Modeling Cracking in Shell-Type Reinforced Concrete Structures

A three-dimensional (3D) hypoelastic material model for modeling material properties of cracked reinforced concrete is proposed. Material properties of multidirectionally cracked reinforced concrete are represented by the material properties of intact concrete and a number of uniaxially cracked concrete with their coupling solids. Cracking effects due to multiple nonorthogonal cracks are traced in each uniaxially cracked concrete. Tension softening and aggregate interlock occurring at the crack interface as well as tension stiffening and compression softening initiated in concrete between cracks due to multiple nonorthogonal cracks are all incorporated explicitly. RC panels under in-plane loading and RC slab under pure torsion have been analyzed. The developed 3D hypoelastic material model has been proved to be efficient and effective in modeling the material behaviors of cracked reinforced concrete in shell-type RC structures. The deformational response, the ultimate strength, and failure mode can be captured reasonably well.     

Numerical Cracking and Debonding Analysis of RC Beams Reinforced with FRP Sheet

Bonding a fiber reinforced polymer (FRP) sheet to the tension-side surface of reinforced concrete (RC) structures is often performed to upgrade the flexural capacity and stiffness. Except for upper concrete crushing, FRP sheet reinforcing RC structure may fail in sheet rupture, sheet peeloff failure due to opening of a critical diagonal crack, or concrete cover delamination failure from the sheet end. Accompanying the occurrence of these failure modes, reinforcing effects of the FRP sheet will be lost and load-carrying capacity of the RC structures will be decreased suddenly. This study is devoted to developing a numerical analysis method by using a three-dimensional elasto-plastic finite element method to simulate the load-carrying capacity of RC beams failed in the FRP sheet peeloff mode. Here, the discrete crack approach was employed to consider geometrical discontinuities such as opening of cracks, slipping of rebar, and debonding of the FRP sheet. Comparisons between analytical and experimental results confirm that the proposed numerical analysis method is appropriate for estimating the load-carrying capacity and failure behavior of RC beams flexurally reinforced with a FRP sheet.     

纵筋锈蚀无腹筋混凝土梁抗剪性能细观数值研究

以钢筋混凝土梁为研究对象,考虑钢筋非均匀锈蚀膨胀效应,建立三维钢筋混凝土梁剪切破坏分析的数值分析模型。通过多阶段分析方法(钢筋锈蚀阶段,构件性能退化阶段)探索锈蚀对结构力学行为的影响。钢筋的非均匀锈蚀膨胀以施加非均匀径向位移的方式模拟,获得保护层的破坏状态,并以此“最终状态”作为之后混凝土梁静载试验的“初始条件”输入,进而模拟构件的力学行为。在验证了多阶段数值模型合理性的基础上,分析了纵筋锈蚀、剪跨比对无腹筋混凝土梁抗剪性能的影响规律。结果表明,纵筋锈蚀使混凝土梁产生明显的纵向裂缝。纵筋锈蚀率增大,保护层开裂区域增加,梁的抗剪承载力下降严重。另外,剪跨比对梁的抗剪承载力产生影响,剪跨比对未锈蚀梁的影响明显大于对锈蚀梁的影响程度。最后,基于模拟结果对相关设计规范中的抗剪承载力计算公式进行了讨论,发展建立了考虑锈蚀影响的无腹筋混凝土梁抗剪承载力计算方法。      

Seismic Behavior of Concrete Columns Reinforced by Steel-FRP Composite Bars

Steel-fiber-reinforced polymer (FRP) composite bars (SFCBs) are a novel reinforcement for concrete structures. Because of the FRP’s linear elastic characteristic and high ultimate strength, they can achieve a stable postyield stiffness even after the inner steel bar has yielded, which subsequently enables a performance-based seismic design to easily be implemented. In this study, lateral cyclic loading tests of concrete columns reinforced either by SFCBs or by ordinary steel bars were conducted with axial compression ratios of 0.12. The main variable parameters were the FRP type (basalt or carbon FRP) and the steel/FRP ratio of the SFCBs. The test results showed the following: (1)?compared with ordinary RC columns, SFCB-reinforced concrete columns had a stable postyield stiffness after the SFCB’s inner steel bar yielded; (2)?because of the postyield stiffness of the SFCB, the SFCB-reinforced concrete columns exhibited less column-base curvature demand than ordinary RC columns for a given column cap lateral deformation. Thus, reduced unloading residual deformation (i.e., higher postearthquake reparability) of SFCB columns could be achieved; (3)?the outer FRP type of SFCB had a direct influence on the performance of SFCB-reinforced concrete columns, and concrete columns reinforced with steel-basalt FRP (BFRP) composite bars exhibited better ductility (i.e., a longer effective length of postyield stiffness) and a smaller unloading residual deformation under the same unloading displacement when compared with steel-carbon FRP (CFRP) composite bar columns; (4)?the degradation of the unloading stiffness by an ordinary RC column based on the Takeda (TK) model was only suitable at a certain lateral displacement. In evaluating the reparability of important structures at the small plastic deformation stage, the TK model estimated a much smaller residual displacement, which is unsafe for important structures.     

Calculation of Moisture Distribution in Early-Age Concrete

The moisture content in concrete pores is a critical parameter for most of the degradation processes suffered by concrete, such as concrete shrinkage and related cracking. The objective of this paper is to present the formulation of a general moisture distribution model for young-age concrete. In the modeling, both cement hydration and moisture diffusion resulted humidity variations are taken into account synchronously. The effect of initial water distribution (after concrete casting) on the development of moisture distribution is considered by introducing a critical time parameter. The simulation of humidity reduction produced from self-desiccation is based on cement hydration degree that taking the effect of temperature into account by using the equilibrant age concept. During modeling the moisture diffusion, a multilinear model was adopted to simulate the moisture dependent diffusivity. The developed model and finite deferential method can well predict the moisture distribution as well as its variations with time. Good agreement between model predictions and experimental results is found. These results can subsequently be used in shrinkage induced stress field analyses, and further be used for cracking control of concrete structures.     

Simplified Methodology for the Evaluation of the Residual Strength of Corroded Reinforced Concrete Beams

Steel corrosion in reinforced concrete (RC) structures leads to change of steel mechanical properties, longitudinal cracking in the concrete cover, and other related effects that weaken the serviceability and load capacity of the composites. It is therefore extremely important to have methods targeted to the evaluation of the structural damage induced by corrosion for estimating the residual load capacity of a structure, and then for inspection procedures and strengthening the maintenance interventions. This paper presents a simplified methodology capable of providing estimates of the residual life of corroded RC beams. The proposed method uses damaged material properties, and accounts for the length of partial corrosion and the amount of corrosion, concrete loss and change of bond strength within this specified length. A comparison of the model predictions with the experimental results published in the literature shows the validity of the model. It is also concluded that the ultimate flexural moment of corroded RC beam will not significantly influenced by the partially corroded or unbonded length and the bond characteristics over this partial length as long as the tensile steel of the beam can reach its yield strength. In addition, although complete loss of bond over the partial length is assumed to asses the residual strength of corrosion-damaged RC beam, neglecting the influence of bond strength within the corroded length may lead to underestimate the ultimate flexural capacity of the damaged beam, especially when the corrosion level of tensile steel of the RC beam is not very high.     

Toward a Physical Damage Variable for Concrete

Continuum damage mechanics models, while elegant and useful, suffer from what are typically highly idealized relationships between model and material. In this technical note, using three-dimensional (3D) measurements of internal cracking, direct, albeit simple relationships were made between the quantity of cracking and a corresponding scalar damage variable. Geometric properties of internal cracks were measured through 3D image analysis of in situ microtomographic scans of small concrete specimens subject to compression. A scalar damage variable was determined from the changes in stiffness measured in successive loading cycles. Results showed a nearly linear relationship between the damage variable and the volume of new cracks formed. In contrast, results showed a nonlinear relationship between the damage variable and the crack surface area. Such relationships can potentially lead to a more physical basis for continuum damage formulations.     

Scale Transition in Steel-Concrete Interaction. I: Model

This paper deals with the analysis of reinforced concrete (RC) structures with special emphasis on modeling of the interaction between concrete and reinforcement. A new mode for consideration of the response of the composite material at the member (structural) scale is proposed. It is obtained from extension of the fracture energy concept, originally developed for the simulation of cracking of plain concrete, to reinforced concrete. Hereby, the fracture energy related to the opening of primary cracks is increased in order to account for bond slip between steel and concrete. This increase is determined from the distribution of bond slip by means of a one-dimensional composite model introduced at the bar scale. The model consists of steel bars and the surrounding concrete. Between these two components, a nonlinear bond stress–bond slip relation is considered. The obtained results at the bar scale, such as the average crack spacing between adjacent cracks and the load-displacement response of the composite material, form the basis for determination of the increase of the fracture energy at the member scale. The performance of the proposed transition of the steel-concrete interaction from the bar scale to the member scale is assessed by means of reanalysis of experiments performed on RC bars. The application of the respective material model for reinforced concrete to real-life engineering structures is reported in Part II of this series.     

Modeling Cover-Cracking due to Reinforcement Corrosion in RC Structures

Service life of concrete structures is limited by the susceptibility of the reinforcement to corrosion. Oxidation of iron leads to the formulation of various products (such as ferrous and ferric oxides), some of which occupy much greater volume than the original iron that gets consumed by the corrosion process. As corrosion progresses, these products accumulate, thereby generating expansive pressures on the surrounding concrete. The pressure builds up to levels that cause internal cracking around the bar and eventually leads to through cracking of the cover and spalling. Loss of cover marks the end of service life for corrosion-affected concrete structures, because at that stage the reinforcement loses its ability to develop its forces through bond and is no longer protected against further degradation from corrosion. In this paper, a simple analytical model is formulated to demonstrate the mechanical consequences of corrosion-product buildup around the bar. Service life is estimated as the time required for through cracking of the cover, which is identified in the model by a sudden drop of the internal pressure exerted by the corroding bar eventually relaxing to zero. Cracking time is found to be a function of cover, material properties of the surrounding concrete, and rust product, and is controlled by the rate of rust accumulation. In formulating the associated boundary-value problem, the governing equation expressed in terms of radial displacements is discretized using finite differences, whereas cracked concrete is treated as an orthotropic material. Calculated cracking times are correlated against published experimental data. The parametric sensitivity of the model is established with reference to published experimental evidence, and the role of the important design variables in the evolution of this mechanical problem is identified and discussed.     

Design Approach for Calculating Deflection of FRP-Reinforced Concrete

Deflection of reinforced concrete is typically computed with an effective moment of inertia Ie that accounts for nonlinear behavior after the concrete cracks. Existing expressions for Ie tend to overpredict the member stiffness of concrete reinforced with fiber-reinforced polymer (FRP) bars, and an alternative expression is used as the basis for developing a practical design approach to compute deflection. The proposed expression has a rational basis that incorporates basic concepts of tension stiffening to provide a reasonable estimate of deflection for both steel and FRP-reinforced concrete without the need for empirically derived correction factors. Calculation of deflection with the proposed expression for Ie is recommended using the code value for the elastic modulus Ec of concrete because computed values of deflection are relatively insensitive to variations in Ec, and shrinkage restraint is taken into account by using a reduced cracking moment less than the code-based value of the cracking moment Mcr. Ie is conservatively based on the moment at the critical section (where the member stiffness is lowest), unless more accuracy is required with an integration-based expression that gives an equivalent moment of inertia Ie′ to account for the variation in stiffness along the member length. Recommendations are validated by comparison with a database of deflection test results for FRP-reinforced concrete.     

Finite-Element Analysis of Chemical Transport and Reinforcement Corrosion-Induced Cracking in Variably Saturated Heterogeneous Concrete

Reinforcement corrosion owing to chemical attack could lead to premature steel-mortar debonding, concrete cracking, and catastrophic failure of structures if not well attended. In conventional design and maintenance practices, heterogeneous concrete matrix is commonly treated as a homogeneous medium when the evolution of chemical ingress and concrete cracking need to be determined. Such oversimplification has caused significantly inaccurate prediction and evaluation of structural service life. This paper presents a finite-element (FE) model developed to evaluate the service life of reinforced concrete (RC) structures in three key steps: chemical ingress, steel corrosion, and concrete cracking. The mass conservation principle is employed in the first step to model the ingress of multiple chemical species into variably saturated heterogeneous concrete matrix. By using Faraday’s law, steel corrosion and the incurred diametric expansion are then formulated as a transient displacement boundary condition for subsequent analysis of concrete cracking. The cracking pattern of concrete under the expansion force of corrosion products is finally characterized by using a cohesive-fracture approach. The FE model is validated with laboratory experiments.     

Coupled Environmental-Mechanical Damage Model of RC Structures

The evaluation of strength reduction of RC structures subjected to mechanical damage process and chemical attack is carried out, with regard to concrete deterioration and steel corrosion. A coupled environmental-mechanical damage model, developed as an extension of that previously published is presented. Two independent scalar mechanical damage parameters are introduced, each of them representing the degradation mechanisms occurring under tensile and compressive stress conditions. The stiffness recovery upon loading reversal, which is manifest when passing from tension into compression, is fully captured by the proposed model. The environmental damage is strongly related to the diffusion process, as well as to the evolution of the chemical reaction between pollutant and cementitious constituents. An enhanced local method is proposed to regularize the problem of nonobjectivity of the finite-element solution due to the strong strain softening behavior of concrete material. The splitting test of a concrete specimen and a static analysis of an RC frame subjected to mechanical loads and chemical attacks are carried out, and the damage evolution is analyzed in detail.     

组合式钢框架内填预制RC墙结构静力性能有限元分析

钢框架内填预制钢筋混凝土剪力墙结构是新型混合式结构,由钢框架与内填墙组成双重防线,具有良好的抗侧力能力,同时预制构配件和预制装配建筑有利于推动住宅产业化发展.考虑大尺寸内填预制RC墙运输和安装困难的情况,提出竖向和横向组合式钢框架内填RC墙结构,采用ABAQUS建立有限元模型进行结构受力分析.通过分析荷载位移曲线,构件应力分布和变形情况,研究结构破坏特点和受力性能.结果表明,全螺栓结构因其合理的传力路径,有良好的承载力和延性;竖向组合式具有较好的初始刚度和整体承载力,与全螺栓连接预制RC墙有近似的受力性能,便于运输和安装;而横向组合式由于上下板缺乏有效传力路径,初始刚度和最终承载力都明显低于全螺栓和竖向组合式,不利于实际工程应用.      

Deflection Prediction for FRP-Strengthened Concrete Beams

Due to increasing popularity of using fiber-reinforced polymer (FRP) for external strengthening of concrete structures, an urgent demand for understanding the structural behavior of FRP-strengthened structures has been emerging. Unlike conventional reinforced concrete (RC) structures, FRP-strengthened members can exhibit additional flexural capacity in the postyielding stage. This makes RC models for predicting deflection inapplicable in case of FRP-strengthened structures. Therefore, some models have been explicitly developed for evaluating deflection of the strengthened structures. However, most existing models are empirically based, verified with limited experimental results, and require in some cases sophisticated calculation procedures. Accordingly, there is still a demand for a rational and more convenient model for predicting deflection of FRP-strengthened beams. In the current paper, Bischoff’s model, originally proposed for RC and FRP reinforced structures, was extended. Consequently, the developed model is applicable to FRP-strengthened concrete beams besides its validity to both RC and FRP reinforced beams. Validation of the model with some available test data confirmed its accuracy.     

Transverse Cracking of Concrete Bridge Decks: Effects of Design Factors

Early transverse cracking is one of the dominant forms of bridge deck defects experienced by a large number of transportation agencies. These cracks often initiate soon after the bridge deck is constructed, and they are caused by restrained shrinkage of concrete. Transverse cracks increase the maintenance cost of a bridge structure and reduce its life span. Most of the past efforts addressing transverse bridge deck cracking have focused on changes over the years in concrete material properties and construction practices. However, recent studies have shown the importance of design factors on transverse bridge deck cracking. This paper presents results of a comprehensive finite-element (FE) study of deck and girder bridge systems to understand and evaluate crack patterns, stress histories, as well as the relative effect of different design factors such as structural stiffness on transverse deck cracking. The results of this study demonstrate the development of transverse deck cracking and emphasize the importance of these design factors. They also recommend preventive measures that can be adopted during the design stage in order to minimize the probability of transverse deck cracking.     

Transverse Thermal Expansion of FRP Bars Embedded in Concrete

Fiber reinforced polymers (FRPs) have a thermal expansion in the transverse direction much higher than in the longitudinal direction and also higher than the thermal expansion of hardened concrete. The difference between the transverse coefficient of thermal expansion of FRP bars and concrete may cause splitting cracks within the concrete under temperature increase and, ultimately, failure of the concrete cover if the confining action of concrete is insufficient. This paper presents the results of an experimental investigation to analyze the effect of the ratio of concrete cover thickness to FRP bar diameter (c/db) on the strain distributions in concrete and FRP bars, using concrete cylindrical specimens reinforced with a glass FRP bar and subjected to thermal loading from ?30?to?+80°C. The experimental results show that the transverse coefficient of thermal expansion of the glass FRP bars tested in this study is found to be equal to 33 (×10?6?mm/mm/°C), on average and the ratio between the transverse and longitudinal coefficients of thermal expansion of these FRP bars is equal to 4. Also, the cracks induced by high temperature start to develop on the surface of concrete cylinders at a temperature varying between +50 and +60°C for specimens having a ratio of concrete cover thickness to bar diameter c/db less than or equal to 1.5. A ratio of concrete cover thickness to glass fiber reinforced polymers (GFRP) bar diameter c/db greater than or equal to 2.0 is sufficient to avoid cracking of concrete under high temperature up to +80°C. The analytical model, presented in this paper, is in good agreement with the experimental results, particularly for negative temperature variations.     

Active Confinement of Reinforced Concrete Bridge Columns Using Shape Memory Alloys

This paper presents experimental and analytical work conducted to explore the feasibility of using an innovative technique for seismic retrofitting of RC bridge columns using shape memory alloys (SMAs) spirals. The high recovery stress associated with the shape recovery of SMAs is being sought in this study as an easy and reliable method to apply external active confining pressure on RC bridge columns to improve their ductility. Uniaxial compression tests of concrete cylinders confined with SMA spirals show a significant improvement in the concrete strength and ductility even under small confining pressure. The experimental results are used to calibrate the concrete constitutive model used in the analytical study. Analytical models of bridge columns retrofitted with SMA spirals and carbon fiber-reinforced polymer (CFRP) sheets are studied under displacement-controlled cyclic loading and a suite of strong earthquake records. The analytical results proves the superiority of the proposed technique using SMA spirals to CFRP sheets in terms of enhancing the strength and effective stiffness and reducing the concrete damage and residual drifts of retrofitted columns.     

Theoretical Study on Short-Term and Long-Term Deflections of Fiber Reinforced Polymer Prestressed Concrete Beams

This paper presents the methods for predicting the short-term and time-dependent deflections of fully or partially prestressed concrete beams with fiber reinforced polymer (FRP) tendons under sustained bending moment and axial force. The age-adjusted effective modulus method is used to model the creep behavior in the concrete and the relaxation in the FRP prestressing tendons. A tension-stiffening model is proposed to evaluate the stiffness of the section after cracking. The analytical values are compared to the test results and it is found that the analytical values are in good agreement with the experimental results.     

New Directions in Concrete Health Monitoring Technology

The NSF-sponsored Center for Advanced Cement-Based Materials is actively involved in research aimed at the development of technologies for health monitoring and nondestructive evaluation of the concrete infrastructure. This paper summarizes pertinent research performed at the center. Basic findings from several new laboratory-based nondestructive evaluation techniques for concrete are reported. The described techniques are based on measurements of mechanical waves that propagate in the concrete. First, ultrasonic longitudinal wave (also called the L-wave or P-wave) signal transmission (attenuation) measurements are shown to be sensitive to the presence of damage in the form of distributed cracking in concrete. Next, experimental procedures that enable practical one-sided wave signal transmission measurements to be performed on concrete structures are described. The utility of the signal transmission measurement is demonstrated by two experimental test series; the depths of surface-opening cracks in concrete slabs are estimated and the extent and nature of autogenous healing in concrete disks are studied. Finally, an approach by which fatigue-induced damage in concrete structures is nondestructively monitored is described. Vibration frequencies are shown to be sensitive to the presence of fatigue-induced cracking in concrete specimens; changes in the vibration frequency of a concrete specimen during fatigue tests are related to the remaining fatigue life of the test specimens.     

退化钢筋混凝土桥梁概率耐久性评估方法

提出了考虑时间、空间变异特性的退化钢筋混凝土桥梁耐久性概率评估的随机有限元方法.首先,通过考虑钢筋与混凝土之间时变的粘结滑移关系及腐蚀钢筋的应力应变关系,采用弥散裂纹方法对退化钢筋混凝土桥梁进行有限元分析.然后,提出了退化钢筋混凝土桥梁耐久性概率评估的随机有限元分析方法,基于文献及现场调查的数据,采用蒙特卡罗仿真方法对钢筋均匀及点锈蚀、混凝土保护层厚度、表面氯离子含量、氯离子扩散系数及腐蚀率等进行随机抽样,考虑这些时变及空间变异的因素对钢筋混凝土桥梁可靠度的影响.最后,以天津滨海新区的一座钢筋混凝土梁桥为例分析了所提方法的应用.