EXTERNAL POST-TENSIONING RETROFITTING AND MODELLING OF STEEL-CONCRETE BOX-GIRDER BRIDGES

Bursi S.O.a, Bonelli A.b, Mammino A.c, Pucinotti R.d, Tondini N.e a,b,e Department of Mechanical and Structural Engineering, University of Trento, Italy

c S.I.GE.S. s.a.s Povegliano (Tv), Italy d Department of Mechanics and Materials, Mediterranean University of Reggio Calabria, Italy

Abstract: This paper reports the study of the Montevideo viaduct retrofit by means of exter-nal post-tensioning. The FE 3D model of the bridge was developed. The dynamic analysis of the structure was carried out by means of a modal response spectrum analysis which allowed to identify the sensitive details. One retrofit solution with parabolic and one with rectilinear cables were investigated. The second solution was selected: it consists of a group of straight cables lying on the bottom of the steel box. The positions of the anchorages were conceived in order to obtain a stepwise constant bending moment diagram very close to that obtained by the parabolic solution. In parallel with the retrofit design a dynamic analysis was carried out in order to identify the sensitive details; in particular by means output-only ambient vibration tests the Finite Element (FE) model was validated.

1. INTRODUCTION

Steel-concrete composite bridges benefits by a strong growth in rail and highway. In fact it represent a design option that is being increasingly adopted: i) in road networks; ii) in areas prone to high-intensity seismic events. The success of this design solution is due to the advan-tages that composite elements offer in terms of stiffness, resistance and ductility; moreover, the rapid erection, long span capability, economics, and aesthetics of these girders make them more favorable than other structural systems. The structural service-life has assumed a big importance in the design of structures, underlining the fact that the durability concept should be considered in the choice both of the material and of the structural typology.

The durability of structural systems can be defined as the capacity to preserve the initial performance. It is thus linked to the capacity of the material of construction to keep its physi-cal and mechanical properties unchanged within a given environment and under given work-ing conditions. The steel-concrete composite action is particularly advantageous for bridges as it leads to enhanced stiffness, ultimate capacities and ductility. On the other hand, their non-homogeneity leads to significant problems at service conditions. Furthermore, it has to be considered that, for bridge structures, environmental conditions and types of loads increase the degradation of the material and in particular the most common degradation phenomenon

2 7th International Conference on Steel Bridges is related to the corrosion of rebars in the concrete slabs. Bridges are, in fact, subjected to fa-tigue which leads to an increase of the cracks which, in turn, give rise to the penetration of the aggressive agents (e.g. chlorides, de-icing salts). In addition, an inaccurate maintenance, es-pecially of the expansion joints, could lead to aggressive environments in closed box-girder composite bridges which could undermine the structural steel owing to corrosion.

In this framework, an interesting technique for the rehabilitation and the retrofit of bridges is the post-tensioning by means of external slipping cables which can be straight or draped along the steel beam by means of deviators. Moreover, a peculiar issue is the lack of an accu-rate knowledge about dynamic effects, in particular in end-diaphragms and bearing regions which result to be very sensitive parts owing to stress concentrations. In fact, they can be widely damaged when subjected to strong dynamic loadings, like earthquakes; in addition, dynamic effects induce vibrations owing to traffic loads, which can amplify fatigue phenom-ena.

Many existing bridges have shown structural deficient owing mainly at deterioration of structural elements and at the load increment impose of rules evolution. Conditions assess-ment of bridges, frequently are largely based on visual observations and described by subjec-tive indices which do not permit an accurate evaluation of serviceability and safety.

In this paper, in addition both to the analysis of the actual state of the bridge and the FE model along with the dynamic analysis, the localization of the sensitive details is also de-scribed and a finite-element model updating to identify structural parameters and mechanisms is applied.

Moreover, the retrofit of the bridge by means of external post-tensioning with two solu-tions and different numerical analyses is presented.

2. THE VIADUCT: GEOMETRIC PROPERTY AND DEGRADATION STATE

The Vela viaduct or Montevideo is a steel-concrete box-girder bridge with 7 spans, 75 m

each; it is simply supported and 4 spans are curved with different curvature radius: going along the bridge from east to west the first three spans have R=350 m, while the 7th and last span has approximately R=200 m. The transversal section (Figure 1) consists of 4 lanes corre-sponding to 2 carriageways and 2 footpaths with a total width of the deck of 18 m. The total height of the steel box is 4.10 m with a concrete slab of 30 cm. Moreover, the steel box is composed of transversal truss diaphragms which have different stiffness on the basis of their position along the span. The viaduct built in the early eighties with steel grade S355 and char-acteristic compressive strength of the concrete of 40 MPa. The shear connection system be-tween the steel box and the concrete slab consists of studs and T connectors.

During the construction stages propping structures were used owing the limited height of the viaduct from the ground. This allowed an amount of saved structural steel of about 20%. Therefore, in the analysis of the structure the various stages were taken into account in order to obtain the actual stresses in the bridge [1].

Figure 2 shows a partial view of the vaduct, where it is possible to see the inpact of the structure on the area.

The employed steel in fact is classifiable how COR-TEN steel type. That is becoming more popular by roll formed product end-users. Its unique look and naturally oxidizing finish make it especially desirable for many architectural projects. Steel portions of the bridge have suffered an rapid degradation owing to the corrosion caused to the presence of atmosphere particularly aggressive and unfavourable. Therefore the primary cause of the advanced state of corrosion of the steel box is imputable just to the environmental conditions.

Theme (by the C.C.) 3

4100

1000 16000 1000

60003000 3000

3000 6000 6000 3000

300

Fig. 1: Transversal section at the bearing. Dimensions in mm

Figure 3 shows the degradation of the viaduct owing the corrosion of steel immersed in an

aggressive environment that have caused about 1 mm of decrease of steel plate thicknesses. Table 1 shown the midspan actual stress of a rectilinear span of the steel plates by applying

the loads of the in force rules [2]. It is possible to observe that the stress in the steel is much higher than the yield strength fy=355 MPa owing to the decreased thicknesses of steel plates.

Table 1: Stresses at the bottom of the steel box and in the slab at midspan

Description Maximum stress at the bottom [MPa]

Maximum stress in the slab[MPa]

Maximum bending and torsion 421.40 -15.5

Fig. 2: View of the case study viaduct

b) external detail c) internal detail

Fig. 3: Degradation of the viaduct The necessity of the bridge retrofit by means of an external post-tensioning after only 25 years from its building is determined by essentially 3 factors:

i) the traffic loads given by the national rules have risen in the past years; ii) the thickness of the steel plates which form the box is decreased of approximately 1

mm owing to a widespread corrosion process;

4 7th International Conference on Steel Bridges

iii) the traffic on the bridge cannot be interrupted owing to its strategic importance in the road network.

3. FE MODEL OF THE VIADUCT

The preliminary FE 3D model consists of 7 simply supported spans and was developed by using the SAP2000 program [3]. In the analysis focussed mainly on the horizontal interaction of spans and particular attention were paid on the span with the smallest curvature radius, i.e. R=200 m. The dynamic analysis of the structure was carried out by means of a modal re-sponse spectrum analysis which allowed to identify the sensitive details.

The bridge was discretized with shell elements for modelling the slab and the steel box, while frame elements were used for the truss elements of the transversal diaphragms and of the horizontal bracings. The composite interaction between the concrete slab and the steel box was made effective by body constraints which guarantee a full interaction as established by the European [4] and Italian rules [5]. The FE model of the curved span is shown in Figure 4.

The bridge was dynamically analysed according to the national seismic code OPCM 3431 [6] which incorporates the EC-8 design philosophy. It is important to underline that the stud-ied viaduct is located in Trento in a zone of low seismicity, classified how ZONE 3 according to the OPCM 3431 that fixes new criteria for the seismic classification of the Italian territory. Hence, the bridge was seismically analysed and checked by employing a modal response spectrum analysis with ag=0.15g.

The seismic analysis leads to a satisfactory behaviour of the viaduct in terms of check ac-cording to CNR 10011/88 [7] and CNR 10016/00 [5]; and it has been useful to identify the sensitive details from a dynamic point of view. As expected, the analysis showed that the bearing zone and the end-diaphragm were locally the most stressed ones. In particular, the diagonals and the connections were identified as stress concentration zones to be particularly sensitive; Figure 4b shows the longitudinal stress under the seismic load. Therefore, they could become critical in areas prone to high-intensity seismic events if not properly designed. Moreover, also the fatigue behaviour according to the part 2 of Eurocode 1, Eurocode 2, Eurocode 3 and Eurocode 4 was checked and it resulted satisfactory.

a) 3D FE model of the viaduct b) Longitudinal stress at the end-diaphragm

Fig. 4: 3D FE Model of the viaduct

4. OUTPUT-ONLY AMBIENT VIBRATION TESTS

Theme (by the C.C.) 5

In the previous section, we identified the sensitive details of the bridge starting from a FE model which did not match the actual state of the bridge in terms of mass and stiffness owing to an advanced corrosion of the steel in the box and uncertainties related to time-dependent phenomena. The bridge was tested by ambient vibration measurements. Followed by the three-dimensional FE modelling of the bridge, an eigenvalue sensitivity study is carried out to see the most sensitive parameters to the concerned modes.

The use of output-only techniques is very useful when dealing with bridges, because they can be used without interrupting the traffic flow which is the main vibration source along with the possible presence of wind.

The test was performed with an acquisition system which can acquire till 16 signals and two types of accelerometers with different sensitivities were employed. Two accelerometer configurations, as depicted in Figure 5 (5a and 5b), were conceived for acquiring the most significant modes. The optimal accelerometer locations were selected by means of the AutoMAC matrices [8].

9,8 9,8 9,811,5

11,5

9,8

9,8

9,8

Acquisition system position

Fix vertical accelerometer

Transversal or longitudinal fix accelerometer

Vertical accelerometer

a) Configuration A. Abutment side

9,8 9,8 9,811,5

11,5

9,8

9,8

9,8Accelerometer position on the pier

Fix vertical accelerometer

Transversal or longitudinal fix accelerometer

Vertical accelerometer

Acquisition system position

b) Configuration B. Pier side

Fig. 5: Accelerometer configurations

Table 1 report the comparison between experimental and numerical preliminary frequen-cies obtained by using the SAP2000 program (before model updating).

It is easy to see as, in correspondence of lowest frequencies, the variations between ex-perimental and numerical frequencies exceeds the 70 percent.

6 7th International Conference on Steel Bridges

Table 1: Comparison between experimental and numerical frequencies Shape fexp,i (Hz) fFE,i,1 (Hz) Variation (%) 1.00 1.70 2.96 74.05 2.00 5.10 5.10 0.00 3.00 8.80 9.84 11.72 4.00 9.10 10.99 20.66 5.00 12.01 15.03 25.15

5. MODEL UPDATING Finite element models (FEMs) are typically used in the retrofitting structures. The correla-

tion between an initial FEM and experimental data is often poor. This can arise due to inaccu-rate experimental data or an inadequate FEM. Factors that contribute to poor accuracy of FEMs include poor modelling of the structural elements and components, e.g. omitting inter-action among components like structural joints. Further potential source of errors are changes in the values of physical parameters and material properties. In fact, these can significantly alter FEM predictions.

The aim of the model updating procedure is to improve the correlation of FEM and ex-perimental modal analysis results. Therefore, model updating is used to minimize the ‘differ-ence’ between FEA and reference test data. In this paper the model updating were applied using the following procedure:

1. valuation of initial parameters, joP , ; 2. computation of the sensitivity matrix ][ ijS in order to construct the equation

jiji PSR ∆=∆ ][ , where iR∆ is the residual difference between the ith predicted and ex-perimental modal data, and jP∆ is the jth selected updating parameter;

3. solving for jP∆ : iijj RSP ∆=∆ +][ ; were +][ ijS is the pseudo-inverse matrix of ][ ijS ; 4. introduction of the resulting parameter changes jP∆ into the model and re-

computation of the modal parameters; 5. repeated the procedure until a convergence criterion is satisfied.

In detail as first step we considered as experimental modal data just the first five experimental frequencies and we estimeted sensitivity matrix numerically:

⎪⎪⎪⎪

⎭

⎪⎪⎪⎪

⎬

⎫

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

⎨

⎧

−

−

−

=∆

i

iFEi

i

FE

FE

i

fff

fff

fff

R

exp,

,exp,

exp,

2,2exp,

1exp,

1,1exp,

...,

⎪⎪⎪⎪

⎭

⎪⎪⎪⎪

⎬

⎫

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

⎨

⎧

−

−

−

=∆

jold

joldjnew

old

oldnew

old

oldnew

j

ppp

ppp

ppp

P

,

,,

2,

2,2,

1,

1,1,

...,

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

=

j

iFEi

j

FEFE

j

FEFE

ij

pf

pf

pf

pf

pf

pf

S

,

1

exp,

2,

1

2,

1,

1

1,

...

.........

...

...

][ (1)

The parameters initially chosen for model updating were: • Young’s Modulus of concrete; • Young’s Modulus of steel; • thickness of sidewalk; • span length; • slab thickness.

Theme (by the C.C.) 7

• inferior plate thickness of the box girder The number of parameters to which the model is effectively sensitive, corresponds to the

rank of the sensitivity matrix. The valuation of this rank happens through the valuation of the single value decomposition of the sensitivity matrix. The rank of the sensitivity matrix was 4. Afterwards sensitivity analyses on the five parmeters have allowed to adopt just the subse-quent parameters:

• Thickness of sidewalk; • Span length of the bridge; • Slab thickness. • inferior plate thickness of the box girder

Simultaneously we decided to insert in the FE model the experimental elastic modules of the actual materials (steel and concrete).

Table 2 shows the comparison among experimental frequencies and numerical frequencies obtained by using the SAP2000 program. In particular the second column reports the experi-mental frequencies, while the columns 3 and 4 report numerical frequencies before model up-dating and after some iteration of the model updating procedure respectively. At this moment the model updating procedure is still in course.

Table 2: Comparison between experimental and numerical frequencies Shape fexp,i (Hz) fFE,i,1 (Hz) fFE,i,Last (Hz) Variation (%)

1.00 1.70 2.96 2.88 69.29 2.00 5.10 5.10 5.04 1.14 3.00 8.80 9.84 9.65 9.63 4.00 9.10 10.99 10.85 19.19 5.00 12.01 15.03 14.73 22.71

6. RETROFITTING

The concept of prestressing and post-tensioning is well-known, above all in concrete struc-tures [9]. However, in steel-concrete structures, even though it can show good results, its ap-plication is very seldom and it assumes a slightly different meaning in the sense that we talk about prestressing when the external force is applied only to the steel part before the slab cast while with post-tensioning we mean the external force applied to the whole composite struc-ture [10], [11]. Advantages arise from the prestressing because it is possible to obtain the same benefits with less applied force but it is suitable for new rather than existing structures. For the reason of dealing with an existing bridge, post-tensioning will be provided for. More-over, since this solution is always external, an adequate study of restraint structures and de-viators of forces as well as of possible local instabilities, which could lead to whole collapse of the structure, must be provided. Another important aspect is the choice of an appropriate development of the cables along the span. As a result, in this case two solutions were taken into account:

i) a parabolic solution; ii) a rectilinear solution.

In a simply supported beam a parabolic development in the vertical plane of the cables is the most rational as the sections with higher bending moment are characterized by the maxi-mum cable eccentricity. In fact, the cable is able to produce an equivalent load which is very

8 7th International Conference on Steel Bridges close to an uplift uniform distributed load. Moreover, in correspondence to the bearings the post-tensioning force causes a shear decrease. In this case the cables were deviated also in the horizontal plane in order to avoid interferences with other structures like diaphragms, stiffen-ers etc. As a result, the cable development became quite complex as it is possible to observe in Figures. 6 and 7.

Fig. 6: Cable planimetry with parabolic solution

Fig. 7: Cable altimetry with parabolic solution

This entailed the use of plates with high thickness, till 30 mm, which determined difficul-

ties in the organization of the building site, especially in terms of realization times and as-semblage inside the steel box.

In order to overcome the problems risen from the solution with parabolic cables, a second approach was investigated. It consists of a group of rectilinear cables lying on the bottom of the steel box. In this way the eccentricity of the cable with respect to the centre of the sections is higher and the losses owing to the angular deviations are practically negligible.

However, the benefit of the parabolic cable in terms of shear at the bearings is lost. More-over in this case, in order to get a post-tensioning force proportional to the applied loads the cable anchorages were distributed along the span as depicted in Figure 8.

Fig. 8: Cable planimetry with rectilinear solution

The positions of the anchorages were conceived in order to obtain a stepwise constant

bending moment diagram very close to the one obtained by the parabolic solution with the same number of cables, see Figure 9 (9a and 9b). This positioning allowed a gradual increase of the post-tensioning force from the end to the midspan. Moreover, the critical anchorage received the thrust of only 6 out of 18 cables, this meaning restraint structures less complex and lighter. In fact, there was a steel reduction of 20÷25 percent owing to savings with respect to the steel used to anchor the parabolic cables.

Theme (by the C.C.) 9

Every anchorage consists of a rectangular box (80 cm × 35 cm and variable plate thickness 15 ÷ 25 mm) welded to the bottom of the steel box.

a) parabolic post-tensioning only

b) rectilinear post-tensioning only

Fig. 9: Bending moment, shear and axial force

In Figure 10a is reported a typical restraint structure. The little eccentricity between the

cable and the bottom of the box entails a local bending moment which determined a strength-ening of the box as depicted in Figure 10b.

Finally, this solution had the evident advantage of simplicity so that a standardization of the single parts could be achieved which turned out in a reduction of realization times and as-semblage procedures.

a) transversal diaphragm

b) Section A-A of the anchorage Fig. 10: Anchorage detail

7 Conclusions

The paper reports the study of the Montevideo viaduct retrofit by means of external post-tensioning. The FE 3D model of the bridge was developed and dynamic analysis of the struc-

10 7th International Conference on Steel Bridges ture was carried out by means of a modal response spectrum analysis which allowed to iden-tify the sensitive details. Moreover, the paper presents the FE model updating results of the bridge based on the measured frequencies. In particular, the output-only techniques results are presented. Model updating was conducted with the aim to improve the correlation of FEM and experimental modal analysis results and with the objective to minimize the ‘difference’ between FEA and reference test data. The applications, still in development, have consented to choose the more sensitive parameters. In fact, a total of 6 structural parameters are selected for updating based on a comprehensive eigenvalue sensitivity study. The sensitivity matrix rank obtained is 4; this means that only four of the six parameters considered are valid to be used in the model updating. At the moment, we are improving the modal updating procedure.

Finally, retrofit solutions with both parabolic and rectilinear cables were investigated. In this last solution, that is the more convenient, the positions of the anchorages were conceived in order to obtain a stepwise constant bending moment diagram very close to that obtained by the parabolic solution. Acknowledgments This work has been carried out with a financial contribution of the Italian Earthquake Engi-neering Laboratory Network (RELUIS). References [1] Matildi, G. and Matildi P., Ponti Metallici. Esperienze Vissute, Cimolai, Pordenone,

1990. [2] Consiglio Superiore LL. PP., Testo Unico - Norme Tecniche per le Costruzioni, Roma,

2005. [3] Wilson E. L., Habibullah A., Sap 90 - A Series of Computer Program for the Static and

Dynamic Finite Element Analysis of Structures, Users Manual. Computer & Structures Inc., Berkeley, 1988.

[4] CEN, prEN 1994-2 (Final Draft). Eurocode 4: Design of Composite Steel and Concrete Structures - Part 2: General Rules and Rules for Bridges, Brussels, 2005.

[5] CNR, CNR 10016/00. Strutture Composte di Acciaio e Calcestruzzo: Istruzioni per l'Impiego nelle Costruzioni”, Roma, 2000.

[6] Ordinanza P.C.M. 3431, Norme Tecniche per il Progetto Sismico dei Ponti, Roma, 2005.

[7] CNR, CNR 10011/88. Costruzioni di acciaio: Istruzioni per il Calcolo, l’Esecuzione, il Collaudo e la Manutenzione. Roma, 1988.

[8] Ewins D.J., Modal Testing 2nd Edition, Research Studies Press Ltd, Baldock, 2000. [9] Pozzo E., Teoria e tecnica delle strutture. Volume III. Il cemento armato precompresso,

Pitagora Editrice, Bologna, 1999. [10] Nunziata V., Strutture in Acciaio Precompresso, Dario Flaccovio, Palermo, 2004. [11] Troitsky M.S., Prestressed Steel Bridges. Theory and Design, Van Nostrand Reinhold

Company, New York,1990. [12] CEN, prEN 1993-1-9 (Final Draft). Eurocode 3: Design of Steel Structures - Part 1.9:

Fatigue, Brussels, 2004. [13] CEN, prEN 10025-6 (Final Draft). Hot rolled products of structural steels - Part 6:

Technical delivery conditions for flat products of high yield strength structural steels in the quenched and tempered condition, Brussels, 2003.