be obtained that the observed dierences are negligible.

3.3. Beamcolumn elements

The frame structural systems consist of beams and columns whereas the dual (frame-wall)systems have in addition two reinforced concrete walls. Each structure is modelled as a 2Dassemblage of non-linear elements connected at nodes. The mass is lumped at the nodes andeach node has three degrees of freedom.

Each structure responds dynamically and vibrates independently. Collision occurs when thelateral displacements of the structures at the oor levels exceed the pre-dened gap distance(dg) between the two structures. The actual conditions and the model idealization of the

pounding problem examined in this study are shown in Figure 1.The computer program used in this work is the program package DRAIN-2DX [20]. The

nite element mesh used here for the modelling of each structure uses a one-dimensionalelement for each structural member. Two types of one-dimensional beamcolumn elementswere used: (a) one special purpose element that is employed for the modelling of the columnsof the 8-storey structure; and (b) an element for the modelling of the beams of this structureand for all members of the second shorter structure. The latter element is a common lumped

plasticity beamcolumn model that considers the inelastic behaviour concentrated in zero-length plastic hinges at the elements ends.


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Figure 2. Analysis model for the pounding area (type B).

The special purpose element employed for the columns is one of distributed plasticity typeaccounting for the spread of inelastic behaviour both over the cross-sections and along thedeformable region of the member length. This element performs numerical integration of thevirtual work along the length of the member using data deduced from cross-section analysisat pre-selected locations. Thus, the deformable part of the element is divided into a numberof segments (Figure 2) and the behaviour of each segment is monitored at its centre cross-

section (control section). The cross-section analysis that is performed at the control sectionsis based on the bre model. This bre model accounts rationally for axialmoment (PM)interaction.

In order to accurately model the actual behaviour of the columns in the area that poundingtakes place the deformable height of each column is divided into four segments (see Figure 2).The lengths of the segments have been determined as follows; the length of the inner two equalsegments have been taken as equal to 0:47h whereas the length of the segments at the ends


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of the element are equal to 0:03h, where h is the deformable height of the column (Figure 2).This partition of the columns deformable height can reasonably take into account withoutexcessive increase of the computational eort the following important structural parameters forthe behaviour of a reinforced concrete column. (a) The actual distribution of the quantity of

the longitudinal reinforcement along the column length. (b) The variation of the connementdegree of concrete over the cross-sections and along the length of the column since a higherdegree of connement is usually applied near the elements ends. (c) This partition of thecolumns length also allows for the setting of control sections near the elements ends veryclose to the face of the joints. These parts are considered to be critical zones because theyare areas of potential formation of plastic hinges.

The connement degree in the middle part of the internal columns is rather low and theconnement coecient ranged from K= 1:023 to 1.041, while in the end parts of the samecolumns it ranged from K= 1:213 to 1.305. However, according to the Eurocodes 2 and 8the connement rules for the critical regions of columns are applied for the entire length ofthe external columns. Thus, for the external columns of the examined cases, the degree ofconnement was the same for the entire length and the connement coecient ranged fromK= 1:213 to 1.309.

Furthermore, in this work special attention has been given to the study of the local responseof the column that suers the direct hit of the upper slab of the shorter and stier structurein the case of pounding type B. In this direction, two special purpose elements of distributed

plasticity type are employed for this column. Each element is divided into four unequalsegments in the way that is shown in Figure 2. Thus, there are eight control cross-sectionsalong the height of the critical column. This partition of the columns deformable heightcan reasonably take into account the actual distribution of reinforcement and the connementdegree of concrete and further it allows for the setting of the control cross-sections near theelements critical points.

4. DESIGN OF STRUCTURES

4.1. Eight-storey structures

Two 8-storey frame structures were designed according to Eurocodes 2 and 8 [7, 8], therst one meeting the Ductility Capacity Medium (DCM) criteria and the latter one meetingthe Ductility Capacity High (DCH) criteria of the codes. Behaviour factors for DCM andDCH frames were q= 3:75 and 5.00, respectively. The mass of the structures is taken asM= (G+ 0:3Q)=g (where G= gravity loads and Q= live loads [7]) and the design baseshear force was taken as V= (0:3g=q)M (where q = the behaviour factor of the structure

[8]). Reduced values of member moments of inertia (Ief) were considered in the design toaccount for the cracking; for beams Ief= 0:5Ig (where Ig=the moment of inertia of the grosssection) and for the columns Ief= 0:9Ig. The code provision [7, 8], in most cases, provedto be critical for the dimensioning of the columns, regarding the axial load ratio limitationd60:65 and d60:55 for DCM and DCH frames, respectively, and in a few cases (columnsof the upper storeys) the code minimum dimensions requirements. The structure geometryand reinforcement of the columns of the 8-storey frames are shown in Figure 3.


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Figure 3. Structural system and column reinforcement of the 8-storey frames designed to EC2 and EC8.

4.2. Four-storey and two-storey structures

Two 4-storey and two 2-storey structures were designed according to the codes EC2 andEC8, meeting the DCM design criteria [7, 8]. The rst one of each pair of structures is a

frame structure, whereas the second one is a dual (framewall) structural system. Behaviourfactors used in the design of the frame structures and the framewall structures were q= 3:75and 3.00, respectively. The mass is taken as M= (G+ 0:3Q)=g and the design base shearforce was taken as V= (0:3g=q)M. Reduced values of member moments of inertia (Ief) wereconsidered in the design; Ief= 0:5Ig, Ief = 0:9Ig and Ief = 2Ig=3 for beams, columns and walls,respectively. In most of the cases the code minimum requirements proved to be critical forthe dimensioning of the columns.


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4.3. Three-storey structure

One 3-storey structure is also designed according to the codes EC2 and EC8, meeting theDCM design criteria. The structure is a dual (framewall) structural system. The behaviour

factor is taken as equal to 3.0. The mass and the design characteristics were the same asin the cases of the 4-storey framewall structure. The code minimum dimensions proved tobe critical for the dimensioning of the columns in most of the cases. The height of the rststorey is 4:80 m and the height of the other stories is 3 :20 m.

5. POUNDING TYPE A. POUNDING AT THE FLOOR LEVELS

5.1. Examined cases

Seventy-two pounding cases between structures with equal inter-storey heights designedaccording to EC2 and EC8 are examined and discussed. These are the interaction cases be-

tween the 8-storey frames (DCM and DCH frames) and the shorter and stier structures (two4-storey and two 2-storey structures) mentioned in the previous section. The pounding casesof the 8-storey structures to stationary barriers (very sti structures) are also included. Each

pair of structures is examined for six dierent gap distances between the two structures.Each pounding case is subjected to two dierent natural seismic excitations; the El Cen-

tro 1940 earthquake (duration 15 secs and max = 0:318 g) and the Korinth (Alkyonides)Greece 1981 earthquake (duration 12 secs and max= 0:306 g). The pounding cases were ex-amined and the ratios of the elastic structural stiness and period (k and T, respectively)of the 8-storey frame to the ones of the adjacent less exible structure of each case are pre-sented in Table I. The elastic stiness is evaluated by means of a push-over analysis of thestructures.

5.2. Results

Time history comparative results of the examined pounding cases between the DCM 8-storeyframe and the 4-storey structures (Korinth 1981 excitation) are presented in Figure 4. InFigure 4(a) the displacement time histories of the 4th level (pounding level) of the 8-storeyframe for the cases of pounding with the 4-storey frame structure and the 4-storey stationary

barrier (very sti structure) are presented and compared with the response of the 8-storeyframe vibrating without pounding. In Figure 4(b) the displacement time histories of the 8thlevel of the same structure for the same pounding cases are presented.

In Figures 4(a) and (b) it can be seen that the amplitude of the response displacementsof the 8-storey frame in the cases of pounding with the 4-storey structures is signicant. Itis noted that the peak negative displacement at the pounding level is larger in the case of

pounding with the 4-storey frame (d= 0:105m) than the one in the case where the 8-storeyframe vibrates without pounding problems (d = 0:080 m). The same type of behaviour has

been observed in the case of pounding between the 8-storey frame with the 2-storey frame-wall structure. The responses of the 4-storey and the 2-storey structures were greatly aected

by the pounding that generally decreased the response amplitude of these structures.In this study the inuence of the pounding on the curvature ductility requirements of

the columns of the 8-storey frame in the area of the pounding is primarily examined. The


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Table I. Pounding type A. The examined cases, the rations k (and T) of the pounding structures andcoecients , maximum values yielded from non-linear dynamic analyses for the excitations Korinth,

Alkyonides, Greece 1981 and EI Centro 1940.

Examined casesRatios k (and T)(each pair is examined for 6 dierent gap distances dg between the structures)

4-storey structures 2-storey structures

Frame Dual system Rigid barrier Frame Dual system Rigid barrier 8-storey k= 0:42 k= 0:21 k 0 k= 0:56 k= 0:13 k0DCM-frame (T= 1:36) (T= 2:93) (T) (T= 2:42) (T = 7:85) (T)

8-storey k= 0:48 k= 0:21 k 0 k= 0:64 k= 0:15 k0DCH-frame (T= 1:30) (T= 2:93) (T) (T= 2:30) (T = 7:45) (T)

Coecients for the 5th oor column of the 8-storey frame(pounding between the 8-storey frames and the 4-storey structures (dg= 0))

4-storey 4-storey 4-storey

Frame structure Framewall structure Stationary barrier Top end Bottom end Top end Bottom end Top end Bottom end

cross-section cross-section cross-section cross-section cross-section cross-section

8-storeyDCM-frame 1.95 2.14 2.49 2.78 2.85 4.398-storeyDCH-frame 1.00 1.26 1.63 1.98 2.42 4.78

Coecients for the 3rd oor column of the 8-storey frame(pounding between the 8-storey frames and the 2-storey structures (dg= 0))

2-storey 2-storey 2-storeyFrame structure Framewall structure Stationary barrier

Top end Bottom end Top end Bottom end Top end Bottom endcross-section cross-section cross-section cross-section cross-section cross-section

8-storeyDCM-frame 1.22 1.31 1.30 1.38 1.41 1.428-storeyDCH-frame 1.17 1.10 1.38 1.21 1.40 1.31

cross-section geometry, the strength M+N interaction diagram and the available curvature ofthe upper end of the 5th level column in the pounding area of the 8-storey frame are shownin Figures 5(a), (b) and (c), respectively. The inuence of the pounding and the gap distance

between the adjacent structures on the curvature ductility requirements of the 5th level columnis investigated. The results are presented in Figure 5(d) for the top end cross-sections of thecolumn, in terms of the overstress coecient . The coecient represents the increasedrequirements of the column in curvature ductility due to the pounding eect and is denedas =;dg =, where is the curvature ductility requirement as deduced from seismicanalysis of the 8-storey frame without pounding problems and ;dg is the curvature ductilityrequirement of the same cross-section as deduced from seismic analysis of the 8-storey frame


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0 2 4 6 8 10 12 14

Time (sec)

-0.12

-0.09

-0.06

-0.03

0.00

0.03

0.06

Displacement(m)

without pounding

pounding case with 4-story frame structure

pounding case with 4-story rigid structure (very stiff one)

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0 2 4 6 8 10 12 14

Time (sec)

-0.24

-0.18

-0.12

-0.06

0.00

0.06

Displacement(m)

without pounding

pounding case with 4-story frame structure

pounding case with 4-story rigid structure (very stiff one)

(a)

(b)

Figure 4. Time history comparative results of pounding cases between the DCM 8-storey frame andthe 4-storey structures. Pounding at the oor levels (pounding type A) (for the seismic excitationof Korinth, Alkyonides, Greece 1981): (a) time history of the 4th level of the 8-storey structure;

and (b) time history of the 8th level of the 8-storey structure.

taking into account the inuence of the adjacent structure and considering various values forthe gap distance (dg) between the two structures.

Values of the coecient for the cases of pounding of the 8-storey frames (DCM andDCH) with (a) the 4-storey DCM frame, (b) the 4-storey DCM framewall structure, and(c) the 4-storey stationary barrier for various gap distances (dg) have been evaluated by means

of non-linear dynamic step-by-step analysis. These values for the DCM frame are presentedin Figure 5(d) for the top end cross-sections of the 5th level column of the 8-storey structurein the pounding area.

The ductility requirements of the 5th storey column as deduced from analyses withoutpounding were 1.22 and 1.65 for the upper and the lower connection cross-sections of the5th level column, respectively. From the diagrams of Figure 5(d) indicative values for theinuence of the pounding on the ductility for similar pounding cases can be obtained. Thus,


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Example: Ductility requirement

100 200 300

M (kNm)-1000

1000

3000

5000

N(

kN)

24 6 8 10

ductility-1000

1000

3000

5000

N(

kN)

0 2 4 6 8 10

Gap distance (cm) - dg

1

2

3

4

3

2

1

1. pounding with DCM frame2. pounding with DCM frame-wall structure3. pounding with rigid (very stiff) structure

- without pounding

,req = 1.22

- pounding with frame-wall

structure dg =0.5 cm

,req,dg = .,req =

= 2.25 .1.22 = 2.75

(a) (b) (c)

(d)

Figure 5. Pounding of 8-storey frames with 4-storey structures (Type A). Values of coecients inrelation to the gap distance (dg) of the adjacent structures for the column of the 8-storey frame abovethe pounding area as evaluated from the non-linear seismic analyses. Max. coecient values obtainedfor two seismic motions (Korinth, Alkyonides, Greece 1981 and El Centro 1940): (a) cross-section;(b) interaction diagram M+N; (c) available ductility ;av = 3:87 (curvature ductility); and (d) values

of cocients for the top cross-section of the 5th level column of the 8-storey frames.

in the case of pounding of the DCM 8-storey frame with the 4-storey frame-wall structureand gap distance dg= 0:5cm the ductility requirements can be evaluated based on Figure 5(d)and similar diagrams as

;dg=0:5= = 2:251:2 2 = 2:75 and ;dg=0:5= = 2:001:6 5 = 3:30

for the top and bottom end cross-sections of the column, respectively. Where the value= 2:25 for the top end cross-section is taken from Figure 5(d) and the value = 2:00from similar diagrams for the bottom cross-section [18].

Values for the coecients have been evaluated for all the examined cases for the columnsin the area of the pounding. Values of the coecients for the column of the 5th oor ofthe 8-storey structure for the pounding cases of the DCM and DCH 8-storey frames with the4-storey structures without gap (structures in contact) are presented in Table I. Likewise, thevalues of the coecients for the column of the 3rd oor of the 8-storey structure for the

pounding cases of the DCM and DCH 8-storey frames with the 2-storey structures withoutgap (structures in contact) are also presented in Table I.


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6. POUNDING TYPE B. INTERACTION CASES BETWEEN STRUCTURES WITHUNEQUAL INTER-STOREY HEIGHTSPOUNDING AT THE COLUMNS

6.1. Examined cases

Thirty-six interaction cases between the 8-storey frame and the 3-storey structures with un-equal inter-storey heights are examined and discussed. In these cases it is considered that the

pounding takes place at points of the deformable height of the columns of the more exible8-storey frame structure.

It is expected that the important problem in the case of inter-oor pounding of reinforcedconcrete structures (pounding type B) is the development of critical shear state, since in thesecases the demands of exural ductility can more safely be satised. Furthermore, the factthat the failure of reinforced concrete members due to shear is brittle led the investigation ofinter-oor pounding to the examination of the developing shear forces and their comparisonsto the corresponding shear strength. Pounding at the mid-height of the column produces themaximum exural moment for the element but not the maximum shear force as well; in fact

the two parts of the column (the upper and the down part) suer the same shear force whichis equal to half of the impact force. Thus pounding cases at points of the column dierent tothe mid-height have been chosen for this investigation.

Series 1. Three interaction cases between the 8-storey DCM frame and the 3-storey structureare investigated. Each of these cases is examined for three dierent gap distances betweenthe two structures and is analysed using two seismic excitations. In these interaction casesthe total height of the 3-storey structure is greater than the total height of the 3rd oor andless than the total height of the 4th oor of the 8-storey frame and thus the contact point ofthe two structures lies between the levels of the 3rd and the 4th oor of the 8-storey frame.Each of these cases is examined for three positions of the contact point.

(a) The highest contact point of the two structures lies between the levels of the 3rd andthe 4th oor of the 8-storey frame at 2=3 of the height of the column of the 4th oor.

(b) The highest contact point is located at 1=3 of the inter-storey height of the column ofthe 4th oor of the 8-storey frame.

(c) The total height of the 3-storey structure is equal to the height of the 4th oor of the8-storey frame. This is pounding type A but is included in this series for comparisonreasons.

Series 2. Similarly to the previously mentioned cases of Series 1, pounding cases between the8-storey frame and the 3-storey height stationary barrier (very sti structure) are examined inthis series.

(a) The highest contact point of the 8-storey frame with the 3-storey stationary barrier islocated at 1=3 of the inter-storey height of the 4th oor column of the 8-storey frame.

(b) The highest contact point of the 8-storey frame with the 3-storey stationary barrier islocated at 2=3 of the inter-storey height of the 4th oor column of the 8-storey frame.

(c) The contact point is located at the 4th oor level of the 8-storey frame. This is poundingtype A but is included in this series for comparison purposes.


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All pounding cases are examined: (a) for structures in contact from the beginning(gap distance dg= 0), (b) for initial gap distance between the two structures of dg = 2 cm,and (c) for initial gap distance ofdg = 5 cm. In this case (dg = 5 cm) the structures vibratewithout pounding eect.

Each pounding case is subjected to two dierent natural seismic excitations; the El Centro1940 earthquake (duration 15 secs and max= 0:318g) and the Korinth (Alkyonides) Greece1981 earthquake (duration 12secs and max= 0:306g) (pounding cases type B). The maximumacceleration (max) of these excitations is very close to the design acceleration of the examinedstructures (A= 0:3g).

The ratio (k) of the elastic structural stiness of the 8-storey frame to the one of the3-storey structure is k= 0:22. The ratio (T) of the elastic period of the 8-storey frame tothe one of the 3-storey structure is T = 2:51.

6.2. Results

The results and the conclusions deduced from the analyses are sorted and presented in twoparts. The rst part includes the observed overall response of the 8-storey frame and theductility requirements of its columns. In the second part of the results attention is focused onthe response of the 4th storey column of the 8-storey frame where the pounding takes place.

Ductility requirements. The curvature ductility requirements for the columns of the 8-storeyframe are presented in Figures 6 and 7 for the pounding cases (a) 8-storey frame and 3-storeystructure and (b) 8-storey frame and 3-storey stationary barrier, respectively. In these casesthe seismic excitation of El Centro is used. Each pounding case includes the study of theductility requirements of the external columns at the pounding side of the 8-storey frame for:(a) contact point at 1=3 of the inter-storey height of the 4th oor column of the 8-storeyframe (Figures 6(a) and 7(a)); (b) contact point at 2=3 of the inter-storey height of the 4th

oor column of the 8-storey frame (Figures 6(b) and 7(b)); (c) contact point at the 4th oorlevel of the 8-storey frame.

It is observed that the ductility requirements of the columns of the 8-storey frame, andespecially the ductility requirements of the internal ones, are substantially increased for theoors above the oor of the contact (4th oor). This is probably attributed to a whiplashtype of behaviour of the taller structure; the whiplash type of behaviour can also be deducedindirectly from the ductility distributions with height. This kind of response has been alsoobserved in the interaction cases of pounding type A. The whiplash type of behaviour becomesespecially intense in the pounding cases between the 8-storey frame and the 3-storey stationary

barrier. In this extreme case (k0) the curvature ductility requirements of the upper oorcolumns of the 8-storey frame exceed the available curvature ductilities.

Column that suers the pounding. The most important issue in the pounding type B cases isobviously the local eect on the external column of the tall building that suers impact withthe upper oor slab of the adjacent shorter and stier structure. This impact usually takes

place at a point in the deformable height of the column. The consequences of the impact canbe very severe for the capacity of the column. In this work special attention has been givenfor the study of the local response of this structural member. For this purpose two special


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8th

7th

6th

5th

4th

3rd

2nd

1st

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Floorlevel

Available Required-Structures in contact (dg = 0)

Required without pounding Required for dg = 2cm

Available Required-Structures in contact (dg = 0)

Required without poundi ng Required for dg = 2cm

h/3

2nd

3rd

4th

h

1st

3rd

2nd

hh

h

8th

3rd

4th

2nd

1st

5th

6th

7th

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Curvature ductility,


Floorlevel

h

h

3rd

2nd

1st2nd

3rd

4th

2h/3

h

h

(a)

(b)

Figure 6. Pounding type B. Interaction of 8-storey DCM frame with the 3-storey framewall struc-ture. Ductility requirements of the external columns at the pounding side of the 8-storey frame(seismic excitation El Centro 1940): (a) pounding at the point h=3 of the 4th oor column; and

(b) pounding at the point 2h=3 of the 4th oor column.

purpose elements of distributed plasticity type are used for the simulation of the behaviourof this column (see also Figure 2).

Results concerning the exural and the shear demands of this column are presented andcompared with the corresponding available values for all the examined pounding cases. Forthe pounding case of the 8-storey frame with the 3-storey structure the ductility requirementsof the external columns (pounding side) of the 8-storey frame for the cases of pounding at the

points 1=3 and 2=3 of the column height are presented in Figures 6(a) and (b), respectively.In these gures results are presented for the structures in contact from the beginning (dg=0)and for dg = 2 cm. From these gures it can be observed that the ductility demands for thecolumn that suers the pounding impact (4th storey column) are increased when comparedwith the ones without the pounding eect (Figure 6) and in the cases where the two buildingsare in contact these demands appear to be higher than the available ductility values. In thecases where there is a small gap distance (dg = 2 cm) between the interacting buildings the


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=10.82

(dg=0cm)

=20.29

(dg=0cm)

8th

7th

6th

5th

4th

3rd

2nd

1st

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0


Floorlevel

Available Required-Stuctures in contact (dg = 0)

Required without pounding Required for dg = 2cm

h

3rd

2nd

h

4th

h/3

8th

7th

6th

5th

4th

3rd

2nd

1st

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0


Floor

level

2h/3

2nd

3rd

4th

h

h

Available Required-Stuctures in contact (dg = 0)

Required wi thout pounding Required for dg = 2cm

(a)

(b)

Figure 7. Pounding type B. Pounding of 8-storey DCM frame with the 3-storey stationary barrier.Ductility requirements of the external columns at the pounding side of the 8-storey frame (seismicexcitation El Centro 1940): (a) pounding at the h=3 of the 4th oor column; and (b) pounding

at the 2h=3 of the 4th oor column.

ductility demands of the column are also higher than the ones of the same column with-out the pounding eect (Figure 6) but they appear to be lower than the available ductilityvalues.

The developing shear forces of the critical part of the column that suers the impactfor the pounding case of the 8-storey frame with the 3-storey structure are presented in

Figure 8 for the case of pounding at the point 1=3 of the column height. In these guresresults are presented for the case that the two structures are in contact from the beginning(dg= 0) and for the case where there is a gap distance equal to 2 cm between the twostructures. In these gures each point represents the developing shear force, V, and the axialforce, N, at a step of the seismic analysis, whereas the lateral solid lines show the availablecapacity of the reinforced concrete element for the combination of shear versus axial force(EC2 and EC8 [7, 8]). This way a direct comparison of the developing shear force at the


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-900 900

-2000

N (KN)

V (KN)

Vrd3

Column part A

0.0

El Centrodg = 0.0cm

Pounding at the point 1/3h of the 4th floor column

-900 900

-2000

N (KN)

V (KN)

Vrd3

Column part A

0.0

El Centrodg = 2.0cm


A

B

A

B

Available

Shear Strength

Available

Shear Strength

Each point represents the pair of the developing Shear force and Axial force at a step of the seismic analysis

N : Axial force, V : Shear force

Figure 8. Pounding type B. Pounding of 8-storey DCM frame with the 3-storey framewall structureat the point h=3 of the 4th oor column. Shear forces developed in the critical column (lower part A)

of the 4th storey of the 8-storey frame and available strength.

-900 900

-2000

N (KN)

V (KN)

Vrd3

Column part A

0.0

El Centrodg = 0.0cm


-900 900

-2000

N (KN)

V (KN)

Vrd3

Column part A

0.0

El Centrodg = 2.0cm


Available

Shear Strength

Available

Shear Strength

B

A

B

A

Each point represents the pair of the developing Shear force and Axial force at a step of the seismic analysis

N: Axial force , V: Shear force

Figure 9. Pounding type B. Pounding of 8-storey DCM frame with the 3-storey stationary barrier atthe point h=3 of the 4th oor column. Shear forces developed in the critical column (lower part A)

of the 4th storey of the 8-storey frame and available strength.

steps of the analysis with the available shear strength can be presented. It is noted that inall the examined cases the developing shear forces exceed the shear strength of the columnmany times during the excitation.

Analyses results for the pounding cases between the 8-storey frame and a stationary barrierare presented in Figures 7 and 9. Ductility requirements of the external columns (pounding


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side) for the cases of pounding of the 8-storey frame with the stationary barrier at the points1=3 and 2=3 of the height of the 4-storey column are presented in Figures 7(a) and (b),respectively. From these gures it can be observed that the ductility demands for the columnthat suers the pounding (4th storey column) are increased when compared with the ones

without the pounding eect (Figure 7). In the cases where the two buildings were initiallyin contact these demands appear to be higher than the available ductility values. The devel-oping shear forces of the critical part of the column that suers the impact are presented inFigure 9 for the cases of the pounding at the point 1=3 of the height of the 4th storey column.In these gures results are presented for the structures in contact with the barrier from the

beginning of the excitation (dg= 0) and for the case where there is a gap distance equal to2 cm between the structure and the barrier. It can be observed that in all the examined casesthe developing shear forces exceeded the shear strength of the column many times during theseismic excitation.

7. CONCLUSIONS

An investigation of the inuence of the structural pounding on the ductility requirements andthe seismic behaviour of multistorey reinforced concrete structures with non-equal heights is

presented. Special purpose elements of distributed plasticity are employed for the study of thecolumns and especially for the columns in the area of the pounding.

Two distinct types of the structural pounding problem are identied and examined. Type A:collisions may occur between the oor slabs and consequently between the storey masses. TypeB: the heights of the storey levels of the adjacent structures are not equal and consequentlythe slabs of one structure hit the columns of the other one.

Seventy-two pounding cases of Type A between structures with unequal total heights are ex-amined. The inuence of the pounding on the curvature ductility requirements of the columns

in the area of the contact of the structures is studied and presented in the form of coecients. The coecient represents the ratio of the increased ductility requirements (due to thepounding) to the requirements without the pounding eect. Based on the values of the coe-cient that are yielded from non-linear dynamic step-by-step analyses and are presented in theform of diagrams the following remarks can be deduced. (i) Pounding between frame struc-tures designed according to EC2 and EC8 increased signicantly the ductility requirementsof the columns in the pounding area. Nevertheless, these requirements do not appear to becritical for all the examined cases of the DCM and the DCH 8-storey frames. (ii) Poundingof the 8-storey frames with the 4-storey framewall structures yielded critical values onlyfor the cases were the structures were in contact (dg= 0). (iii) Values of the coecientfor the pounding of the 8-storey frames with 4-storey stationary barriers proved to be criticalin all the examined cases.

Furthermore, based on the examined cases and the presented diagrams it could be suggestedthat for problem cases with similar characteristics the use of the indicative coecients might

be useful in the design process of a structure potentially under pounding.Thirty-six pounding cases of Type B between structures with unequal total heights and

unequal heights of the storey levels are examined. From the results yielded from the non-linear dynamic step-by-step analyses the following remarks can be deduced for the examinedcases. (i) Ductility requirements for the columns of the taller structure and especially for the


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internal ones are substantially increased for the oors above the highest contact storey level.This is probably attributed to a whiplash type of behaviour of the taller structure. This kindof behaviour has also been observed in the examined interaction cases of pounding type A.(ii) The most important issue in the pounding cases of Type B is the local response of the

external column of the tall structure that suers the impact of the upper oor slab of theadjacent shorter and stier structure. (iii) It has been observed that the ductility demandsfor the column that suers the pounding hit are substantially increased compared with theones without the pounding eect. In the cases where the two buildings are in contact thesedemands appear to be critical since they are higher than the available ductility values. In thecases where there is a small gap distance (dg = 2 cm) between the interacting buildings theductility demands of this column are also higher than the ones of the same column withoutthe pounding eect but they appear to be lower than the available ductility values. (iv) It hasto be stressed that in all the examined cases the observed shear forces of the critical part ofthe column that suers the impact exceed the shear strength of the column. Thus, it can beconcluded that in pounding type B the column that suers the impact is always in a criticalcondition due to shear action and, furthermore, in the cases where the two structures are incontact from the beginning this column appears to be critical due to high ductility demandsas well. This means that special measures have to be taken in the design process rst for thecritically increased shear demands and secondly for the high ductility demands.

Thus, it can be summarized that in situations where pounding potentially may occur, ne-glecting its possible eects leads to non-conservative building design or evaluation. This obser-vation becomes critical in cases of pounding type B. The response behaviour trends presentedin this work and especially the indicative coecients may be generalized to other buildinganalyses provided the problem physical characteristics are similar to those used here. Suchextrapolation may be used to assist in the building design process. Attention must be givento the key assumptions inherent to this study regarding their applicability to other situations.

REFERENCES

1. Arnold C, Reitherman R. Building Conguration and Seismic Design. Wiley: New York, 1982.2. Rosenblueth E, Meli R. The 1985 earthquake: Causes and eects in mexico city. Concrete International(ACI)

1986; 8(5):2324.3. Anagnostopoulos SA. Earthquake induced pounding: State of the art. Proceedings of the 10th European

Conference on Earthquake Engineering 1995; vol. 2. pp. 897905.4. Bertero VV. Observations on structural pounding. Proceedings of the International Conference on Mexico

Earthquakes, ASCE, 1986; 264287.5. Anagnostopoulos SA. Building pounding re-examined: How serious a problem is it? Proceedings of the 11th

World Conference on Earthquake Engineering, Acapulco, Mexico, 1996.6. ACI Committee 318. Building code requirements for structural concrete (ACI 318-95) and Commentary (ACI

318R-95), American Concrete Institute, Detroit, 1995.7. Eurocode 2. Design of Concrete StructuresPart 1. General Rules and Rules for Building. CEN, Technical

Committee 250=SG2, ENV 1992-1-1, 1991.8. Eurocode 8. Structures in Seismic Regions, DesignPart 1. General and Building. CEC, Report EUR 12266

EN, May 1994.9. Athanasiadou CJ, Penelis GG, Kappos AJ. Seismic response of adjacent buildings with similar or dierent

dynamic characteristics. Earthquake Spectra 1994; 10.10. Anagnostopoulos SA. Pounding of buildings in series during earthquakes. Earthquake Engineering and

Structural Dynamics 1988; 16:443456.11. Westermo BD. The dynamics of interstructural connection to prevent pounding. Earthquake Engineering and

Structural Dynamics 1989; 18:687699.12. Anagnostopoulos SA, Spiliopoulos KV. An investigation of earthquake induced pounding between adjacent

buildings. Earthquake Engineering and Structural Dynamics 1992; 21:289302.


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13. Liolios AA. A numerical approach to seismic interaction between adjacent buildings under hardening andsoftening unilateral contact. Proceedings of the 9th European Conference on Earthquake Engineering 1990;7A:2025.

14. Papadrakakis M, Mouzakis H, Plevris N, Bitzarakis S. A Lagrange multiplier solution method for pounding ofbuildings during earthquakes. Earthquake Engineering and Structural Dynamics 1991; 20:981998.

15. Stavroulakis G, Abdalla K. Contact between adjacent structures. Journal of Structural Engineering (ASCE)1991; 117(10):28382850.

16. Maison BF, Kasai K. Analysis for type of structural pounding. Journal of Structural Engineering (ASCE)1990; 116(4):957977.

17. Maison BF, Kasai K. Dynamics of pounding when two buildings collide. Earthquake Engineering and StructuralDynamics 1992; 21:771786.

18. Karayannis CG, Fotopoulou MG. Pounding of multistorey RC structures designed to EC8 and EC2. 11thEuropean Conference on Earthquake Engineering (Proceedings in CD form), 1998; Balkema, ISBN 90-5410-982-3.

19. Rahman AM, Carr AJ, Moss PJ. Seismic pounding of a case of adjacent multiple-storey buildings of dieringtotal heights considering soil exibility eects. Bulletin of the New Zealand Society for Earthquake Engineering2001; 34(1):4059.

20. Prakash V, Powell GH, Gampbell S. DRAIN-2DX base program description and users guide. UCB=SEMMReport No. 17=93, 1993; University of California.


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EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2005; 34:2148

Published online 25 October 2004 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/eqe.404

Identication of structural and soil properties from vibrationtests of the Hualien containment model

J. Enrique Luco1;; and Francisco C. P. de Barros2

1Department of Structural Engineering; University of California; San Diego; La Jolla;California 92093-0085; U.S.A.

2Depto. Ciencias Fundamentais; Radiac oes e Meio Ambiente; Instituto Militar de Engenharia=CNEN;Praca General Tiburcio 80; CEP 22290-270; Rio de Janeiro; Brazil

SUMMARY

Measurements of the response of the 14 -scale reinforced concrete Hualien (Taiwan) containment modelobtained during forced vibration tests are used to identify some of the characteristics of the super-structure and the soil. In particular, attempts are made to determine the xed-base modal frequencies,modal damping ratios, modal masses and participation factors associated with translation and rockingof the base. The shell superstructure appears to be softer than could have been predicted on the basisof the given geometry and of test data for the properties of concrete. Estimates of the shear-wavevelocity and damping ratio in the top layer of soil are obtained by matching the observed and theo-retical system frequency and peak amplitude of the response at the top of the structure. The resultingmodels for the superstructure and the soil lead to theoretical results for the displacement and rotationsat the base and top of the structure which closely match the observed response. Copyright ? 2004John Wiley & Sons, Ltd.

KEY WORDS: identication; structures; soils; dynamics; interaction; vibration tests

INTRODUCTION

The extensive data recorded during forced vibration tests of the 14

-scale Hualien, Taiwancontainment model [1, 2] are used to test the possibility of using identication techniquesto determine some of the modal properties of the superstructure and some of the charac-teristics of the top layers of soil. The study focuses on: (i) assessment of the adequacy ofthe experimental forced vibration test program to provide data from which structural and

Correspondence to: J. Enrique Luco, Department of Structural Engineering, University of California, San Diego,La Jolla, California 92093-0085, U.S.A.

E-mail: [email protected]

Contract=grant sponsor: National Science Foundation, U.S.A.; contract=grant number: BCS-9315680Contract=grant sponsor: U.S. Nuclear Regulatory CommissionContract=grant sponsor: CNEN (Brazilian Nuclear Regulatory Commission)

Received 10 February 1997

Revised 3 April 2004Copyright ? 2004 John Wiley & Sons, Ltd. Accepted 3 April 2004

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22 J. E. LUCO AND F. C. P. de BARROS

soil information can be obtained by use of identication techniques, (ii) discussion of vari-ous structural identication techniques in the presence of signicant soilstructure interactioneects, (iii) discussion of a direct approach to obtain some of the soil properties of the toplayers of soil, (iv) assessment of the quality of the basic structural and soil data by compar-

ison with the identied properties, and (v) evaluation of a mathematical model to calculatethe dynamic response of structures including soilstructure interaction eects.

The study starts with a brief description of the Hualien containment model including rele-vant characteristics of the superstructure, foundation and soil. The experimental procedure isthen summarized and followed by a discussion of the characteristics of the observed responseof the structure. The observed response at the top of the structure together with the observedtranslation and rotation of the base are used to isolate and determine some of the xed-basemodal characteristics of the superstructure including modal frequencies, modal dampingratios, modal masses and participation factors associated with the translation and rockingof the base. Next, the characteristics of the top layer of soil are determined by matching theobserved and calculated responses at the top of the structure. Finally, the resulting modelsfor the superstructure and the soil are used to calculate a set of theoretical results which arecompared with the observations.

DESCRIPTION OF THE HUALIEN CONTAINMENT MODEL

Characteristics of the superstructure and foundation

The 14

-scale Hualien containment model is illustrated in Figure 1. The structure has a totalheight of 16:13m, a basal diameter of 10:82m and is founded at a depth of 5:15m belowgrade level. The base slab of diameter 10:82m has a thickness of 3:00m and rests on alayer of lean concrete of 0:15m thickness. The total mass of the foundation (including the

lean concrete) is estimated at 695 103

kg. The reinforced concrete containment shell has anexternal diameter of 10:52m, a height of 11:63m and a uniform thickness of 0:30m. Thecylindrical roof slab has a diameter of 13:28 m and a thickness of 1:50 m and is supported onfour beams with cross-sections of 0:60 m 0:30 m. The top slab has a square 2:20 m 2:20 maccess hole at its center. The mass of the shell and top slab are estimated at 264 103 and505 103 kg, respectively (after the mass of the beams is partitioned between the slab andthe shell). A variety of tests to determine Youngs modulus for the concrete in the shellhave been conducted at the National Taiwan University. These tests have led to estimates of

Ec= 2:61 1010N=m2, 2:82 1010N=m2 and 4:05 1010N=m2 based, respectively, on average

28-day cylinder strength, standard compression tests and resonant frequency tests. The valuesEc= 2:82 10

10 N=m2 (2:88 105 kgf=cm2), = 2400kg=m3 and = 0:16 for concrete wererecommended for the blind prediction exercises.

The wide scatter of the estimates for the Youngs modulus Ec and the lack of information,at the time, on the strain levels during the tests, has led the authors to use the average ofthe compression and resonant frequency test data (Ec= 3:44 1010 N=m2) as the initial valuefor Ec. In the initial model, the containment shell was modeled as a Timoshenko beam forhorizontal-rocking vibrations and as a hollow shaft for vertical and torsional vibrations. Someof the xed-base modal characteristics of the superstructure calculated by use of the initialmodel are listed in Table I. These results were later conrmed by a nite element model of


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VIBRATION TESTS OF THE HUALIEN CONTAINMENT MODEL 23

0.300.30

3.

00

Dimensions in meters

G.L.

2.00 2.501.50

2

.50

2.

65

0.

15

0.150.15

0.60 0.60

3.26 3.262.20

16.

28

1.50

0.

30

1.38 1.38

13.28

10.82 2.65

Figure 1. Schematic representation of the Hualien containment model.

Table I. Initial calculated values for xed-base modal characteristics of thesuperstructure (based on Ec= 3:44 10

10 N=m2).

Type of Modal Fraction of

motion frequency (Hz) total mass M1

Mb

M1Ib

1

1

Horizontal=rocking 12.03 0.822 0.714 1.073 1.012Torsion 24.21 0.891 0.762 1.082 Vertical 34.86 0.899 0.780 1.073

Modes normalized by response at the top.

the shell. The calculated fundamental xed-base mode involving horizontal=rocking vibrationshas a characteristic frequency of 12:03Hz (for Ec= 3:44 1010 N=m2) and accounts for 82

per cent of the total mass. The second horizontal=rocking mode has a frequency of 45:59Hzand accounts for 9.2 per cent of the total mass. The fundamental xed-base torsional andvertical modes have frequencies of 24:2 and 34:9Hz, respectively and account for about 90

per cent of the mass of the superstructure.


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0 200 400 600-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

Shear-Wave Velocity (m/sec)

Depth(m)

0 200 400 600-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

Shear-Wave Velocity (m/sec)

A C B

(a)

5 - 12 m

= 0.47

= 2420 kg/m3

= 0.47

= 0.02

12 - 46 m

= 476 m/sec

= 0.47

= 2420 kg/m3

= 0.02

12 - 46 m

(b)

= 476 m/sec

= 2420 kg/m3

= 0.02

5 - 12 m

= 0.47

= 333 m/sec

= 2420 kg/m3

= 0.02

0 - 2 m,

= 231 m/sec

= 133 m/sec, = 0.38

= 1690 kg/m3, = 0.02

2 - 5 m,

= 1930 kg/m3= 0.02

= 0.48

Figure 2. (a) Shear-wave velocities below the foundation for Models A, B andC; and (b) prescribed free-eld velocities.

Characteristics of the soil

The soil at the Hualien site consists of sands and gravels which have been studied extensively[3] by CRIEPI (Central Research Institute of Electric Power Industry, Japan) and IES (Institutefor Earth Sciences, Taiwan). The characteristics of the free-eld soil over the top 20 m of soilare shown in Figure 2(b). These velocities were obtained by CRIEPI by cross-hole (10 m)

and down-hole (10z20m) measurements. There is some uncertainty about the abruptchange in velocity from 333m=sec to 476m=sec at the depth of 12m. This abrupt changein properties is also shown in the IES down-hole data but is not apparent in the blow countof the penetration tests conducted at the site. Estimates of the shear-wave velocities obtained

by Tajimi Engineering Services [4] on the basis of correlation of shear-wave velocity withblow count and eective overburden suggest an average velocity of about 375m=sec in thedepth range from 12 to 18m instead of 458 to 474 m=sec as obtained by IES and CRIEPI.Overall, signicant dierences exist between the CRIEPI, IES and Tajimi ES estimates ofthe free-eld velocities [5]. The maximum deviations with respect to the mean of the threeestimates amount to 22, 34, 5 and 14 per cent for the 02 m, 25m, 512m and 1218mlayers, respectively.

After excavation to a depth of 5 m and construction of the containment model and prior

to backll of the soil surrounding the foundation, extensive measurements of the shear-wavevelocity immediately below the foundation (in the depth range from 510 m below gradelevel) were undertaken by CRIEPI. The resulting estimates of the shear-wave velocity arewidely scattered over the range from 200 m=sec to 475m=sec and have a weighted averagevalue of 317m=sec.

The participants in the Hualien project [1, 2] were asked to submit blind predictions for theresponse of the containment model to forced vibration tests for two prescribed soil models


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(Models A and B). The soil properties in both models are identical to the CRIEPI free-eldproperties except for the soil in the rst 7 m immediately beneath the foundation (depth rangefrom 5 to 12m). In Model A, the soil beneath the foundation in the depth range from 5 to12m is characterized by the average of the measured shear-wave velocities in that depth range

( =317 m=sec). In Model B, the shear-wave velocities in this area are based on calculationsreecting the changes in conning stress as a result of excavation and subsequent constructionof the model. In our blind predictions we considered a third model (Model C) based on ourown estimates of the eects of changes of conning stress on shear-wave velocity. It was alsosuggested that the eects of strain on the soil shear modulus and damping ratio should not

be considered. Finally, soil damping ratios of 2% were recommended. The characteristics ofthe upper layers of Models A, B and C for the soil column below the foundation are shownin Figure 2(a).

FORCED VIBRATION TESTS AND RESULTS

Description of the forced vibration tests

Harmonic forced vibration tests of the Hualien containment model were conducted by theTokyo Electric Power Corporation [6, 7] in November 1992 before the backll soil was putinto place. The experiment included four tests with a shaker exerting a harmonic horizontalforce in two orthogonal directions at the top and base of the model and one test with theshaker exerting a vertical force at the base of the model. The tests covered frequency rangesfrom 2 to 20Hz and 2 to 25Hz for horizontal and vertical excitations, respectively.

The measured displacement response components for each excitation frequency were pre-sented in the form D =A exp(i) where represents the phase of the response with respect

to the forcing function and A represents the amplitude of the response. Although the shakergenerates a force which varies with the square of the forcing frequency, the amplitude Aprovided to the participants was linearly scaled to a force of amplitude 1tonf (9806N) forall frequencies.

For horizontal excitation, the recorded response appears to show a high degree of cross-axiscoupling whereby a force in the NS direction excites not only vibrations in the NS direction

but also vibrations in the orthogonal EW direction and vice-versa. The perpendicular responsecomponent can be as large as 60 per cent of the parallel response component. In addition,the frequency response curves for both the NS and EW components instead of presenting one

peak show two peaks at frequencies of 4:14:2 and 4:6Hz. The cross-axis coupling and thebimodal characteristics of the response have been ascribed to azimuthal variations of the soilproperties in the vicinity of the foundation. It has been found [6] that the coupling between

the response in two directions could be minimized if the axes are rotated counterclockwiseby = 34 (it should be noted that the nominal North direction is 31:4 to the west of thetrue North).

It must be noted here that the process of scaling the data to a nominal force of 9806 Nand of combining the results of NS and EW main and sub-tests to obtain the response forexcitation in the D1 (N34

W) and D2 (N124W) directions presumed that the structure, soil

and data acquisition system are responding linearly.


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0

50

100

150

200

250

300

Amplitude(m/tonf

)

2 3 4 5 6 7 8-60

0

60

120

180

240

300

Frequency (Hz)

Phase(degrees)

0

25

50

75

100

2 3 4 5 6 7 8-60

0

60

120

180

240

300

Frequency (Hz)

0

1

2

2 6 10 14 18 22 26-60

0

60

120

180

240

300

Frequency (Hz)

Horizontal Force at Top Horizontal Force at Base Vertical Force at Base

(a)

D1

D2

(b)

D1

D2

(c)

D1

D2

(d)

D1

D2

(e)

(f)

UT

H TH

b

Ub

UT

H TH

b

Ub

UT

Ub

Figure 3. Amplitude and phase of the experimental response for horizontal excitation at the top (a, b);horizontal excitation at the base (c, d); and vertical excitation at the base (e, f).

Characteristics of the experimental response

The amplitude and phase characteristics of the rotated response for the conditions prior tobackll are illustrated in Figure 3 which shows the amplitude (a c) and phase (b d) of the totalhorizontal displacement UT, the total rotations HT and Hb at the top and base normalized

by the height H= 13:13m, and the total horizontal displacement Ub at the top of the baseslab. The results labeled D1 correspond to the response in the direction D1=N34

W for ahorizontal force of amplitude 1tonf (9806N) acting at the top (ab) or base (cd) of the

structure in direction D1. The results labeled D2 correspond to the response in the directionD2=N124

W for a force at the top or base of the structure acting in the direction D2. Finally,Figures 3(e) and (f) show the amplitude and phase of the total vertical displacements at thetop UT and base Ub of the structure for a vertical force of amplitude 1 tonf (9806N) appliedat the base of the structure.

All of the phase angle data shown in Figure 3 show signicant uctuations for frequen-cies below 4 Hz. The amplitude data for horizontal excitation at the base (Figure 3(c))


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and for vertical excitation (Figure 3(e)) also show strong uctuations for frequenciesbelow 46Hz.

Prior to backll, the peak response of the model in direction D1 occurs at frequencies of4:1 and 4:2 Hz for horizontal excitation at the top and base of the structure, respectively. The

peak response for horizontal excitation in the D2 direction occurs at a frequency of 4 :6Hzindependently of the location of the shaker. The amplitude of the response in the D1 directionis 20 to 40 per cent larger than the response in the D2 direction, depending on the responsecomponent and on the location. For vertical excitation, the peak response at the top and baseof the structure occur at frequencies of 11:0 and 9:5Hz, respectively.

The eects of soilstructure interaction on the response are quite large. Rigid-body rockingwith respect to the bottom of the base slab accounts for 61 to 69 per cent of the totalresponse at the top of the structure at the fundamental system frequency. Rigid-body swayingof the foundation accounts for 11 to 13 per cent of the total response at the top while thedeformation of the structure only accounts for 21 to 26 per cent of the total response. Forvertical vibrations, the motion of the base accounts for 83 per cent of the total motion atthe top.

IDENTIFICATION OF STRUCTURAL PROPERTIES

Model of the superstructure

To identify structural properties out of forced vibration test results that include a signicantamount of soilstructure interaction it is necessary to consider that the deformation of thesuperstructure depends on the force applied by the shaker and also on the translation androtation of the base. To derive the necessary equations we consider the lumped mass modelshown in Figure 4. In the case shown, the superstructure is excited by the force FTe

i!t thatthe harmonic shaker exerts at the top of the structure. The total translation at the top of the

rigid foundation is represented by Ubei!t and the total harmonic rotation of the base aboutthe horizontal axis is represented by be

i!t.The total harmonic displacement Uje

i!t (j = 1; N) and the total rotation jei!t (j = 1; N)

at the j-th level can be written in the form

Uj= Ub+hjb+Uj (1)

j= b+j (2)

where Uj and j represent the relative displacement and relative rotation at the j-th levelwith respect to a system of coordinates attached to the rigid foundation. In Equation (1), hjdenotes the height of the j-th level with respect to the top of the foundation. Equations (1)and (2) can be summarized in the form

{ U} = {1} Ub+{h}b+{U} (3)

where { U} = (U1; 1; U2; 2; : : : ; UN; N)T and {U} = (U1; 1; U2; 2; : : : ; U N; N)

T representthe total and relative displacement vectors, respectively, {1} = (1; 0; 1; 0; : : : ; 1; 0)T and {h} =(h1; 1; h2; 1; : : : ; hN; 1)

T.


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Figure 4. Lumped mass model for derivation of identication approach.

The equation of motion of the superstructure in terms of the generalized relative displace-ment is given by

(!2[M] +i![C] + [K]){U} = {F}+!2[M]({1} Ub+{h}b) (4)

where [M], [C] and [K] are the xed-base mass, damping and stiness matrices, and {F}

= (0; 0; : : : ; 1; 0)T

FT represents the force vector acting on the superstructure.Now, for vibrations in the vicinity of the fundamental xed-base natural frequency of the

superstructure we can approximate the deformation of the superstructure by

{U} = {(1)}UT (5)

where UT= UN is the relative translational displacement at the top of the superstructure and{(1)} is the fundamental xed-base mode normalized so that the translation at the top isequal to one. Substitution from Equation (5) into Equation (4), pre multiplication by {(1)}T

and use of Equation (1) for j =N lead to

UT= Ub+Hb+

FT1!2M1

+1 Ub+1Hb

(!1=!)2 1 + 2i1(!1=!) (6)

where UT= UN= UT+ Ub+ Hb is the total displacement at the top of the structure andH= 13:13 m is the height from the top of the base mat to the top of the roof slab. The modalmass M1 and the participation factors 1 and 1 appearing in Equation (6) are given by

M1= {(1)}T[M]{(1)} (7a)


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1= 1

M1{(1)}T[M]{1} (7b)

1=

1

HM1 {(1)

}T

[M]{h} (7c)

The xed-base natural frequency !1 and the xed-base modal damping ratio 1 are given by

!21= 1

M1{(1)}T[K]{(1)} (8a)

1= 1

2M1!1{(1)}T[C]{(1)} (8b)

The term 1 appearing in Equation (6) represents a correction that needs to be incorporatedwhen the shaker acts at a location dierent from that of the observation point at the top of the

structure. The term 1 is dened as the ratio of the amplitude of the translational componentof the mode shape {(1)} at the location of the shaker divided by the corresponding amplitudeat the location of the observation point at the top of the structure. In the present case, whenthe shaker is acting at the top of the structure 1= 1:0345.

During forced vibration tests the total displacements UT and Ub and the total rotation bare measured at dierent frequencies ! for a known force FT. All or some of the structural

propertiesM1, 1, 1, !1 and 1 can then be determined by tting Equation (6) to the observeddata. In here we note that if the shaker is acting on the oor slab (base excitation) then theterm (FT=!

2M1) appearing in Equation (6) should be deleted (1= 0). In addition, for verticalexcitation the term involving b should be deleted from Equation (6).

Approximate identication approach (Method 1)

To start the process of identication of structural properties on the basis of the observedresponse during forced vibration tests we consider Equation (6) at the system frequency !1.From Equation (6) we obtain

(!1=!1)2 1 = Re

FT1

!21M1UT+1

UbUT

+1Hb

UT

!1

(9)

where UT= UT Ub Hb is the relative displacement at the top of the structure.Since UT, Ub and Hb are approximately in phase at the system frequency !1 and are90 out of phase with respect to FT (Figure 3), we nd that

!1 !1UT+1

Ub+1HbUT

!1

(10)

which reduces to

!1 !1

UT

UT

!1

(11)


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Table II. Inferred modal properties by dierent identication methods.

Top force Base forceModal Average Base forceproperty Method D1 D2 D1 D2 horizontal vertical

f1 (Hz) 1 9.06 9.72 8.32 9.72 9.21 26.762 9.25 9.25 9.70 9.70 9.48 27.603 9.05 9.67 9.39 9.74 9.46 27.354 9.23 8.81 9.29 9.72 9.26

1001 3 6.83 4.42 0.64 0.57 3.12 3.114 4.24 11.08 1.07 0.16 4.14

1 3 1.359 1.561 1.460 4 1.311 1.195 1.253

1 3 1.169 1.216 1.203 1.071 1.165 1.0094 1.147 0.940 1.444 1.011 1.136

1 3 0.975 1.188 1.063 1.027 1.063 4 0.950 0.803 1.242 0.955 0.988

after the approximations 1 1 and 1 1 are introduced. An alternative derivation of Equa-tion (11) has been presented by Luco et al. [8, 9].

Applying Equation (11) to the data for the vibration tests prior to backll (FVT-1) leads tothe results forf1= !1=2 listed in Table II. The obtained values off1 for horizontal=rockingvibrations range from 8:32 to 9:72Hz, while the theoretical value based on the initial model ofthe superstructure was 12:03 Hz. For vertical vibrations, the identied value off1 is 26:76 Hzwhich must be compared with the theoretical value of 34 :86 Hz based on the initial model ofthe superstructure.

The large dierences between the estimates of the xed-base natural frequenciesf1 based onthe FVT-1 data and the initial theoretical values suggest that the assumed value for concretesYoungs modulus Ec was largely overestimated or that the structure as built diers from theinitial plans. To match the vertical frequency of 26 :76 Hz it would be necessary to reduce Ecfrom 3:44 1010N=m2 to 2:02 1010N=m2 which would be 28% lower than the recommendedvalue of 2:82 1010 N=m2.

Identication frequency-by-frequency (Method 2)

A second identication approach [8, 9] assumes that the modal properties M1, 1 and 1 areknown. In this approach Equation (6) is written in the form

(!1=!)2 1 + 2i1(!1=!) =A(!) (12)

where

A(!) =1

FT1!2Mb

+1 Ub+1Hb

UT UbHb(13)


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and 1=Mb=M1 in which Mb= 769 103 kg is the total mass of the superstructure. The term

A(!) involves known or measured quantities. Taking real and imaginary parts of Equation (12)results in

!1= !

1 +ReA(!) (14)

and

1= ImA(!)

2

1 +ReA(!)(15)

which lead to independent estimates of !1 and 1 for each forcing frequency. Again, ifthe force is applied at the base then the term FT=!

2Mb should be deleted from Equa-tion (13). In the case of vertical vibrations the terms involving b should also be deleted from

Equation (13).The results of applying Equations (14) and (15) to the FTV-1 data prior to backll areshown in Figure 5 as a function of the excitation frequency f. The calculations for horizontalexcitation are based on 1= 1:400, 1= 1:073, and 1= 1:012. The parameter1 takes values1= 1:0345 for excitation at the top and 1= 0 for excitation at the base. For vertical excitationat the base the only required parameter is 1= 1:073. The estimate of the fundamental xed-

base frequency for vertical vibration is about 27:6Hz and this estimate is quite stable forexcitation frequencies above 8 Hz. For horizontal vibrations induced by a horizontal forceat the base of the structure, the estimates of f1 in the directions D1 and D2 converge to avalue of f1= 9:70Hz for excitation frequencies above 8 Hz. The estimates of f1 from testsinvolving a horizontal force at the top of the structure lead to values that oscillate between8:0 and 10:5Hz with a best estimate of f1= 9:25Hz.

The fact that the results for f1 obtained from tests with excitation at the base which donot involve the term FT=!

2M1UT in Equation (13) are more stable at high frequencies thanthose involving a force at the top suggest that there may be some error in the experimentalvalues of the phase of the response with respect to the forcing function. This phase dierenceaects the estimates of f1 and 1 for forces at the top of the structure but not for forces atthe base.

The results obtained for the xed-base damping ratio 1 for horizontal=rocking vibrationsare quite erratic. There is some indication that the damping ratio for horizontal excitation atthe base is less than 2 per cent, while larger values would apply to the case of excitationat the top. The result for vertical excitation would correspond to a damping ratio inversely

proportional to the cube of the forcing frequency. In general, it seems that data for therelative phase between response components and the external force are not accurate enough

for a precise identication of the damping ratio within the superstructure.

Identication by use of the amplitude of the frequency response (Method 3)

In a third approach we attempt to determine all of the modal properties M1=Mb, 1, 1, !1and 1 by imposing Equation (6) at all of the observation frequencies. In particular, we


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earthquake engineering & structural dynamics

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