Performance-based design and assessment of critical

Performance-based design and assessment of critical facilities considering soil-structure interaction

Anastasios SextosProfessor of Earthquake Engineering

Length: 850m (left branch), 640 (right branch) Deck: continuous, box-shaped, prestressed concrete

Curvature: 450m radius (the larger curved bridge in Greece) Number of spans: 10

Maximum pier heightConstruction method: Incremental launching

Foundation: piles

SSI: Large scale numerical modelling

Introduction

q Questionable accuracy

q Intensity or frequency

independent

q limited to the most common

scenarios

Analytical solution of the PDE equations

Direct FEM simulation

Simplified closed form

approximationsq Capable of simulating

complex behaviorq High Computational

Cost

Kwon et al (2008)

Seismic Reliability-Based Design Optimization

Fragility assessment of structures

Presence of soil can have a detrimental impact on the behaviour of a structure.

Khatibinia et al (2015)

FEM method non viable under the framework of:

SSI: Analytical LPM modelling

Direct FEM simulation

Model Order Reduction

computationally viable

q Global Stability IssuesqLimited to Viscous-Elastic Systems

us usReduction of sub soil domain through internal DOF elimination in the

frequency domain

Finite element formulation

Lumped Parameter (LP) modeling Method

Dyn

amic

Stif

fnes

s

Frequency (Hz)

Target IF Real PartTarget IF Imag PartLP approximation Real PartLP approximation Imag Part

Lesgidis, N., Sextos, A.G. and Kwon, O.-S. (2018) “A frequency- and intensity-dependent macroelement for reduced order soil-structure interaction analysis”, Earthquake Engineering and Structural Dynamics (available online, DOI: 10.1002/eqe.3063).

https://rdcu.be/R3Wq

Stability issues in LP method

( ) ( )( )

( ) ( )( ) ( )NNo

NNo

LPLPLPsqsqqspsppS

sQsPSsS

×++×+

×++×+×=×=

++

!

!

1

111

0,0,

LP model represented as a polynomial fraction in the frequency domain:

Polynomial coefficients calibrated for:

Translation to an ODE system (decomposition of polynomial fraction and term by termtranslation to physical components):

Sufficient condition to emulate the Steady state behavior. It will not necessarily lead to an ODE system with stable complementary solutions.

( ) ( )sSsS tarLP =

( ) ( )ååå-+

=

-+

== ÷øöç

èæ +-

-+

÷øöç

èæ +-

-+

-==

2/1

22

2/1

221)(

)( MN

Mi ii

i

i

iMN

Mi ii

M

i i

i

s

q

s

srsq

sQsP

ba

bb

a

ba

a ii

Example of 1st

order term:Example of 2nd

order term:

Use of a predefined LPmodel:

Restriction of usedcomponents on positiveregion through boundconstraints in thecalibration process.

Bridge deck

SLP,ry

SLP,gy

SLP,gx-cx

SLP,gx

SLP,gx-x

SLP,gy-y

Expansion joint gap δy

Bearing Connection System

SLP,z

SLP,cx

SLP,cy

SLP,y

SLP,rx

Expansion joint gap δx

Bearing located after

the gap

SLP,rz

SLP,x

Pier base region:

Abutment-Embankment region:

6x6 dynamic stiffness matrix

9x9 dynamicstiffness matrix

Proposed Stable LP method

Frequency-dependent SSI effect on system fragility

Case Study: investigation of the impact of frequency dependence for different bridge SSI configurations in their fragility.

Pedini Overpass: Bridge PropertiesOverall length 78

Span Arrangement 19.00m -32.00m -19.00m Deck Section box girder, non prismatic

Piers(P1,P2) solid circular section, height : 8.50 m

Abutments ( A1,A2) laying on PTFE pot bearings

Different soil

ScenariosSoil type

S1 Soft ClayS2 Loose SandS3 Medium ClayS4 Medium SandS5 Hard Clay

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2

Spec

tral

acc

elar

atio

n/Pg

a

Period T ( sec)

mean Responsespectrummean ± standardDeviation

a/v <0.8

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2

Spec

tral

acc

elar

atio

n/Pg

a

Period T ( sec)

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5 1 1.5 2

Spec

tral

acc

elar

atio

n/Pg

a

Period T ( sec)

0.8<a/v <1.2 1.2<a/v

Excitation sets based on the frequency content:

8

FE Modeling

Pier: Reinforced concrete Fiber Model

Pier interface Region: (a) Kelvin Voigt Assembly (b) LP model Assembly

interface node P1

interface node A1

Interface node A2

Interface node A3

Interface node A4

Pot Bearing: Velocity dependent friction model

Seismic Isolation: Non linear Gap Model

Abutment interface Region: (a) Kelvin Voigt Assembly (b) LP model Assembly

Transverse interface Node

A2 (y)

longitudinal interface Node

A4 (x)

Transverse interface

Node A1 (y)

interface Node A3

(x,y,z,rx,ry,rz) Young Modulus Distribution

60 m

37.1 m

FEM model in OpenSees.

Extraction of dynamic

Impedance functions from

FEM model formulation.

9

Error induced when neglecting frequency-dependence

(a)

m

LS1 -Serviceability

LS3 – Collapse prevention

(b)

m

(c)

m

LS2 – Damage control

Percentage error in probability of reaching threshold limit states:

10

Inelastic LP modeling method

Selection and extraction of representative properties of target dynamic system:

Extraction of Dynamic stiffness matrix for selected variable states in

inelastic range

Extraction of dynamic returning force matrix for selected variable

states in inelastic range

Complementary Component:(M.1): Externally controlled Spring

(M.2):Conventional spring

Base Component:Macroelement

Complementary Component:Conventional Mass

Complementary Component:Conventional Dashpot

( ) compbasebasecompcomp uukF !! ×= ,α

( )nbasebasen

obasebase

n

o

basebasecomp

uif

Unloadingoruif

k

kuk

cαc

cαα

<<

<

ïî

ïí

ì=

T-

T

][

][

,1

,

, !

Frequency- and intensity- dependent LPMs


Lesgidis, N., Sextos, A.G. and Kwon, O.-S. (2018) “A frequency- and intensity-dependent macroelement for reduced order soil-structure interaction analysis”, Earthquake Engineering and Structural Dynamics

-650

-450

-250

-50

150

350

-0.0012 -0.0007 -0.0002 0.0003

Mom

ent M

y (KN

m)

rotation θ (rad)

Fo=800KN

FxMy

Fo

Verification example

d = 1.6m

H=50m

L=6 m

Soil Propeties:fy=100 MPav=0.409E=169090 MPaHo=20000

xm !!×

Sample of Dynamic Properties in the Frequency domain:

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14

Dyn

amic

Stif

fnes

s Kx

Rea

l Par

t (K

N/m

)

Frequency (Hz)

Simp. LP method (M.2) vs.2-vs.9Complete LP method (M.1) vs.2-vs.9FEM solution vs.2-vs.9Simp. LP method (M.2) vs.1Complete LP method (M.1) vs.1FEM solution vs.1

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14

Dyn

amic

Stif

fnes

s K

x Im

ag P

art (

KN

/m)

Frequency (Hz)

Static Properties Calibration:

-450.0

-350.0

-250.0

-150.0

-50.0

50.0

150.0

250.0

350.0

450.0

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Mom

ent a

t Fou

ndati

on (K

Nm)

Foundation Rotation (mrad)

-80.0

-60.0

-40.0

-20.0

0.0

20.0

40.0

60.0

80.0

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Hor

izon

tal F

orce

at F

ound

atio

n (K

N)

Foundation Displacement (mm)

FEM solutionComplete LP model (M.1)Simp. LP model (M.2)NL Macroelement

Model verification results:

13

High intensity dynamic response (F-d & d(t))

High intensity dynamic response (F-d & d(t))

15

BRAIS: Bridge Risk Assessment Integrated System

•Smooth automations to minimize the time required for pre-processing.

•Expert decision making at every step of the simulation and order reduction process.

•Computationally optimized stochastic sampling procedures for the assessment of the conditional probability failure.

•Ad-hoc developed 3D visualization engine that allows the inspection of the fragility assessment results.

16

Ground Motion Selection Module

Preliminary selection:

Final Selection:

• specific bridge structure (site faults properties

known- M and Re)

• portfolio representative bridge (site faults

properties generated by the system)

Development of greedy search algorithm with constrained scaling

17

Automated FE model construction module

Procedural knowledge Base

Element type selection rules

Mesh refinement selection rules

Constitutive law selection rules

reduced regions selection rules Damage state selection rules

User Interface

Inference Engine

bridge structuredescription

Pier i (a) elements type, (b) mesh Refinement, (c)

constitutive laws.(d)

Span i (a) elements type, (b) mesh Refinement, (c)

constitutive laws (d)

Interconnection regions , (a)Modelling approach (b)

constitutive laws

(a) Line fiber element(b) EDP selection(c) Mesh refinement (d) Constitutive laws

Box section overpass Bridge

(a) Line element(b) Mesh refinement

(a) Bearing model(b) Gap/bounce model(c) EDP selection

Modelling OptionsBridge Description by User

Flow chart of modelling expert system Architecture.

Illustration of Bridge description and Model

generated by the integrated System.

18

Order reduction moduleSuperstructure FEM model

Abutment “B” soil domain FEM model

Abutment “A” soil domain FEM model

Pier Foundation soil domain FEM model

Reduced orderLP models

Order reduction in accordance to previously presented LP methods.

Automated construction of FEM models of subsoil interface

regions.

19

Fragility assessment


-1.20E+00

-1.00E+00

-8.00E-01

-6.00E-01

-4.00E-01

-2.00E-01

0.00E+00

2.00E-01

5 5.2 5.4 5.6 5.8 6 6.2 6.4

Disp

lace

men

t (Nr

omal

ized)

Time (sec)

MeasurementsLP modelWinkler Model

Project objectives

• R&I project implemented via secondments

• Brain circulation between Europe, US, Canada; Academia and Industry

• Have a big structural effect in EU

• Shift from research culture to innovation culture

• Establish sustainable networking

Challenges

Limited EU & US design guidelines for construction and assessment of NG pipelines is seismic areas

• In Eurocodes there is no procedure prescribed as to mitigate seismic risk of NG pipelines

• No means for quick inspection and rehabilitation in case of an earthquake event.

• Guidelines too general (summarized in 4 pages)

• Wave-induced earthquake loading in 2 pages informative Annex based 1967 Newmark method

Challenges

Spatially variable earthquake induced displacements along the pipeline axis are ignored

• Seismic loading is not deemed critical for buried pipelines

• Deformations are not uniform along the pipe length

• (particularly for abruptly changing and/or liquefiable soil profiles)

• Analytical and experimental justification is required

Challenges

Soil-pipeline interaction modeling is simplified

• Only bi-linear, force-displacement relationships, similar to those adopted by

ALA(2001) document in the U.S. are most commonly used

• Challenge is to develop reliable cyclic force-deformation relationships for (a) axial,

(b) transverse horizontal and (c) transverse vertical springs

Challenges

Experimental verification of failure modes is very limited

• Need for reliable laboratory testing of soil-pipe systems

Cross-section distortion (e.g. section ovalization)

Local bucklingAxial strain-rupture

Upheal buckling

Challenges

Empirical fragility assessment of

natural gas pipelines

• Current fragility curves are empirical

based on the Repair Ratio

• Few works on local damage (tension

cracks; local buckling; beam buckling)

• No consideration of spatially variable

ground displacements and soil-pipeline

interaction

• Fragility expressions for the

Metering/Regulating stations linking the

High Pressure Natural Gas Transmission

System to the local Natural Gas

Distribution Network are only empirical.

Challenges

Need for optimal pre-earthquake retrofitChallenges

&

Pre-quake Post-quake

National Research Council (2011) National Earthquake Resilience, Washington, DC

The less vulnerable the critical components (pipeline segments. connections) -> the less the initial functionality loss

The more efficient the post-earthquake mitigation-> the faster the functionality recovery

=f(t)due to aging

Hybrid experimentation on principle failure

modes of the soil-pipeline systemStructure

WP02

SSI: nonlinear numerical modelling

Scenario 1 Scenario 2


Ux

σyy σyy

Ux

SV- waves

P- waves

tcr

Time-variation of εa,gat the surface of the equivalent-linear site axial displacement (top), vertical displacement

(bottom) at tcr

2( )S ext=F u p

( )( )

( ) ( )

j

Sj j¶D =

¶u

F uu R

u( 1) ( ) ( )j j j+ = + Du u u

3D soil-pipe interaction analysis

x

,g yu

,g xu

40

( );g g crx t=u u

zx

y ( )xu t!!

‘Global’subdomain

‘Local’subdomain

,( ) ( ) ( ) ( )g g g r s r bt t t V u tr+ + =Μu Cu Ku J!! ! !

2D plane strain site response analysis

Instantaneous ground motion X-profiles

tcr whenεg,xx = min

crt t=

crt t=

FirmSoft

SSI: FEM substructuring

Nick Psyrras, PhD student

zx

y

R(mm)

t(mm)

R/t(-)

σy(MPa) P/Py

hemb(m)

εu(%)

450 12 37.5 450 0.63 1000 4

( )0.5 ~ 0.9 tanµ j=(O’Rourke & El Hmadi, 1988)


Psyrras, N., Gerasimidis, S., Kwon, O-S. & Sextos, A.G. (2018) “Can a buried natural gas pipeline buckle locally during earthquake ground shaking?”, Soil Dynamics and Earthquake Engineering (accepted for publication).


SSI: probabilistic assessment of geohazards (including seismic risk and loss)

De Risi, R., De Luca, F. Kwon, O.-S., Sextos, A.G. (2018) “Post-earthquake risk assessment for buried gas pipelines at regional scale”, ASCE Journal of Pipeline Systems (accepted for publication).

SSI: experimental investigation (shaking table + shear stack)


• Modal analysisEmpty: fo,1 = 2.97 Hz (after tuning of rubber stiffness)

Full: fo,1 = 18.03 Hz

Mode 1

Mode 2


• Minimum required pipe anchorage length

Mode 1Lan = ?

Po

Free pipe ends

tu

ou an o an

u

Pt L P Lt

= Þ =

( )1 2 23

ou

Kt H R Rµg p+æ ö= +ç ÷è ø

hcov

hcov

Exact expression

21 243

oK Rµg +æ ö+ ç ÷è ø

Prototype scale

R

t

P

,maxp p

anL L³,max

4.8 4.8

pp pan

m

LL LnL

= = =!



SSI: experimental investigation (soil isolation)

Nick Alexander, Anastasis Tsiavos, Anastasios Sextos

SSI: hybrid testing

Static DOFDynamic DOFBearing modeled numericallyBearing physically tested

Bousias, S., Sextos, A.G., Kwon, O.-S., Taskari, O., Elnashai, A., Evangeliou, N. and Di Sarno, L. (2017) “Intercontinental Hybrid Simulation for the Assessment of a Three-span R/C Highway Overpass”, Journal of Earthquake Engineering

ConcreteCompressive

Strength fc (MPa) 35

Tensile Strength ft (MPa) 2

Modulus of Elasticity (GPa) 28

Poisson's Ratio 0.2Strain at

compressivestrength

0.0035

Density (kg/m3) 2500Steel

Modulus of Elasticity (GPa) 200

Yield Stress (MPa) 460Density (kg/m3) 7850

SSI: geometrically nonlinear numerical modelling

SSI: FEM substructuring & effect on equipment

Sextos, A.G., Manolis, G.D., Ioannidis, N., Athanasiou, A. (2016) “Seismically induced uplift effects on nuclear power plants. Part I&II: Containment building rocking spectra”, Nuclear Engineering and Design

Sextos, A.G., Manolis, G.D., Ioannidis, N., Athanasiou, A. (2016) “Seismically induced uplift effects on nuclear power plants. Part I&II: Containment building rocking spectra”, Nuclear Engineering and Design

SSI: FEM substructuring & effect on equipment

SSI: geometrically nonlinear numerical modelling

National Soil-Foundation-Structure Interaction Laboratory

UKCRIC has the ambition to build a £500m national research programme, over the next 10 years.

The £12m National Soil-Foundation-Structure Interaction (SoFSI) Facility, is a nationally shared facility to be hosted at the University of Bristol.

SoFSI will be a core component of the Government’s £138m UK Collaboratorium for Research in Infrastructure and Cities (UKCRIC) initiative, which will drive forward the national infrastructure research investments for the next 30 years and beyond.

Earthquake Shaking Table at the existing lab

3m by 3m platform supported by 8 hydraulic actuators that carry up to 15t Acceleration up to 5g with peak displacements of ±150mm

Documents

Performance-based design and assessment of critical