Dynamic Tests of Pony Truss Railway Bridge Under Normal Operation

One of the methods used to assess the technical condition of a structure is the studies under test load [3], [4]. Such studies require the bridge to be closed. The load tests consist of two types of tests, static and dynamic [5].

The static test identifies the effects of static load, i.e. the most frequent subsidence and displacements arising from such loads.

Dynamic tests usually involve making a series of passages at different speeds of an arbitrarily selected train vehicle or the entire train. The observation involves the dynamic effects, displacements, and accelerations caused by the passage of the test rolling stock. Analysis of a dynamic test is limited to a simple analysis of signals [6]. This approach may prove effective in the case of simple bridges with well-separated forms of free vibration, but this involves two main limitations. The key limitation is the necessity of closing traffic on the examined object and on the adjacent section of the railway line, which allows the required speed of the test rolling stock to be reached. Another, not less significant limitation, involves the cost of renting and insuring the test railway vehicle.

As an alternative to typical dynamic test loads, we propose tests in normal traffic using all available, random, uncorrelated excitation, i.e., operational modal analysis [7–11]. The experiment described in the paper was carried out using the said OMA analysis.

In the research with the application of OMA technology, for the purposes of identification, we make use of vibrations caused by normal operation and vibrations induced by other, unknown excitation forces such as, e.g. wind or movement under the bridge span. Tests under ongoing traffic conditions allow us to make observations of the dynamic behaviour of the structure under real operating conditions. Identification encompasses the entire dynamic system, i.e., the span and its actual rather than idealised support system conditions.

In research under normal traffic, the impact exerted by the presence of vehicles on the bridge on the estimated modal parameters is becoming more important. In the described example, the weight of the locomotive is almost twice the mass of the span. For this reason, the signals recorded when the locomotive is on the deck cannot be used to estimate the modal parameters of the structure. However, signals recorded after the load has left the deck contain useful information and the vibrations induced by the passage have amplitudes higher than vibrations typically induced by other excitations. In the analysed structure only part of the recorded response was used for modal parameters estimation, the part containing only free vibrations excited by the tran passage. In this way, possible variability of modal parameters due to changing total mass of the system was addressed.

It is well known that there is a significant impact of environmental conditions on the estimated modal parameters. A change in ambient temperature or other environmental parameters can cause a change in the observed dynamic response [12].

The identification of modal parameters (which most frequently consists of three quantities: frequency, the form of free vibrations, and the corresponding damping [13]) is understood in OMA as a process that correlates the dynamic characteristics of a mathematical model with the physical properties of the system obtained from the measurement data. In OMA, the measurement data obtained from the dynamic response under normal operation are used to estimate the parameters of the model that describe the observed behaviour of the structure. In the experiment presented in the paper, the stochastic subspace identification algorithm based on correlation functions (SSI-COR) described in the paper [14] was used to identify the modal parameters.

The supporting structure of the bridge, under the active railway track, is made of simple supported single-track truss spans with a bottom ride of the theoretical span of 30.0 m. The bridge across the Nysa Łużycka River belongs to the popular in the 20^th century type of bridge structures used to cross medium-span obstacles – halfframe truss systems. The structure was built in the 1950s and has been used for more than 70 years. The specificity of this type of structure is that the upper flanges of the truss girders are not transversely braced (Fig. 2). Computational analyses of this type of structure usually demonstrate that the load-bearing capacity of the system is determined by the buckling of the compressed upper flange of the truss girder.

Figure 2.

Cross section of the the sixth span of discussed bridge with spatial transducer layout; suffix y denotes the transverse uniaxial sensor, z denotes the vertical uniaxial sensor and yz denotes the transverse and vertical biaxial sensor

The sixth span, located on the territory of Germany, was selected for the study. The choice of span was dictated by its availability and by the fact that during the examination of the structure, no significant differences were observed between successive spans and bridge supports.

The bridge was built diagonally with respect to the obstacle and that is why the truss girders are shifted with respect to each other by a 3 m long field. Such a shift affects the shape of the observed vibration forms described in the following part of the paper.

Two models of the structure were prepared, a preliminary model for the planning and realisation needs of the experiment in the Autodesk Robot Structural Analysis (ARSA) programme and a model taking into account the research results in the Midas Civil programme. For the purposes of this work, only the results of the preliminary model were addressed.

The structure of the sixth span was modelled using finite elements (Fig. 4). Steel bridges with riveted joints are characterised by a high uncertainty in estimation of the stiffness of the joints. At the same time, riveted joints are a source of non-linearity, which is reflected in the estimated modal parameters [15]. The quoted model allowed for the articulated joint of the stringer supporting the track with cross beams, due to the susceptibility of the connection of these two members, which is difficult to assess. Boundary conditions represented theoretical boundary conditions derived from the visual inspection of the structure. The FE model lacks representation of some local stiffening elements found in the real structure. The toal mass of the structural and non-structural elements was also taken into consideration, because of its importance when it comes to modal analysis results.

The distribution of the measurement points in the cross section of span no. six is presented in Fig. 2. Two inductive sensors of linear displacements were placed in the middle of the span (P61 and P62). In turn, the accelerometers were placed in three sections along the length of the span (15 single-axis transducers). During the experiment, the fifth span was observed, but the scope of the measurements was smaller. The measurement consisted only of vertical displacements in the middle of the span (P51 and P52) and vertical accelerations at four points on the deck. The observation of the fifth span was supposed to find possible differences in the dynamic response of the neighbouring spans. The presentation of a detailed sensor layout for span no. five was omitted. A general spatial layout of the measurement points for both spans (five and six) is presented in Fig. 3. The spatial arrangement of the sensors is clearly represented in this figure. The studies did not include observations of supports or points of the structure in the immediate vicinity of the support points. Only the highlighted nodes are those observed with accelerometers.

Figure 3.

Accelerometer layout in spans no. five (on the right) and six (on the left)

The identification experiment was carried out on one day in stable weather conditions with low wind and without rain. Structure is located away from effective, environmental sources of excitation forces, namely a busy road, etc. Additionally, its size is relatively small, so it is not so prone to being excited by wind. As a consequence identification of less-excites, higher forms of free vibrations is proven to be difficult.

A limited number of available accelerometers enforced the measurements on the tested span to be carried out in two setups: In the first setup (U1), the sensors were placed at the measurement points A01: A08 (Fig. 3); in the second setup (U2), the sensors were placed at the measuring points A01: A04 and A09: A12. During the measurements, a total of almost 5h of signals were recorded.

Through the two application of the mentioned accelerometer setups, we could observe the vibrations of 15 degrees of freedom of the sixth span. It also afforded the possibility to observe higher-order vibration forms. We must remember that any change in the location of the sensors is time-consuming and it enforces a break in the recording process of measurement signals. In addition, the described tests had to be performed in one day, and the client expected only basic information about the behaviour of the structure loaded with real trains. The tests were carried out in consultation with the railway line operator. Thus, we had access to the parameters of the passing rolling stock and to the estimated time of their passage. The recorded passages are summarised in Tab. 1.

The numerical model allows for obtaining many forms of vibration. Their number corresponds to the total number of degrees of freedom that all nodes have in the numerical model. Due to technical, time, and organisational limitations, the vibrations in the examined object were recorded only at a few points of the structure and along with the selected directions. This results in the observability being limited to several pre-selected forms of vibration. It also means that inappropriate placement of sensors can prevent the detection of significant forms of vibration in the tested structure.

The applied distribution of vibration transducers allowed us to explicitly identify several basic forms of free vibrations. The identification results are summarised in Table 2. The modes related to local vibrations were not included in the above summary (thus some of the local vibration modes are missing in Table 2). The identified frequency of free vibrations of a given form (n_OMA) was determined as the arithmetic mean of several estimations based on various available signals. The same was done with the fraction of critical damping (ξ). The expanded experimental uncertainty (n_OMA and Uξ) of both of these quantities was also determined to the be equal to double standard deviation of the estimates used to determine the mean value. Some modes were not detected in all estimates. This indicates a weak excitation of these forms of vibration and may highlight a lack of certainty of estimation. In most cases, the uncertainty of the damping estimate is much higher than the uncertainty of the estimate of the frequency of free vibration. Table 2 shows quite close resemblence of OMA vs. FEM mode frequencies. The model can be further improved, but its further improvement is of limited value from an engineering standpoint. Differences in frequency for global vertical modes are of order of not more than 8%. For fundamental horizontal mode, 19% difference is of limited interest for us and can in our opinion be accepted.

Fig. 4 presents two examples of the correctly detected vibration mode shapes. One basic and one higher-order mode of vibration associated with the upper flange of the truss girder. The visualisation of the shape of the form was prepared on a single setup of accelerometers. This is due to the fact that the signal-to-noise ratio in most of the recorded signals was low. Merging the signals from two sensor setups did not give satisfactory results. Propper assemblage of mode shape pair, OMA and FEM, was performed only on visual inspection of mode shapes. No formal way of mode shape comparision, e.g. Modal Assurance Criterion, was implemented.

Figure 4.

Comparison of mode shapes estimated from experimental data and calculated using the FE model; a) low order mode shape; b) higher order mode shape

Fig. 5 presents the displacements of the fifth and sixth spans caused by the passage of a single heavy locomotive (Tab. 1). The signals were prefiltered with a low-pass digital filter of the cutoff frequency of 32 Hz. The comparable displacements of the two observed spans are visible. Fig. 6 shows the vertical displacements from the beginning of the passage of a freight train pulled by the same heavy locomotive as in the previous graph. This time, the maximum displacements under the locomotive are different in the two spans. Similarly, wagons cause displacements of different amplitudes. No explanation was found for the observed differences. Additional smoother time waveforms were obtained after applying the 0.5 Hz filter. They were used to estimate the dynamic amplification factor (DAF) as the ratio of the signal filtered out with a filter of 32 Hz cutoff frequency and that filtered out with a filter of 0.5 Hz cutoff frequency. In none of the registered passages, the DAF determined in this way does not exceed the value of 1.04.

Figure 5.

Vertical displacements induced by a heavy locomotive (L1); span 6 – on the left, span 5 – on the right

Figure 6.

Vertical displacements induced by a locomotive of a freight train (T3); span 6 – on the left, span 5 – on the right

The presented results (Tab. 2) speak of the difficulty in unambiguously identifying the forms of vibration associated with the transverse movement of the upper truss flanges. We can see small number of the parameter which in turn shows how easy or hard the given mod was to detect. This is due to the insufficient number of measuring points on the top flange. We can also observe that, in the case of small, weakly excited structures, not all expected forms reveal themselves to the extent that their detection.

The results presented involve a short-term measurement campaign. Long-term measurements using a vibration monitoring system could provide more information on the variability of the dynamic response of the structure as environmental conditions change. The weather conditions on the day of the study were recorded and are part of the research records report. This should allow one to relate the information obtained in effect of the described experiment to future results obtained under similar conditions. Significant differences may be a premise that indicates a change in structure.

The scope of the experiment was limited to observing one of the six spans. This may significantly undermine the legitimacy of transferring the conclusions from the research of a single span onto the remaining structures of the same type, even though all spans had been examined and no significant differences had been detected. The potential variability of the results of OMA identification experiments for individual spans could be an indicator of significant differences between individual trusses not detected during the examination.