Brussels, 18-20 February 2008 Dissemination of information workshop 1 EUROCODE EN1998-2 SEISMIC DESIGN OF BRIDGES Basil Kolias
Basic Requirements Brussels, 18-20 February 2008 Dissemination of information workshop 2 Non-Collapse Retain structural strength + residual resistance for emergency traffic. Limit damage to areas of energy dissipation. Damage Minimization Under probable seismic effects.
Analysis Methods Brussels, 18-20 February 2008 Dissemination of information workshop 3 Equivalent Linear Analysis: Elastic force analysis (response spectrum) forces from unlimited elastic response divided by global behaviour factor = q. design spectrum = elastic spectrum / q
Analysis Methods Brussels, 18-20 February 2008 Dissemination of information workshop 4 Stiffness of Ductile Elements: secant stiffness at the theoretical yield Secant stiffness M y Yield of first bar
Analysis Methods Brussels, 18-20 February 2008 Dissemination of information workshop 5 Non-linear Dynamic Time-History Analysis: In combination with response spectrum analysis without relaxation of demands. For irregular bridges. For bridges with seismic isolation. Non-linear Static Analysis (Push-Over): For irregular bridges.
Seismic behaviour of bridges Brussels, 18-20 February 2008 Dissemination of information workshop 6 Ductility Classes Limited Ductile Behaviour: q 1.50 Ductile Behaviour: 1.50 < q 3.50
Compliance Criteria for Elastic Analysis Brussels, 18-20 February 2008 Dissemination of information workshop 7 Limited Ductile Behaviour: Section verification with seismic design effects A Ed Verification of non-ductile failure modes (shear and soil) with elastic effects qa Ed and reduction of resistance by γ Bd = 1.25
Compliance Criteria for Elastic Analysis Brussels, 18-20 February 2008 Dissemination of information workshop 8 Ductile Behaviour: Flexural resistance of plastic hinge regions with design seismic effects A Ed. All other regions and non-ductile failure modes (shear of elements & joints and soil) with capacity design effects A C. Local ductility ensured by special detailing rules (mainly confinement).
Compliance Criteria for Elastic Analysis Brussels, 18-20 February 2008 Dissemination of information workshop 9 Control of Displacements: Assessment of seismic displacement d E d E = ημ d d Ee. d Ee = result of elastic analysis. η = damping correction factor. μ d = displacement ductility as follows: when T T 0 =1.25T C : μ d = q when T<T 0 : μ d = (q-1)t 0 / T + 1 5q - 4
Compliance Criteria for Elastic Analysis Brussels, 18-20 February 2008 Dissemination of information workshop 10 Provision of adequate clearances for the total seismic design displacement: d Ed = d E + d G + 0.5d T d G due to permanent and quasi-permanent actions. d T due to thermal actions. For roadway joints: 40% d E and 50% d T
Compliance Criteria for Non-linear Analysis Brussels, 18-20 February 2008 Dissemination of information workshop 11 Chord rotation: θ = θ y + θ p L θ M L p Plastic hinge
Compliance Criteria for Non-linear Analysis Brussels, 18-20 February 2008 Dissemination of information workshop 12 Ductile Members: Deformation verification Plastic chord rotations of plastic hinges: demand design capacity θ p,e θ p,d, θ p,d = θ p,u / γ R,p, γ R,p = 1.40 θ p,u = probable (mean) capacity from tests or derived from ultimate curvatures
Compliance Criteria for Non-linear Analysis Brussels, 18-20 February 2008 Dissemination of information workshop 13 Non-ductile members: Force verification as in elastic analysis for regions outside plastic hinges and nonductile failure modes, with capacity design effects replaced by: γ R,Bd1 A Ed with γ R,Bd1 = 1.25 Design resistances: R d = R k / γ M
Seismic Action Brussels, 18-20 February 2008 Dissemination of information workshop 14 Two types of elastic response spectra: Type 1 and 2. 5 types of soil: A, B, C, D, E. 4 period ranges: short, constant acceleration, velocity and displacement. Design spectrum = elastic spectrum / q. 3 importance classes: γ I = 1.3, 1.0, 0.85.
Seismic Action Brussels, 18-20 February 2008 Dissemination of information workshop 15 Elastic Spectrum Type 1 (ξ = 0.05) Se/A g 4 3 2 E D C B A 1 0 T B T C 1 T D 3 (s)
Seismic Action: Spatial Variability Brussels, 18-20 February 2008 Dissemination of information workshop 16 Spatial variability model should account for: Propagation of seismic waves Loss of correlation due to reflections/refractions Modification of frequency content due to diff mechanical properties of foundation soil
Seismic Action: Spatial Variability Brussels, 18-20 February 2008 Dissemination of information workshop 17 Rigorous model in Inf. Annex D: Simplified method: Uniform support excitation + pseudostatic effects of two sets of displacement (A and B) imposed at supports. Sets A and B applied in the two principal horizontal directions but considered independently
Seismic Action: Spatial Variability Brussels, 18-20 February 2008 Dissemination of information workshop 18 Displacement sets defined from: d g = 0.025 a g ST C T D : max particle displ. corresponding to the ground type (EC8-1) L g is the distance beyond which seismic motion is completely uncorrelated Ground Type Recommended Values of L g (m) A B C D E L g (m) 600 500 400 300 500
Seismic Action: Spatial Variability Brussels, 18-20 February 2008 Dissemination of information workshop 19 Displacement set A uniform expansion/contraction displacement of support i relative to support 0 d ri = ε r L i d g 2 ε r = d 2 g L g
Seismic Action: Spatial Variability Brussels, 18-20 February 2008 Dissemination of information workshop 20 Displacement set B with opposite directions at adjacent piers d = ± Δ / 2 = ground type i d i Δ d = ±β ε L i r r av, i β r 0.5 1.0 same different
Regular / Irregular Bridges Brussels, 18-20 February 2008 Dissemination of information workshop 21 Criterion based on local required force reduction factors r i of the ductile members i : r i = qm Ed,i /M Rd,I = q x Seismic moment / Section resistance A bridge is considered regular when the irregularity index: ρ ir = max(r i ) / min( r i ) ρ 0 = 2 Piers contributing less than 20% of the average force are not considered
Regular / Irregular Bridges Brussels, 18-20 February 2008 Dissemination of information workshop 22 For regular bridges: equivalent elastic analysis is allowed with the q-values specified, without checking of local ductility demands Irregular bridges are: either designed with reduced behaviour factor: q r = q ρ o / ρ ir 1.0 or verified by non-linear static (pushover) or dynamic analysis
Capacity Design Effects Brussels, 18-20 February 2008 Dissemination of information workshop 23 Correspond to the section forces under permanent loads and a seismic action creating the assumed pattern of plastic hinges, where the flexural overstrength: M o = γ o M Rd has developed with: γ o = 1.35 Simplifications satisfying the equilibrium conditions are allowed.
Detailing Rules Brussels, 18-20 February 2008 Dissemination of information workshop 24 Confinement reinforcement Increasing with: Normalised axial force: η k = N Ed / (A c f ck ). Axial reinforcement ratio ρ (for ρ > 0.01). Not required for hollow sections with: η k 0.20 and restrained reinforcement. Rectangular hoops and crossties or Circular hoops or spirals or overlapping spirals
Detailing Rules Brussels, 18-20 February 2008 Dissemination of information workshop 25 Restraining of axial reinforcement against buckling max support spacing: s L δø L 5 δ = 2,5 (f t / f y ) + 2,25 6 minimum amount of transverse ties: A t /s T = Σ A s f ys /1,6f yt (mm 2 /m)
Detailing Rules Brussels, 18-20 February 2008 Dissemination of information workshop 26 Hollow piers In the region of the plastic hinges Limitation of wall slenderness ratio: b / t or D / t 8 Pile foundations Rules for the location and required confinement of probable plastic hinges
Detailing Rules Brussels, 18-20 February 2008 Dissemination of information workshop 27 Bearings and seismic links. Holding down devices. Shock transmission units (STU). Min. overlap lengths at movable supports. Abutments and retaining walls. Culverts with large overburden. γ s /2 γ s /2 γ s = v g /v s
Bridges with Seismic Isolation Brussels, 18-20 February 2008 Dissemination of information workshop 28 The isolating system arranged over the isolation interface reduces the seismic response by: either lengthening of the fundamental period. or increasing of the damping. or (preferably) by combination of both effects.
Bridges with Seismic Isolation Brussels, 18-20 February 2008 Dissemination of information workshop 29 Design properties of the isolating system Nominal design properties (NDP) assessed by prototype tests, confirming the range accepted by the Designer. Design is required for: Upper Bound design properties (UBDP). Lower Bound design properties (LBDP). Bounds of Design Properties result either from tests or from modification factors.
Bridges with Seismic Isolation Brussels, 18-20 February 2008 Dissemination of information workshop 30 Analysis methods Fundamental or multi mode spectrum analysis (subject to specific conditions). Non-linear time-history analysis.
Bridges with Seismic Isolation Brussels, 18-20 February 2008 Dissemination of information workshop 31 Substructure Design for limited ductile behaviour: q 1.50
Bridges with Seismic Isolation Brussels, 18-20 February 2008 Dissemination of information workshop 32 Compliance criteria Isolating system Displacements increased by factor: γ IS = 1.50 Sufficient lateral rigidity under service conditions is required.
Bridges with Seismic Isolation Brussels, 18-20 February 2008 Dissemination of information workshop 33 Lateral restoring capability (revision) Governing parameter: d cd /d r d cd = design displacement d r =F 0 /K p = maximum residual displ. Force F 0 d r d r K p Displ. Condition (1): insignificant residual displ.: Or Condition (2): adequate capacity for accumulated residual displ.: dmi do,i + γ du d bi, d ρ d 1 ρd = 1+ 1.35 1+ 80 ( d / d ) y ( d / d ) 1. 5 cd cd r 0.6 dcd δ dr δ = 0.5 γ du = 1.20
Bridges with Seismic Isolation Brussels, 18-20 February 2008 Dissemination of information workshop 34 Lateral restoring capability
Seismic Deformation Capacity of Piers Brussels, 18-20 February 2008 Dissemination of information workshop 35 Ultimate Displacement Monotonic Loading F Rd < - 0.2F 5th cycle Rd d y d u
Deformation Capacity of Piers Brussels, 18-20 February 2008 Dissemination of information workshop 36 Chord rotation θ u = θ y + θ p Plastic chord rotation θ p derived: Directly from appropriate tests From the curvature, by integration
Deformation Capacity of Piers Brussels, 18-20 February 2008 Dissemination of information workshop 37 Ultimate curvature: Φ u = ε su ε d cu Reinforcement: ε su = 0.075 (EN1992-1-1) Unconfined concrete: ε cu = -0.0035 (EN1992-1-1) Confined concrete: εcu,c = 0.004 1.4ρ s f ym ε su f cm,c
Deformation Capacity of Piers Brussels, 18-20 February 2008 Dissemination of information workshop 38 Mean material properties Reinforcement f ym /f yk = 1.15, f sm / f sk = 1.20, ε su = ε uk Concrete f cm = f ck + 8 (MPa), E cm = 22(f cm /10) 0.3 Stress-strain diagram of concrete Unconfined concrete: ε c1 = -0.0007f cm 0.31
Deformation Capacity of Piers Brussels, 18-20 February 2008 Dissemination of information workshop 39 Confined concrete - Mander model f cm,c f cm Unconfined concrete Confined concrete E cm E sec ε c1 ε cu1 ε c1,c ε cu,c c
Deformation Capacity of Piers Brussels, 18-20 February 2008 Dissemination of information workshop 40 Chord rotation: θ u = θ y + θ p,u θ p,u = (Φ u Φ y )L p (1 L p 2L ) F Rd L θ Φ u Φ y L p M L p Plastic hinge
Deformation Capacity of Piers Brussels, 18-20 February 2008 Dissemination of information workshop 41 100000 90000 80000 ρ=4% First yield of confined concrete Confined concrete reaches peak stress Confined concrete fails First yield of longitudinal steel Longitudinal steel fails Moment X (knm) M u 70000 60000 M50000 Rd 40000 ρ=3% ρ=2% Φ y ε sy = 2.1 d 30000 20000 ρ=1% Y 10000 X 0 Φ y 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 Curvature (1/m)
Deformation Capacity of Piers Brussels, 18-20 February 2008 Dissemination of information workshop 42 Calibration with test results Database: 64 tests on R/C pier elements. 31 circular, 25 rectangular, 8 box sections Curvature analysis for each test specimen Non-linear regression for the coefficients of: L p = 0.10L + 0.015f yk d s
12 10 θp,exp/θp,prd No of exp. : 64 Average : 1.09 St. Dev.: 0.18 θ p,exp =1.09 θ p,prd Predicted θ p 8 6 4 2 5% fract. (S.F.=1.25) S.F.=1.40 0 0 2 4 6 8 10 12 Experimental θ p (%)
Non-linear Static Analysis Brussels, 18-20 February 2008 Dissemination of information workshop 44 Based on the equal displacements rule Analysis directions: x: Longitudinal y: Transverse
Non-linear Static Analysis Brussels, 18-20 February 2008 Dissemination of information workshop 45 Horizontal load increased until the displacement at the reference point reaches the design seismic displacement of elastic response spectrum analysis (q = 1), for Ex + 0.3Ey and Ey + 0.3Ex Reference point is the centre of mass of the deformed deck
Non-linear Static Analysis Brussels, 18-20 February 2008 Dissemination of information workshop 46 Load distribution Load increment at point i at step j ΔF i,j = Δα j G i ζ i distribution constant along the deck: ζ i = 1 distribution proportional to first mode shape
Brussels, 18-20 February 2008 Dissemination of information workshop 47 Thank you!!!