Rebar-reinforced coarse aggregate ultra-high-performance concrete (R-CA-UHPC) has been used in the construction of new structures and strengthening of deteriorated aged infrastructures, and it inevitably sustains tension. To study the tensile behavior of R-CA-UHPC members, axial tensile tests for dog-bone-shaped specimens were designed and conducted. The investigated variables included reinforcement ratio in terms of rebar quantity/diameter, and concrete type (CA-UHPC vs. normal concrete). The test results showed that the improved rebar/CA-UHPC bond property prevents the emergence of splitting cracks, but intensifies the crack localization for CA-UHPC and strain concentration for rebar after yielding. Moreover, the restrained effect of rebar on free shrinkage of CA-UHPC leads to a decrease in the first cracking strength for R-CA-UHPC members. Based on the established development functions of elastic modulus, autogenous shrinkage, and tensile creep for CA-UHPC, the restrained effect was quantified according to Dischinger's-differential-equation-based theoretical analysis. Finally, the models to predict the first cracking stresses/strains and the yielding loads of the R-CA-UHPC members were developed and validated.@en

Corrosion and shear cracking are frequently observed near supports of pretensioned bridge girders in coastal climates, so non-linear finite element analysis was used to study the effect of corrosion on shear performance in a real case study. Varying degrees of corrosion and various locations (top strands, bottom strands, vertical stirrups and girder-slab interface) were considered. The analyses included construction phases, concrete creep and shrinkage, and the effects of corrosion on the properties of prestressing and reinforcing steel, concrete, and the bond between concrete and reinforcement. The study shows that high (20%) corrosion in the bottom layer of strands can modify the failure mode from concrete crushing in the web to strand slippage or crushing of concrete in the support zone with limited cracking. Although severe strand corrosion significantly compromises girder capacity and ductility, failure occurs only when there is overloading. The predicted failure mode was also sensitive to material parameters, in particular the corrosion-induced crack widths used for modelling the reduced concrete strength. Nevertheless, some similarities were noticed between observed and predicted cracking occurrence. For moderate corrosion (10%), girder capacity was limited by strand fracture, but extensive flexure and shear cracking would appear before failure. 20% corrosion in the vertical stirrups in the web seems to have potentially smaller effect on the shear capacity than 20% corrosion in the strands in support, while corrosion in the top strands or stirrups in the girder-slab interface did not affect the girder capacity.

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This study investigated the effect of fire on the ultimate load-bearing capacity of reinforced concrete (RC) slabs. The structural response of RC circular specimens subjected to static load conditions after exposure to a hydrocarbon fire on one side of the specimen was examined. Two fire exposure times were considered (60 and 120 min) in addition to reference non-exposed specimens. The static response was evaluated in the damaged specimens in residual conditions after natural cooling from the elevated temperatures. The temperature distribution across the thickness of the slabs and their load–displacement response was measured. The decrease in the stiffness of the slabs due to the thermal exposure was studied by means of direct ultrasonic pulse velocity (UPV) measurements made before and after the fire tests. The decrease in global stiffness was partially accounted for by UPV measurements. The experimental results showed two peaks in the load-deflection response of the slabs. The first peak was related to an arching mechanism introduced by the specific set-up used. The second peak, corresponding to the ultimate load, occurred due to tensile membrane action at large deflections. While the former was strongly affected by the fire exposure, with the load being halved after the 120-min exposure, the latter was not greatly affected by either the presence of fire or the exposure time. Simplified mechanical models were used to explain the behavior of the RC slabs during the tests.

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Alkali–silica reaction (ASR) in concrete causes expansion and degradation of the material, which might give adverse structural consequences. From the structural engineer point view, the greatest concern is if ASR leads to loss of structural integrity. Two natural questions arise when assessing existing concrete structures affected by ASR: (1) how to calculate the ASR-induced stresses, and (2), when the ASR-induced stresses are calculated, what is the residual capacity when accounting for the material deterioration caused by ASR? This study aimed to contribute in answering the first question. The ASR-induced stresses can be calculated in a structural analysis that includes a concrete material model that incorporates the effects of ASR on the material behaviour, i.e. expansion and material deterioration. Many such models exist. However, these models rely on predefined field variables, e.g. moisture and temperature, which are (generally speaking) unknowns for an existing structure. Consequently, structural analysis of ASR-affected concrete structures involves dealing with unknown field variables. From this background, we developed a material model and a suitable structural analysis method. The material model relies on only one predefined, howbeit unknown, field variable —the free ASR expansion. The structural analysis method is based on solving an inverse problem, which is to back-calculate the free ASR expansion field from a set of measured displacements. The material model and the structural analysis method were applied in a structural analysis of an ordinary reinforced beam bridge in Norway. Then, the imposed deformations and stresses due to ASR were investigated to increase the understanding of the structural consequences of ASR in ordinary reinforced continuous beam bridges.

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Advanced numerical modeling of high-strength concrete (fc>60 MPa) structures designed to withstand severe thermal conditions requires detailed and reliable information on the mechanical properties of the material exposed to elevated temperatures. The only uniaxial compressive strength variation with temperature is not enough to satisfy the large number of parameters often required by advanced nonlinear constitutive models. For this reason, a complete experimental investigation is required. The paper takes a commonly used high-strength concrete (fc=73 MPa) as an example to describe a comprehensive experimental approach instrumental to the parameter definition and calibration of common constitutive models for concrete. The present study not only studied the overall compressive and tensile behavior of the case study material, but also investigated the effect of elevated temperatures on the specific fracture energy and the evolution of internal damage, in residual conditions after a single thermal cycle at 200°C, 400°C, and 600°C.

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Material modelling, from the micro to the macro level, of concrete affected by alkali–silica reaction (ASR) has been devoted a lot of research. However, the application of the material models in structural analyses of reinforced concrete (RC) structures, showing the structural implications/consequences of ASR, has got little attention in the literature. This paper aims to show the relevance of the constitutive model on the calculated load effects—induced by ASR—in statically indeterminate beam structures. For the purpose of the study, a three-span RC beam, inspired by a real bridge in Norway, is analysed. The RC beam is modelled using Euler–Bernoulli beam theory, and numerical solutions are obtained with the finite element method. The effects of ASR on the concrete are accounted for in an expansion based (macro) constitutive model, which also accounts for cracking, creep and compressive non-linearity. In this way, ASR gives an imposed deformation similar to thermal dilation and shrinkage, for which structural effects have been widely studied. As imposed strain gradients tend to cause higher load effects than uniform strains, the effect of ASR gradients, owing to e.g. a moisture gradient, is addressed. It is shown that linear structural analyses (using a linear material model), give conservative results (the greatest load effects) when an ASR strain gradient is imposed. Among the non-linear material effects investigated, it is shown that stress dependent ASR expansion and concrete cracking are important to consider. The stress dependency of the ASR expansion is shown to have a smoothing effect on the imposed ASR strain field, and as a result, reduces the load effects induced by ASR, while cracking results in crack/plastic hinges releasing the stresses in the system.@en

Reinforced concrete (RC) submerged floating tunnels (SFTs) represent a possible solution for crossing wide, deep fjords, and is considered for the E39 highway route along the Norwegian west coast. With regard to SFTs, the specific accidental scenario that is under investigation is the combined action of fire and subsequent internal explosion, as this is a crucial safety design condition for this type of structure. To assess the structural performance of reinforced concrete structures under combined fire and blast actions, gas burner equipment and a shock tube device were used to generate high temperature and blast loading, respectively, on RC circular slabs. A proper set of instruments consisting of thermocouples embedded in the specimens, accelerometers and ultrasonic pulse velocity (UPV) equipment made it possible to capture the behaviour of the slabs under the combined fire and blast actions and to distinguish the specific role of fire and blast. Simplified numerical tools such as an equivalent elastic single degree of freedom (SDOF) model and a linear elastic finite element (FE) model were used to interpret the experimental results. By considering all combinations of three fire exposure times and two shock waves, the effect of damage accumulation from a combined action of fire and subsequent internal explosion was mapped. A reliable benchmark for numerical models was obtained.

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The cracking behaviours of reinforced-concrete (RC) ties are investigated by conducting virtual experiments using non-linear finite-element analysis. The assumptions in the model are verified by benchmarking the classical experiments of B. Bresler and V. V. Bertero as conducted in 1968 and P. J. Yannopoulos, conducted in 1989, which shows good agreement in the comparison of steel strains, development of crack widths and crack spacing. Furthermore, virtual experiments on four different RC ties show that the size of the cover and not the bar diameter governs the crack spacing and thus implicitly the crack width. An increase of the bar diameter has a beneficial effect in reducing the steel stress and the associated steel strains, which in turn reduces the crack width. Finally, a single bond-slip curve is sufficient in describing the average bond transfer of an arbitrary RC tie.

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The most common methods for detecting chloride-induced corrosion in concrete bridges are half-cell potential (HCP) mapping, electrical resistivity (ER) measurements, and chloride concentration testing, combined with visual inspection and cover measurements. However, studies on corrosion detection in pretensioned structures are rare. To investigate the applicability and accuracy of the above methods for corrosion detection in pretensioned bridge girders, we measured pretensioned I-shaped girders exposed to the Norwegian coastal climate for 33 years. We found that, even combined, the above methods can only reliably identify general areas with various probabilities of corrosion. Despite severe concrete cracking and high chloride content, only small corrosion spots were found in strands. Because HCP cannot distinguish corrosion probability in the closely spaced strands from other electrically connected bars, the actual condition of individual strands can be found only when concrete cover is locally removed. Wet concrete with high chloride content and accordingly low HCP and low ER was found only in or near the girder support zones, which can therefore be considered the areas most susceptible to chloride-induced corrosion. We conclude by proposing a procedure for the inspection and assessment of pretensioned girders in a marine environment.

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This paper formulates an analytical calculation model for predicting the cracking behavior of reinforced concrete ties to provide more consistent crack width calculation methods for large-scale concrete structures in which large bar diameters and covers are used. The calculation model was derived based on the physical behavior of reinforced concrete ties reported from experiments and finite-element analyses in the literature. The derivations led to a second order differential equation for the slip that accounts for the three-dimensional effects of internal cracking by using a proper bond-slip law. The second order differential equation for the slip was solved completely analytically, resulting in a closed-form solution in the case of lightly loaded members and in a non-closed-form solution in the case of heavily loaded members. Finally, the paper provides a solution strategy to facilitate a practical and applicable method for predicting the complete cracking response. Comparison with experimental and finite-element results in the literature demonstrated the ability of the calculation model to predict crack widths and crack spacing consistently and on the conservative side regardless of the bar diameter and cover.

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The alkali silica reaction (ASR) in concrete causes internal localized swelling and micro cracking, which result in expansion and correlated deterioration of the concrete material. The stress state of the concrete is known to affect expansion due to ASR, with an anisotropic stress state giving rise to anisotropic expansion. Similarly, the orientation and extent of micro cracking have a directional effect on the concrete mechanical behaviour. This research studied the effect of sustained uniaxial compressive stress on the evolution of the mechanical behaviour of concrete in compression. Concrete cubes of 230 mm side length were uniaxially restrained and stored in accelerated conditions, with cores drilled in two directions for mechanical tests: a cyclic test in compression, i.e. a stiffness damage test (SDT) and a complete stress-strain test. A clear directional dependency of the mechanical characteristics was found. Furthermore, the results indicate that reduction in modulus of elasticity is well correlated with the expansion in the test direction. On the other hand, the damage indices obtained from the SDT merely relate to the expansion, which puts in question the SDT's ability to predict ASR expansion in stressed concrete and therefore in concrete structures.

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Ferry-free coastal route E39 is a project that aims to design a coastal highway without ferry connections. Wide and deep fjords along the Norwegian coast make submerged floating tunnels (SFT) an alternative to conventional structures. In the unfortunate situation of accidental events, the SFT reinforced concrete (RC) structure may become damaged, affecting its load carrying capacity. RC shells can be a representative component of the SFT concrete structure, and it is relevant to study if RC shells can carry the combination of fire and subsequent blast load. An experimental program has been performed in conjunction with numerical simulations in order to enable the risk analysis and the feasibility study of SFT in the E39 project. A shock tube equipment has been used to evaluate the influence of high temperature on the blast load carrying resistance. In addition, static and material tests have been performed for further understanding of the slab behaviour. Nonlinear analyses for static loading and preliminary dynamic analyses have been performed, in combination with standard fire curve load effects. Temperature-dependent material properties have been used based on the results from the material tests. This paper gives an exemplary overview of (sometimes preliminary) results. Both the experimental and numerical results have revealed that high temperature leads to a significant internal damage of the material, affecting the response of RC slabs. In addition, statics tests results for slabs subjected to high temperatures show a significant reduction of the load carrying capacity.

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This study was based on findings from the Norwegian Public Roads Administration's Bridge Management System and field investigations on corrosion damage in pretensioned Norwegian standard I-beam (NIB) girders in 227 coastal climate bridges. The main durability design parameters are summarized and related to regulations over the last 80 years. Environmental exposure is discussed in the light of the global, local, and micro climate. We found that 51% of the bridges have girder corrosion damage. The percentage is highest for bridges built when the cover thickness required was lowest. Cover thickness below that required (resulting from production faults) caused 74% of corrosion damage. Most of the severe chloride-induced corrosion damage in bridges was found in the inner NIB girders, particularly in the support-zones and their vicinity. This can be due to interaction between geometry and exposure. Corrosion of reinforcement in support-zones can impact structural behavior, particularly NIB girder shear performance.

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The strain profile over the cover in reinforced concrete ties subjected to tension is investigated in this paper. This is normally neglected in the crack width calculation methods recommended by Eurocode 2 and fib Model Code 2010, meaning that it is assumed uniformly distributed over the cover. However, this assumption is questionable in the case of large covers. A pragmatic approach of accounting for the non-uniform strain profile over the cover in an analytical crack width calculation model can be by using the concept of the strain variation parameter ψ, which relates mean concrete strains over the cover to concrete strains at the steel bar surface at an arbitrary section over the bar length, x. Virtual experiments on six cylindrical concentrically reinforced concrete specimens were thus conducted by using nonlinear finite element analysis to establish a better understanding of the strain profile over the cover and, if possible, to obtain a proper value for ψ(x). The results show that ψ more or less remains constant over the bar length, except for the region close to the loaded end. This means that assuming a constant value for ψ seems reasonable. The practical significance of this finding is that the non-uniform strain profile over the cover can be properly accounted for in deriving and solving the second order differential equation for the slip between concrete and steel. This would ultimately yield an analytical crack width calculation model that predicts crack widths consistently, also in cases for large covers and bar diameters.

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The modified cracked membrane model (MCMM) presented in this paper was formulated to facilitate a mechanical calculation model that predicts crack widths in reinforced concrete (RC) structures subjected to in-plane loading for all cracking stages. It was formulated using the basic concepts of the existing cracked membrane model (CMM). Furthermore, a generalized approach for predicting the tension stiffening normal to a crack was formulated, an approach currently lacking in Eurocode 2 and fib Model Code 2010. A simplified approach for predicting the cracking behaviour of RC membranes was also proposed. Comparison with a total of 101 maximum crack widths measured experimentally on 37 test specimen from the literature showed that the MCMM provided good and consistent crack width predictions even for the cases of large rebars and covers, at which the CMM was seen to struggle. The results in this paper suggests that both the MCMM and the simplified approach show great potential for yielding reliable crack width predictions in RC membranes.@en

This paper theoretically and experimentally investigates the semi-empirical formulas recommended by Eurocode 2 (EC2), fib Model Code 2010 (MC2010), and Eurocode 2 with the German National Annex (DIN) for calculating crack widths in reinforced concrete. It is shown that the formulas can be derived from the principles for the idealized behavior of RC ties. However, instead of explicitly solving the resulting differential equations, the use of simplifications leads to inconsistent formulas. An experimental study was carried out involving the testing of eight RC ties to discover the modeling uncertainty of the formulas. It was found that EC2 substantially overestimated the crack widths for the RC ties. MC2010 and DIN seemed to predict the crack widths better, but gave rather a large number of nonconservative crack width predictions. These experimental results, combined with the theoretical study, suggest that a more consistent calculation model should be formulated by explicitly solving the resulting differential equation.

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The background theory for the crack width calculation methods according to Eurocode 2 and fib Model Code 2010 is discussed to evaluate the applicability for the more general case of relatively thick beams, slabs and shells. Essentially, the formulas originate from the maximum transfer length and the difference in steel and concrete strains over this length. It is shown that the formulas are based on both a slip and a no-slip theory, two theories using exactly opposite assumptions. The slip theory assumes that a physical slip occurs in the interface between concrete and steel and, also, that plane sections remain plane. The no-slip theory assumes that no physical slip occurs between concrete and steel and, thus, that plane sections no longer remain plane. The theories were merged pragmatically in an attempt to describe the physical reality related to cracking. This resulted in a formula for the transfer length composed by two linear terms. Such a formulation, however, leads to inconsistencies that opposes the basic principles in solid mechanics. It is argued that these inconsistencies limits the application for the more general case. The observations in this paper suggests that a more robust and consistent calculation method should be formulated. A possible way is by improving the bond assumptions in the interface between concrete and steel, and thoroughly studying the geometry and configuration of cracks experimentally and theoretically.@en

This paper presents a modelling approach for fibre-reinforced concrete elements in which the fibre structure is taken into account in simulating the mechanical behaviour. The fibre structure is discretized in volumes and two fibre parameters are defined for each discrete volume: the dominant fibre orientation and the fibre volume fraction. These parameters are incorporated in a numerical model that uses a single-phase material definition dependent on the fibre parameters. The first part of this paper describes the methodology and constitutive modelling. The second part addresses the simulation of two beams that exhibited large differences in bending because of uneven fibre distribution. Data on the fibre structure was obtained using Computed Tomography scanning. The modelling approach captured the large difference in the flexural response of the two beams and provided an adequate prediction of the location and propagation of the critical cracks.

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Concrete structures shall be designed and constructed to limit cracking and crack widths for durability, functionality and aesthetic reasons. Current design methods and requirements are, however, only in a limited manner verified for large-scale concrete structures and long service life, as well as for new binder and concrete types. To facilitate an improved design basis for large-scale reinforced concrete structures, the present project on evaluation and improvement of calculation methods for large-scale concrete structures in Service Limit State has been initiated. Initially, the occurrence of shear cracks and excessive deformations in concrete cantilever bridges has been investigated. A calculation model based on the Modified Compression Field Theory was established under the assumption that creep in principal compression direction may cause the occurrence of diagonal shear cracks in webs of the cross section. In a shear cracked state, the shear stiffness will be significantly reduced, which further results in increase of shear deformations. The calculation model was applied to, and verified on a real segmentally cast cantilever bridge: the Sålåsund Bridge with main span L = 120 m, where this type of cracking was observed.@en

Innovative structures can be designed with flowable concrete. A homogenous fibre distribution has to be assured by adequate mix design, whereas the fibre orientation depends on the flow and casting conditions, fibre length and rheological properties. Important work has been carried out during the past years on test methods and methods for non-destructive testing highlighting the necessity for on-site assessment of material behaviour of fibre concrete. The translation of results of small scale specimens tested in bending or in uniaxial tension is not necessarily straightforward and easy to execute considering a larger number of affecting parameters in the case of flowable concrete. This paper reviews the progress in understanding of how test results of small scale specimens relate to the structural behaviour of flowable fibre reinforced concrete. Results of recent studies reported in literature and carried out by members of fib Task Group 8.8 are considered.@en