Measures for reducing the effect of pounding between adjacent buildings during near-source earthquakes

Uemuet Goerguelue Graduate School of Computational Engineering, Ruhr University Bochum, Germany, and Graduate School of Natural Science and Technology, Okayama University, Okayama, Japan

Nawawi Chouw Department of Civil and Resource Engineering, University of Western Australia, Crawley, Australia; Gledden Fellow, on leave from Faculty of Environmental Science and Tech., Okayama University, Okayama, Japan

ABSTRACT: In this study friction device, viscous damper, and elastic spring are used as a measure to mitigate the pounding between adjacent structures. In the numerical analysis structures are modeled by using a finite element method. In order to simulate the pounding link elements with a possible gap between the structures is applied. Results show that link element with gap, friction device, viscous damper and elastic spring, can reduce the effect of pounding. The friction device itself can limit the pounding force. In the considered ground motions link element without gap and with viscous damper improves the dynamic behavior of structures. However, the installation location of the link elements, and the damping constant must be determined properly.

KEYWORDS: Near-source earthquake, pounding mitigation, friction device, viscous damper

1 INTRODUCTION

Pounding occurred in many major earthquakes, e.g. the 1964 Alaska Earthquake, the 1971 San Fernando Earthquake, the 1985 Mexico Earthquake, the 1989 Loma Prieta Earthquake, the 1985 Kobe Earthquake, the 1999 Taiwan Chi-Chi Earthquake, and the 1999 Turkey Earthquake. Pounding can happen if the structures are not far enough, and if they vibrate out-of-phase. Even when the structures are far apart pounding can also take place due to collapse of the neighbouring structures. In the past earthquakes pounding caused severe damages at the structures, and consequently it can cause loss of human life.

In order to understand and prevent poundings many researches were done for decades. So far suggestions for preventing and mitigating the pounding effect can be categorized in three groups: measures at the possible pounding locations, minimum separation distance between the structures, and link of the structures.

Anagnostopoulos and Spiliopoulos (1992) investigated the pounding behaviour of series of buildings and analysed the collision walls for mitigating the pounding. This measure is also suggested in the European codes (Anagnostopoulos, 1996). Jankowski, Wilde and Fujino (2000) analysed hard rubber bumpers between bridge girders, and their results showed that placing of rubber bumpers decreased the forces at the bridge piers.

Kasai (1996) studied seismic separation gap, and he suggested the spectral difference method. Penzien (1997) suggested a complete-quadratic-combination method for determining the necessary separation distance between the structures. This measure, seismic separation gap, has been required also in many codes (American UBC 1993, NEHRP 1991, Canadian NBCC 1990, Chinese GBJ11-89).

Westermo (1989) investigated analytically the seismic behaviour of adjacent buildings connected by rigid links with hinges. Luco and De Barros (1998) determined the optimal value of uniformly installed viscous dampers between the adjacent structures. Zhang and Xu (1999) presented a procedure for estimating the modal damping ratios in order to reduce the response of buildings by connecting them with viscoelastic dampers. Yang and Xu (2003) performed experimental

investigations to determine the effect of the number and location of viscous dampers between the adjacent structures. Rosskamp and Vielsack (2002) examined experimentally and numerically the effect of friction dampers on the pedestrian bridges between the buildings under a harmonic load.

Seismic separation gap is not applicable in some cases, for example, if the structures are already built very close to each other. In such a case we can either install equipment at the possible pounding locations or we can connect the structures.

This paper addresses the possible measures for reducing the pounding effect. In order to apply the measures, structures are connected with link elements that can have a gap, viscous damper, friction device and elastic spring. The influence of considered measures on the structures under the 1994 Northridge earthquake and the 1999 Turkey earthquake is examined.

2 MODELLING OF THE SYSTEM

Figure 1a and b show the time history of the Northridge and Turkey ground acceleration in the north-south direction, respectively. Their peak ground accelerations are 4.44m/s2 and 3.30 m/s2, and occur at 4.09s as well as 8.72s, respectively.

-3

-2

-1

0

1

2

3

4 9 14-5

-2.5

0

2.5

5

0 5 10Time [s]

a [m/s2] a [m/s2]

(a) (b)Time [s]

Figure 1 (a) and (b). Time history of the (a) Northridge Earthquake and (b) Turkey Earthquake

The considered model comprises two adjacent frame structures with a bridge link. This link can also have a function of pedestrian bridge (Chouw, 2002). Figure 2 shows the bridge link at the top floor of the right structure. The material data is given in Table 1. It is assumed that the system is fixed at the base, and the structures experience the same ground acceleration. The first natural frequency of left and right structures is 1 Hz and 1.25 Hz, respectively.

Figure 2. Frame structures with link element

No of the Structural Member

Mass [kg/m]

EA [106 kN]

EI [103 m2]

(1) 67 1.72 21 (2) 33 0.837 9.8 (3) 2447 3.19 200 (4) 2358 3.19 200 (5) 1209 3.19 110

Link Element 314 vary 0

Table 1. Material properties

The link element can comprise an elastic spring, a gap, a friction device and a viscous damper as indicated in Figure 3. It has equal lumped mass at each end. The friction device consists of a friction element and a spring. If the activated force exceeds the defined spring force, friction takes place.

If friction and gap exist, the link element behaves non-linearly. In order to calculate the non-linearity the Newton-Raphson iteration technique is used (Cook, 1989). If the material properties change abruptly, the convergence in the iteration needs to be improved by line-search and arc-length methods. The line search is achieved by scaling the solution vector with a scalar value (Forde, 1987). The arch-length method involves the tracing of a complex path in the load-displacement response with a defined spanned curve (Figure 4).

Displacement

Load

Figure3. The link element

Lumped mass

Figure 4. Iterative procedure of the Arc-Length method

In the investigation we consider the link element with gap and without gap. Twelve different cases are taken into account. The cases are defined in Table 2. In the first case there is no interaction between the structures. In cases two to seven the link element with a gap is used, and pounding takes place. In cases eight to twelve the link element without gap is considered.

3 NUMERICAL

In order to compare ( −x

100)

1

1 ⋅x

xi,

where x is the maxim2), and the subscripamplification and rereference.

Case Gap [m] Stiffness [MN/m]

Damping constant [Ns/m]

Friction force [kN]

I ∞ 0 0 0 II 0.1 274.426 0 0 III 0.1 1372.131 0 0 IV 0.1 274.426 100 0 V 0.1 274.426 10000 0 VI 0.1 274.426 0 600 VII 0.1 274.426 10000 600 VIII 0 274.426 0 0 IX 0 274.426 0 60 X 0 274.426 10000 60 XI 0 274.426 10000 0 XII 0 0 10000 0

Table 2 Properties of a link element

RESULTS

the results the maximum horizontal displacement ratios are calculated as (1)

um horizontal displacement of the structure at the roof level (uL and uR in Figure t is the number of the case. The positive and negative value means respectively duction of the response of the structures. The first case results are taken as a

-3.6 -4.11

-4.38 -21.32

-26.13

2.28

31

25.26

-8.76-10.73

-8.74-8.9

-7.341-11.588

-4-11.791

-11.34-22.75-34.4

58.465.12

58.562.11

32.1335.21

8867.3967.59

468.23(b)

32.80.61

14.469.25

13.32

1.14

-27.4 -2-35 9.5 8.13

Left Structure Right Structure case Left Structure Right Structure (a)

32.11

-4.52 -4.1

-0.411

Figure 4 (a) and (b). Ratio of the maximum displacement in case of the (a) Turkey, and (b) Northridge Earthquake

3.1 Investigation of the effect of link with a gap

Pounding can modify the dynamic behaviour of structures. The displacement responses of the structures either increase or decrease depending on the dynamic properties of the structures and the characteristics of the loading (Figure 4, caseII). If we use friction device, viscous damper and elastic spring simultaneously (case VII) compared to the cases II to VI, we can decrease the structural response. The pounding force itself can be limited by the friction device (Figure 5).

The result shows that in case pounding cannot be avoided, a simultaneous application of friction device, viscous damper and elastic spring at the possible pounding locations is a useful measure to improve the response of the structures. Additionally, we can control the impact forces.

0 0

0

800

1600

4 5 6 7 8 9 10

F [kN]

Time [s]

case 2

4 5 6 7 8 9 10

case 3

4 5 6 7 8 9 10(c) (b) (a)

F [kN] F [kN]

800 800

1600 1600

Time [s] Time [s]

case 6case 7

Figure 5 (a) – (c). Pounding force F at uR

3.2 Investigation of the effect of link without gap

Another possible measure for mitigating the pounding effect is to link the adjacent structures. The result shows that the response of the stiffer right structure increases, while the one of the flexible left structure decreases (Figure 4). Viscous damper (case XII) proved to be the best measure for reducing the response of structures.

3.2.1 Effect of the damping constant and the location of the viscous damper In the considered cases the viscous damper is installed at the first, second, third, and at all floor levels. Damping value is varied in the range from 102 to 108 Ns/m.

Figure 6 shows the influence of the location and the damping value on the displacement ratio. As the damping constant increases, the two structures vibrate in phase. The more the damping constant decreases, the more out-of-phase the structures will vibrate. The result shows that in order to have an optimum response for both structures the damping constant should be limited in a certain range.

In order to determine the optimum damping value, the effect of the various damping constant is examined. The indicated area in Figure 6 shows the range of the optimum damping value in case viscous dampers are installed at all floor levels. Damping value in this range can provide more reduction of the flexible structure response (Figure 6(a) and (b)), and less response amplification in the stiffer structure (Figure 6(c) and (d)). If the damping value is very large, no more reduction of the structural response can be achieved, and even amplification can take place. For example, in case of the Northridge Earthquake (Figure 6 (a) and (c)) an further increase of the damping value from the optimum range causes a strong amplification of the displacement of the stiffer structure, and it does not further reduce the response of the flexible structure. If the damping value is low, responses of the structures are not changed. The result shows that the optimum damping should be calculated by considering all modes of the structures. However, in common design procedures the viscous damping ratio is determined based on the information of certain mode, normally the fundamental mode of the flexible structure. This common approach can indeed provide a reduction of the structural response. The damping value is also in the indicated range, however it is not the optimum one as defined by the value at the right end of the range. This is because of the assumption that the structural response is mainly determined by their fundamental modes. However, the higher modes might play an important role in the structural response, especially, when they are partially restraint at certain height location due to the installation of the viscous dampers.

(c) (d)

Reduction [ % ] Reduction [ % ]

Damping constant [Ns/m] Damping constant [Ns/m]

Link atall floors

1st floor 1st floor

2nd floor

1st floor

2nd floor

2nd floor (a)

3rd floor

0

20

40

0

20

40

102 104 106 108 102 104 106 108

3rd floor

0

20

40

0

50

100

Link at all floors

2nd floor

3rd floor

3rd floor

1st floor

Amplification [ % ] Amplification [ % ]

Link at all floors

(b)

all floorsLink at

Figure 6 (a) - (d). Reduction of the maximum displacement ratio for left structure due to (a) Northridge Earthquake and (b) Turkey Earthquake, and amplification of the displacement ratio for right structure due to (c) Northridge Earthquake and (d) Turkey Earthquake

In order to investigate the effect of the location of the viscous dampers the maximum horizontal displacements of structures are considered. In Figure 7(a) the response of the structures for different viscous damper locations are displayed. The damping constant is 104Ns/m. When the structures are linked at all floor levels, compared to other link conditions the response of the flexible structure decreases. The relative displacement along the height of structure also becomes smaller (Figure 8(a)).

In case of horizontal ground motions we can expect that the fundamental mode of the structures will determine the response. Therefore we can expect that uniformly distributed viscous dampers will control the response effectively. If we install the viscous dampers at lower levels their effectiveness will decrease. In order to compensate this disadvantage a higher damping value has to be used. In Figure 7(b) the maximum response of the left structure is presented as a function of the damping value. The result shows that viscous dampers at all floors with the value of 104Ns/m, at third floor with the value of 104.3Ns/m, at second floor with the value of 104.5Ns/m, and at the first floor with high value of

105Ns/m, all dampers cause almost the same response. As a reference the response without any damper is also displayed.

14 10

0

468

101214

0 0.1 0.2 0.3 0.4 0.5

2468

12

0 0.1 0.2 0.3 0.4 0.5

c [Ns/m] Link at 104.5 2nd floor 105 1st floor

c = 104 [Ns/m] Link at all floors

3rd floor

H [m]

without viscous damper

c [Ns/m] Link at 104 all floors 104.3 3rd floor

umax [m]

H [m]

1st floor 2nd floor

(b) 0(a)

2Without viscous damper umax [m]

Figure 7 (a) and (b). Effect of the location of the viscous dampers on the maximum structural response due to Northridge Earthquake. (a)Response at the right and left structure, and (b) Influence of the damping value

Dampers at lower level with higher damping value can indeed reduce the maximum response. However, the relative displacement between the floors can become larger, especially, at the top floor levels, as we can see from the comparison between Figure 7(b) and 8(b).

c = 104 [Ns/m]

02468

101214

0 0.05 0.1 0.15 0.20

24

68

1012

14

0 0.05 0.1 0.15 0.2

without viscous damper

c [Ns/m] Link at 104 all floors 104.3 3rd floor 104.5 2nd floor

105 1st floor

3rd floor

without viscous damper

2nd floor

1st floor

Link at all floors

(a) urel [m]

H [m]

(b)

H [m]

urel [m]

Figure 8 (a) and (b). Influence of the location of the viscous damper on the maximum relative displacement due to the Northridge Earthquake. (a) Displacement with damper at different locations, and (b) Displacement with different damping values

4 CONCLUSION

In the investigation of the pounding mitigation measures the effect of the near-source earthquakes are considered. The investigation of the effect of the link with a gap reveals:

Pounding can cause amplification or reduction of the response of the adjacent structures. The viscous damper, friction device and elastic spring can reduce the structural response. The friction device itself can limit the pounding force.

The investigation of the influence of the link without gap indicates:

The displacement of the flexible structure decreases, and the response of the stiffer structure increases.

In order to improve the effectiveness of the viscous dampers not only the damping constant but also their location should be chosen properly. Uniformly distributed viscous dampers can reduce the structural response with lower damping

value. If a viscous damper is used at the lower location, higher damping value has to be used to have the same effectiveness.

ACKNOWLEDGMENTS

The authors would like to express their gratitude to the DAAD (German Academic Exchange Service) for the support that makes this research work possible. The second author is grateful to the University of Western Australia for the Gledden Fellowship.

REFERENCES

Anagnostopoulos, S. A. and Spiliopoulos, K.V. (1992) An investigation of earthquake induced pounding between adjacent buildings, Earthquake Engineering and Structural Dynamics, Vol. 21, pp. 289-302

Anagnostopoulos, S.A. (1996). Building pounding re-examined: How serious a problem is it? Proceedings of 11th world conference on earthquake engineering, Mexico, paper 2106, 8 pp

Berterro, V. V. (1987) Observation on structural pounding. Proceedings of the international conference Mexico earthquake 1985 “, Mexico City, ASCE, pp. 264-287

Chouw, N. (2002) Influence of soil-structure interaction on pounding response of adjacent buildings due to near-source earthquakes, Journal of Applied Mechanics, Vol. 5, pp. 543-553

Cook, R., Plesha, E., and Malkus, D. S. (1989). Concepts and application of finite element analysis, 3rd Edition Forde, W. R. B. and Stiemer, S. F. (1987) The improved arc length orthogonality methods for non-linear finite

element analysis. Computers and Structures, Vol. 27, No. 5, pp. 625-630 Kasai, K., Jagiasi, A.R., Jeng, V. (1996) Inelastic vibration phase theory for seismic pounding mitigation Journal

of Structural Engineering. ASCE, pp.1136-1146 Jankowski, R., Wilde, K., Fujino, Y. (2000). Reduction of pounding effects in elevated bridges during

earthquakes. Earthquake Engineering and Structural Dynamics, Vol. 29, pp. 195-212 Luco, J. E., De Barros, F. C. P. (1998). Optimal damping between two adjacent elastic structures, Earthquake

Engineering and Structural Dynamics, Vol. 27, pp. 649-659 Rosskamp, C., Vielsack, P. (2002). Friction damping of coupled frames, In: Structural Dynamics, Eurodyn2002,

Swets & Zeitlinger, Lisse, pp.1597-1599 Penzien J. (1997). Evaluation of building separation distance required to prevent pounding during strong

earthquakes, Earthquake Engineering and Structural Dynamics, Vol. 26, pp. 849-858 Westermo B.D. (1989) The dynamics of inter-structural connection to prevent pounding. Earthquake

Engineering and Structural Dynamics, Vol: 18, pp. 680-699 Xu, Y. L., Zhan, S., Ko, J.M. and Zhang, W.S. (1999). Experimental investigation of adjacent buildings

connected by fluid damper. Earthquake Engineering and Structural Dynamics, Vol. 28, pp. 609-631 Yang, Z., Xu, Y. L., Asce, M. and Lu, X. L. (2003) Experimental seismic study of adjacent buildings with fluid

dampers, Journal of Structural Engineering, Vol: 129, No. 2, pp. 197-205