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Final Report

PTDC/ECM/117618/2010

February, 2016

Authors:

Corneliu Cismasiu (IR) Filipe Amarante dos Santos Alfredo Campos Costa Paulo Candeias Luís Guerreiro

SUPERB

Seismic Unseating Prevention Elements for Retrofitting of Bridges

Table of Contents

Table of Contents

Introduction .............................................................................................................................. 1

Dissemination of Knowledge ................................................................................................ 2

Advanced Training ............................................................................................................... 3

Publications .......................................................................................................................... 4

Seismic Unseating Prevention ................................................................................................. 6

Topic introduction ................................................................................................................. 6

Research team ..................................................................................................................... 6

Objectives and work planning .............................................................................................. 7

Dynamic characterization of footbridges ............................................................................... 10

Introduction ........................................................................................................................ 10

Experimental campaign ..................................................................................................... 10

Numerical modeling of footbridges ........................................................................................ 26

Finite element updating ...................................................................................................... 26

Implementation of the finite element updating procedure .................................................. 27

FE updating of the PP3141 numerical model .................................................................... 28

Updated FE models ........................................................................................................... 32

Case studies .......................................................................................................................... 35

Numerical simulations using the AEM ............................................................................... 35

Numerical simulations using the FEM ................................................................................ 44

Experimental program ........................................................................................................... 48

Shear behavior of the connection between girder and pile ............................................... 48

Characterization of the superelastic elements ................................................................... 57

Conclusions ........................................................................................................................... 59

References ............................................................................................................................ 61

Introduction

Introduction Nowadays, it is generally accepted that, for a modern transportation system to be reliable, the

design process must ensure an acceptable earthquake risk for the bridge infrastructures. In

the case of existing structures, unacceptable seismic safety conditions must be clearly

identified and promptly corrected. Past earthquakes have demonstrated that the damage

induced in bridges can assume a multitude of different forms, depending, among others, on

factors like the ground motion itself, conditions depending on the building site, the adopted

bridge structural solution and its specific detailing provisions. Unseating of the bridge

superstructure at in-span hinges, or at simple supports, is one of the most severe forms of

seismic damage, leading to eventual collapse. This type of failure is either due to shaking or

to differential support movement associated with ground motion. The problem of unseating is

generally associated with inadequate seat lengths or restraint and it is worsened by skewed,

curved, or complex bridge configurations. In order to reduce the seismic response of bridge

structures, they can be provided with special restraining devices called seismic links.

According to EC8, these connection devices may be responsible for the partial or full

transmission of the design seismic action, provided that dynamic shock effects are mitigated

and taken into account in the design. They are designed to ensure the structural integrity of

the bridge and avoid unseating under extreme seismic displacements, while allowing the non-

seismic displacements of the bridge to develop without transmitting significant loads. While

the new design strategies contemplated in EC8 aim to mitigate potential unseating problems

in new bridges, there are still many existing bridges susceptible to span unseating, due either

to the lack of adequate seismic detailing, like the shorter seats usually associated with old

constructions, either to potential stronger shaking than the one considered in the original

design. These structures require seismic retrofitting and several solutions are currently used,

namely steel restrainer cables, metallic dampers and seat extenders. In order to overcome

some of the limitations presented by these devices, and taking advantage of recent advances

in Material Science, the use of new materials has been proposed in the literature. Among

them, the shape memory alloys (SMAs), a class of metallic alloys exhibiting two important

properties: the shape-memory effect, which allows the material to recover its original

geometry during heating, even after severe deformation, and the superelasticity, which

enables the material to withstand large cyclic deformations, without residual strains, while

dissipating energy. The main objective of this project is to study a seismic retrofitting solution

for existing bridges in Portugal, using seismic links built up of superelastic NiTi SMA restrainer

cables to reduce the deck’s response and therefore the risk of span unseating during

earthquakes. Several activities are planned to be executed during the project. First, taking

Introduction

advantage of the information stored in the EP's archives, a database was be created and

populated with relevant data regarding the dynamic characteristics of existing footbridges

located in the Southern part of Portugal, a region with significant seismic activity. This

database supported the definition of several typical footbridge structural models that were

analyzed numerically in order to assess their seismic vulnerability. If needed, the structures

were equipped with superelastic NiTi SMA restrainers and analyzed again to assess the

effectiveness of this type of retrofitting. Finally, taking advantage of the exquisite facilities

available at LNEC, a large scale experimental test program was implemented aiming to

confirm the feasibility of the application of SMAs on bridge structures retrofitting. To establish

the supporting conditions necessary to guarantee the accomplishment of all project goals, the

research team is composed by specialists with large expertise in seismic analysis of structures

(IST, LNEC, FCT), bridges maintenance, retrofitting and rehabilitation (EP), numerical

modelling of complex SMA constitutive models (FCT). Professor Reginald DesRoches from

the Georgia Institute of Technology, well known researcher in Earthquake Engineering, design

and analysis of bridge structures and structural applications of smart materials, Professor Álex

Barbat from Polytechnic University of Catalonia, prestigious researcher in seismic vulnerability

and risk assessment and Professor Jason P. McCormick from the University of Michigan,

experimented researcher in large-scale tests aiming to reduce the seismic vulnerability of

structures through innovative systems, including shape-memory alloys, contributed with their

knowledge to the successful conclusion of the project by acting as external consultants. The

expertise gained during the project help training young post-graduate researchers and ensure

the longevity of the achievements of this research, and also constitute a pool of knowledge for

all involved partners and the bridge community at large.

Dissemination of Knowledge

Organization of conferences and workshops

1. 15the World Conferences on Earthquake Engineering (15WCEE), Lisbon,

September 24-28, 2012. One of the team members, Professor Luís Guerreiro,

act as the Secretary General of the Local Organization Committee.

2. Workshop: Dynamic Performance Assessment & Rehabilitation of Structures

(October 31, 2014). This workshop, organized by the team members of the

project had as main speakers Professor Alex H. Barbat (External consultant

- UPC, ICNME Barcelona), Engineer Alfredo Campos Costa (Team member

- LNEC), Engineer Carlos Filipe Sanches Pimentel (Special guest - EP),

Professor Jason McCormick (External consultant - University of Michigan),

Professor Álvaro Alberto de Matos Ferreira da Cunha (Special guest - FEUP),

Introduction

Professor Luís Manuel Coelho Guerreiro (Team member - IST) and Professor

Filipe Pimentel Amarante dos Santos (Team member FCT-UNL).

Reports

1. "Relatório Nº1 - projeto PTDC/ECM/117618/2010: Ensaios de

Caracterização Dinâmica de Passagens Superiores de Peões", P. Saldanha,

F.P.Amarante dos Santos, C. Cismasiu, M.A. Gonçalves da Silva.

UNIC/FCT/UNL, 2012. (http://sites.fct.unl.pt/superb/pages/relatorio)

2. "Relatório Nº2 - projeto PTDC/ECM/117618/2010: Modelação em Elementos

Finitos e Análise do Comportamento Dinâmico da Passagem Superior de

Peões 3141. Implementação de elementos de reforço compostos por ligas

com memória de forma.” P. Saldanha, F.P.Amarante dos Santos, C.

Cismasiu, M.A. Gonçalves da Silva. UNIC/FCT/UNL, 2013.

(http://sites.fct.unl.pt/superb/pages/relatorio)

3. "Relatório Nº3 - projeto PTDC/ECM/117618/2010: Análise Não Linear do

Comportamento Sísmico da Passagem Superior de Peões 2787", L.

Rodrigues, V. Bernardo, C. Cismasiu, FPl Amarante dos Santos.

UNIC/FCT/UNL, 2014. (http://sites.fct.unl.pt/superb/pages/relatorio)

4. Relatório Nº4 - projeto PTDC/ECM/117618/2010: “Análise preliminar das

simulações na mesa sísmica do LNEC”. André Emanuel Bicho Lourenço de

Oliveira, Vasco Miguel Serrano Bernardo. FCT/UNL, 2014.

(http://sites.fct.unl.pt/superb/pages/relatorio)

5. Relatório bolsa Maio-Julho 2014. André Emanuel Bicho Lourenço de Oliveira.

FCT/UNL, 2014. (http://sites.fct.unl.pt/superb/pages/relatorio)

Advanced Training

MSc Thesis

1. Krus, Tiago de Carvalho Almeida Palma. (2012), Análise dinâmica e controlo

passivo de vibrações de uma ponte pedonal, MSc Thesis, Faculdade de

Ciências e Tecnologia (http://run.unl.pt//handle/10362/8875)

2. Valentim, Nilton Leonardo. (2012), Análise do comportamento dinâmico em

pontes pedonais, MSc Thesis, Faculdade de Ciências e Tecnologia

(http://run.unl.pt//handle/10362/8580)

3. Fernandes, João Filipe Figueira. (2012), Solução de controlo passivo de um

passadiço pedonal pré-fabricado, submetido a acções sísmicas, MSc Thesis,

Faculdade de Ciências e Tecnologia (http://run.unl.pt//handle/10362/7787)

http://sites.fct.unl.pt/superb/pages/relatorio



http://run.unl.pt/handle/10362/8875

http://run.unl.pt/browse?type=author&value=Valentim%2C+Nilton+Leonardo


http://run.unl.pt/browse?type=author&value=Fernandes%2C+Jo%C3%A3o+Filipe+Figueira


Introduction

4. Ferreira, Ana Cláudia Narciso. (2013), Identificação modal e actualização de

modelos de elementos finitos, MSc Thesis, Faculdade de Ciências e

Tecnologia (http://run.unl.pt/handle/10362/11225)

5. Rodrigues, Ana Isabel Malveiro (2013), Modelação e análise não-linear do

comportamento dinâmico de um passadiço pedonal, MSc Thesis, Faculdade

de Ciências e Tecnologia (http://run.unl.pt/handle/10362/12193)

Short stays

1. Short stay (March 4-22, 2013) of one team member (Pedro Manuel Saldanha

Santos) to Georgia Institute of Technology - Civil & Environmental

Engineering under the supervision of Professor Reginald DesRoches, one of

the project external consultants.

Participation in conferences

1. Second European Conference on Earthquake Engineering and Seismology

(2ECEES), Istambul, Turkey, August 24-29, 2014

(http://www.2eceesistanbul.org/)

2. 6th International Conference on Bridge Maintenance, Safety and

Management (IABMAS 2012), Stresa, Lake Maggiore, Italy, July 8-12, 2012

(http://www.iabmas2012.org/)

3. 4.º Congresso Nacional sobre Segurança e Conservação de Pontes

(ASCP2015), Lisbon, Portugal, July 25-26, 2015 (http://ascp2015.ascp.pt/)

4. 5ªs Jornadas Portuguesas de Engenharia de Estruturas, o Encontro Nacional

de Betão Estrutural 2014 e o 9º Congresso Nacional de Sismologia e

Engenharia Sísmica (JPEE2014), Lisbon, Portugal, November 26-28, 2014

(http://jpee2014.lnec.pt/)

5. 3.º Congresso Nacional sobre Segurança e Conservação de Pontes

(ASCP2013), Porto, June 26-28, 2013 (http://ascp2013.ascp.pt/)

Publications

Papers in international journals

1. Amarante dos Santos, F. P., Cismaşiu, C. and Pamies Teixeira, J. (2013),

Semi-active vibration control device based on superelastic NiTi wires. Struct.

Control Health Monit., 20: 890–902. doi: 10.1002/stc.1500

http://run.unl.pt/browse?type=author&value=Ferreira%2C+Ana+Cl%C3%A1udia+Narciso


http://run.unl.pt/browse?type=author&value=Rodrigues%2C+Ana+Isabel+Malveiro


http://www.2eceesistanbul.org/

http://www.iabmas2012.org/

http://jpee2014.lnec.pt/

Introduction

2. Cismaşiu, C., Narciso, A., and Amarante dos Santos, F. (2014).

"Experimental Dynamic Characterization and Finite-Element Updating of a

Footbridge Structure." J. Perform. Constr. Facil., 10.1061/(ASCE)CF.1943-

5509.0000615, 04014116.

Comunications in international meetings

1. Cismasiu, C., and Amarante F. P. dos Santos. "Towards a semi-active

vibration control solution based on superelastic shape memory alloys." 15th

WCEE. Lisbon, Portugal 2012

2. Amarante dos Santos, F. P., and C. Cismasiu. "Bridge Hinge-Restrainers

Built up of NITI Superelastic Shape-Memory Alloys." New Trends in Smart

Technologies. Eds. Christian Boller, and Hartmut Janocha. Saarbrücken:

Fraunhofer Verlag, 2013. 195-203.

3. Cismasiu, Corneliu, and Filipe Pimentel Amarante dos Santos. "Shape

Memory Alloys in Structural Vibration Control. Research at

UNIC/DEC/FCT/UNL." International Conference "Tradition and Innovation".

60 Years of Civil Engineering Higher Education in Transilvania. Cluj-Napoca,

Romania: UTCN, 2013.

4. Cismasiu, Corneliu, Filipe Amarante P. dos Santos, and Ana I. M. Rodrigues.

"Experimental and FE updating techniques for the unseating vulnerability

assessment of a footbridge structure." The 4th International Conference on

Dynamics, Vibration and Control. Shanghai, China: Shanghai Institute of

Applied Mathematics and Mechanics, 2014.

Comunications in national meetings

1. Bernardo, Vasco, André Oliveira, Filipe Amarante dos Santos, and Corneliu

Cismasiu Vulnerabilidade e reforço sísmico de uma passagem superior

pedonal pré-fabricada. 5as Jornadas Portuguesas de Engenharia de

Estruturas. Lisboa, 2014.

http://docentes.fct.unl.pt/cornel/publications/towards-semi-active-vibration-control-solution-based-superelastic-shape-memory-a

http://docentes.fct.unl.pt/cornel/publications/towards-semi-active-vibration-control-solution-based-superelastic-shape-memory-a

http://docentes.fct.unl.pt/cornel/publications/bridge-hinge-restrainers-built-niti-superelastic-shape-memory-alloys-0

http://docentes.fct.unl.pt/cornel/publications/bridge-hinge-restrainers-built-niti-superelastic-shape-memory-alloys-0

http://docentes.fct.unl.pt/cornel/publications/shape-memory-alloys-structural-vibration-control-research-unicdecfctunl



http://docentes.fct.unl.pt/cornel/publications/experimental-and-fe-updating-techniques-unseating-vulnerability-assessment-footb

http://docentes.fct.unl.pt/cornel/publications/experimental-and-fe-updating-techniques-unseating-vulnerability-assessment-footb

http://docentes.fct.unl.pt/cornel/publications/vulnerabilidade-e-reforco-sismico-de-uma-passagem-superior-pedonal-pre-fabricada

http://docentes.fct.unl.pt/cornel/publications/vulnerabilidade-e-reforco-sismico-de-uma-passagem-superior-pedonal-pre-fabricada

Seismic Unseating Prevention


Topic introduction

Structural continuity is of utmost importance in order to guarantee an adequate seismic

behavior for bridge decks. In fact, well-designed monolithic structures have also the added

advantage of lower maintenance costs since joints and bearings represent some of the major

maintenance problems on bridges today. If structures are not continuous and monolithic, they

must be tied together at deck joints, supports and abutments, preventing them from pulling

apart and collapsing during an earthquake. The research of restraining solutions for seismic

linkage in existing footbridges, aims to mitigate their vulnerability to span unseating, by

controlling the corresponding deck displacements during an earthquake event. The traditional

approach for this type of restraining systems usually relies on the use of steel cables, which,

if designed to remain elastic, lack the ability to dissipate energy and are responsible for the

transmission of large seismic forces to other structural components. After yielding, these

elements tend to accumulate plastic deformations in repeated loading cycles that can also

result in unseating. Several other devices have been presented in the past decades as

unseating prevention devices for bridges, namely in the form of fluid-viscous dampers and

metallic dampers [AN07]. Although these devices are able to dissipate energy, they lack the

capacity for re-centering, which is a very important asset in order to control hinge opening in

bridges during seismic actions [DE04a, DE04b]. The installation of external hinge extenders

prevents the supported section of the superstructure from dropping off from its support but

has no effect on controlling the deck displacements, which may lead to structural damage in

other important components. Several authors have studied the retrofit and rehabilitation of

bridges using an alternative solution for bridge hinge restrainers, built up of superelastic (SE)

cables and bars [DE02, DE03].

Research team

The FCT-UNL research team has been developing active work in the superelastic field over

the last years, mainly addressing the numerical simulation of structures with SE elements

subjected to dynamic excitations [CI08, SA10]. Novel SE restraining devices for seismic

hazard mitigation has also been proposed by this team [CI10] and successfully simulated,

allowing the accumulation of a solid background in modelling the complex superelastic

behavior. LNEC has long tradition of interaction with medium and large research teams,

participating and coordinating several projects or networks research activities, funded by

National organizations or by the European Commission. Presently the Earthquake

Engineering Research Division of LNEC (NESDE) conducts earthquake engineering


research, from laboratory experiments and field testing, structural monitoring and analytical

modeling of structures, to seismic hazard and risk analysis. LNEC is from the beginning a

component of the European Large Scale Facilities, offering Transnational Access, with its 3D

Shaking Table (LNEC-3G) operating since 1996. Furthermore LNEC has been in charge of

drafting the Portuguese regulations for seismic design and holds from the beginning the

Permanent Secretariat of CEN/TC250/SC8, the CEN Subcommittee for Eurocode 8. The

responsible for the research team of LNEC contributing to this project, the Head of NESDE,

with a long experience in earthquake engineering, has been involved in many research co-

operations [CA04, CO05, FA05, FA08, FA08a], at National and European level, having acted

frequently as leader of research groups; is Technical Secretary of CEN/TC250/SC8, member

of the Portuguese Committee for the Implementation of Eurocodes and Vice-President of the

Portuguese Association for Earthquake Engineering. The team expertise in seismic analysis

of bridges was ensured by the presence of a very experienced researcher and IST professor.

In the last decade his research was focused in Earthquake Engineering and the seismic

behavior and structural control of bridges [GU97, VI00, BR00, GU03]. Besides a valuable

personal experience in the field, his contribution to the international dissemination of the

research developed in this project was essential, as, together with another team member of

the project, were part of the organizing committee of the 15th World Conference on

Earthquake Engineering that took place in Lisbon in September of 2012 (www.15wcee.org).

In order to establish the supporting conditions necessary to guarantee the accomplishment of

the project goals, the research team was assisted by one of the most prestigious world

specialists in design and analysis of bridge structures and structural applications of smart

materials, Professor Reginald DesRoches from Georgia Institute of Technology, who acted

as external consultant. In his previous research, he has broadly studied the efficacy of SE

based seismic damping devices [DE03a, AN05, AN07], aimed to concentrate energy

dissipation in specific bridge locations. To guarantee that the research related to the project

activities is strongly anchored in the Portuguese reality, the team members counted with an

important institutional partner, the EP – Roads of Portugal. This public limited company is the

concessionaire of the Portuguese National Road Network and, as responsible for the

maintenance and rehabilitation of the existing bridges, detains in its archives exclusive

information of crucial importance for the project.

Objectives and work planning

Bridges are important lifeline projects and therefore, their collapse during a disaster such as

an earthquake will cause significant casualties and properties losses. The moderate-to-strong

earthquakes occurred in the past two decades showed that one of the most common type of

failure in bridges is unseating. For example, during the 1971 San Francisco earthquake, this


type of failure was observed in many damaged bridges and as a consequence, the California

Department of Transportation started a highly active retrofitting campaign [AN07]. Although

the seismic hazard of the Portuguese territory is moderate and despite the new design

strategies, like the ones contemplated in EN 1998 EC8, aiming to mitigate the potential

unseating problems in new structures, there are still many existing bridges with high seismic

vulnerability, susceptible to span unseating, due either to the lack of adequate seismic

detailing, like the shorter seats usually associated with ancient constructions, either to

potential stronger shaking than the one considered in the original design. One mention that,

the Portuguese National Road Network includes more than 6000 bridges and/or viaducts

under the direct or indirect management of EP – Roads of Portugal. Among them, 206 have

been already retrofitted within a national campaign that started in 2001, and other 101 required

emergency interventions. According to the partial results of the ongoing national inspection

program, 306 more bridges and/or viaducts are expected to be intervened by 2015. The main

objective of this project is to study the effectiveness of a relatively new seismic retrofitting

solution for existing footbridges in Portugal, based on seismic links built up of superelastic NiTi

SMA restrainer cables, aiming to reduce the deck’s response and consequently, the risk of

span unseating during earthquakes. In order to ensure the needed expertise that guarantee

the fulfilling of the proposed objective, four of the top prominent Portuguese institutions in

areas like seismic analysis of structures, bridges maintenance, retrofitting and rehabilitation

and numerical modelling of complex SMA constitutive models, namely FCT/UNL, IST, LNEC

and EP, joined forces and create a highly qualified research team. The activities that planned

to be executed during the project were divided in four main tasks:

Task 1 – Dynamic characterization of footbridges. The objective of this first task, planned to

be executed in parallel with Task 2 in the first year of the project, is to develop a database with

relevant information regarding the dynamic characteristics of several footbridges existing in

the Southern part of Portugal, as well as their existing unseating prevention devices, if any.

The activities in this task were of utmost importance as allowed to adapt the research to the

Portuguese reality and therefore preparing the project outputs for the immediate

implementation in real life.

Task 2 - Numerical modelling of footbridges. The activities in this task, planned to be executed

in parallel with the first task during the first year of the project, being a natural continuation of

the work initiated at FCT/UNL in 2006 [CI08, SA10], reflected the strategy of developing

numerical models able to perform MDOF dynamic non-linear analysis of structures including

superelastic restrainers. The resulting models were used in the later part of the research to

analyze the performance of a superelastic retrofitting system when implemented in typical

footbridge structures and to prepare the experimental program.


Task 3 – Case studies. Using the outputs resulting from the first two tasks, the activities in this

task, were planned to be executed during the second year of the project, yielding FE models

of typical footbridges existing in Portugal. Using these FE models, the team members

associated to this task have simulated the presence of superelastic NiTi SMA restrainers and

analyze their seismic response to assess their effectiveness. These numerical tests allowed

to identity, among the great variety of existing footbridges in Portugal, potential targets for this

type of seismic retrofitting.

Task 4 - Experimental program. Taking advantage of the exquisite facilities available at LNEC,

a series of large scale experimental test were conducted in this last stage of the project, aiming

to validate the conclusions resulting from the numerical simulations performed during Task 3.

As already reported in the literature [TY07a, TY07b], experimental tests on NiTi coupon

specimens provide only limited information in terms of the full-scale behavior. Therefore, these

full-scale tests, using relevant earthquake-type loading, are essential for the full understanding

of the effectiveness of superelastic NiTi restrainers retrofitting in real life bridge structures.

Dynamic characterization of footbridges


Introduction

It is well known that lifelines interruption as a result of natural disasters can have major

economic and social impacts, leading to much higher losses than the value of damage to the

infrastructure itself. Therefore, although the footbridges are not usually considered as critical

lifeline structures, their collapse during a disaster such as an earthquake can be critical, as it

might cause severe lifelines interruption, like the examples illustrated in Figure 1.

Figure 1: Lifeline interruption due to footbridges collapse

Despite the new design strategies, like the ones contemplated in Eurocode 8, the Portuguese

National Road Network includes many footbridges with high seismic vulnerability, susceptible

to span unseating, due either to the lack of adequate seismic detailing, like the shorter seats

usually associated with ancient constructions, either to potential stronger shaking than the one

considered in the original design. In order to guarantee successful structural interventions, the

numerical models to be used in the design stages of their retrofitting solutions must be

validated using experimental measurements on the existing structures.

In 2012, within the SUPERB research project, an experimental campaign has been launched,

collecting relevant dynamic records of 17 footbridges located in the Southern part of Portugal,

a region with significant seismic activity. Subsequent application of experimental modal

identification techniques has enabled the accurate identification of their structural properties

and provide reliable data to support calibration, updating and validation of the corresponding

numerical models.

Experimental campaign

The basic principles in experimental modal analysis and its evolution from input-output to

output-only identification techniques have been presented by many authors, as for example,

Ljung [LJ99], Cunha and Caetano [CU05, CU06], Ibsen and Liingaard [IB06] or Haritos

[HA10]. Nowadays, the output-only modal testing and identification is becoming a widespread


tool for solving a broad range of engineering problems. Its main advantages and limitations

are extensively discussed by Brincker and his co-workers in [BRI00, BRI03, BRI07]. A

literature review reveals many applications of output-only modal identification techniques to

Civil Engineering structures in general [CU05, CU06, PE01, BRI01, AR02, TA02, EL04, GE06,

BR07, JU08, BE08, RE08, SA09, FO12] and footbridges in particular [CA04a, GA05, ZI06,

ZI07, CR09, LA11].

Based on the expertise reported in the consulted literature, between May and July, 2012, an

experimental campaign has been designed and carried out on 17 typical pedestrian crossing

in the Faro district in the Southern part of Portugal, see Figure 2.

Figure 2: Location of the studied footbridges

Among them, as illustrated in Figure 3, several pedestrian crossing are located in a particularly

sensitive area, close to the Faro airport and railways station, 3 hospitals, 2 fire departments,

a large shopping center, a large university and several schools.

The structures are simply supported footbridges with the main span between 26 and 34 m and

a vertical clearance between 5.2 to 5.6 m, composed of two I-shaped prestressed girders with

1.20 m height, connected by an inferior deck slab. The deck slab, which is built up of a 0.06

m precast slab and a cast-in-place concrete topping with 0.06 m, is supported by the bottom

flanges of the main girders, as illustrated in Figure 4(a). The connection of the main girders to

the piles, see Figure 4(b), is materialized by a set of two steel dowels, with a diameter of 20


mm each, and an elastomeric bearing. The girders have vertical ducts in order to

accommodate the dowels, which are filled with a non-shrink grout.

Figure 3: Footbridges located in a particularly sensitive area

The main piles, as shown in Figure 4(c), are precast reinforced concrete elements, with a

variable rectangular cross-section, ranging from 0.60×0.50m2 to 1.00×0.50m2, with superficial

precast foundations. The access to the bridges is materialized by a set of lateral precast

reinforced concrete ramps and/or stairs, which are mainly built up of ribbed slabs supported

by prestressed corbels, rigidly connected to the columns.

Figure 4: Typical design details of the footbridges

During the ambient vibration tests (AVT), the velocity response was acquired using three

MR2002-CE vibration monitoring systems from SYSCOM, each consisting of one MS2003+

triaxial velocity sensor and one vibration recorder, see Figure 5. The MR2002-CE is equipped


with a digital signal processor to filter the signals coming from the sensor. Using its default

filter algorithm, the signal is cut-off at 80% of Nyquist frequency, meaning that a data

acquisition sampling-rate of 100 samples per second, value that was used in these tests,

allows the identification of frequencies as high as 40 Hz. To ensure synchronized data

acquisition, the MR2002 clock is automatically updated using a GPS receiver.

Preliminary SAP2000 finite element models, built based on the structural drawings, were used

to provide estimates for the expected modal characteristics of the structures. These results

were used to decide the data acquisition sampling-rate, the reference channel locations and

the configurations of the roving sensors. As only 3 triaxial vibration monitoring systems were

available, one was kept in the same location, the mid-span of the footbridge, to guarantee 3

reference channels. The remaining roving sensors were used in several setups in order to

cover all defined grid points, see an example in Figure 6. For each setup, ambient vibration

data were acquired for 15 minutes.

Figure 5: SYSCOM MR2002-CE vibration monitoring systems equipped with MS2003+ triaxial velocity sensors


Figure 6: Grid points defined for the AVT measurements of a footbridge

Images captured during the experimental campaign are available on the project webpage

(http://sites.fct.unl.pt/superb/). For illustration purposes, several images captures during the

AVT recordings on several pedestrian crossings are given in the following figures.

Figure 7: AVT on PP3141

http://sites.fct.unl.pt/superb/


Figure 8: AVT on 2723





Subsequent data processing using the Enhanced Frequency Domain Decomposition (EFDD)

and the Unweighted Principal Component version of the Stochastic Subspace Identification

(SSI-UPC) algorithms, both implemented in the operational modal analysis software

ARTeMIS, yields the estimates for the modal properties of the footbridge.

The EFDD [BRI00, BRI01a, BRI01b, GA06] is a non-parametric method developed in the

frequency domain, which estimates the modal parameters directly from signal processing

calculations. It is an extension of the Frequency Domain Decomposition (FDD), algorithm that

estimates the Eigen-modes, in the condition of a white noise input and a lightly damped

structure, by performing a singular value decomposition of the system’s spectral density

spectra, to obtain power spectral densities of a set of several single-degrees-of-freedom

systems, each corresponding to an individual mode. The EFDD is a technique that allows the

estimation not only of the mode shapes and their frequencies but also of the corresponding

damping ratios.

The Stochastic Subspace Identification (SSI) techniques [VA96, AN--, BRI06] is a parametric

method developed in the time domain, that uses weighted time series data resulting from the

output-only measurements, to identify a stochastic state space model that describes the linear

vibrations of the structure. The Unweighted Principal Component (UPC), an algorithm that

works best with data having modes with comparable energy level, is the simplest version, as

no weighting is performed at all. For each set-up, a set of models with different parameters

are identified and a stabilization diagram is established, discriminating between stable,

unstable and noise modes.


Table 1: Experimental modal properties of PP3141

Mode EFDD SSI-UPC

Frequency (Hz) Damping (%) Frequency (Hz) Damping (%)

Longitudinal 1.933 1.081 1.929 1.230

Lateral 2.522 0.856 2.515 0.807

1st Vertical 3.016 0.597 3.013 1.590

1st Torsional 5.203 0.583 5.197 0.874

2nd Torsional 8.176 1.197 8.371 2.486

2nd Vertical 11.220 0.410 11.220 0.727

As an example, the identified modal properties of PP3141 are resumed in Table 2. The

singular values of the spectral density matrices obtained using the EFDD algorithm, on all test

setups, are presented in Figure 18(a). The corresponding stabilization diagrams, in the case

of the application of the SSI-UPC algorithm, as well as the correlation between EFDD and

SSI-UPC, are shown in Figures 18(b) and (c), respectively.


Figure 18: PP3141 – Results of the Operational Modal Analysis (OMA)

The entries in the Modal Assurance Criterion (MAC) matrix, presented in Figure 18(c), indicate

a good correlation between identified modes using the two algorithms at stake. However, one

must note two particular aspects.

The first one, is related to the slight drift that can be observed in the entry associated with the

first mode, indicating some problems in the convergence of the two algorithms for this

particular vibration mode. Analyzing the processed data presented in Figure 4(a) and (b), one

can clearly observe two closed picks near 1.9 Hz, the source of this convergence problem.

Their presence is explained by the existence of signals associated with the longitudinal

response of the footbridge having a non-stationary amplitude during the recording period. This

can be verified in Figure 19, where one of the recorded data sets is presented for three

orthogonal directions.


Figure 19: Velocity time history for one MR2002 SYSCOM station

One can see that, for the case of Channel X, corresponding to the longitudinal direction, two

zones with different mean amplitudes can be identified. The data associated with the larger

amplitudes generate a lower frequency while the data associated with the lower amplitudes

generate a slightly larger frequency, corresponding to the two picks near 1.9 Hz, identified in

Figure 18(a) and (b).

The second aspect worth to be mentioned here is the fact that some of the frequencies

identified by the SSI-UPC algorithm, were not detected using the EFDD technique. It was

verified by the finite element simulations that the vibration modes associated with these

frequencies are mainly related to the access ramps and therefore, the corresponding

vibrations transmitted to the main deck are only residual. This explains the difficulty of the

EFDD algorithm in detecting these frequencies.

All the relevant dynamic characteristics obtained during the identification campaign were

collected in a modular, flexible and easily expandable web-oriented database, specially

created within the activities of this task, using MySQL management system and PHP scripting

language.

A resume of the 17 pedestrian crossing location, main span and identified principal

frequencies is given in Table 2.

Table 2: Experimental campaign – Ambient Vibration Tests, May – July, 2012

CC.STB-IC32.001+187.PP.3779.0#0.0

IC32 at km 1,187 - PSP

Span: 29.57m

Natural frequencies (Hz):

L 2.973; T 3.662; V 3.503


EP.FAR-125-10 (EN).000+420.PP.3141.0#0.0

EN125-10 at km 0+420 - PSP

Span: 29.00m

Natural Frequencies (Hz):

L 1.943; T 2.527; V 3.017

EP.FAR-125-10 (EN).001+250.PP.3149.0#0.0 EN125-10 at km 1+250 - PSP

Span: 33.60m


L 1.854; T 2.574; V 2.175

EP.FAR-125-10 (EN).001+750.PP.3152.0#0.0 EN125-10 at km 1+750 - PSP

Span: 30.60m


L 1.671; T 2.261; V 2.454

EP.FAR-125-10 (EN).002+600.PP.3164.0#0.0

EN125-10 at km 2+600 - PSP

Span: 26.00m


L 2.365; T 2.762; V 3.494


EP.FAR-270 (ER).044+100.PP.3082.0#0.0

ER 270 at km 44+100 - PSP

Span: 29.80m


L 9.725; T 4.364; V 4.111

EP.FAR-IC 1.703+073.PP.3886.0#0.0

IC1 at km 703+073 - PSP

Span: 22.50m


L 1.998; T 3.292; V 4.469

EP.FAR-IC 4.000+100.PP.2793.0#0.0

IC4 (EN125-4) at km 0+100 - PSP

Span: 27.50m


L 3.313; T 3.094; V 3.327

EP.FAR-IC 4.002+500.PP.2854.0#0.0

IC4 (EN125-4) at km 2+500 - PSP

Span: 25.80m


L 3.440; T 3.426; V 3.495


EP.FAR-IC 4.097+700.PP.2730.0#0.0

IC4 (EN125-4) at km 97+700 - PSP

Span: 22.20m


L 2.307; T 3.669; V 5.121

EP.FAR-IC 4.098+050.PP.2723.0#0.0

IC4 (EN125-4) at km 98+050 - PSP

Span: 22.50m


L 2.185; T 4.009; V 3.296

EP.FAR-IC 4.098+480.PP.2719.0#0.0

IC4 (EN125-4) at km 98+480 - PSP

Span: 28.50m


L 2,034; T 2.934; V 3,068

EP.FAR-IC 4.098+850.PP.2816.0#0.0

IC4 (EN125-4) at km 98+850 - PSP

Spans: 12.30m; 22.00m; 10.50m


L 2.305; T 2.594; V 4.551


EP.FAR-IC 4.099+250.PP.2697.0#0.0

IC4 (EN125-4) at km 99+250 - PSP

Span: 28.50m


L 1.805; T 2.267; V 3.013

EP.FAR-IC 4.100+400.PP.2787.0#0.0

IC4 (EN125-4) at km 100+400 - PSP

Spans: 16.70m; 24.70m; 16.70m


L 1.794; T 2.058; V 2.594

EP.FAR-IC 4.101+050.PP.2757.0#0.0

IC4 (EN125-4) at km 101+050 - PSP

Spans: 25.80m; 17.90m


L 2.295; T 2.301; V 2.828

EP.FAR-IC 4.102+150.PP.6136.0#0.0

IC4 (EN125-4) at km 102+150 - PSP

Span: 32.95m


L 1.610; T 1.734; V 1.851

Numerical modeling of footbridges


Finite element updating

Once identified the modal properties of the analyzed footbridges, these results are used to

update and validate the finite element models to be used, in a later stage, to check if the

structure is satisfying the actual building codes and, in the case it does not, to design

retrofitting solutions.

A general description of the finite element modal updating procedure applied to structural

dynamic problems can be found in [AS71, MO35, EW00, JA05, RE10]. Several practical

applications are reported in the literature, related, for example, to bridges [EL04, 39, GE06],

grandstands [SA09] and footbridges [CA04a, ZI06, BA09]. The procedure is usually performed

by comparing the numerical with the experimental natural frequencies and mode shapes.

When significant discrepancies are found, one seeks to correct inaccurate parameters, , in

the finite element model, in order to improve the agreement between the numerical estimates

and the experimental results.

(1)

From a practical point of view, one has to solve an optimization problem, in which the optimal

values of the parameters are obtained by minimizing an objective function, J(). The objective

function considered in the present project, is computed based on the identified modal

parameters of the N observed modes. The first term in equation (1) represents the difference

between the measured i, and the computed bar(i), frequency of the i-th mode, while the

second term, based on the modal assurance criterion [AL03], represents the difference

between the measured i, and the computed bar(i), mode shape components of the i-th

mode. Note that, when the estimated and the identified modes are alike, the objective function

tends to zero.

When implementing equation (1), one must note, however, that while the mode shapes

resulting from the FE analysis are usually real, the identified modes are complex, as a result

of the non-proportional damping in the system. For lightly damped structures, the damping

effects can be neglected and a set of real modes could be extracted and used to compare

with the numerical estimations. Several algorithms that can be used to convert the complex

mode shapes into real ones are available in the literature, as, for example in [IB83, NI84,


ZH87, ZH87a, IM93]. The approach used in the present paper, appointed as the best strategy

for extracting real modes from complex ones [IM93, AH95], assumes that the optimum real

mode shape corresponding to a complex one, is the one which has maximum correlation with

this mode. It is proved [AH95] that the most correlated real vector with a complex mode shape

is the real part of the complex mode, when rotated so that the norm of its real part is

maximized. In [AH95] it is shown that the corresponding rotating angle , can be readily

computed from equation (2), where R and I are the real and imaginary part of the complex

mode shape, respectively.

(2)

Using the solution of equation (2), which maximizes the real part of the complex mode shape,

one can finally compute the real part of the rotated mode, which is given by R cos + I sin.

Applying this procedure for all identified complex mode shapes, one obtains real measured

mode shapes, that are used for comparison with those obtained using the finite element model

and in the definition of the objective function given in equation (1).

Implementation of the finite element updating procedure

Although is common practice to perform the finite element updating manually, procedure

adopted also during the present project for the most of the FE models, a numerical framework

was designed and implemented, combining an optimization routine based on the NLPQL

algorithm presented by Schittkowski [SC86], with SAP2000, the general purpose finite

element program, to allow for the automatic performing of the finite element updating

procedure, when this computational program is used.

To run the finite element updating, the numerical model must be defined using a set of

physically meaningful parameters related to constants associated with a certain degree of

uncertainty, as for example material properties like the Young’s modulus, Poisson ratio or

mass density/distribution, physical dimensions of the structural elements or boundary

conditions and connections between components, which are seldom understood with

certainty. A previous sensitivity analysis might help the user to decide, among these

parameters, which are the best to be used in the optimization process.


FE updating of the PP3141 numerical model

As an example, the complete FE updating procedure applied to PP3141 is given next.

Preliminary SAP2000 tridimensional finite element parametric models were defined, based on

the structural drawings of the footbridge. While the deck was modeled using variable cross-

section four-node quadrilateral shell elements with six degrees of freedom per node, all the

other structural elements, namely the piles and the access ramps, were modeled using 3D

frame elements. The resulting finite element model is presented in Figure 6.

Figure 20: PP3141 - SAP2000 FE model

The original design indicates that a C35/45 class concrete was used for the prestressed

elements of the deck and a C25/30 class concrete was used in all the remaining structural

elements. The values of the Young’s modulus used in the finite element model were chosen

accordingly to the general material prescriptions for these two concrete classes, i.e., 34 and

31 GPa, respectively. The same Poisson ratio of 0.2 and volumetric weight of 25 kN/m3 were

considered for all structural elements. The connections between the deck and the piles, and

between the access ramps and the main structure of the footbridge, are simulated using linear

link elements. Their stiffness was computed taking into account the neoprene elastomeric

laminated bearings and the existing steel dowel connectors. The structure is assumed to be

clamped on a rigid foundation.


Figure 21: Modal Assurance Criterion - correlation between EFDD and SAP2000

Although this model was used to provide estimates for the expected modal characteristics of

the structure, essential to prepare the experimental campaign, one can readily see from the

values presented in Figure 21, that the finite element estimates for the modal properties of the

footbridges are not consistent with the identified values. According to the MAC matrix, the

second and the third modes of the main deck shift places in the numerical model. The other

modes are not very accurate (the values on the main diagonal of the MAC matrix are drifted

away from the unity) and there is an important error in the frequency values, with a maximum

error of about 17% for the lateral mode.

If this finite element model is to be used predictively in a later stage, for untested loading

conditions or modified structural configurations, a previous finite element updating is required.

Sensitivity analysis

The aim of the model updating is to modify the values of some, physically meaningful,

parameters in order to obtain a better agreement between the numerical results and the

experimental data. These parameters are usually chosen among geometric and material

constants, boundary conditions and inter-elements connections, which are not known with

certainty. Before starting the finite element updating procedure, and in order to improve its

performance, a set of numerical simulations are usually performed, as to understand the

sensitivity of the finite element results to changes in these parameters.

The first parameter considered uncertain for the structure at stake, was the bending stiffness

of the main girders. As expected, a sensitivity analysis considering the variation of this

parameter alone proves that it directly affects the first two vertical vibration modes of the deck.

The best values for the corresponding frequencies were obtained when the bending stiffness

of the main girders was increased by 24%, as shown in Table 3 (note that in the preliminary

FE model, the contribution of the rebars to the global stiffness of the RC elements was not

taken into account).


Table 3: Sensitivity to bending stiffness of the main girders

Mode Experimental Preliminary FE model Updated FE model

(Hz) (Hz) Error (%) (Hz) Error (%)

1st Vertical 3.016 2.785 7.66 3.020 0.13

2nd Vertical 11.220 10.348 7.78 11.225 0.04

As no geotechnical data were available, another uncertainty is related with the boundary

conditions to be used in the FE model, to simulate the ground connections of the piles and the

access ramps. The piles were considered connected to a rigid foundation by different springs

in different directions, being their stiffness the parameters to be optimized. All the access

ramps were considered simply supported on the ground. As expected, a sensitivity analysis

proves that these boundary conditions massively affects the longitudinal and the lateral

vibration modes, while have practically no influence on the vertical modes of the deck. The

best values obtained for the corresponding frequencies are reported in Table 4.

Table 4: Sensitivity to ground connections



Longitudinal 1.933 1.800 6.88 1.919 0.73

Lateral 2.522 2.949 16.93 2.452 2.77

Automatic finite element updating

Completed the sensitivity tests, an automatic finite element updating was performed using the

implemented algorithm, using the six identified vibration modes of the main deck. The bending

stiffness of the main girder, the spring connections between the piles and the rigid foundations

and the stiffness of the neoprene elastomeric laminated bearings (including the steel dowel

connectors) between the main girders and the piles were considered simultaneously, as

optimization parameters. The best values obtained during the sensitivity tests were

considered as initial approximations and a ±10% variation was allowed for all these

parameters.

A comparison between the FE numerical estimates for the main frequencies of the deck and

the corresponding experimental values is presented in Table 5. One can readily see that while

the estimates produced using the preliminary FE model have an average error of about 11%,

the updated FE model produce much better estimates, reducing the average error to about

3%.


Table 5: Comparison between the experimental and the updated FE frequencies



Longitudinal 1.933 1.800 6.88 1.915 0.93

Lateral 2.522 2.949 16.93 2.419 4.08

1st Vertical 3.016 2.785 7.66 3.029 0.44

1st Torsional 5.203 5.881 13.02 5.286 1.58

2nd Torsional 8.176 7.094 13.24 7.154 12.50

2nd Vertical 11.22 10.348 7.77 11.266 0.40

In what concerns the corresponding vibration modes, the MAC matrix presented in Figure 22,

indicates that, except for the two torsional modes, the updated finite element estimates are

now consistent with the identified values.

Figure 22: MAC - correlation between experimental and the optimized FE model

The graphical representation of the six, identified (ARTeMIS) and estimated (Updated

SAP2000 FE model), vibration modes of the deck is presented in Figure 23.

To conclude, one must recall that the FE predictions, based on models developed using

existing design data, are often disbelieved when they are in conflict with experimental results.

In such cases, FE updating techniques are available to correct the FE model based on

dynamic response records of the real structure.

The first six vibration modes of the PP3141 footbridge were identified using ambient vibration

tests and compared with their estimates from a preliminary SAP2000 FE model. Important

errors were revealed, both in the natural frequencies and the corresponding mode shapes.

A manual sensitivity analysis of several meaningful but uncertain parameters, such as the

bending stiffness of the main girders of the deck, the boundary conditions used to simulate

the ground connections of the piles and the stiffness of the neoprene bearings between the

main girders and the piles, allows to reduce the initial errors and to enable an automatically

update of the FE model, using the implemented algorithm.


This automatic procedure further improves the FE estimates for the modal properties of the

structure, leading to values which present a very good correlation with the experimental

measurements. Taking also into account that all parameters changes were within physically

acceptable limits, one may conclude that the updating process was successful.

Figure 23: PP3141 - Principal vibration modes of the main deck

Updated FE models

Numerical models of three representative footbridge structures having one (PP3141), two

(2757) and three (2787) spans were developed in a series of computational programs

(SAP2000, OpenSees, SeismoStruct and ELS).


Some of the optimized numerical models, resulting from the finite element updating, are

presented in Tables 4 to 8.

Table 4: PP3141 – OpenSees updated numerical model

3D numerical model MAC

Table 5: PP3141 – SeismoStruct updated numerical model


Table 6: PP3141 – ELS updated numerical model


Case studies

Case studies A statistical analysis of the database created in Task 1 allowed to identify the typical dynamic

characteristics of the footbridges under analysis. Representative one (PP3141), two (PP2757)

and three (PP2787) span footbridges were chosen and their calibrated numerical models used

to test their seismic vulnerability in different seismic scenarios. When necessarily, the

presence of superelastic NiTi SMA restrainers was simulated as well, in order to assess the

effectiveness of this type of seismic retrofitting.

Numerical simulations using the AEM

Complex modeling of the representative footbridges, including the dowel connection, was

performed using the Applied Element Method [ME99, ME00a, ME00b, ME00c, ME01, ME02]

based computational program, Extreme Loading for Structures (ELS).

Based on the design drawings, the structural elements were accurately modeled, as illustrated

in Figures 24 to 28.

Figure 24: Main girders rebar arrangement

A500 steel Y1860 steel

Case studies

Figure 25: Deck slab

Figure 26: Main piles

(a) Geometry (b) Rebar

(a) Geometry (b) Rebar (c) Complete model

Case studies

Figure 27: Piles of the access ramps/stairs

(a) Complete model (b) Rebar (c) Geometry

Case studies

Figure 28: Connection between the main girders and the piles using two 20mm steel dowels and a neoprene bearing pad

The dowel connection is of extremely importance as to prevent the unseating of the deck and

to ensure the global structural stability. Therefore, its modeling must be performed as accurate

as possible. In this phase of the project, the maximum shear force that can be transmitted by

this connection was estimated through a pushover analysis and compared with the design

codes requirements.

232

Case studies

Figure 29: Numerical estimates for the pushover analysis

Table 5: Maximum shear force for the dowels

Dowels 20 MC2010* BS8110

Maximum dowel shear force (kN) 56.19 94.20

* dowel effect included

The results, illustrated in Figure 29 and Table 5, were promising and encouraged the use of

these numerical models in further analysis. However, one must note that these values were

updated in a later stage of the project, when the results of the large scale experimental tests

were available.

Final numerical models

The final numerical models, obtained after performing a manual updating procedure, were in

good agreement with the identified modal parameters, as illustrated by the MAC matrices

presented in Tables 6.

The configurations and the natural frequencies of the principal vibration modes of the three

footbridges, as resulted from the numerical simulations, are illustrated in Tables 7 to 9.

Case studies

Table 6: MAC for the final ELS models

PP3141 (one span)

PP2757 (two spans)

PP2787 (three spans)

Table 7: PP3141 - Modal configuration of the principal vibration modes

1.901 Hz 2.620 Hz 3.044 Hz

Case studies


2.243 Hz 2.358 Hz

3.935 Hz 7.666 Hz


1.803 Hz 1.962 Hz

4.037 Hz 8.073 Hz

Case studies

Collapse mechanism for high values of PGA

The three calibrated numerical models were used next to check eventual unseating

vulnerability of the footbridges when subjected to the design earthquake. The performed

non-linear analysis proved that all structures are safe in what respect the unseating and

integrity of principal structural elements.

Further analysis aimed to check the collapse mechanism in the case of stronger seismic

excitation. This type, the footbridges were subjected to a PGA of 0.6g, roughly two times the

design earthquake. The Figures 30 to 32 illustrate that, although the structures collapsed, the

failure was not caused by unseating.

Figure 30: Collapse mechanism of the one span PP3141 footbridge

Figure 31: Collapse mechanism of the two span PP2757 footbridge

Case studies

Figure 32: Collapse mechanism of the three span PP2787 footbridge

Collapse mechanism for cascading aftershocks scenario

To check the potential of the cumulative damage and of the cumulative relative displacements

between the deck and the piles to initiate the unseating and therefore, the collapse of the

structures, another scenario was considered. This time, a design earthquake with a PGA value

of 0.3g was considered as a main shock, together with a 0.2g foreshock and a 0.2g aftershock.

The results of the numerical simulations show that, is such a scenario, all three structures are

susceptible to unseating. A high probability of occurrence of this failure mechanism is

expected for multi-span footbridges, which are associated with inadequate seat lengths. An

example is illustrated in Figures 33. In such cases, the implementation of a strengthening

solution is considered mandatory.

Case studies

Figure 33: Unseating mechanism of the three span PP2787 footbridge

Numerical simulations using the FEM

To assess the effectiveness of an eventual retrofitting solution comprising superelastic NiTi

SMA restrainers, further numerical simulations were performed using OpenSees computing

program due to its ability to include in the analysis superelastic elements.

The structural vulnerability of the retrofitted footbridges was compared with the structural

vulnerability of the original structures. Moreover, a comparison was made to enhance the

better performances of the superelastic solution when compared with the classical steel

connectors. This comparison is illustrated in Figures 34 to 36 for the one span footbridge

(PP3141), structure that is known to be less sensitive to this scenario. Even in this case, the

effectiveness of the superelastic solution is clearly emphasized.

Case studies

Figure 34: Seismic response of the original footbridge structure

Figure 35: Seismic response of the retrofitted structure - 4 STEEL rods (0.4m, 10mm)

Case studies

Figure 36: Seismic response of the retrofitted structure - 4 SMA rods (0.4m, 11mm)

Conclusions

The estimates of the performed numerical simulations must be confirmed, in a later stage,

using the results obtained during the large scale experimental campaign. However, several

conclusions can be drawn.

In what respect the original footbridge structure:

It presents no unseating vulnerability for the design earthquake;

The plastic deformation are concentrated at the dowels connection;

However, the connection has no recentring capabilities;

The structure is highly vulnerable to unseating in the case of cascading aftershocks.

In the case of the structure retrofitted structure with steel rods:

Small part of the plastic deformation is distributed to the piles;

Large energy dissipation concentrated in the seismic links;

However, the connection has no recentring capabilities;

The structure presents moderate unseating vulnerability in case of cascading

aftershocks.

In the case of the structure retrofitted structure with SMA rods:

Only a small part of the plastic deformation is distributed to the piles;

Case studies

Moderate energy dissipation in the seismic links;

The connection has recentring capabilities avoiding cumulative relative

displacements;

The structure is safe in a scenario of cascading aftershocks.

Experimental program


Shear behavior of the connection between girder and pile

Experimental setup

The main objective of the proposed experimental tests was to analyse the shear behaviour of

the connection between the deck main girders and the piles, when subjected to monotonic

and cyclic shear loads. The connection is built up of two 20 mm steel dowels and a neoprene

bearing pad.

The prototype, designed to be representative of a typical footbridge connection, consisted on

a short girder supported on a reinforced concrete seating, with 10 mm thickness neoprene

pads and the corresponding dowels. The reinforced concrete prototype was rigidly connected

to the seismic table using steel supporting apparatus. The girders were actuated longitudinally

by the table itself, using an additional metallic strut which was supported on a reaction wall. In

Figure 24 is presented a general scheme of the experimental prototype, with its main

components.

Figure 37: General scheme of the experimental prototype

For the girders, an inferior reinforcement of 5𝜙12 was adopted, with a transversal

reinforcement of 𝜙8//0.10m, as shown in Figure 38. For the seating, both superior and inferior

reinforcements of #𝜙12//0.10m were adopted. The connection between the girder and its

Load

cell

RC seating

Steel supporting apparatus

Small girder Metallic

strut

Seismic Table Reaction wall


seating is materialized by two steel dowels with 𝜙20 mm, which are placed inside two circular

ducts filled with a high resistance mortar.

Figure 38: Reinforcement detailing for the concrete elements

Construction of the prototype

The construction of the prototypes was performed during August, 2015 in the facilities of the

Earthquake Engineering and Structural Dynamics Division (NESDE) of LNEC. Figures 38 to

43 illustrate some of the key phases of the construction process.

Figure 38: Floor leveling structure and bottom formwork


Figure 39: Vertical formwork and shoring

Figure 40: Positioning of the negative molds


Figure 41: Positioning of the rebar


Figure 42: Concreting process

Figure 43: Concrete release

Figure 44: Prototype ready to be tested on the NESDE seismic table


Monotonic loading

The monotonic loading consisted in a quasi-static test during which the displacements were

imposed to the seating through the seismic table. The velocity of the imposed displacements

was sufficiently low to prevent the occurrence of inertia forces and the associated dynamic

effects. The direction of the loading remained constant during the whole test. The resulted

force-displacement diagram is presented in Figure 45. During this test, the maximum shear

force in the connection was 142.12 kN, which is consistent with the values given by the design

codes (EC2 and MC10). For the case of the EC2, the relative error was about 9%.

One can see through the obtained force-displacement diagram that the connection is

characterized by a high ductility. For the imposed level of displacements, failure occurs both

in the concrete of the girder and of the seating, see Figure 46 (a) e (b), as well as in the dowels

themselves, see Figure 46 (d). The degradation of the neoprene pad is shown in Figure 46(c).

One can see that a significant degradation of the bearing pad occurred during the test, with a

complete tearing of this element in an alignment defined by the dowels.

-40-20

020406080

100120140160180

0 10 20 30 40 50 60 70 80

Fo

rce

[k

N]

Displacement [mm]

Figure 45: Force-displacement diagram obtained during the monotonic test

Displacement (mm)

Sh

ea

r fo

rce (

kN

)


(a) Concrete failing in the girder (b) Concrete failure in the seating

(c) Degradation of the neoprene pad (d) Failure of the dowels

Figure 46: Degradation of the prototype after the monotonic test


Cyclic loading

To understand and characterize the connection cumulative damage and the corresponding

stiffness loss, typical for earthquake scenarios, quasi-static cyclic displacements of growing

amplitude were imposed to an identical prototype. The load history is presented in Figure 47.

Figure 47: Time history of the imposed displacements

The structural response of the prototype connection is presented in Figure 48, being

characterized by hysteretic cycles where one can see the increased degradation both in terms

of stiffness and resistance.

Figure 48: Force-displacement diagram obtained during the cyclic test

Dis

pla

cem

en

ts (

m)

Time (s)

Sh

ea

r fo

rce (

kN

)

Displacement (mm)


In this test it was observed that the resistance of the connection decreased for growing levels

of displacements, with the number of applied cycles. The results are not quite symmetrical

with a slight higher resistance associated with the push direction. Regarding the degradation

observed during the experimental test, and illustrated in Figure 49, the girder presented some

cracks, while the seating suffered a significant concrete failure, similar to the one occurred in

the monotonic test.

(a) Girder with little degradation

(b) Failure of the concrete in the seating

(c) Cracks on the girder

Figure 49: General state of the prototype after the cyclic test

During the cyclic tests, the dowels were essentially mobilized in flexion, with their failure

occurring for a displacement of approximately 40 mm. One of the dowels has failed in two

distinct places, associated with the formation of two plastic hinges, see Figure 50. The

distance between these hinges was about 70 mm.

Figure 50: Failure of the dowel associated with the formation of two plastic hinges

The results of the cyclic tests clearly illustrate the presence of cumulative damage in the

connection, with evident consequences in the seismic structural vulnerability of the footbridge

as a whole. Therefore, the numerical models that are used to assess their non-linear dynamic

response to earthquakes, must be calibrated with results obtained through experimental

cyclic/dynamic tests.


The ability of the numerical models used during the project to simulate the footbridges

responses to replicate these experimental curves was successfully proven, as illustrated in

Figure 51.

Figure 51: Dowel hysteretic cycle - Experimental and simulated cyclic tests

Characterization of the superelastic elements

Cyclic uniaxial tensile tests were conducted on a Zwick-Roell Z50 tensile testing machine to

characterize the superelastic properties of the 1.6 mm diameter NiTi wires provided by Memry

Inc. Twenty consecutive uniaxial tensile cycles, with a speed of 0.3%/s and a maximum strain

of 5% were performed on the specimens, tested as received.

The machine’s gripping jaws during testing, the extensometers used to measure the sample

strains and the wire sample itself are illustrated in Figure 52.


Figure 52: Zwick-Roell Z50 gripping jaws, extensometers and wire sample

The tensile tests in the superelastic specimens showed a cumulative degradation in terms of

accumulated residual strains, and a decrease on the critical stress to induce martensite. As

illustrated in Figure 53, this degradation eventually stabilized, leading to a forward

transformation plateau of about 400 MPa.

Figure 53: Stress-strain diagram of the superelastic wires

The stress-strain experimental diagram can and will be used to calibrate the superelastic

material constitutive model to be used in the numerical simulation of retrofitted footbridges

subjected to seismic loading.

Conclusions

Conclusions Analyzing the outputs of the activities performed during the project and despite some inherent

difficulties related to the budget execution, all the proposed scientific objectives of the project

were fulfilled. The main achievements of the SUPERB project are highlighted below:

As a result of an extensive and successful experimental campaign of modal

identification from ambient vibration responses, a web-oriented database was

created, collecting relevant structural and dynamic characteristics of 17 footbridges in

the Southern part of Portugal. Besides of major importance for the current project, the

database can support future research initiatives in this area, as it is public available

(http://sites.fct.unl.pt/superb).

A high-performance computational program was developed, allowing the non-linear

dynamical analysis of MDOF systems comprising SMA elements. The rate dependent

constitutive model used to simulate the behavior of the superelastic elements

guarantees accurate results of the numerical simulations for an extensive range of

forcing frequencies, yielding a numerical tool that can help the civil engineers to

understand the complex seismic response of structures containing superelastic kernel

elements.

Complex non-linear dynamical analysis using SAP2000 (www.csiportugal.com),

OpenSees (opensees.berkeley.edu), SeismoStruct ( www.seismosoft.com) e ELS

(www.extremeloading.com) performed on statistically relevant footbridges subjected

to significant ground motions, selected as to cover a meaningful range of peak ground

accelerations, duration and frequency content for Portugal, reveal no unseating

vulnerability of these structures for the design seismic action. However, this is only

true if the dowels are in a good state of conservation and when pre and after-shocks

are not considered in the analysis. In such cases, especially in the case of multi-span

structures, cumulative damage lead to larger relative displacements between the deck

and the pile and unseating can occur. In such a scenario, superelastic retrofitting

devices proved, numerically, to be extremely effective.

The results of the large scale seismic experimental program allow to completely

characterize the complex failure mechanism of the dowel connection between the

deck and the piles for cyclic loading. The outputs of this experimental program,

together with cyclic experimental tests on samples of shape-memory alloy wires

allowed to calibrate the numerical models in order to increase the confidence in the

numerical estimates.

Related to training and dissemination actions one recall the participation of team

members in the organization of the 15the World Conferences on Earthquake

http://sites.fct.unl.pt/superb

http://www.csiportugal.com/

http://www.extremeloading.com/

Conclusions

Engineering (2012) and the Workshop: Dynamic Performance Assessment &

Rehabilitation of Structures (2014), the short stay of one team member at Georgia

Institute of Technology and participation of several team members in international and

national conferences related to the main topics of the project (ASCP-2015, 2ECEES,

ICDVC-2014, JPEE-2014, ASCP-2013, WCEE-2012, IABMAS-2012).

Related to publication, the activities related to the project yielded 2 papers in

international journals, 4 communications in international meetings, 1 communication

in a national meeting, 5 reports and 5 MSc thesis.

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http://www.dec.fct.unl.pt/projectos/SUPERB/PAPERS/VI05.pdf



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