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PROTA 28th Anniversary Symposium “Seismic Isolation Methods and Practices” Ankara, Feb. 28 & March 1, 2013
Seismic Isolation Principles and Practice in the Context of European Standards Michael N. Fardis University of Patras, Greece
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European Standards (ENs) Design standards : The Eurocodes Material standards (steel, ETAs: European Technical concrete, etc.) Approvals Product standards (Special isolation or (Structural bearings, dissipation devices, FRPs, Antiseismic devices, etc.) prestressing systems, etc.) Execution standards (e.g., standards for the execution of concrete or steel structures) Test standards
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THE EN-EUROCODES EN 1990 Eurocode: Basis of structural design
EN 1991 Eurocode 1: Actions on structures EN 1992 Eurocode 2: Design of concrete structures EN 1993 Eurocode 3: Design of steel structures
EN 1994 Eurocode 4: Design of composite (steel-concrete) structures EN 1995 Eurocode 5: Design of timber structures
EN 1996 Eurocode 6: Design of masonry structures EN 1997 Eurocode 7: Geotechnical design EN 1998 Eurocode 8: Design of structures for earthquake resistance
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EN 1999 Eurocode 9: Design of aluminium structures
INTERRELATION OF EUROCODES EN1990
Structural safety, serviceability and durability
EN1991
Actions on structures
EN1992
EN1993
EN1994
EN1995
EN1996
EN1999
EN1997
EN1998
Design and detailing
Geotechnical and seismic design
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• •
• •
• •
FLEXIBILITY IN THE EUROCODE SYSTEM Eurocodes (ECs) or National Annexes cannot allow design with rules other than those in the ECs. National choice can be exercised through the National Annex, only where the Eurocode itself explicitly allows: 1. Choosing a value for a parameter, for which a symbol or range of values is given in the Eurocode; 2. Choice among alternative classes or models detailed in the Eurocode. 3. Adopting an Informative Annex or referring to alternative national document. Items of national choice in 1-2: Nationally Determined Parameters NDPs National choice through NDPs: – Wherever agreement on single choice cannot be reached; – On issues controlling safety, durability & economy (national competence) & where geographic or climatic differences exist (eg. Seismic Hazard) For cases 1 & 2, the Eurocode itself recommends (in a Note) a choice. The European Commission will urge countries to adopt recommendation(s), to minimize diversity within the EU. If a National Annex does not exercise national choice for a NDP, designer will make the choice, depending on conditions of the project.
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EC8 Parts EC8 Part
Title
CEN date
1: EN1998-1 General rules, seismic actions, rules for buildings
Dec. 04
2: EN1998-2 Bridges
Nov. 05
3: EN1998-3 Assessment and retrofitting of buildings
June 05
4: EN1998-4 Silos, tanks, pipelines
July 06
Foundations, retaining structures, geotechnical 5: EN1998-5 aspects
Nov. 04
6: EN1998-6 Towers, masts, chimneys
June 05
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EN 1998-1:2004 General rules, seismic actions, rules for buildings No. of NDPs 1. General _ 2. Performance Requirements and Compliance Criteria 2 3. Ground Conditions and Seismic Action 8 4. Design of Buildings 7 5. Specific Rules for Concrete Buildings 11 6. Specific Rules for Steel Buildings 6 7. Specific Rules for Steel-Concrete Composite Buildings 4 8. Specific Rules for Timber Buildings 1 9. Specific Rules for Masonry Buildings 15 10. Base Isolation 1 Annex A (Informative): Elastic Displacement Response Spectrum 1 Annex B (Informative): Determination of the Target Displacement for Nonlinear 1 Static (Pushover) Analysis Annex C (Normative): Design of the Slab of Steel-Concrete Composite Beams at Beam-Column Joints in Moment Resisting Frames
Total:
_ 57
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EN 1998-2:2005: Bridges no of NDPs 1. Introduction 2. Performance Requirements and Compliance Criteria 8 3. Seismic Action 4 4. Analysis 2 5. Strength Verification 3 6. Detailing 6 7. Bridges with Seismic Isolation 4 Annex A (Informative): Probabilities related to the reference seismic action 1
Guidance for the selection of the design seismic action during construction Annex B (Informative): Relationship between displacement ductility and curvature 1 ductility factors of plastic hinges in concrete piers 1 Annex C (Informative): Estimation of the effective stiffness of reinforced concrete ductile members Annex D (Informative): Spatial variability of earthquake ground motion: Model and 1 methods of analysis Annex E (Informative): Probable material properties and plastic hinge deformation 1 capacities for non-linear analyses Annex F (Informative): Added mass of entrained water for immersed piers 1 Annex G (Normative): Calculation of capacity design effects Annex H (Informative): Static nonlinear analysis (Pushover) 1 Annex J (Normative): Variation of design properties of seismic isolator units 2 Annex JJ (Informative): -factors for common isolator types 1 Annex K (Informative): Tests for validation of design properties of seismic isolator units1 Total: 38
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Application of EN1998 rules for seismic isolation The rules in Section 10 of EN 1998-1: apply to buildings (and building-like structures). The rules in Section 7 and Annexes J, JJ & K of EN 1998-2: apply to bridges only; are more detailed & up-to-date than those in EN1998-1. The parts of Eurocode 8 on tanks, silos, pipelines, towers, etc: do not include specific rules for seismic isolation; for such structures the rules in EN 1998-1, EN 1998-2 on seismic isolation may be applied by analogy.
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From EN1990 (Eurocode – Basis of structural design): «Seismic design situation»:
G j 1
k, j
"" P"" AEd "" 2,i Qk ,i i 1
Gk , j : Permanent actions (characteristic or nominal values) j 1 : Prestressing P
2,iQk ,i : Quasi-permanent values of variable actions (live loads) AEd AEk : Design Seismic action AEk: Characteristic Seismic action, : Importance factor of structure
From EN1990:
AEk :«Reference Seismic action» («Reference» exceedance probability PR in design life TL of structure, or «Reference» return period TR).
ψ 2,i: Residential & office buildings: 2 =0.3;
Shopping or congregation areas in buildings: 2 =0.6; Storage areas in buildings:2 =0.8; Roofs: 2 =0.0 (but 2 =0.2 for snow, at altitudes >1000m or in Scandinavia); Bridges of motorways/roads of national importance:2=0.2 on uniform load; Bridges for intercity rail links or high speed trains: 2 =0.3; Other bridges and footbridges: 2 =0.
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Design seismic action in Eurocode 8 • The Reference Return Period of the Reference Seismic action is a NDP, with recommended value of 475yrs (Reference Probability of Exceedance in a design life of 50yrs: 10%). • The Reference Seismic action is described (in the national zonation maps) in terms of a single parameter: the Reference Peak Ground Acceleration (PGA) on Rock, agR. • The design ground acceleration on rock, ag, is the reference PGA times the importance factor: ag = γIagR
• In addition to the Reference Peak Ground Acceleration on Rock, the Reference Seismic action is defined in terms of the Elastic Response Spectrum for 5% damping.
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Elastic Spectra in Eurocode 8 Spectral shape: Given in National Annex as NDP as function of: Ground type (surface layers, a few tens of m) Earthquake Magnitude (possibly) deep geology below surface deposits. Spectral shape: Has regions of: Constant response spectral pseudo-acceleration Constant response spectral pseudo-velocity Constant response spectral displacement • Recommended: Two types of horiz. spectra from S.European data: Type 1: High & moderate seismicity (distant EQs, Ms> 5.5); Type 2: Low seismicity; local EQs (Ms< 5.5). (High amplification at low T; falls-off sooner with T). Detailed ground classification (5 standard ground types defined on the basis of shear-wave velocity in top 30m, plus 2 special ones). Site specific spectra required for Importance Class IV isolated buildings (“essential”) near potentially active faults giving Ms>6.5
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Standard Ground types
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Standard elastic response spectral shape • Ranges of constant spectral pseudo-acceleration, pseudo-velocity, displacement, start at corner periods TB, TC, TD. • Uniform amplification of spectrum by soil factor S (including PGA at soil surface, to Sag). • Damping correction factor: • Constant spectral acceleration = 2.5 times PGA at soil surface for horizontal, 3 times for vertical. • TB, TC, TD, S: NDPs
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Recommended horizontal elastic spectrum, Type 1, ξ=5% 4
E
D C
Se/ag
3
B A
2 1
0 TB TC Ground motion max acceleration: agS
1
max velocity: vg = agSTC/(2π)
TD
3 (s)
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max displacement: dg = 0.025 agSTCTD
Recommended vertical elastic spectra, ξ=5%
• Corner periods TB, TC, TD: NDPs • Recommended: – Independent of ground type (no
– – – –
data) TB = 0.05s TC = 0.15s TD = 1.0s Peak vertical ground acceleration • avg = 0.9ag, if Type 1 spectrum used; • avg = 0.45ag, if Type 2 spectrum.
• Vertical component mandatory: – for all isolated bridges; – if avg > 0.25g in buildings. • .
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Ground motion records for time-history analysis
• Historic or simulated records preferred over artificial ones. – Simulated records: from mathematical model of the source
dominating the seismic hazard (rupture event, wave propagation via the bedrock to the site and via the subsoil to the ground surface). – Historic records: from seismic events with magnitude, fault distance & mechanism of rupture consistent with those dominating the hazard for the design seismic action. Travel path & subsoil conditions of recording station should resemble those of the site. – Artificial (“synthetic”) records: mathematically derived from the target elastic spectrum (unrealistic if rich in all frequencies in the same way as the target spectrum; perfect matching of spectrum to be avoided). • Component records scaled so that the elastic spectra values are ≥ 90% of the code spectra (in the range of 1.5x to 20% of the fundamental period along the component). For pairs of horiz. components this is applied to SRSS of spectral values, taking 0.9√2 ~1.3. • ≥ 7 independent seismic events (component or pair time-histories) needed if analysis results for peak response quantities are averaged; • 3-6 if most adverse peak response from all the analyses is used.
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Strong discontinuity in heightwise distribution of lateral stiffness uncouples deformations in the superstructure from the ground motion
Superstructure
Isolation device/unit
Isolation system @ isolation interface
Isolation device/unit
Substructure
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Isolation strategies to reduce lateral forces on the superstructure damping↑
acceleration
Period T
resistance↓
Period T
displacement
Period ↑
displacement
acceleration
Period ↑
damping ↑
Flexible isolators lengthen period & reduce forces. Damping reduces displacements @ Period T isolation interface damping ↑
Limiting the force resistance of isolators reduces the force input (cf. capacity design). Damping reduces displacements @ Period T isolation interface
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Sd (m)
Sa (m/sec2)
Acceleration, Displacement & ADRS (Acceleration-Displacement) Type 1 elastic response spectra recommended in EC8 (for damping ξ = 5% & PGA = 1m/sec2 on Soil A – rock) 4
Soil A Soil B Soil C Soil D Soil E
3.5 3 2.5
Sd Sa T
2
2
2π
0.16 0.14 0.12 0.1 0.08
1.5
0.06
1
0.04
0.5
0.02
0
0
0.5
1
1.5
2
2.5
3
3.5
4
Period (sec)
• Spectrum reduction factor for damping in EC8:
10 (5 %) • η ≥ 0.55 (ξ ≤ 28%) in buildings. • η ≥ 0.40 (ξ ≤ 57%) in bridges.
Sa (m/sec2)
0
4
Soil A Soil B Soil C Soil D Soil E
0 0.5 T=0.25 T=0.50
1
1.5 T=1.0
3.5
2
2.5 3 3.5 4 Soil A Period (sec) Soil B
Soil C Soil D
3
Soil E
2.5
T=1.5
2 1.5
T=2.0
1
PROTA T=3.0 T=4.0
0.5 0 0
0.02 0.04 0.06 0.08
0.1
0.12 0.14
Flexibility strategy • Common and relatively inexpensive. • Isolators ~elastic and re-centering: – Elastomeric (rubber) bearings: • with low damping (~5%, LDRB), or high damping a) (10-20%, HDRB). – If damping is low, supplemental damping (eg, fluid viscous dampers) may be used to reduce the displacements.
• Less effective if: – motion is rich in low-frequencies (eg, on soft soils); or – superstructure is flexible (high-rises); or – substructure is flexible (tall/flexible piers, flexible piles).
Force-limitation strategy • • • • •
More effective in the cases where flexibility strategy is less effective. Convenient for retrofitting superstructures with low force resistance. Isolators with force limitation (eg, flat sliding isolators). No re-centering. Supplemental damping may be used to reduce the displacements if energy dissipation (eg, by friction) is low.
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Combination: Flexibility after force limit • Most common in practice. • Possibly more expensive. • Isolators: – Lead-Rubber Bearings (LRB); – Units with spherical sliding surface(s); – Sliding surface with yielding (elasto-plastic) steel device; etc.
• Hysteretic energy dissipation after force limit exceeded. • Re-centering depends on details of the hysteretic loop. • Don’t need supplemental damping.
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Isolator hysteretic behavior idealized as bilinear Basic parameters F0: Force at zero displacement Ke: elastic stiffness Kp: post-elastic stiffness Derived parameters Fy: yield force = F0/(1-Kp/Ke) dy: yield displacement = (F0/Ke)/(1-Kp/Ke) Response (& design) values 1 ED ξ eff dd (or dbd): design displacement 2π Fmaxd d Fmax: maximum force = F0+Kpdd ED: dissipated energy/cycle at displacement dd (area inside hysteresis loop) = 4F0(dd-dy) ξeff: damping =(2/π)(Fy/Fmax-dy/dd)
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Analysis methods in EN 1998 Reference method (always applicable): – Non-linear time-history analysis in 3D.
Simplifications (subject to certain conditions): – Equivalent-linear analysis: • Multi-modal equivalent-linear spectral analysis; • Simplified equivalent linear ("fundamental mode" spectral)
In bridges, the displacements & forces from any analysis are scaled up to reach at least 80% of the displacement at center of isolation system & of the total base shear from a fundamental mode analysis (per hor. direction, if the piers are tall or the longitudinal eccentricity of deck mass to the stiffness center of isolation system is > 0.1L).
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Non-linear time-history analysis • Only the isolators are modelled as nonlinear. • Two concurrent horizontal components, considering interaction of response in the two horizontal directions and the effects of overturning moments; masses moved by ±accidental eccentricities. • The effects of the vertical component may be computed separately and linearly - with the response spectrum approach and combined to those of the horizontal via the 1:0.3:0.3 rule. • Raleigh damping (C = αΚ + βΜ) should not interfere with the hysteretic damping of the isolated modes (with longest T); it should dampen-out very short periods: – β = 0; – α > ξT/π = 0.1x0.05/π = 0.0016 give ξ>5% for T<0.1 s 20.0% 17.5%
Damping ξ
15.0% 12.5% 10.0%
7.5% 5.0% 2.5%
0.0% 0.0
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1.0
1.5
2.0
2.5
3.0
3.5
4
Equivalent linear analysis • Linear static or modal analysis with: – the total effective stiffness Keff & damping eff of the system computed from the secant stiffness and dissipated energy of the individual devices at their displacement which corresponds to the design displacement dd at the stiffness center of the isolation system, – =5% for higher modes in modal, – torsional response due to accidental eccentricity computed statically. • Applicability condition: – ξeff ≤30%; • Additional condition for bridges (EN1998-2): – Ground types A, B, C, E (not D, S1, S2). • Additional conditions for buildings & structures ≠ bridges (EN1998-1): – Isolators: LDEB, HDEB, elastoplastic with bilinear hysteresis; – Keff(at dd) ≥ 0.5Keff(at 0.2dd); – force-displacement features of isolation system do not vary by >10% due to loading rate or vertical load variations in the range of the design values; – when displacement of isolation system increases from 0.5dd to dd, its force increases > 2.5% of total superstructure gravity (for certain recentering).
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Iterative equivalent linear analysis
Assume dcd,a dbd,i From device i monotonic F-d relation: Fmax,i Keff,i=Fmax,i/dbd,i,
Fmax Fy
Kp
F0 Ke
ED: dissipated energy/cycle at dbd,i
Effective period & damping:
dy
Iterations till dcd,r ≈ dcd,a.
2 1 ( 1 p)(μ 1) ~const. π μ 1 p(μ 1)
dbd
ED
ΣED,i M 1 Teff 2π ,..ξ eff K eff,i 2π ΣFmax,id bd,i dcd,r from displacement spectrum: 10 ≤ 0.55 in buildings ηeff 5 ξ eff (%) ≤ 0.40 in bridges
Nb: ξ eff
Keff
for ↑μ
p=Kp/Ke:
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Multi-modal equivalent linear spectral analysis • Full modal analysis of complete structural system, separately in the two horizontal directions (also separately for the vertical). – to capture possibly significant contributions of higher modes. • Isolators i with their effective stiffness, Keff,i, from the fundamental mode method in the direction considered. • The substructure & superstructure w/ their normal stiffness (uncracked in bridges, 50% of uncracked in buildings). • Modal damping ξ = 5% in all modes with T < 0.8Teff – Teff from fundamental mode method; – ξeff of that mode for all modes w/ T >0.8Teff. • Torsional response due to accidental eccentricities computed statically and superimposed to results of modal analysis.
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Simplified equivalent linear analysis ("fundamental mode" spectral in EN1998-2)
• Superstructure rigid (forces on it proportional to spectral acceleration & mass) • Buildings & structures ≠ bridges: – 2 DOFs: uncoupled horiz. translations of isolation system stiffness center, with static torsional effects (about the vertical) on isolation system due to natural & accidental eccentricities, but neglecting overturning effects . – If horiz. eccentricities ex, ey between mass center & isolation stiffness center (incl. accidental) 7.5% of plan dimensions: • Torsional effects of eccentricities ex, ey (natural & accidental) by 2 2 multiplying isolator displacements by: δxi 1 e y yi / ry ,..δ yi 1 ex xi / rx (rx, ry: torsional radius of isolation system in x, y) – Consider vertical component & DOF (separately) only if avg > 0.25g. • Bridges: – 3 DOFs: 2 uncoupled horiz. translations & one vertical; – static torsional effects (about the vertical) on isolation system due to longitudinal eccentricity ex (natural & accidental) of transverse earthquake ex (y) by multiplying transverse isolator displacements etc by: δ yi 1 xi (r: radius of gyration of superstructure mass about vertical). rrx • Combination of components w/ SRSS or 1:0.3(:0.3) rule.
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Applicability of simplified equivalent linear analysis ("fundamental mode" spectral, in EN1998-2) Conditions for bridges (EN1998-2) – Distance >10km from potentially active faults.
Conditions for structures ≠ bridges (EN1998-1) – – – – –
Distance >15km from potentially active faults producing Ms 6.5 Max plan dimension 50 m Rigid substructure All isolators: above substructure elements supporting vertical load Effective period Teff 3s & ≥3-times1st mode period on fixed base.
Additionally, for buildings (EN1998-1): – – – –
Superstructure stiffness regular & symmetric in plan Negligible rocking at the base of the substructure Vertical-to-horizontal stiffness ratio of isolation system Kv/Keff 150 1st vertical vibration period: Tv 0.1 s
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Low Damping Elastomeric Bearings (LDEB) in EN1998-2 • “Normal” laminated elastomeric Bearings per EN 1337-3 (rubber layers & bonded steel plates) • Narrow hysteresis loops, ~elastic. • Damping ξ not much larger than 5%. 50
200
45
Rubber Bearing Force(kN)
150 100 50 0 -50 -100 -150
PGA:25% (#5 Couple)
40 35 30
7.5% KM 15% KM 20% KM 20% 10KM 20% 0.1KM 20% 0.5KM 20% 2KM 20% 2KM (repeated) 25% KM 25% KM (repeated) 25% 10KM 25% 0.5KM 25% 2KM
25 20 15 10
0.5
PGA:25% (#1 Couple) PGA:20% (#4 Couple)
5
PGA:20% (#1 Couple)
-200
3.5 7.5% KM 15% KM 3 20% KM 20% 10KM 20% 0.1KM 2.5 20% 0.5KM 20% 2KM 2 20% 2KM (repeated) 25% KM 25% KM (repeated) 1.5 25% 10KM 25% 0.5KM 25% 2KM 1
G (MPa)
Equivalent Viscous Damping (%)
250
PGA:15% (#4 Couple) PGA:15% (#1 Couple) PGA:7.5% (#1 Couple)
0
PGA:7.5% (#1 Couple)
-250 -150
-120
-90
-60
-30
0
30
Displacement (mm)
• • • •
60
90
120
150
0
25
50
75
100
125
Strain (%)
150
175
200
0
0 225
25
50
75
100
125
Strain (%)
150
175
d
200
b Fb Horizontal stiffness Kb=GbAb/tb Ab: plan area, tb: elastomer thickness Gb: shear modulus (≈ 0.9 to 1.3 MPa, “scragging” if Gb<0.6MPa) “Normal” LDEB cheap; not manufactured specifically for seismic use: in strong earthquakes they may not sustain the large shear strains. – Accept some damage & replace, or combine with viscous dampers
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225
High Damping Elastomeric Bearings (HDEB) in EN1998-2 • Per EN 15129 (“Antiseismic devices”) • Broader hysteresis loops, thanks to special elastomer mixed with special aggregates: – Damping ξ = 10 to 20% • Impact of deformation history (scragging), esp. for low-G elastomer: – Significant drop in shear stiffness after 1st cycle at peak strain. – Initial stiffness ~fully recovered with time (months-years). – Risk: underestimate G by testing scragged bearings. – EC8-2: Test unscragged bearings, use average G in first 3 cycles.
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Force (k
0
-50
Stiffness, LDE: KR=GRAR/hR; Lead core: KL=GLAL/h Stiffness LRB: elastic: Ke=KR+KL, post-elastic: Kp=KR Yield force LRB: Fy=FLy(1+KR/KL) Displacement (mm) Parameters AR, AL: wide range of bilinear loops -100
25% 2M 25% 0.5M 25% M
-150
-200 -140
-105
-70
-35
0
35
70
105
140
20 15
Force (kN)
10
200 150
Force (kN)
100
5 0
-5 -10 -15
50
-20 -15
0
-10
-5
0
5
10
15
Displacement (mm)
-50 -100 25% 2M 25% 0.5M 25% M
-150 -200 -180
-120
50 15% 15% 15% 15% 15% 20% 25% 25% 25% 25% 25% 20% 25% 30%
45 40 35 30 25 20
KM 10KM 01KM 05KM 2KM KM KM 10KM 01KM 05KM 2KM KM second KM unscragged KM second
10 5 0
30
60
90
Strain (%)
120
150
0
60
120
180
High stiffness & damping at shear strains < 30%: good for frequent actions (wind); Minimum stiffness & damping for shear strains of 100-150% (~design earthquake)
180
4000
Strain (%)
15
0
-60
15% 15% 15% 15% 15% 20% 25% 25% 25% 25% 25% 20% 25% 30%
3600 3200 2800
Keff(kN/m)
Equivalent Viscous Damping (%)
Lead Rubber Bearings (LRB) in EN1998-2
2400 2000 1600 1200 800 400 0
0
KM 10KM 01KM 05KM 2KM KM KM 10KM 01KM 05KM 2KM KM second KM unscragged KM second
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60
90
Strain (%)
120
150
180
Fluid viscous dampers (supplemental damping) in EN1998-2 Force Vs. Velocity Constitutive Law
Force (kN)
Velocity governed: F = Cvα 4000 3500 3000 2500 2000 1500 1000 500 0
At max displacement: v=0, F=0, Keff=0 (no contribution damper to the stiffness of the isolation system) For sinusoidal motion: db=dbdsin(ωt) with ω=2π/T F=Cvα =Fmax(cos(ωt))α Fmax=C(dbdω)α Depend strongly ED=λ(α)Fmaxdbd on ω if α>>0
α=0.15, C=3000kN/(m/sec)α
0
0,5
1
1,5
2
Velocity (m/s)
}
λ(α) 2 α
2 α
Γ 2 (1 0.5α) , Γ (2 α)
0.01 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.50 2.00
λ(α) 3.988 3.882 3.774 3.675 3.582 3.496 3.416 3.341 3.270 3.204
π
2.876 2.667
( ): gamma function
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If α<<1: Fmax≈C, λ(α)≈4
Fluid viscous dampers & LDEBs, approach viaduct of Rio-Antirio bridge, GR (design PGA 0.48g)
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Rio-Antirio main bridge: fluid viscous dampers in transverse direction, between deck (suspended from pylon tops) & piers Characteristics
Pylons
Transition Piers
Prototype
Damper Series
OTP350/3500
OTP350/5200
OTP350/1800
Stroke (mm)
-1650/+1850
± 2600
± 900
Pin-to-Pin Length (mm)
10520
11320
6140
Total Length (mm)
11310
12025
6930
Max. Diameter (mm)
500
550
500
Damper Weight (kg)
6500
8500
3300
Total Weight (kg)
9000
11000
286
560
560
2252
5500 Courtesy of GEFYRA SA
560
286
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Courtesy of GEFYRA SA
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Tests of prototype: Caltrans SRMD facility, UCSD
Courtesy of GEFYRA SA
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•
•
• • • • •
Flat sliding bearings in EN1998-2 Frictional behavior with limiting force: Fmax = μdNSdsign ( d ) bd • μd: dynamic friction coefficient ≠ static or breakaway • NSd: vertical force • dbd: velocity No restoring capability: • Need to combine in isolation system with fully re-centering components (eg, LDEBs). Commonly: Lubricated PTFE on stainless steel with very low minμd ≈0.005-0.02. If PTFE unlubricated: μd ≈0.05-0.1. Conformity to EN1337-2 gives controlled upper bound of μd, but no reliable lower limit. Device damping ξ=2/π, but Energy dissipation: ED=4μdNsddbd≈0.
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Example: Flat sliding bearings used with elastomeric bearings for restoring force Twin bridges over Corinth Canal (GR): • Flat sliding bearings on top of the piers; • Elastomeric bearings at the abutments
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Two pairs of elastomeric bearings per abutment
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One flat sliding bearing at the top of each pier
Bearings with spherical sliding surface in EN1998-2 Fmax
• Significant restoring force • Stainless steel surfaces; special surfacing material for low friction • μd=0.05-0.10 • Device damping: ξ=(2/π)/(1+μddbd/Rb) • Energy dissipation: ED=4μdNsddbd.
NSd dbd μdNSdsign ( d bd) Rb
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424 units w/ spherical sliding surface under 2 LNG tanks Revithousa island, Greece
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Bearings with two spherical sliding surfaces
• Covered by EN 15129, not mentioned in EN1998-2. • Equivalent radius: Rb=R1+R2-h1-h2 • Displacement capacity: d1(1-h1/R1)+d2(1-h2/R1) • No other difference in behavior w.r.to single spherical surface.
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Bearings with 3 spherical sliding surfaces (not in EN15129 or EN1998)
Schematic Cross Section
Photo of Triple PendulumTM Bearing
Schematic Cross Section
μ1=μ4=μd μ2=μ3<μd
Concaves and Slider Components Concaves and Slider Assembly
Photo of Triple PendulumTM Bearing
Regimes I & II: minor earthquakes, -dy*≤ d ≤dy*, F ≤μ2Nsd Motion in d2, d3. High stiffness, good re-centering
Concaves and Slider Components
Schematic Cross Section
Regime V: >design earthquake, d>dlim, Motion in remaining part of d2, d3.
Regimes III & IV: ≤ design earthquake. dy*≤ dlim. Motion within d1 & d4.
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Properties of isolation systems exclusively of sliding isolators (normally with spherical sliding surface) For bearing i: Fbi =NSd,i(db,i/Rb+μd) = kiNSd.i If the isolation system:
• is supported on a rigid diaphragm; and • supports the superstucture via a rigid diaphragm (or the superstucture is horizontally rigid) all db.i are equal ⇨ all ki are equal ⇨ no twisting about the vertical. [Strictly speaking this is always the case for flat sliders, which have Rb=∞ but are never used alone in an isolation system]. If db,i/Rb>>μd the period is T ≈2π√(Rb/g) ~ independent of the mass of the superstucture.
PROTA
Layout of isolators per EN1998 • To minimize twisting: effective stiffness center of isolation system as close as possible to the horizontal projection of the center of mass of the superstructure (met automatically for sliding isolators). • To minimize differential behavior of isolators: they should share ~uniformly the gravity loads of the superstructure. • Rigid diaphragm above isolation interface - in buildings, below it as well. • Sufficient space around isolating devices for inspection, maintenance, replacement. • Use dampers, shock-absorbers, etc., if shocks is an issue.
PROTA
Design properties of isolators used in analysis
Nominal (“mean”) design properties are determined via tests of prototype devices, to confirm the range specified in the design. The variation of design properties due to aging, temperature, contamination, cumulative travel/wear, scragging, etc, considered; design is carried out using both: • Upper Bound Design Properties (UBDP), for maximum forces in the superstructure & substructure; and • Lower Bound Design Properties (LBDP), for maximum displacements of the isolators & the superstructure. The Bounds of Design Properties from tests, or modification (λ) factors (Annex J of EN15129, J & JJ of EN1998-2, from AASHTO Guide Specs). Properties obtained for the quasi-permanent variable actions, but for temperature the frequent value is taken into account. In bridges, multimode spectral or nonlinear time-history analysis may be based just on nominal design properties, if the displacements from Fundamental mode analyses with UBDPs & LBDPs differ from those for the nominal ones by < 15%.
PROTA
Increased reliability required of the isolation system Why? • The superstructure and the substructure have safety margins, because their ULS resistance is calculated from characteristic (5%-fractile) values of material strengths divided by the material partial safety factors (1.5 for concrete, 1.15 for steel). • By contrast, the ULS of isolators is defined by their nominal displacement capacity, without margins. • Thanks to redundancies in the superstructure and the substructure, attainment locally of their ULS resistance does not have catastrophic consequences. • By contrast, failure of isolators may be catastrophic for the superstructure.
How? • Multiplicative factor applied on the seismic displacement of the isolators from the analysis, dE, with recommended values: • γx = 1.2 in buildings; • γIS= 1.5 in bridges. dE,a = (γx or γIS) dE
PROTA
Verifications – “Full isolation” Superstructure: Verified at the ULS for forces from the analysis reduced by (behavior factor) q=1.5 for overstrength - even for nonlinear time-history analysis.
Foundations & substructure: Verified at the ULS for forces from the analysis (reduction or behavior factor q=1), except for bridges, where the piers are designed in flexure for q=1.5 & detailed as "limited ductile“(but in shear, q=1).
No detailing for ductility (except in bridge piers) or capacity design Horiz. clearance between superstructure & surrounding elements dEd= dE+dG+0.5dT dG: due to permanent & quasi-permanent actions (shrinkage, creep) dT: due to design thermal actions.
Isolating system: Accommodate total displacement:
dEd= dE,a+dG+0.5dT [dE,a=(γx or γIS)dE ] Interstory drifts in buildings for “damage limitation” earthquake:
PROTA <0.5% for non-structural partitions, <1% if only structural frame.
Product Standards for the devices 1. EN 15129:2009 Antiseismic devices. 2. EN 1337-3:2005 Structural bearings - Part 3: Elastomeric bearings 3. EN 1337-2:2000 Structural bearings - Part 2: Sliding elements 4. etc. Specify: – functional requirements and design criteria for the devices (2 & 3: for non-seismic actions), – material characteristics, – manufacturing and conformity, – installation and maintenance requirements, – etc.
PROTA
Additional requirements in EN1998-2 for devices •
For elastomeric bearings: Shear strain in elastomer < 200% under resultant of horizontal displacements of bearing (SRSS or 1:0.3 combination for dE,x dE,y): dEd,x=γIS dE,x+dG,x+0.5dT,x, dEd,y= γISdE,y+dG,y+0.5dT,y
•
Restoring capability of isolation system: – Option 1: Design displacement at stiffness center of isolation system: dcd ≥ 0.5dr = 0.5F0/Kp
– Option 2: Displacement capacity of isolator: ≥dG+0.5dT+(γduρd)(γISdE)
γ du 1.20,
1 d y /d c d
0. 6
ρ d 1 1.35 1. 5 1 80d c d/d r
PROTA
dcd/dr
Factor for displacement capacity of isolator, against 80%-fractile accumulated residual displacements in sequence of earthquakes ρd
dy/dcd
dm ≥dG+0.5dT+(γISdEi)( γduρd)
ρ d 1 1.35
1 d y /d c d
0.6
1 80d c d/d r
1.5
γ d u 1.20
d /d PROTA cd
r
Application example to a bridge
http://www.aces.upatras.gr/node/191
PROTA
EXAMPLE: bridge with composite (steel-concrete) deck and seismic isolation Elevation
Piers - transverse section
Deck cross-section
Pier head & bearings
Piers in elevation
PROTA
Seismic design spectra – Ground Motions • Ordinary importance: γΙ=1.0 • High Seismicity: agR=0.40g , ag=γI agR = 0.40g • Ground Type B Horizontal spectrum S=1.2, TB=0.15s, TC=0.5s, TD=2.5s
Vertical spectrum S=1 avg=0.9ag, TB=0.05s, TC=0.15s, TD=1s
2.00
Average SRSS spectrum of ensemble of earthquakes 1.3 x Elastic spectrum
1.80
Spectral acceleration (g)
1.60
Damping 5%
1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00 0.0
0.5
1.0
1.5
2.0
2.5 3.0 Period (sec)
3.5
4.0
4.5
5.0
• 7 ground motion triplets (2 horizontal, one vertical component) • Artificial records by modulating historic ones to fit the spectra
PROTA
Plan layout and properties of isolators Y
:
C0_L
P1_L
P2_L
C3_L
C0_R
P1_R
P2_R
C3_R
Bearings with spherical sliding surface Two bearings per abutment, size 0.9m x 0.9m x 0.4m Two bearings per pier, size 1.2m x 1.2m x 0.4m μd = effective friction coefficient = 0.061 ± 16% = 0.051 - 0.071 R = effective radius =1.83m Dy = effective yield displacement = 0.005m
PROTA
X
Isolator Upper & Lower Bound Design Properties (UBDP, LBDP) Force at zero displacement F0/W - nominal value range: 0.061±16%=0.051~0.071 LBDP: (F0/W)min= minDPnom = 0.051 UBDP: per EN 1998-2 Annex J & JJ Minimum temperature for seismic design: Tmin,b=ψ2Tmin+ΔΤ1=0.5x(-20oC)+5oC
=-5oC (ψ2=0.5: combination factor for thermal actions, Tmin=-20oC: minimum shade air temperature @ site, ΔΤ1=5oC for composite deck) λmax factors: f1-ageing: λmax,f1=1.1 (Table JJ.1, for normal environment, unlubricated PTFE, protective seal) f2-temperature: λmax,f2=1.15 (Table JJ.2 for Tmin,b=-10oC, unlubric. PTFE) f3-contamination: λmax,f3=1.1 (Table JJ.3 – unlubr. PTFE, sliding surface facing both upwards & downwards) f4-cumulative travel λmax,f4=1 (Table JJ.4 - unlubr. PTFE , cum.travel ≤1km) Combination factor ψfi: ψfi=0.7 for Importance Class Ordinary (Table J.2) Combination value of λmax factors: λU,fi=1+(λmax,fi-1)ψfi f1 - ageing: λU,f1=1+(1.1-1)x0.7=1.07 f2 - temperature: λU,f2=1+(1.15-1)x0.7=1.105 f3 - contamination λU,f3 =1+(1.1-1)x0.7=1.07 f4 - cumulative travel λU,f4=1+(1.0-1)x0.7=1.0 Effective UBDP: UBDP =maxDPnomλU,f1λU,f2λU,f3λU,f4: (F0/W)max=0.071x1.07x1.105x1.07x1=0.09
PROTA
Fundamental Mode analysis with LBDP - 1st iteration Weight: W= 36751kN Assumed value for design displacement: dcd=0.15m
Effective Stiffness of Isolation System (ignoring the piers):
Keff=F/dcd=W(F0/W+dcd/R)/dcd=36751x(0.051+0.15/1.83]/0.15=32578kN/m Effective period of Isolation System:
Teff 2π
Dissipated energy per cycle:
m 36751/9.81 2π 2.13 s K eff 32578
ED=4W(F0/W)(dcd-dy)= 4x36751kNx(0.051)x(0.15-0.005)=1087kNm Effective damping: ξeff=ΣED,i/(2πKeffdcd2)=1087/(2π x 32578 x 0.152)=0.236 η=√[0.1 /(0.05+ξeff)]=0.591 Design displacement dcd dcd=(0.625/π2)agSηTeffTC= (0.625/π2)x(0.4x9.81)x1.2x0.591x2.13x0.5=0.188m Check assumed displacement Assumed displacement 0.15m; Calculated 0.188m Another iteration
PROTA
Fundamental Mode analysis with LBDP – 2nd iteration
Assume new value for design displacement: dcd=0.22m
Effective Stiffness of Isolation System:
Keff=F/dcd=W(F0/W+dcd/R)/dcd=36751x(0.051+0.22/1.83)/0.22=28602kN/m Effective period of Isolation System:
Teff 2π
Dissipated energy per cycle:
m 36751/9.81 2π 2.27 s K eff 28602
ED=4W(F0/W)(dcd-dy)= 4x36751kNx(0.051)x(0.22-0.005)=1612kNm Effective damping: ξeff=ΣED,i/(2πKeffdcd2)=1612/(2π x 28602 x 0.222)=0.185 η=√[0.1 /(0.05+ξeff)]=0.652 Design displacement dcd dcd=(0.625/π2)agSηTeffTC= (0.625/π2)x(0.4x9.81)x1.2x0.652x2.27x0.5=0.22m Converged. Spectral acceleration Se Se=2.5(TC/Teff)ηagS=2.5x(0.5/2.27)x 0.652x0.4x1.2= 0.172g Seismic shear force Vd=Keff dcd=28602x0.22=6292kN
PROTA
Fundamental Mode analysis with UBDP – Final results Assumed design displacement: dcd=0.14m Effective Stiffness of Isolation System:
Keff=F/dcd=W(F0/W+dcd/R)/dcd=36751x(0.09+0.14/1.83)/0.14=43708kN/m Effective period of Isolation System:
Teff 2π
Dissipated energy per cycle:
m 36751/9.81 2π 1.84 s K eff 43708
ED=4W(F0/W)(dcd-dy)= 4x36751kNx(0.09)x(0.14-0.005)=1799kNm Effective damping: ξeff=ΣED,i/(2πKeffdcd2)=1799/(2π x 43708 x 0.142)=0.33 η=√[0.1 /(0.05+ξeff)]=0.512 Design displacement dcd dcd=(0.625/π2)agSηTeffTC= (0.625/π2)x(0.4x9.81)x1.2x0.512x1.84x0.5=0.14m Convergence. Spectral acceleration Se Se=2.5(TC/Teff)ηagS=2.5x(0.5/1.84)x 0.512x0.4x1.2= 0.166g Seismic shear force Vd=Keff dcd=43708x0.14=6119kN, Per abutment: Vd= 569kN; per pier: Vd= 2479kN
PROTA
Non-linear time-history analysis
PROTA
0 -2000.000
0.100
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PROTA
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EQ5
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Force (KN)
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EQ3
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0 0.000 -200
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300 200 100 0 -1000.000 0.050 0.100 0.150 0.200 -0.200 -0.150 -0.100 -0.050 -200 -300 Displ. (m) -400
-0.300
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Direction Y
400 300 200 100 0 -0.200 -0.150 -0.100 -0.050-1000.000 -200 -300 -400
Force (KN)
-0.300
0 -0.100 0.000 -200
0.050
-400 500 400 300 200 100 0 -1000.000 -200 -300
Force (KN)
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EQ2
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0 -0.100 0.000 -200
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Force (KN) Force (KN)
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EQ1
400
400
Force (KN)
EQ7
-0.300
-400
-0.300
0.300
UBDP
Direction X
600
Force (KN)
EQ6
0.200
600
-0.200
Direction Y
200
Force (KN)
EQ5
-0.300
0.100
Force (KN)
EQ4
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EQ3
-0.200
Force (KN)
EQ2
LBDP
Direction X
400 300 200 100 0 -1000.000 -200 -300 -400
Force (KN)
EQ1
Hysteresis loops for abutment bearing, time-history analysis
0.150
Displ. (m)
600 400 200
0 -0.200 -0.150 -0.100 -0.050 0.000 -200
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EQ6
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0 -5000.000
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1500 1000 500 0 -0.250 -0.200 -0.150 -0.100 -0.050-5000.000 -1000 0.100 0.150 -1500 Displ. (m) -2000
EQ5
500 0 -0.050 0.000 -500
Displ. (m)
1500
Displ. (m)
1000
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1000
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0.200 -0.100
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2000 1500 1000 500 0 -500 -0.100 0.000 -1000 -1500 -2000
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EQ4
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0.100
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Force (KN)
500
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500 0.100
1500 1000 500 0 -0.200 -0.150 -0.100 -0.050-5000.000 0.200 -1000 -1500 Displ. (m) -2000
EQ3
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0.300 -0.200
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1500
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0 -0.200 -0.150 -0.100 -0.050 0.000 0.050 0.100 0.150 0.200 -500
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UBDP
-1500
Displ. (m)
-1500
PROTA Force (KN)
Displ. (m)
-1500
0.100
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Direction Y
Force (KN)
-0.200
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1500 EQ1 1000 500 0 -0.200 -0.150 -0.100 -0.050-5000.000 -1000 0.200 0.300 -1500 Displ. (m) -2000
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EQ7
0.200
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EQ6
0.100
2000 1500 1000 500 0 -0.100 -5000.000 -1000 -1500
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EQ5
0 -5000.000
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EQ4
-0.100
Direction X
LBDP
500
Force (KN)
EQ3
-0.200
Direction Y
1000
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EQ2
Direction X
1500
Force (KN)
EQ1
Hysteresis loops for abutment bearing, time-history analysis
0.050
0.100
1500 1000 500
0 -0.200 -0.150 -0.100 -0.050-5000.000
0.050
0.100
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-1000 Displ. (m)
-1500
Displ. (m)
Global seismic action effects - check of 80% lower limit Mean peak action effects from t-history LBDP analyses (design displacement dcd, seismic shear force Vd):
Peak displacement in X: dcdx = 193 mm (concurrent dcdy =63 mm) Peak displacement in Y: dcdy = 207 mm (concurrent dcdy =57 mm) Peak seismic shear in X: Vdx = 6929 kN. Peak seismic shear in Y: Vdy = 6652 kN.
Action effects from t-history analysis ≥ 80% of Fundamental Mode results ? Displacement in X: dcdx/dfx =193/220=0.88 >0.8 OK. Displacement in Y: dcdy/dfy =207/220=0.94 >0.8 OK. Total shear in X: Vdx/Vfx =6929/6292=1.10 >0.8 OK. Total shear in Y: Vdy/Vfy =6652/6292=1.06 >0.8 OK.
PROTA
Displacement demand on isolators: dEd=dE,a+dG+0.5dT o o
• Design uniform ΔΤ: –45 C/+55 C. • Fixed point of thermal expansion/contraction at one pier: • Expansion/contraction LT: 140 m for abutments, 80 m for pier bearings. • Thermal movement 0.5dT at pier (+ towards abutment, - towards bridge center): • 0.5LTαΔΤ=0.5×80000×1.0×10–5×(-45) or ×(+55)= -18 mm or 22 mm • 0.5dT at the abutments: • 0.5LTαΔΤ=0.5×140000×1.0×10–5×(-45) or ×(+55)= -31.5 mm or 38.5 mm • Displacements dG due to (quasi-)permanent actions (shrinkage, creep): • At the piers: -3 mm • At the abutments: -8 mm • Offset displacements dG+0.5dT at the piers: • Towards bridge center: -3-18=-21 mm • Towards abutments: +22 mm • dG+0.5dT at abutments: • Towards bridge center: -8-31.5=-39.5 mm • Towards abutment: +38.5 mm Total resultant displacement for combined components - LBDP analysis: Longitudinal, pier bearings: dm =√[(1.5x193+22)2+(1.5x63)2] = 325 mm Longitudinal, abutment units: dm =√[(1.5x193+39.5)2+(1.5x63)2] =342mm Transverse, pier bearings: dm =√[(1.5x57+22)2+(1.5x207)2] = 329 mm Transverse, abutment units: dm =√[(1.5x57+39.5)2+(1.5x207)2] = 335 mm
PROTA
Restoring capability of isolation system Ratio dcd/dr ≥ 0.5 ?
Maximum static residual displacement dr=F0/Kp
Post-elastic stiffness Kp =W/R
dr=F0/Kp=Wx(F0/W)/(W/R)=(F0/W)xR
Longitudinal direction - LBDP: dcd/dr=0.193/(0.051x1.83)=2.07>0.5.
Transverse direction - LBDP: dcd/dr=0.207/(0.051x1.83)=2.22>0.5.
Longitudinal direction - UBDP: dcd/dr=0.149/(0.09x1.83)=0.90>0.5.
Transverse direction - UBDP: dcd/dr=0.138/(0.09x1.83)=0.84>0.5.
UBDP more unfavorable, as dr larger and dcd smaller. Sufficient restoring capability without increasing the displacement capability of devices
PROTA
Thank you !
PROTA
