SEISMOLOGICAL INFORMATION FOR DISPLACEMENT-BASED SEISMIC DESIGN A STRUCTURAL ENGINEER S WISH LIST

Transcription

1 SEISMOLOGICAL INFORMATION FOR DISPLACEMENT-BASED SEISMIC DESIGN A STRUCTURAL ENGINEER S WISH LIST Nigel Priestley Rose School Pavia, Italy

2 1. FORMULATION OF THE DIRECT DISPLACEMENT-BASED (DDBD) APPROACH DDBD is based on the observation that damage is directly related to strain (structural effects) or drift (nonstructural effects), and both can be integrated to obtain displacements. Hence damage and displacement can be directly related. It is not possible to formulate an equivalent relationship between strength (force) and damage. This is one of the major deficiencies of current force-based seismic design)

3 FUNDAMENTALS OF DIRECT DBD

4 INITIAL AND SECANT STIFFNESS F u =K e Δ D F m e F u F n rk i H e K i K e Δ y Δ D (a) SDOF Simulation (b) Initial and Secant Stiffness Initial Stiffness: K i with (5%) elastic damping (traditional) Secant Stiffness: K e with effective (e.g.16%) damping (new)

5 ASPECTS OF DDBD (c) Equivalent Damping vs Ductility (d) Design Displacement Spectra Ductility Damping; Damping+Displacement Period T e 2 K e = 4"! M T 2 e Fu =K e Δ D

6 TOPICS DISPLACEMENT SPECTRA CHARACTERISTICS DESIGN VERIFICATION USING NON-LINEAR TIME-HISTORY ANALYSIS (SEISMOLOGY ASPECTS)

7 SEISMOLOGISTS: Probability Theory; PSHA (a mystery to structural engineers); statistical data STRUCTURAL ENGINEERS: Deterministic approach: Pass/Fail; Right/Wrong. (e.g. If the building is 2% below code strength it is unsafe; if it is 2% above code strength it is safe) The need to design to prescriptive seismic design codes encourages this approach. Thus, structural engineers take probabilistic data from seismologists and are forced to treat it deterministically. This causes obvious problems to the thought processes of structural engineers.

8 1. SEISMOLOGISTS AND STRUCTURAL ENGINEERS CHARACTERIZE SEISMICITY DIFFERENTLY Seismologist appear primarily interested in short-period response, while structural engineers are more interested in the medium-period, and increasingly the long-period response. Note that design codes, which define prescriptive building periods which are typically less than 40% of true periods are partly to blame.

9 Different Presentations of Elastic Acceleration Response Spectra Spectral Acceleration (g) Period (sec) (a) Seismologists Preference Spectral Acceleration (g) Period (sec) (b) Structural Engineers preference Note: 4-storey frame building: T i 1.0 sec, T eff 2.0 sec sec 8-storey wall building: T i 1.6 sec, T eff 3.2

10 Different Presentations of Elastic Acceleration Response Spectra 1 1 Spectral Acceleration (g) Range of Interest Spectral Acceleration (g) Range of Interest Period (sec) Period (sec) (a) Seismologists Preference (b) Structural Engineers preference Note: 4-storey frame building: T i 1.0 sec, T eff 2.0 sec 8-storey wall building: T i 1.6 sec, T eff 3.2 sec

11 Different Presentations of Elastic Displacement Response Spectra 0.5 Spectral Displacement (m) Period (sec) 0.5 Spectral Displacement (m) Period (sec) (a) Seismologists Preference (b) Structural Engineers preference Note: 4-storey frame building: T i 1.0 sec, T eff 2.0 sec 8-storey wall building: T i 1.6 sec, T eff 3.2 sec

12 Different Presentations of Elastic Displacement Response Spectra Spectral Displacement (m) Range of Interest Spectral Displacement (m) Range of Interest Period (sec) Period (sec) (a) Seismologists Preference (b) Structural Engineers preference Note: 4-storey frame building: T i 1.0 sec, T eff 2.0 sec 8-storey wall building: T i 1.6 sec, T eff 3.2 sec

13 2. GENERAL FORM OF ELASTIC 5% DISPLACEMENT SPECTRUM, FROM EC8 Δ max Plateau? Displacement Corner Period Linear? Δ PG T C Period T D T E T C? Period T D T E

14 2. RESPONSE SPECTRA STRUCTURAL NEEDS 5% Spectral Shape as Influenced by Magnitudeis the linearity with period valid? Reduction of Displacement Spectral ordinates for different damping levels is the reduction independent of period? Is the current CEB equation reasonable (US expressions are different) Corner period and corner displacement Is the concept valid? Need to reconcile the big difference between European and US expressions for TC Characteristics for Subduction EQ s?

15 RESPONSE SPECTRA STRUCTURAL NEEDS (Continued) Near field (forward directionality effects) spectral shape, and reduction for higher damping levels How should forward directionality be considered in PSHA? Presumably backward directionality has equal probability of occurrence, and designing for just forward directionality implies design to a lower annual probability of exceedence (?)

16 3. DISPLACEMENT RESPONSE SPECTRA- A STRUCTURAL ENGINEER S APPROXIMATION The following slides provide a structural engineer s VERY tentative attempts to provide interim information, in a form useful for structural designers

17 .DESIGN DISPLACEMENT SPECTRA (1) Can be approximately generated from design acceleration spectra (5% damping) using accelerationdisplacement relationships: Δ (T,5) = (T 2 /4π 2 ).g.a (T,5) Values for damping other than 5% can be generated from relationships such as: Normal records, Current CEB Velocity pulse records (Forward directionality) (Very tentative!)

18 DESIGN DISPLACEMENT SPECTRA (2) However, design acceleration spectra tend to be inaccurate (and often excessively conservative) in the long-period range. Also, relationships between pseudo displacement and acceleration are inaccurate in the long-period range. An alternative approach is to generate displacement spectra directly from source mechanics, and recent digital records (e.g. Bommer, 2001, Faccioli et al,2002). An approach developed from Faccioli et al,2002 is used here:

19 DESIGN DISPLACEMENT SPECTRA (3) CHARACTERISTICS: (My interpretation of Faccioli et al) 5% displacement spectrum increases linearly to a corner period, then remains constant (large earthquakes), or decreases (moderate earthquakes) at longer periods. (In fact, at very large periods (T>10sec) it must reduce to the peak ground displacement) Soil amplification of displacement occurs throughout the period range. Corner period is not significantly affected. Soft soil amplification is more pronounced at longer distances (30 50 km) for both moderate and large earthquakes.

20 DESIGN DISPLACEMENT SPECTRA (4) Based on Faccioli s observations,the corner period T c appears to increase almost linearly with moment magnitude. For earthquakes with M W > 5.7, the following expression seems conservative: seconds Peak displacement at the corner period can be estimated from the following expression (firm ground): mm r = nearest distance to fault plane (km)

21 5% Damped Spectra Resulting from the Equations, at r = 10km

22 5% Damped spectra, Resulting from the Equations, at r = 20 km

23 5% Damped spectra Resulting from the Equations, at r = 40 km

24 DESIGN DISPLACEMENT SPECTRA Note that the method for generating design spectra is PRELIMINARY and TENTATIVE, and applies to FIRM GROUND. It also applies to strike/slip earthquakes (i.e. not to subduction events). Firm Ground: Approximate modification factors for other ground conditions: Rock: Multiply by 0.7 (???) Advice Please! Soft Soil: Multiply by 1.5 (???)

25 16 12 Corner Period (sec) 8 4 NEHRP Faccioli et al (2002) EC Moment Magnitude M W DIFFERENT ESTIMATES OF RELATIONSHIP BETWEEN CORNER PERIOD AND MAGNITUDE

26 16 12 Corner Period (sec) NEHRP Faccioli et al (2002) EC Moment Magnitude M W Example of Consequences: Frame building, 60m high,t el 6 sec M W =7; PGA=0.4 Acceleration plateau ends at 0.5 sec Design Elastic displacement response: EC8: 250mm Faccioli: 530 mm NEHRP: 880 mm This uncertainty is of extreme concern to the structural engineer

27 DRS from attenuation relation for M W 6 at various distances (km), D = 0.05 e m e c a l p s i d l a r t c e p S M Structural period [s] Courtesy Prof. Faccioil, Aug 29,2006

28 DRS from attenuation relations for M W 7 at different distances (km) e m e c a l p s i d l a r t c e p S M Structural period [s] Courtesy Prof. Faccioli, Aug 29, 2006

29 Exploring the feasibility of a simplified DRS model (II) The a g values controlling the ascending branch can be suitably chosen so as to fit the mean osberved DRS shapes The d g values controlling the constant branch were taken here as the mean between the spectral maximum and D < M < km Sd [cm] km km km T [s] Real spectra shown are the mean ones from the worldwide database for the indicated M and distances Courtesy Prof. Faccioli, Aug 29,2006

30 16 12 Corner Period (sec) 8 4 NEHRP Faccioli et al (2002) EC8 Faccioli, Moment Magnitude M W DIFFERENT ESTIMATES OF RELATIONSHIP BETWEEN CORNER PERIOD AND MAGNITUDE

31 Long-Period Spectral Displacements (Courtesy Prof. Bommer, Sept.2, 2006) Required for direct displacement-based seismic design and the seismic design of very tall buildings, long-span bridges and base-isolated structures Results are highly sensitive to the processing (filtering) applied to the accelerograms Key issue is identifying the maximum usable period of the filtered data, which is less than the filter cut-off

32 Rock - Analog (Elastic 5%) 1.0 n = % Confidence X = S d,proc /S d,uproc T/Tc Stiff - Analog (Elastic 5%) 1.0 n = 4 P(0.9 < X < 1.1) Rock - Digital (Elastic 5%) 1.0 n = % Confidence X = S d,proc /S d,uproc T/Tc Stiff - Digital (Elastic 5%) 1.0 n = 4 For analogue records, maximum usable period about of filter cut-off For digital records, increases to of filter cut-off % Confidence X = S d,proc /S d,uproc T/Tc P(0.9 < X < 1.1) % Confidence X = S d,proc /S d,uproc T/Tc In both cases, much shorter for INELASTIC spectral ordinates (Akkar & Bommer, 2006)

33 Courtesy Prof Bommer Sept.2,2006

34 INFLUENCE OF DAMPING AND DUCTILITY ON SPECTRAL DISPLACEMENT RESPONSE Current EC8: 1993 EC8: Newmark and Hall 1987: Independent analyses by Priestley et al, Kowalsky et al, Sullivan et al, support the 1993 EC8, not the 2003 Eqn,nor Newmark and Hall. Tentative Expression for Forward Directivity, Near field

35 1 0.8 Reduction Factor Damping Modifiers to Elastic Spectral Displacements Forward Directivity(?) Newmark+Hall EC8 (new) EC8 (old) Damping ratio (%) Analysis of spectrum-compatible records indicates reasonable period independence, but it is not clear real records agree. What is appropriate for design?

36 INFLUENCE OF DAMPING ON DISPLACEMENT RESPONSE

37 Note that designing for Velocity Pulse spectra of the type in the previous slide using Direct Displacement-Based Design automatically results in a reduced effective period, and hence an increased seismic design force to limit the displacements to the design value. This is one of the advantages of Direct Displacement-Based Design

38 Displacement Spectra related to Ductility 0.5 µ=1 0.5 µ=1 0.4 Displacement (m) µ=2 µ=3 µ=4 µ= µ=2 µ=3 µ=4 µ= Period (seconds) (a) EPP (Equal Displacement) Period (seconds) (b) EPP (Time-history Analysis) (r=post-yield stiffness ratio; loop shape irrelevant) Results from inelastic timehistory analysis give different results!

39 4. REPRESENTATION OF SEISMICITY FOR DESIGN VERIFICATION: INELASTIC TIME- HISTORY ANALYSIS: CHOICE OF ACCELEROGRAMS Artificial Accelerograms Recorded Accelerograms (scaled to fit design spectrum at critical period(s) Recorded accelerograms manipulated to fit spectrum over entire spectrum. (Note) recorded accelerograms should represent the relevant site characteristics (strike/slip, or subduction; velocity pulse if near field, etc)

40 ACCELEROGRAMS SCALED OVER PERIOD RANGE Displ. error Period shift Spectral matching Disp.duct.=3 T 3 T 1 Period Spectrum matching is required not just over the ELASTIC period range of relevance, but also for the softened first mode period

41 NUMBER OF RECORDS FOR TIME HISTORY ANALYSIS ENVELOPE RESPONSE FROM AT LEAST 3 RECORDS AVERAGE RESPONSE FROM AT LEAST 7 RECORDS QUESTION: If I generate 14 spectrum-compatible records, can I select which 7 I use? (Trick question!) QUESTION: If the risk at the site is partly from near-field and partly from more distant earthquakes, how should I select the base records? QUESTION: If 2-component input is required, should BOTH components match the design spectrum?

42 AVERAGING OF RESULTS FROM 7 ACCELEROGRAMS Deck Displacements (ins) for plastic hinge strains Δ Positive Δ Negative Rebar tension strain Concrete compression strain Average: Average of Maxima (Green) = ins (178.4mm) Overall Average =5.858 ins (148.8mm)

43 AVERAGING OF RESULTS FROM 7 ACCELEROGRAMS (Conflicting Arguments) Peak displacements in opposite directions should not be averaged, if damage potential is considered (e.g. plastic hinge compression strain, movement joint opening). But the polarity of the earthquake accelerogram is arbitrary, and hence the displacement signs are arbitrary Hence displacements in opposite directions SHOULD be averaged. BUT This implies considering polarity of BOTH +1 and -1, implying 14 accelerograms, and selecting the seven most critical. All 14 should be averaged, in this case, giving a LOWER (5.858 in) displacement.

44 MULTI-AXIS EXCITATION: SCALING HORIZONTAL COMPONENTS OPTIONS: 1. Rotate recorded components to get principal axes. Scale maximum to the design spectrum Problem: Uncertainty about direction (with respect to the structure) to apply the H1 and H2 components. Need multiple analyses with different orientation 2. Scale H1 and H2 so both match design spectrum (which is in fact an average spectrum). Since cross-correlation is low, spectrum in all directions is close to design spectrum (i.e. directionally independent; one analysis OK)

45 PORT OF LOS-ANGELES MARGINAL WHARF STUDY CLE 5% DAMPING 40% of Risk from Near-field (Palos Verdes) fault, 60% from distant faults: 3 records (each 3-component) near field, 4 distant.(from EMI)

46 1.0 second 3.0 second 1.5 second 2.0 second 4.0 second 5.0 second target Average, 7 spectrum compatible records CLE PEAK ELASTIC DISPLACEMENTS AT DIFFERENT BEARINGS AND PERIODS (5% DAMP.) (from EMI)

47 A: critical pile C. Of stiffness C.of mass dyke Marginal wharf Marginal Wharf with Sloping Dyke

48 2-SEGMENT MARGINAL WHARF PLAN VIEW A Land-Side Shear Key Water-Side Potential Impact Peak vectorial displacement at A found from the maximum of SRSS combination of X and Y displacements at each time step. QUESTION: Is it valid to average these peak displacements, given different directions? (Clearly averaging X and Y peaks and taking SRSS is wrong)

49 2-SEGMENT MARGINAL WHARF PLAN VIEW A Land-Side Shear Key Water-Side Potential Impact In Fact, displacements for each record must be calculated at each time step at each of (say) 24 different bearings (i.e. 15 degree intervals. The peak displacements for each bearings are averaged over the 7 records, and the critical bearing, and maximum average displacement are found.

50 CONCLUSIONS Structural Periods are longer than previously calculated for most structural types. This is not a function of changing structural forms, but of improved structural understanding. Response periods in the range seconds are of greatest interest regardless of whether initial-stiffness or displacement based design philosophies are used Better information on medium-long period response seismicity is urgently needed. Existing codified information is extremely poor Structural engineers need help in appreciating the probabilistic nature of seismic design spectra. Design codes require us to adopt a pass/fail mentality when designing our structures, when only an infinitesimal increase in risk may be involved Techniques currently employed for averaging results from multiple time-history analyses appear to us to be incompatible with reliability theory