Keywords: masonry arch bridge, dynamic tests, identification, model updating.

A 19th multi-span masonry arch bridge over the Tanaro River, in the city of Alessandria, Piedemont, in the north-western Italy, was a railway bridge between Turin and Genoa. It has 15 spans of about 10 m, and the total length of the bridge is about 185 m. The rise of the bridge is about 1.7 m, and their radial thickness is about 0.81 m. They are supported by the short and stiff piers and their thickness and height are about 2.5 m and 4.0 m, respectively. The arch bridge was composed of three arch decks having an almost equal width and the total width of the bridge is about 12.9 m. These arch decks were fastened by transversal rods.

Several dynamic tests have been carried out to evaluate the structural characterization of the remaining two span masonry arch bridge, other spans were demolished. The present study deals with the dynamic identification and model updating of the remaining two span masonry arch bridge and a comparison of the fundamental frequencies and mode shapes identified by the eigensisytem realization algorithm (ERA) technique [1,2] and the results determined by finite element analysis (FEA) based on the inverse eigensensitivity method (IEM) [3] is discussed.

In order to obtain data on the dynamic structural properties the acceleration time histories due to the impulsive vertical and horizontal loading are measured in the vertical direction in the two cases, without fill materials and without fill materials and spandrels. The total number of measuring points is 33 and 36, respectively.

Four principal modes in the vertical direction are estimated by experimental measurements and dynamic identification and the following can be inferred:

1. Although the profile of the remaining two span masonry arch bridge is symmetric in the longitudinal direction, the asymmetric mode shapes appear for all modes. These asymmetric mode shapes are probably caused by the inhomogeneous material of the piers and, or the problem of foundations including unequal settlement.
2. The discontinuous mode shapes appear for all modes. The arch is composed of three arch decks fastened by the transversal rods. These discontinuous mode shapes are probably caused for this reason.

The FE model is composed of eight-node isoparametric solid elements. The total number of nodes and elements is 1644 and 916, respectively. The boundary conditions of the three piers are assumed to be fixed.

The correction procedure uses four experimental frequencies and mode shapes obtained from dynamic identification [4]. Since the initial FE model is excessively idealized, errors of up to 23.2% between the measured and estimated frequencies obtained by the FE model are significant. After updating, the differences between the experimental and analytical frequencies are less than 1.21% for all the modes. The values of the MAC between the measured and analytical modes of the updated model become a little bit larger than those of the initial model for all modes.

With the model updated according to the experimental measurements, it is possible to determine the variations in the stiffness of the structural elements. From the results of the numerical model updating based on IEM, the following can be inferred:

1. The stiffness of the elements at the base of the piers is reduced to almost 80% probably due to the effect of bridge-soil interaction.
2. The stiffness of the elements at the mortar between the arch decks is decreased and the discontinuous mode shapes appears. This means the arch decks are really not well connected.
3. The stiffness of the elements at the arch decks near the first pier, the thickness is larger than others, is increased probably due to the effect of the abutment.
4. The cross-wise heterogeneity of the piers is also confirmed.

Fortunately several dynamic tests were carried out during the demolition of the multi-span masonry arch bridge, the numerical updated model obtained can simulate the real behaviour of the remaining two span masonry arch bridge and allow the analysis of the structural dynamic response of the particular and complicate masonry arch bridges. This bridge studied here is not special, most masonry arch bridges are the same kind of structures.

1

J. Juang, R.S. Pappa, "An Eigensystem Realization Algorithm for Modal Parameter Identification and Model Reduction", Journal of Guidance, Control and Dynamics, 8(5), 620-627, 1985. doi:10.2514/3.20031

2

T. Aoki, T. Komiyama, D. Sabia, D. Rivella, "Theoretical and Experimental Dynamic Analysis of Rakanji Stone Arch Bridge, Honyabakei, Oita, Japan", in "Proceeding of the 7th International Conference on Motion and Vibration Control MOvIC'04", St. Louis, 8-11 August, 1-9 (CD-ROM) , 2004.

3

H. Jung, D.J. Ewins, "Error Sensitivity of the Inverse Eigensensitivity Method for Model Updating", in "Proceedings of the 10th International Modal Analysis Conference", San Diego, 992-998, 1992.

4

M.I. Friswell, J.E. Mottershead, "Finite Element Model Updating in Structural Dynamics", Dordrecht, Kluwer Academic Publishers, 1995.

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