A model to simulate the moment-rotation and crack width of FRC members reinforced with longitudinal bars

The present work describes a model for the determination of the moment–rotation relationship of a cross section of fiber reinforced concrete (FRC) elements that also include longitudinal bars for the flexural reinforcement (R/FRC). Since a stress–crack width relationship (σ–w)(σ–w) is used to model the post-cracking behavior of a FRC, the σ–w directly obtained from tensile tests, or derived from inverse analysis applied to the results obtained in three-point notched beam bending tests, can be adopted in this approach. For a more realistic assessment of the crack opening, a bond stress versus slip relationship is assumed to simulate the bond between longitudinal bars and surrounding FRC. To simulate the compression behavior of the FRC, a shear friction model is adopted based on the physical interpretation of the post-peak compression softening behavior registered in experimental tests. By allowing the formation of a compressive FRC wedge delimited by shear band zones, the concept of concrete crushing failure mode in beams failing in bending is reinterpreted. By using the moment–rotation relationship, an algorithm was developed to determine the force–deflection response of statically determinate R/FRC elements. The model is described in detail and its good predictive performance is demonstrated by using available experimental data. Parametric studies were executed to evidence the influence of relevant parameters of the model on the serviceability and ultimate design conditions of R/FRC elements failing in bending.

Crack width control in RC elements with recycled steel fibres and applications to integral structures : theoretical and experimental study

El presente trabajo trata de elementos reforzados con barras de armadura y Fibras Metálicas Recicladas (FMR). El objetivo principal es mejorar el comportamiento a fisuración de elementos sometidos a flexión pura y a flexión compuesta, aumentando en consecuencia las prestaciones en servicio de aquellas estructuras con requerimientos estrictos con respecto al control de fisuración. Entre éstas últimas se encuentran las estructuras integrales, es decir aquellas estructuras sin juntas (puentes o edificios), sometidas a cargas gravitatorias y deformaciones impuestas en los elementos horizontales debidas a retracción, fluencia y temperatura. Las FMR son obtenidas a partir de los neumáticos fuera de uso, y puesto que el procedimiento de reciclado se centra en el caucho en vez que en el acero, su forma es aleatoria y con longitud variable. A pesar de que la eficacia del fibrorefuerzo mediante FMR ha sido demostrada en investigaciones anteriores, la innovación que representa este trabajo consiste en proponer la acción combinada de barras convencionales y FMR en la mejora del comportamiento a fisuración. El objetivo es por tanto mejorar la sostenibilidad del proyecto de la estructura en HA al utilizar materiales reciclados por un lado, y aumentando por el otro la durabilidad. En primer lugar, se presenta el estado del arte con respecto a la fisuración en elementos de HA, que sucesivamente se amplía a elementos reforzados con barras y fibras. Asimismo, se resume el método simplificado para el análisis de columnas de estructuras sin juntas ya propuesto por Pérez et al., con particular énfasis en aquellos aspectos que son incompatibles con la acción de las fibras a nivel seccional. A continuación, se presenta un modelo para describir la deformabilidad seccional y la fisuración en elementos en HA, que luego se amplía a aquellos elementos reforzados con barras y fibras, teniendo en cuenta también los efectos debidos a la retracción (tension stiffening negativo). El modelo es luego empleado para ampliar el método simplificado para el análisis de columnas. La aportación consiste por tanto en contar con una metodología amplia de análisis para este tipo de elementos. Seguidamente, se presenta la campaña experimental preliminar que ha involucrado vigas a escala reducida sometidas a flexión simple, con el objetivo de validar la eficiencia y la usabilidad en el hormigón de las FMR de dos diferentes tipos, y su comportamiento con respecto a fibras de acero comerciales. Se describe a continuación la campaña principal, consistente en ensayos sobre ocho vigas en flexión simple a escala 1:1 (variando contenido en FRM, Ø/s,eff y recubrimiento) y doce columnas a flexión compuesta (variando contenido en FMR, Ø/s,eff y nivel de fuerza axil). Los resultados obtenidos en la campaña principal son presentados y comentados, resaltando las mejoras obtenidas en el comportamiento a fisuración de las vigas y columnas, y la rigidez estructural de las columnas. Estos resultados se comparan con las predicciones del modelo propuesto. Los principales parámetros estudiados para describir la fisuración y el comportamiento seccional de las vigas son: la separación entre fisuras, el alargamiento medio de las armaduras y la abertura de fisura, mientras que en los ensayos de las columnas se ha contrastado las leyes momento/curvatura, la tensión en las barras de armadura y la abertura de fisura en el empotramiento en la base. La comparación muestra un buen acuerdo entre las predicciones y los resultados experimentales. Asimismo, se nota la mejora en el comportamiento a fisuración debido a la incorporación de FMR en aquellos elementos con cuantías de armadura bajas en flexión simple, en elementos con axiles bajos y para el control de la fisuración en elementos con grandes recubrimientos, siendo por tanto resultados de inmediato impacto en la práctica ingenieril (diseño de losas, tanques, estructuras integrales, etc.). VIIIComo punto final, se presentan aplicaciones de las FMR en estructuras reales. Se discuten dos casos de elementos sometidos a flexión pura, en particular una viga simplemente apoyada y un tanque para el tratamiento de agua. En ambos casos la adicción de FMR al hormigón lleva a mejoras en el comportamiento a fisuración. Luego, utilizando el método simplificado para el análisis en servicio de columnas de estructuras sin juntas, se calcula la máxima longitud admisible en casos típicos de puentes y edificación. En particular, se demuestra que las limitaciones de la práctica ingenieril actual (sobre todo en edificación) pueden ser aumentadas considerando el comportamiento real de las columnas en HA. Finalmente, los mismos casos son modificados para considerar el uso de MFR, y se presentan las mejoras tanto en la máxima longitud admisible como en la abertura de fisura para una longitud y deformación impuesta. This work deals with elements reinforced with both rebars and Recycled Steel Fibres (RSFs). Its main objective is to improve cracking behaviour of elements subjected to pure bending and bending and axial force, resulting in better serviceability conditions for these structures demanding keen crack width control. Among these structures a particularly interesting type are the so-called integral structures, i.e. long jointless structures (bridges and buildings) subjected to gravitational loads and imposed deformations due to shrinkage, creep and temperature. RSFs are obtained from End of Life Tyres, and due to the recycling process that is focused on the rubber rather than on the steel they come out crooked and with variable length. Although the effectiveness of RSFs had already been proven by previous research, the innovation of this work consists in the proposing the combined action of conventional rebars and RSFs to improve cracking behaviour. Therefore, the objective is to improve the sustainability of RC structures by, on the one hand, using recycled materials, and on the other improving their durability. A state of the art on cracking in RC elements is firstly drawn. It is then expanded to elements reinforced with both rebars and fibres (R/FRC elements). Finally, the simplified method for analysis of columns of long jointless structures already proposed by Pérez et al. is resumed, with a special focus on the points that conflict when taking into account the action of fibres. Afterwards, a model to describe sectional deformability and cracking of R/FRC elements is presented, taking also into account the effect of shrinkage (negative tension stiffening). The model is then used to implement the simplified method for columns. The novelty represented by this is that a comprehensive methodology to analyse this type of elements is presented. A preliminary experimental campaign consisting in small beams subjected to pure bending is described, with the objective of validating the effectiveness and usability in concrete of RSFs of two different types, and their behaviour when compared with commercial steel fibres. With the results and lessons learnt from this campaign in mind, the main experimental campaign is then described, consisting in cracking tests of eight unscaled beams in pure bending (varying RSF content, Ø/s,eff and concrete cover) and twelve columns subjected to imposed displacement and axial force (varying RSF content, Ø/s,eff and squashing load ratio). The results obtained from the main campaign are presented and discussed, with particular focus on the improvement in cracking behaviour for the beams and columns, and structural stiffness for the columns. They are then compared with the proposed model. The main parameters studied to describe cracking and sectional behaviours of the beam tests are crack spacing, mean steel strain and crack width, while for the column tests these were moment/curvature, stress in rebars and crack with at column embedment. The comparison showed satisfactory agreement between experimental results and model predictions. Moreover, it is pointed out the improvement in cracking behaviour due to the addition of RSF for elements with low reinforcement ratios, elements with low squashing load ratios and for crack width control of elements with large concrete covers, thus representing results with a immediate impact in engineering practice (slab design, tanks, integral structures, etc.). Applications of RSF to actual structures are finally presented. Two cases of elements in pure bending are presented, namely a simple supported beam and a water treatment tank. In both cases the addition of RSF to concrete leads to improvements in cracking behaviour. Then, using the simplified model for the serviceability analysis of columns of jointless structures, the maximum achievable jointless length of typical cases of a bridge and building is obtained. In XIIparticular, it is shown how the limitations of current engineering practice (this is especially the case of buildings) can be increased by considering the actual behaviour of RC supports. Then, the same cases are modified considering the use of RSF, and the improvements both in maximum achievable length and in crack width for a given length and imposed strain at the deck/first floor are shown.

Tensile stress–crack width law for steel fibre reinforced self-compacting concrete obtained from indirect (splitting) tensile tests

In this work, the fracture mode I parameters of steel fibre reinforced self-compacting concrete (SFRSCC) were derived from the numerical simulation of indirect splitting tensile tests. The combined experimental and numerical research allowed a comparison between the stress-crack width (σ - w) relationship acquired straightforwardly from direct tensile tests, and the σ - w response derived from inverse analysis of the splitting tensile tests results. For this purpose a comprehensive nonlinear 3D finite element (FE) modeling strategy was developed. A comparison between the experimental results obtained from splitting tensile tests and the corresponding FE simulations confirmed the good accuracy of the proposed strategy to derive the σ – w for these composites. It is concluded that the post-cracking tensile laws obtained from inverse analysis provided a close relationship with the ones obtained from the experimental uniaxial tensile tests.

Modelo para calcular a contribuição da fibra na resistência à punção de lajes em concreto reforçado com fibra de aço

Neste artigo, formulações analíticas são desenvolvidas para calcular a resistência à punção de lajes lisas de concreto reforçado com fibras de aço (CRFA) e que também são reforçadas à flexão por barras de aço (reforço convencional). A partir de análises estatísticas sobre um banco de dados que reúne resultados experimentais de caracterização do comportamento pós-fissuração do CRFA, equações são estabelecidas para avaliar parâmetros da resistência residual à tração na flexão (fRi) a partir de informações fundamentais que caracterizam a fibra de aço. O parâmetro de resistência fRi, proposto pelo ModelCode10 foi usado para definir a lei tensão-abertura da fissura (σ-w) que simula o mecanismo de reforço da fibra em um material cimentício. A segunda parte do artigo descreve uma formulação analítica baseada nos conceitos propostos por Muttoni e Ruiz, onde a lei σ-w é convenientemente integrada para simular a contribuição da fibra de aço na resistência à punção de lajes em CRFA. A partir de um banco de dados, composto de 154 ensaios de punção, o bom desempenho da proposta apresentada é demonstrado. O desempenho do modelo também é evidenciado comparando-se os seus resultados a outros modelos.

Prestress losses in NSM-CFRP flexurally strengthened RC beams

The use of prestressed near surface mounted fibre reinforced polymers (NSM-FRP) has been long acknowledged to be a suitable approach to strengthen and retrofit existing reinforced concrete structures. The application of a certain amount of prestress to the FRP prior to its installation provides a number of benefits, mainly related to crack width and deflection requisites at serviceability limit state conditions. After transferring the prestress to a structural element, some of the existing cracks can be closed, decreasing the vulnerability of the element to corrosion and, a certain amount of deflection can be recovered due to the introduced negative curvature. However, these benefits can only be assured if the prestress is properly preserved over time. In this context, three series of reinforced concrete beams, in a total of 10 beams, were strengthened with a prestressed carbon FRP laminate (CFRP) and monitored for about 40 days. The data obtained from these tests is in this paper presented and analysed. The observed losses of strain in the CFRP laminate were found to be mainly located in the extremities of the bonded length, while in the central zone most of the initial strain was well-preserved over time. Additionally, the highest CFRP strain losses were observed in the first 6 to 12 days after prestress transfer, suggesting that the benefits of prestressed NSM-FRP will not be considerably lost over time.

Influence of casting condition on the anisotropy of the fracture properties of Steel Fibre Reinforced Self-Compacting Concrete (SFRSCC)

Identification of the tensile constitutive behaviour of Fibre Reinforced Concrete (FRC) represents an important aspect of the design of structural elements using this material. Although an important step has been made with the introduction of guidance for the design with regular FRC in the recently published fib Model Code 2010, a better understanding of the behaviour of this material is still necessary, mainly for that with self-compacting properties. This work presents an experimental investigation employing Steel Fibre Self-Compacting Concrete (SFRSCC) to cast thin structural elements. A new test method is proposed for assessing the post-cracking behaviour and the results obtained with the proposed test method are compared with the ones resulted from the standard three-point bending tests (3PBT). Specimens extracted from a sandwich panel consisting of SFRSCC layers are also tested. The mechanical properties of SFRSCC are correlated to the fibre distribution by analysing the results obtained with the different tests. Finally, the stress-crack width constitutive law proposed by the fib Model Code 2010 is analysed in light of the experimental results.

Strength and serviceability performance of beams reinforced with GFRP bars in flexure

Glass fiber reinforced polymer (GFRP) rebars have been identified as an alternate construction material for reinforcing concrete during the last decade primarily due to its strength and durability related characteristics. These materials have strength higher than steel, but exhibit linear stress–strain response up to failure. Furthermore, the modulus of elasticity of GFRP is significantly lower than that of steel. This reduced stiffness often controls the design of the GFRP reinforced concrete elements. In the present investigation, GFRP reinforced beams designed based on limit state principles have been examined to understand their strength and serviceability performance. A block type rotation failure was observed for GFRP reinforced beams, while flexural failure was observed in geometrically similar control beams reinforced with steel rebars. An analytical model has been proposed for strength assessment accounting for the failure pattern observed for GFRP reinforced beams. The serviceability criteria for design of GFRP reinforced beams appear to be governed by maximum crack width. An empirical model has been proposed for predicting the maximum width of the cracks. Deflection of these GFRP rebar reinforced beams has been predicted using an earlier model available in the literature. The results predicted by the analytical model compare well with the experimental data

Behavior of geopolymer concrete exposed to elevated temperatures

The research in the area of geopolymer is gaining momentum during the past 20 years. Studies confirm that geopolymer concrete has good compressive strength, tensile strength, flexural strength, modulus of elasticity and durability. These properties are comparable with OPC concrete.There are many occasions where concrete is exposed to elevated temperatures like fire exposure from thermal processor, exposure from furnaces, nuclear exposure, etc.. In such cases, understanding of the behaviour of concrete and structural members exposed to elevated temperatures is vital. Even though many research reports are available about the behaviour of OPC concrete at elevated temperatures, there is limited information available about the behaviour of geopolymer concrete after exposure to elevated temperatures. A preliminary study was carried out for the selection of a mix proportion. The important variable considered in the present study include alkali/fly ash ratio, percentage of total aggregate content, fine aggregate to total aggregate ratio, molarity of sodium hydroxide, sodium silicate to sodium hydroxide ratio, curing temperature and curing period. Influence of different variables on engineering properties of geopolymer concrete was investigated. The study on interface shear strength of reinforced and unreinforced geopolymer concrete as well as OPC concrete was also carried out. Engineering properties of fly ash based geopolymer concrete after exposure to elevated temperatures (ambient to 800 °C) were studied and the corresponding results were compared with those of conventional concrete. Scanning Electron Microscope analysis, Fourier Transform Infrared analysis, X-ray powder Diffractometer analysis and Thermogravimetric analysis of geopolymer mortar or paste at ambient temperature and after exposure to elevated temperature were also carried out in the present research work. Experimental study was conducted on geopolymer concrete beams after exposure to elevated temperatures (ambient to 800 °C). Load deflection characteristics, ductility and moment-curvature behaviour of the geopolymer concrete beams after exposure to elevated temperatures were investigated. Based on the present study, major conclusions derived could be summarized as follows. There is a definite proportion for various ingredients to achieve maximum strength properties. Geopolymer concrete with total aggregate content of 70% by volume, ratio of fine aggregate to total aggregate of 0.35, NaOH molarity 10, Na2SiO3/NaOH ratio of 2.5 and alkali to fly ash ratio of 0.55 gave maximum compressive strength in the present study. An early strength development in geopolymer concrete could be achieved by the proper selection of curing temperature and the period of curing. With 24 hours of curing at 100 °C, 96.4% of the 28th day cube compressive strength could be achieved in 7 days in the present study. The interface shear strength of geopolymer concrete is lower to that of OPC concrete. Compared to OPC concrete, a reduction in the interface shear strength by 33% and 29% was observed for unreinforced and reinforced geopolymer specimens respectively. The interface shear strength of geopolymer concrete is lower than ordinary Portland cement concrete. The interface shear strength of geopolymer concrete can be approximately estimated as 50% of the value obtained based on the available equations for the calculation of interface shear strength of ordinary portland cement concrete (method used in Mattock and ACI). Fly ash based geopolymer concrete undergoes a high rate of strength loss (compressive strength, tensile strength and modulus of elasticity) during its early heating period (up to 200 °C) compared to OPC concrete. At a temperature exposure beyond 600 °C, the unreacted crystalline materials in geopolymer concrete get transformed into amorphous state and undergo polymerization. As a result, there is no further strength loss (compressive strength, tensile strength and modulus of elasticity) in geopolymer concrete, whereas, OPC concrete continues to lose its strength properties at a faster rate beyond a temperature exposure of 600 °C. At present no equation is available to predict the strength properties of geopolymer concrete after exposure to elevated temperatures. Based on the study carried out, new equations have been proposed to predict the residual strengths (cube compressive strength, split tensile strength and modulus of elasticity) of geopolymer concrete after exposure to elevated temperatures (upto 800 °C). These equations could be used for material modelling until better refined equations are available. Compared to OPC concrete, geopolymer concrete shows better resistance against surface cracking when exposed to elevated temperatures. In the present study, while OPC concrete started developing cracks at 400 °C, geopolymer concrete did not show any visible cracks up to 600 °C and developed only minor cracks at an exposure temperatureof 800 °C. Geopolymer concrete beams develop crack at an early load stages if they are exposed to elevated temperatures. Even though the material strength of the geopolymer concrete does not decrease beyond 600 °C, the flexural strength of corresponding beam reduces rapidly after 600 °C temperature exposure, primarily due to the rapid loss of the strength of steel. With increase in temperature, the curvature at yield point of geopolymer concrete beam increases and thereby the ductility reduces. In the present study, compared to the ductility at ambient temperature, the ductility of geopolymer concrete beams reduces by 63.8% at 800 °C temperature exposure. Appropriate equations have been proposed to predict the service load crack width of geopolymer concrete beam exposed to elevated temperatures. These equations could be used to limit the service load on geopolymer concrete beams exposed to elevated temperatures (up to 800 °C) for a predefined crack width (between 0.1mm and 0.3 mm) or vice versa. The moment-curvature relationship of geopolymer concrete beams at ambient temperature is similar to that of RCC beams and this could be predicted using strain compatibility approach Once exposed to an elevated temperature, the strain compatibility approach underestimates the curvature of geopolymer concrete beams between the first cracking and yielding point.

Rissbildung und Zugtragverhalten von mit Stabstahl und Fasern bewehrtem Ultrahochfesten Beton (UHPC)

Ultrahochfester Beton (UHPC) ist ein sehr gefügedichter zementgebundener Werkstoff, der sich nicht nur durch eine hohe Druckfestigkeit, sondern auch durch einen hohen Widerstand gegen jede Form physikalischen oder chemischen Angriffs auszeichnet. Duktiles Nachbruchverhalten bei Druckversagen wird meist durch die Zugabe dünner kurzer Fasern erreicht. In Kombination mit konventioneller Betonstahl- oder Spannbewehrung ermöglicht UHPC die Ausführung sehr schlanker, weitgespannter Konstruktionen und eröffnet zugleich neue Anwendungsgebiete, wie zum Beispiel die flächenhafte Beschichtung von Brückendecks. Durch das Zusammenwirken kontinuierlicher Bewehrungselemente und diskontinuierlich verteilter kurzer Fasern ergeben sich unter Zugbeanspruchung Unterschiede gegenüber dem bekannten Stahl- und Spannbeton. In der vorliegenden Arbeit wird hierzu ein Modell entwickelt und durch eine umfangreiche Versuchsreihe abgesichert. Ausgangspunkt sind experimentelle und theoretische Untersuchungen zum Verbundverhalten von Stabstählen in einer UHPC-Matrix und zum Einfluss einer Faserzugabe auf das Reiß- und Zugtragverhalten von UHPC. Die Modellbildung für UHPC-Zugelemente mit gemischter Bewehrung aus Stabstahl und Fasern erfolgt auf der Grundlage der Vorgänge am diskreten Riss, die daher sehr ausführlich behandelt werden. Für den elastischen Verformungsbereich der Stabbewehrung (Gebrauchslastbereich) kann damit das Last-Verformungs-Verhalten für kombiniert bewehrte Bauteile mechanisch konsistent unter Berücksichtigung des bei UHPC bedeutsamen hohen Schwindmaßes abgebildet werden. Für die praktische Anwendung wird durch Vereinfachungen ein Näherungsverfahren abgeleitet. Sowohl die theoretischen als auch die experimentellen Untersuchungen bestätigen, dass der faserbewehrte UHPC bei Kombination mit kontinuierlichen Bewehrungselementen selbst kein verfestigendes Verhalten aufweisen muss, um insgesamt verfestigendes Verhalten und damit eine verteilte Rissbildung mit sehr keinen Rissbreiten und Rissabständen zu erzielen. Diese Beobachtungen können mit Hilfe der bisher zur Verfügung stehenden Modelle, die im Wesentlichen eine Superposition isoliert ermittelter Spannungs-Dehnungs-Beziehungen des Faserbetons und des reinen Stahls vorsehen, nicht nachvollzogen werden. Wie die eigenen Untersuchungen zeigen, kann durch ausreichend dimensionierte Stabstahlbewehrung zielgerichtet und ohne unwirtschaftlich hohe Fasergehalte ein gutmütiges Verhalten von UHPC auf Zug erreicht werden. Die sichere Begrenzung der Rissbreiten auf deutlich unter 0,1 mm gewährleistet zugleich die Dauerhaftigkeit auch bei ungünstigen Umgebungsbedingungen. Durch die Minimierung des Material- und Energieeinsatzes und die zu erwartende lange Nutzungsdauer lassen sich so im Sinne der Nachhaltigkeit optimierte Bauteile realisieren.

Serviceability behaviour of fibre reinforced polymer reinforced concrete beams

El uso de materiales compuestos de matriz polimérica (FRP) emerge como alternativa al hormigón convencionalmente armado con acero debido a la mayor resistencia a la corrosión de dichos materiales. El presente estudio investiga el comportamiento en servicio de vigas de hormigón armadas con barras de FRP mediante un análisis teórico y experimental. Se presentan los resultados experimentales de veintiséis vigas de hormigón armadas con barras de material compuesto de fibra de vidrio (GFRP) y una armada con acero, todas ellas ensayadas a flexión de cuatro puntos. Los resultados experimentales son analizados y comparados con algunos de los modelos de predicción más significativos de flechas y fisuración, observándose, en general, una predicción adecuada del comportamiento experimental hasta cargas de servicio. El análisis de sección fisurada (CSA) estima la carga última con precisión, aunque se registra un incremento de la flecha experimental para cargas superiores a las de servicio. Esta diferencia se atribuye a la influencia de las deformaciones por esfuerzo cortante y se calcula experimentalmente. Se presentan los aspectos principales que influyen en los estados límites de servicio: tensiones de los materiales, ancho máximo de fisura y flecha máxima permitida. Se presenta una metodología para el diseño de dichos elementos bajo las condiciones de servicio. El procedimiento presentado permite optimizar las dimensiones de la sección respecto a metodologías más generales.

Fadiga em dormentes de concreto reforçados com fibras de aço

A prestressed concrete monoblock railroad tie was designed to attend the characteristics of a Brazilian railroad track with 1,600 mm gauge and 320 kN axle load. Concrete ties specimens were manufactured without and with steel fibers in a volume fraction of 60 kg/m3 (0.76 % by volume), and three different initial prestress forces. Static and fatigue tests were carried out on the ties. Static tests showed that steel fibers increase the first crack and ultimate bending moments, increase significantly the slip force of the prestressing tendons, reduce crack width, add higher ductility to the ties and decrease the stress in the prestressing tendons. Under dynamic loading the steel fibers decreased the stress in the prestressing tendons by about 50%, which improved significantly the fatigue strength of the tie. A tie without fibers failed after only 150,000 cycles. However, a similar tie, with fibers, resisted 3,000,000 cycles without suffering fatigue failure.

Avaliação de tubos de concreto reforçados com fibras de aço segundo a NBR 8890

Pós-graduação em Engenharia Civil - FEIS

Obtaining carbonation depth of concrete used two different procedures standard EHE-08

In the Standard EHE 08, for the first time, durability acquires the status of Limit State. Article 8 provides that the term Durability limit state, produced by physical and chemical actions, different loads and actions of structural analysis, which can degrade the concrete and reinforcement to unacceptable limits. The verification of this limit state can be done through a procedure set out in the provisions of the Standard. This procedure is based on the use of tables that, depending on the aggressiveness of the environment in which the structure is the concrete strength and the life of the project, setting the quality of the concrete cover (minimum thickness and maximum water cement ratio of concrete used) and the maximum crack width. This procedure, simple in its application, provides highly secure solutions. In addition, on Annex 9, the Standard EHE 08 offers models for testing the durability limit state in cases of corrosion of reinforcement due to carbonation of concrete or entry of chloride ions. The results obtained with these models are tighter than those obtained with the procedure of the articles. In this paper we use both methods in the study of reinforced concrete structures with potential problems of corrosion of reinforcement due to carbonation of concrete. Later checking the results obtained by both procedures. Results demonstrate that the use of the models listed in Annex 9 of Standard EHE 08 offer cheaper solutions than those obtained using the procedure of the articles

Coupled model of initiation and propagation of corrosion in reinforced concrete

Corrosion of reinforcing steel in concrete due to chloride ingress is one of the main causes of the deterioration of reinforced concrete structures. Structures most affected by such a corrosion are marine zone buildings and structures exposed to de-icing salts like highways and bridges. Such process is accompanied by an increase in volume of the corrosión products on the rebarsconcrete interface. Depending on the level of oxidation, iron can expand as much as six times its original volume. This increase in volume exerts tensile stresses in the surrounding concrete which result in cracking and spalling of the concrete cover if the concrete tensile strength is exceeded. The mechanism by which steel embedded in concrete corrodes in presence of chloride is the local breakdown of the passive layer formed in the highly alkaline condition of the concrete. It is assumed that corrosion initiates when a critical chloride content reaches the rebar surface. The mathematical formulation idealized the corrosion sequence as a two-stage process: an initiation stage, during which chloride ions penetrate to the reinforcing steel surface and depassivate it, and a propagation stage, in which active corrosion takes place until cracking of the concrete cover has occurred. The aim of this research is to develop computer tools to evaluate the duration of the service life of reinforced concrete structures, considering both the initiation and propagation periods. Such tools must offer a friendly interface to facilitate its use by the researchers even though their background is not in numerical simulation. For the evaluation of the initiation period different tools have been developed: Program TavProbabilidade: provides means to carry out a probability analysis of a chloride ingress model. Such a tool is necessary due to the lack of data and general uncertainties associated with the phenomenon of the chloride diffusion. It differs from the deterministic approach because it computes not just a chloride profile at a certain age, but a range of chloride profiles for each probability or occurrence. Program TavProbabilidade_Fiabilidade: carries out reliability analyses of the initiation period. It takes into account the critical value of the chloride concentration on the steel that causes breakdown of the passive layer and the beginning of the propagation stage. It differs from the deterministic analysis in that it does not predict if the corrosion is going to begin or not, but to quantifies the probability of corrosion initiation. Program TavDif_1D: was created to do a one dimension deterministic analysis of the chloride diffusion process by the finite element method (FEM) which numerically solves Fick’second Law. Despite of the different FEM solver already developed in one dimension, the decision to create a new code (TavDif_1D) was taken because of the need to have a solver with friendly interface for pre- and post-process according to the need of IETCC. An innovative tool was also developed with a systematic method devised to compare the ability of the different 1D models to predict the actual evolution of chloride ingress based on experimental measurements, and also to quantify the degree of agreement of the models with each others. For the evaluation of the entire service life of the structure: a computer program has been developed using finite elements method to do the coupling of both service life periods: initiation and propagation. The program for 2D (TavDif_2D) allows the complementary use of two external programs in a unique friendly interface: • GMSH - an finite element mesh generator and post-processing viewer • OOFEM – a finite element solver. This program (TavDif_2D) is responsible to decide in each time step when and where to start applying the boundary conditions of fracture mechanics module in function of the amount of chloride concentration and corrosion parameters (Icorr, etc). This program is also responsible to verify the presence and the degree of fracture in each element to send the Information of diffusion coefficient variation with the crack width. • GMSH - an finite element mesh generator and post-processing viewer • OOFEM – a finite element solver. The advantages of the FEM with the interface provided by the tool are: • the flexibility to input the data such as material property and boundary conditions as time dependent function. • the flexibility to predict the chloride concentration profile for different geometries. • the possibility to couple chloride diffusion (initiation stage) with chemical and mechanical behavior (propagation stage). The OOFEM code had to be modified to accept temperature, humidity and the time dependent values for the material properties, which is necessary to adequately describe the environmental variations. A 3-D simulation has been performed to simulate the behavior of the beam on both, action of the external load and the internal load caused by the corrosion products, using elements of imbedded fracture in order to plot the curve of the deflection of the central region of the beam versus the external load to compare with the experimental data.

Experimental and numerical study of cracking of concrete due to reinforcement corrosion

La corrosión del acero es una de las patologías más importantes que afectan a las estructuras de hormigón armado que están expuestas a ambientes marinos o al ataque de sales fundentes. Cuando se produce corrosión, se genera una capa de óxido alrededor de la superficie de las armaduras, que ocupa un volumen mayor que el acero inicial; como consecuencia, el óxido ejerce presiones internas en el hormigón circundante, que lleva a la fisuración y, ocasionalmente, al desprendimiento del recubrimiento de hormigón. Durante los últimos años, numerosos estudios han contribuido a ampliar el conocimiento sobre el proceso de fisuración; sin embargo, aún existen muchas incertidumbres respecto al comportamiento mecánico de la capa de óxido, que es fundamental para predecir la fisuración. Por ello, en esta tesis se ha desarrollado y aplicado una metodología, para mejorar el conocimiento respecto al comportamiento del sistema acero-óxido-hormigón, combinando experimentos y simulaciones numéricas. Se han realizado ensayos de corrosión acelerada en condiciones de laboratorio, utilizando la técnica de corriente impresa. Con el objetivo de obtener información cercana a la capa de acero, como muestras se seleccionaron prismas de hormigón con un tubo de acero liso como armadura, que se diseñaron para conseguir la formación de una única fisura principal en el recubrimiento. Durante los ensayos, las muestras se equiparon con instrumentos especialmente diseñados para medir la variación de diámetro y volumen interior de los tubos, y se midió la apertura de la fisura principal utilizando un extensómetro comercial, adaptado a la geometría de las muestras. Las condiciones de contorno se diseñaron cuidadosamente para que los campos de corriente y deformación fuesen planos durante los ensayos, resultando en corrosión uniforme a lo largo del tubo, para poder reproducir los ensayos en simulaciones numéricas. Se ensayaron series con varias densidades de corriente y varias profundidades de corrosión. De manera complementaria, el comportamiento en fractura del hormigón se caracterizó en ensayos independientes, y se midió la pérdida gravimétrica de los tubos siguiendo procedimientos estándar. En todos los ensayos, la fisura principal creció muy despacio durante las primeras micras de profundidad de corrosión, pero después de una cierta profundidad crítica, la fisura se desarrolló completamente, con un aumento rápido de su apertura; la densidad de corriente influye en la profundidad de corrosión crítica. Las variaciones de diámetro interior y de volumen interior de los tubos mostraron tendencias diferentes entre sí, lo que indica que la deformación del tubo no fue uniforme. Después de la corrosión acelerada, las muestras se cortaron en rebanadas, que se utilizaron en ensayos post-corrosión. El patrón de fisuración se estudió a lo largo del tubo, en rebanadas que se impregnaron en vacío con resina y fluoresceína para mejorar la visibilidad de las fisuras bajo luz ultravioleta, y se estudió la presencia de óxido dentro de las grietas. En todas las muestras, se formó una fisura principal en el recubrimiento, infiltrada con óxido, y varias fisuras secundarias finas alrededor del tubo; el número de fisuras varió con la profundidad de corrosión de las muestras. Para muestras con la misma corrosión, el número de fisuras y su posición fue diferente entre muestras y entre secciones de una misma muestra, debido a la heterogeneidad del hormigón. Finalmente, se investigó la adherencia entre el acero y el hormigón, utilizando un dispositivo diseñado para empujar el tubo en el hormigón. Las curvas de tensión frente a desplazamiento del tubo presentaron un pico marcado, seguido de un descenso constante; la profundidad de corrosión y la apertura de fisura de las muestras influyeron notablemente en la tensión residual del ensayo. Para simular la fisuración del hormigón causada por la corrosión de las armaduras, se programó un modelo numérico. Éste combina elementos finitos con fisura embebida adaptable que reproducen la fractura del hormigón conforme al modelo de fisura cohesiva estándar, y elementos de interfaz llamados elementos junta expansiva, que se programaron específicamente para reproducir la expansión volumétrica del óxido y que incorporan su comportamiento mecánico. En el elemento junta expansiva se implementó un fenómeno de despegue, concretamente de deslizamiento y separación, que resultó fundamental para obtener localización de fisuras adecuada, y que se consiguió con una fuerte reducción de la rigidez tangencial y la rigidez en tracción del óxido. Con este modelo, se realizaron simulaciones de los ensayos, utilizando modelos bidimensionales de las muestras con elementos finitos. Como datos para el comportamiento en fractura del hormigón, se utilizaron las propiedades determinadas en experimentos. Para el óxido, inicialmente se supuso un comportamiento fluido, con deslizamiento y separación casi perfectos. Después, se realizó un ajuste de los parámetros del elemento junta expansiva para reproducir los resultados experimentales. Se observó que variaciones en la rigidez normal del óxido apenas afectaban a los resultados, y que los demás parámetros apenas afectaban a la apertura de fisura; sin embargo, la deformación del tubo resultó ser muy sensible a variaciones en los parámetros del óxido, debido a la flexibilidad de la pared de los tubos, lo que resultó fundamental para determinar indirectamente los valores de los parámetros constitutivos del óxido. Finalmente, se realizaron simulaciones definitivas de los ensayos. El modelo reprodujo la profundidad de corrosión crítica y el comportamiento final de las curvas experimentales; se comprobó que la variación de diámetro interior de los tubos está fuertemente influenciada por su posición relativa respecto a la fisura principal, en concordancia con los resultados experimentales. De la comparación de los resultados experimentales y numéricos, se pudo extraer información sobre las propiedades del óxido que de otra manera no habría podido obtenerse. Corrosion of steel is one of the main pathologies affecting reinforced concrete structures exposed to marine environments or to molten salt. When corrosion occurs, an oxide layer develops around the reinforcement surface, which occupies a greater volume than the initial steel; thus, it induces internal pressure on the surrounding concrete that leads to cracking and, eventually, to full-spalling of the concrete cover. During the last years much effort has been devoted to understand the process of cracking; however, there is still a lack of knowledge regarding the mechanical behavior of the oxide layer, which is essential in the prediction of cracking. Thus, a methodology has been developed and applied in this thesis to gain further understanding of the behavior of the steel-oxide-concrete system, combining experiments and numerical simulations. Accelerated corrosion tests were carried out in laboratory conditions, using the impressed current technique. To get experimental information close to the oxide layer, concrete prisms with a smooth steel tube as reinforcement were selected as specimens, which were designed to get a single main crack across the cover. During the tests, the specimens were equipped with instruments that were specially designed to measure the variation of inner diameter and volume of the tubes, and the width of the main crack was recorded using a commercial extensometer that was adapted to the geometry of the specimens. The boundary conditions were carefully designed so that plane current and strain fields were expected during the tests, resulting in nearly uniform corrosion along the length of the tube, so that the tests could be reproduced in numerical simulations. Series of tests were carried out with various current densities and corrosion depths. Complementarily, the fracture behavior of concrete was characterized in independent tests, and the gravimetric loss of the steel tubes was determined by standard means. In all the tests, the main crack grew very slowly during the first microns of corrosion depth, but after a critical corrosion depth it fully developed and opened faster; the current density influenced the critical corrosion depth. The variation of inner diameter and inner volume of the tubes had different trends, which indicates that the deformation of the tube was not uniform. After accelerated corrosion, the specimens were cut into slices, which were used in post-corrosion tests. The pattern of cracking along the reinforcement was investigated in slices that were impregnated under vacuum with resin containing fluorescein to enhance the visibility of cracks under ultraviolet lightening and a study was carried out to assess the presence of oxide into the cracks. In all the specimens, a main crack developed through the concrete cover, which was infiltrated with oxide, and several thin secondary cracks around the reinforcement; the number of cracks diminished with the corrosion depth of the specimen. For specimens with the same corrosion, the number of cracks and their position varied from one specimen to another and between cross-sections of a given specimen, due to the heterogeneity of concrete. Finally, the bond between the steel and the concrete was investigated, using a device designed to push the tubes of steel in the concrete. The curves of stress versus displacement of the tube presented a marked peak, followed by a steady descent, with notably influence of the corrosion depth and the crack width on the residual stress. To simulate cracking of concrete due to corrosion of the reinforcement, a numerical model was implemented. It combines finite elements with an embedded adaptable crack that reproduces cracking of concrete according to the basic cohesive model, and interface elements so-called expansive joint elements, which were specially designed to reproduce the volumetric expansion of oxide and incorporate its mechanical behavior. In the expansive joint element, a debonding effect was implemented consisting of sliding and separation, which was proved to be essential to achieve proper localization of cracks, and was achieved by strongly reducing the shear and the tensile stiffnesses of the oxide. With that model, simulations of the accelerated corrosion tests were carried out on 2- dimensional finite element models of the specimens. For the fracture behavior of concrete, the properties experimentally determined were used as input. For the oxide, initially a fluidlike behavior was assumed with nearly perfect sliding and separation; then the parameters of the expansive joint element were modified to fit the experimental results. Changes in the bulk modulus of the oxide barely affected the results and changes in the remaining parameters had a moderate effect on the predicted crack width; however, the deformation of the tube was very sensitive to variations in the parameters of oxide, due to the flexibility of the tube wall, which was crucial for indirect determination of the constitutive parameters of oxide. Finally, definitive simulations of the tests were carried out. The model reproduced the critical corrosion depth and the final behavior of the experimental curves; it was assessed that the variation of inner diameter of the tubes is highly influenced by its relative position with respect to the main crack, in accordance with the experimental observations. From the comparison of the experimental and numerical results, some properties of the mechanical behavior of the oxide were disclosed that otherwise could not have been measured.