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Soil-Structure Interaction of High-rise

Building Resting on Soft Soil

Mao-guang YueState Key Laboratory of Costal and Offshore Engineering

Dalian University of Technology

ymg2004@126.com

Ya-yong WangInstitute of Earthquake Engineering

China Academy of Building Research

yayongwang@sina.com

ABSTRACTTaking one real high-rise frame shear-wall structure in Fujian province of China as an

example, the influences of soil-structure interaction on the super-structure are studied with

ABAQUS procedure. The peak response of absolute acceleration, story drift, moments at

beam ends, as well as inner force of columns and shear walls are analyzed under two

orthogonal horizontal directions seismic excitations. Then the influences of field nonlinearity

on seismic response of high-rise building are summarized and the rationality of reduction

factor for soil-structure interaction calculation specified in Chinese seismic code is discussed.

It is concluded that its usually safe for most stories of the high-rise frame shear-wall structurewhen the soil-structure interaction considered according to Chinese seismic code; however,

the seismic response of structural member may be amplified in some stories, so it is unsafe in

such regions.

KEYWORDS: Soil-structure interaction; seismic response; field nonlinearity.

INTRODUCTION

Extensive studies on pile-soil-structure interaction have been carried out (Lou, 1999), the

scopes of which include not only theory research but also strong earthquake observations(Trifunac, 1999 & 2001; Ivanovie, 1999) and shaking table tests (Chen, 2001; Lv, 2002). Theseresearches indicate that the fundamental period and damping of structures may be prolongedwhen soil-structure interaction is considered. So the seismic force and story drift response ofstructure can be reduced according to the response spectra advised by Code for Seismic Design

of Buildings (GB 50011-2001, Chinese seismic code for short). Correspondingly the story driftmay be diminished and acceleration amplitude at basement may be smaller than that at adjacentfree-field. Therefore, it is specified in Chinese seismic code that the influences of soil-structureinteraction can be neglected for most cases in building design. Nevertheless, Li (2002) indicates

that soil-structure interaction calculation is close to the specifications of Chinese seismic code

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only when structural response dominated by the first mode; but there are large differences whenthe influence ofhigher modes cant be neglected, and even the response may be increased insteadof reduced in some stories (Han, 1992). As a result, specifications of interaction calculation inChinese seismic code not always approach to safety.

At present, there still exist many problems in the pile-soil-structure interaction calculationdue to its complexity (Mylonakis, 1997; Carrabba, Finn and Makoto, 1996; Li, 2002):

Although the structure and ground soil adjacent to foundation may work in plastic rangeunder strong earthquake, most of the present studies are aimed at elastic systems.

Some studies are focusing on the systems elastoplastic response, but the constitutiverelationship of soil is simulated by Mohr-Coulomb model or Drucker-Prager model which issuitable for monotonic loading simulation, so large errors may be produced for dynamic loading

like earthquake.

Two-dimensional finite element models are employed in most soil-structure interactionanalysis, so the characteristics of multi-dimensional seismic excitation cant be reflected. In thefew analyses with three-dimensional model subjected to multi-component seismic excitation,simple frame structure or further simplified mass-lumped model is used, so the influences of

structural integrity cant be reflected.

Based on problems mentioned above, taking one real high-rise frame shear-wall structure inFujian province as an example, pile-soil-structure interaction is analyzed. First of all, detailed 3-

dimensional finite element model of soil and high-rise building is established with ABAQUSprocedure; then the absolute acceleration response, story drift, moments at beam ends, as well as

the inner force of column and wall are analyzed under bidirectional horizontal seismicexcitations; finally, influences of field nonlinearity on high-rise building are summarized, and the

rationality of reduction factor in interaction calculation of Chinese seismic code is discussed.

PROJECT OVERVIEW AND FINITE ELEMENT MODEL

1. Soil Model

The engineering field lies in an alluvial island of river Jin. According to Chinese seismic

code, the seismic fortification intensity is 7 (peak acceleration in design is 0.15g) and the designearthquake group belongs to the1st group. Site class of the field is III and characteristic period is0.4s specified by the geological exploration. The overlay soil includes artificial fill, medium sand

(1), silty sand, medium sand (2), silt, cobble gravel, strongly weathered rock and moderatelyweathered rock. The principal parameters of soil layers are listed in Table 1. In the overlay soil,

backfilling sand, medium sand and medium-course sand belong to soft ground, so the field isdisadvantage for seismic fortification. In addition, the minimum distance between river bank andhigh-rise building to be constructed is only 18m, which cant meet to the provisions of Chinese

seismic code (when lateral expansion or now sliding is possible due to liquefaction, no permanentbuildings should be constructed within 100m of the normal waterline). Therefore, double-row

piles shoring scheme is adopted in the project (Yue, 2009).

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As the undulation of each soil layer is not large, it is simplified to isotropic stratified soilwith constant thickness in the finite element model. Parameters of all the layers are listed in Table1, in which shear velocity of strongly weathered rock is greater than 500m/s, therefore it can beconsidered as bedrock according to Chinese seismic code. In the model, only soil over strongly

weathered rock layer is simulated. Total depth of model is 27.1m and seismic acceleration isapplied at the bottom of cobble-gravel layer. The soil is simulated by solid element with 1mlength in principal region and refined at near pile region. The element length is increasedgradually far form the principal region, and the maximum length is 6m.

Finite element method is only suitable for finite region analysis, while the foundation soil of

interaction system is a half infinite space. So the soil must be cut off and artificial boundaryshould be added to simulate horizontal infinity. Typical artificial boundaries include cutoff

boundary, viscous boundary, penetrate boundary, as well as coupling of finite element andinfinite element (or boundary element). But most of them are only appropriate for analysis infrequency domain. For real nonlinear problems in time domain, there is no better method exceptmaking the soil boundary as far as possible (Zhuang, 2006). In order to eliminate the influence of

free boundary, about 5 times length of the principal region is extended in horizontal direction(Chen, 2006). Free boundary condition is adopted in the soil model: vertical free and horizontalconstrained in static analysis step, and then changed to vertical constrained and horizontal free intime-history analysis step.

Table 1: Layers and principal parameters of the soil

Soil LayersDepth

(m)

Gravity

(kN/m3)

Poissons

Ratio

c

(kPa)()

Shear Velocity

(m/s)

Elastic

Modulus (Pa)

Artificial fill 1.60 18.5 0.30 25 19.0 118 6.69e7

Medium sand (1) 11.60 18.5 0.30 1.2 28.9 156 1.17e8

Silty sand 16.20 17.9 0.35 11 18.3 130 8.17e7

Medium sand (2) 19.20 19.2 0.30 1.2 28.9 200 2.00e8

Silt 21.10 17.0 0.35 6.5 14.4 130 7.76e7

Cobble gravel 27.10 21.5 0.25 5 40.0 340 6.21e8

Strongly

weathered rock35.30 20.0 0.20 -- -- 522 9.81e8

Moderately

weathered rock40.30 26.2 0.20 -- -- 817 3.15e9

The constitutive relationship of soil is very complex with characteristics of significantnonlinearity, elasto-plasticity, viscoelasticity, shear dilatability, anisotropy and deformationcumulating. For accurate simulation of the dynamic characteristics, a constitutive model withviscous-plastic memorial nested yield surface is adopted (proposed by Zhuang, 2006, ZHY model

for short). At the end of any increment, the inverted loading surface, the failure surface and theinitial loading surface which was tangent with the inside of inverted loading surface were

memorized, and dynamic behavior of yield surface was defined by these surfaces. The yieldsurface equation of the model is as follow:

( )( ) / 2 0ij ij ij ijf p S S k (1)

In which, k and are computing factor of the yielding face; ij and Sij denote kinematic

hardening parameter and deviatoric stress component respectively.

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1 2 3( ) / 3p (2)

Relationship between stress and strain is:

2

( )2 (2 ) ( )

2( )

ij ij

ij kk ij ij t kl kl kl

Sd Bd Gde G H S d

k p

(3)

B denotes bulk modulus and Ht represents elastoplastic shear modulus. The relationship of

Ht, G (shear modulus) andH(plastic hardening modulus) is:

1 1 1

2t

H G H (4)

If the relationship between stress and strain expressed by hyperbolic curve at load beginning,

then:

2

,max max(1 / )t tH H r r (5)

Combined equation (4) and (5):

,max max2tH G (6)

Where, Gmax is the maximum shear modulus which can be determined by in situ wavevelocity method or indoor test.

2. Model of high-rise buildingThe building to be constructed in the engineering field is a frame shear-wall structure with

total 25 stories and 2-story basement, the total height of aerial part is 90m, and the size ofbuilding plane is 43.2m20.7m. Plane layout of the building is shown in Fig. 1 and the basic

information is listed in Table 2. The primary dimension of beam section is 250mm400mm,250mm500mm, 250mm600mm; and column dimension is 600mm600mm at lower portionand 400mm400mm at upper potion; the thickness of shear wall is 400/300mm at bottom and

250/200mm at upper portion. Pile-raft foundation is taken to support the super structure, in whichthe bored pile is 800mm in diameter and the raft foundation is 1.5m in thickness. The supportinglayer is moderately weathered rock. As to supporting piles, 0.6~1D (D is pile diameter) of pile

length at top should be inserted to the supporting layer.

According to the information of engineering field and tall building introduced above, a 3-dimensional finite element model is assembled and displayed in Fig. 2. As completely nonlineardynamic analysis with great time consuming will be carried out for soil, the super structure is

considered as elastic. In the model, supporting piles, pile foundation, beam and column ofbuilding are simulated with elastic beam element; retaining wall of bank, raft plate and shear wall

of building are simulated with elastic shell element. In order to discuss the interaction influenceson seismic response of building, two different models are constructed, one of which is systemwith pile foundation, soil and super structure (SSI model for short), and the other one is over-

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ground portion of building based on rigid foundation hypothesis (NSSI model). The interactionbetween supporting pile, soil, retaining wall and basement of structure are simulated withembedded command, and connections between beam, column, shear wall top and floor aresimulated with Tie command. Because the floor is minor object, the mesh is very course and no

any result outputted in calculation.

(a) Arrangement of two stories at bottom

(b) Arrangement of standard story

Figure 1: Diagram of structural arrangement

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Table 2: Basic information of the high-rise frame-shear wall structure

Story

No.

Story

Height

(m)

Total

Height

(m)

Strength Grade of

ConcreteColumn

Section

(mmmm)

Thickness

of Wall

(mm)

Thickness

of Floor

(mm)Beam Column Wall

B2 3.8 3.8

C35 C40 C40 600600 400/300 120B1 3.25 7.05

1 3.6 10.65

2 3.6 14.25

3

3.6

17.85

C35 C40 C40 600600 300 120~ ~

6 28.65

7

3.6

32.25

C30 C35 C35 600600 250 120~ ~

13 53.85

14

3.6

57.45

C25 C30 C30 400400 200 120~ ~25 97.05

(a) Soil (b) Retaining wall (c) Supporting piles

(d) Pile-raft foundation (e) Structure (f) System of pile-soil-foundation-structure

Figure 2: Finite element model of the system

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KINETIC EQUATION AND SEISMIC EXCITATION

In the simulation, total 3 analysis steps are set. Gravity load, floor load (dead load and live

load are considered together, 5kN/m

2

for basement and first two stories and 4kN/m

2

for the otherstories) and seismic load are applied in the three sequence steps. As great time consuming, only30s of the earthquake wave are cut off. As to SSI model, geostatic analysis should be carried outunder gravity load first of all. The balance of ground stress is considered to be reached whenvertical displacement at ground surface is 10-5 order.

For interaction analysis of pile-soil-structure system, kinetic equation is similar to super structureanalysis except interface interaction must be considered, the equation as follow:

( ) ( ) ( ) ( )Mu t Cu t Ku t F t (7)

Where ( )u t and ( )u t are node acceleration and velocity respectively. M, C, K and F(t) are

systems mass matrix, damping matrix, stiffness matrix and node load vector respectively . Theyare matrix or vector integration of pile, soil and member in structure.

The model is excited at two orthogonal directions with a recorded wave and an artificialwave, the shapes of which excited in X direction of SSI model and NSSI model are shown in Fig.

3. The scale of peak acceleration at ground surface in X and Z direction is 1:0.85. For SSI model,it is excited at soil bottom, and the frequency components of acceleration response at groundsurface shall be consistent with that of standard spectra. The peak acceleration shall be scaled toabout 0.15g at ground surface in accordance with the fortification intensity of the field. As to

NSSI model, it is excited at structural bottom, and the input wave is acceleration response of the

corresponding free field in SSI model.

0 5 10 15 20 25 30-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Acceleration(m/s2)

Time (s) 0 5 10 15 20 25 30

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Accleration(m/s2)

Time (s)

(a) Recorded wave in SSI model (b) Artificial wave in SSI model

0 5 10 15 20 25 30-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Acclera

tion(m/s2)

Time (s) 0 5 10 15 20 25 30

-1.5

-1.0

-0.5

0.0

0.5

1.0

.

Acceleration(m/s2)

Time (s)

(c) Recorded wave in NSSI model (d) Artificial wave in NSSI model

Figure 3: Time histories of acceleration excitation in X direction

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SOIL-STRUCTURE INTERACTION ANALYSIS

In order to study the soil-structure interaction, absolute acceleration, relative story drift,

moments at beam ends, as well as inner force of column and shear wall in the two models arecompared. For convenience, response ratio is defined as below:

Response ratio = (peak response of structure in SSI model) / (peak response of structure in

NSSI model).

1. Natural Vibration Characteristics

For ZHY constitutive relationship model, the hysteretic damping and viscous damping areintroduced in soil model. The hysteretic damping has been implied in the restoring force, and the

viscous damping is considered by Rayleigh damping, which is expressed by equation (8).

[ ] [ ] [ ]C M K (8)

andare Rayleigh damping factors.

According to the orthogonality between system mode and damping matrix:

2 2

2 2

2( )

2( )

j i i j i j

i j

i i j j

i j

(9)

On the assumption of 5% damping for the first two modes, factors of Rayleigh damping arecalculated with equation (9). The first 6 vibration periods and damping factors of the first twomodels are listed in Table 3.

Table 3: First 6 natural vibration periods and factors of Rayleigh damping

Model

Natural vibration period (s) Damping factors

1 2 3 4 5 6

SSI 1.87 1.32 0.89 0.61 0.61 0.58 0.1970 0.0123

NSSI 1.79 1.05 0.81 0.53 0.25 0.25 0.2212 0.0105

The fundamental vibration period can also be estimated according to Load code for thedesign of building structures (2006), in which empirical formula of RC frame shear-wall

structure is given as below:

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3 2 30.25 0.53 10 /T H B (10)

HandB are the height and width of the building respectively.

So that T=0.25+0.5390210-3/20.7-1/3=1.81s. The estimated period is very close to the result

of NSSI model. So the finite element model is reasonable. The data in table 3 indicate that natural

period will be prolonged when the field effect is considered, and the period can be increased byone more times for high modes especially. Therefore more modes are attributed to the response ofSSI model.

2. Horizontal Absolute Acceleration Response

Distributions of peak horizontal acceleration and acceleration response ratio along thestructural height are presented in Fig. 4, from which we can conclude:

oPeak acceleration variation of super structure in X and Z direction is not in coincidence.Acceleration distributions in X-direction have a clear S shape, that is, value of acceleration

increased gradually in the lower 12 stories and decreased in the 12th~19

thstories and then

increased in the rest stories. The acceleration reaches its minimum at the 19th story and reaches itsmaximum at the top of structure. Acceleration in Z-direction shows no much changes below the15th story (slightly decrease from the 10th to the 15th story), but increased gradually in stories

above 15. Acceleration in Z-direction reaches its maximum at the top of structure.

o Acceleration response in the upper floors is no longer comply with the scale (1:0.85) ofwhich at ground surface, and in some floors the acceleration in X direction is even higher thanthat in Z direction especially for recorded wave excitation.

o Variation of acceleration along the structural height of SSI model is similar to that ofNSSI model. Acceleration response at floors has a trend of degrading except several stories (the19th and 20th stories for recorded wave). When field nonlinearity is considered, distributions of

acceleration along the structural height become more uniform.

o Fig. 4(c) shows that peak acceleration response in super-structure is not always amplified.The acceleration response ratio is usually lower than 1 (0.55-0.9) except the 19th and 20th stories

when excited by recorded wave.

0

5

10

15

20

25

0 1 2 3 4 5 6 7

SSI, X-direction

SSI, Z-direction

NSSI, X-direction

NSSI, Z-direction

Acceleration (m/s2)

to

ry

o.

0

5

10

15

20

25

0 1 2 3 4 5 6 7

SSI, X-direction

SSI, Z-direction

NSSI, X-direction

NSSI, Z-direction

Acceleration (m/s2)

StoryNo.

0

5

10

15

20

25

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.

Recorded wave

in X-direction

Recorded wave

in X-directionArtificial wave

in X-direction

Artificial wave

in Z-direction

Acceleration Ratio

StoryNo.

(a) Recorded wave excitation (b) Artificial wave excitation (c) Acceleration response ratio

Figure 4: Distributions of peak horizontal acceleration and acceleration response ratio

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3. Story Drift Response

Distributions of peak story drift and story drift response ratio along the structural height arepresented in Fig. 5. It is shown that:

o Peak story drift variation of super structure in X-direction is not coincident with that in Z-direction. Distributions of story drift in X-direction are W-shaped while they nearly increasealong the structural height in Z-direction.

o The story drift reaches its maximum at the 20th story. The maximal value in X and Zdirection is 9.1mm and 14.4mm respectively for NSSI model, and the corresponding term is

7.5mm and 4.2mm for SSI model.

o When the effects of field nonlinearity are considered, story drifts will not always decreasecompared with that of NSSI model. Such as the 8th~15th stories in X-direction and the lower 10stories in Z-direction for recorded wave, and the lower 6 stories in Z-direction for artificial wave.

o Similar to the acceleration response, distributions of story drift along the structural heightalso become more uniform when the field nonlinearity is considered. Interaction of pile-soil-structure has a clear peak-reduction effect.

o Fig. 5(c) shows that story drift response ratio of super-structure in X-direction has a W-shaped distribution while it has no much changes in Z-direction except the 2 bottom stories(much greater than 1). Story drift ratio in Z-direction is higher than one in the middle of structureheight, about from the 10th story to the 14th story. The story drift response ratio reaches to itsmaximum at the 5th story, which is 0.68.

0

5

10

15

20

25

0 2 4 6 8 10 12

SSI, X-direction

SSI, Z-direction

NSSI, X-direction

NSSI, Z-direction

Story Drift (mm)

StoryNo.

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10

SSI, X-direction

SSI, Z-direction

NSSI, X-direction

NSSI, Z-direction

Story Drift (mm)

StoryNo.

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8

Recorded wave

in X-direction

Recorded wave

in Z-direction

Artificial wave

in X-direction

Artificial wave

in Z-direction

Drift Ratio

StoryNo.

(a) Recorded wave excitation (b) Artificial wave excitation (c) Story drift response ratio

Figure 5: Distributions of peak story drift and drift ratio

4. Moment Response at Beam Ends

The beam moment response is analyzed in this section. Beam-1 and beam-2 marked with redin Fig. 1 are taken as example, which lie in X and Z direction respectively. Distributions of peakmoment response and moment response ratio at beam ends along the structural height aredisplayed in Fig. 6. It is indicated that:

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Variation of peak moment along the structural height in SSI model is similar to that in NSSImodel. Peak moment distribution of beam-1 is W-shaped while inverted W-shape is for beam-2,in which breaks with small amplitude appears in the 14th and 23rd stories.

The nonlinear response of filed can generally reduce the moment response at beam ends, andclear peak-reduction effect is displayed in beam-1.

Moment ratio at beam ends may greater than one in lower stories. The maximum value ofwhich is 1.26, and the corresponding minimum value is about 0.7.

0

5

10

15

20

0 2 4 6 8 10 12 14 16 18 20Moment (kN.m)

Sto

ryNo.

SSIRecorded

wave, end-1

SSIRecorded

wave, end-2

NSSIRecorded

wave, end-1

NSSIRecorded

wave, end-2

SSIArtificialwave, end-1

SSIArtificial

wave, end-2

NSSIArtificial

wave, end-1

NSSIArtificial

wave, end-2

0

5

10

15

20

25

0 5 10 15 20 25 30 35Moment (kN.m)

StoryNo.

(a) Peak moment of beam-1 (b) Peak moment of beam-2

0

5

10

15

20

25

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4Moment Ratio

StoryNo. Recorded wave,

end-1

Recorded wave,

end-2

Artificial wave,end-1

Artificial wave,

end-2

0

5

10

15

20

25

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Recorded wave,

end-1

Recorded wave,

end-2

Artificial wave,

end-1

Artificial wave,

end-2

Moment Ratio

StoryNo.

(c) Moment ratio of beam-1 (d) Moment ratio of beam-2

Figure 6: Distributions of peak moment and moment ratio at beam ends

5. Inner Force of Column

In the following portion, seismic response of column will be introduced, which include axial

force, shear force and moment at column end. The analysis objects are corner column, sidecolumn and interior column lined out with pink in Fig. 1. According to variation of response ratio

of axial force, shear force and moment, influences of field nonlinearity on the seismic response ofcolumn is analyzed.

(1) Axial force response of column

Distributions of peak axial force and axial force response ratio for the three kinds of columnare presented in Fig. 7. It is shown that:

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o The axial force is nearly reduced linearly along with the structural height.o The influence of interaction on axial force response of side column and interior column

can be neglected as the axial force ratios of the columns are approximate to one in all through the

structural height.

o The influences of interaction on axial force response of corner column are moresignificant. Compared with NSSI model, the peak axial force of corner column is not alwaysdiminished in SSI model. The peak axial force of corner column is amplified in the lower 7stories but diminished in the other stories. The maximum and minimum value of axial force ratiois 1.12 and 0.88 respectively.

o When the interaction of pile-soil-structure is considered, the peak axial force distributionsof column along the structural height become more uniform.

0

5

10

15

20

25

0 1000 2000 3000 4000

Recorded wave, SSI

Recorded wave, NSSI

Artificial wave, SSI

Artificial wave, NSSI

Axial Force (kN)

StoryNo.

0

5

10

15

20

25

0 500 1000 1500 2000 2500 3000

Recorded wave, SSI

Recorded wave, NSSI

Artificial wave, SSI

Artificial wave, NSSI

Axial Force (kN)

StoryNo.

(a) Peak axial force of corner column (b) Peak axial force of side column

0

5

10

15

20

25

0 1000 2000 3000 4000

Recorded wave, SSI

Recorded wave, NSSI

Artificial wave, SSI

Artificial wave, NSSI

Axial Force (kN)

StoryNo.

0

5

10

15

20

25

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Recorded wave,

corner column

Recorded wave,

side column

Recorded wave,

inner column

Artificial wave,

corner column

Artificial wave,

side column

Artificial wave,

inner column

Axial Force Ratio

StoryNo.

(c) Peak axial force of interior column (d) Axial force response ratio

Figure 7: Distributions of peak axial force and axial force ratio at column end

(2) Shear force response at column end

Distributions of peak shear force and shear force response ratio for the three kinds of column

are presented in Fig. 8. It is concluded that shear force at column end is increased in turns fromcorner column, side column to interior column, except for few stories in structural bottom. Theshear force distributions have two sharp breaks in the 7th and 14th story, especially near the 14thstory. Such breaks are resulted from changes of concrete strength grade or cross-sections ofcolumn, which are listed in Table 2. Compared with concrete strength changes assigned in the 7 th

story, both of the concrete strength and cross section are changed in the 14th

story, so larger

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breaks appeared in this story. Influences of field nonlinearity on shear force reaction in X-direction are more significant than that in Z-direction. When the interactions of soil-structure areconsidered, distributions of shear force reaction at X-direction along structural height becomemore uniform except interior column in the 14 th story when excited by recorded wave. Peak shear

force reaction in Z-direction of side (or interior) column in SSI model is nearly superposed onthat of NSSI model.

Distributions of shear force response ratio in X-direction have a shape of >. The ratiochanges in a large scope (0.71~1.25), which is greater than one in the 10

th~15

thstories. Shear

force response ratio under artificial wave excitation changes in a relatively small scope, which is

less than one except bottom stories.

Distributions of shear force response ratio in Z-direction have a shape of L. The ratio isgreater than one in lower 7 stories, and the maximum value is 1.25 appeared in corner columnwhen excited by recorded wave. In stories over 7, the shear force response ratio for side columnand interior column is approximate to one, which indicates that influences of soil-structure

interaction are negligible. On the other hand, response ratio for corner column is obviouslysmaller than one in stories above 7, and the minimum ratio is 0.84 for artificial wave excitation.

In general, when the field nonlinearity is considered, shear force response of column is notalways decreased compared with that in NSSI model. Shear force of middle stories in X-directionand bottom stories in Z-direction may be amplified. Regions where material strength or column

section changed will become weak layers.

0

5

10

15

20

25

0 100 200 300 400 500Shear Force (kN)

StoryNo.

Recorded wave, SSI, corner column

Recorded wave, NSSI, corner column

Artificial wave, SSI, corner column

Artificial wave, NSSI, corner column

Recorded wave, SSI, side columnRecorded wave, NSSI, side column

Artificial wave, SSI, side column

Artificial wave, NSSI, side column

Recorded wave, SSI, inner column

Recorded wave, NSSI, inner column

Artificial wave, SSI, inner column

Artificial wave, NSSI, inner column

0

5

10

15

20

25

0 10 20 30 40 50 60 70 80 90Shear Force (kN)

StoryNo.

(a) Peak shear force at X-direction (b) Peak shear force at Z-direction

0

5

10

15

20

0.4 0.6 0.8 1.0 1.2 1.4Shear Force Ratio

StoryNo.

Recorded wave,

corner column

Recorded wave,

side column

Recorded wave,

inner column

Artificial wave,

corner column

Artificial wave,

side column

Artificial wave,

inner column

0

5

10

15

20

25

0.6 0.8 1.0 1.2 1.4Shear Force Ratio

StoryNo.

(c) Shear force ratio at X-direction (d) Shear force ratio at Z-direction

Figure 8: Distributions of peak shear force and shear force ratio at column end

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(3) Moment response at column end

Fig. 9 shows the distributions of peak moment at column end and moment response ratioalong the structural height.

It is indicated in Fig. 9 (a-c) that distributions of peak moment in X-direction are clearly C-

shaped, that is, peak moment is larger in bottom and top stories than in middle stories. As thechanges of material strength or cross-section, slight breaks appeared in the 7

thand 14

thstory.

Compared with corner and side column, peak moment in interior column is much higher.

Distributions of peak moment in Z-direction have a lean W shape shown in Fig. 9 (d-f).The peak moment of column in middle stories and bottom stories is greater than that in top

stories. Contributed to the whiplash effect, moment in the top of structure is increased suddenly.In Z-direction, moment reaction in corner column is greater than that of side column and interior

column. When field nonlinearity is considered, distributions of peak moment along the structuralheight become more even, so interaction of soil-structure has a peak-reduction effect evidently.

The moment ratio distributions in X-direction along the structural height are W-shaped

approximately. Nearly all the moment ratio in X-direction is lower than one except the top andbottom stories. Moment ratios of corner column and side column in X-direction have a sudden

increase in the 5th story, and the maximum value reaches to 1.74. The minimum moment ratio inX-direction is 0.59 which appears in the interior column.

As to moment ratio in Z-direction, it is greater than one in bottom stories for corner column

and side column, and so is it in stories of 6-8, 13-16 and 23-25 for interior column, while it islower than 1 for other cases. The maximum and minimum ratio at Z-direction is 1.32 and 0.63

respectively.

In brief, column moment is not surely diminished in through the structural height when fieldnonlinearity is considered, and the peak moment can be increased by 70% especially for cornercolumn and side column in bottom stories.

0

5

10

15

20

25

0 5 10 15 20 25 30

Recorded wave, SSI

Recorded wave, NSSI

Artificial wave, SSI

Artificial wave, NSSI

Moment (kN.m)

StoryNo.

0

5

10

15

20

25

0 5 10 15 20 25 30

Recorded wave, SSI

Recorded wave, NSSI

Artificial wave, SSI

Artificial wave, NSSI

Moment (kN.m)

StoryNo.

0

5

10

15

20

25

0 10 20 30 40 50 60

Recorded wave, SSI

Recorded wave, NSSI

Artificial wave, SSI

Artificial wave, NSSI

Moment (kN.m)

StoryNo.

(a) Moment of corner column atX-direction

(b) Moment of side column atX-direction

(c) Moment of interior columnat X-direction

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0

5

10

15

20

25

0 10 20 30 40 50 60

Recorded wave, SSI

Recorded wave, NSSI

Artificial wave, SSIArtificial wave, NSSI

Moment (kN.m)

Sto

ryNo.

0

5

10

15

20

25

0 2 4 6 8 10 12 14 16 18

Recorded wave, SSI

Recorded wave, NSSI

Artificial wave, SSI

Artificial wave, NSSI

Moment (kN.m)

StoryNo.

0

5

10

15

20

25

0 2 4 6 8 10 12 14

Recorded wave, SSI

Recorded wave, NSSI

Artificial wave, SSI

Artificial wave, NSSI

Moment (kN.m)

Sto

ryNo.

0

5

10

15

20

25

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Moment Ratio

StoryNo.

Recorded wave,

corner column

Recorded wave,

side column

Recorded wave,

inner column

Artificial wave,

corner column

Artificial wave,

side columnArtificial wave,

inner column

0

5

10

15

20

25

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4Moment Ratio

StoryNo.

(g) Moment response ratio at X-direction (h) Moment response ratio at Z-direction

Figure 9: Distributions of peak moment and moment ratio at column end

6. Inner Force of Shear Wall

The shear force of two pieces of wall (W1 and W2 shown in Fig. 1) will be analyzed in this

section, where W1 is in X-direction and W2 is in Z-direction. According to the inner force

comparisons between the two models, the influences of field nonlinearity on seismicresponse of shear wall are analyzed. Here, the inner force means force per unit width in

plane.

(1) Axial force response of shear wall

Fig. 10 displays the distributions of peak axial force and axial force response ratio of the twopieces of wall. It can be concluded from the Figure:

o Axial force of the shear wall nearly decreases along with the structural height except thebottom stories.

o As for the model of rigid foundation assumption, the axial force reaches its maximum atthe bottom story. When soil-structure interaction is considered, the corresponding maximumvalue appears in the 3rd story. Axial force in the first and second story is diminished in SSI model

because the number of shear wall in the two bottom stories is more than that in above stories.

o The overall axial force response ratio of W1 is less than one except the 23 rd story (theratio is 1.08) when excited by recorded wave. The ratio of W1 reduces quickly below the 3

rd

story, and the minimum value is 0.51.

(d) Moment of corner column at

Z-direction(e) Moment of side column at Z-

direction(f) Moment of interior column at

Z-direction

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o The axial force response ratio of W2 in the overall structural height is less than orapproximate to one. It is slightly greater than one of W2 between the 2nd~6th stories, and the peakvalue is 1.05 and 0.67 respectively.

0

5

10

15

20

25

0 500 1000 1500 2000 2500 3000 3500

Recorded wave, SSI

Recorded wave, NSSI

Artificial wave, SSI

Artificial wave, NSSI

Axial Force (kN)

StoryNo.

0

5

10

15

20

25

0 500 1000 1500 2000

Recorded wave, SSI

Recorded wave, NSSI

Artificial wave, SSI

Artificial wave, NSSI

Axial Force (kN)

StoryNo.

0

5

10

15

20

25

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Recorded wave,

shear wall-1

Recorded wave,

shear wall-2

Artificial wave,

shear wall-1

Artificial wave,

shear wall-2

Axial Force Ratio

StoryNo.

(a) Peak axial force of W1 (b) Peak axial force of W2 (c) Axial force response ratio

Figure 10: Distributions of peak axial force and axial force ratio of shear wall

(2) Shear force response of wall

Fig. 11 is the distributions of peak shear force and shear force response ratio along the

structural height of shear wall. It is indicated that:

o Great differences of shear force distributions exist in the two orthogonal directions.Except for several stories at bottom, the peak shear force of W1 nearly increases along thestructural height while that of W2 is W-shaped.

o The shear force in the two bottom stories changes greatly for the number of shear wallincreasing. As to the NSSI model, the peak shear force reaches its maximum at the bottom story.When soil-structure interaction is considered, the corresponding maximum value appears in the

3rd story.

o The shear force response ratio of W1 is less than one except the 3 rd story (the ratio is1.16) when excited by recorded wave. The ratio of W1 is reduced quickly below the 3

rdstory, and

the minimum value is 0.24.

o The shear force response ratio of W2 is less than one except the 23 rd story (the ratio is1.14) when excited by recorded wave, and the minimum value is 0.30.

0

5

10

15

20

25

0 100 200 300 400 500 600

Recorded wave, SSI

Recorded wave, NSSI

Artificial wave, SSI

Artificial wave, NSSI

Shear Force (kN)

Story

No.

0

5

10

15

20

25

0 50 100 150 200 250

Recorded wave, SSI

Recorded wave, NSSI

Artificial wave, SSI

Artificial wave, NSSI

Shear Force (kN)

StoryNo.

0

5

10

15

20

25

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Recorded wave,

shear wall-1

Recorded wave,

shear wall-2

Artificial wave,shear wall-1

Artificial wave,

shear wall-2

Shear Force Ratio

StoryNo.

(a) Peak shear force of W1 (b) Peak shear force of W2 (c) Shear force response ratio

Figure 11: Distributions of peak shear force and shear force ratio of shear wall

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(3) Moment response of wall

Fig. 12 displays the distributions of peak moment and moment response ratio along with thestructural height of shear wall. It is indicated that:

o As the number of shear wall increased at bottom stories, peak moment response changesgreatly. Distributions of moment peak along structural height have a W shape approximatelyexcept the two bottom stories.

o Peak moment distributions near the 7th and the 14th story have a certain breaks as materialstrength or section dimension changes.

o In general, influences of field nonlinearity on moment response of shear wall are notserious. The moment response ratio at bottom and mid-upper stories may larger than one while itis lower than one in stories of 5-14.

0

5

10

15

20

25

0 1 2 3 4

Recorded wave, SSI

Recorded wave, NSSI

Artificial wave, SSI

Artificial wave, NSSI

Moment (kN.m)

StoryNo.

0

5

10

15

20

25

0 1 2 3 4

Recorded wave, SSI

Recorded wave, NSSI

Artificial wave, SSI

Artificial wave, NSSI

Moment (kN.m)

StoryNo.

0

5

10

15

20

25

0.0 0.4 0.8 1.2 1.6 2.0 2.4

Recorded wave,

Shear wall-1

Recorded wave,

Shear wall-2

Artificial wave,

Shear wall-1

Artificial wave,

Shear wall-2

Moment Ratio

StoryNo.

(a) Peak moment of W1 (b) Peak moment of W2 (c) Moment response ratio

Figure 12: Distributions of peak moment and moment response ratio of shear wall

In short, the inner force of shear wall is not surely diminished in through structural heightwhen soil-structural interaction is considered. The inner force response ratio may obviouslygreater than one in some structural position. In regions where material strength, sectiondimension or shear wall numbers changed, the inner force distributions of member may havesudden breaks, so we must be cautious in design.

7. Discussion of the Results

(1) Simplification of Chinese seismic code on interaction calculation

It is very complex of pile-soil-structure interaction calculation and there exist many

influencing factors. In simplification, it is specified in Chinese seismic code (2001) that the soil-structure interaction may be ignored generally in seismic computation. For tall buildings in

intensity 8 or 9, which lie in Site-class III or with box type or a relatively rigid raft foundation,

the influences of soil-structure interaction can be considered when the fundamental period ofstructure is within the scope of 1.2~5 times of the characteristic period of site. The story drift can

be calculated according to the reduced story shear force. For structures with height/width ratioless than 3, the reduction factor of horizontal seismic shear of each floor may be determined bythe following equation:

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0.9

1

1

T

T T

(11)

Where: is seismic shear reduction factor considering the soil-structure interaction; T1 is thefundamental period of structure with rigid base assumption; T is the additional period afterconsidering the soil-structure interaction.

For structures with height/width ratio not less than 3, the seismic shear of the structuralbottom may be reduced according to equation (11), but no reduction at the top. In middle floors,

the seismic shear may be reduced according to the linear interpolation values.

(2) Comparison of calculated results with Chinese seismic code

The height/width ratio of structure in this paper is greater than 3, and the fundamentalperiods of NSSI model and SSI model are 1.79s and 1.87s respectively. According to Chinese

seismic code, the reduction factor at bottom is = (1.79/1.87)

0.9

=0.96, and no reduction at thetop. In middle floors, the value shall be linearly interpolated.

Compared the soil-structure interaction calculation in this research with specifications inChinese seismic code, it is shown that:

o Moment at beam ends, inner force of column and shear wall have much reduction in somefloors when interaction is considered and sometimes it is much less than 0.96, so specifications inChinese seismic code approach to safety in such region.

o The seismic response of structural member may be amplified in some stories when theinteraction is considered, so the reduction in these stories is not safe.

o Interaction influences on corner column, side column and interior column is different, soit is not suitable to take the same reduction factor.

o Interaction influences on story drift and shear force is different, so single reduction factoradopted in Chinese seismic code is irrational.

o Under bidirectional seismic excitation, interaction influences on member force in the twodirections are different, so the larger reduction factor should be adopted.

o In stories where material strength or member section changed, the seismic force responseis very complex. Those stories may become weak layer when soil-structure interaction is

considered, so it must be cautious in design.

CONCLUSION

In this paper, the influences of soil-structure interaction on seismic response of structure are

analyzed taking one real project as an example.

In conclusion, it is usually safe for seismic design according to Chinese seismic code in moststories of the high-rise frame-shear wall structures with considering soil-structure interaction.

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However, seismic response of structural member may be amplified in some stories, so it is unsafein such regions. Under bidirectional horizontal seismic excitations, the larger reduction factorshall be taken as the influences of field nonlinearity on seismic response at the two directions aredifferent. The reduction factors have great differences for different terms of structural response

and the variation along the structural height is also not linear, therefore, constant or linearinterpolated reduction factor specified in Chinese seismic code is irrational. In addition,influences of soil-structure interaction on members in different position are diverse, so differentreduction factors shall be adopted in member seismic design.

It can be concluded in this research that the soil-structure interactions is very complex.

Extensive studies are still needed to ascertain a rational reduction factor. It may be not safe forsome members and stories purely reduced according to the existing Chinese seismic code.

Therefore, finite element analysis and shaking table test are advised to carry out for importanthigh-rise buildings or very complex structures, so that it is clear on the seismic force in whichstories or members can be reduced and where should be strengthened.

ACKNOWLEDGEMENTThe authors would like to express their thanks to the financial supports from Key Seismic

Technique Research and Demonstration of Large and Important Buildings, Sub-topics of

Eleventh Five-Year National Scientific Support Plan (No. 20070106110141014). We alsogreatly thanks to the support from Innovation Group of Education Ministry (IRT0518) andZhuang Haiyang of Nanjing University of Technology for supplying the constitutive relationshipmodel of soil.

REFERENCE1. Lou M.L., Wu J.N. Seismic response analysis of pile foundation structure system.

China Civil Engineering Journal 1999; 32(5): 56-61.

2. Trifunac M.D., Hao T.Y. 7-story reinforced concrete building in Van Nuys,California: Photographs of the damage from the 1994 Northbridge earthquake.Report CE 01-05, July, 2001, Los Angeles, California.

3. Trifunac M.D., Ivanovie S.S., Todorovska M.I. Instrumented 7-story reinforcedconcrete building in Van Nuys, California: Description of the damage from the 1994

Northbridge earthquake and strong motion data. Report CE 99-02, July, 1999, Los

Angeles, California.

4. Ivanovie S.S., Trifunac M.D., Novikova E.I. etc. Instrumented 7-story reinforcedconcrete building in Van Nuys, California: Ambient vibration surveys following the

damage from the 1994 Northbridge earthquake. Report CE 99-03, July, 1999, Los

Angeles, California.

5. Chen Y.Q., Lv X.L. and Li P.Z. et al. Shaking table testing for layered soil-foundation -structure interaction system. Earthquake Engineering and Engineering

Vibration 2001; 21(3): 104-112.

6. Lv X.L., Chen Y.Q. Study on effect of soil-structure interaction by shaking table test.Earthquake Engineering and Engineering Vibration 2002; 22(2): 42-48.

7/27/2019 Ppr0937w

20/20

Vol. 13, Bund. D 20

7. Lou M.L., Wang W.J. and Ma H.C. et al. Study on soil-pile-structure interactionsystem by shaking table model test. Journal of Tongji University 2001; 29(7): 763-768.

8.

Code for seismic design of buildings GB 50011-2001. Beijing: China Architecture &Building Press, 2001.

9. Li Y.M., Sun G.F. and Wang S.T. et al. Dynamic interaction of pile-soil-framestructure. Journal of Building Structures 2002; 23(1): 75-81.

10.Han Y.C., Vaziri H. Dynamic response of pile groups under lateral loading. SoilDynamic and Earthquake Engineering 1992; 11: 87-99.

11.Mylonakis G., Nikolaou A., Gazetas George. Soil-pile-bridge seismic interaction:kinematic inertial effects. Part I: soft soil. Earthquake engineering and structuredynamics, 1997; 26: 337-359.

12.Carrabba P., Maugeri M. Nonlinear effects during dynamic loading on piles. Proc. ofthe 11th WCCE, Acapulco, Mexico.

13.Finn W.D.L., Wu G. Nonlinear seismic analysis of pile foundations. Proc. of the 11thWCCE, Acapulco, Mexico.

14.Makoto K. Study on nonlinear dynamic analysis method of pile subjected to groundmotion. Proc. of the 11th WCCE, Acapulco, Mexico.

15.Yue M.G., Wang Y.Y. and Lv Z.L. et al. Analysis on seismic stability of bank inengineering field. Building Structure; (accepted).

16.Zhang H.Y. Study on nonlinear dynamic soil-underground structure interaction andits large-size shaking table test. Nanjing: Nanjing University of Technology, 2006.

17.Chen C.B., Lou M.L. and Tao S.F. Discussions on two-dimensional finite elementanalysis of seismic response. Technology for Earthquake Disaster Prevention 2006;1(4): 292-301.

18.Load code for the design of building structures GB 50009-2001. Beijing: ChinaArchitecture & Building Press, 2006.

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