1 INTRODUCTION

The modal analysis, both analytical and experimental, offers the excellent tools for studding the dynamical behaviour of structures. Although most physical problems are non-linear, and the modal analysis is linear by nature, still a huge number of applications for which linear approximation is acceptable exist. In this paper the part of work that has been done within a frame of Smart Structure Marie Curie RTN project is presented. The main goal of the specific part of project was to turn a large, safety-critical civil engineering structure that was equipped with a monitoring system into “smart structure” that could autonomously provide a continuous update on its health. In scope of work, the experimental modal analysis techniques were applied in order to identify the mode shapes, frequencies, and the damping of considered system, and for preparation of so called reference model. In the computational stage, the finite element model of structure was built and subjected to the analytical modal analysis. The reference model was exploited to produce more reliable numerical model. It was achieved by altering the FE model and comparing experimentally obtained mode shapes and frequencies with the results of simulations.

Numerical model derivation of the composite high-speed train viaduct based on the experimental data

M. Kahsin LMS International, Leuven, Belgium

B. Peeters LMS International, Leuven, Belgium

ABSTRACT: Due to the considerable advantages regarding the design, construction time, durability and costs, composite steel-concrete bridges are commonly used in high-speed lines of the European railway network. Generally, the nature of bridge-like civil structures does not allow to build a prototype. Therefore, in case of analyses aiming to remove uncertainties on dynamic effects and interaction phenomena, derivation of fatigue loadings, structural modelling, fatigue life and damage assessment of steel-concrete composite high-speed railway bridges, an appropriate numerical model representing the dynamical state of the construction is needed. This paper covers the derivation of a numerical model of the Sesia Viaduct located on the new Italian high-speed line between Torino and Milano. More specifically, issues related to complex material data, asymmetries in the construction, asymmetries in the supporting condition, and model reduction will be addressed and resolved. Finally, the numerical model has been updated with the use of experimental data acquired by means of Operational Modal Analysis under ambient and train excitation conditions.

38 IOMAC'09 – 3rd International Operational Modal Analysis Conference

2 THE OBJECT OF INVESTIGATION - SESIA VIADUCT

As an object of investigation the steel-concrete composite Sesia Viaduct has been chosen. The viaduct is located on the Turin-Milan Italian high-speed railway line near Novara on the homonymous river.

2.1 The Description of Structure

Figure 1 : The view of Sesia Viaduct.

The viaduct is a box girder steel-concrete composite bridge designed in 2003 and it consists of seven 46 m long spans for a total length of 322 m, see Fig. 1. Each simply supported girder span has the same double box cross section: the bottom steel box is composed by lower flanges and three webs, see Fig. 2; the concrete slab has geometrical dimension of 13.6 m width and 0.4 m thickness and it is formed by supporting pillar with an integrating cast and stud connections to the steel box. The steel box is formed by three parts, each about 15 m long and joined together by welded connection. The bearings scheme is formed by fix, mono-directional and bi-directional supports, see Figs. 2-3. It has been designed in order to avoid internal stress due to thermal actions. The supporting piers are realized in a reinforced concrete solution and they are founded on piles. As it could be seen in Fig. 2, the viaduct structure is unsymmetrical, both in the cross-section (middle flange) and the bearings. The bearings configuration provides static decoupling of spans, although some coupling effects could be expected due to the rail-ballast action between spans.

Figure 2 : The Sesia viaduct cross-section (left). The span support layout (right).

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Figure 3 : The Sesia viaduct bearings (multi-directional - mono-directional - multidirectional).

2.2 The Experimental Identification of Viaduct Dynamics – Preparation of Reference Model

Due to the large extend of investigated structure only part of Sesia Viaduct has been instrumented with sensors, see Fig. 4. The choice of sensor types and positions was such that the global and local structural behaviour, both in vertical and horizontal direction, could be analyzed. Totally, accelerations were measured in 103 directions, i.e. 12 on the first span, 86 on the second and 5 on the third span. A total amount of 33 accelerometers (10 PCB capacitive and 23 PCB piezoelectric ICP accelerometers) was available, which required to measure the viaduct in multiple runs with the majority of the sensors moving positions between the runs, while keeping a few of them at fixed locations during all runs (the so-called reference sensors).

Figure 4 : Positions of acceleration sensors and measured directions on Sesia Viaduct.

The acquisition system consisted of an LMS SCADAS 305 front-end controlled by LMS Tes.Lab Spectral Testing software. The power was supplied by a generator, with a double back up provided by a UPS system and the internal batteries of the laptop and the SCADAS 305 front-end.

The acceleration response measurement included two types of excitation: ambient (wind-excitation); and train set passage. The identification of system dynamics by means of modal

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analysis could be performed for wind-excited condition only. The reasons for this was lack of information about excitation amplitude during train passage, and a potential loss of system observability caused by over 11% of train mass contribution to the total mass of the system. Because of “randomness” of the ambient excitation it could be treated as white noise. In such case the modal parameters estimation (i.e. eigenfrequencies, damping ratios, mode shapes) of viaduct could be performed with use of Operational Modal Analysis (OMA). Both Stochastic Subspace Identification and Operational PolyMAX - Peeters et al. (2007), as implemented in LMS Test.Lab - LMS International (2008) have been applied to the 4 runs of ambient vibration. An example of registered acceleration data is presented in Fig. 5. More information on the data pre-processing, the parameter identification and the combination of the results from the 4 different runs is given in – Chellini et al. (2008). Figs. 6-7 show the first six identified mode shapes. The final reference model consists of these six modes. It could be seen that this mode shapes are almost identical on the second span; the difference is in the interaction with the neighbouring spans. This situation could be caused by coupling effects of rails and ballast.

Figure 5 : An example of registered data from accelerometer at position 2b06 (see Fig. 4) in vertical

direction. Two train passage events have been recorded.

Figure 6 : The first two identified mode shapes of Sesia Viaduct. The mode shapes are almost identical for the second span; the difference could be seen while comparing the motion of neighbouring spans.

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Figure 7 : Mode shapes 3-6 of Sesia Viaduct. The mode shapes are almost identical for the second span;

the difference could be seen while comparing the motion of neighbouring spans.

3 THE VIADUCT’S MODEL DERIVATION

The 3D CAD model has been built with use of LMS Virtual.Lab software basing on the provided viaduct’s drawings. The 3D model of one span is presented in Fig. 8.The CAD level of detailing was affected by the facts that further on developed FE model was meant to be used in durability simulation.

Figure 8 : The 3D CAD model of single span.

To avoid excessive model complication, no riveted, bolted nor welded connections have been considered. However, such connections could be investigated with use of sub-structuring techniques on the basis of derived model. It was also decided that no geometrical representation

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of supporting pillars and bearings should be included. The steel parts of viaduct have been modelled as the surfaces, while the concrete and the ballast have been modelled as solids.

3.1 The FE Model of One Span

The FE model of one span has been built basing on the 3D CAD model and with use of LMS Virtual.Lab software. The 3D model of one span is presented in Fig. 9. For the steel parts of viaduct 2D linear shell elements have been used, while the concrete and ballast parts have been modelled with use of 3D linear solid elements. The initial values of material data and element properties are presented in Table 1.

Figure 9 : The finite element model of single span.

Table 1: Materials and elements properties of FE model.

Material Elastic Modulus

Poisson’s Ratio

Density Element Type

Element Thickness

- GPa 1/1 kg/ m3 - Mm Floor Steel 205.6 0.3 7850 Shell 20/30 Walls Steel 205.6 0.3 7850 Shell 20 Ribs Steel 205.6 0.3 7850 Shell 20 Sections Steel 205.6 0.3 7850 Shell 10/16/18/25 Slab Concrete 31.41 0.2 2500 Brick - Ballast Equiv. 1.588 0.2 1750 Brick - Rails-Pads-Sleepers Equiv. 12 0.2 2500 Shell 7.686

The Fe model does not include riveted, bolted nor welded connections; overlaying shell, and contacting 3D (ballast-concrete) elements share common nodes; interface between steel and concrete has been realized with the rigid bar elements. For the support additional spider-web of rigid elements has been applied in the proximity of the bearings. The master node of the spider-web for each bearing has been restrained in appropriate direction, see Fig. 2. The rails-pads-

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sleepers system has been regarded as 2D shell elements witch equivalent properties. All materials in the model are assumed to be isotropic.

3.2 The Modal Analysis of FE Model

Initially, the one-span model was solved for normal modes with use of Lanczos normal mode extraction procedure (NASTRAN’s SOL 103), preceded by static analysis that allowed to include viaduct’s pre-stress (self-weight) effect. On the basis of FE modal analysis results, the verification model has been built. The verification model in conjunction with the previously mentioned reference model was used for a Modal Assurance Criterion (MAC) analysis. The MAC values ranges from 0 to 1, and are correlation factors for each pair of analytical and experimental mode shape. In case of normal modes it could be presented i.e. Eq. (1):

][][

2][

FEVT

FEV

TestVT

TestV

FEVT

TestV

TestFEMAC

⋅⋅

⋅= (1)

where MACTestFE = MAC value, VTest = test mode shapes and VFE = mode shapes from FE analysis. The ideally correlated modes should produce diagonal pattern with values 1. A MAC matrix for the one-span model and first mode shape are presented in Fig. 10.

Figure 10 : The MAC matrix and first mode shape for the one span model.

From the MAC matrix it could be seen that in the analysed Sesia Viaduct case the one-span FE model does not represent properly dynamical behaviour of real structure. Although the initial MAC values are on acceptable level (the values with not yet updated physical properties of FE model), the one of bending modes is missing. It could not be stated whether if it is the one with symmetrical or anti-symmetrical boundary conditions at the piers, without taking in to account the action of neighbouring spans. According to this observation more modified FE models have been investigated. The idea was to modify numerical model in such a manner that

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it shoul represent action of neighbouring spans while keeping model size within reasonable size The first bending mode shapes of investigated FE models are presented in Fig. 11.

Figure 11 : The first bending mode shapes of investigated FE models. a – the first model consisting of

one span, b – the one-span model with spring elements on the end interfaces of ballast and rail path, c – the model consisting of one full span and the two halve-spans, d – the model including all seven spans, e

– the three-spans model.

The first altered model, see Fig. 11b, contains additional sprig elements attached to the nodes at the ends of ballast and rail path. It was assumed that implementing additional stiffness which values have been derived as an equivalence of redundant spans stiffness (i.e. one from the right side of viaduct, and five on the left side), should allow to properly imitate the dynamical behaviour of whole structure. Nevertheless, the situation was analogous to the original one-span model – no second bending moment could have been excited. In the third approach, see Fig. 11c, instead of spring elements, halve-spans were applied at the original span interfaces. The reason for this was to not include too many additional degrees of freedom in the FE model. In the results of modal analysis for this configuration both first mode shapes were bending modes. However the situation at the lower frequencies improved, the higher modes were no longer in agreement with the test results. It was impossible to state what kind of restrains at the ends of halve-spans should be applied due to the asymmetry of supporting of bearings. Such approach will also create a solution with nonphysical values of halve-spans material and geometrical properties in case of tuning the system with use of optimisation method. Next, the seven-span model has been used for identifying the overall structure’s dynamical behaviour, in order to determine the influence of rail-ballast coupling effects on the performance of individual spans, see Fig. 11d. With this model good agreement between test and simulation data has been established. In this case all the mode shapes from the test had their counterparts in the simulation results. The major problem concerning this model was that its size (over three million DOFs) made it impossible to use in further analyses (i.e. system level durability – basing on the viaduct flexible representation and the multi-body system dynamics representation of train set). The last investigated configuration of FE model, based on the information about rail-ballast coupling properties obtained from seven-span case results, consisted of three spans, see Fig. 11e. The three-spans model fulfilled goals related to reproducing measured dynamics of viaduct while having reasonable size. In comparison to seven-span model, the mode shapes of three-span were less distinctive, i.e. MAC for three-span model in case of two first bending modes frequencies has lower and almost equal values. Surprisingly, the frequencies differences, especially for the higher occurrences, have been improved. The change of mode shapes order and differences in frequencies are presented in Fig. 12.

The summary of results from different FE models is presented in Table 2.

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Figure 12 : The MAC matrices for the altered FE models: a – the one-span model; b – the one-span model

with spring elements on the end interfaces of ballast and rail path; c – the model consisting of one full span and the two halve-spans; d – the seven-span model, e – the three-span model.

Table 2: The summary of results for different FE models.

Description of model Max. freq. difference Modes representation

acc. to test (MAC)

Remarks

% - - One-span model 52% - first bending

mode poor One of the firsts bending

modes, and both second bending modes have no

counterparts in the simulation mode set

One-span model with attached spring

13.9% first bending mode

very poor The one of the first bending modes in simulation is missing.

Scattered MAC. Full-span with attached halve-spans

8% - both first modes in the first pair of

bending and torsional modes

poor Both first bending modes are present; modes above 10.4Hz

from simulation have no counterparts in test data.

Three-span model Full model of the viaduct

10% - first in the first pair of torsional

modes

the best among all

analysed cases

The simulated modes mimic double nature of first bending,

first torsional, and second bending modes. Distinction in modes order is troublesome.

Seven-span model 15% - the second of first pair of bending

modes

good All the pairs of modes are present in simulation. In this model modes are the most distinctive in comparison to other models. The huge number of DOFs.

Additional remark concerns modes that are not present in the reference model. It is obvious that the FE modal basis will contain modes that can not be excited during the measurements, especially of higher frequencies, but in case of OMA it should be of special concern due to the very weak excitation (i.e. wind). For the Sesia Viaduct no other techniques but OMA could

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have been undertaken due to the fact that the structure must been continuously operational. With to many missing modes in test data it could be hard to determine if modes obtained from the FE simulation are in proper order. For further exploitation, the three-span model has been chosen as the one best satisfying accuracy and size requirements. Due to the frequencies differences between test and simulation eigenfrequencies and poor distinction of mode shapes among the paired modes, the additional optimizing procedure has been carried on. Description and results of model updating with optimization methods exceeds scope of this paper and will not be discussed in more detail (Author, in prep.).

4 CONCLUSIONS AND OUTLOOK

This paper presented the preparation process of numerical model for the large-compound civil structure on basis of the high-speed Sesia Viaduct example. The comparison of simulated and measured modes clearly states that appropriate numerical representation of such structure is hardly ever obtainable without simultaneous comparison with the experimental data. The OMA with use of wind excitation is very good option for the dynamics identification of bridge-like structures under continuous operational condition, nevertheless it should be noticed that due to the nature of excitation some of modes could be not present in-between experimental modal basis. The uncertainties concerning: the appropriate completeness of experimental modal basis, structural and material parameters; the unknown and hart to predict dynamical behaviour of span-to-span coupling are the most important sources of difficulties during modelling, simulation and updating stages. Some trial optimisation runs have been carried out before changing FE model structure. It has been done to improve representativeness of the one-span FE model. Unfortunately all of these attempts failed to produce satisfactory results (Author, in prep.). The more realistic dynamical model of the viaduct has been derived after intensive study of FE mesh composition. In the analysed case the best way to obtain the adequate FE model representing dynamics of single span of viaduct was to apply additional structure. The selected three-span model is characterized by reasonable agreement with the experimental mode shapes and frequencies. Additionally, it realizes the non-excessive model assumption. However, the supplementary action in order to improve the simulation results has been planed, i.e.: the three-span model updating with use of global optimization method; and the study of bearings stiffness influence on the calculated mode shapes and frequencies.

REFERENCES

Chellini, G. and Nardini, L. and Liu, K. and Reynders, E. and Peeters, B. and De Roeck, G. and Salvatore, W. and Sorrentino, G. and Tisalvi, M. 2008. Experimental dynamic analysis of the Sesia Viaduct, a composite highspeed railway bridge. Proc. 26th Int. Modal Analysis Conference (IMAC-XXVI), p. 150-162.

LMS INTERNATIONAL. 2009 LMS Test.Lab Structures Rev 9A. LMS INTERNATIONAL. 2009 LMS Virtual.Lab Rev 8B. Peeters, B. and Marton, S and Chellini, G. and Nardini, L. and Salvatore, W. and Sorrentino, G. and

Tisalvi, M. 2008. A 24-bit permanent monitoring system for bridges: development and initial results. Proc. 4th European Workshop of Structural Helth Monitoring, p. 230-245.