Simulation of Corrosion-Induced Cracking of Reinforced Concrete Based on Fracture Phase Field Method

Accurate simulation of the cracking process caused by rust expansion of reinforced concrete(RC)structures plays an intuitive role in revealing the corrosion-induced failure mechanism.Considering the quasi-brittle fracture of concrete,the fracture phase field driven by the compressive-shear term is constructed and added to the traditional brittle fracture phase field model.The rationality of the proposed model is verified by a mixed fracture example under a shear displacement load.Then,the extended fracture phase model is applied to simulate the corrosion-induced cracking process of RC.The cracking patterns caused by non-uniform corrosion expansion are discussed for RC specimens with homogeneous macroscopically or heterogeneous with different polygonal aggregate distributions at the mesoscopic scale.Then,the effects of the protective layer on the crack propagation trajectory and cracking resistance are investigated,illustrating that the cracking angle and cracking resistance increase with the increase of the protective layer thickness,consistent with the experimental observation.Finally,the corrosion-induced cracking process of concrete specimens with large and small spacing rebars is simulated,and the interaction of multiple corrosion cracking is easily influenced by the reinforcement spacing,which increases with the decrease of the steel bar interval.These conclusions play an important role in the design of engineering anti-corrosion measures.The fracture phase field model can provide strong support for the life assessment of RC structures.

Effect of Shrinkage Reducing Agent and Steel Fiber on the Fluidity and Cracking Performance of Ultra-High Performance Concrete

Due to the low water-cement ratio of ultra-high-performance concrete(UHPC),fluidity and shrinkage cracking are key aspects determining the performance and durability of this type of concrete.In this study,the effects of different types of cementitious materials,chemical shrinkage-reducing agents(SRA)and steel fiber(SF)were assessed.Compared with M2-UHPC and M3-UHPC,M1-UHPC was found to have better fluidity and shrinkage cracking performance.Moreover,different SRA incorporation methods,dosage and different SF types and aspect ratios were implemented.The incorporation of SRA and SF led to a decrease in the fluidity of UHPC.SRA internal content of 1%(NSRA-1%),SRA external content of 1%(WSRA-1%),STS-0.22 and STE-0.7 decreased the fluidity of UHPC by 3.3%,8.3%,9.2%and 25%,respectively.However,SRA and SF improved the UHPC shrinkage cracking performance.NSRA-1%and STE-0.7 reduced the shrinkage value of UHPC by 40%and 60%,respectively,and increased the crack resistance by 338%and 175%,respectively.In addition,the addition of SF was observed to make the microstructure of UHPC more compact,and the compressive strength and flexural strength of 28 d were increased by 26.9%and 19.9%,respectively.

Quantitative crack evaluation in slender reinforced concrete walls with rectangular section

Past earthquakes have shown that cracking affects post-earthquake functionality and accounted for huge repair costs for reinforced concrete(RC)wall buildings,even though the code-compliant seismic design prevents col-lapse.Engineers should know the maximum residual flexural crack width and volume of repair material needed for the flexural cracks to determine the damage degree and the repair cost.This paper presents the experimental campaign on four RC slender walls that investigated the effect of confining reinforcement and thickness of the wall on flexural crack parameters under quasi-static reversed cyclic loading.The width of all flexural cracks was measured when reaching each cycle peak drift and when unloading to zero lateral loads.Crack widths at peak and residual states increased with increasing peak drift.Based on the experimental observations,it was found that the maximum residual crack width is obtained as a simple function of the extreme tension fiber elongation of the wall tensile fiber within±30%error.In addition,this paper outlines methods to calculate the volume of repair material for flexural cracks from the extreme tension fiber elongation of the wall.With the funda-mental rules found from the experiment in this paper,it will become possible to obtain the maximum crack width and the volume of repair material from simple numerical analysis tools such as a multi-spring line element model.

Analytic model of non-uniform corrosion induced cracking of reinforced concrete structure

In order to perfectly reflect the dynamic corrosion of reinforced concrete (RC) cover in practical engineering,an analytic model of non-uniform corrosion induced cracking was presented based on the elastic-plastic fracture mechanics theory.Comparisons with the published experimental data show that the predictions given by the present model are in good agreement with the results both for natural exposed experiments and short-time indoor tests (the best difference is about 2.7%).Also it obviously provides much better precision than those models under the assumption of uniform corrosion (the maximal improved precision is about 48%).Therefore,it is pointed out that the so-called uniform corrosion models to describe the cover cracking of RC should be adopted cautiously.Finally,the influences of thickness of local rusty layer around the reinforcing steel bar on the critical corrosion-induced crack indexes were investigated.It is found that the thickness of local rusty layer has great effect on the critical mass loss of reinforcing steel,threshold expansion pressure,and time to cover cracking.For local rusty layer thickness with a size of a=0.5 mm,the time to cover cracking will increase by about one times when a/b (a,semi-minor axis;b,semi-major axis) changes from 0.1 to 1 mm.

Probabilistic Lifetime Assessment of Marine Reinforced Concrete with Steel Corrosion and Cover Cracking

In order to study the durability behavior of marine reinforced concrete structure suffering from chloride attack, the structural service life is assumed to be divided into three critical stages, which can be characterized by steel corrosion and cover cracking. For each stage, a calculated model used to predict the lifetime is developed. Based on the definition of durability limit state, a probabilistic lifetime model and its time-dependent reliability analytical method are proposed considering the random natures of influencing factors. Then, the probabilistic lifetime prediction models are applied to a bridge pier located in the Hangzhou Bay with Monte Carlo simulation. It is found that the time to corrosion initiation to follows a lognormal distribution, while that the time from corrosion initiation to cover cracking t~ and the time for crack to develop from hairline crack to a limit crack width t2 can be described by Weibull distributions. With the permitted failure probability of 5.0%, it is also observed that the structural durability lifetime mainly depends on the durability life to and that the percentage of participation of the life to to the total service life grows from 61.5% to 83.6% when the cover thickness increases from 40 mm to 80 mm. Therefore, for any part of the marine RC bridge, the lifetime predictions and maintenance efforts should also be directed toward controlling the stage of corrosion initiation induced by chloride ion.

Tensile Strength Characteristics of GFRP Bars in Concrete Beams with Work Cracks under Sustained Loading and Severe Environments

To investigate the effect of different environmental conditions of GFRP bars in concrete beams with work cracks subjected to sustained loads, the beams were exposed in indoor, freeze/thaw cycles and immersed in alkaline solution at elevated temperature. The bars were carefully extracted from the beams and tested in order to evaluate residual tensile properties. The results show that the tensile strength decreased significantly in the highly aggressive conditions but not in the natural conditions. The effect of GFRP bars casting in concrete beams demonstrated approximately 2.5% decrease of tensile strength caused by pore water environment in concrete beams on basis of those of the original bars. The effect of sustained loading plus work cracks demonstrated about 10.5% tensile strength decrease on basis of those of the bars only casted in concrete beams. The effect of environments under sustained loading plus work cracks demonstrated about 17% tensile strength decrease caused by a saturated solution of Ca（OH）2 and 60-2 ℃ tap water （pH=12-13） and about 8% tensile strength decrease caused by freezing and thawing cycle （F/T）, both on basis of those of the bars of the indoor beams only under sustained loading plus work cracks. The results demonstrate the effects of the tensile strengths under different environmental conditions of GFRP bars in concrete beams with work cracks subjected to sustained loads.

Assessment of early-age cracking of high-performance concrete in restrained ring specimens

High-performance concrete （HPC） is stronger and more durable than conventional concrete. However, shrinkage and shrinkage cracking are common phenomena in HPC, especially early-age cracking. This study assessed early-age cracking of HPC for two mixtures using restrained ring tests. The two mixtures were produced with water/binder mass ratio （mw/mB） of 0.22 and 0.40, respectively. The results show that, with greater steel thickness, the higher degree of restraint resulted in a higher interface pressure and earlier cracking. With steel thickness of 6 mm, 19 mm, and 30 mm, the age of cracking were, respectively, 12 days, 8 days, and 5.4 days with the mw/mB = 0.22 mixture; and 22.5 days, 12.6 days, and 7.1 days with the mw/mB= 0.40 mixture. Cases of the same steel thickness show that the ring specimens with a thicker concrete wall crack later. With the mw/mB = 0.22 mixture, concrete walls with thicknesses of 37.5 mm, 75 mm, and 112.5 mm cracked at 3.4 days, 8.0 days, and 9.8 days, respectively; with the mw/mB = 0.40 mixture, the ages of cracking were 7.1 days, 12.6 days, and 16.0 days, respectively.

Seismic stability analysis of concrete gravity dams with penetrated cracks

The seismic stability of a cracked dam was examined in this study. Geometric nonlinearity and large deformations, as well as the contact condition at the crack site, were taken into consideration. The location of penetrated cracks was first identified using the concrete plastic-damage model based on the nonlinear finite element method （FEM）. Then, the hard contact algorithm was used to simulate the crack interaction in the normal direction, and the Coloumb friction model was used to simulate the crack interaction in the tangential direction. After verification of numerical models through a case study, the seismic stability of the Koyna Dam with two types of penetrated cracks is discussed in detail with different seismic peak accelerations, and the collapse processes of the cracked dam are also presented. The results show that the stability of the dam with two types of penetrated cracks can be ensured in an earthquake with a magnitude of the original Koyna earthquake, and the cracked dam has a large earthquake-resistant margin. The failure processes of the cracked dam in strong earthquakes can be divided into two stages： the sliding stage and the overturning stage. The sliding stage ends near the peak acceleration, and the top block slides a long distance along the crack before the collapse occurs. The maximum sliding displacement of the top block will decrease with an increasing friction coefficient at the crack site.

Effect of Concrete Cracks on Dynamic Characteristics of Powerhouse for Giant-Scale Hydrostation

With the increase of capacity and size of the hydro-generator unit, the spiral case becomes a more super-giant hydraulic structure with very high HD value, where H and D denote water head and maximum intake diameter of spiral case, respectively. Due to the induced lower stiffness by the more giant size and adverse operation conditions, dynamic performances of the powerhouse and the supporting structure for the giant units have become more important and attracted much attention. If the manner of steel spiral case embedded directly in concrete is adopted, on some locations of the concrete surrounding the spiral case, distributed and concentrated cracks will emerge due to high tensile stress. Although the concrete is reinforced well to control the maximum crack width, definitely these cracks will reduce the local and entire stiffness of the powerhouse. Under dynamic loads such as hydraulic forces including water pressure pulsation in flow passage acting on the structure, effect of the cracks on the dynamic characteristics of the local members and entire structure needs to be evaluated. However, research on this subject is few in hydroelectric engineering. In this paper, Three-Gorge Project was taken as an example to evaluate effect of such cracks on natural frequencies and the vibration responses of the powerhouse under hydraulic and earthquake forces in detail. Results show that cracks only reduce the local structural stiffness greatly but have little effect on the entire powerhouse especially the superstructure; vibrations of powerhouse with cracks in concrete surrounding the spiral case are still under the design limits. Results in this paper have been verified by practice of Three-Gorge Project.

Finite element analysis of road structure containing top-down crack within asphalt concrete layer

In this paper, a four-layered road structure containing a top-down crack is investigated by performing finite element analyses in ABAQUS. In this study, in addition to the vertical load of a vehicle wheel, the horizontal load as well as its position with respect to the crack is also considered in the analyses, and the crack tip parameters including stress intensity factors(SIFs) and T-stress are then calculated. Moreover, influence of elastic modulus and thickness of the pavement layers on the crack tip parameters is studied. Results show that the horizontal and vertical loads along with their position with respect to the crack, elastic modulus and thickness of the road layers influence the crack tip parameters(KⅠ, KⅡ and T-stress) significantly. It was also found that for the cases that the vehicle wheel is positioned near the crack plane, only the shear deformation mode is observed at the crack tip;while, for the vehicle wheel positions far from the crack, only the opening mode is observed, and between these positions, both the opening and shear deformation modes(i.e., mixed mode Ⅰ/Ⅱ) are observed at the crack tip.

Evaluation method of cracking resistance of lightweight aggregate concrete

The cracking behavior of lightweight aggregate concrete(LWAC) was investigated by mechanical analysis, SEM and cracking-resistant test where a shrinkage-restrained ring with a clapboard was used. The relationship between the ceramsite type and the cracking resistance of LWAC was built up and compared with that of normal-weight coarse aggregate concrete(NWAC). A new method was proposed to evaluate the cracking resistance of concrete, where the concepts of cracking coefficient ζt(t) and the evaluation index Acr(t) were proposed, and the development of micro-cracks and damage accumulation were recognized. For the concrete with an ascending cracking coefficient curve, the larger Acr(t) is, the lower cracking resistance of concrete is. For the concrete with a descending cracking coefficient curve, the larger Acr(t) is, the stronger the cracking resistance of concrete is. The evaluation results show that in the case of that all the three types of coarse aggregates in concrete are pre-soaked for 24 h, NWAC has the lowest cracking resistance, followed by the LWAC with lower water absorption capacity ceramsite and the LWAC with higher water absorption capacity ceramsite has the strongest cracking resistance. The proposed method has obvious advantages over the cracking age method, because it can evaluate the cracking behavior of concrete even if the concrete has not an observable crack.

Chloride diffusivity in flexural cracked Portland cement concrete and fly ash concrete beams

In order to examine the effect of load-induced transverse cracks on the chloride penetration in flexural concrete beams, two different concretes, Portland cement concrete(PCC) and fly ash concrete(FAC), were tested with various crack widths. Total 14 reinforced concrete(RC) beams, ten of which were self-anchored in a three-point bending mode, were immersed into a 5% NaCl solution with the condition of dry-wet cycles. Then, the free chloride ion contents were determined by rapid chloride testing(RCT) method. Based on the proposed analytical models of chloride penetration in sound and cracked concrete subjected to dry-wet cycles, the apparent chloride diffusion coefficient and chloride diffusivity of concrete were discussed. It can be found that the performance of chloride diffusivity in both concretes will be improved with the increase of crack width, and that the influence of convection action will also be augmented. Based on the two samples obtained in sound concrete after 15 and 30 cycles, the time-exponent, m, for chloride diffusion coefficient was determined to be 0.58, 0.42, 0.62 and 0.77 for PCC1, PCC2, FAC1 and FAC2 specimens, respectively. Finally, two influencing factors of fly ash content and crack width on chloride diffusivity were obtained by regression analysis of test data, and it can be seen that factors kf and kw can be expressed with quadratic polynomial functions of fly ash content, f, and crack width, w, respectively.

Analytical Modeling for Corrosion-Induced Cover Cracking of Corrosive Reinforced Concrete Structures

An analytical model for predicting the corrosion-induced cracking of concrete cover of reinforced concrete(RC) structures was developed.The effects of influence factors such as practical initial defects,corrosion rate,strength and elastic modulus of concrete on the corrosion-induced cracking of concrete cover were investigated.It was found that the size of practical initial defects was the most effective factor.Therefore,improving the compactness of concrete is an effective way to improve the durability of RC structures.It was also demonstrated that the accelerated corrosion tests may be unfavorable in the study of the relationship between cracking time and crack width.

Hydration Process and Crack Tendency of Concrete Based on Resistivity and Restrained Shrinkage Crack

Hydration process, crack potential and setting time of concrete grade C30, C40 and C50 were monitored by using a non-contact electrical resistivity apparatus, a novel plastic ring mould and penetration resistance methods, respectively. The results show the highest resistivity of C30 at the early stage until a point when C50 accelerated and overtook the others. It has been experimentally confirmed that the crossing point of C30 and C50 corresponds to the final setting time of C50. From resistivity derivative curve, four different stages were observed upon which the hydration process is classified; these are dissolution, induction, acceleration and deceleration periods. Consequently, restrained shrinkage crack and setting time results demonstrated that C50 set and cracked the earliest. The cracking time of all the samples occurred within a reasonable experimental period thus the novel plastic ring is a convenient method for predicting concrete＇s crack potential. The highest inflection time（t_i） obtained from resistivity curve and the final setting time（t_f） were used with crack time（t_c） in coming up with mathematical models for the prediction of concrete＇s cracking age for the range of concrete grade considered. Finally, an ANSYS numerical simulation supports the experimental findings in terms of the earliest crack age of C50 and the crack location.

The Performance of SUF High Effective Concrete Crack-patching Material

The physical properties and microstructure of SUF are investigated to develop a highly effective cement matrix crack-patching material for concrete cracks. The SEM and XRD determination of hardened SUF shows that the microstructure of SUF is dense and compact with a lot of C-S-H gels and ettringite. Also, the mechanism of shrinkage compensating is discussed.

Reliability analysis for anchorage of reinforced concrete beams with longitudinal cracks due to corrosion at anchorage zone

An anchorage reliability analysis approach for simply supported reinforced concrete beams under corrosion attack in the anchorage zone is developed.The first-order second-moment method is employed to analyze the effects of various factors on the anchorage reliability.These factors include both the length and width of cover cracking due to reinforcement corrosion,the cover thickness,the anchorage length,and the stirrup ratio.The results show that the effect of corrosion-induced crack length on the reliability index for anchorage,β0,is negligible when the crack on the concrete surface is just appearing,but with the crack widening,the β0 value is reduced significantly;the considerable changes in β0 result from a variation in cover depth and anchorage length;the effect of changes in the diameter or space of stirrups on the anchorage resistance is very limited,and the variation in β0 is also very low.

Reflective cracking viscoelastic response of asphalt concrete under dynamic vehicle loading

In order to investigate the mechanical response of reflective cracking in asphalt concrete pavement under dynamic vehicle loading, a finite element model is established in ABAQUS. The viscoelastic behavior is described by a prony series which is calculated through nonlinear fitting to the creep test data obtained in the laboratory. Based on the viscoelastic theory, the time-temperature equivalence principle, fracture mechanics and the dynamic finite element method, both the Jintegral and the mix-mode stress intensity factor are utilized as fracture evaluation parameters, and a half-sine dynamic loading is used to simulate the vehicle loading. Finally, the mechanical response of the pavement reflective cracking is analyzed under different vehicle speeds, different environmental conditions and various damping factors. The results indicate that increasing either the vehicle speed or the structure damping factor decreases the maximum values of fracture parameters, while the structure temperature has little effect on the fracture parameters. Due to the fact that the vehicle speed can be enhanced by improving the road traffic conditions, and the pavement damping factor can become greater by modifying the components of materials, the development of reflective cracking can be delayed and the asphalt pavement service life can be effectively extended through both of these ways.

Effect of Pulse Parameters on Deposition in Concrete Crack using Pulse Current Electro-deposition

To evaluate the effect of pulse parameters on the formation of electrodeposits in concrete cracks, five different types of pulse current were set up, and ZnSO_4 and MgSO_4 solutions were used as the electrolytes. The rate of weight gain, rate of surface coating, rate of crack closure and crack filling depth were measured. Scanning electron microscopy was used to assess the morphology of the electrodeposits, and energy dispersive spectroscopy was used to analyze the mineral composition of the electrodeposits in the cracks. The experimental results demonstrate that, among five different pulse parameters, when T_（on）/T_（off）=0.8 ms/0.8 ms, the healing effect of electro-deposition is the best. The pulse mode hardly affects the mineral composition of the electrodeposits but changes the micromorphology. In addition, for both ZnSO_4 and MgSO_4 solutions, when T_（on）/T_（off）=0.8 ms/0.8 ms, the crystal structure of the electrodeposits is the most uniform and the densest.

Lifetime Reliability Analysis of Flexural Cracking for Prestressed Concrete Bridge

Time-dependant reliability is analyzed for the flexural cracking of prestressed concrete bridges under service limit state. The limit state function and random variables are derived from Chinese highway bridge design specifications. For deterioration of structural performances, chloride-induced reinforcement corrosion is emphasized. Through integrating first order reliability method （FORM） and time discretized approach, the time-variant reliability is evaluated. For illustrative propose, the reliability of a typical simply supported prestressed concrete beam is exemplified.

Characterisation of Bacteria⁃Based Concrete Crack Rejuvenation by Externally Applied Repair

Microbiologically⁃induced calcite⁃precipitation(MICP)has been increasingly studied in structural repair including self⁃healing and external applications.Among various MICP pathways,enzymatic urea hydrolysis is suggested to be applied as external repair instead of self⁃healing.This study comprehensively characterised the enzymatic urea hydrolysis pathway in physical,impermeable,and mechanical rejuvenation of concrete cracks.The visual quality of repaired structures was presented,and the importance of humidity in the remediation of cracks was demonstrated.Moreover,this study investigated the differences in the effectiveness of repair between premixing bacteria with urea and without any premixing.With premixing,there was a concern that the accelerated reactions would precipitate calcite in the shallow spaces of the cracks and impede deeper healing.However,the observed results indicated that neither physical nor impermeable rejuvenation of concrete cracks repair would be detrimentally affected.The results obtained from this study will allow further development in commercialisation since the effectiveness of repair has been confirmed with an improvement in its efficiency.