Acta Polytechnica CTU Proceedings https://doi.org/10.14311/APP.2024.47.0084 Acta Polytechnica CTU Proceedings 47:84–88, 2024 © 2024 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague CONCRETE AND RELIABILITY OF EXISTING PRESTRESSED BRIDGE STRUCTURES Aleš Mezera∗, Milan Holý, Miroslav Sýkora Czech Technical University in Prague, Klokner Institute, Šolínova 7, Prague 166 08, Czech Republic ∗ corresponding author: ales.mezera@cvut.cz Abstract. A large number of post-tensioned concrete bridges were built in the second half of the last century. They have often been insufficiently maintained during their lifetime (usually around 50 years). Nowadays, these structures exhibit significant deterioration, mainly due to leakages and also due to various other deficiencies such as a small concrete cover. Their load-bearing capacity needs to be verified. This paper focuses on estimating the load-bearing capacity calculation of existing post-tensioned concrete bridges. In the engineering practice, this is carried out using the partial factor method according to the currently valid standards (Czech standards ČSN and the Eurocodes), which often impose more stringent requirements than the original standards. The partial factor method then often leads to low load-bearing capacities. This study deals with the bridge for which a very low load-bearing capacity has been determined. For this reason, a comparative probabilistic analysis was performed, allowing for a better description of the uncertainties in the resistance and load effect variables. The probabilistic approach appears to be less conservative and yields a higher load-bearing capacity. Keywords: Concrete, bridge, partial factor method, reliability, load-bearing capacity. 1. Introduction In the second half of the last century, the post- tensioned bridges in Czechoslovakia developed inten- sively, largely utilising standardized structural mem- bers and systems. This was a response to the growing needs of transport and infrastructure, where the main goal was to connect regions as efficiently as possible and to provide for the efficient transport of persons and goods. The choice of this structural system was motivated by the ability to build quickly and use materials efficiently, therefore several systems of post- tensioned precast beam bridges were developed and standardised [1]. This study specifically focuses on the KA type post- tensioned precast beams. These beams were manu- factured off-site under controlled conditions, which guaranteed the high quality of the concrete and pre- stressing elements. The method was well standardised, which enabled many bridges to be built quickly and economically. The beams were commonly manufac- tured in several segments to facilitate transportation. In the present territory of the Czech Republic, a large number of bridges were built from the KA beams, and subsequently, during the operation, the deficien- cies of this technology gradually became apparent: • imperfect grouting of cable ducts and poor protec- tion of prestressing reinforcement; • low concrete cover of the reinforcement; • closed hollows that are difficult to survey and can collect water (often the drainage holes of the hollows were not drilled and surveys revealed that in some cases the hollows were full of water); • the beams were assembled on site in several seg- ments and thus contain joints without passing- through reinforcement, thereby creating weak sec- tions of the structure; • in the transverse direction, joints between the in- dividual beams allow for rotation between the in- dividual beams and this behaviour often results in damage to waterproofing and leaking into the structure, even early after commissioning [2]. It should be pointed out that imperfect grouting is particularly dangerous as it does not protect the pre- stressing reinforcement against corrosion and, further- more, creates conditions for moisture condensation that can lead to reinforcement corrosion [3]. 2. Bridge under investigation The bridge under investigation was built in 1964 and carries the 2nd class road over a small water stream. The superstructure is made of nine post-tensioned precast beams KA-61/18 (Figure 1) and acts as a simply supported beam with span of 19 m. Width of the bridge is 9.18 m. At both sides of the cross-section there are 0.75 m-wide precast reinforced concrete cor- nices with railings. The bridge deck surfacing is made of asphalt and width between the safety barriers is 7.68 m. The one-sided transversal slope of 3 % was created by a variable thickness of concrete deck. Relia- bility analysis of the critical edge beam (Figure 2 and Figure 3), which exhibits the most severe corrosion weakening, is presented in detail. According to long- term experience gained by surveys of these bridges, 84 https://doi.org/10.14311/APP.2024.47.0084 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en vol. 47/2024 Concrete and reliability of existing prestressed bridge structures Figure 1. Cross-section at mid-span and longitudinal section of half of beam KA 61/18 with prestressing tendons [1]. Figure 2. Cross-section of bridge (critical beam marked in red). Figure 3. View of bridge. edge beams generally prove to be the most exposed to corrosion weakening of prestressing tendons [4, 5]. The material characteristics of the concrete were determined by a structural survey carried out by the Klokner Institute of CTU in Prague. The characteris- tic value of the concrete compressive strength was de- termined by tests on samples as fck = 40 MPa and the mean value of the concrete compressive strength was fcm = 57.4 MPa. For the application of the partial fac- tor method, concrete strength class C 35/45 is consid- ered, which well corresponds to the original documen- tation [1] (concrete class B500 according to the past classification). The prestressing tendons consist of patented wires of 4.5 mm diameter with a guaranteed ultimate strength fpk = 1 650 MPa and yield strength σ0 .2 = 1 200 MPa. According to [1], yield strength was increased by applying a prestress equal to the yield stress for two minutes. In this way yield strength was increased to σ0 .2 = 1 350 MPa. In reliability analysis, yield strength fp0 .1k = 0 .935σ0 .2 = 1 262 MPa accord- ing to [6] was then considered. The wires and tendons approximately correspond to relaxation class 1 accord- ing to EN 1992-1-1 [7]. The prestress losses in the time of assessment – after 59 years – were determined by TDA analysis in SCIA Engineer v. 21.1 [8] with a value of 25.1 % at mid-span. 3. Partial factor method Reliability analysis of existing structures is com- monly based on the principles of ISO 1382 [9] and ČSN 73 0038 [10]. The partial factor method is widely applied when calculating the load-bearing capacity of existing bridges. ČSN 73 6222 [11] provides supple- mentary guidance in accordance with the Eurocodes. In the partial factor method, the basic reliability condi- tion for the determination of the load-bearing capacity can be written using the load combination rule (6.10a, b) according to EN 1990 [12] as follows: 85 A. Mezera, M. Holý, M. Sýkora Acta Polytechnica CTU Proceedings γG(Gk0 +Gk) + γQψ0δnomVn,P F M ≤ R(fpk/γP , fck/γC , fsk/γS , b, ...) (1) γGξj(Gk0 +Gk) + γQδnomVn,P F M ≤ R(fpk/γP , fck/γC , fsk/γS , b, ...) (2) Maximum of the load effects in Equation 1 and Equation 2 is considered. Based on a survey and inspection of the bridge, the actual condition of the structure is taken into account. Due to incomplete information and large uncertainties, weakening of the prestressing reinforcement area up to 25 % of the cross-sectional area is conservatively considered, tensile strengthening of the prestressing reinforcement is ignored, and weakening of the shear reinforcement up to 5 % of the cross-sectional area is taken into account. The permanent loads are based on the nominal dimensions of the structure and densities of the ma- terials according to EN 1991-1-1 [13]. Traffic loads for the determination of the load-bearing capacity are considered according to ČSN 73 6222 [11]. The load cases are considered so as the variable loads are always placed in the most unfavourable position as determined from influence line graphs. The capacity in the critical cross-section is esti- mated considering the ultimate limit state (ULS) – bending and shear. Considering that the prestressed structure was designed using the theory of allowable stresses, it was also necessary to assess it for the serviceability limit states (SLS) – stress and crack width limitations. In the former, the normal stresses are verified for the characteristic, frequent and quasi- permanent load combinations and crack widths are verified for the characteristic load combination. Ta- ble 1 provides load-bearing capacities for shear and bending and the individual load combinations in the ultimate and serviceability limit states. Note that in this study, only normal load-bearing capacity is dis- cussed, i.e. the vehicle on the bridge is not restricted in terms of speed and position. Load combination Vn,PFM [t] ULS – shear (6.10a) 41.3 ULS – shear (6.10b) 36.8 SLS – shear (characteristic combination 76.4– verification of crack width) ULS – bending (6.10a) 10.8 ULS – bending (6.10b) 16.0 SLS – bending (verification of stress limitation) 11.7 Table 1. Load-bearing capacity for considered load combinations. It follows from Table 1 that the critical failure mode is mid-span bending with a very low load-bearing ca- pacity Vn,PEM = 10.8 t. For example, an unloaded Tatra 815 weighs approximately 15 t. This is why a probabilistic approach is also applied to better de- scribe the uncertainties in the resistance of the critical section and the load effects of permanent and traffic loads. 4. Probabilistic method The probabilistic approach relies on the determination of the reliability index β or, equivalently, probability of failure pf . For existing structures, according to ISO 13822, tab. F.1 [9] the target reliability level is β= 3.8. The limit state function reads: g(x) = θRR(fp, fc, fs, b, . . . )− θE(G0 +G+ δVn,P M ) (3) The symbols and probabilistic models of the basic variables are given in Table 2. Probability of failure was estimated by the Monte Carlo method. Note that the mean value of the bending resistance of the prestressed section is Rm = 1 960 kNm and the characteristic value is Rk = 1 744 kNm (Rk/Rm = 0.89). The coefficient of variation VR = 0.071 corresponds approximately to the coefficient of variation of the prestressing force taking into account the prestressing losses. The load-bearing capacity VVn,PM = 22 t is esti- mated iteratively to achieve a reliability index of β= 3.8. The resulting load-bearing capacity is, there- fore, approximately doubled in comparison to the value determined by the partial factor method. 5. Discussion It is assumed that the difference in load-bearing ca- pacities can be attributed to: • conservative value of the partial factor γG – for an existing bridge it is possible to measure the dimensions of structural members and thicknesses of pavement layers, specify material densities, and therefore to significantly reduce the uncertainties and subsequently update (reduce) the partial factor according to the procedure in ČSN 730038 [10], • a conservative value of the partial factor γQ – in the determination of the load-bearing capacity, the uncertainties associated with the effects of vehicle loading on the bridge are lower than for the traffic flow considered in the design; therefore, the value of the partial factor 1.35 could be reduced. 6. Conclusion Post-tensioned prestressed concrete bridges built in the second half of the last century have often been poorly maintained; nowadays their age reaches mostly cca 50 years. These structures exhibit significant degradation (mainly due to adverse long-term effects of leakages and various other deficiencies such as a 86 vol. 47/2024 Concrete and reliability of existing prestressed bridge structures Symbol Variable Characteristic Xk/µX Distribution Coefficient Source value Xk of variation VX b width of beam 0.98 m 1 - - [1] h height of beam 0.85 m 1 - - [1] fc concrete compressive strength 43 MPa 0.75 LN0 0.115 - fp prestressed force 1 327 kN 0.88 N 0.075 - L span length 19 m 1 - - [1] γC partial factor for concrete 1.50 - - - [12] γG partial factor for permanent actions 1.35 - - - [12] γQ partial factor for traffic load 1.35 - - - [12] γS partial factor for reinforcement 1.15 - - - [12] δ dynamic factor 1.20 1 LN0 0.05 - G0 self-weight load 493 kNm 1 LN0 0.04 - G other permanent loads 421 kNm 1 LN0 0.10 - Vn,P M Vn (normal load-bearing capacity) 330 kNm 1 N 0.05 [14] θE model uncertainty for action effects 1 1 LN0 0.10 [15] θR model uncertainty for resistance 1 0.98 LN0 0.06 [16] Table 2. Probabilistic models of basic variables. low concrete cover) and their load-bearing capacity needs to be verified. Focusing on an example of the representative bridge, the verification by the partial factor method reveals that the mid-span bending fail- ure (with a load-bearing capacity of 10.8 t) is the decisive ULS. Since this is a very low value, a probabilistic method was also applied to better describe the uncertainties in resistance and load effects. The load-bearing capac- ity was determined iteratively to achieve the target reliability index β= 3.8. The load-bearing capacity, 22 t, is approximately doubled in comparison to that obtained by the partial factor method. The differ- ence between the load-bearing capacities is attributed to the conservative values of the partial factors for the permanent and variable loads. The probabilistic analysis further shows that the variability of the resis- tance of the critical section is mainly determined by the variability of the prestressing force including the effect of prestress losses. However, it is important to note that the determination of the corrosion weaken- ing of prestressing reinforcement is a largely uncertain parameter, since surveys reveal conditions of prestress- ing steel only in a limited number of locations. The obtained results should therefore be considered as in- dicative only; further research will specifically focus on better characterisation of corrosion effects. Acknowledgements This study has been supported by the Czech Science Foun- dation under Grant 23-06222S. References [1] Prefabrikované cestné mosty svetlosti 9–12–15–18–21m montované z predpatých nosníkov KA–61 [Prefabricated road–bridges of span clearance 9–12–15–18–21 m assembled from post-tensioned beams KA–61]. Dopravoprojekt Bratislava, 1964. 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Partial factor methods for existing concrete structures. Federation internationale du béton (fib), 2016. 88 https://doi.org/10.1680/cien.2001.144.6.8 https://doi.org/10.1080/15732479.2011.581673 Acta Polytechnica CTU Proceedings 47:84–88, 2024 1 Introduction 2 Bridge under investigation 3 Partial factor method 4 Probabilistic method 5 Discussion 6 Conclusion Acknowledgements References