Jianping Han and Xiaoyun Sun - risedr.tongji.edu.cnrisedr.tongji.edu.cn/7th_Kwang-Hua_Forum/files/Parallel_1B/...Ø Reliable and rational inelastic response analysis of structures

Key Laboratory of Disaster Prevention and Mitigation in Civil Engineering of GansuWestern Engineering Research Center of Disaster Mitigation in Civil Engineering of

Ministry of Education,

Lanzhou University of Technology

Jianping Han and Xiaoyun Sun

Duration effect of spectrally matched ground motion records on collapse resistance capacity

evaluation of RC frame structures

2017-1-6 The Seventh Kwang-Hua Forum on Innovations and Implementations in EE Research 1

Outline

Significance to account for duration effect

Measures for ground motion duration

Ground motion records based on spectral matching

Collapse resistance capacity evaluation of infilled RC frame

Conclusion and suggestion

2017-1-6 2The Seventh Kwang-Hua Forum on Innovations and Implementations in EE Research


Wenchuan Earthquake in China, 2008

Chile Earthquake, 2010 Tohoku Earthquake in Japan, 2011 Recent earthquakes remind us that ground motion with long duration really occur at some specific sites, and it is obvious that some structures collapse due to impact by long-duration ground motion.


Ø Due to the cyclic damage accumulation, ground motion duration is intuitively expected to influence the response of structures especially when the structures deform beyond their linearly elastic range.

Ø Reliable and rational inelastic response analysis of structures is necessary. It is the fact that absorbed hysteretic energy and fatigue damage increased during long duration ground motions, and ground motion duration significantly affects the ductility demand of structures with stiffness degradation and the effect increases as the strength of the structure degrades.

Ø Up to now, the prescriptive provisions on how to account for the effect of ground motion duration are not clear in the current seismic design codes around the world.





Figure 1. The schematic diagram of definition for bracketed duration of ground motion.

a

bDt

0a

is the time elapsed between the first and last excursions of the accelerogram above a certain acceleration threshold (commonly used thresholds are 0.05g and 0.1g).

bD

Although the definition of is relatively simple, the selection of the thresholds is subjective and the selection of the thresholds has a significant impact on the results.

bD

Measures for ground motion durationØ Bracketed duration


is the sum of the time interval at which the acceleration value reaches or exceeds the specified value. The specific definition of uniform duration is shown in Figure 2.

Figure 2. The schematic diagram of uniform duration definition of ground motion.

uD

a

t

0a

1t 2t 3t 4t

i

iu tD

Ø Uniform duration

Some research results have shown that has a good correlation with structural response. In contrast to , the specified threshold has slight impact to . But it is not a continuous duration and it is not convenient for use in seismic analysis.

uD

uDbD



is defined based on the accumulation of energy in the accelerogram represented by the integral of the square of the ground acceleration, velocity or displacement. If the integral of the ground acceleration is employed then the quantity is related to the Arias intensity, . The Arias intensity is defined as

AI

2

0( )

2maxt

AI a t dtg

is a continuous time interval considering the characteristics of ground acceleration, so it is more convenient for time history analysis. Bradley concluded that the significant duration is suited better than others in structural response analysis.

As shown in Figure 3, Trifunac and Brady defined 90% significant duration, , namely the time interval from 5% of Arias intensity of the ground motion to 95% of total energy.

5 95%sD

Ø Significant durationsD


sD


The Eq.10, CHICHI.03_TCU129N component of ground acceleration at TCU129 station during Chi-Chi earthquake in 1999 and the computation of 5-95% significant duration are shown in Figure 3.

0 4 8 12 16 20-5

0

55

t /s

a /g

0 4 8 12 16 20205

95

Ds5-95%=13.16sAI/%

t /s


Ø Significant duration



1( )aS T

Ø60 ground motion records with different duration were selected.

Ø In order to eliminate the effect of frequency content of ground

motion on structural response, the pseudo-acceleration spectrum

of these records were matched based on the acceleration response

spectrum in Chinese seismic design code.

Ø was taken as intensity measure and all records are scaled to

have the same =0.5g. The 5-95% significant duration is

used to quantify ground motion duration.

ØThe 5-95% significant duration data of partial selected records are

shown in Table 1.

1( )aS T


Table1. Partial selected ground motion records

5 95%sD No.Earthquake events

Station Component /sPGA

/gName Magnitude Year

Eq. 1 San Fernando, USA 6.6 1971 Castaic - Old Ridge Route SFERN_ORR021 16.76 0.275

Eq. 2 San Fernando, USA 6.6 1971 Santa Felita Dam (Outlet) SFERN_FSD172 23.03 0.067

Eq. 3 San Fernando, USA 6.6 1971 UCSB - Fluid Mech Lab SFERN_SBF042 50.25 0.021

Eq. 4 Kocaeli, Turkey 7.5 1999 Arcelik KOCAELI_ARE000 11.05 0.21

Eq. 5 Kocaeli, Turkey 7.5 1999 Arcelik KOCAELI_ARE090 12.71 0.083

Eq. 6 Kocaeli, Turkey 7.5 1999 Afyon Bay KOCAELI_AFY000 60.232 0.012

Eq. 7 Kocaeli, Turkey 7.5 1999 Tosya KOCAELI_TOS090 75.08 0.012

Eq. 8 Kocaeli, Turkey 7.5 1999 Aydin KOCAELI_AYD090 91.61 0.018

Eq. 9 Chi-Chi, Taiwan 7.6 1999 TCU045 CHICHI_TCU045-E 11.34 0.473

Eq. 10 Chi-Chi, Taiwan 7.6 1999 TCU129 CHICHI.03_TCU129N 13.16 0.224

Eq. 11 Chi-Chi, Taiwan 7.6 1999 CHY024 CHICHI.04_CHY024N 14.936 0.248

Eq. 12 Chi-Chi, Taiwan 7.6 1999 CHY006 CHICHI.04_CHY006N 16.776 0.125

Eq. 13 Chi-Chi, Taiwan 7.6 1999 TCU076 CHICHI.06_TCU076N 17.956 0.092

Eq. 14 Chi-Chi, Taiwan 7.6 1999 CHY029 CHICHI_CHY029-E 32.275 0.289

Eq. 15 Chi-Chi, Taiwan 7.6 1999 TCU098 CHICHI_TCU098-E 33.63 0.064




rN

Take significant duration 30s as the threshold to identify long- or short-duration record for all 60 ground motion records in Table 1, so the number of long- and short-duration record is 30, respectively. The numbers of ground motion records with different 5-95% significant duration are shown in Figure 4. The response spectrum in the Chinese 2010 code for seismic design of buildings was adopted as the target spectrum, and all 60 ground motion records were matched spectrally.

Figure 4. The number of ground motion records with different 5-95% significant duration.


Figure 5. The comparison of pseudo-acceleration response spectra of the spectrally matched ground motion records with different 5-95% significant duration.


Take Eq.28 ( ) and Eq.51 ( ) as examples.

The comparison of pseudo-acceleration response spectra of these ground

motion records after matching was shown in Figure 5.

5-95% 20.47ssD 5 95% 103.95ssD

3002

1

( )0.05

300

i ii

M TRMSE


The investigated building is an infilled reinforced concrete frame structure with 4 storeys and 2 bays, which was designed according to the requirements of 7 degree of seismic fortification with a peak ground acceleration of 0.10g in current seismic design.

1200 600

900

900

1800

CKZ-1

820×510Window

Window420×510

4020

020

042

040

Door 200×400

50 mm thick filler wall

B

A

1

KZ-1

2

KZ-1

3

820×510820×510Window

KZ-180×80

KZ-1

KZ-1

KZ-1

820×510820×510Window

18001200 600

900

900

1800

CKZ-1

820×510Window

Window420×330

4020

020

042

040

Door200×400

B

A

1

KZ-1

2

820×510820×510Window

KZ-180×80

KZ-1820×330Window

50 mm thick filler wall

50 mm thick and 250 mm high wall

3

KZ-1

KZ-1

KZ-1

1800

(a) Ground floor plan (b) Standard floor plan Figure 6. The shaking table test model of 4-storey RC frame structure.

Collapse resistance capacity evaluation of infilled RC

Ø Numerical model of the multi-storey infilled RC frame


Figure 9. Concrete02 concrete constitutive model.

E

Fy

sh

Fu

E s

sh su

fSR f0

f0

y max

p max= - y

Figure 7. ReinforcingSteel model.

Figure 8. Strength deterioration pattern of ReinforcingSteel model.



E0 fEts

t

pcu

f pcu

f pc

pc

l Constitutive models of reinforcing steel and concrete


Figure 10. Proposed infill model using beam-column elements with fiber discretization.

l In-plane and out-of-plane interaction of infill walls3 32 2

1.0N H

N0 H0

M PM P

where, is the out-of-plane bending strength with in-plane force, and is the out-of-plane bending strength without in-plane force. is the in-plane axial capacity with out-of-plane force, and is the in-plane axial capacity without out-of-plane force.

NM N0MHP

H0P

PH

PN

xyz

Midpoint node without-of-plane mass

Beam-columnelements

Surroundingframe element

Surroundingframe element



Kadysiewski S, Mosalam KM. 2009. Modeling of unreinforced masonry infill walls considering in-plane and out-of-plane interaction. Report PEER 2008/102, Pacific Earthquake Engineering Research Center, University of California: Berkeley, CA.


Figure 11. The series model considering the axial-shear-flexure interaction.

• The model of the fiber beam-column element in connection with shear spring attached to its ends along the vertical axial direction of the column, for simulating the coupling with flexure and shear mechanism, and the Shear Limit Curve and Limit State Material were chosen to simulate shear spring.

• The axial spring attached to the fiber beam-column element along the axial direction of the column was applied to simulate the axial deformation of the column, and the axial spring was modeled by using Axial Limit Curve and Limit State Material definition. V

H

VP

V

P

l Axial-shear-flexure interaction



Elwood KJ. 2004. Modelling failures in existing reinforced concrete columns. Canadian Journal of Civil Engineering 31(5):846–859.


As the shear spring shown in Figure 11, its limit state backbone curve in series with beam-column elements can be defined by the limit state material model, as shown in Figure 12. Based on the drift capacity model, the following equation was used to define the Shear Limit Curve.

Figure 12. The backbone of limit state uniaxial material model.

F

DKRF

Pre-failure backbone

Failure detectedPost-failure backbone

3 1 1 14100 40 40 100

s

c g c

v pL f A f

cf





The model assumes that shear failure has already occurred and that axial

failure results from sliding along a critical inclined shear crack. The

model suggests that the drift at axial failure, , is inversely

proportional to the axial load supported by the column and directly

proportional to the amount of transverse reinforcement, as shown in the

Equation:

AxialL

21 tan4100 tan ( / tan )Axial st yt c

θL p s A f d





Based on of the structure, the ground motion records in Table 1 were scaled and the incremental dynamic analysis was carried out on the model. The geometric means of the IDA curves for both long- and short-duration record sets, in terms of maximum inter-story drift ratio and ground motion intensity , are shown in Figure 13.

1( )aS T

max(0.42s,5%)aS

maxFigure 13. Geometric mean IDA curves for long- and short- duration record sets.


Ø Results of incremental dynamic analysis



Ø Results of incremental dynamic analysisAs shown in Figure 13, the structural response caused by both record sets is similar at first. But curves begin to diverge after value reaches about 0.02, which coincides with the point where the steel reach their peak strengths and begin to strain-soften. This trend indicates that the influence of ground motion duration on is observed only at intensity levels large enough to produce non-linear deformations that extend into the post-peak softening range of inelastic response. This observation helps reconcile the results of this study with many previous studies, which used numerical models that did not incorporate deterioration, and hence, found no influence of duration on peak deformation demands. The long-duration sets make the model produce larger geometric mean of maximum inter-story drift, when the is the same.

max

(0.42s,5%)aS

max


,r max

(a) Maximum residual inter-story drift ratio (b) Maximum residual roof displacement Figure 14. Correlation of maximum residual displacement responses with significant duration

before collapse.

In order to obtain more steady residual displacement results such as maximum residual inter-story drift ratio and maximum residual roof displacement of the structure, the zero ground acceleration series with 20s duration was added at the end of original acceleration series to all scaled records.

,r max

The results show that both and of the structure tend to increase gradually with the increase of significant duration.

,r max,r max



Ø Evaluation of collapse resistance capacity

Figure 15. Correlation of collapse capacity with 5-95% significant duration.


In this paper, DM-IM criterion was used to evaluate the collapse resistance capacity. And corresponding to 20% initial slope and constitute as the collapse criteria. When the model begins to collapse, the correlation between 5-95% significant duration and the is shown in Figure 15.

1/ 20DM maxC

, (0.42s,5%)a collapseS

1( )aS T

Collapse resistance capacity tends to decrease with the increase of . So the ground motion records with longer duration are likely to cause the structure collapse easily.

5 95%sD


The collapse probability curves in terms of are shown in Figure 16.

(0.42s,5%)aS

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

Sa(0.42s,5%)/g

Col

laps

e pr

obab

ility

Short-duration setShort-duration set Long-duration setLong-duration set

Figure 16. Collapse probability curves of long- and short- duration ground motion records with different intensity.

On average, the longer duration of ground motion with respect to the other, the higher collapse probability it predicts, which implies that taking into account the of the ground motion records decrease the collapse resistance capacity of the RC frame structure.

5 95%sD

Ø Evaluation of collapse resistance capacity




ØNonlinear seismic responses such as maximum inter-story drift ratio, maximum residual inter-story drift ratio and maximum residual roof displacement of the structure are higher under long-duration ground motion records than short-duration ground motion records.

ØThe larger the difference of 5-95% significant duration is, the higher the collapse probability caused by the long-duration record with respect to the short-duration record is.

ØThe ground motion duration has a significant influence on the structural inelastic response and the energy dissipation capacity. So the increase of ground motion duration will decrease the collapse resistance capacity and increase the collapse probability definitely.



This study highlights the need to account for the effect of ground motion

duration for nonlinear analysis and collapse resistance capacity evaluation,

in addition to ground motion intensity and spectral shape. ØWe should therefore pay attention to ground motion duration

characteristic and provide clear provisions in the seismic design code about ground motion duration.

ØThe relation of the seismic hazard analysis and the ground motion attenuation should be combined for further study on the correlation between ground mot ion durat ion and other ground mot ion characteristics, between the damage and collapse of structures and the ground motion duration.


Thank you for your attention！

Duration effect of spectrally matched ground motion records on collapse resistance capacity

evaluation of RC frame structures

Jianping Han and Xiaoyun Sun - risedr.tongji.edu.cnrisedr.tongji.edu.cn/7th_Kwang-Hua_Forum/files/Parallel_1B/...Ø Reliable and rational inelastic response analysis of structures

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