TYPOLOGY OF SEISMIC MOTION AND SEISMIC ENGINEERING DESIGN

Transcription

1 COST C6: Urban Habitat Constructions under Catastrophic Events WG: Earthquake resistance Workshop Prague, March 3-3, 7 TYPOLOGY OF SEISMIC MOTION AND SEISMIC ENGINEERING DESIGN E. Mistakidis R. Apostolska (Petrusevska), D. Dubina, W. Graf, G. Necevska-Cvetanovska, P. Nogueiro, S. Pannier, J.-U. Sickert, L. Simões da Silva, A. Stratan, U. Terzic

2 Introduction Earthquake forces on structures a characteristic case where an action can be exceptional and therefore lead to catastrophic events. It is admitted that there exists a high probability that the value of the seismic forces will at some time exceed the value prescribed in the design. Inherent uncertaint nature of the seismic action Incomplete or inadequate knowledge of the structural behavior.

3 Seismological aspects It has been demonstrated that the characteristics of the ground motions vary between recording stations. Two main regions with different types of ground motions are considered (Gioncu et al ). The far-source region. The near-source region. The vertical component could be greater than the horizontal ones. The significance of higher vibration modes increases Due to the pulse characteristics of the actions, the ductility demands could be very high. After Kobe earthquake it has been verified that earthquake loading conditions in the near-source region subject buildings to more severe conditions than previously assumed.

4 Influence of the ground conditions The following parameters influence the amplification or attenuation of the seismic action on the structures the thickness of the soft and stiff soil layers, the shear wave velocities of the rock and soil layers, the soil/rock impedance ratio, the layering properties of the soil layers etc. Attention to landsliding, liquefaction surface fault rupture

5 Structure related items Magnification of the seismic action on short period structures Connections in steel structures have been identified as crucial for the structural response after the Kobe and Northridge earthquakes. Concrete structures suffer from micro-cracks induced by relatively moderate earthquakes that influence the structural response under design-level earthquakes. The case of old existing structures has to be identified as one where the seismic events may be catastrophic due to the fact they were designed (if so) with old codes, proved to be inadequate.

6 Overview of the presentation First part (ground motion uncertainty) Seismic motions with specific characteristics that lead to exceptional actions on structures. Near-fault ground motions and the local site parameters are examined and the latest developments in the field are presented. Modeling of the ground motion specifically for the needs of the seismic analysis of structures. Behaviour of structures in the short period range and the corresponding magnification of the seismic action that has been observed. Uncertainty in structural analysis (uncertainty in the seismic motion parameters and uncertainty in the model parameters). Second part (structural behaviour) Performance based design as a tool for the analysis of the structural behaviour under extreme seismic events. Influence of the connection behaviour in steel structures Capacity design methodology for the design and evaluation of the seismic resistance of reinforced concrete structures. Direct displacement-based design approach for the design of reinforced concrete structures.

7 Near-fault ground motions Near-field (distance to fault < -6 km): site position with respect to the focus is important Forward directivity - rupture propagates toward a site: large period, high-amplitude velocity pulse of short duration Backward directivity - rupture propagates away from a site: short period, low-amplitude motion, long duration

8 Near-fault ground motions Near-fault regions: large period, high-amplitude velocity pulse large vertical component Near-fault in design codes: scarcely represented when considered (by an amplification coefficient - UBC97), does not account for change in frequency content of the ground motion

9 Local site conditions Important parameters affecting ground motion characteristics. Basin effects seismic wave may be "trapped" inside the basin amplification and increase of duration of the seismic motions Surface topography: amplification of seismic motion for irregular topographies crest canyon slope

10 Local site conditions Frequency content of the ground motion Stiff soil: amplification of spectral accelerations in the short-period range Soft soil: amplification of spectral accelerations in the long-period range Seed et al, 976 (NEHRP )

11 Influence of the frequency content on the inelastic structural response Structures designed for seismic forces lower than the ones corresponding to an elastic response Components of the force reduction factors R=R μ R S : ductility-related R μ (major contribution) overstrength R S Frequency content strongly influences inelastic structural response: 8 T<T C : "equal displacements" T>T C : "equal energy" 6 T ( ) 4 μ + for T TC R T μ = C μ for T > TC Ground motions with control period larger than the system s period impose large ductility demands R μ VR77-INC-NS 5 5 μ Bucharest 977 record (T c =.4sec) F elastic EPP Elastic EPP, T=. EPP, T=.5 EPP, T= EPP, T=.5 EPP, T=

12 Seismic motions with high T C values Soft soils Directivity effect in case of near-field earthquakes Check: (Stratan 3) 496 European records 6.5<M w <7.8 PGA>.9 m/s Values of T C computed and records divided into two groups:.3<t C <.4.<T C <.7 All motions Motions recorded on soft were soils or were near-field recorded on records (<35 km) rock or firm soil

13 Seismic force reduction factors In spite of the strong relationship between R μ and the frequency content of the ground motion, code force reduction factors are constant: R empirically based on structural performance in past earthquakes larger overstrength of low-period structures smaller ductility-related force reduction factor for low-period structures R R μ R S T C T This simplification may not be correct for ground motions with large values of control period T C : soft soil conditions directivity effects in near-fault ground motions

14 MODELLING OF GROUND- MOTION AND SEISMIC ANALYSIS OF STRUCTURES

15 Time history representation of ground motion For many years the structural design was performed with elastic analysis and reduced seismic forces. The recently introduced nonlinear methods (pushover, time-history nonlinear analysis) require the accurate representation of the ground motion. Recorded accelerograms: should be adequately qualified with regard to the seismogenetic features of the sources and to the soil conditions appropriate to the site. Simulated accelerogram: generated through physical simulation of seismic source, travel path, and local site conditions. Artificial accelerograms: generated so as to match the code elastic spectrum. Simple pulses can be used to model ground motion (especially useful in case of near-fault ground motions).

16 Magnification of seismic action on short period structures

17 Reliability of the Displacement Coefficient Method Force F e The DCM is based on the statistical analysis of the results obtained by the time history analysis of SDOF oscillators of various types. The target displacement is given by the equation δ e δ t C δ t =C C C C 3 S a g (T/π) : relates the spectral displacement with the displacement of the upper level of the building. C :takes in to account the magnification of the maximum displacement due to inelastic behaviour. C =/R+(-/R)T g /T, με C < γιά T<.sec, C = για T>T C R : elastic strength ratio T g : characteristic period (dependent on the soil) C : takes into account the quality of the hysteretic response C 3 : takes into account the increased displacements when the second-order effects become significant. F t Displacement

18 RECORDS USED IN THE ANALYSIS Selection from a database of records with earthquakes between 98 and 994 according to the following criteria: Peak ground acceleration (PGA) >.g Magnitude M L >4.4 in the Richter scale Αρ Code Date Magnit. Station Comp PGA (g) Char.period(sec) ARGO83-7//983 Μ L =6.5 Argostoli L.7.35 ATHENS- 7/9/999 Μ L =5.9 Halandri Τ ΑΤΗΕΝS-3 7/9/999 Μ L =5.9 KEΔΕ T ATHENS-4 7/9/999 Μ L =5.9 ΓΥΣ L ARGO83-7 3/3/983 Μ L =5.7 Argostoli Τ ΖΑΚ88-4 6//988 Μ L =5.5 Zante Τ ΚΑL86-3/9/986 Μ L =5.5 Kalamata Τ EDE9- //99 Μ L =5.4 Edessa L..4 9 ΑRGO83-8 4/3/983 Μ L =5. Argostoli Τ.35.4 PAT393-4/7/993 Μ L =5. Patras T.4.35 LEF94-5//993 Μ L =5. Lefkas T.36.4 KYP87- /6/987 Μ L =5. Kyparissia Τ ΑRGO9-3//99 Μ L =5. Argostoli L PYR93-8 6/3/993 Μ L =5. Pyrgos L ΚΑL86-5/9/986 Μ L =4.8 Kalamata Τ LEF88-4/4/988 Μ L =4.5 Lefkas T ΙΕR83-3 6/8/983 Μ L =4.4 Ierissos Τ.78.5

19 Models used in the analysis F F F Δ Δ Δ a) b) c) Type Α Elastoplastic model with 5% hardening. Corresponds to perfect response and is used here as a reference model. Type Β Elastoplastic model with 5% hardening but with reduced stiffness. Characteristic for wall systems with dominant the bending response. It s typical for new buildings designed according to newer theories. Type C Elastoplastic model with softening behaviour (-%) and with reduced stiffness. It s typical for masonry systems where, for increased displacements, the strength is reduced.

20 Two types of dynamic analyses were performed In the first type the displacement ductility μ was considered as constant (μ=,4,6,8) In the second type the strength reduction factor R was considered as constant (R=,3,4,5,6). The ratio d n /d e is monitored, where d n : maximum displacement of the non-linear oscillator d e : maximum displacement of the elastic oscillator having the same stiffness with the initial stiffness of the non-linear oscillator.

21 Type A model Results for constant μ F d n / d e Πλαστιμότητα μετακινήσεων - Displacement ductility μ= Δ T (sec) d n / d e 3.5 Πλαστιμότητα μετακινήσεων - Displacement ductility μ=4 As the ductility increases, the scattering increases as well. For T >.4-.6 sec, the mean values are very close to T (sec) The scattering increases for lower values of the period. For Τ <.4-.6sec, the increase of the ductility leads to larger mean values

22 Type B model Results for constant μ F Δ d n / d e Πλαστιμότητα μετακινήσεων - Displacement ductility μ= T (sec) d n / d e 3.5 Πλαστιμότητα μετακινήσεων - Displacemenτ ductility μ= T (sec) The mean values for periods between.-.4 sec tend to be greater than the corresponding ones for the type A model

23 Type C model Results for constant μ F Δ d n / d e Πλαστιμότητα μετακινήσεων - Displacement ductility μ= T (sec) d n / d e 4 Πλαστιμότητα μετακινήσεων - Displacement ductility μ= T (sec) The scattering increases (values between.4 and 6.5) The mean values for Τ between.-.4 sec are significantly higher than those of the type Α model.

24 Mέσοι όροι, Μοντέλο Α Mean values, Μοdel A μ= /d e μ=4 d n μ=6.5 μ=8.5.5 T (sec) dn/de Mέσοι όροι, Μοντέλο B Mean values, Μοdel B.5.5 T (sec) μ= μ=4 μ=6 μ=8 dn/de Mέσοι όροι, Μοντέλο Γ Mean values, Μοdel C.5.5 T (sec) μ= μ=4 μ=6 μ=8.4 Tυπική απόκλιση, Μοντέλο Α Standard deviation, Μοdel A.4 Τυπική απόκλιση, Μοντέλο Β Standard deviation, Model B.6 Τυπική απόκλιση, Μοντέλο Γ Standard deviation, Model C...4 dn/de μ= μ=4 μ=6 μ=8 dn/de μ= μ=4 μ=6 μ=8 dn/de μ= μ=4 μ=6 μ= T (sec).5.5 T (sec).5.5 T (sec) The mean values are smaller than for large periods (the linear systems overestimate the displacements of the non-linear systems). In the short period range, the results differ according to the ductility level. The mean values are greater than even for high periods (especially for large values of the displacement ductility) in the results of Model C The values of the standard deviation in Model C are greater than the corresponding values of the type A and B models.

25 Type A model Results for constant R F Δ d n / d e R= Frequency ν Τhe results are close to until a frequency of about.5. After that value, a great scattering occurs. R=4 d n / d e Frequency ν

26 Type B model Results for constant R F Δ d n / d e d n / d e R= Frequency ν R= Frequency ν The mean values are increased with respect to the values that correspond to model A.

27 Type C model Results for constant R F These models are vulnerable to collapse From the 7 examined oscillators (7 ground motions x frequency values x 5 levels for R), 69 oscillators failed. Δ d n / d e d n / d e 5 R Failed oscillators Percentage % R= Frequency ν R= Frequency ν Structures exhibiting negative hardening (softening) should remain elastic in order to avoid collapse

28 Mέσοι όροι, Μοντέλο Α Mean values, Model A Τυπική απόκλιση, Μοντέλο Α Standard deviation, Model A dn/de R= R=3 R=4 R=5 R=6 dn/de R= R=3 R=4 R=5 R= Frequency ν Frequency ν Mέσοι όροι, Μοντέλο B Mean values, Model B Τυπική απόκλιση, Μοντέλο B Standard deviation, Model B dn/de R= R=3 R=4 R=5 R=6 dn/de R= R=3 R=4 R=5 R= Frequency ν Frequency ν The mean values are close to for v<.5, for all R levels. For ν>.5, the mean values increase, depending on R. Large values of the standard deviation appear in the high-frequency range.

29 R= R= DCM, T=.4 MODEL-A 6 DCM, T=.4 MODEL-A PROPOSITION 5 PROPOSITION dn /de.5 dn /de Frequency ν Frequency ν dn /d e DCM, T=.4 MODEL-A PROPOSITION R=6 For (v<.5) the values of C are reliable. For high frequencies, there is a strong dependance on R C cannot describe effectively the response of inelastic systems with large R values in the high frequency range Frequency ν Proposal C = + (R-)(T g /T - )/ για Τ g < T <.sec

30 Uncertainty in structural earthquake assessment and simulation

31 Fuzziness Uncertainty in engineering analysis In general data and models are uncertain. This fact has a significant influence for the results of the analysis. Uncertainty has to be described with suitable models and considered within the analysis. Classification of uncertainty Stochastic uncertainty A random result (e.g. of an experiment under identical boundary conditions) are observed almost indefinitely Informal uncertainty The system overview is incomplete or if only a small number of observations are available. Lexical uncertainty The uncertainty is quantified by linguistic variables, transformed onto a numerical scale. Examples of fuzziness earthquake loading storm loading impact loads aging processes damage material parameters

32 Modelling of uncertainty with fuzzy variables fuzzy set {( A ( )) } A% = x; μ x x X ~ triangular fuzzy number A and α-levels: μ A (x) μ A (x) membership function μ A (x) α α-level x x x 3 x ~ support S(A) Expresses the certainty with which a quantity is known From the fuzzy quantity crisp sets A α = {x X μ ( x ) α } k k may be extracted for real numbers a k (, ]. These crisp sets are called a-level sets.

33 Solution technique cartesian product fuzzy input value ~ ~ x = A μ A (x ). K% = A% A% A% K ~ =... n [ x = (x;x;...;xn ); μk (x) = μk (x;x;...;xn )] x X ; μ (x) = min[ μ (x )];i = ;...;n i i K (interaction of fuzzy quantities) Ai i. x μ K (x). x ~ ~ ~ K = A x A ~ ~ fuzzy input value x = A μ A (x ).. x. x

34 Solution technique ~ ~ ~ generation of an uncertain input subspace (bunch parameters s,, s,, s,3 ) μ(s, ) μ(s, ) μ(s,3 ) α = α i α = α i α = α i s,;αl s,;αr s, s,;αl s,;αr s, s,3;αl s,3;αr s,3 s, s,;αr s,3 n-dimesional uncertain input subspace s,;αl s,3;αl s,3;αr s,;αl s,;αr s,

35 Solution technique ~ ( % j,r ) (% % ) v% = g..., s,... = g s, s fuzzy input value s fuzzy input value s s s ~ s, α k s, α kr s, α kl s s, α k mapping operator s s, α k s, α kr vj vj, μ(s ) α k μ(s ) α-level optimization. α κ.. α κ. s, α kl s, α k μ(v j ). ακ v j, α k fuzzy result value ~ v j. v j, α kl v j, α kr v j

36 Illustrative example Loads Dead load 3. kn/m Live load 5. kn/m Seismic papameters Spectral acceleration:.6g, Soil type: B, Effective damping: 5% Importance factor. Foundation factor:. Beams upper reinforcement 8.cm Lower reinforcement 4.cm Columns Total amount of the longitudinal reinforcement.4cm (uniformly distributed along the perimeter of the column). Analysis Elastoplastic (pushover) Determination of target displacement (ATC4)

37 Input quantities Fuzzy numbers representing the steel yield stress and the concrete compressive strength Response quantities H/V.4 Fuzzy capacity curve..3 Certainty Elastic Point "Fuzzy" capacity curve Steel yield stress (Mpa) Displacement (m).. Fuzzy top-horizontal displacement.75 Certainty Concrete compressive strength (Mpa) Certainty Horizontal displacement (cm)

38 Capacity Design Methodology for Design and Evaluation of Seismic Resistance of RC Building Structures

39 RESIST-INELA Methodology [Author: Golubka Necevska-Cvetanovska, IZIIS, 99] MAIN PURPOSE: Define strength and deformability capacity of the structure Define nonlinear behaviour of the structure for a given earthquake effect Evaluation of seismic resistance STEP STEP STEP 3 STEP 4 STEP 5 Definition of the structural system of the building and determination of the quantity and quality of the built-in material. Determination of the Q- Δ diagram for each element and the storey Q- Δ diagrams (RESIST computer program). Definition of the seismic parameters and the design criteria. Nonlinear dynamic analysis of the structural system for a given earthquake effect (INELA computer program). Selection of an optimal system in newly designed structures and evaluation of the seismic resistance for the existing structures

40 Application of RESIST-INELA Methodology Settlement Kapistec

41 Application of RESIST-INELA Methodology Settlement Jane Sandanski

42 Application of RESIST-INELA Methodology Settlement Novo Lisice

43 Application of RESIST-INELA Methodology Settlement John Kennedy

44 Correlation with Modern Design Codes To conceive particular aspects of EC8 for frame structural systems and compare them with the requirements and criteria prescribed with our national existing seismic regulations (SP-8), and methodology developed at Institute of Earthquake Engineering and Engineering Seismology Skopje, several structures were analyzed. Presented here are the results from the analysis of structure B-, Unit 4, "Vardar" settlement Skopje, (fyrepublic of Macedonia). Characteristic plan and weights of building storeys

45 Correlation with Modern Design Codes X-X direction Y-Y direction Storey 5 4 Storey IZIIS EC-8 SP- 8 3 IZIIS EC-8 SP S eismic forces [kn] 5 5 Seismic forces [kn] Seismic forces obtained according to SP-8, EC8 and IZIIS Methodology

46 Correlation with Modern Design Codes 8 Ulcinj (Albatros) Amax=.4g x-x direction 8 Ucinj (Albatros) Amax=.4g y-y direction Storey EC-8 SP-8 IZIIS Storey EC-8 SP-8 IZIIS Required displacement (cm) Required displacement (cm) Required displacements for Ulcinj (Albatros) Earthquake

47 Direct Displacement Based Design Approach for Design of RC Frame Building Structures

48 Displacement-Based Seismic Design, DBD Displacement-Based Design vs. Forced -Based Design Displacement-based seismic design is defined broadly as any seismic design method in which displacement-related quantities are used directly to judge performance acceptability. Concrete cracking and reinforcement yielding Formation of flexural plastic hinge The extent of damage is related to the amount of deformation (turn to displacement) in plastic hinge Insignificant change of forces despite change of wall behaviour from elastic to deeply nonlinear

49 Direct Displacement-Based Seismic Design, DDBD The most developed and the most important method in the field of direct displacement-based design of RC building structures, both with frame and with shear wall lateral bearing system is the Priestley s method, (Priestley,, ). Substitute structure approach, (Shibata and Sozen, 975)

50 Design Example RC Frame Building In order to determine the effort needed for direct displacement-based design of a RC frame building, an example structure is designed using the Priestley s method (Priestley,, ) with minor changes that do not affect the essence of the original. Later, an example structure is analyzed using a nonlinear static procedure, (Terzic, 6). B B Layout of typical storey and cross-section of the structure

51 Assume dimensions of elements Determine storey yield drift θ y For each performance level transform MDOF system into equivalent SDOF system and calculate base shear V B Design Example Applied Method Select target performance levels according to FEMA 356 and for each performance level select critical drift θ u, corresponding earthquakes probability of occurrence and design Sd-T diagram Determine design displacements at different storeys Δ i Determine design displacement Δ d for SDOF system Determine yield displacement Δ y at the height of the resultant lateral seismic force Determine ductility μ s Performance Level IO LS Probability of earthquake occurrence %/5 year %/5 year Return Period (yrs) Critical Drift θ u (%) CP %/5 year 5 4 Determine effective damping ξ e Distribute base shear force vertically in proportion to the storey mass and displacement profile Calculate required longitudinal reinforcement in structural members assuming that beams have stiffness at maximum response, and columns cracked-section stiffness and hinges at base with base resisting moment applied Determine effective mass m e Determine effective period T e from Sd-T diagram Calculate effective stiffness K e Calculate design base shear V B Determine transverse and column longitudinal reinforcement applying capacity design approach Earthquake d (m) y (m) m e (kg) μ ξ T e (s) K e (kn/m) V B (kn) %/5 years END OF DESIGN %/5 years %/5 years

52 Analysis Results for Target Drifts Target drifts-ddbd Drift (%) Percentage of Members Achieving State Earthquake IO LS CP %/5 year.4 39 %/5 year.6 66 %/5 year.43 Target drifts-ec8 Drift (%) Percentage of Members Achieving State Earthquake IO LS CP %/5 year.39 %/5 year.66 6 %/5 year.5 Base Shear (kn) %/5 year EC %/5 year EC %/5 year EC %/5 year DDBD %/5 year DDBD IO Demand %/5 year DDBD LS Demand Displacement (m) CP Demand Capacity curve for building designed according to DDBD and EC8

53 Influence of connection behaviour on the seismic response of structures

54 J4 E9, 3.5m 3.5m E9, E,4 E,6 E,3 E,5 E,8 E, E,7 E,9 E, E,4 E, E,3 E9,6 E9,5 HEA HEB3 HEB3 J4 Base IPE3 IPE45 IPE45 HEB3 HEB3 HEB3 HEB8 HEB4 HEB3 HEB8 HEB4 HEB8 HEB4 IPE36 IPE4 HEB3 IPE45 HEB3 IPE45 J J J3 J4 J4 J J J3 J4 J4 J J J3 J4 J4 HEB3 Base Base. Influence of pinching J IPE3 J IPE36 J3 IPE4 3.m Composite section 4.m 3.m 3.m 3.m m/sec sec 5.8m m/sec sec 5.8m m/sec sec 7.5m 7.5m 7.5m 7.5m Hysteretic curve for external E9 connection Hysteretic curve for internal E connection

55 Performed analyses Dynamic N (uniform) N (modal) Analysis results Connections rot. (mrad) rot. (mrad) rot. (mrad) dynamic N (uniform) N (modal) E 9, E, J3E/J J53EF/J-X Conclusion For study of the behaviour of the connections, the monotonic methods have some limitations, because they give insufficient hysteretic information.

56 . Comparative effect of extreme event Influence of the connections simulated with semi-rigid behaviour and partial strength with rigid behaviour and full strength V* [KN] Sa [m/s ] Espectro EC8,5 g Bilinear 6.m 9.m 6.m Floor m 4.35m Floor 7 Floor 6,,,4,6,8, Top Disp.* [m],,,,3,4,5,6,7 Sd [m] 4.35m Floor 5 V* [KN] Sa [m/s ] Espectro EC8,5 g Bilinear 4.35m 4.35m 4.35m 4.35m 4.335m Floor 4 Floor 3 Floor Floor Ground Floor,,,4,6,8, Top Disp.* [m],,,,3,4,5,6,7 Sd [m]