Change of the Grade Line of Bridges Constructed with Cantilever Concreting Technology

The cantilever concreting technology was used first time in 1951 by U. Finsterwalder to construct the bridge over the Lahn Bulduinstein River. Hence most of bridges constructed with this technology have not exceeded half of the expected service life of 100 years. Until present times thousands of such bridges were made in the world. In Poland between 1963 and 1973 the cantilever method was used for the construction of three bridges (in two casess the prefabricated assembly was used). The next big group of those bridges had been evident since 1998, when the bridge in Torun was built. It seems, that Polish experience regarding this technology is in initial phase.

The cantilever concreting (or assembly) technology is one of present techniques of bridge construction. The fundamental features of this method are saving of materials and construction costs (especially of scaf-folding and of formwork) and first of all a possibility of carrying out the construction of the span in many spots at the same time. The latter, especially the cyclical concreting of bridge segments results in a shorter construction time. This technology is effective for the bridges, whose span length is between 50 and 250 meters.

The characteristic feature of those bridges is the external appearance, which is showed in Figures 1 and 2. The geometrical profiles are determined by the applied technology and by the distribution of loads – especially, in the construction phase. In such long-span pre-tensioned concrete bridges the distribution of internal forces is mainly influenced by static behaviour pattern of cantilevers in construction phase.

Figure 1.

Figure 2.

Characteristic feature of post-tensioned long-span concrete bridges are excessive deflections. By the excessive deflections are meant those exceeding the deflection coefficient ω = 1.250‰. That coefficient is calculated with the use of the following formula: (1) ω = w L [ ‰ ] , w [mm] is a displacement at the mid-point of the bridge span L [m].

Problem of excessive deflections considered in this paper is a common one. One of the best documented examples of the analyzed problem is the bridge Støvset [2], Fig. 2. The designer used in the middle of the span light concrete LC55, like in the Stolma Bridge, which spans at amazing length L = 301 m. Hence, this method could be used to build long-span bridges. Nevertheless, already 8 years after the completion of the structure, the deflection w was over the design value 200 mm! It was believed that the main reason was underestimation of the deformation of the light concrete, used to build that bridge [2].

One of negative examples of reduction of excessive deflections is the Koro-Babelthaupt Bridge with span L = 241 m. The deflections of this bridge were measured after 12 years of service and they reached the value w = 1200 mm, corresponding to ω = 4.98‰. After 18 years the span deflection increased to ω = 1390 mm, so now ω = 5.77‰. It shows that the deflection coefficient very much exceeded the allowable value (1). The reinforcing of the bridge – post-tensioning – did not help and after short service the structural failure occurred.

In spite of the fact, that the rheological behavior of the concrete was studied over the whole 20^th century, the problem of excessive deflections of post-tensioned concrete bridges remains unsolved. It seems, that during the designed service time of 100-years the rheological effects do not reach any final, constant value. The excessive deflections problem is quite well recognized by monitoring of the span-bridge deflection [1]. In this paper the deflection w(t) is represented as a function of the service time of the bridge structure, calibrated by the results of monitoring of the bridge deflection for the cantilever concreting constructions. However, the experience from a number of bridges shows that some bridges show excessive deflections but a great majority of bridges work very well.

During the construction process of the cantilever spans the uplift is used, which is the initial elevation of the longitudinal axis of the bridge with respect to the grade line of the bridge. The purpose of that initial elevation is the reduction of deflection, which results from sustained loads after connection of spans, especially from the forced deflection during the cantilever span connection, post-tensioning for river span, equipment loads. In some cases the rheological processes occurring during the service time are taken into account. Because of relatively big own weight of the structure, as compared with service loads, in this paper the arising span deformations are regarded as rheological effects, rather than as the results of variable loads.

In the Tab. 1 as well as in the Fig. 3 two different examples of bridges over Odra River (in Poland) are compared. In comparison with similar bridge structures, these bridges have more varying height of the box girder. Because of the used construction technology – concrete scaffolding, the bridge spans over the river usually have constant height of box girder. Along the bridge, the grade line is a circle of radius R, where the highest value occurs in the longest span.

Figure 3.

The technology – uplift of span –, which was applied in the structure located in Opole Fig. 3a is usually used to erect the structure with the cantilever concreting technology. In the Fig. 3a. two curves of the bridge grade line are presented, the first one – planning phase, which is determined as the section of the circle of the radius R and the second one – the curve, which is the result of the surveying measurements during service. These curves show that after 10 years of service, the bridge elevation of 60 mm remaining from the applied uplift still existed, the span length being 150 m. The difference, which is seen between both lines (design phase – surveying measurement) is the provided excess, which was designed to minimize the rheological processes occurring in the bridge structure.

Fig. 3b presents the case, where the designer did not apply the uplift of the span, in the middle of that (x = 190 m) the recess occurred, which amounted to 130 mm. It turned out that the allowable deflection coefficient for this type of bridges is ω = 1.25‰, and it was reached already after 8 years of service. Comparison of those deflections (rheological process) with the deflection due to service loads, which were measured during the commissionig loading test of the Kedzierzyn-Kozle Bridge showed that the ω coefficient from the rheological processes is bigger than the ω coefficient from service loads, where deflection equals w = 59.9 mm, which gives ω = 0.43‰.

Characteristic feature of these bridges are large long-term deflections of span, especially during the initial phase of service life. Some measurement results of the deflections for the bridge structures in Japan are shown in Fig. 4. On the basis of these, the formula (2) is drawn, which can be used to determine the deflection coefficient dependent on time t[years] for bridges constructed with cantilever concreting technology.

Figure 4.

Development of the deflection of a span constructed with the cantilever technology may be regarded in 3 different ranges of time. At the beginning – few years after putting into service – the increase of deflections is the biggest. From the curve in Fig. 4 it can be seen, that in the first year the increase of the deflection is the largest, and during the subsequent years the deflections get stabilized. During the second period in Fig. 5, the development of deflections is more balanced. The third, the longest period of bridge service life (75% of service time) could be only forecast (predicted), because of lack of measurement results.

Figure 5.

In the paper [1] results of deflection measurements of 56 bridges constructed with cantilever concrete method are presented. These bridges were made of different concretes as well as in various climatic zones. Also the static schemes (mainly the span length L) of these bridges are diverse. Therefore the deflection coefficient, as given by formula (1), rather than the deflection itself is presented.

With the aid of the results given in [1] 10 groups of coefficients were made depending on the time evolution of ω(t). In the Tab. 2 the characteristics of chosen structures for these groups are listed, where the range of span length was 95 m < L < 142 m. On the grounds of the results of measurements (for short service time) the following approximate formula was established (3) ω ( t ) = a ln ( l + b t ) [ ‰ ] , where a and b are coefficients listed in Tab. 2 and t denotes time (in years), measured from completion of the constrution process. These functions are plotted in Fig. 5. Table 2.

Parameters of bridges spans

The results presented in Tab. 2 as well as in Fig. 5 show, that the deflection formula results are scattered. It means, that many approximate functions ω(t) could be proposed. In this paper some selected examples of these formulas referring to four-span Zvikov-Otava Bridge (nr 7), L = 84 m are given. For this bridge, similar plots of deflection were obtained from formula (3) for each span. The values of parameters in formula (3) are listed in the Tab. 3, the graphs are shown in the Fig. 6.

Figure 6.

The formula (3) is regarded as the initial formula. As the approximation of deflection, during first 30 years, t < 30 years also the following function can be used (4) ω ( t ) = c t [ ‰ ] .

For example, for the Zvikov-Okava Bridge good results are obtained for c = 0.24, as compared with the Japanese bridges (analyzed before in Fig. 4), magnitude of deflection coefficient c is two times smaller.

As next example, the formula (5) is given, which is more complex than (3). The results obtained from that formula are equally accurate as from (3) (5) ω ( t ) = d ⌊ ln ( e + t ) − e − f ⋅ t ⌋ ‰ , where d = 0.3701 and f = 0.06994. The simple formula (6) given below (6) ω ( t ) = ln ( t ) − g h ‰ , where g = 0.3023 and h = 2.413 is not useful.

The effectiveness of approximate formulas (3) to (6) is compared in Fig. 7. The data was taken from the measurements of Zvikov-Otava Bridge.

Figure 7.

The purpose of establishing formula for ω(t) is to estimate the deflection of the span during the whole service time of the structure, assumed usually for 100 years. The functions useful for an early phase of bridge service time are not necessarily so useful for long-term deflection. For examle, if the value of coefficient deflection for t = 10 years was equal, the results obtained from formula (3) and (4) would be the same, i.e. w ₁₀(3) = w ₁₀(4). Then for t = 100 it would be 7 w 100 ( 3 ) = ln ( l + 30 , 86 ) ln ( l + 3 , 086 ) w 10 = 2 , 46 w 10 where a = 0.554 and b = 0.3086.

And from the formula (4) the following is obtained 8 w 100 ( 4 ) = 100 10 w 10 = 10 w 10 = 3 , 16 w 10

If we assume, that the formula (3) is a reliable deflection extrapolation, the results in Tab. 2 can be taken as final results after service time t = 100. As we can see the coefficient ω₁₀₀ that means for t = 100 years, for the goups 3–9 (Table 2) has exceeded the allowable value ω(t) < 1.25‰. For bridges of groups 5, 6, 8, 9 the values of coefficients have reached very high levels, which is comparable with the Koror-Bablthaupt deflection.

Characteristic feature of behaviour of bridges constructed with cantilever concreting method, resulting from large span lengths, is excessive long-term deflections of the bridge (w > L/800), due to rheological processes in the concrete and in the pre-tensioning steel. For example, if we take the results from Fig. 6, it can be easily said, that the deflection increase is not proportional to the final value w ₁₀₀ = 155 mm, t = 100 years: 25% of the value is already reached after 4 yers of service; w ₄ = 38.75 mm, 50 % of final results after 13 years; w ₁₃ = 77.50 mm, 75% after 32 years; w ₃₂ = 116.25 m. It shows that, the reological procceses (as regards deflections) do not approach any final value after 100 years of predicted service life, these processes continue.

Fundamental feature of the cantilever bridges is the large scatter of the measurements results, which is caused by many random factors like: construction technology, duration of construction process, concreting time, climate, concrete strength, used aggregate, quantity of reinforced steel and the important/rheological processes. In this paper the formula (3) for deflection depending on service time of the structure is proposed, which is based on the measurements of bridges constructed with the use of the cantilever concreting method. Analyses presented in the paper are going to be used to establish rheological models of reinforced steel and concrete. The current aim of the paper is not the assessment of rheological models of concrete and of reinforced steel, but the demonstration of complexity of the problems of large long-term deflections. It should be pointed out, that the bridges with hinges at the midspan are much more sensitive to long-deflections than continous bridges. That knowledge should be used during the designing phase of bridges. The problem of maintaining the grade line of reinforced concrete bridges in appropriately designed line is still not solved.