Strengthening and Rehabilitation of U-Shaped RC Bridges Using Substitute Cable Ducts

Research Article Strengthening and Rehabilitation of U-Shaped RC Bridges Using Substitute Cable Ducts Adam Svoboda , Ladislav Klus´ aˇ cek, and Martin Olˇ s´ ak Institute of Concrete and Masonry Structures, Brno University of Technology, Veveˇ r´ ı331/95, 602 00 Brno, Czech Republic Correspondence should be addressed to Adam Svoboda; [email protected] Received 23 July 2019; Revised 20 September 2019; Accepted 23 October 2019; Published 30 November 2019 Academic Editor: Mohammad A. Hariri-Ardebili Copyright ©2019 Adam Svoboda et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The presented paper deals with strengthening and rehabilitation of U-shaped reinforced concrete bridges from the period of 1905–1930 using post-tensioning, which is a suitable, reliable, and durable method. These bridges have two main beams pulled over the bridge deck, which is supported by cross girders. The cross girders connect the two main beams forming a half-frame in the transverse direction, which provides spatial rigidity to the structure. The spans of these bridges are usually between 15 and 25 m. The high efficiency of post-tensioning can be seen on many implemented applications for bridge reconstructions worldwide. However, in this paper, the post-tensioning method is extended by a unique structural system of substitute cable ducts that allows for significantly expanding applicability of this method on existing concrete bridges. This method is highly recommended due to minimization of interventions into the constructions, unseen method of cable arrangement, and hence the absence of impact on appearance, which is appreciated not only in case of valuable historical structures but in general as well. In conclusion, the posttensioning by monostrands in substitute cable ducts is a highly efficient method for strengthening of existing bridges in order to increase their load-bearing capacities in terms of current traffic load and to extend their service life. This method was also verified by monitoring the behavior of rehabilitated bridges before and after strengthening. 1. Introduction Reinforced concrete beam bridges have been built since the very beginnings of reinforced concrete. Both simple and continuous parapet bridges represent a suitable structural option of beam bridges because of their small construction height (U-shaped bridges, camelback bridges, and trough girder bridges). These structures have been developed near Michigan, USA, and soon they have spread in Europe as well [1]. There is still a couple of hundred of these structures around the roadways in the Czech Republic [2]. The oldest U-shaped bridges were built between 1905 and 1915, and they were designed in accordance with the Austrian Ministry of Railways Bridge Standard of August 1904 [3]. At that time, the largest load the road bridges had to endure on the primary roads was an 18 t(180 kN) steamroller or a uniformly distributed load of 460 kg/m2 (4.6 kN/m2) over the surface of the bridge [4]. This bridge type was very popular up until 1930, but from the standpoint of current traffic demands upon bridge structures, it usually does not comply because of its load-bearing capability and an efficient strengthening and total reconstruction has to be performed upon bridge structure [5]. These concrete bridges are also valuable from the historical standpoint because they represent a legacy of the first generation of reinforced concrete bridge engineers. 1.1. Reinforced Concrete Bridge Strengthening Using the Substitute Cable Duct Method. Post-tensioning is a suitable, reliable, and durable method for reinforced concrete bridge strengthening. A strengthening system using post-tensioning effects has also been discussed in previous studies and applications; for example, Recupero et al. [6, 7] presented an application of external prestressing technique for strengthening a single-span concrete railway bridge in Italy. The effect of strengthening was also researched with the help of numerical simulations. Nilimaa et al. [8] focused on Hindawi Advances in Materials Science and Engineering Volume 2019, Article ID 8920718, 21 pages https://doi.org/10.1155/2019/8920718 strengthening of concrete railway bridges (in Sweden) in the transverse direction using prestressed bars installed in additionally drilled holes in the existing concrete. Petrangeli et al. [9] published a paper focused on strengthening of the continuous reinforced concrete bridge in 1976 in Ethiopia across the Gibe river using external prestressing tendons. Daly and Witarnawan in articles [10, 11] presented two applications of strengthening composite (steel-concrete) bridges in Indonesia using external prestressing and also discussed key parameters for designing such a system. Woodward and Daly [12] examined the effect of external prestressed tendons within an experiment on a bridge model of a 1 : 4 scale. The experimental load tests have shown that the post-tensioning method provides a safe and stable method of strengthening. Dai et al. [13] examined the strengthening technique with double-layer prestressed steel wire ropes (PSWRs) to enhance the serviceability of an existing concrete box girder. Miyamoto et al. [14] studied the behavior of prestressed beams strengthened with external tendons. In the presented paper, simply supported prestressed composite girders with alternating prestressing levels, eccentricity of tendons, and tendon properties are examined. Mimoto et al. [15] developed a strengthening system using post-tensioned tendons with internal anchorages in the existing concrete. The internal anchorage hole is made using a special drilling machine, and the system provides joints between the existing and additionally cast concrete parts. Other researchers focused on post-tensioning of concrete using FRP elements; for example, Lee et al. [16] and Jung et al. [17] presented a post-tensioned FRP near-surface mounted system for strengthening of existing structures without changing its dimensions. The strengthening effect was investigated both experimentally and numerically. Aravinthan and Heidt [18] studied innovative methods for strengthening of bridge headstocks using posttensioned fibre composite wraps as an alternative to steel prestressing tendons. Some scientists deal with the comparison of prestressing methods using steel tendons or FRP elements; for example, Choi [19] examined effective stresses of concrete beams strengthened using CFRP and external prestressing tendons. The strengthening effect of external tendons was found to be significantly greater in comparison with CFRP. Also, RC beams strengthened with external tendons showed small difference between the analysis and experimental results compared to beams strengthened by the CFRP method. However, none of the cited authors applied the posttensioning method for strengthening the described U-shaped RC bridges. Researchers at the Brno University of Technology (Czech Republic) have developed the substitute cable duct method, whose structural design pushes the limitations of historical structure prestressing. Basic structural arrangement of prestressing cables in beam bridge strengthening using the method of substitute cable ducts is shown in Figure 1. After a previous detailed diagnostics, usable spaces between reinforcement are determined and substitute cable ducts are drilled through the beams. The direction and distribution of ducts is intentionally selected so that the anchorage area could be created above or behind the bearing axis, and the distribution of saddles was selected at 1/5 to 1/4 from the theoretical support in compliance with the static calculation. Preparatory works for cables are finished by creating the saddles in such a manner that the radial forces of the cables are directed straight into the concrete of the retrofitted structure, and the complex and unclear transformation of forces is not performed. After prestressing, the anchoring areas are filled with concrete and the cables (monostrands) on the bottom side of the beams are covered with an additional concrete covering layer, or they are hidden in the reconstructed original covering layer. The suitability of the method was confirmed for both simple and continuous U-shaped bridges with span lengths from 8 to 25 m [20]. 1.2. Cables in Substitute Ducts in Original Beams. Using the substitute cable duct method leads to a placement of posttensioning cables and monostrands directly into the concrete of the original beams. The essential requirement of this method is a favourable distribution of the original main load-bearing reinforcement, which provides abundant space for suitable drilling of substitute ducts in the available spaces between the original reinforcements without its interruption, or with just a small decrease in strength, which can be included in the strengthening design calculations and which can be compensated by the post-tensioning effects. This requirement is met relatively often (in most cases resolved by post-tensioning, suitable spaces could be found between the original reinforcements), which is given by the design customs from the time of construction. Use of the substitute cable duct method then provides significant advantages: (1) Through saddles, the cables lean directly on the concrete of the beams, and therefore, the radial effects of cables directly affect the original structure (practically in the vertical axis of the beams). Therefore, they do not have to be rather intricately transformed by weldments placed on beam sides, or with separately cast blocks with duct saddles. (2) The saddles can be created very simply as steel sheets (strap steel) bent into the prescribed radius of 1.2 m to 1.5 m, which are mounted into high-strength microconcrete with a full-area anchored saddle. (3) The prestressing reinforcement (cables composed of monostrands) is completely protected against mechanical damage after subsequent filling of ducts with injection. If this protection is further complemented with additionally anchored cable sheathing in a straight section between saddles on the bottom surface of beams, then the entire prestressing set is hidden in the original concrete and in the newly constructed cover. Therefore, the requirements for perfect mechanical protection of the plastic sheaths of individual monostrands are met. If the stable conditions for primary and secondary protection of prestressing reinforcement are observed, long lifetime (long-term reliability) of this type of strengthening is guaranteed. 2Advances in Materials Science and Engineering Substitute cable ducts require drilling of holes into concrete and masonry in lengths multiple times longer than the commonly manufactured machines and tools allow. A special positioning drilling device—a drilling support—was designed and manufactured for this purpose. The main parts of the device are guiding bars and a drilling cart. The cart allows defined clamping of drilling machines and a transfer of force for provision of the necessary drilling thrust. Together with the cart, the guiding bar allows prolongation of drilling shafts. This device (Figure 2) composed of the cart and the guiding bars provides machine guidance for the drilling machine and decreases strain of the operators of the drilling machine to an acceptable level. Secondly, it also increases the accuracy of drilled cable duct trajectory to the highest degree possible. Thirdly, it allows the operators to set a completely arbitrary trajectory because they can set any angle in both the horizontal plane and the vertical plane (usually an angle towards the longitudinal axis of the load-bearing structure). The drilling support can be axially equipped with both diamond and impact drilling technology, and these can be swapped even during the drilling of a single cable duct. Another advantage of the drilling support is that it can be attached to the retrofitted structure itself. Figure 3 shows a deployment of the drilling support with diamond drilling technique. Both simple and continuous reinforced concrete beam structures can be strengthened using cables in substitute ducts. In the case of simple structures (usually simply supported beams), the ducts and prestressing reinforcements are arranged in accordance with Figure 1; in the case of continuous structures, they are arranged in accordance with Figure 4. Continuous structures can be efficiently tensioned with continuous raised cables, tensioned from both sides. In accordance with static requirements, these cables can be complemented with noncontinuous cables, anchored in a composite slab or in anchoring blocks (extensions), which will be placed between the original beams. In monostrand prestressing, the coefficient of friction μ, which is used only in saddles in this distribution, has the value of 0.06 to 0.10, which was repeatedly verified during prestressing of structures strengthened in this manner by comparing the calculated and the achieved monostrand extension sizes. The friction does not apply in direct sections of cable trajectories (in such case, monostrands mostly lead almost linearly from saddle to saddle, through air and without friction). Substitute cable ducts can be drilled into the structure very accurately and with very little damage to the original beam reinforcement. Site diagnostic of beam reinforcement, which provides information on the most suitable space for duct drilling, is necessary for drilling the cable duct. The designer defines the position of theoretical points (TP) only in the longitudinal direction, and they let the exact outlets of ducts in the transverse direction of the beams up to the construction process. In many cases, the concrete of the strengthened structure is more damaged by corrosion in the area of the bottom face of the beams that the concrete cover layer has already fallen off and the distribution of reinforcements is 5.0° 15.0° Figure 2: Scheme of the drilling support for drilling substitute cable ducts of relatively small diameters (ϕ�35 ∼52 mm) into the concrete of the existing bridge structure. It allows adjustment of both vertical and horizontal drilling angles. The picture shows a support fitted with a drill using the impact technology. Longitudinal section A-A Cross section B-B A A B B L/4~L/5 L Figure 1: The basic scheme of cable arrangement in the case of strengthening a simple span bridge by post-tensioning using the substitute cable duct method. Figure 3: A realization of drilling substitute cable ducts on the bottom side of a U-shaped bridge using a drilling support [21]. The photo shows the use of invented drilling support equipped with a drilling machine with the diamond drilling technology. The drilling machine, clamped into a cart, is led by guiding bars in the required angle (both vertical and horizontal) relative to the bottom face of the structure while drilling a duct. Advances in Materials Science and Engineering 3 clearly visible. In other cases, in the area of future saddles, the original cover can be removed because after prestressing, the cables will be protected by the anchored cover and the surfaces of the entire structure are usually retrofitted with a special layer. Figure 5 shows an example of a duct outlet between beam reinforcements of a strengthened continuous beam structure in accordance with project documentation. It shows that suitable space could always have been found and that the substitute ducts could have been prepared without or with minimum damage to the original profiles of the main load-bearing reinforcement. 2. Strengthening of U-Shaped Bridges U-shaped bridges have two main girders extending above the roadway, and the bridge deck is supported by cross girders. The cross girders connect both main girders, and together with them, they form a half-frame in the transverse direction; the half-frame provides spatial rigidity to the structure. These bridges can also be efficiently strengthened using the substitute cable duct method both in the longitudinal and transverse directions [22]. The spans of these structures are between 15 and 25 mm, and the described strengthening was used in the realized designs, e.g., [21, 23]. The main girders are usually reinforced with the original reinforcement in the amount of 8 to 12 pieces with ϕof 35 to 50 mm in two or three rows. This provides enough space for substitute ducts. The main girders of U-shaped bridges are regularly strengthened with two to four cables with three to four monostrands in every cable. Similarly to main beams, the transverse girders can be strengthened with cables in substitute ducts anchored on side areas of main girders. Basic distribution of post-tensioning cables is shown in Figures 6 and 7. U-shaped bridges, built between 1905 and 1930, are suitable structures for strengthening using the substitute cable duct method, which is given by the following structural particularities: (1) Girder front sides are available for cable anchoring in the main girders (U-shaped). Cable lines can be designed with zero end eccentricity above the supports. The tensioning set can be best anchored in the center of gravity of girders, which contributes to high efficiency of post-tensioning and to a good distribution of forces in anchors into the concrete of the original girders. (2) Completely free side areas of main girders are available for anchoring of transverse cables (cables strengthening the transverse beams). On the free side areas, the anchoring areas can be created either with cut bearing surface (older system) or in the form of cast concrete extension (currently used system, which guarantees both primary and secondary protection of the entire lengths of cables including anchors). In the U-shaped girder, cables are led through space crossways with regard to both the horizontal and the vertical planes so that the anchors would act in the vicinity of the center of gravity of the end cross section (in the crosssectional core). The location of cross girder anchors has to be selected carefully because the prestressing forces affect the transverse semiframe; the anchors have to be placed in the center of gravity of projection of the cross girder into the main beam or slightly below it. Then the additional set of forces will be balanced with regard to the semiframe, and it will not stress it adversely in the transverse direction. Prestressing will efficiently create conditions for the additionally cast composite slab, which, in accordance with the requirements of the investor, strengthens the original bridge deck to as high a load as the U-shaped girders and cross girders can be strengthened. Figure 6 shows the shape and arrangement of the prestressing system for strengthening the U-shaped bridge with a span length of l�16.4 m on a secondary road for load-bearing class B in accordance with ˇ CSN 73 6203 [24]. The main girders were sufficiently prestressed with four cables; cross girders were prestressed with two cables. Therefore, conditions have been created to carry the weight of an additionally cast composite slab, which strengthened the original bridge deck. This case is also an example of L1L2L3 Figure 4: The basic scheme of cable arrangement in the case of strengthening a continuous span bridge by post-tensioning using the substitute cable duct method. Also, it is an example of the usage of multiple phases of post-tensioning. The first phase (on the picture described by red dashed lines) creates a possibility for casting an additional concrete composite slab for slab strengthening. The second phase (on the picture described by blue dashed lines) increases the overall load-bearing capacity of the critical middle span. Figure 5: An example of a substitute cable duct (ϕ52 mm) outlet at the bottom side of the beam in a suitable position in a gap between the existing reinforcement. 4Advances in Materials Science and Engineering anchoring using the single-strand wedge with bearing plates without observing the primary protection in anchors (older way). The secondary protection was guaranteed by the usual casting of anchor holes. Figures 8 and 9 show the characteristic details of this strengthening: cable saddles in U-shaped beams and the anchors at the end of these beams [21]. Figure 7 shows the shape and distribution of the prestressing system in strengthening of a U-shaped bridge with variable height of the main beam and a length span of l� 14.1 m on a tertiary road also to the load-bearing class B [24]. The main girders were post-tensioned with two cables of four monostrands, the cross girders were post-tensioned with one cable of monostrands. Once again, conditions to carry the weight of an additionally cast composite slab were created. However, this is an example of anchoring using the encapsulated anchor system with an observance of primary protection in anchors (newer, regularly used bridge anchoring system). The secondary protection was once again guaranteed by the usual casting of anchor areas in concrete. Figure 10 shows characteristic details of cable anchors in the main girder and the cross girder anchors at the sides of the main girder [23]. Strengthening of the U-shaped bridges with post-tensioning using the substitute cable duct system generally brings many advantages: (1) In contrast to the glued reinforcement, which is activated only after load, and therefore does not contribute to the transfer of forces from the permanent load, transfer of prestressing into the structure balances a significant portion of internal forces created by the permanent load; this efficiently improves the condition, in which the structure is not stressed by live load and a necessary reserve is created for the transfer of effects of live load. (2) The increase of load-bearing capacity by this method is significant, regularly 200%–300%, which is an effect, higher almost by an order than the use of glued reinforcement, for which general experience speaks on an achievable increase of approximately 30% [19]. (3) Cracks created by static or dynamic load in the tension flanges of reinforced concrete beams significantly accelerate the process of reinforced concrete corrosion significantly. The transfer of pressure forces by prestressing leads from a partial to a complete closure of cracks and a subsequent Longitudinal section A-A Cross section B-B B B A A 16.25m 9.45m 7.95m 2.45m Figure 6: Cable arrangement in the longitudinal and transverse directions for strengthening of a U-shaped bridge with straight girders, built in Tˇ rebechovice in 1932, according to project documentation [21]. Longitudinal section A-A Cross section B-B B B A A 14.15m 7.50m 5.98m 2.59m Figure 7: Another example of cable arrangement in the longitudinal and transverse directions for strengthening the U-shaped bridge with curved girders which was built in Vraˇ zn´ e in 1928 according to project documentation [23]. Figure 8: An example of the anchorage areas made directly in the existing concrete of the main girders of U-shaped bridge. The strengthening was implemented in 2002, so the old type of anchors was used [21]. Advances in Materials Science and Engineering 5 prolongation of the concrete structure resistance against corrosion. (4) Most construction works connected to this technology can be created without interruption of the traffic on the bridge or only with a partial limitation. (5) When we strengthen bridges by prestressing, we use the entire prestress level interval. In the case of beam bridge strengthening, the interval usually achieves values of λ�0.15∼0.25 (in accordance with Bachmann [25]). (6) For bridges seemingly irreparable due to their static condition, or if the requested load-bearing capacity cannot be achieved with other methods, and when the bridges are usually demolished and a new structure is built, the required parameters can be achieved using this very method of load-bearing capacity increase for a mere third or half of the price of the new structure [26]. The actual design and performance of strengthening must emphasize the fact that the static strengthening is usually a part of a total reconstruction and of retrofitting of the bridge. It must create prerequisites for reliability and durability of the selected design. That is why the below mentioned measures have to be considered and proposed: (1) A thorough treatment of the degraded concrete of the entire bridge (surface areas including the plaster), first mechanically and then using a rotating highpressure water jet. (2) Careful cleaning of the exposed and corroded steel reinforcing bars in the entire bridge structure, first mechanically and then with a high-pressure water single-jet tool. (3) Protection of the steel reinforcing bars with silicate materials. (4) The actual post-tensioning of the bridge structure by both transfer of prestressing and by the composite slab. (5) Application of the adhesion primer coat on the whole surface of the retrofitted concrete of the bridge. (6) Rough and finish reprofiling of the bridge loadbearing structure. (7) Application of a protective and unifying coating on the inner and upper areas of the U-shaped girders. 3. Static Effect of Prestressing Cables in Strengthening by Post-Tensioning Static effect of prestressing cables, additionally built into the original reinforced concrete structures, is basically the same as the effect of a prestressing reinforcement in regular prestressed concrete [27]. This is achieved because the post-tensioned cables are built into the cross section of strengthened structures using the substitute cable ducts in a manner similar to the new, mostly fully prestressed structures. There are almost no differences in the service stage; in this case, radial effects of the additionally built-in prestressing set manifest themselves positively, while the favorable effect of the actual prestressing force manifests itself as well, but not so clearly. This is given by small, but sufficient prestressing degrees λ�0.12∼0.25 [25]. In the stage of ultimate limit state, the main difference lies in the fact that cables composed of monostrands appear to be free (without cohesion with concrete), even if built-in and injected in a cross section. However, the ultimate limit states increase as well by the very additional effect of prestressing forces, which transfer the former sections in pure bending to sections in eccentric compression [28]. 3.1. Decrease of Dead Weight Effects. The basic static function of thus designed beam bridge strengthening is shown in Figure 11. It is depicted on a simple structure, and the used approach can be analogically extended to a continuous structure as well. The radial effect of additional Figure 10: Realization of the additional anchorage areas of both main girders and cross girders. In this implementation, a new type of encapsulated single-strand anchors was used (2008). The anchors are covered and protected in concrete extensions [23]. Figure 9: Prestressing tendons composed of individual monostrands (black HDPE sheaths) on the bottom side of the girder after curvature of their trajectories in saddles [21]. After the prestressing of tendons, the bottom side of the girder is provided with the anchored protective concrete cover layer (the second corrosion protection). The appearance and the concrete character of the bridge are then preserved. 6Advances in Materials Science and Engineering cables leads to a decrease in the effect of the dead weight. Therefore, the LBM (load balancing method) is subsequently applied [27]. The beam bridge structure is loaded by its own weight g0, other permanent load g1(long-term live load, the weight of all layers of the roadway with possible additional load by the raised and over-layered roadway), and live load q. The live load is usually determined as the load-bearing capacity of the bridge in accordance with the relevant technical standard before the beginning of the retrofitting preparations [29]. The load-bearing capacity of a bridge is defined here; it is determined by the following values: normal load-bearing capacity Vn, reserved load-bearing capacity Vr, and an exceptional load-bearing capacity Ve. In accordance with the respective technical standard, a bending moment of ultimate limit state can be determined for the critical sections of the structure (i.e., the limit, to which the section can be loaded in order not to exceed the maximum load on concrete and steel, set by the standard) [30]. Figure 11 shows which part of the bending moment of the ultimate limit state can be used for the moment of determining the load-bearing capacity of the bridge. The load decisive for the load-bearing capacity of the bridge before strengthening can cause the highest bending moment Mq, and its total effect is increased by the dynamic coefficient of a moving load δ. In accordance with calculations and studies of several dozens of beam bridges built between 1915 and 1950, the load-bearing capacities of the original bridges come out to be very low. Normal load-bearing capacities Vnare between 8 and 15 t, and reserved load-bearing capacities Vrusually constitute 15 to 30 t, expressed with regard to the moment of bending moment of ultimate limit state; 1/4 to 1/3 of a bending moment of an ultimate limit state of a section can be used for the load-bearing capacity. In the case of overfilled bridges, i.e., bridges, whose roadway was simply raised with other layers of asphalt concrete in the past, this number can be even lower, often 1/10 to 1/4 of the bending moment of ultimate limit state. We can often encounter paradoxic situations, in which the entire moment of ultimate limit state can be consumed by the weight of the bridge itself, or the limit can be even lower. In terms of calculations, such a structure cannot even carry its own weight. It is clear that a collapse will not occur because of the internal reserves in the materials and sections, but the structures exploited in this way then lack the safeties guaranteed by standards and even a regular traffic overloads them and all the related negatives ensue (sagging, cracks, and vibration). This leads to a decrease of lifetime of such overloaded structures. As shown in Figure 11, bending moment effects of suitably designed post-tensioning efficiently decrease bending moments from permanent load. The following inverse proportion applies to the bending moment stress determining the load-bearing capacity of the bridge: the decrease of bending moment effects of permanent loads (g0, g1) caused by bending moments since prestressing MPis inversely proportional to the portion of the total bending moment of the ultimate limit state which can be used. Even with a small level of prestressing, the bending moment gain of thus-strengthened structures is significant and many times larger portion of the bending moment of ultimate limit state than before strengthening can be used for the determining bending moments of the ultimate limit state after structure prestressing. It can be stated that MRd,new �(2∼3)MRd,old,(1) where MRd,new is the largest moment determining the load-bearing capacity for structures strengthened with prestressing, MRd,old is the largest moment determining load-bearing capacity on the original, nonprestressed structure. If the usable moments MRd,new after strengthening are multiple times larger than moments MRd,old before strengthening, the load-bearing capacity of thus-strengthened beam bridges increases as well. The load-bearing capacity can commonly be increased by 200 to 300% in comparison with the original values before strengthening. Slab bridges were also strengthened, and in their case, 10 times higher normal load-bearing capacity values and 6 times higher reserved load-bearing capacity have been achieved. PP PP Pv Pv Mg0+g1 Mg0+g1 + MP Mg0+g1 + MP MRd,new MRd,new MRd,old MP MPMRd,old Mg0+g1 + = δMq δMq q q g0 + g1 After strengthening Before strengthening Figure 11: The basic scheme of prestressing static effect on the simple span bridge (reduction of dead load bending moments—application of LBM). Prestressing creates a much bigger reserve of bearing capacity which can be used for traffic load, and therefore, the load-bearing capacity is increased. The efficiency of this method is up to 300%. Advances in Materials Science and Engineering 7 3.2. Section Load-Bearing Capacity Increase. Axial component of prestressing force has a minor effect upon real section strengthening and therefore on the increase of the bending moment of the ultimate limit state. In accordance with Figure 12, the section originally in pure bending changes to a section in eccentric compression, which is accompanied by an expansion of the compressed area of concrete section x. This fact causes a minor increase in the bending moment of ultimate limit state in accordance with Figure 13. Prior to strengthening, the bent bridge beam section is characterized by a pair of internal forces N�0;M�MRd,old. In accordance with the size of the moment Min effect, its current stress can be expressed only on the horizontal axis of the failure function π. After strengthening, stressing force Pis transferred into the section. In accordance with the achieved degree of prestressing λ,any horizontal line in the marked area inside the failure function πapplies to the strengthened section. The intersection of this line and the failure function π is given by the pair N�P;M�MRd,new. The following statement must apply to every horizontal line in the marked area (thus for every nonzero P) on the basis of shape of the failure function π: MRd,new >MRd,old,(2) where Pis a prestressing force transferred by post-tensioning during strengthening, MRd,old is the section bending moment of ultimate limit state prior to strengthening, and MRd,new is the section bending moment of ultimate limit state after strengthening with prestressing force P. Increase of height of the compressed area xof the strengthened section increased the ideal moment of inertia around the most stressed sections. Theoretically, this leads to a decrease in structure sagging (the structure becomes stiffer), which was also experimentally measured and confirmed (paragraphs 5.1 and 5.2 of this article). Attention should be paid to the fact that, for the used low levels of prestressing, the movement of the neutral axis is relatively small and the corresponding increase of the ideal moment of section inertia is only 10 to 15% in comparison with the original. We can never expect full prestressing of the sections. Their deformation behavior after strengthening is basically the same as before (crack openings occur again in the tensioned flange because of the other, nonbalanced portion of permanent loads and live loads), but their widths will decrease and sagging will slightly decrease because of the effect of the live loads. It is clear that even in low levels of prestressing, the effects of beam bridge strengthening are significant. The load-bearing capacity values increase to multiples of the original values after strengthening. Even the mere decrease of influence of the dead weight of the structure (for example, by removing the overfilled layers of roadway), which also releases a part of the bending moment of ultimate limit state, can be surprisingly used very scarcely. The vertical alignment of the roadway is mostly the decisive factor because it is given by the connection before and after the bridge. Its decrease on the bridge causes large and therefore financially demanding modifications of long stretches of the road. Alongside the beam strengthening, the bridge deck often has to be strengthened as well so that it could withstand the wheel pressure of the cars. Additionally cast slabs, which can be efficiently designed to the very structure strengthened by prestressing, can be used for this purpose because the increase of the dead weight with an additionally cast slab can be eliminated by the very posttensioning. The intents to only increase the load-bearing capacity of a bridge with minimum costs because of the limited financial means are also frequent. In such cases, this is a very efficient method because all the layers of the original roadway can be kept on the structure. The fact that this strengthening can be performed under almost normal operation of the bridge with minimum demands upon traffic limitation is also worth mentioning. Substitute cable ducts as well as saddles are mostly created from the bottom part of the structure, usually with no interruption of operation of the bridge. The performance of the anchoring areas and prestressing can be performed gradually (one half of the bridge after another) because the character of post-tensioning using the subsequent cable duct method is structurally similar to the assembled structure. 3.3. Shear Forces Reduction. Similarly, the shear forces are efficiently reduced by prestressing. The reduction is depicted in Figure 14. The section above includes an example of a typical basic course of shear forces to permanent loads and a load corresponding with the Vn set. The middle section describes a course of shear forces from prestressing which has the opposite sign. The resulting reduced course of the shear forces is stated in the section below. The larger is the distance between the saddle and the support, the smaller is the angle of the cable against the axis of the beam and the smaller are the shear forces, which are able to reduce the original shear forces and which are affected by the prestressing cable. From the standpoint of the shear forces, it would be better to create saddles closer to the support; from the standpoint of bending moment, it would be better for the saddles to be as far away from the support as possible. Even though the specific design depends on many other factors of structures generally very diverse in terms of dimensions and composition, the results of as-yet designed and realized strengthenings lead to a discovery that the ideal distance for distribution of saddles in a length is in the interval from 1/5 to 1/4. This applies to both simple and continuous structures [31]. Structures with haunches require special attention. If the haunches are linear, then the beginnings of haunches mostly correspond to the abovementioned recommendation. In the substitute cable duct method, the saddles can be placed in the haunch ends. If the haunches are longer (for example, parabolic haunches often reach l/3), it is necessary to use separately cast blocks between beams and place those in the recommended spaces. 8Advances in Materials Science and Engineering 4. Diagnostics, Design, and Strengthening Performance Process 4.1. Diagnostics of the Current Bridge Structure. In the diagnostics for bridge strengthening, it is necessary to determine the following: (i) Reinforcement of the current sections of beams, cross girders, and slabs in the center of their length, or above the supports of the continuous structure. It is necessary to determine the amount, diameter, and locations of the individual reinforcement profiles including spaces between them as the source data for decision whether the substitute cable duct method can be used. (ii) Reinforcement of the current sections of beams, cross girders, and slab in supports. It is necessary to determine the amount, diameter, and locations of the individual reinforcing profiles in order to determine the number of raised shear reinforcement. The raised shear reinforcement (bent profiles) can be swung out from the vertical plane, and they can partially intersect with the trajectory of the substitute cable duct. That is why it is better to select those spaces between reinforcements which are not trimmed with bends. In bridge slabs, it is necessary to determine how much reinforcement is raised in the support; this usually constitutes 1/3 or 1/2 of the total amount of profiles. (iii) Strength of the concrete of the load-bearing structure at least with nondestructive impact method (Schmidt) with specification using test core drilling. The NDT itself is not sufficient because, in older structures, it usually provides concrete strengths of one or two classes higher than the final ones after specification. The permissible stress of concrete under anchors has to be derived from the determined strengths. The concrete strength significantly codetermines the bending moment of ultimate limit state of the current section. (iv) The concrete elastic modulus has to be determined if a verification of behavior of the bridge structure after strengthening with a stress test can be expected. In the case of historical bridge constructions, the modulus of elasticity varies depending on the possibilities of concrete production at that time and especially on the placing, processing, and compacting of the concrete mixture. In practice for + = After strengthening Before strengthening Vg0+g1 + VP Vg0+g1 VP Figure 14: The basic scheme of reduction of shear forces due to the radial effects of prestressing cables in polygonal trajectory in the case of strengthening the simply supported beam according to Figure 11. Mg0+g1 + δMq Xold MRd,old Cg (a) Mg0+g1 + δMq P MRd,new Xnew MP Cg (b) Figure 12: Expression of the prestressing effect on the beam structure cross section. The beam cross section and its internal forces (pure bending) (a) before and (b) after application of prestressing force. The cross section is now eccentrically in compression (a combination of bending moments and axial force), thus increasing the load-bearing capacity of the cross section. P N (kN) M (kNm) λ = 0.10~0.25 [N = P; MRd,new] ∏ = [NRd; MRd] [N = 0; MRd,old] Figure 13: Increase of the load-bearing capacity of the cross section in the interval of partially prestressed concrete λ�0.12∼0.25 expressed by the interaction diagram (failure function π[25]). Advances in Materials Science and Engineering 9 (a) (b) (c) Figure 21: Static load test of the U-shaped bridge built in 1928 after strengthening [23]. The position of heavy vehicles (vehicles front and rear axles) in the longitudinal and transverse directions is described on the pictures. 0.5 1 1.5 20 Time (hour) –1 –0.5 0 0.5 1 Deformation (mm) 1st test 2nd test Test load: 2 × 20tonnes Figure 25 T2-right girder (a) −4 −2 0 2 4 Deformation (mm) 02468 Time (hour) Prestressing of the right girder Sign convention: + = sag, − = hog Total force = 784kN T2-right girder (b) Figure 22: Continued. 16 Advances in Materials Science and Engineering 0.5 1 1.5 20 Time (hour) –1 –0.5 0 0.5 1 Deformation (mm) 1st test 2nd test Test load: 2 × 20tonnes Figure 25 T2-right girder (c) Figure 22: Graphs of the right girder (see sensor T2 in Figure 20) deflections (a) before strengthening (static load test with two load cases—heavy vehicles), (b) during prestressing, and (c) after strengthening (static load test with an identical load before strengthening). 0.5 1 1.5 20 Time (hour) 1 0 –1 2 Deformation (mm) 1st test 2nd test Test load: 2 × 20tonnes Figure 26 T3-cross girder (a) 24680 Time (hour) −4 −2 0 2 4 Deformation (mm) Prestressing of the cross girder Sign convention: + = sag, − = hog Total force = 392kN T3-cross girder (b) Figure 23: Continued. Advances in Materials Science and Engineering 17 show examples from an extensive set of measured saggings and hoggings during prestressing and during the load test using the two test vehicles [23]. Within the evaluation of the strengthening effect, the measured values were averaged. The summary of the resulting values is stated in Figure 24. On the basis of the measured data, strengthening of the load-bearing elements of the U-shaped bridge can be evaluated as follows: (1) Main girders strengthening: the change of internal forces, which led to an increase of load-bearing capacity of the main girders, and therefore the entire bridge, will manifest itself in the hogging of the main girders and in the ratio of the measured sagging before and after strengthening. During prestressing, the main girders have hogged (bent upward) by 2.4 mm. In the absolute value, this value is a 4.6x higher positive deformation effect than the effect caused by two Tatra vehicles weighing 2 ×22 t. This proves the high efficiency of the performed strengthening. (i) After strengthening, the measured sagging of the main girders loaded by identical vehicles has decreased to 86% of sagging before strengthening (Figure 25). This proves the reinforcement of the main girders achieved by the performed strengthening. This is the proof of increase of deformation stiffness of main girders, even if at a low level of prestressing (λ�0.14)[25]. (2) Cross girder strengthening: the change in internal forces has also manifested itself in the ratio of measured sagging before and after cross girder strengthening. The cross girders hogged (bent upwards) by 3.0 mm during the prestressing. In the absolute value, this value is a 2.4x higher positive deformation effect than the effect caused by two Tatra vehicles weighing 2 ×22 t. This is also an example of the high static efficiency of the performed strengthening. After strengthening, the measured sagging of the cross girders loaded by identical vehicles has decreased to 91% of sagging before strengthening (Figure 26). This once again proves the cross girder reinforcement achieved by the performed strengthening. This is the proof of increase of deformation stiffness of cross girders, even if at a low level of prestressing (λ�0.12)[25]. Deflections of the U-shaped bridge structure (mm) Part of the structure Before strengthening During strengthening After strengthening Ratio of average deflections after/before strengthening Main girder T1 0.50 –2.60 –0.47 0.86 Main girder T2 0.54 –2.20 –0.43 Cross girder T3 1.75 –5.60 1.50 0.91 Cross girder T4 1.78 –5.20 1.70 Figure 24: Assessment of deflections before and after the strengthening of the U-shaped bridge in Vraˇ zn´ e, built in 1928 [23]. Note: downwards +; upwards −. 0.5 1 1.5 20 Time (hour) 1 0 –1 2 Deformation (mm) 1st test 2nd test Test load: 2 × 20tonnes Figure 26 T3-cross girder (c) Figure 23: Graphs of cross girder (see sensor T3 in Figure 20) deflections (a) before strengthening (static load test with two load cases—heavy vehicles), (b) during prestressing, and (c) after strengthening (static load test with exact the same loading like before strengthening). 18 Advances in Materials Science and Engineering 6. Recommendations for Design and Performance of Strengthening by PostTensioning On the basis of already designed and realized structures and on the basis of measurements performed during prestressing and subsequently during structure loading, the below mentioned recommendations regarding design and the actual performance of the post-tensioning using the substitute cable duct method can be provided. 6.1. Values for Prestressing Losses. If the cables used are composed of monostrands, the coefficient of friction decreases significantly. This is caused by the lower friction of the plastic protective sheaths and the metal components of the saddle and also by the greasing effect of the anticorrosive passivating filling between the monostrand wires and the protective sheath. The passivating filling contains grease or paraffin wax, which limits friction efficiently. Even though the standard documents state the value of the coefficient of friction in a bend to be 0.06 for cables composed in this way, during practical tests performed during tensioning of the strengthened bridges, the value of 0.10 was determined. This value can be recommended for this post-tensioning system, in which the monostrands individually lean on the saddle reinforcement [31]. Single-strand encapsulated anchor systems are used regularly in bridge strengthening (e.g., [34]). The anchoring is performed using self-locking three-jaw wedges in the conical opening of the anchor. During their use, their slipping was measured at 2.60 mm to 2.90 mm while tensioning with the maximum forces of 200 kN. In consideration of slipping losses, 3.0 mm can be considered a safe value. In such a small size, the slipping reach is not significant and the slipping usually disappears already around the location of the first saddle. This allows a design of continuous cables over three or even four span lengths of continuous structures. Tensioning from both sides is used for these cables (respectively, tensioning from one side of the cable, and after anchoring, the cable is tensioned from the previously nontensioned end), and in such case, friction losses remain acceptably low at the center of the cable (usually within 15%). The losses caused by the elastic shortening of concrete losses are negligible. This is given by the low level of prestressing (average prestressing in the section achieves 1.5 to 3.0 MPa) and therefore also by the very small elastic deformation of the concrete and the entire structure during prestressing. Because the number of tensioned cables is not large, repeated tensioning of already anchored monostrands can completely exclude this loss even in cases in which the exclusion is not advisable. Relaxation losses can be determined the same in a new structure as from prestressed concrete. In regular cases, in which low relaxation monostrands are used almost exclusively, the losses can be disregarded [27]. Losses caused by concrete shrinking can be completely disregarded because during strengthening, the prestressing is being used on concrete structures 80 to 100 years old. Only in the case of strengthening of a combination of posttensioning and an additionally cast composite slab, the load from prevented concrete shrinking of a new slab should be included in the calculation. Losses caused by concrete creeping can be disregarded in most cases as well. This is Time Before strengthening After strengthening 0 0.2 0.4 0.6 Deformation (mm) Figure 25: A comparison of the measured deflections of the main girder before and after the strengthening with the same test vehicles in the same position on the U-shaped bridge built in Vraˇ zn´ ein 1928 [23]. Time Before strengthening After strengthening 0 0.5 1 1.5 Deformation (mm) Figure 26: A comparison of the measured deflections of the cross girder before and after the strengthening with the same test vehicles in the same position on the U-shaped bridge built in Vraˇ zn´ ein 1928 [23]. Advances in Materials Science and Engineering 19 caused by the low level of transferred prestressing and the decrease of compressive stress in the compressed area of the original sections, which is achieved by the very balancing of a part of permanent load of the structure. Alternatively, they can be quantified more specifically using creeping models used by separately developed computer programs for time-dependent analysis of concrete structure creeping [36]. 6.2. Recommendations for Structural Details. As regards the saddle radii, we recommend observation of the minimum radius of r�1.2 m and a creation of haunches on the steel strap with a minimum length of 150 mm and a radius of r�r/4. Regular sheet steel saddles can transfer radial forces from one to four monostrands without larger structural issues. The saddle shape should be adapted width-wise for the insertion into the cable duct. Saddle length should not be smaller than 400 mm (without haunches) for practical reasons so that it could even be mounted including the required tolerances. The same radii are applied to tube saddles. Tube saddles should be equipped with haunches in the shape of a hollow cone [31]. The diameters of drilled ducts are supposed to be as small as possible, e.g., ϕof 35 mm is sufficient for single-strand cables and ϕof 52 mm is sufficient for multistrand cables up to four monostrands. In beam structure strengthening, it is suitable to allow for weakening by interruption of one or two profiles of the original reinforcement in the static design. Cables with even larger number of monostrands are used rarely, and in such case, they must be placed outside of the section (e.g., [6, 9]). Deviations have to be prescribed for duct drilling and for saddle mounting, and the deviations must be fulfilled. The design of additional concrete covers always has to include anchoring into the original structure. Anchoring with mere cohesion cannot be considered sufficient because of temperature changes of the cables, elastic sagging of the structure, etc. The covering layer also has to be reinforced with welded wire mesh so that the forces would be distributed from the anchors to the entire covering layer. 7. Conclusion The described method is suitable for rehabilitation (increase of load-bearing capacity, reconstruction, and prolongation of durability) of reinforced concrete U-shaped bridges, which were built between 1905 and 1930 and the original structure of which almost renders other strengthening methods impossible. Efficiently, the main beams and cross girders can be strengthened, and in that manner, the increase of the dead weight connected to the use of a composite slab to strengthen the bridge deck can be balanced. The static strengthening is significant, and it is accompanied with increase of deformation stiffness, which was proven by the performed load tests. In the case of U-shaped bridges, there is no other option to effectively improve their structural behavior without affecting appearances of these unique historical concrete structures. The presented method of substitute cable ducts can also be used to strengthen other types of concrete bridges with different static schemes and cross-sectional shapes. It can be used for structural securing of the prestressed bridges and masonry vaults. Data Availability The data used to support the findings of this study are available from the corresponding author upon request. Disclosure This paper has been worked with the support of the program Competence of Technology Agency of the Czech Republic (TAˇ CR) within the Centre for Effective and Sustainable Transport Infrastructure (CESTI), Project No. TE01020168. This paper has been created during the solution of Specific Junior Research FAST-J-19-5989 Analysis of verification static loading tests of reinforced concrete bridges strengthened by post-tensioning. Conflicts of Interest The authors declare that they have no conflicts of interest. References [1] N. Holth, “Michigan’s unique concrete camelback bridges,” 2019, https://historicbridges.org. [2] Road and Motorway Directorate of the Czech Republic, Statistical Overviews of the Bridge Database Information System, Prague: Road and Motorway Directorate of the Czech Republic, Prague, Czech Republic, 2018. [3] Austrian Ministry of Railways Bridge Standard, New Bridge Standard: Technical Standard, Wien: Austrian Ministry of Railways Bridge Standard, Wien, Austria, 1904. [4] Czech Office for Standards, First Czechoslovakia Bridge Standard: Technical Standard, Czech Office for Standards, Prague, Czech Republic, 1923. 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