BOĞAZİÇİ UNIVERSITY KANDILLI OBSERVATORY AND EARTHQUAKE RESEARCH INSTITUTE CHANGING NEEDS OF ENGINEERS FOR SEISMIC DESIGN

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1 BOĞAZİÇİ UNIVERSITY KANDILLI OBSERVATORY AND EARTHQUAKE RESEARCH INSTITUTE CHANGING NEEDS OF ENGINEERS FOR SEISMIC DESIGN Erdal Şafak Department of Earthquake Engineering Kandilli Observatory and Earthquake Research Institute Boğaziçi University, Istanbul, Turkey

2 PERFORMANCE-BASED SEISMIC DESIGN OF STRUCTURES

3 INELASTIC RESPONSE OF STRUCTURES Backbone curve F elastic Elasto-plastic model Force Load reduction factor: R=F elastic /F plastic Ductility: µ= x plastic/ /x yield F plastic Deformation FORCE 1 k Dynamic force-deformation hysteresis x yield x elastic x plastic = µ x yield DISPLACEMENT Seismic load or moment Limited damage Life safety No collapse No damage Displacement or rota/on

4 PERFORMANCE-BASED DESIGN

5 SENSITIVITY OF INELASTIC RESPONSE TO YIELD LEVEL AND YIELD TIME

6 ELASTO- PLASTIC RESPONSE OF A 2.0 Hz SDOF OSCILLATOR

7 ACC.=F / m ELASTO- PLASTIC RESPONSE OF A 2.0 Hz SDOF OSCILLATOR

8 FORCE- DEFORMATION PLOTS OF ELASTO- PLASTIC RESPONSE FOR DIFFERENT DUCTILITY LEVELS (Note that the plots have the same axis limits) μ=1 μ=2 μ=4 μ=6

9 SENSITIVITY OF INELASTIC RESPONSE TO INPUT AND YIELD LEVEL DISPLACEMENT (m) # Yield /mes: t=4.95 s. t=6.75 s. t=6.76 s. ELASTIC RESPONSE Yield level E-Lim=0.9*E-Lim E-Lim= E-Lim=1.1*E-Lim TIME (s) 0.3 GROUND ACCELERATION ACCEL. (g) TIME (s) Force E- Lim Displ.

10 SENSITIVITY OF INELASTIC RESPONSE TO INPUT AND YIELD LEVEL: VARIATION OF FORCE AND DISPLACEMENT DISPLACEMENT # TIME VARIATION OF DISPLACEMENTS 0.9*E-lim 1.0*E-lim 1.1*E-lim TIME TIME VARIATION OF FORCE 0.9*E-lim 1.0*E-lim FORCE *E-lim TIME

11 SENSITIVITY OF INELASTIC RESPONSE TO INPUT AND YIELD LEVEL: VARIATION OF FORCE-DISPLACEMENT HYSTERESIS 0.02 FORCE - DISPLACEMENT HYSTERESIS Duct = Duct = Duct = FORCE DISPLACEMENT #10-3

12 IMPORTANCE OF SURFACE WAVES FOR LONG-PERIOD STRUCTURES

13 DISPLACEMENTS OF A 17- STORY BUILDING IN LOS ANGELES DURING A M=4.9 EARTHQUAKE End of the earthquake record from a triggered sta4on.

14 N-S, E-W, AND VERTICAL ACCELERATIONS AT GROUND LEVEL N-S, E-W, AND VERTICAL DISPLACEMENTS AT GROUND LEVEL

15 EFFECTS OF SURFACE WAVES ON BUILDING RESPONSE

16 μ=2.75 μ=6.63

17 ROTATIONAL EXCITATION DUE TO SURFACE WAVES

18 FORCES ON A TALL BUILDING SUBJECTED TO SURFACE WAVES v(x,t) θ ( xt, ) = vxt (, )/ x u(x,t)

19 RAYLEIGH WAVES ON THE SURFACE OF UNIFORM HALF SPACE

20 HORIZONTAL AND VERTICAL DISPLACEMENTS AND ROTATIONS DUE TO RAYLEIGH WAVES (Note that horizontal and rota/onal mo/ons are in phase)

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22 IMPORTANCE OF HIGH-PASS FILTER CORNER ON LONG-PERIOD STRUCTURAL RESPONSE (From: Becky, R., K. Buyco, and T. Heaton (2017). Filtered data is less likely to introduce collapse in tall buildings than raw records, SSA Annual Meeting in Denver, CO, April 2017) Ground Displacement Displacement response spectra Inter-story drifts in a 20-story building The data processing method used in NGA database (i.e., 10 sec. non-causal, zero-phase Butterworth filter) removes the tilt effects from the record and may cause under-estimation of P-Δ effects and collapse probability in long-period structures.

23 SOFT-FIRST-STORY BUILDINGS AND P-Δ RESPONSE SPECTRA

24 SOFT STORY DAMAGE TO A TYPICAL APARTMENT BUILDING WITH SOFT FIRST STORY DURING THE M=7.4, 1999 KOCAELI, TURKEY EARTHQUAKE

25 P-Δ EFFECTS ON SOFT-FIRST-STORY BUILDINGS P Δ P H + Failure M=P Δ Σ H Σ H PΔ Σ P P-Δ Effects due to soft 1 st story

26 RESPONSE SPECTRA WITH P-Δ EFFECTS

27 REDUCTION OF NATURAL FREQUENCY DUE TO P- Δ EFFECTS Additional parameters needed for response spectra: P/P cr and vertical accelerations.

28 DISPLACEMENT RESPONSE SPECTRA WITH P- Δ EFFECTS

29 TALL BUILDING RESPONSE TO LARGE DISTANT EARTHQUAKES

30 M=7.8; 16 April 2013

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32 RECORDED GROUND ACCELERATIONS

33 T x =3.85 sec. LeN side Y X Right side 5 min. 10 min. 15 min.

34 T x =7.14 sec. LeN side Y X Right side 5 min. 10 min. 15 min.

35 Istanbul M=6.5; 24 May 2014 North East 62- story Sapphire Tower The tallest building in Istanbul

36 3.33 min. T x =4.54 sec min. T x =4.54 sec.

37 3.33 min. T x =6.20 sec min. T x =6.20 sec.

38 CALCULATED DAMPING RATIOS DISPL. (cm) DISPL. (cm) DISPL. (cm) NORTH SIDE, EAST DIRECTION, FIRST MODE DISPLACEMENTS NORTH SIDE, NORTH DIRECTION, SECOND MODE DISPLACEMENTS NORTH SIDE, EAST DIRECTION, THIRD MODE (TORSION) DISPLACEMENTS TIME (sec) ξ 1 =0.006 ξ 2 =0.007 ξ 3 =0.008

39 From Satake at.al, 2003

40 SOME SUGGESTIONS FOR NEW APPROACHES: Ø Utilize data from dense urban networks to supplement GMPEs Ø Use a probabilistic approach to calculate response spectra Ø Use energy and energy flux for ground motion description and structural response

41 CAN WE UTILIZE DATA FROM DENSE URBAN NETWORKS TO LOCALIZE GMPEs? Example: Istanbul Ø Ø Ø Ø Ø real-time strong-motion stations (700 more are currently being installed) Over 7,000 records from M>3.00 earthquakes Well known fault path Topography seems to be important in shaking distribution Can a calibrated 3D seismic model be an alternative to GMPEs? 41

42 ω 0, ξ 0 PROBABILISTIC APPROACH TO CALCULATE RESPONSE SPECTRA: DISTRIBUTION OF PEAKS OF A SDOF OSCILLATOR x(t) Relative displacement with respect to ground P3 P1 P2 P4 a(t) p(x) 0.6 σ x Distribution of peaks (Rayleigh distribution) p(x)= x σ exp x 2 2 x 2σ x 2 E(x)= 1.25σ x Var(x)= 0.43σ x 2 σ x x

43 Standard Response Spectra The rate of decay of amplitudes with increasing peak number gives a measure of duration.

44 INFORMATION THAT CAN BE EXTRACTED FROM PROBABILISTIC RESPONSE SPECTRA η Given: Distribution of peak displacements relative to base. 2 2 Number of crossings of level per unit time: ( ) 2 exp 2 Number of cycles (i.e., zero crossings) per unit time: (0) 2 Probability of exceeding a specified displacement level : F( ) ( y N f N f p η η η σ η η = = = 0 0 ) Displacement level corresponding to a specified probability of exceedance: inv ( ) d p d η η η η η η η =

45 RANDOM VIBRATION APPROACH TO STRUCTURAL RESPONSE π Power Spectral Density of ground accelerations: S a (ω ) = lim T T E F (ω ) 2 a 2 where S a (ω ) dω = σ a S a (ω) 1 Effective frequency band S 0 ω 1 ω 2 Freq ω 1 ω 2 ω σ a2 = S a (ω ) dω = S 0 (ω 2 ω 1 ) ω σ a 2 S 0 = ω 2 ω 1 x(t) ω 0, ξ 0 σ x2 S 0 4π 2 ξ 0 ω 0 3 S 0 is the best single parameter to characterize ground shaking for engineering purposes. a(t)

46 ENERGY-BASED FORMULATION OF RESPONSE m, c, k x(t) m!!x(t)+ c!x(t)+ k x(t)= m a(t) Dividing by m and denoting: k /m = ω 02 and c /m = 2ξ 0 ω 0 : a(t)!!x(t)+2ξ 0 ω 0!x(t)+ω 02 x(t)= a(t) (ξ 0 and ω 0 vary with x and t if nonlinear) By integrating over the relative displacement with respect to base:!!x(t) dx + 2ξ 0 ω 0.!x(t) dx + ω 02 x(t) dx = a(t) dx x x x x " $ # %$ " $$ # $$ % " $ # $$ % " $ # $ % E k =Kinetic Energy E D =Damping Energy E A =Absorbed Energy E I =Input Energy E K + E D + E A = E I (all for per unit mass) where E D,E A includes energies absorbed due to elastic and inelastic behaviors. Energy response spectrum is the plot of (E I ) max against T 0 = 2π /ω 0 for given a(t) and ξ 0.

47 ENERGY FLUX Amount of energy transmitted through a cross section per unit time. A=1 v(t) V, ρ E(t) Energy Flux = 1 2 (mass density) (ground velocity)2 (wave propagation velocity) E(t) = 1 2 ρ [v(t)]2 V

48 PROPAGATION OF ENERGY FLUX IN A MULTI-STORY BUILDING Layer j+1 D j+1 U j (t) = A j 2( f ) [α j 1 ( f ) D j (t τ j ) + β j 1 ( f ) U j 1 (t τ j )] U j+1 Interface j D j (t) = A j 2( f ) [α j ( f ) U j (t τ j ) + β j ( f ) D j+1 (t τ j )] Layer j Interface j-1 Layer j-1 U j U j- 1 D j D j- 1 α, β = Energy reflection and transmission coefficients τ = Wave travel time in the layer A( f ) = exp πτ f Q - Energy loss due to damping

49 EXAMPLE: Energy flux in a 10-story building on two-layer soil media 10th story Parameters required: E I : Upgoing input energy (or velocity) from ground τ : Wave travel times in layers. r : Wave reflection coefficients at layer interfaces. Q : Damping in each layer. 1st story Soil layer 1 Soil layer 2 E I Bedrock

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51 References: Becky, R., K. Buyco, and T. Heaton (2017). Filtered data is less likely to introduce collapse in tall buildings than raw records, SSA Annual Meeting in Denver, CO, April M.J.N. Priestley, G.M. Calvi, M.J. Kowalsky (2007). Displacement Based Seismic Design of Structures, IUSS Press, Pavia, Italy. Safak, E. (1988). Analytical approach to calculation of response spectra from seismological models of ground motion, Earthquake Engineering & Structural Dynamics, Wiley Inter-Science, Vol.16, No.1, January 1988, pp Safak, E., C. Mueller, and J. Boatwright (1988). A simple model for strong ground motions and response spectra, Earthquake Engineering & Structural Dynamics, Wiley Inter-Science, Vol.16, No.2, February 1988, pp Safak, E. (1998). 3D Response Spectra: A method to include duration in response spectra, Proceedings of the 11 th European Conference on Earthquake Engineering, Paris, France, September 6-11, 1998, A.A. Balkema Publishers, Rotterdam, Netherlands. Safak, E. (2000). Characterization of seismic hazards and structural response by energy flux, Soil Dynamics & Earthquake Engineering, Elsevier Science Ltd., Vol. 20, No. 1-4, pp Satake,N., K-I Suda, T. Arakawa, A. Sasaki, and Y. Tamura (2003). Damping Evaluation Using Full-Scale Data of Buildings in Japan, ASCE Journal of Structural Engineering, Vol. 129, Issue 4, April Uang, C.-M. and V.V. Bertero (1990). Evaluation of seismic energy in structures, Earthquake Engineering & Structural Dynamics 19(1):77-90 January 1990.

52 SOME CONCLUSIONS: Performance- based design requires the control of inelas/c deforma/ons, which are very sensi/ve to the ini/al build- up of ground accelera/ons and the yield point of the structure. Surface waves from distant large earthquakes can be cri/cal for long- period structures because of rota/onal excita/ons and P- Δ effects. Dura/on of vibra/on of a structure is related to its natural frequency and damping, and does not always correlate with the dura/on of earthquake. Collapse of son- first- story structures is also controlled by P- Δ effects and ver/cal ground accelera/ons. - Damping in tall buildings decrease with increasing height, and can be as low as 1%. - - Probabilis/c response spectra provide much more informa/on than standard response spectra. Energy- based representa/on of ground shaking and structural response can be a powerful alterna/ve to current seismic design methods.