Bridge analysis, design + assessment

Case Study

Seismic Assessment of the Mustafa Inan Viaduct

  • Seismic re-assessment study following earthquake damage
  • Linear and nonlinear dynamic analysis using 3D thick beam elements
  • Very good correlation achieved between previously measured and calculated modal frequencies

In August 1999, the Kocaeli earthquake in Turkey damaged a number of structures on the Trans-European Motorway. In all, 20 viaducts, 5 tunnels, and a number of overpasses were affected. Damage varied from concrete spalling, shifting of girders from their seats, pier tilting, approach fill settlement, and for some structures total deck collapse. Gebze Institute of Technology, with the permission of and in cooperation with the Turkish general Directorate of Highways, have used LUSAS Bridge to study the effects of the earthquake on a number of the structures including a seismic assessment study of the Mustafa Inan viaduct - located just 5km from the epicentre.


The Mustafa Inan viaduct consists of two carriageways - both of 10 equally spaced, 40m long, cell box girders resting on elastomeric bearings and simply supported on what, at the time of its construction in 1982, where the tallest piers ever built, at 90m in height. Seismic buffer stops restrain the girders. Because of the great variation in lateral stiffness of the piers the bridge exhibits a complex dynamic behaviour. Apart from damage to the seismic buffers located at the second longest pier in the central span the viaduct appears to be structurally intact following the earthquake.

General Arrangement, LUSAS Model and Critical Mode Shape


Ambient vibration test data obtained from sensors before the earthquake hit helped to derive the dynamic characteristics of the undamaged structure and assisted in the calibration of the LUSAS model. 3D thick beam elements were used to represent the girders and piers. Whilst girders were simply supported between the piers, they were modelled as being continuous to simplify the model. In order to investigate the influence of out-of-phase movements on potential pull-off and drop collapse effects, the elastomeric bearings were modelled as linear spring elements with appropriate end constraints. For nonlinear modelling, 3D co-rotational, thick-beam elements were used. This type of element allows assignment of elastic perfectly plastic material characteristics and a solution procedure taking into account large geometrical deformations. An implicit method with the Hilber-Hughes-Taylor integration scheme with a time step of 0.025 sec was chosen because it is unconditionally stable. Input acceleration data for a site just 2 km south of the viaduct was used in the analyses.


Modal shapes and corresponding frequencies were found to be very sensitive to the variation in spring stiffness of the pier-to-deck connection. Participation factors, calculated by LUSAS, indicated that the lower-frequency modes (0.4 - 1.0 Hz) contributed 90% of the overall response of the structure. Comparison of results from linear and nonlinear transient dynamic analyses indicated that the shorter piers are more likely to sustain larger moments and shear forces than the longer mid-piers. In addition, inspection of the deformed shape of the viaduct in the time domain revealed considerable snap-through behaviour in the longer piers at middle spans, leading to amplified second-order effects. As a result, geometric nonlinearity must be taken into consideration for a more accurate representation of the real behaviour.

By using LUSAS Bridge very good correlation was achieved between the calculated and measured modal frequencies. The research study indicated that the viaduct exhibits three different dynamic behaviours in three different frequency bands.

  • In the first (low) frequency range of 0.4- 1Hz, relatively large displacements are of major concern and the structure appears to be very sensitive to displacements. The structure is subjected to proportional damping in lower modes since the piers exhibit in-phase motion. The calculated participation factors indicate that the first three modes contribute about 90% of the structure. Thus, the out-of-phase motion in higher modes (above 1Hz) were ignored, and a Rayleigh-type proportional damping was assumed. Results of the spectral analysis indicated excessive shear forces in the piers close to the supports.

First frequency range 0 - 1Hz

  • The second frequency range of between 1.0 and 2Hz, corresponds to the higher longitudinal and transverse modes. Displacements near the dominant frequency of the structure decreased toward the supports, and a substantial amount of energy was shifted to the frequency range 1–1.5 Hz. This was due to the response of the side frame at 1.5 Hz and to other high-frequency effects - confirming that the structure is more sensitive to velocity than to displacement. At frequencies between 1.2 and 1.5 Hz pull-off and drop-collapse effects could occur due to out-of-phase motion of the side and central frames. This critical range may be important for the response of the structure in future earthquakes, where short duration and high acceleration may dominate.

Second frequency range 1 - 2 Hz

  • The third frequency range lies above 3 Hz, and includes the response of the floating structure sitting on its elastomeric bearings at 3.7 Hz.

The out-of-phase motion of the side and central frames was identified in both the experimental and numerical studies. The nonlinear analyses showed that the earthquake would cause an expansion in the deck containing the expansion joint, indicating a possible drop-collapse behaviour or a contraction of the symmetrical side, indicating a possible failure of the seismic buffer stops. This was confirmed by the preliminary damage reports of the viaduct.

There is a reported 70% chance of another major earthquake within 30 years in the region so results from dynamic tests and finite element analysis studies are necessary to adequately model the behaviour of these structures and to help enhance the earthquake resistant design codes used for these kinds of highway bridges. 

Mustafa viaduct

Gebze Institute of Technology gratefully acknowledge the logistical and technical support provided by the Turkish Highways 1st Division and Kandilli Observatory Earthquake Research Institute in their research work which will be extended to other essential highway structures located in the region to improve design and analytical techniques, to identify structural damage, and to make decisions on structural strengthening needs.


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