Evaluation of crack width in FRC structures and application to tunnel linings

When steel bars are placed in a concrete structure, the evaluation of crack width and crack spacing is generally required in the serviceability stage. According to more or less aggressive conditions, crack width shall be limited in order to avoid, for instance, the corrosion of steel reinforcement. The presence of fibers in the concrete cast may help to achieve this goal, since fibers remarkably increase the bridging actions across a crack. However, new mechanical models are needed to evaluate these effects, which are generally neglected by classical approaches. Code requirements are based on semi-empirical formulae, in which the average structural performances are analyzed by referring to a single cross-section, instead of a wide portion of an R/FRC or RC element in bending. To evaluate crack patterns more accurately, a suitable block model is therefore introduced in this paper. With the new approach, the bridging effects of fibers, as well as the bond-slip mechanism between steel bars and FRC in tension, are taken into account. By means of such model, it is possible ble to predict at one time the values of crack width, crack spacing, and crack depth, and compare them to data obtained by bending tests on concrete beams. Moreover, to evaluate the possible crack patterns in R/FRC tunnel linings, the proposed block model has been extended to the serviceability stage of massive structures subjected to combined compressive and bending actions. This paper follows a previous work by the same authors (Chiaia et al. Mater Struct 40(6):593–694, 2007) and completes the design procedures for FRC cast-in-place tunnel linings.     

Structural effects of FRC creep

Research studies in the last 20 years allowed to obtain reliable rules for designing structures made of fiber reinforced concrete (FRC). However, design aspects like the long-term behavior of FRC, especially when synthetic fibers are adopted, require further research. Long-term behavior includes aging and creep. Aging represent the change of fiber properties into the concrete environment, which may reduce the structural bearing capacity; when present, it is an important issue for the structural safety, especially when fibers are the only reinforcement. Aging of fibers must be proven by experimental tests. Creep is a complex phenomenon, roughly considered by building codes even for traditional reinforced concrete (RC) structures. The introduction of fibers do not change anything in concrete matrix and, before cracking, in the material concrete creep behavior is not expected any change. After cracking, the structural effect of FRC creep depends on the degree of structural redundancy and on the presence of rebars since creep produces a stress redistribution in the structure or from FRC to the rebars. When FRC post-cracking resistance is necessary for equilibrium requirements, in structures with cracked sections in service conditions the structural deferred response has to be analyzed by considering the FRC creep behavior. When FRC is used for resisting secondary actions and rebars are present for equilibrium requirements, the response of a FRC element (with rebars and fibers) will be identical to a conventional RC; FRC contributes by controlling the crack development under both short and long term loading.     

采用通用有限元程序的弥散裂缝模型和分层壳单元模拟钢筋混凝土构件裂缝宽度

该文基于弥散裂缝模型,采用通用有限元程序的分层壳单元计算钢筋混凝土构件裂缝宽度的方法。讨论了理论基础,Bazant和Oh提出的经典裂缝带理论主要针对素混凝土构件,严重的局部化效应导致显著的网格依赖性,而将裂缝带理论拓展到工程常用的配筋混凝土构件时,由于多裂缝分布发展的特点,裂缝带宽应修改为平均裂缝间距而使计算结果与网格无关。在理论基础讨论的基础上,给出了采用通用有限元程序的弥散裂缝模型和分层壳单元计算钢筋混凝土构件裂缝宽度的计算流程,其中,平均裂缝间距将有限元分析中的“应变”概念和工程设计中的“裂缝宽度”概念紧密联系起来,是计算流程中最关键的参数。以某承受负弯矩的简支组合梁混凝土板开裂分析为例,验证并讨论了网格相关性、大软化模量导致数值收敛困难的应对策略、平均裂缝间距的决定性作用等重要问题。     

Strain compatibility between HPFRCC and steel reinforcement

To build reinforced concrete structures able to mitigate steel corrosion produced by environmental attack, a reduced crack width should appear in tensile concrete. At least in the serviceability stage, fibers added to ordinary concrete could be a way to satisfy this requirement. Depending on the type, on the volume content and on the aspect ratio of fibers, FRC (fiber reinforced concrete) can show a higher ductility and sometimes a higher tensile strength than ordinary concrete. However, with or without fibers, concrete cannot produce tensile strains totally compatible with those of the steel rebars. To overcome this problem, new FRCs, called High Performance Fiber-Reinforced Cementitious Composites (HPFRCC), have been recently tailored to develop an ultra-high ductility. In these composites, since the strain at maximum stress is higher than the steel strain at yielding, strain incompatibility vanishes. In the present paper, in order to prove the existence of compatible strains between steel and HPFRCC, numerical results and experimental measurements are compared. This is possible by introducing a mechanical model of tension-stiffening, and by referring to tests to reinforced HPFRCC elements in tension. The good agreement between theoretical and experimental results is also found for reinforced HPFRCC beams in bending.     

Cracking behaviour of concrete beams reinforced with a combination of ordinary reinforcement and steel fibers

The paper presents an experimental and theoretical study on the cracking behaviour of concrete beams having longitudinal tension reinforcement and various combinations of volume and aspect ratio of steel fibers. Five full-scale beams with a concrete compressive strength of 42 MPa were tested. The mechanical properties of the steel fiber concrete under tension were determined by means of the four-point bending test specified in the Belgian standard NBN B15-238. The experimental results show that the addition of steel fibers decreases both the crack spacing and the crack width. A modification of the model of Nemegeeret al. to predict crack widths is suggested.     

钢筋钢纤维自密实混凝土梁裂缝宽度试验研究

通过9根钢筋钢纤维自密实混凝土梁的四点弯曲试验,分析了钢纤维体积率、配筋率对钢筋钢纤维自密实混凝土梁裂缝形态、裂缝宽度以及裂缝间距等参数的影响。结果表明：在自密实混凝土梁中掺加钢纤维可有效限制裂缝的扩展,掺入体积率为0.38%和0.64%的钢纤维,可使自密实混凝土梁在正常使用阶段的最大裂缝宽度减小31%~56%,平均裂缝间距减小15%~28%,纵筋应变减小40%~56%。考虑钢纤维在试验梁开裂截面的分布以及应力传递机理,结合试验数据提出了钢筋钢纤维自密实混凝土梁最大裂缝宽度的计算公式,并与MC 2010、RILEM TC-162 TDF及CECS 38：2004的公式进行了对比。计算结果表明：该文建议公式计算的最大裂缝宽度与试验值吻合较好,可用于钢筋钢纤维自密实混凝土梁最大裂缝宽度的分析与验算。     

预应力铝合金筋嵌入式补强钢筋混凝土梁裂缝分析与计算

完成了7根预应力7075铝合金筋嵌入式补强混凝土梁试件的四点弯曲静载试验,应用非接触式数字图像相关法对混凝土加固梁的裂缝形成、分布、裂缝宽度和间距进行分析,研究了铝合金加固量、预应力以及预应力水平对嵌入式补强混凝土梁试件破坏模式和裂缝特性的影响。试验研究表明:铝合金筋嵌入式补强法可以显著提高混凝土梁的承载能力,施加预应力进一步增强加固梁的强度并延缓混凝土开裂和钢筋屈服;端部锚固有效避免了加固梁试件发生剥离破坏,提高高强铝合金强度利用率;施加预应力、增大加固量和提高预应力水平,均可以有效控制裂缝扩展,减小裂缝宽度和间距;根据中国《混凝土结构设计规范》(GB 50010?2010)对嵌入式非预应力/预应力铝合金筋补强混凝土梁的裂缝宽度和分布进行了计算,理论计算值与试验结果吻合良好,结果表明:中国混凝土结构设计规范给出的正常使用状态下最大裂缝宽度计算方法能够较好地考虑预应力、加固筋数量以及预应力水平对最大裂缝宽度的影响,适用于嵌入式补强钢筋混凝土受弯构件的裂缝计算与分析。     

Design provisions for crack spacing and width in RC elements externally bonded with FRP

Verification of serviceability is a key issue in reinforced concrete (RC) elements; for RC elements externally bonded with fibre reinforced plastic (FRP) laminates and sheets cracking phenomena are usually verified by adopting the same approach used for steel RC elements. The available code provisions for crack width and spacing in steel RC elements are reviewed in this paper in order to ascertain the reliability of their application to RC elements strengthened with FRP sheets. Experimental results belonging to test programmes performed by the authors and other researchers on RC elements externally bonded with FRP were compared with existing code provisions in terms of crack width and spacing.A new formula for crack spacing, calibrated on the experimental results, is proposed for use in the expression given by the published version of EC2 for calculating crack width in RC elements externally bonded with FRP.     

Cracking characteristics of reinforced steel fiber concrete beams under short- and long-term loadings

In this paper, an analytical method for the prediction of maximum crack width in reinforced steel fiber concrete (SFC) beams under short-term loading is first presented. The method accounts for the enhanced cracking strength, restraint against crack growth, and reduced tensile steel strains due to the presence of steel fibers. Based on a correlation analysis, a semiempirical formula for the long-term crack widths in reinforced SFC beams under sustained loads is also proposed. Tests were carried out on 10 beams to investigate the effect of steel fiber content on the cracking characteristics in both the short- and long-term. The results indicated that the use of steel fibers greatly reduced the maximum crack widths in reinforced concrete beams. Good agreement was generally obtained between the analytical predictions and test results.     

Development of kenaf fibre reinforced polymer laminate for shear strengthening of reinforced concrete beam

Fabrication of green fibre composite laminate for strengthening of reinforced concrete structure is one of the current interests in the field of construction industry. The aim of this research was to develop kenaf fibre reinforced polymer (KFRP) laminate for shear strengthening of reinforced concrete beam. Comprehensive design and theoretical models were also proposed for KFRP laminate shear strengthened beam. In the experimental programme, KFRP laminate had been fabricated with various fibre content to obtain optimal mix ratio. Physical and mechanical properties of KFRP laminates were experimentally investigated. Three reinforced concrete beam specimens were prepared for structural investigations. Results showed that KFRP laminate with maximum fibre content had the highest tensile strength and the laminate was found to be elastic isotropic in nature. The KFRP laminate strengthened beam had 100 % higher shear crack load and 33 % ultimate failure load as compared to un-strengthened control beam. It reduced the numbers and width of cracks and had shown strain compatibility behavior with shear reinforcement. The failure load, ductility, crack patterns and strain characteristics of KFRP laminate strengthened beam were found to be closely comparable with CFRP laminate strengthened beam. The experimental results satisfactorily verified the proposed design and theoretical models.     

Crack width for thick offshore plates

Using thick concrete covers in offshore and nuclear containment applications is increasing because it is a durability issue. Most crack width models indicate that increasing concrete covers results in increased crack spacing and hence increased crack width this means that thick concrete covers are detrimental to crack control. In this paper, tests were conducted on two groups of thick plates. Group I, included five specimens that had two concrete covers, 60 and 70 mm. Group II, included four thick heavy reinforced specimens; all specimens in this group had a clear concrete cover of 70 mm. Using thick concrete covers is a common practice in offshore and containment structures for nuclear power generation. The objective of testing both groups is to measure flexural crack widths under different load levels and, most importantly, under service loads. Group I was intended primarily to investigate the effect of increasing the cover and bar spacing on the crack width. Group II represents a unique experimental investigation in assessing the magnitude of crack width in full-scale thick plates under service loads. An analytical investigation is presented in this work. The main focus of this study is to evaluate the available codes’ models for estimating the crack width of thick concrete plates having thick concrete covers used for offshore and nuclear containment structure applications. It was concluded that crack control can still be achieved by limiting the spacing of the reinforcing steel despite using thick concrete covers.     

Design and structural applications of stress-crack width relations in fibre reinforced concrete

The stress-crack width relationship has been shown to be the key to an understanding of fracture propagation in and mechanical behaviour in tension of fibre reinforced concrete materials and structures. A model is derived for the stress-crack width relationship for randomly oriented short fibre composites which takes hybrid fibre systems and possible fibre rupture into account. It is shown how this stress-crack width relationship can be included in a structural model for the prediction of crack widths in reinforced concrete structures. With this combination of models a rational design tool for the design of composite materials and structures has been established. It is shown how different fibre systems can be tested for structural applicability and how combined material and structural optimization can take place.     

A design model for fibre reinforced concrete beams pre-stressed with steel and FRP bars

This paper presents a design oriented model to determine the moment–curvature relationship of elements of rectangular cross section failing in bending, made by strain softening or strain hardening fibre reinforced concrete (FRC) and reinforced with perfectly bonded pre-stressed steel and fibre reinforced polymeric (FRP) bars. Since FRP bars are not affected by corrosion, they have the minimum FRC cover thickness that guaranty proper bond conditions, while steel bars are positioned with a thicker FRC cover to increase their protection against corrosion. Using the moment–curvature relationship predicted by the model in an algorithm based on the virtual work method, a numerical strategy is adopted to evaluate the load–deflection response of statically determinate beams. The predictive performance of the proposed formulation is assessed by simulating the response of available experimental results. By using this model, a parametric study is carried out in order to evaluate the influence of the main parameters that characterize the post cracking behaviour of FRC, and the pre-stress level applied to FRP and steel bars, on the moment–curvature and load–deflection responses of this type of structural elements. Finally the shear resistance of this structural system is predicted.     

Short and long-term cracking behaviour of GFRP reinforced concrete beams

A total of ten simply supported beams reinforced with different amounts of GFRP and steel bars were subjected to two consecutive test phases in order to evaluate their short and long-term cracking behaviour. The beams were initially tested up to service load and subjected to two additional load cycles. Subsequently, the specimens were subjected to two different levels of sustained load for 250 days. The effect of cyclic load during short-term tests resulted in an increase in crack width up to 25% more than the initial value. The sustained load led to an increase in crack width up to 2.9 times larger than that measured under the corresponding short-term load. A similar cracking behaviour was observed when reinforcing solutions with similar stiffness (GFRP or steel bars) were used.Existing models to estimate crack spacing and crack width for FRP and steel reinforced concrete elements, including ACI 440.1R-06, Eurocode 2 and Model Code 2010 are discussed and their performance is assessed against the experimental results. Model Code 2010 was found to yield more accurate predictions of the cracking behaviour of the test specimens under both short-term and long-term loading.     

Experimental study and code predictions of fibre reinforced polymer reinforced concrete (FRP RC) tensile members

Due to their different mechanical properties, cracking and deformability behaviour of FRP reinforced concrete (FRP RC) members is quite different from traditional steel reinforced concrete (SRC) having great incidence on their serviceability design. This paper presents and discusses the results of an experimental programme concerning concrete tension members reinforced with glass fibre reinforced polymer (GFRP) bars. The main aim of the study is to evaluate the response of GFRP reinforced concrete (GFRP RC) tension members in terms of cracking and deformations. The results show the dependence of load-deformation response and crack spacing on the reinforcement ratio. The experimental results are compared to prediction models from codes and guidelines (ACI and Eurocode 2) and the suitability of the different approaches for predicting the behaviour of tensile members is analysed and discussed.     

Crack profile in RC,R/FRCC and R/HPFRCC members in tension

The theoretical approaches used for the evaluation of crack width in reinforced concrete (RC) structures, are generally based on the hypothesis of parallel crack surfaces. In this way, crack width measured on the concrete cover should be equal to that on the bar surface. The results of several experimental analyses, developed during the past years in many Research Institutes, do not justify this assumption. On the contrary, even in RC members under tensile actions, crack width appears wider on external surface than on rebar–concrete interface. To better define the effective crack profile of RC structures, a new model, able to analyze the whole structural response of RC ties, is here presented. In the proposed approach, all the physical phenomena involved in the cracking process are taken into account: the bond-slip behavior between steel rebar and tensile concrete, the nonlinear fracture mechanics of concrete in tension, and the mechanism of aggregate interlock. Crack profiles computed with this model seem to be in accordance with those experimentally measured in RC elements in tension. A good agreement between numerical results and experimental data is also found both in case of steel rebar and ordinary fiber reinforced cementitious composites (R/FRCC), and in case of steel rebar and high?performance fiber reinforced cementitious composites (R/HPFRCC).     

钢纤维混凝土带裂状态下抗弯承载力的计算方法

在混凝土中加入钢纤维,可使开裂后的混凝土仍能在开裂面传递拉应力,但钢纤维所传递的拉应力随裂缝宽度的增加而发生变化.因此以前认为钢纤维混凝土抗拉强度与裂缝宽度无关的设计方法,并未反映钢纤维混凝土的真实受力特性.本文通过四点弯曲试验,得到荷载与裂缝张开位移的关系.然后用受力平衡的方法,反算出钢纤维混凝土开裂后拉应力与裂缝宽度的关系,即拉伸软化曲线.通过分析发现,典型的钢纤维混凝土拉伸软化曲线,可以用其四个关键点的直线段描述.并根据实验数据,给出各段直线的确定方法.最后根据裂缝宽度和拉伸软化曲线,可以确定在指定裂缝宽度下,钢纤维混凝土的抗弯承载力.     

An experimental study on the tensile strength of steel fiber reinforced concrete

This paper deals with steel fiber reinforced concrete mechanical static behaviour and with its classification with respect to fibers content and mix-design variations. A number of experimental tests were conducted to investigate uniaxial compressive strength and tensile strength. Different mixtures were prepared varying both mix-design and fiber length. Fibers content in volume was of 1% and 2%. Mechanical characterization was performed by means of uniaxial compression tests with the aim of deriving the ultimate compressive strength of fiber concrete. Four-point bending tests on notched specimens were carried out to derive the first crack strength and the ductility indexes. The tensile strength of steel fiber reinforced concrete (SFRC) was obtained both from an experimental procedure and by using an analytical modelling. The experimental tests showed the different behaviour of SFRC with respect of the different fiber content and length. Based on the experimental results, an analytical model, reported in literature and used for the theoretical determination of direct tensile strength, was applied with the aim of making a comparison with experimental results. The comparison showed good overall agreement.     

Fatigue life prediction of fiber reinforced concrete under flexural load

This paper presents a semi-analytical method to predict fatigue behavior in flexure of fiber reinforced concrete (FRC) based on the equilibrium of force in the critical cracked section. The model relies on the cyclic bridging law, the so-called stress–crack width relationship under cyclic tensile load as the fundamental constitutive relationship in tension. The numerical results in terms of fatigue crack length and crack mouth opening displacement as a function of load cycles are obtained for given maximum and minimum flexure load levels. Good correlation between experiments and the model predictions is found. Furthermore, the minimum load effect on the fatigue life of beams under bending load, which has been studied experimentally in the past, is simulated and a mechanism-based explanation is provided in theory. This basic analysis leads to the conclusion that the fatigue performance in flexure of FRC materials is strongly influenced by the cyclic stress–crack width relationship within the fracture zone. The optimum fatigue behavior of FRC structures in bending can be achieved by optimising the bond properties of aggregate–matrix and fiber–matrix interfaces.     

基于粘结-滑移的FRP筋钢纤维轻骨料混凝土梁裂缝宽度计算方法

将纤维增强筋(FRP筋)混凝土梁裂缝的开展过程视作FRP筋由两侧混凝土中拔出的过程,建立了基于粘结-滑移的FRP筋轻骨料混凝土梁裂缝宽度微分方程。根据规范给出的裂缝宽度限值,合理确定滑移量上限,提出并引入了适用于梁正常使用阶段的FRP筋钢纤维轻骨料混凝土“低滑移”阶段粘结-滑移本构模型。进而,在明确最大裂缝间距l_max、裂缝宽度放大系数h₂/h₁与裂缝截面纤维混凝土残余应力σ_fib等特征参数的基础上,利用迭代算法建立了FRP筋钢纤维轻骨料混凝土梁最大裂缝宽度计算模型。基于正常使用阶段裂缝宽度实测数据对建议模型的适用性进行评估,结果表明:裂缝宽度限值0.5 mm内,建议模型能够准确预测FRP筋钢纤维轻骨料混凝土梁的最大裂缝宽度。