The new railway hybrid bridge in Dąbrowa Górnicza: innovative concept using new design method and results of load tests

In order to understand the problems concerning the applied solution, one can refer to [48] and use the analogy to the tied-arch bridge using composite tie. Concrete cracking is one of the most complicated issues in modeling composite structures. For standard composite sections, the rules given in Eurocode 4 are based on an extensive and a complex theory supported by testing [41]. Contrary to the classic solution according to Eurocode 4, accepting an uncracked cross section is not always safe for longitudinal shear design [3]. In the case of the object in question, the problem of concrete cracking and the effect of tension-stiffening affect the deformation of the system, that is, in practice, vertical displacement under load (1) and the values of longitudinal shear in appropriate limit states (2). In the case of composite dowels, it is especially important in the fatigue limit state (FLS): for this the fatigue limit state actually governed the design of steel parts. Due to the lack of knowledge and experience, two extreme cases in design were conservatively assumed for longitudinal shear design, that is, a fully cracked section and uncracked (Fig. 5). Considering the CHC in the span under sagging bending, it can be seen that the distribution of tensile stresses transferred jointly by T-section and the cracked concrete slab depends strongly on the degree of cracking of this slab, and this influences distribution of longitudinal shear flows (web-T and web-slab). The ration of concrete versus steel area in the tensile part of the CHC is greater in the case of span sections than in the case of supports for the structure in question. Therefore, at this stage of the analysis, the focus was on the former, while in the case of the latter, adopting a full crack does not lead to a significant impact on the steel wear in the upper section. The determination of the degree of plate cracking in the FLS is a key issue and the main challenge standing in the way of optimizing the solution. The most reliable measure of the degree of concrete cracking and the first point of reference for further analyses are measurements under the real load of a real object, and so, it was done in this case and this is presented in the paper. Measurements of vertical displacements were made and the obtained results were compared with the predictions from various numerical models to draw first conclusions. In parallel, during the tests, a visual assessment of the degree of cracking was carried out, that is, crack observation (morphology and crack width). The conclusions regarding stiffness of a new type of structure considering tension-stiffening effect based on displacements measured on site have been drawn. The results are presented and discussed in the later paragraphs on the background of the theory for classic reinforced concrete.

The structure uses a new solution that consists of the application of two types of shear connection (CDs and PBLs) in one steel web. This creates parallel “statically indeterminate” shear flows (Fig. 17, right); hence, it is not known what part of the shear flow is transferred to the steel bottom flange via CDs and what part of the shear flow is transferred via PBLs. Fig. 17 explains this task. The point of reference here can be filler beam railway bridges, in which holes are used in the lower part of the steel beams to guide the transverse reinforcing bars. For the design of the bridge, the following shear transfer was conservatively assumed (Fig. 17, left): the shear flow from the concrete web (1) passes to the T-section via the CDs (I) and to the plate (3) via the inner part of the web below the CDs’ level (1b). The influence of outer web (1a) and PBLs (II) is negligible. In reality (Fig. 17, right), it is difficult to determine what portions of the shear flow are transmitted by the elements 2, 1a, and 1b; it is noted that the shear flow separation depends not only on the shear capacity of elements (webs 2, 1a, and 1b and shear connections I and II), but also on their stiffness, so the model depends on the considered limit state (ultimate limit state ULS, serviceability limit state SLS, fatigue limit state FLS). As a consequence, it is difficult to determine what part of the shear flow is transferred by the PBLs (II), therefore this shear was conservatively omitted in the design analysis for longitudinal shear.

The problem of concrete cracking in the bottom plate described in section 4.1 affects the division of the shear flows (an uncracked plate takes up less force than a cracked one). Bearing in mind the authors’ conclusion resulting from the design of the bridge that the assumption of steel sections is essentially determined by the fatigue conditions (FLS), it becomes clear that the stiffness of the cracked plate (adequate to the FLS conditions) and the division of the shear flows are inextricably linked problems. To sum up, Fig. 22 is shown to open a discussion. It is justified to assume that the big part of shear flow goes through PBLs and it would significantly influence the design of shear connection in the FLS (decisive criterion). The use of the parallel shear transfer mechanism (CDs + PBs) in the hybrid cross section is a new issue; such a solution was used in the construction for the first time.

The presented structure is the first engineering structure which used the division of the shear force into the part carried by the steel T-sections and the part carried by the concrete web according to the lever arm concept proposed in [3]; such an approach will be implemented in the CEN-TS design regulations that are just being developed [44]. It was presented at the SC4 meeting in December 2021 [45]. The theory of hybrid section concept is presented in [43]. (Earlier, an intuitive and engineering version of the method proposed in [3] and sanctioned in [43] was used on the Wierna Rzeka [6] bridge; it is presented in [43].) It is shown below how the concept to be used for simple hybrid cross section [44] has been applied to the combined (double composite) hybrid cross section. According to [15], the reduced effective depth of a cross section d_v (according to Eurocode 2) should be used for calculation of the inner lever arm of internal forces to be used for the determination of required reinforcement and design of the diagonal strut. In practice, in the case of the considered structure, it is about determining the dimensions of the stirrups A_s1 (Fig. 18) and the application of the concept according to [15] would lead to an irrational and greatly overestimated reinforcement A_s1. Moreover, there is no indication as to whether the reinforcement A_s2 should be taken into account when transferring the transverse force and for the vertical splitting at the same time. Here, the approach was used (formally for the first time) where the lever arm Z_H was used, which was calculated using an effective depth of the hybrid cross section d_H taken as the distance from the top surface of the upper surface of the girder to the centroid of the tensile part of the cross section made of structural steel. As the bridge is conservatively designed in the elastic domain, the lever arm can be determined for such a case from the formula Z_H = Z = I/S [4]. The lever arm of forces Z_H was used to determine the amount of reinforcement needed to transfer the transverse force in the girder and to determine the resistance of the compressed struts in concrete web (the entire procedure is as for a concrete cross section in accordance with Eurocode 2 [43]). The reinforcement A_s2 was taken into account for transferring the transverse force and for the vertical splitting at the same time. Thus, the total reinforcement assumed to transfer the vertical shear force in one girder is the sum of A_s1 and A_s2 (based on the experience from the bridge in Elbląg [1,37]). When determining the cross-sectional characteristics, it was necessary to take the effective width (see b₁ in Fig. 18) of the bottom slab and the premises here were followed as for the standard for concrete structures, that is, Eurocode 2 [21].

Figure 18

Both cracked and uncracked sections were analyzed; x in Fig. 18 is height of uncracked concrete zone for sagging bending (in such a case, reinforcement A_sd is considered at b₁ width). As can be seen, the issue of concrete cracking is of key importance in the case of the considered structure, not only for the transmission of the bending moment, but also for the transverse shear. The use of the hybrid cross section concept includes the assumption that the transverse force is divided into parts down: in the case of the design of the described structure, part of the transverse force is transmitted through the upper tee, some through the section of the concrete web connecting the steel T-sections, some through the lower T-section, and some through the inner bottom part of the concrete web (Fig. 17, left). Designing CDs with regard to steel failure (plastic design, at ULS [25,26,44]) provides at the same time a condition for the transfer of a part of the shear force through the webs of the steel T-sections, and the reinforcement of the main part of concrete web (Fig. 17, position 1) has been checked at the level of the hybrid cross section. This is the idea of designing for vertical shear force according to the hybrid cross section concept [43]. Selected design issues with regard to the bending moment and the issues of detailed modeling of the structure using finite element method (FEM) are presented in the subsequent paragraphs. The key issue is how to model the type of structure presented in this article. The problem of modeling (Fig. 19) is presented in [42] and this article shows how modeling with various techniques influences the results of the calculations which were compared to the values of displacements measured during real studies of the object on a natural scale (aim 4). In addition to these four main issues, other issues were considered, which are presented later in the text (they are cognitively important and often complicated, but, according to the authors, are of a lesser scientific importance). At the time of writing the article for printing, the draft of the guidelines introducing the design of hybrid cross sections [31] is basically finished.

Figure 19

The issues related to the design and construction of the bridge were first presented at the Wrocławskie Dni Mostowe (WDM) conference [10]. Attention is drawn to the fact that the transverse T-sections used in Spergau were abandoned in order to eliminate the problem of tension acting composite dowels in transversal element [20]. As a result, member characteristics (like the moment of inertia) can be assigned globally to the entire bridge cross section. Thus, a structure was obtained that can be modeled globally at the element level as a prismatic bar using concrete channel section with reinforced steel parts at the corners. In such a cross section, the effects of both free and restrained torsion play an important role. At the same time, it was necessary to determine whether the global analysis is performed on a cracked model (as for composite structures) or on a uncracked model (as for concrete structures).

The analyzed case is a new type of cross section and this question had to be answered. In the case of a beam model, it was necessary to determine the concept according to which the effective width is assumed [21]; here, it was done according to Eurocode 2 (ad hoc). A different concept is valid for composite structures and a different one for concrete structures, and the convergence of these concepts for the new version of Eurocode 4 was discussed in [21] and this is a complex problem. These two issues already show how important it is from the designer's point of view to qualify a new type of structure: is it a “rather” concrete or “rather” composite structure? As presented already, a key issue is the influence of concrete cracking and the tension-stiffening effect on the longitudinal shear forces in the shear connection when designing this connection on fatigue. Especially in the case of a field section, it is an important issue, where the reinforced bottom plate is an important element of the composite cross section (as opposed to the solution according to [6, 7]). In order to answer the question about modeling issues, a research project was conducted in parallel with the design work, under which a number of analyzes of various models were carried out. Various concepts of shell and beam models, cracked and uncracked, were analyzed and then, after gathering construction experience, mainly concerning the qualitative and quantitative issues of concrete cracking (shrinkage cracks of the new element and cracks resulting from creep effect), models which ensure the best representation of realistic superstructure issues were chosen. The numerical models done by external consulting (next to the models by design office) are shown in [10], and, here, probably, the most cognitively important part of the research work is presented, that is, the results of measurements under real load and their comparison to FEM models are done by the design office.

In order to verify design assumptions, regarding the response of the superstructure under static and dynamic loads, test load procedure was performed. During static test load, locomotive SM31 weighing 116.6 t (1143.46 kN) was used. A dynamic test load was carried using locomotive SM31 and ET22 (1177.20 kN) also. (Fig. 20). In a nonlinear analysis, apart from locomotive weight, self-weight of the superstructure and the equipment load were applied to the finite element models. Specific gravity of the superstructure-reinforced concrete (C40/50) was set in programs to 26 kN/m³. It was assumed that a deck is loaded with weight of a layer of rumble 0.63 m thick, layer of isolation 0.02 m thick, and track weight. Weight of sidewalks of both sides was also applied to main girders as an additional linear load. A sum of the equipment load applied to the whole span is equal 78.06 kN/m (68.67 + 1.53 + 6.00 + 1.86).

Figure 20

Girders’ deflection measurements were made using dial gauges, inductive sensors, and precise leveling. During static test load of the structure, strains in steel and concrete were also measured with the use of optical fibers. One optical fiber was attached to the bottom surface of steel flange of T-girder. The second one was attached to the side surface of concrete web of the main girder at the distance circa 5 cm from the bottom surface of the web (Fig. 21). In order to check the dynamic response of the superstructure, two accelerometers were used. Their job was to measure acceleration of two points on the main girders in the middle of the span during dynamic test load.

Figure 21

In order to analyze and check test load measurements, several finite element models were created. For this purpose, two programs were used: Midas Civil (design office during design process) and SOFiSTiK (external consulting and independent own analysis of B. Bartoszek for purposes of PhD dissertation). Structural modeling problems are presented in [10] where models by external consultancy check are presented. For the purposes of this study, additional models (Fig. 22: S00–S70, M40 UCR/CR) were made. Two models were prepared in Midas Civil for linear analysis of the superstructure in uncracked (M40 UCR) and cracked (M40 CR) conditions. In these models, only T-shaped steel sections are represented by beams. The deck and concrete webs are designed as shell elements. Eight different additional models were prepared in SOFiSTiK. In the first one (S00), the whole span is represented by one beam element with tapered cross section. In the second one (S10), the main girders and the deck are represented by a grid of beams. The whole span is divided into five elements in transversal direction (two girders and three longitudinal deck beams). Because of a vertical offset between the longitudinal deck bars and the main girders, rigid connections between bars were created. In the third model (S20), the deck was modeled by shell elements and main girders containing steel T-sections and concrete web by beams connected with the deck by rigid links. The fourth model (S30) also used concrete deck modeled as a shell element connected with the main girders introduced as bars. In this case, the T-sections and concrete web were divided into three parts connected via rigid links. In the fifth model (S40), all elements, which means concrete deck and webs, apart from steel T-beams, are implemented as shell elements. Steel beams are connected via rigid links with the top and bottom edges of concrete webs. The next model (S50) uses the same elements, but steel sections are connected with concrete webs at the real level of composite dowels in the middle of the concrete web. In comparison to that, in the sixth model (S60), additional division of concrete webs is implemented on a transversal direction. It means that concrete webs are split into two on both sides of steel T-sections (see Fig. 17, left). This allows to control lateral shear distribution and use or not bars going through steel webs as a composite. The last model (S70) uses beam elements only as the representation of steel flanges of T-sections. All the other elements, concrete deck, steel, and concrete webs, are modeled as shell. In all cases, linear and nonlinear analyses were conducted to get deflection, internal forces, and stress in superstructure in uncracked and cracked conditions. Load application was adjusted individually for all of the models.

Figure 22

As part of the static test load, one scheme of locomotive load was considered. A location of the locomotive was set to acquire maximum deflection value in the first span, whose length is equal 21.30 m. According to this, many locations along the span were analyzed using finite element models. Span deflection was measured in four points in the middle of each span on the bottom surface of steel T-girders. The location of all measure points is presented in Fig. 23.

Figure 23

Before static load test, the locomotive was set away from the flyover and default values of measurements were set. Next, locomotive SM31 entered the flyover and was set in designated place, which generates the biggest deflection values in span length 21.30 m. Static test load lasted 60 min. Deflection values in the middle of spans were measured every 15 min. Strain values in optical fibers were measured 12 times every 5 min. Acquired measured values were compared to the results of analysis of cracked and uncracked finite element models. Linear results for all models were highly convergent, while differences in nonlinear results were noticeable. Models S00–S30 do not allow to take into account realistic crack zones’ range, due to shear transfer in cross section, because steel and concrete are not defined separately. This means that nonlinear results from these models ensure lower accuracy than the models S40–S70 obviously. Results from model S60 and S70 are almost the same because the only difference between them concerns the method of modeling the steel member. The above comparison of deflection values is presented in the graphs for Midas Civil models M40 UCR/CR (Fig. 24–25) and SOFiSTiK models S40–60 (Fig. 26–27) also. Results from models S00–S30 were also checked and discussed, but in order to ensure better clarity of charts and taking into consideration the complex character of a nonlinear behavior of the superstructure, they were not included in the charts.

Figure 24

Figure 25

Figure 26

Figure 27

The numerical analyses performed showed that the measured values of girder's deflections exceed just slightly the results obtained for uncracked models. Test load values are also much lower than the results obtained according to nonlinear analysis, representing the superstructure in a cracked condition. Maximum values of girder's deflection obtained from the test load measures are equal to 2.81 mm at point D1-1 and 2.82 mm at point D2-1. Deflection values in these points obtained from Midas uncracked model are equal to 2.72 mm (D1-1) and 2.49 mm (D2-1). In comparison, deflection of cracked span obtained from Midas model is equal to 5.07 mm (D1-1) and 4.81 mm (D2-1). It can be seen that the value of girder deflection obtained from nonlinear model S40 is bigger than that obtained from model S50 and even bigger than the value of deflection of model M40 CR. This difference is probably caused mainly by shear deformation of the concrete web (see element 1a in Fig. 17 left) because the primary difference between S40 and S50 FE models is localization of shear connection between the steel girder and the concrete web. Stiffness reduction in model M40 CR assumed axial stiffness reduction of concrete deck and web, but the shear deformation was omitted in this case, so deflection of nonlinear analysis may be more accurate. It is worth noting that deflection models like S40 should be always higher than the real structure because in the real structure, the axial force from steel sections is provided approximately 500 mm (in this particular case) from the concrete edge, and therefore, the real height of shear-deformed web is much lower than 1800 mm. Realistic localization of shear connection is implemented in models S50, S60, and S70. Application of a concrete web split in two pieces by steel web in models S60 and S70, provides realistic representation of shear transfer in the cross section. So, these models should ensure the highest accuracy of results. The next step is to analyze the strain and stress values measured by optic fibers. In this case, the test load values are very close to the results obtained from uncracked Midas models. Comparison of values from Midas models (design office models) and optic fibers results is presented in Fig. 28–29.

Figure 28

Figure 29

In order to check the dynamic response of superstructure, dynamic test load was designed. Regarding this, the acceleration and deflection of points (D1-1 and D2-1) in the middle of the span of 21.30 m were measured during passage of the locomotive in both directions.

In this case, two different locomotives were used. First, on 05.08.2019, locomotive SM31 drove over the flyover with speeds 10, 20, 40, and 70 kph. In the second test, on 05.11.2019, locomotive ET22 drove over the span with speeds 10, 30, 50, 70, 90, and 120 kph (design speed). The maximum value of acceleration reached during tests was equal to 0.39 m/s² for speed 120 kph. This number is much lower than the maximum required due to pt. A 2.4.4.3.2 PN-EN 1990 A1 (Table A2.9), which is 1.0 m/s². So, the superstructure ensures very good comfort for the passengers. Dynamic factors of span in design analysis were calculated due to pt. 6.4.5.2 PN-EN 1991-2 and Annex C of PN-EN 1991-2 based on results of the first natural bending frequency of span. Results of these analysis for Midas Civil and SOFiSTiK are presented in Tables 1 and 2. Real dynamic factors reached during dynamic test load were estimated based on static and measured deflection of girders, while the locomotives were going over the span. Comparison of analytically calculated and test values is presented in Fig. 30. Based on dynamic test load, the value of the first natural frequency was established at a level 5.43 Hz, which is within the range (3.36–8.09 Hz) defined according to pt. 6.4.4 PN-EN 1991-2.

Figure 30

This value is slightly lower than any frequency obtained from numerical analysis, where the biggest frequencies were reached for M40 UCR (4.90 Hz), S50, and S00 (4.83 Hz) models. This difference may be caused by smaller real values of dead load applied to the superstructure than it was assumed in numerical analyses. Additionally, stiffness of rumble, track, and friction between them and the superstructure were neglected in the analyzed FE models. In reality, these phenomena may have influenced the global dynamic response of the structure.

Additional measurements using optical fibers were performed and comparison of steel and concrete bottom surfaces strains can be seen in Fig. 31. High picks of strains in optical fibers attached to concrete surface (S03) mean that discontinuity appears and should be interpreted as cracks in concrete. These results led authors to estimate crack localization on concrete webs. In Fig. 36, strains for steel bottom surface and concrete web are compared, which means that the mean values of strain in optical fibers are presented.

Figure 31

Figure 32

It was initially explained why the stress level in the lower chord is small under the test load. It is generally difficult to achieve a high degree of effort under the actual service load of short span railway structures. The lower chord effort level (about 200 MPa in the span at the ultimate limit state) results not only from the designers’ conservatism in their approach to this innovative structure: the bottom steel flange area is correlated with the thickness of the steel web (rolled HL sections) and the thickness of the steel web in railway bridges using composite dowels [6,9,12] usually results from the fatigue limit conditions (FLS) for steel dowels [56], and the same was true for the structure in question. Thus, assuming a cracked state in the dimensioning both in terms of bending and longitudinal shear resulted in oversizing of the structure due to bending in the span (relatively big steel flanges). In addition, a much lower operational load does not even significantly induce the concrete cracking in the bottom plate and results in a very low level of stress in the steel bottom chord (but also with low longitudinal shear). With the present state of knowledge [3, 43, 44], it simply could not be designed less conservatively and the test load results show a far-reaching conservatism, and this is the crux of the influence of concrete cracking on dimensioning that the authors wanted to show. In order to draw conclusions as to the behavior of an innovative structure, one should have a point of reference. In this respect, reference is made to the results obtained during measurements of standard bridge structures. On the other hand, the slight effort of the structure is justified. As test loads in Poland are performed as standard for new bridges, this valuable reference point was used. The reference point is the bridges made of reinforced concrete as well as those made of filler beam decks (in the case of steel structures, there is a high compliance of the measurement results with the theoretical models and standard composite solutions are not a good reference point). The point of reference is the conclusions and experiences of the person having big experience in first load tests in Poland [50, 51]. In the case of filler beam decks in railway bridges, the obtained deflections are smaller [51] or close to those obtained for the uncracked cross section [50]. The method of modeling elements other than the girders themselves plays an important role, and in the case of a relatively accurate model, values close to those calculated for the uncracked model are usually obtained [50]. Railway bridges with a reinforced concrete structure generally have a small span, up to 10 m, and are stressed during loading at the level of about 50% of the characteristic load according to [51]. Statistically speaking, the displacements obtained correspond to about 70% of the theoretical displacements obtained for the uncracked model. Thus, not only do they “work as if they are not cracked,” but also the influence of equipment elements not included in the model is also visible (attention is paid to the small span). Reinforced concrete road structures are usually structures with a span of less than 20 m (prestressed concrete is usually used above). The level of their effort during the test loads is higher than the railway bridges, and usually about 75% of the characteristic load [51] is achieved. Usually, about 90%–100% of the displacement values calculated as for the uncracked model are obtained [51]. Since equipment elements (such as sidewalk slabs) are not taken into account in the calculations and cracks in concrete are observed, it can be concluded that these objects reach the level of effort corresponding to the beginning of the cracked phase, but, in general, it should be summarized that their stiffness corresponds to the uncracked phase (note that a similar result was obtained for the structure in question and its span exceeds that used in reinforced concrete railway bridges and corresponds to the upper limit for road structures). The deflections obtained in road bridges are essentially elastic. Against this background, a specific conclusion can be drawn: the behavior of the structure corresponds to that of reinforced concrete bridges; it works like almost uncracked, but due to the relatively low level of stress in the steel bottom flange of the structure, one should be careful with drawing far-reaching conclusions. The values of the measured deflections under static load are significantly lower than the analytically determined values for the cracked models and only slightly higher than for the uncracked models. This allows us to conclude that the structure exhibits greater stiffness than conservatively assumed (cracked) at the design stage. The results constitute an important premise to indicate the justification for modeling hybrid structures in an uncracked state for FLS. The value of the natural vibration frequency determined from the tests is higher than for uncracked models, which may be caused by the cooperation of the span with the railway track surface. The values of the dynamic coefficients determined on the basis of the tests are lower than the values determined analytically according to standard design procedures; thus, it is confirmed that the assumptions made in the design calculations concerning the dynamic coefficient allow for the safe design of this type of structure. The acceleration values are significantly lower than the maximum values allowed by [52], thanks to which the structure ensures adequate comfort for passengers. Summarizing the first load test, relatively small cracking of the concrete structure and relatively high stiffness of the innovative hybrid superstructure as well as very good dynamic properties were observed. The obtained unique results constitute the first and basic point of reference for further analyses.