seismic analysis of bridges part i

Lezione n°26 Università degli Studi Roma Tre – Dipartimento di IngegneriaCorso di Teoria e Progetto di Ponti – A/A 2013-2014 - Dott. Ing. Fabrizio Paolacci

Seismic analysis of BridgesPart I


IntroductionThe evaluation of the risk associated to the seismic vulnerability of the transportation infrastructure, and in particular to that of bridge structures has been the object of quite large number of researches. This has stimulated the authorities to think about a code expressly dedicated to bridges. In Italy, two are the seismic events in which bridges suffered important damages

• Friuli Earthquake (1976) with limited damages have been observed in the bridges

• Irpinia Earthquake (1980) the bridges on the Highway A16 suffered some damages, essentially due to inadequacy of the bearing devices, which has been changed with isolation devices


Introduction

Loma Prieta Earthquake 1989Cypress viaduct

3

A proper seismic design have to start from the analysis of the behaviour of the structures during seismic events. Typical observed dameges are:

Kobe Earthquake 1995Nishinomiya-ko

Insufficient length of the supportsPounding between adjacent spansInsufficient design of the bearings


Introduction

Loma Prieta Earthquake 1989Cypress viaduct

4


Kobe Earthquake 1995Nishinomiya-ko

Insufficient length of the supportsPounding between adjacent spansInsufficient design of the bearings


Introduction

5


Insufficient length of the supportsPounding between adjacent spansInsufficient design of the bearingsInsufficient design of piers

Higashi-Kobe

San Fernando Earthquake 1971


IntroductionThe damages of the piers are often due to the lack of ductility and/or shear strength of the sections

Gothic Avenue Viaduct, Northdridge

1994

Gothic Avenue Viaduct

Wushi viaductChi-Chi, Taiwan 1999


Introduction

Shinkansen Viaduct Kobe, 1995

The damages of the piers are often due to the lack of ductility and/or shear strength of the sections


Introduction

Urban Viaduct Hanshin, Kobe1995

Example of complete collapse


Seismic codesIn Europe the Eurocodes system includes a normative document for the seismic design of new bridges, which is at least partially based on the recent concepts of performance-based design: Eurocode 8 Part 2. For the existing structures there is the Eurocode 8 part 3 that regards only existing buildings.

In Italy two main documents regards design of new bridges

OPCM 3441

NTC 2008

Within a wide research program funded by RELUIS and in particular from the research line 3 (existing bridges) new guidelines of existing bridges has been proposed.


Seismic codesThe philosophy of the new seismic codes includes the definition of performance levels mainly related to the importance of the structure (performance-based design)

The safety requirements and the limit statesDefinition of the seismic input:

Elastic SpectraNatural records and artificially generated accelerograms) - Scaling and combination rules

Evaluation of the safety levelStructural modelsAnalysis Methods (linear and non-linear static and dynamic analysis)Evaluation of the members capacityVerification Format


Safety requirements and Limit States


Safety requirements and LSThe safety (protection level) is defined for a specific limit state for a given seismic level intensity characterized by a probability of occurrence PVR in a given time (Nominal Life VR).

The nominal life depends on the type of construction (provisional, ordinary, strategic)

The probability of occurrence is defined by the Return Period TR

R

R

R

TV

V eP

1


Safety requirements and LS

R

R

R

TV

V eP

1

Distribution of the number of earthquakes (x)in a given interval of time t (Poisson distribution)

Probability of occurance of an earthquake with intensity S < Sa

is mean rate of occurrence of the events (probability of occurrence in the unit time) and is equal to the inverse of the arrival time Tr = 1/ Tr

tn

e!nt)Saa|nN(P

tTRe)SaS|N(P)SaS(P1

0

tTRe)SaS(P1

1

Probability of occurrence of an earthquake with intensity S > Sa is the complementary probability


Safety requirements and LS: Return Period

R

R

R

TV

V eP

1

Comment:

This determinist approach contains actually the random nature of the earthquake. The most probable earthquake it considered


Safety requirements and LS: Limit States

ULS SLSFEMA 356


Safety requirements and LS : Limit States

For non-strategic bridges only the Life Safety or Collapse prevention have to be verified, whereas for strategic bridges the SLD o SLO have also to be taken into account

Operational level

FEMA 356


Safety requirements and LS : Limit States

NTC08


Safety requirements and LS : Limit StatesEN1998:1In EN1998:1 only 3 limit states are required

(the operational level is missed)


Safety requirements and LSEvaluation of the return period of bridges following NTC08:

Tipo di costruzione Vita nominale (anni) Opere provvisorie, fasi di costruzione ≤ 10 Opere ordinarie ≥ 50 Opere strategiche ≥ 100

Limit state PVR

Stati limite di Esercizio SLE SLO (operatività) 81% SLD (danno) 63%

Stati limite Ultimi SLU SLV (salvaguardia della vita) 10% SLC (collasso) 5%

RVRR PlnVT 1

NUR VCV

(Return Period)


Safety requirements and LS


Safety requirements and LSExample 1: return Period calculation

Evaluation of the return period of an ordinary bridge, for the SLV limit state (Life Safety) following NTC08:

Nominal life: Vn> 50 Years (ordinary bridge)class: II VR = CU Vn = 1 x 50 = 50 yearsProbability of occurrence : Pr = 10% Tr = - 50 / ln0.9 = 475 years

Example 2: return Period calculation

Evaluation of the return period of a strategic bridge, for the SLD and SLV limit states

Nominal life: Vn> 100 Years (strategic bridge)class: IV VR = CU Vn = 2 x 100 = 200 yearsSLV: Probability of excedence: Pr = 10% Tr = -200/ln0.9=1898 yearsSLD: Probability of excedence: Pr = 63% Tr = -200/ln0.37=201 years


Seismic Input


Seismic Input : response spectra Lo spettro di risposta

Per il progetto di una struttura soggetta ad un terremoto, generalmente non è necessario conoscere l’intera storia temporale della forza Fs, quanto piuttosto il suo valore massimo. Ciò è possibile costruendo degli Spettri di Risposta elastici. Uno spettro elastico è definito come quel diagramma che in funzione del periodo proprio della struttura e dello smorzamento, fornisce il valore massimo di uno dei parametri della risposta dell’oscillatore elementare.

Spettro di risposta in pseudo-accelerazione


Seismic Input : response spectra

La costruzione di uno spettro di risposta ad un determinato terremoto, può essere facilmente effettuata calcolando per la risposta massima di un oscillatore elementare al variare del periodo proprio e dello smorzamento.

xg

k1

mm

mm

mk2

k3

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.5 1 1.5 2 2.5 3

PSa

T (sec)

TCU120STURNO270

OPCM1OPCM2

ARC090DCZ180

Lo spettro di risposta


Seismic Input : response spectra Lo spettro di risposta: Caratteristiche

• per T=0 (strutture rigide) Sa è pari all’accelerazione sul terreno

• Per T= (strutture flessibili) Sa è nulla• Esiste una zona entro la quale Sa

subisce un amplificazione che in rapporto all’acc. sul terreno può variare tra 2 e 3

• All’aumentare dello smorzamento l’amplificazione dimunuisce

• per T=0 (strutture rigide) lo spostamento Sd è nullo

• Per T= (strutture flessibili) lo spostamento Sd è pari allo spostamento sul terreno

• Esiste una zona entro la quale lo spostamento subisce un amplificazione

• All’aumentare dello smorzamento l’amplificazione dimunuisce


Seismic Input : response spectraUsually the seismic intensity is defined starting from the seismic hazard of the site in which the bridge has been built, expressed in terms of response spectrum.

Horizontal spectra (EC8)

ag = agR, S=soil factor, =damping correction factor

Importance factor

Hazard

(EN1998-1: General rules, seismic actions and rules for buildings)


Seismic Input : response spectra(EN1998-1: General rules, seismic actions and rules for buildings)



Ground Types



Importance classes

Description I

I Low importance 0.85

II Normal importance 1

IIIcomprises bridges of critical importance for maintaining communications, especially in the immediate post-earthquake period

1.3

IMPORTANCE FACTOR FOR BRIDGES (SUGGESTED VALUES)


Seismic Input : response spectra(NTC 08)

TSg SSa

0FSSa TSg

BBTSg T

TFT

TFSSa 11

00

TTFSSa C

TSg 0

20 TTTFSSa DC

TSg

55.0510

3.2.VI tabelladalla 3.2.V tabelladalla ,

1 tabellaall.B da ,, *0

T

cS

Cg

SCS

TFa

*CCC TCT

3CB TT 6.10.4 gaT gD

TSg SSa

0FSSa TSg

BBTSg T

TFT

TFSSa 11

00

TTFSSa C

TSg 0

20 TTTFSSa DC

TSg

55.0510

3.2.VI tabelladalla 3.2.V tabelladalla ,

1 tabellaall.B da ,, *0

T

cS

Cg

SCS

TFa

*CCC TCT

3CB TT 6.10.4 gaT gD

T

Sa

The parameters of the elastic spectra are defined according to seismic hazard defined in terms of return period, which if function of the adopted performance level. The return period is defined with reference to a very refined grid (10 km x 10 km )

N.B.: the importance factor is not explicitally defined but is included in the definition of the importance classes

Elastic spectrum


Seismic Input : response spectra(NTC 08)

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,0 1,0 2,0 3,0 4,0

Periodo T (s)

Sa (g

)

Ponte ordinario (Vr = 50, Tr=475)

Ponte strategico (Vr = 200, Tr = 1828)

Barberino del Mugello, Italy


Seismic Input: response spectra(NTC 08)

In order to verify the bridge supports or the application of the displacement-based design approach, elastic spectrum of displacements can be defined starting from the acceleration spectrum.

2

2

TTSe

DCTSgg TTSSad 025.0

CTBT DT ET sTF 10

0Fdg

gd

EF

Eg TT

TTFFd 00 1DeS

2

2

TTSe

DCTSgg TTSSad 025.0

CTBT DT ET sTF 10

0Fdg

gd

EF

Eg TT

TTFFd 00 1DeS

224TSS a

d

Displacement spectrum


Seismic Input : accelerograms(NTC 08)

For time-history analyses the base motion is represented by natural or artificially generated accelerograms. In any case the following coherence condition has to be respected:

• From EC8: “no value of the mean 5% damping elastic spectrum, calculated from all time histories, should be less than 90% of the corresponding value of the 5% damping elastic response spectrum”

For the artificially generated accelerograms additional conditions have to be respected:

• The duration of the accelerograms shall be consistent with the magnitude and the other relevant features of the seismic event

• The minimum duration Ts of the stationary part of the accelerograms should be equal to 10 s.

The minimum number of natural record is 10 and artificial accelerogram is 5


Seismic Input : accelerograms(NTC 08)


Seismic Input: accelerograms(NTC 08)

Evento Data Mag. Stazione Dist. (Km)

Filtro (Hz)

Sigla

Duzce, Turkey 12/ 11/ 99 7.1 1061 15.6 0.07 1061 Chi-Chi, Taiwan 20/ 09/ 99 7.6 CHY029 15.3 0.03 CHY029

Chi-Chi, Taiwan 20/ 09/ 99 7.6 TCU045 24.1 0.03 TCU045

Chi-Chi, Taiwan 20/ 09/ 99 7.6 TCU070 19.1 0.03 TCU070

Landers 28/ 06/ 92 7.3 23 Coolwater 21.2 0.1 CLW

Landers 28/ 06/ 92 7.3 12149 Desert Hot Springs 23.2 0.07 DSP

Cape Mendocino 25/ 04/ 92 7.1 89486 Fortuna 23.6 0.07 FOR

Northridge 17/ 01/ 94 6.7 90058 Sunland 17.7 0.05 GLE Northridge 17/ 01/ 94 6.7 24688 LA - UCLA 15.0 0.08 UCL Imperial Valley 15/ 10/ 79 6.5 6604 Cerro Prieto 26.5 0.1 H-CPE

0 2 4 6 8P erio d o (s)

0

0 .2

0 .4

0 .6

0 .8

1

Acc

eler

azio

ne (g

)

Target elastic spectrum

List of selected natural records(10 dir x +10 dir y)

An example of selection of natural records


Seismic Input: Combination(NTC 08, EN1998:1)

222dZdYdXd EEEE

dZdYdXd EEEE 3.0""3.0""0.1

SRSS method

100-30-30 method

In tridimensional problems, in order to get the maximum response quantities we need to combine the responses to the earthquakes in the all the three principal directions.For this purpose we can adopt two different formulas (only for elastic analysis. For non-linear analysis the maximum response in both directions is taken


Structural modeling


Structural ModelingMaterial models: concrete


Structural ModelingMaterial models: concrete – Kent & Park

Parabolic

Linear

Confinement parameters

sh


Structural ModelingMaterial models: concrete – Popovic - Mander

cc1cu1c

cE

secE

cf

ccf

cuc c

c

cc1cu1c

cE

secE

cf

ccf

cuc c

c

rcc

c

xrxr

f

1

cccx 1

secEEEr cc

ccccfE 1sec

cccc ff

254.1294.71254.2 c

e

c

ec ff

151002.01 ccc

For the definition of this constitutive law is enough to know strength fc and elastic modulus Ec, for non-confined concrete, and also the transversal geometrical percentage of reinforcement and the relative yielding fy

Confinementtension


Structural ModelingMaterial models: concrete – Popovic - Mander

Parameters governing the confinement tension

bc

hc

Dc


Structural ModelingMaterial models: Steel


Structural ModelingMaterial models: Steel – Menegotto Pinto Model

RRbb1

**** 11

rr 0*

rr 0*

210 aaRR

b

*

*

2

1

1

1

0R

2R

1R

b

*

*

2

1

1

1

0R

2R

1R

EP : used in monotonic static analysis

MP : used non-linear dynamic analysis


Structural ModelingStiffness of Elements

For the elements of the deck (beams, transverses, slabs, etc..) the stiffness is related to the no-cracked elastic behaviour of the sections

When linear or non-linear analysis with plastic hinges are used the stiffness of the piers has to be calculated using the characteristics of the cracked sections

y

Reffc

NMIE

MR (N) is the ultimate moment of the section calculated for a normal force due to the gravity load, usually calculated using the moment curvature relationship


Structural ModelingPlastic hinge models

Moment-Rotation

lp 0.1 H + yield penetration

The moment-rotation (M-) relationship in given to the column base and is relative to a limited part of the element length lp. It can be determined starting from the Moment-Curvature law (M-) of the base column section. After that it is enough to multiply it for the length lp. Usually the axial force is constant, especially for simply supported bridges. So it is not necessary to determine the Moment-Axial force interaction domain.


Structural ModelingFiber Models

The section is subdivided into several fibers along the principal directions. Applying the virtual work principal it is possible to express the stiffness K (displacement approach) or the flexibility F (force approach) matrix of the element. Today the force formulation is the most used because the shape functions are determined imposing equilibrium conditions, that are exactly.

(Spacone Filippou Taucer Earthquake Engineering and Structural Dynamic vol 27, 1996) )


Structural ModelingLevel of dynamic modeling


Analysis methods


Analysis methodsSimply supported deck bridges

7.5 m

50 m 50 m

2.0 m

2.0 m 0.5 m

MA Single DOF model can be usedTaking into account eventual eccentricities


Analysis methodsSimply supported deck bridges: Longitudinal direction


Analysis methodsSimply supported deck bridges: Transversal direction


Analysis methodsSuperposition Modal analysis: continuous deck bridges

Mode I Mode II Mode III

gx MIKXXCXM

1 23

Eigenvalue problem

MatrixStiffnessMatrixDamping

matrixmass

KCM

0KXXM tie ΦX 02 MK

Equation of Motion

02 MK Eigenvalues and Eigenvectors


Analysis methodsSuperposition Modal analysis: continuous deck bridges

Mode I Mode II Mode III

gx MIKXXCXM

gTTTT x MIYKYCYM

gTiiiiiii xyyy MI 22

n

ii y,11YX

Modal partecipation factor

1 23

seismic analysis of bridges part i

Documents

ponti aa

teoria e progetto

seismic events

kobe earthquake

seismic vulnerability

bridges irpinia earthquake

fabrizio paolacci5introduction

fabrizio paolacci6introduction