Modelação numérica do escorregamento de armaduras em elementos de betão armado / Numerical modelling of bond-slip effects in reinforced concrete elements

Reinforced concrete (RC) framed structures subjected to seismic loading often show localized deformations at the extremities of the members associated with the slippage of reinforcing bars along their anchorage length. Despite this phenomenon being responsible for up to 40% of the total lateral deformation of RC members, the numerical simulation of this behaviour still presents several limitations. This paper introduces a modelling strategy wherein, for the first time, an explicit bond-slip model is developed to be used in connection with a fibre-based beam-column element through a zero-length link element. The proposed element adopts an advanced bond stress-slip constitutive relation capable of representing the effects of cyclic degradation or rebar yielding, among others. The numerical model is validated through a comparison with experimental results, evidencing a remarkable efficiency, accuracy and numerical stability.

A fibre-based frame element with explicit consideration of bond-slip effects

João Saraiva Esteves Pacheco de Almeida

Reinforced concrete (RC) frames subjected to seismic loading often depict localized member-end deformations due to strain penetration effects between adjacent members, such as beam-column and column-footing joints. Past experimental programs indicate that the bond-slip deformations occurring at the interface between the reinforcement and the surrounding concrete can contribute up to 40% of the lateral deformation of the RC members. The employment of advanced bond-slip models within detailed finite element formulations, capable of simulating continuous domains with highly discretized meshes, has witnessed great advances over the recent years with encouraging results. Nonetheless, this modelling approach is computationally heavy and hence inapplicable for practical seismic (nonlinear) analysis of structures. Alternatively, the use of beam-column elements with lumped or distributed plasticity is a more computationally efficient and engineering-friendly modelling approach. Unfortunately, the elements of this type available in conventional numerical packages did not yet consider an explicit simulation of the interface between the reinforcing bars and the surrounding concrete along their embedment length. The present study aimed at overcoming the foregoing limitation by developing an explicit bond-slip model applicable to general fibre-based beam-column elements. Using a state-of-the-art bond-slip constitutive model, the current paper introduces a zero-length element that computes the localized member-end deformations accounting for the bond-slip response at each reinforcing bar of a given RC section. Along with the material properties and anchorage conditions, the proposed nonlinear model also accounts for cyclic degradation and rebar yielding effects. Validation studies conducted with the proposed numerical formulation reveal a good agreement with past experimental tests, evidencing an important stability and accuracy at the expense of an acceptable additional computational effort.

2017

Structural Response of R-UHPFRC - RC Composite Members Subjected to Combined Bending and Shear

Talayeh Noshiravani

The addition of a thin overlay of Ultra-High Performance Fibre Reinforced Concrete (UHPFRC) to Reinforced Concrete (RC) members is an emerging technique to strengthen and protect existing structures and to design durable new structures. Combining UHPFRC with closely spaced, small-diameter steel rebars in Reinforced UHPFRC (R-UHPFRC) layers improves the UHPFRC's strain hardening behaviour. For reasons of practicality, R-UHPFRC layers are cast or glued (in the case of prefabricated elements) on top of RC members, thus changing the latter into R-UHPFRC - RC composite members. The high strength and deformation capacity of R-UHPFRC elements make them a suitable external flexural reinforcement for RC members over intermediate supports, e.g., bridge decks and slabs or beams in buildings. Over reinforcement of RC beams and slabs with tensile flexural reinforcement can result in their shear failure at either a lower resistance or deformation than the associated values for member failure in flexure. A comprehensive experimental program was conducted to study the flexure-shear behaviour of R-UHPFRC - RC composite beams. The program comprises two test series on cantilever beams and continuous beams. The test parameters include shear span-depth ratio (a/d), the amount of transverse reinforcement ( ρν), the amount of longitudinal reinforcement, and the strength and bond condition of the R-UHPFRC rebars. The experimental results reveal the different failure modes of R-UHPFRC - RC composite members and the contribution of the R-UHPFRC elements to the member resistance, ductility and capacity to redistribute the internal stress. It was shown that in R-UHPFRC - RC beams with ribbed rebars and a shear span to depth ratio greater than 2.5 the stresses are carried by beam action. Depending on the degree of longitudinal reinforcement, all but two of the beams with 3.0≤a/d≤3.4 and ρν≤0.17 had a flexure-shear failure; the rest failed in flexure. The flexure-shear failure of the composite beams was at an approximately equal rotation level as their RC reference beam but at a resistance 2.3 times that of the RC beam. This is due to (1) the debonding interface zone between the elements that allows the R-UHPFRC - RC beams to rotate more freely and (2) the out-of-plane resistance of the R-UHPFRC element that contributes to the shear resistance. The internal flow of forces and the structural response of composite members strongly depend on the bond condition between the R-UHPFRC and RC, the UHPFRC and its rebars, as well as the concrete and its rebars. Cracking of the concrete along the interface zone causes bond reduction, i.e., softening of the shear connection, between the two elements. In presence of high shear stresses and diagonal flexure-shear cracks, interface zone softening is observed between the elements prior to the maximum resistance, while UHPFRC is strain hardening. The cause of this softening behaviour is the prying action due to the relative rotational movement of the RC rigid bodies separated by the flexure-shear cracks. Static and kinematic solutions of the theory of plasticity for RC beams are extended to predict the collapse load of R-UHPFRC - RC composite beams at the ultimate limit state. A mechanical model for predicting the structural response of composite beams is proposed. In combination with truss models, the concept of an R-UHPFRC - RC plastic hinge is introduced to calculate the force-displacement response of composite beams. The failure criterion based on the collapse mechanisms (kinematic solutions) sets the limit of the force-displacement response. The model is corroborated by the experimental results. This model provides a tool for analysis of RC members reinforced with an added tensile R-UHPFRC element.

EPFL2012

Etude expérimentale des couplages viscoélasticité-croissance des fissures dans les bétons de ciment

Emmanuel Denarié

Viscoelasticity and crack growth govern the long-term deformability of concrete and thus its service behaviour and its durability. For low load levels, viscoelasticity behaves quasilinearly and crack growth is inactive. On the other hand, for high load levels, cracks grow and interact with viscoelasticity. Numerous authors have long demonstrated the influence of microcracking on creep qualitatively. Moreover, rate effects on the fracture behaviour of concrete are clear for low and high loading rates. Nevertheless, the mechanisms involved in these effects are not yet clearly determined. Cohesive crack approaches extended to time dependent parameters, give some elements of explanation, although without providing a general tool capable of explaining all the phenomena. The dissipative nature of crack growth and viscoelasticity naturally encourages one to model their couplings by means of an energybased approach to fracture. This is the meaning of the continuum thermodynamics of dissipative multicracked granular bodies developed by Huet (1997). This theoretical formalism puts the emphasis on the effect of viscoelasticity on the driving (reactive) part of the propagation criteria (energy release rate). The aim of this experimental research was to investigate coupling effects between viscoelasticity and crack growth in concrete. With this aim in view, 4 different types of fracture test have been performed on the same material (concrete with a maximum aggregate size of 8 mm), with a constant specimen geometry (rectangular wedge splitting specimens 20 by 20 by 10 cm). The first type of test consisted of performing a series of successive relaxations, at various increasing load levels, before, on and after the peak force, following the envelope of failure. Special attention was devoted to the influence of the control parameter ("active": with respect to displacements measured on the specimen, or "passive": crosshead displacement) and loading history. The results showed a progressive deviation from the linear viscoelastic behaviour starting from a load level of approximately 50 % of the peak force, before the peak. This deviation was significantly higher with crosshead control ("passive"). It depended on the loading history. After the peak, in "active" displacement control, relative relaxations tended to be similar whatever the load level. The displacement parameters (other than control) measured on the specimen or crosshead during relaxation, showed an evolution dependent on the control parameter. This effect was significant at the beginning of the relaxation and tended to disappear later. Furthermore, acoustic emissions could be detected at the beginning and during some relaxations, for high load levels (nearby peak force and after). The second type of test consisted of one or more successive creep levels up to eventual failure under sustained force. In certain cases, during creep levels leading to fracture, alternating secondary and tertiary creep with multiple concavity changes correlated with measured acoustic emissions could be observed. The tertiary creep leading to fracture developed over several minutes. Unstable sudden crack propagation was only seen at the end of the tertiary creep levels, accompanied by a sudden and very fast increase of the number of acoustic emissions. Moreover, during tertiary creep, an increase of the crack length measured on the specimen's surface by means of a conductive crack graphite gauge could be observed, correlated with the evolution of the creep displacements. The third type of test was performed under constant displacement speed (displacement measured on the specimen in the axis of the splitting force) with a range of speeds from 5 x 10-4 to 5 x 10-1 mm/minute. The results show a clear influence of the displacement speed on the response in terms of force-displacement curve, in the vicinity of the peak. The maximum force decreases with the displacement speed. On the other hand, the displacement at peak force was not significantly influenced by the displacement speed. Surface crack length measurements by means of a conductive graphite gauge enabled the determination of the surface crack speed as a function of the imposed displacement. The obtained surface crack speed depended quasi linearly on the imposed displacement speed. The fourth type of test, complementary to the former ones, was especially for the study of the evolution of internal micromechanical parameters during crack growth. Two wedge splitting specimens were equipped internally, near to the potential crack path with optical strain gauges (Bragg gratings). The internal strain measurements, revealed two zones of very different behaviour, with similar tends for the two specimens. Optical strain gauges close to the fracture plane (less than 5 mm from gauge axis) measured high strains (around 1000 με) significantly greater than the ultimate tensile strain of normal concrete (0.1‰ or 100 με) and mostly irreversible. At the contrary, optical strain gauges farther from the fracture plane (over 10 to 15 mm) measured strains that were always smaller than 100 με , and mostly reversible. Finally, two types of computer simulation (homogeneous materials) were performed in order to complement the interpretation of experimental results. A linear viscoelastic calculation, for a constant crack pattern, was used to illustrate quantitatively the progressive deviation from linearity observed in the experimental successive relaxations. A non-linear calculation of the propagation of a discrete crack with softening behaviour, in a linear elastic material, accurately predicted some of the strains measured with optical strain gauges during crack propagation. The experimental results demonstrated many indications of crack growth activity during creep as well as relaxation levels. These measurements confirm the significant contribution of propagation and coalescence of microcracks to the non-linear viscoelastic response of concrete. Indications of microcrack growth during relaxation can be explained by unstable propagation phenomena triggered by the small size of the microcracks. These phenomena could be amplified by viscoelastic effects of the redistribution of internal stresses in the heterogeneous structure of concrete. All the work performed clearly shows the need to complement macroscopic measurements such as the reaction force of a specimen or external displacements, with the measurement of micromechanical parameters in order to distinguish the contributions of the different active phenomena and of their coupling.

EPFL2000