Transverse prestressing and reinforced concrete as the key to restoration of masonry arch bridges

Engineering Structures 245 (2021) 112898 0141-0296/© 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct Transverse prestressing and reinforced concrete as the key to restoration of masonry arch bridges Ladislav Klusáček, Radim Nečas, Michal Požár, Robin Pěkník, Adam Svoboda∗ Institute of Concrete and Masonry Structures, Brno University of Technology, Veveří 331/95, 602 00 Brno, Czech Republic ARTICLE INFO Keywords: Arch bridge Transverse prestressing Wall Restoration Post-tensioning Masonry ABSTRACT There is still a large number of masonry arch bridges on the road and railway network. More than 80 % of arch bridges are over 100 years old so their service life has been exceeded significantly. The general focus of the paper is to show the method for strengthening and restoration of these bridges, especially if they have been damaged by longitudinal cracks. The restoration is performed using new spandrel walls from reinforced concrete stabilized by transverse prestressed cables. This paper illustrates the strengthening process with four examples of restored road or railway bridges. In addition, it includes examples of basic cable arrangements and a design of the new concrete walls, which are used as anchorage areas for transverse prestressing. The efficiency of this method will be determined using data measured during the prestressing and a load test. The measurements have shown an extremely favourable effect of the addition of horizontal prestressing within the new reinforced concrete walls. After an evaluation of the deformation of the top cross-section reduced up to 40 % of the values before strengthening. 1. Introduction In the road and rail network, there are still tens of thousands of bridge arches made of stone or brick masonry throughout Europe (Fig. 1) older than 120 years. Many bridges do not meet the current standards and have reached the end of their theoretical durability [1]. However, the replacement of all these structures is economically unrealistic, since the disposition, flow profile and masonry quality of the arch bridges often comply with the respective standards. However, they are too narrow and their lateral alignment tends to be broken by longitudinal cracks, most often caused by the earth pressures of the road embankment, as well as by transverse tensile stresses, occurring around the centre and at the edges of the arches, caused by overlaying and increased live load (multiple increase of vehicle axle loads and traffic intensity). Transverse prestressing represents one option of reinforcement of such damaged arches. This option is effective for cylindrical road bridges and rail arches, which are, contrary to the arches in building construction, damaged by longitudinal crack systems. The cracks break the arch not only at the connecting points of the spandrel walls and the arch, but also in the middle of structure width, roughly in the axis of the transferred road. Restoration of arch bridges using the post-tensioning method presented in this paper is partially derived from post-tension techniques ∗Corresponding author. E-mail addresses: [email protected] (L. Klusáček), [email protected] (R. Nečas), [email protected] (M. Požár), [email protected] (R. Pěkník), [email protected] (A. Svoboda). for strengthening of reinforced concrete bridges, as shown for example in [2]. This technique of additional prestressing is based on the drilled substitute ducts which enable acting of radial forces directly to the mass of the structure without any anchored weldments or auxiliary mechanical devices. The substitute cable duct technique is rather unique while the standard external prestressing technique using external tendons is very well known around the world. For example, in articles [3] and [4] Recupero et al. presented an application of external prestressing technique for strengthening of a single span concrete railway bridge in Italy. Petrangeli et al. [5] published a paper focused on strengthening of continuous reinforced concrete bridge across the Gibe river in Ethiopia also using external prestressing tendons. In articles [6] and [7] Daly et al. presented two applications of strengthening composite bridges in Indonesia using external prestressing. In his thesis, Nilimaa et al. [8] focused on strengthening of concrete railway bridges (in Sweden) in transverse direction using prestressed bars installed in additionally drilled holes in the existing concrete to prevent shear failure. It is also possible to see the use of an external post-tensioning system using prestressed cables in order to reduce structural vulnerability and to preserve the artistic and aesthetical values of historical structures. In article [9] is discussed the rigid block analysis for modelling such https://doi.org/10.1016/j.engstruct.2021.112898 Received 1 February 2021; Received in revised form 13 July 2021; Accepted 21 July 2021 Engineering Structures 245 (2021) 112898 2 L. Klusáček et al. a system. Other information about strengthening using prestressing method can be found in [10,11] or [12]. The seismic protection of masonry structures by implementation of vertical prestressing at key locations is presented in researches [13–15] and [16] . The main idea of this prestressing technique is to improve the seismic performance by the application of a uniform distribution of compressive stresses which is very favourable for these structures. Other techniques use modern composite materials (FRP, CFRP, GFRP) for strengthening of structures, for example [17–21] or [22]. The technique of GFRP was also researched experimentally for the purposes of strengthening of RC arch bridge as shown in article [23]. The research of application of the FRP method for strengthening of masonry vaults is presented in [24] and an example of usage of the CFRP method for strengthening of masonry vaults is presented in [25]. Design approaches for calculating of the additional strengthening of masonry arches using the Strut-and-Tie model and the applicable standards and their comparison to the experiments can be found in [26]. In paper [27] a non-linear continuum model for the analysis of masonry arches strengthened with FRP composites is presented. The proposed numerical models for one unstrengthened and one FRP-strengthened masonry arch were calibrated based on experimental tests. Also the FEM model was than used for theoretical research of strengthening of Prestwood bridge for which experimental data from a destructive test was available. Another innovative approaches for strengthening masonry arches used in experimental studies are FRCM (fibre reinforced cementitious matrix) or SFRM (steel fibre reinforced mortars) method. The advantage of these methods is that they can be easily applied in intrados the vaults while the bridge structure is in operation. The effectiveness of FRCM strengthening is examined in [28] and comparison between both is shown in [29]. Arch bridges have a rather significant load-bearing capacity for vertical loads. Research of the load-bearing capacity of these bridges to resist horizontal impact is presented in [30]. If reinforced concrete spandrel walls are used, post-tensioning represents a significantly safer method for robust capture of spandrel walls in comparison to other methods. Lower probability of realization errors and simultaneous active correction of the current condition of the structure are other advantages of post-tensioning. Horizontal transverse prestressing completely restores the existing structure of the arch bridge (after a previous injection of cracks). The cracks are being sealed and a general improvement of the condition of the load-bearing structure caused by the introduction of stress reserve occurs. In comparison to other methods, the robustness of this method lies in the fact that the tensile stress in the masonry of the original structure in the transverse direction can be completely eliminated. Passive methods such as FRCM, FRP and SFRM are surely appropriate under certain structural conditions, but if longitudinal cracks are already opening and degraded spandrel walls already lean out, the introduction of pressure force through newly built concrete spandrel walls with anchor areas for post-tensioning is virtually the only option for their conservation and complete restoration. 2. Causes of bridge arches damage Damage typical for these bridges is shown in Fig. 2. The arches are damaged by cracks in planes parallel to the road axis of (with the span plane), i.e. by longitudinal cracks. The width of these cracks can be up to several tens of mm and these longitudinal cracks then divide the arch into several separate arch strips. The bearing strength of such arches in the longitudinal direction determined on common calculation models tends to be high; the arches in the longitudinal direction have a sufficient load-carrying capacity to meet traffic requirements. Both the effect of elevated earth pressure on the spandrel walls and the spatial effect of the structure can be identified as a cause of the longitudinal cracks in the course of the survey of damaged structures. Fig. 1. Example of stone masonry arch bridge. Historical masonry arch bridges were designed in accordance with frame models and therefore, the entire transverse tension was neglected, respectively, these effects were considered negligible. Nevertheless, these structures have been serving for 100 or more years, and the transverse tensions are caused by the long-term effect of constant stress in which the centre of the arch is stressed by the embankment (other constant stress) more than the edges. In fact, the structure works as a shell system and the deflection line in the transverse direction is bulging downward. This means that transverse moments and transverse normal force, which cause tensile normal stresses in the transverse direction of the arches, occur within the structure. Therefore, around the centre of the structure, the cracks were predominantly caused by the spatial effect of the structure. Cracks observes in arch edges (approx. 0.5 m to 1.5 m from the outer edge) can also be supported by the long-term stress in addition to the spatial effect, the effects of earth pressure on the spandrel walls and by the effects of the temperature stresses. In the arch edges, the shell rigidity prevents free expansion of spandrel walls and that is how tensions are created even in these areas. The effect of the traffic is compounded with the aforementioned effects of constant stresses (the weight itself, other constant stresses, earth pressures), fatigue and climate stresses (especially those caused by the temperature). Computational options of today allow us to switch from the frame model to the spatial (shell) model, which, contrary to the original assumptions, manifests transverse tensions and transverse moments with tensions on the bottom strands which can be analysed in this way. The additionally inserted prestressing reinforcement is usually led affine to the deflection line of the transverse direction, which is very suitable. Increased earth pressure occurs especially in road arches, whose levels have been increased by continuous overlaying by up to 1,2 m (Fig. 3). The increase of the earth pressure is further supported by the increased axle pressures of current vehicles, which go directly to the edges of the bridge, and by the traffic intensity, which is several times higher than in the time of the bridge construction (see [31]). Increased earth pressure of the embankment above the arch gradually pushes away the spandrel walls, which damage outer edges of the arches with widths ranging from 0.8 to 1.5 m. In case of railway arches, overlaying of embankments or live load stresses near the arch edges do not occur, but they are often damaged by longitudinal cracks passing through the centre of the arches, not by the causes mentioned above. Instead, transverse thrusts and transverse bending moments resulting from the spatial effect of the arch causes these cracks, which can be illustrated by a spatial numerical shell or volume models (Fig. 17). Observations from service load testing indicate that the development of cracking and non-linearities under service loads can be a significant indicator of the capacity of the structure [32]. Engineering Structures 245 (2021) 112898 3 L. Klusáček et al. Fig. 2. Typical damage in arch bridges caused by longitudinal cracks. Fig. 3. Example of increased road level by asphalt overlay. Longitudinal cracks create natural crevices for penetration and permanent drainage of rainwater. Massive erosion of the embankment above the arch and behind the supports can often be recorded. The expansion of longitudinal cracks accelerates with time, mainly because of the effects of ice in flooded cracks in winter. Leaving the structure without repair leads to a collapse of edges of the arches and to necessary emergency measures, although their function in the longitudinal direction is unimpaired. It is clear that longitudinal cracks often eliminate even some arch bridges with sufficient load-bearing capacity out of service and that a reliable restoration of these cracks, i.e. strengthening the arches in the transverse direction, is desirable. The paper is focused on arch bridges with unaffected longitudinal direction. 3. Design of repair Transverse prestressing of the arches can be applied as a part of a structural system consisting of new spandrel walls and prestressing cables (Figs. 4–6) [33]. Connection of these two features is beneficial, because in the new reinforced concrete spandrel walls, the cables can be anchored in a proven way and an almost uniform distribution of forces in the anchors to the arch masonry can be achieved. Stability of the new walls is ensured by the forces in the anchors, by the wall stiffness of the abutments and by the spatial stiffness of the already reinforced arch. In this use case, the new reinforced concrete spandrel walls fulfil 3 possible roles: Fig. 4. Arch bridge with a new spandrel wall. Fig. 5. Transverse post-tensioning arrangement. 1. They provide restoration and stability for the original crumbling spandrel walls. 2. They allow anchoring of transverse prestressing, which can thus be designed in compliance with procedures according to technical standards. 3. If necessary, they also allow expansion of the operational space, which is often very desirable in case of historical roadway arches. In new reinforced concrete walls, cantilever structures for walkways or even for expansion for sake of transferred roadway can easily be constructed. The principle of the design is based on the approach of considering the anchors as elastic supports and on the design of the prestressing forces, which must include appropriate safety margins and still exceed the active effects of reactions in supports in the numerical model. In the aforementioned applications, the forces in anchors are designed using a slab model (or a shell one), which is supported with elastic supports in the expected anchoring locations of the additional prestressing reinforcement. The model is under constant stress, earth pressure of the embankment and the added stress caused by traffic is being taken into consideration. The strengths of the support reactions on the aforementioned design model then state the necessary sizes of prestressing forces in the given locations. The actual prestressing force is then derived from these reactions while allowing for safety coefficients and prestressing changes. The forces in the anchors form an equilibrious system in the horizontal direction. Transverse prestressing system uses available common construction details and procedures of the substitute cable duct method. In addition to the stability of the spandrel walls, it is necessary to check the maximum amount of prestressing in the arch wall and the abutments, which act in parallel to the bed joint of the masonry. New walls can be designed as relatively thin reinforced concrete walls, but the predominant stress is of a slab type. Their weight during construction is transferred by small flat foundations (individual or continuous footings). After prestressing using the masonry arch, the stress is gradually redistributed, and their weight is transferred by the foundations of the original bridge supports. Shape of the spandrel walls can be easily adapted to the obstacle (cross draining canal, etc.). A great advantage of this construction system lies in the easy expansion of the Engineering Structures 245 (2021) 112898 4 L. Klusáček et al. Fig. 6. Arch with newly reinforced spandrel walls and prestressing cables — perspective model. Fig. 7. Example of the reconstruction — masonry arch road bridge in Semtín (the Czech Republic). roadway on the bridge, eventually in a construction of pavements by means of massive cantilevers that can easily be placed on both sides of the spandrel walls. Figs. 7,8,24,27 and 43 show examples of completed reconstructions of arched bridges on roads. Mechanical compatibility of the additional system is based on a correct solution to anchor areas in new concrete spandrel walls (standard proposal). In addition, it is based on such an amount of transverse prestressing, which usually represents a 0.2–0.3 multiple of the strength of the masonry in tension perpendicularly to the bed joint, which is a very safe limitation (verified by realizations). Compatibility of the original structure with the additionally applied system is also based on the transfer of radial forces from deviators through the arch strength. In terms of materials, the compatibility is based on an injection of all cracks in the masonry so that parasite movements, which could damage the arch structure, were eliminated. Through the application of prestressing, tensile stresses, which are the only ones which damage the arch masonry, are eliminated. Transversally led prestressing cables are protected against corrosion, because cables of the monostrand type are used as well as the closed system including the ‘‘encapsulated’’ anchors. Edge local pressures, which damage the monostrand sheath, are eliminated by the use of deviators with the suitable radius of curvature. 3.1. Design of spandrel walls and prestressing forces Magnitude of the overstraining forces is connected to the stability of the spandrel walls. The new spandrel walls are stabilized by the Fig. 8. Example of the reconstruction — stone masonry arch road bridge in Ransko (the Czech Republic). Fig. 9. Locations of prestressing forces. forces in the anchors that push them to the original walls, eventually to the arch itself. These forces can be examined as forces in the intended supports, which are the anchors on the actual structure. Supports must be modelled as nonlinear (only pressure) in order to properly simulate leaning of the wall against the arch and not to hinder its deformation in the direction away from the arch. The forces in the anchors must be designed to be larger than the support reactions examined. In standard cases, the new spandrel walls can be examined as slabs subjected to the earth pressure of the road body and embankment, supported in the Engineering Structures 245 (2021) 112898 5 L. Klusáček et al. Fig. 10. Loads on spandrel wall. very anchor sites and on the foundation level (Figs. 9 and 10). The earth pressure must be increased by the effect of the live load. The earth pressure pattern is then trapezoidal and increases linearly with depth. For safety purposes, the stiffness of the original spandrel walls is neglected. Because of the variable shape of the spandrel walls and the increasing load with the depth of the embankment, it is recommended to model the spandrel walls using the Finite Element Method (FEM) and to choose a slab element which considers the shear effect as the basic element. On this model, the support reactions and internal forces (moments) for the reinforcement design are determined. The model can also be used to verify deformations of new spandrel walls (Fig. 17). It can be recommended that the deformation of the spandrel wall end does not horizontally exceed the value 𝑤ℎ=𝑙𝑠 350 (1) where 𝑙𝑠is the span of a substitute horizontal cantilever with a rigid support in the arch axis. The intensity of the transverse prestressing in the cross-section of the arch can be assessed in the same way as masonry structures. In typical cases, 20% of the calculated compressive strength of the masonry should not exceed perpendicular to the loading area. The intensity of the transverse prestressing in the arch can be easily determined in the same manner as in a cross-section: the area of the resisting crosssection is the area of the longitudinal cross-section of the arch and the abutments, the acting force is the resultant force from all the anchors, and the point of action is the centre of gravity of all anchors. More specifically, the intensity of the prestressing force can once again be determined on the shell arch model using FEM programs that model the arch including the new spandrel walls. 3.2. Construction solution When reinforcing the structures with additional prestressing, it is necessary to apply the appropriate construction details so that all conditions for reliable operation of both the original reinforced structure and the additionally attached overstraining system are maintained. This can be achieved with a proper design and performance of construction details. Without proper details, neither can the effect of additional reinforcing in accordance with theoretical assumptions be ensured, nor can the long-term reliability of the applied prestressing be guaranteed [34]. 3.2.1. Substitute cable ducts Prestressing cables (mostly single-strand cables; sometimes multistrand cables) are arranged in a polygonal trajectory. Substitute cable ducts form a part of the trajectory, and the central part of the trajectory is guided in carved slots on the obverse side of the arch (Fig. 11). This solution significantly improves the productivity of the preparatory Fig. 11. Slots on the obverse side of the arch. Fig. 12. Anchorage area in new monolithic reinforced spandrel walls. works by reducing drilling lengths. Ducts can be drilled using an impact or a diamond drilling. Drilling with a diamond drill is used for multirope cables without exception. Radial forces at the deviator location do not endanger the masonry of the arch because the radial forces are small when duct slopes are used with 𝛼= 5◦to 8◦. The cables are arranged approximately uniformly over radial planes of the arch in distances ranging from 600 to 1200 mm. Theoretically, the entire length of the cable can be stored in a cable duct alternately created by diamond drilling at the level of the centre of gravity of the arch cross-section, but this is not economically advantageous or statically necessary. 3.2.2. Deviators The design of the prestressing system must also include the design of the deviators, indicating all the parameters necessary for the design and construction of the deviator [35]. Diamond drilling is required to make the flanging surfaces of the grooves and deviators, especially because of the gentle approach to the arch masonry. Investigation of ultimate strength of curved strand tendons is also presented in [36]. 3.2.3. Anchors New monolithic reinforced concrete spandrel walls also perform the function as anchorage areas. Reinforcement of anchoring areas can then be designed and realized according to the rules commonly applied in Engineering Structures 245 (2021) 112898 6 L. Klusáček et al. Fig. 13. Newly made reinforced concrete spandrel wall. case of prestressed concrete. Bridge arches are structures exposed to environments with increased aggressiveness, so it is essential to use encapsulated anchor systems. Anchors of the individual strands are distributed in the pass of the spandrel wall. For this purpose, anchoring weldments are used, which provide anchor positions during pouring of concrete or grouting and distribute forces from the anchors into the concrete of the spandrel wall (Fig. 12). 3.2.4. Monolithic walls The structural design of the reinforcement of the arches by transverse prestressing relies on the newly made reinforced concrete spandrel walls, which, in addition to reinforcing themselves, also restore the original stone spandrel walls (Fig. 13). Thus, the thickness of the new wall fluctuates, and therefore, filling of possible caverns and fixing of loose blocks of the original masonry will occur. The original brick spandrel walls form a leave-in-place formwork. New spandrel walls may be relatively thin (400 to 600 mm); their stability is ensured by the resultant forces of the prestressing cables in the anchors. A thickness of at least 500 mm is recommended because of the one-sided approach for mounting of the reinforcement. 3.2.5. Possibilities of bridge widening By utilizing the overhang of the cantilevers, the existing arch can be advantageously widened in accordance with the requirements of the reconstruction. The cantilevers can be designed as massive, preferably with haunches, which is aesthetically pleasing with regard to the massiveness of the original arch structure (Figs. 4,5and 14). As a result, the arches can be expanded by up to 2.5 m on each side of the bridge. 3.2.6. Prestressing reinforcement For transverse prestressing, cables distributed every 1.2 to 1.5 m along the perimeter of the arch can be used; static analysis of the structure provides the number of strands necessary. It is usually possible to use three-rope or four-rope cables made up of monostrands (Figs. 4– 6). The use of protected reinforcement (monostrands) is a requirement because of the ambient aggressiveness and humidity. Absence of coherence between the original masonry and the prestressing cables does not cause any difficulties since the elastic deformations of the arch and the abutments in the transverse direction caused by the live load are completely negligible. The used prestressing levels are low and the analysed prestressing losses (verified with an experimental measuring) are under 15%. Fig. 14. The existing arch can be advantageously expanded. 3.2.7. Crack injection Cracks must be filled before the overstraining force is introduced (Figs. 15 and 16). The formation of cracks has occurred over a long period of time and with a contribution of the masonry creeping. Therefore, they cannot be closed by prestressing, as this would lead to undesirable displacements of the separated parts of the arch and the supports, as well as to an emergence of new cracks. By filling the cracks, all unwanted movements and shifts during prestressing are minimized, and with a slight horizontal pressure tension, restoration of the monolithic character and integrity of the damaged masonry will be ensured. Injection of cracks with width above 0.5 mm is usually performed with a cemented activated injection mixture. Smaller cracks virtually cannot be injected. Alternatively, injection of non-foamy polyurethane resin (tensile strength in a bend over 100 MPa) can be used. 3.3. Material characteristics The reinforcement of the arches using the aforementioned structural system is necessarily dependent on the characteristics of the used material. The main condition is the sufficient quality of the arch masonry as it determines the further service life of the reinforced bridge and for the transfer of the transverse pressures from the prestressing. The characteristics of the used material must be determined with a detailed construction diagnostics. Examples of non-destructive masonry testing are presented in [37]. Diagnostics are the necessary input for reconstruction design. Within the diagnostics, a general knowledge of cracks (mapping of the entire structure) and their development must be achieved. This information is necessary for a compilation of a defect mechanism, whose knowledge is the key for the actual restoration design. Information of the material characteristics of the individual building materials, mortar and the actual masonry in accordance with the usual procedures based on procedures according to technical standards (‘‘eurocodes’’) are another necessary output of the diagnostic research. The diagnostic Engineering Structures 245 (2021) 112898 7 L. Klusáček et al. Fig. 15. Grouting of cracks. Fig. 16. Grouted area in the back side of the arch bridge. research usually also includes some drilling for probes for the purpose of determination of otherwise inaccessible dimensions (dimensions of supports, height of arch cross section, thickness of the original spandrel walls). Examples of material characteristics of strengthened bridges obtained by diagnostic surveys are given in Table 1. Unlike concrete, masonry is an anisotropic material, i.e. a material whose properties vary in different directions. Sometimes it is referred to as orthotropic, i.e. a material whose properties are different in two perpendicular directions. For masonry, it is usually vital to test its mechanical properties in two main, mutually perpendicular directions, respectively perpendicularly to the bed joints of the masonry (usually in the vertical direction) and parallel to them (usually in the horizontal direction). Basic deformation properties of masonry include the modulus of elasticity and the creep coefficient. The structure diagnosis before the design of repair must identify the following data: •The quality of the arch masonry in terms of its long-term use: The arch bridges are made of stone or brick masonry. Stone masonry uses granite, gneiss, limestone, slate and sandstone; brick masonry most often used burnt full bricks with increased resistance to water absorption and frost breakdown. It is precisely the resistance to damage caused by frost breakdown that is the decisive condition for a further use of the arch structure and for strengthening of the arches at all. Masonry consisting of bricks from igneous and metamorphic rocks; sediment rocks are suitable conditionally. The masonry can also be formed from sandstone or greywacke, which are completely unaffected by frost even in the conditions of several years of leakage into the masonry arch from the roadway. In contrast, some less cohesive sandstones can be damaged by breakdown by frost action to a depth of 80 mm or more. Similarly, brick masonry is generally highly absorbent and thus poorly resistant. Frost breakdown occurs as a result of road leakage. The original insulation of the bridge arches was made of layers of compacted clay. After more than 100 years, these layers are already washed out and do not fulfil the insulation function any more. A new waterproofing layer is established as a part of the reconstruction by transverse prestressing; therefore, the issue of further leakage is not important at the moment of and shortly after the reconstruction. Therefore, we can summarize that arches from stone masonry (granite, gneiss, limestone, sandstone) are suitable for strengthening and widening of arches; the condition of mortar is often not a crucial factor. Brick masonry arches are conditionally appropriate because they almost always require roadway excavation and implementation of waterproofing. •The strength of the masonry supporting structure of the arch: the classification of the bricks and the mortar has to be performed according to the standards and using in situ strength measurements. The strength of the bricks can be determined by a non-destructive rebound method or by taking samples for pressure testing in a press. Mostly, just the non-destructive method is sufficient because the variation in the strength of the building material leads to minimum differences in the resulting design strength of the masonry. In order to determine the strength of the masonry, we have to determine the strength of the mortar, for example by using a modified drill-based testing. From the acquired strengths of the bricks and the mortar, the design strength of the masonry is determined. The strength of the masonry tension is usually defined vertically to the bed joint. In the parallel direction to the bed joint, the tension is very small, hard to measure or not defined at all. In periodically stressed masonry structures or structures stressed for a long period of time, the tensile strength in the direction parallel to the bed joint is almost zero. •The thickness of the roadway and all layers above the arch, including the precise determination of the arch thickness: Layer size determination should be done by drilling trial pits into the road using diamond cutting technology or by bore holes. Moreover, it is necessary to drill a bore hole through the arch to determine the arch thickness. Determination of the actual dimension of the arch is necessary because the thickness of the arch inside the structure may not be identical to the arch depicted on the original spandrel wall. •Defects and failures of the bridge arch before reinforcement and reconstruction: These include determining the extent and source of leaking into the arch. These are the default data for the final design of water-proofing of the reverse side of the arch. 3.4. Numerical model In order to verify the arch behaviour and repair design, the ideal approach is to perform a three-dimensional (3D) discrete analysis using the finite elements method with nonlinear material behaviour. Such analysis will allow calculation of limit states and determination of failure mechanisms, but it is very demanding in terms of input parameters — construction geometry, masonry properties, backfill soil properties and contact element parameters [38–40]. Creation of a three-dimensional spatial model consisting of planar and beam elements is sufficient for use in practice (Fig. 17 — arch bridge in Rybná nad Zdobnicí). This sample numerical model was created from 302 Engineering Structures 245 (2021) 112898 8 L. Klusáček et al. Table 1 Material characteristics of strengthened arch bridges after diagnostic surveys. Material characteristics Location of the arch bridge Semtín Ransko Brno-Špitálka Rybná nad Zdobnicí Compressive strength of building material 𝑓𝑢25 MPa (burnt clay b.) 120 MPa (granite b.) 25 MPa (burnt clay b.) 60 MPa (sandstone b.) Compressive strength of mortar 𝑓𝑚1.2 MPa (lime m.) 0.4 MPa (lime m.) 1.4 MPa (lime m.) 1.2 MPa (lime m.) Compressive strength of masonry 𝑓𝑘3.6 MPa 6.2 MPa 3.8 MPa 5.2 MPa Secant modulus of elasticity (short-term) 𝐸3.6 GPa 6.2 GPa 3.8 GPa 5.2 GPa Fig. 17. Shell model deformation caused by static load (arch bridge in Rybná nad Zdobnicí). beam elements, 6716 shell elements and a total of 7202 nodes. The basic element size was chosen to be 0.3 m. Examples of material properties used in shell model of arch bridge in Rybná nad Zdobnicí are shown in Table 2, where 𝐸is modulus of elasticity, 𝐺is modulus of shear, 𝜈is the Poisson’s ratio, 𝛾is density and 𝛼is thermal expansion coefficient. Materials can be entered as isotropic, elastic and linear into this model. In case of homogenized masonry, it is necessary to check the tensile stress so that no tensile bearing strength is exceeded in any direction (the usual value is 0.05–0.1 MPa). There is a parallel contact between the existing stone spandrel wall and the new reinforced concrete, in which the transmission of forces is expected because of the applied prestressing and the friction between the surfaces. It is advisable to create a simplified slab model to design the thickness of the spandrel walls and prestressing cables (see Section 3.1). The prestressing cables are modelled using beam elements. Prestressing is introduced into the structure through anchors in new reinforced concrete walls and builtin deviators. In the case of deviators, it is necessary to check to avoid local contact breaking of the masonry. In this model, it is also necessary to capture the behaviour of the surrounding backfill, which affects the load distribution on the masonry arch and the boundary conditions of the model, i.e. supports. Generally, the soil exhibits a softer response to the load than the arch. Therefore, if the maximum load on the masonry arch is not exhausted, the surrounding soil has minimum effect on the model. If the tensile load-bearing capacity is exceeded, a Fig. 19. Cracks between spandrel wall (blocks) and masonry caused by buckling. mechanism is created, and the arch interacts with the surrounding soil. In these cases, it is not enough to model only the corresponding stiffness of the foundation, but you also have to model a complete elastic– plastic backfill. For these needs, it is necessary to provide a detailed hydrogeological survey to determine all the necessary parameters for the numerical model. The model is supported by nonlinear supports with adequate stiffnesses, which are ineffective in tension. The inability of the masonry arch to resist tensile stresses was simulated by inserting linear joints and thus the non-linear behaviour of the historical masonry of the bridge arches was substituted. Tensile stresses are completely eliminated by the transverse prestressing and at the same time, compressure intentionally induced by prestressing is designed at low levels with regard to the masonry strength. Therefore, use of elastically linear model complies completely with the resulting behaviour of the structure. This basic presumption of structures reinforced in this way was verified by the measuring. Fig. 18. Road bridge in Semtín, reconstruction by post-tensioning. Engineering Structures 245 (2021) 112898 9 L. Klusáček et al. Table 2 Examples of material properties used in numerical shell model of arch bridge in Rybná nad Zdobnicí (Fig. 17). Type of material Material properties E [GPa] G [GPa] 𝜈[–] 𝛾[kN/m3]𝛼[1∕◦C] Masonry (sandstone, lime mortar) 15 5.7 0.3 24.0 9.0E06 Reinforced concrete (C30/37) 33 13.7 0.2 25.0 1.0E05 Prestressing tendon (Y1860-S7-15.7) 195 75.0 0.3 78.5 1.0E05 Fig. 20. Measuring of horizontal strain during post-tensioning. 4. Deformation of arch masonry during prestressing An important question is how does the masonry of the original arch and the masonry of supports react to the horizontal prestressing, i.e. parallel to the bed joint of the bricks. It is necessary to know the masonry strain for a correct estimation of prestressing losses. Because of the low prestressing levels (up to 20% of masonry strength, 0.1 to 0.3 MPa in practice), the strain can be expected to not be large and rather similar to the strain in case of a stress applied in a perpendicular direction upon the loading surface. The interaction of the adjacent embankments and backfills behind the arch or support is also unknown as well as the interaction of the base of foundation. The authors of the article are probably the first to conduct a shortterm measurement of a deformation response to horizontal prestressing of bridge arches. The obtained results are presented for two cases of strengthening of the arch bridge. 4.1. Bridge arch in the city of Semtín The bridge consists of a cylindrical arch with a centre line in the shape of a circular segment of brick masonry with a thickness of 450 mm. Sandstone blocks form the support of arch masonry on each side of the bridge span. The original spandrel walls and supports were made of stone masonry. The original mortar is lime, partly washed out, of the 0.2 to 0.4 MPa strength class. The arch span is 4.5 m, the arch width is 10 m, and the length of the newly made spandrel walls is 18.4 m. Schematic sections of the structure are shown in Fig. 18. The basic reason for the reconstruction was the leaning out of both spandrel walls of the bridge and ledges, followed by the formation of longitudinal cracks between the arch and spandrel walls with a width of 20–30 mm on the downstream side of the bridge (Fig. 19) and around 10 mm wide on the upstream side. In accordance with the nature of the defects mentioned above, the reinforcement of the arch was designed in such way so that new reinforced concrete walls Fig. 21. Relative strain of arch masonry during horizontal prestressing. Fig. 22. Road bridge in Ransko, reconstruction by post-tensioning. Engineering Structures 245 (2021) 112898 16 L. Klusáček et al. Fig. 40. Relative strains at the top of the arch during crossing on track no. 2 (before and after strengthening). Fig. 41. Relative strains at the top of the arch during crossing on track no. 1 (before and after strengthening). minimum of −174.10 μm/m to −68.36 μm/m on the reverse side and from the measured minimum of −34.68 μm/m to −10.59 μm/m on the obverse side. The increase of the arch stiffness in the transverse direction before and after the restoration can be stated proportionally as 2.55:1 for the reverse side of the arch and as 3.27:1 for the obverse side of the arch. Generally, it can be stated that the stiffness of the arch in place of track no. 2 above the mounted MA1 increased approximately three times. Similarly to the track no. 1 above the mounted MA2, when the train was crossing on the track no. 2, the strain almost did not change on the obverse side of the arch (tensile forces were created), and on the reverse side of the arch, the strain decreased from the measured minimum −86.31 μm/m to −30.19 μm/m, i.e. in the ratio of 2.86:1. Crossings on track no. 1 — MA2 (Fig. 41) On the basis of the measured values, it is clear that when crossing track no. 1 above the mounted mechanical amplifier MA2, the arch in the place of the mounted MA1 was pushed on the reverse side and pulled on the obverse side before and after the restoration. After strengthening, the relative strain was reduced from the measured minimum of −28.59 μm/m to −12.33 μm/m on the reverse side of the arch. The relative strain on the obverse side of the arch decreased from the measured maximum of 10.94 μm/m to 3.15 μm/m. The increase of the arch stiffness in the transverse direction before and after the restoration can be proportionally stated as 2.32:1 for the reverse side of the arch and as 3.47:1 for the obverse side of the arch. In general, it can be stated that the stiffness of the arch in the place of mounted MA1 was increased approximately three times. In the case of track no. 1 above the mounted MA2, the strain was reduced while crossing on track 1 from the measured maximum of 51.61 μm/m to 10.51 μm/m of the arch obverse side, i.e. in the ratio of 4.91:1. On the reverse side of the arch, the relative strain was reduced from the measured minimum of −430.57 μm/m to −89.53 μm/m, i.e. in the ratio of 4.81:1. The performed measurement confirmed the high efficiency of the restoration by introducing the prestressing into the bridge arch. By introducing the prestressing in the transverse direction, the stiffness has been proven to increase, and the separated parts of the bridge arch once again act as a single unit — continuously and mutually dependent. Fig. 42. Arch bridge in Rybná nad Zdobnicí — before reconstruction. Fig. 43. Reinforced arch bridge in Rybná nad Zdobnicí with new spandrel walls. The restoration has significantly reduced the strain at the top of the arch during crossing of trains to about 1/2 to 1/5, which results in an prolonged service life of the structure. 6. The effect of temperature upon measuring During the measurement, there are deviations from the theoretical assumptions in the record. These deviations range from units of hto units of %. The rotation of the mechanical amplifiers, changes of the ambient temperature, the vibrations caused by the technical seismicity, and the human factor, to name a few, are among the most critical factors influencing the accuracy of the measured data. The compensation of the influence of temperature changes during the measurement can be shown in the behaviour of the bridge arch in the city of Rybná nad Zdobnicí, Czech Republic [42]. The main reason for the reconstruction of the bridge arch was the leaning out of both the spandrel walls by up to 180 mm, followed by a disintegration of the masonry and falling out of the stone blocks. The stability of both spandrel walls was disrupted, and the stability of the entire structure was endangered. The bridge arch was also disrupted by longitudinal cracks of a thickness from 2 to 5 mm, which divided the arch into self-acting sections. Engineering Structures 245 (2021) 112898 17 L. Klusáček et al. Fig. 44. The mechanical amplifiers were installed at two places on the arch. Fig. 45. Mechanical amplifier installed at the top of the arch. Fig. 46. A fully loaded truck was used as a burden for static and dynamic measurements. 6.1. Description of measured bridge, performed measurements and tests The supporting structure of the bridge consists of an original stone arch with a clear span of 5.7 m and a clear camber of 2.85 m (Fig. 42). The height of the arch base above the reinforced bank of the stream is 3.2 m, and the height of the arch top above the stream is 7.43 m. The arch thickness is approximately 0.65 m. The new spandrel walls are 0.6 m thick and are made of C- / 28 concrete and reinforcing steel 10505 (R). The reconstruction also included an increase in the free width to 12.0 m using suitably shaped spandrel walls and ledge linings Fig. 47. Relative strain on the outer fibres of the arch without filtering out the temperature. Fig. 48. Development of surrounding temperature in the course of the measurement. on which sidewalks are placed (Fig. 43). Replacement cable ducts with a diameter of 52 mm were placed into the original stone arch to accommodate the prestressing cables. These were created by precision drilling with diamond core drills and diamond cutting machines. The deviators were designed from strip steel with a radius of R = 2.0 m. All the cracks in the arch and supports had been filled with grout before the monostrands were stretched. Also, a sealing injection of 0.5 ×0.5 m grid was carried out, which, to date, continues to prevent water flowing into the supporting structure. The measurement of the arch was designed so that was possible to find out the synergy of the arch in the transverse direction and at the same time to refine the calculation model for static analysis and evaluation of results. Measurements using the previously described mechanical amplifiers were performed at two locations of the arch. The first location was in the middle of the arch width; the second location was in the 1/4 of the stone arch width (Figs. 44 and 45). The arch deflection was also measured in the middle of the arch width to verify the arch behaviour. In several locations around the structure and near the arch and sensors, temperature was measured so that the 41 effects of the temperature could be compensated for. Both static and dynamic load measurements were performed on the structure. A fully loaded Liaz 150 truck was used as a burden (Fig. 46). Total vehicle weight was 18.14 tons (rear axle 11.6 tons; front axle 6.54 tons). In the static load test, the vehicle was placed in the right lane twice, in the middle of the road twice, and in the left lane once. The rear axle has always been positioned above the centre of the arch span. Dynamic measurements during crossings were performed twice at 30 km/h in the right lane and twice in the middle of the road. Engineering Structures 245 (2021) 112898 18 L. Klusáček et al. Fig. 49. Relative strain after filtering out of the effects of volume changes of the arch caused by temperature. Fig. 50. Relative strain during axle test no. 3 — vehicle in the middle of the road above MA1. 6.2. Measurement evaluation Correcting the record for the effects of temperature change can be divided into two basic groups. During the measurement, because of temperature fluctuations, the measuring device is influenced, but also the masonry structure itself is subject to volume changes because of thermal inertia. In Fig. 47, it is possible to see the relative strain on the outer fibres of the bridge arch without filtering out the volume changes of the masonry bridge arch. The red and blue colours show the results from mechanical amplifier no. 1 in the centre of the span and the green and orange colours show the results from mechanical amplifier no. 2 in the 1/4 of the stone arch width. It is also possible to easily identify individual static front axle tests and dynamic test load crossings from the figure. Positive strains of the cross-section between the individual front axle tests (after removal of the load) were measured without filtering out of the volume changes of the masonry arch. These tensile strains are caused by varying temperature. In our case, during the measurement, the ambient environment was cooled down (Fig. 48), which led to volume changes of the masonry arch. Moreover, because the mechanical amplifiers are mounted on the outer surface, positive strains are immediately recorded. The actual strain of the arch farther from the surface will be different because of the temperature inertia of the massive cross-section. Therefore, the measured values have been adjusted to compensate for this temperature effect. Cooling of the ambient environment causes the pressure reserve to be pumped out in the top of the arch and has an almost affine course to temperature development. After filtering out the effects of volume changes of the arch caused by temperature (Fig. 49), the values of the strains in the upper and Fig. 51. Deflection during the dynamic crossings. lower fibres are as expected — positive strains (elongation) on the surface and negative strains (shortening) on the reverse side of the arch. The measured values on both surfaces are almost identical in absolute values (Fig. 50) — inaccuracies are caused by the variable arch thickness and the contribution of the surrounding embankment, which shifts the cross-sectional centre of gravity further from the outer surface of the arch. Fig. 50 shows the measured values from the front axle test no. 3 when the vehicle stops in the middle of the arch (Fig. 46). During the front axle test, locally elevated cross-sectional strain values caused by the regular traffic can be seen; the traffic could not be eliminated during the measurement, only limited and slowed down to the left outer lane of the road. During the dynamic crossings at a speed of 30 km/h, it was possible to measure strain and deflection from the individual axles of the vehicle used as a burden. Fig. 51 illustrates the deflections in the middle of the bridge arch in all four crossings. First, there is approximately half the deflection from the lighter front axle and then the deflection increases because of the heavier rear axle. After crossing of the vehicle, the measured values return to zero, so there is no permanent deformation of the arch. 7. Conclusion The described method of strengthening and widening of a masonry bridge arch using thin reinforced concrete spandrel walls stabilized by transverse prestressing cables has several advantages. It is simultaneously simple, durable and effective. It can be carried out with traffic limited to a single lane through the centre of the bridge in case of road arches, or with traffic limited to only one track in case of railway arches. The restoration with only a partial limitation of traffic is welcomed by both bridge managers and investors. On average, the costs of reconstruction represent 40% of the price of the new bridge. If the quality of the masonry is satisfactory (stone masonry is almost always satisfactory, brick masonry is conditional on quality), it can always be recommended. The authors of the paper prove the reliability and longterm lifetime of this method with practical realizations, and the oldest application has been in operation without any defects for more than 15 years. The described structural system is also advantageous because there is no need to demolish any part of the existing structure in the course of the application of the new system. The original spandrel walls become a permanent shuttering for new reinforced concrete spandrel walls, which will cover the original ones (including their defects) thus automatically causing a restorative effect of the additional structure. Engineering Structures 245 (2021) 112898 19 L. Klusáček et al. The strain of the arch during the prestressing process, which has been verified experimentally, manifests very small to negligible prestressing losses and the predictability of the static calculations used. By using a larger number of mechanical amplifiers across the arch, it is possible to study in more detail the synergy of the parts of the arch arc separated by cracks. The monolithic character of the arch has been achieved by the additional lateral prestressing. The described methodology can be used for complex monitoring of the behaviour of the whole structure, evaluating its damage and refining the computational model according to the current state of the damaged structure. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 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