Study on the effects of bonded stress between concrete and corroded rebar

Study on the effects of bonded stress between concrete and corroded rebar Study on the effects of bonded stress between concrete and corroded rebar Study on the effects of bonded stress between concrete and corroded rebar

I NTRODUCTIONS

Reinforced concrete (RC) has been widely invented and used since the mid- 19th century because of their flexibility, durability and economy

Corrosion and deterioration of reinforced concrete (RC) structures, particularly in marine environments, pose significant challenges, especially in hot and humid climates with high ionic content These conditions lead to varying degrees of rust, jeopardizing the longevity and integrity of construction projects Over the past century, countries worldwide have documented the actual durability of RC structures, highlighting the critical need for effective maintenance and protective measures.

- In the non-corrosive environment, RC structures can work sustainably for over 100 years

- In an aggressive marine environment, corrosion of reinforcement and concrete leading to cracking and destruction of reinforced concrete structures may appear after 10, 30 years of use

The reliability of reinforced concrete structures is significantly influenced by environmental cavitation levels and the quality of materials utilized Key factors include concrete strength, waterproofing standards, corrosion resistance, types of cement, and additives Additionally, the type of reinforcement, design quality, construction practices, management, and maintenance measures play crucial roles in ensuring structural integrity.

In fact that, there are two main reasons that causes of reinforcement corrosion in reinforced concrete structures: Carbonation of concrete due to cavitation air ingress and cavitation of ions

In the first case , CO 2 in the air penetrates into the concrete through a network

2 of pores and fissures In the presence of a liquid phase present in concrete and cement hydration products, especially Ca OH ( ) 2 , carbonation reactions take place to form

CaCO 3 (limestone) The pH of the medium decreases from about 12.5 → 13.5 to approximately 9, resulting in the breakdown of the passive membrane that protects the reinforcement

The presence of a liquid phase allows Cl− ions to infiltrate the concrete structure, altering the protective environment around the reinforcement and transforming the passive membrane This process accelerates corrosion within the structure Data indicates a significant frequency and cost associated with repairs for deterioration and damage resulting from corrosion.

A study conducted in Japan revealed that 90% of buildings exposed to marine environments, despite having a protective concrete layer, were inadequately sized Additionally, a significant proportion of structures that were only 10 years old exhibited considerable damage.

In the United States, based on the monitoring of 586,000 expressway bridges, 15% of which the structure have weakened, mainly due to the strong development of corrosion

In Vietnam, corrosion impacts are significantly more severe than in many other countries, driven by factors such as elevated temperatures, high humidity, prolonged wet conditions, and a high concentration of chloride ions As a result, numerous buildings experience substantial deterioration within a short period of use, highlighting the urgent need for effective corrosion management strategies.

(a) Cua Cam Port – Hai Phong City (b) Trade Port – Vung Tau City

Fig 1 1 Current status of reinforcement corrosion on some real projects [4]

The current condition of key port structures in Vietnam reveals significant deterioration: Cua Cam Port in Hai Phong, located 25km from the sea and in operation for 30 years, and Trade Port in Vung Tau, which has been used for 15 years, both exhibit severe corrosion levels of up to 45% Notably, the steel reinforcements in various areas are fractured, and the protective concrete layers are either peeling or damaged.

Corrosion of reinforcement leads to significant damage to the surface of structures, resulting in cracked and peeling protective concrete layers that negatively impact the aesthetics and architecture of buildings Additionally, the loss of weight and reduction in the effective working area of the corroded reinforcement pose serious risks to both safety and operational functionality.

In Vietnam, numerous seaside construction sites established since the 1960s have adhered to standard construction regulations, often neglecting the corrosion protection requirements outlined in TCVN 9346:2012.

[5] Researches on corrosion problems and effects have not been widely disseminated, the corrosion time is done in units of years

This study presents an experimental procedure for rapidly creating reinforced concrete structures subjected to various corrosive environments in a laboratory setting, utilizing the electrochemical corrosion acceleration method.

Tests will be conducted on specimens to assess how corrosion resistance of reinforcement influences the bond stress between concrete and reinforcement The findings will be calculated and analyzed to understand the impact of corrosion rate on adhesion stress Subsequently, simulation methods will be employed to validate the results and enhance the objectivity of the study.

L ITERATURE REVIEW

The impact of bond force on the adhesion between concrete and reinforced materials is a compelling area of research for scholars globally, employing various models and methodologies to explore this relationship.

4 a) 21% corrosion b) 20% corrosion c) 16% corrosion d) 21% corrosion prior to cleaning

Fig 1 2 The bond sections displaying the reduction in observed cross section [6]

Fig 1 3 Relationship between bond stress and displacement in the experiment [6]

Kivell et al conducted a study to assess the impact of corrosion-induced bond loss in reinforcement, performing 24 experiments that examined the effects of rebar cross-section reductions between 15% and 25% Their findings revealed that even a 15% reduction in cross-sectional area due to corrosion can lead to a bond stress decrease of over 50% Additionally, the study highlighted that when exposed to cyclic loads, the bond stress deterioration rate is significantly higher than anticipated compared to a non-corrosive reference sample.

Alhawat and Ashour [7] investigated the bond performance of recycled coarse aggregate (RCA) concrete with un- corroded/corroded reinforcing steel bars, with the

The study involved testing 60 pull-out specimens with varying percentages of Recycled Concrete Aggregate (RCA), specifically 0%, 25%, 50%, and 100% The main parameters analyzed included RCA content, corrosion level, bar diameter, and embedment length, with specimens featuring steel bars of two diameters: 12mm with embedment lengths of 60mm and 167mm, and 20mm with an embedment length of 100mm.

The study tested steel bars with diameters of 12 mm and 20 mm at various embedment lengths to assess corrosion levels through electrochemical exposure over 2, 5, 10, and 15 days The bond strength between recycled aggregate concrete (RAC) and both un-corroded and corroded steel was compared to existing codes and research findings Results indicated that higher corrosion rates in steel bars correlated with increased replacement levels of recycled concrete aggregates (RCA), attributed to their greater porosity and water absorption While RCA had minimal impact on the bond strength of un-corroded specimens compared to conventional concrete, the bond strength in RAC was significantly influenced by corrosion products Specifically, bond strength improved slightly at corrosion rates up to 2%, but then decreased sharply with longer corrosion durations, mirroring trends in conventional concrete Notably, the degradation rate of bond strength between RAC and corroded steel bars was markedly faster than that of corroded conventional concrete.

Recent studies by Lim et al and Blomfors et al have focused on the bonding model of corroded steel, emphasizing the development of models to assess the anchoring capacity of corroded steel Their innovative model is grounded in the local bond-slip stress relationship outlined in the Fib Model Code and has been specifically adjusted to account for corrosion mechanisms The findings indicate significant insights into the behavior of corroded steel in structural applications.

The inherent dispersion among experimental bonds is significant, even within groups exhibiting the same corrosion degree However, the new development model demonstrates a notable reduction in steel anchoring capacity and offers improved experimental data compared to its predecessor Unlike many existing experimental models, this model effectively illustrates the physical responses and the complete local cohesion-shear relationship, enabling a more accurate estimation of the anchoring ability of corrosive concrete structures.

Kallias and Imran Rafiq conducted a study on the corrosion performance of flexible reinforced concrete beams using the responsive surface method (RSM) and nonlinear finite element analysis (NLFEA) They calculated the effects of corrosion through experimental and semi-experimental models based on specific parameters Their findings revealed that low-order polynomial RSM models effectively determined the working limit deflection, flexural resistance, and corrosion behavior coefficient (LD) of the beams when appropriate tests were applied.

Wang et al [11] investigated the impact of ice on the bond strength between concrete and reinforcement through the Fiber model Their findings indicate that the bonding efficiency between concrete and reinforcement is considerably diminished, and that material degradation is uneven across different locations within the concrete structure when subjected to freeze-thaw cycles.

Gu et al conducted an experimental study on the uneven distribution of cross-sectional areas and mechanical properties of steel bars corroded in a chloride environment, utilizing 19 slabs of prefilled steel bars for accelerated corrosion They employed 3D simulation to develop a geometrical model of the corroded steel bars, which led to the creation of a probability distribution model for the spatial transform factor R, effectively illustrating the impact of corrosion on the structural integrity of steel.

This study utilizes signal processing methods and statistical analysis to examine the mechanical behavior of bars under tensile loads, particularly focusing on the R coefficient, which represents the ratio of the average cross-sectional area to the minimum area The research establishes a link between the mechanical properties of steel and the R coefficient to assess the critical state of brittle failure A key innovation of this study is the ability to calculate the time-dependent reliability of corroded free-bearing reinforced concrete beams Findings indicate that uneven corrosion significantly impacts the time reliability of these beams, and alterations in the failure mode of corroded steel can drastically diminish their reliability.

Zhu and Francois [13] [14] evaluated the shape and tensile strength of corroded reinforcement by experiment (Fig 1.5 and Fig 1.6) Mechanical property tests were carried out on eroded

Fig 1 5 Comparison of the corroded and non-corroded tensile bars [14]

A study conducted on steel bars from reinforced concrete beams exposed to chloride environments for 26 and 28 years examined the impact of corrosion on tensile strength through experimental simulations The research focused on three corrosion types, analyzing various residual cross-section shapes, including both homogeneous and heterogeneous sections Findings revealed that the shape of the remaining cross-section significantly influences the tensile strength of the steel bars Notably, steel bars with symmetrical cross-sections demonstrated the highest tensile strength under the same simulated corrosion conditions.

Wu et al [15] conducted an experimental study to analyze the bonding stress reduction between reinforcement and concrete using steel diameters of D12, D16, D20, and D25 mm Their investigation focused on the coupling effects of weathered concrete and corroded reinforcement The findings revealed that the primary failure mode of the test samples was split failure, and as the corrosion rate increased, the bond between the eroded concrete and steel bars became less distinct Overall, the study highlighted the impact of weathering on bonding strength.

In a study illustrated in Figure 1.7, it was found that the bond strength between cracked concrete and heavily corroded steel bars varies with the diameter of the steel, where smaller diameters initially increased before cracks appeared, then decreased, while larger diameters showed a linear decrease due to a reduced protective concrete layer The author developed a model to quantify this bond strength, incorporating key parameters such as the corrosion rate of the steel bars, the compressive strength of the concrete, the width of the cracks, and the coefficient of friction between the weathered concrete and the corroded steel.

Fang et al [16] conducted experimental research on the bond force between corroded reinforcement and concrete under cyclic loads Their findings indicate that cyclic loading can severely deteriorate this bond, particularly when the reinforcement is corroded The study examined the bond-shear stress behavior of corroded reinforcement in concrete, focusing on variables such as corrosion level, horizontal compression, steel type, and loading process Results revealed a significant reduction in bonding behavior under cyclic loading, with ribbed bars exhibiting less bonding reduction compared to plain bars during the initial load cycle, although this difference diminished over time.

The study reveals that corrosion significantly reduces performance during the initial five cycles, but its impact diminishes as the load increases This indicates that the relationship between bond stress and slip is influenced by the loading process.

R ESEARCH OBJECTIVES

Study on the effects of bond stress between concrete and eroded steel reinforcement by experiment and simulation

Topic as a basis for assessing the reliability of real works as well as a premise for predicting the life of the project

To investigate the effect of different parameters on the bond performance of the bond stress

To conduct an analytical model using non-linear finite element analysis taking into consideration the interfacial behaviour between the bond concrete and steel bar.

R ESEARCH CONTENT

This research investigates the effects of corrosion on three types of reinforcement within concrete, examining three corrosion levels and varying concrete strength It focuses on the influence of adhesion stress between concrete and reinforcement, including evaluations of adhesion when using FRP composite materials for corroded structures The study aims to assess the corrosion characteristics of reinforcing sections in concrete as they deteriorate over time.

Evaluation of many aspects such as corrosion type, weight loss of reinforcement, diameter depth of corrosive reinforcement

Analysis and evaluation of experimental results achieved in combination with ANSYS simulations showed the effect of reinforcement corrosion on bond stress between concrete and reinforcement

Based on the collected data such as: corrosion level, diameter of reinforcement, bond stress, constructing an assessment algorithm, predicting the lifespan of real structures using artificial intelligence (AI )

Proposing next research directions for the topic to achieve higher science, more contribution to construction technology

A PPROACH , RESEARCH METHOD

Refer to some domestic and international studies on the field of corrosion on the relevant reinforced concrete structures Design experiments for samples in the laboratory

This research utilizes general theory and laboratory experiments, complemented by simulations conducted with ANSYS software, to assess the reliability of the findings By integrating real-world statistics with research outcomes, the study develops assessment algorithms aimed at predicting project lifespan effectively.

The developed analytical model is employed to investigate the impact of various parameters through two distinct approaches: one involving test work and the other focusing on analysis, as illustrated in Figure 1.16 The test work comprises two phases, with the initial phase assessing the electrochemical corrosion rate of 324 steel samples.

The tests include the following test parameters: Steel bar type, diameter of steel bar, aggregate, steel bar length, binder type (cement), electrolyte solution

The second stage consists of an bond determination of 324 samples have the following test parameters: Relationship of bond stress and slip displacement of diameter steel D12, D16 and D20

Analysis work entails the development of an analytical model designed for use with commercially available non-linear finite element programs, such as ANSYS, to analyze and predict the cohesive behavior of concrete and reinforcement The model's efficiency and accuracy are calibrated against experimental results, ensuring reliable outcomes Additionally, these analytical models facilitate the investigation of various parameters affecting performance.

R ESEARCH N OVELTY

This study explores the development of experimental models that incorporate varying levels of corrosion in reinforcement, concrete, and steel anchor lengths By integrating reinforcement with composite materials, it aims to provide a more comprehensive understanding of how corrosion impacts the adhesion between concrete and reinforcement, surpassing the insights offered by earlier research.

This study focuses on constructing an ANSYS model to simulate the interaction between concrete and reinforcement subjected to corrosion, utilizing actual data to evaluate the reliability of the findings It involves developing simulation programs to analyze bond stress between corroded concrete and reinforcement using the finite element method within ANSYS software.

Evaluating results is essential for enhancing the actual data set when analyzing reinforced concrete structures The development of AI algorithm models plays a crucial role in assessing and predicting the structural reliability over time.

C ORROSION P ROCESS OF REINFORCEMENT IN CONCRETE

Steel reinforcement corrosion is an electrochemical process where steel reverts to its original ore form by forming iron oxides, commonly known as rust In natural environments, this corrosion occurs slowly due to the protective concrete cover that serves as a physical barrier and the thin oxide passive layer created by the high alkalinity of the concrete, with a pH level around 12.5.

Aggressive environmental factors, particularly chloride ions, penetrate concrete through its pores, compromising protective mechanisms and initiating corrosion Once chloride concentration reaches a critical threshold, it disrupts the passive layers of reinforcement, triggering the electrochemical corrosion process The resulting rust occupies a volume 2 to 6 times greater than the original mass, generating tensile stresses in the surrounding concrete, which leads to cracking and spalling of the cover Consequently, this deterioration significantly impacts the bond between steel and concrete, ultimately degrading the bearing capacity of reinforced concrete (RC) elements.

Fig 2 1 Cracking development and spalling of concrete cover due to oxidation of steel reinforcement [40]

2.1.1 Environmental Severity Factors Influencing Corrosion

Corrosion primarily refers to the degradation of materials, commonly recognized as "rust" on steel and the oxidation of various metals It encompasses the deterioration caused by environmental factors such as sun exposure, mold, mildew, wind, and more Multiple severity factors contribute to the rate of corrosion, including these environmental influences.

Microbiological activity significantly influences material degradation in various ways, with each factor presenting unique challenges If left unaddressed, these impacts can lead to severe consequences Corrosion, in particular, poses a threat to metals, wood, pavements, fabrics, roofs, and overall building systems.

Understanding the risks linked to environmental severity factors is crucial, as local climate conditions, industrial influences, and high solar exposure can lead to corrosion rates that exceed expectations based solely on chloride presence.

2.1.2 Identifying And Recognizing Common Forms Of Corrosion

The common forms of corrosion include [44] (Fig 2.2 , Fig 2.3):

Corrosion can manifest in various forms, including exfoliation, environmentally assisted cracking, and corrosion fatigue, which are prevalent across different environments One of the most common types is uniform (general) corrosion, characterized by its consistent occurrence over the entire exposed surface of a metal To effectively mitigate this type of degradation, applying a barrier coating is a widely used method.

Pitting is a form of localized corrosion that occurs when a corrosive medium attacks a metal at specific points and results in deep cavities in the metal

Crevice corrosion occurs when an electrolyte becomes trapped and stagnant in specific areas like joints, corners, and beneath debris This type of corrosion is often difficult to detect and can be highly aggressive, leading to significant pitting rates and unexpected failures.

Fig 2 2 Common Depictions of Corrosion [44]

Galvanic corrosion occurs when dissimilar metals with different electrical potentials form a galvanic cell in the presence of an electrolyte This type of corrosion can be highly aggressive; however, it is also relatively easy to detect and prevent.

Erosion corrosion occurs when the deterioration of a material accelerates due to the dual impact of corrosion and the repetitive motion of the surrounding environment This phenomenon is commonly observed in high-velocity areas or in fluids that contain abrasive substances.

Intergranular corrosion targets the grain boundaries of materials and can arise from galvanic couples between different phases within the material To prevent this type of corrosion, it is essential to avoid using susceptible alloys or specific heat treatments.

Selective leaching, also known as de-alloying, is a localized corrosion process where specific elements within a material are preferentially removed This phenomenon is particularly common in various copper alloys, making them vulnerable to such attacks.

Stress Corrosion Cracking (SCC) occurs when susceptible materials are exposed to a corrosive environment while under sustained tensile stress Additionally, Solar Ultraviolet Degradation affects organic-based polymers used in construction, leading to photolytic and photo-oxidative reactions when exposed to solar UV radiation.

Environmentally Assisted Cracking occurs when tensile stress interacts with a corrosive environment and a susceptible material, leading to the disruption of protective films at the crack tip This corrosion process produces atomic hydrogen, which diminishes the material's resistance to cracking Typically, this phenomenon is observed in high-strength materials, particularly fasteners.

Corrosion fatigue significantly diminishes the fatigue resistance of various materials, particularly in corrosive environments The corrosion processes that take place at the tips of cracks accelerate the growth rate of fatigue cracks, impacting structural materials like aluminum and steel.

Fig 2 3 Additional images of corrosion forms [44]

The Alkali Silica Reaction (ASR) in concrete develops over time when highly alkaline cement paste interacts with reactive amorphous silica present in various aggregates, particularly in the presence of moisture This chemical reaction results in the expansion of the altered aggregates, leading to spalling and a significant reduction in the concrete's strength, ultimately culminating in structural failure.

2.1.3 Electrochemical cell and corrosion in concrete

B OND STRESS OF CONCRETE AND REINFORCEMENT

The ability to bond between reinforcement and concrete is the factor that ensures the deformation and mutual impact work

Bond refers to the interaction between reinforcing steel and the surrounding concrete, which allows transferring of tensile stress from the steel into the concrete

It is the mechanism that allows the anchorage of straight reinforcing bars and influences many other important features of structural concrete such as crack control and section stiffness [48]

The bond between concrete and the development length of reinforcing steel is crucial for effective composite action in reinforced concrete construction Utilizing deformed bars significantly improves the bond capacity between steel and concrete The bond strength is primarily influenced by three key components related to the adjacent ribs of the reinforcement bar.

The bond strength of bars in concrete is primarily influenced by three factors: shear stresses from adhesion along the bar surface, bearing stresses created by the mechanical interlock against the rib faces, and friction between the bars and the surrounding concrete in the rib dales Notably, mechanical interlock plays the most significant role in enhancing bond strength.

The bond strength between concrete and steel is an important factor from which to determine a sound design for the reinforced concrete

2.2.1 Bonding between concrete and reinforcement

- The interlocking bond between concrete and the reinforcement is formed when the bonded reinforcement forms a sturdy skeleton surrounded by concrete

- The steel bars act as tensile and the concrete plays the role of compression, thereby helping the reinforced concrete structures withstand a greater force when they work alone

A larger contact surface area enhances the stability of the bond between concrete and reinforcement Key mechanisms such as adhesion and friction significantly contribute to the bonding ability, effectively preventing slip between the two materials.

Corrosion of reinforcement is a prevalent issue in reinforced concrete structures While the hydration process enhances the concrete's strength, it simultaneously lowers the pH levels, diminishing the passive anti-corrosion properties of the reinforcing steel Over time, harmful agents like chloride ions penetrate the concrete, directly affecting the reinforcement and leading to corrosion.

Corroded reinforcement significantly impacts the mechanical performance of a structure by diminishing its bearing capacity due to the loss of reinforcement area compared to the original design Additionally, corrosion leads to reduced stiffness, as it weakens the bond between the concrete and the reinforcement, ultimately resulting in increased deflection when the structure is compromised.

2.2.2 Factors that contribute to bonded – stress

Factors that contribute to bonded – stress include:

- Friction: When the concrete dries, Due to its shrinking effect, the concrete embraces the reinforcement, create friction

- Bond: ribbed reinforcement, concrete under the edges will prevent the reinforcement from sliding

- Bonded – stress: adhesive in concrete acts as the surface adhesive of the reinforcement to the concrete

Concrete does not chemically react with reinforcement during fabrication or use, ensuring durability Solid concrete acts as a protective barrier against rust, shielding the reinforcement from corrosive elements Additionally, the thermal expansion coefficients of both concrete and reinforcement are nearly identical, contributing to their compatibility and structural integrity.

The adhesion between reinforcement and concrete is crucial for their effective collaboration, allowing both materials to deform together and facilitating mutual force transmission In structural applications, the adhesion force at the interface between reinforcement and concrete enables them to function cohesively.

But for, the reinforcement to work with all its calculated strength, the contact area of the steel bar in the concrete must be greater than the minimum contact

Factors influencing bonded – stress include:

- Bearing state: compressive reinforcement has greater bonded – stress than tensile reinforcement

- Length of l : when changing length l then  max does not change values but have changed because change l the complete chart coefficient reduced

Fabricated by embracing the reinforcement by concrete and preventing their bonding at the ends

The length of the section (l) in the test for separating reinforcement from concrete must be limited to prevent the reinforcement from exceeding its yield point, which can lead to pulling or compression without slipping This study adhered to the ACI 440.3R standard, utilizing a length of l_b = 5d_b.

Relationship between adhesion stress and sliding displacement of steel bar according to the model of CEB-FIP (2010), is shown in (Fig 2.7) [51] The maximum

Fig 2 7 Model bond – stress and slip displacement relationship of rebar used CEB-

FIP MC2010 [51] bonded – stress is determined after the steel bar slides in the concrete by a distance from S 1 to S 2

Maximum bonded – stress in best condition according to European CEB- FIP MC2010 is calculated as follows [51]:

 ' f c is the characteristic compressive strength of concrete

In this study, we examine low and medium strength concrete, focusing on an average applied force (F_b) to assess the bonded stress (τ_b) during the measurement of steel reinforcing bar slip displacement within the range of S_S1 to S_S2 in the test samples.

In which  b : Bonded – stress ( MPa ) ; F b : The average applied force ( ) kN ; A b : the area of concrete surrounding the rebar segment ( ) mm 2 ; d b : diameter of rebar bar

( mm ) ; l b : bond length of rebar bar ( mm )

2.2.5 The purpose of the experiment is to determine the properties of concrete and reinforcement when it is corroded

Bonding between concrete and rebar is one of the key properties of concrete used in reinforced concrete structures The technical features of reinforced concrete structures depend on this property

Bond strength refers to the interaction between reinforcing rods and concrete, facilitating the transfer of forces from the reinforcement to the surrounding concrete Reinforced concrete is viewed as a composite material formed by these two elements However, the bond surface is recognized as one of the weaker points in the composite structure of steel and concrete.

Bond strength is influenced by various factors, including the compressive and tensile strength of the concrete, the thickness of the protective concrete layer, the arrangement of other steel bars, the condition of the steel bar surface, and the shape of the steel bar.

This property is crucial for determining the deployment length of reinforcement and the transmission length of prestressing reinforcement in prestressed concrete structures, as well as influencing the distance between cracks and their widths.

- The types of adhesion damage before the steel bar slip occurs are chemical bond damage;

Fig 2 8 Relationship of bond stress and slip displacement steel bar [52]

- Development of horizontal cracks in the surrounding concrete layer in the early stage of the load;

- Separate the surrounding concrete when the radial stress at the steel edges is greater than the tensile stress in the concrete

The process of moving the reinforcing bar in concrete according to the stages

[52] is shown in (Fig 2.8) Starting the process of sliding steel bar is the break of chemical bonded, then starting to horizontal cracking of concrete and breaking the surrounding concrete.

S IMULATE THE P ULL O UT EXPERIMENT BY THE F INITE E LEMENT M ETHOD

Bonded behavior with reinforcement is a crucial characteristic of concrete utilized in reinforced concrete structures, influencing the deployment length, reinforcement transmission length, and the dimensions of cracks This behavior is essential for analyzing and calculating the anchoring area of concrete structures The transmission length is established through the "Push-In" experiment, while the deployment length is determined via the Pull-Out experiment.

Through experimental results, conduct simulation computations using ANSYS finite element software to check the result as well as solution the limitations occurring in the experiment

- Build experimental models in accordance with reality.

- Investigation of reinforcement slidling , stress and deformation at the contact area between reinforcement and the concrete side

- Compare simulation results with experimental results and make general conclusions

At present , there are many powerful tools to help solve complex equations that

34 we cannot solve by hand In this study, commercial software ANSYS version 18.2

[53] will be used to solve the problem posed

ANSYS software, developed by the renowned American company ANSYS Inc since the 1970s, is based on the fundamental principles of the finite element method This approach divides complex objects into simpler components, allowing the application of mathematical finite element equations to analyze and provide approximate results that reflect real-world behavior.

ANSYS is an essential software tool for addressing complex practical challenges, enabling highly realistic simulations that yield reliable results Scientists and manufacturers alike recognize its significant impact on their work, as ANSYS facilitates informed decision-making, reduces costs, and enhances overall economic efficiency.

Inheriting the outstanding features of finite element method, ANSYS shows that it has good applicability in many fields Especially in of construction field it is strongly used to:

- Research on properties and behavior of new structures and materials such as: Composite materials, hollow belly beams, green concrete

- Comment on effects and development of cracks in reinforced concrete structures

- Fatigue and longevity of the project

- ANSYS supports many types of elements with characteristics suitable for each computational requirement, this is a very strong point of ANSYS compared to other software

This study employs a linear parallel material model to illustrate the stress-deformation relationship of reinforcement, utilizing two essential parameters: the modulus of steel elasticity (E_s) and the steel yield strength (f_y).

The simple stress-deformation relationship of concrete with polylinear isotropic form proposed by Kachlakev et al [54], with two necessary parameters is concrete elastic modulus ( ) E c and compressive strength ( ) f c '

This article explores the application of the Von Mises criterion to analyze the stress response that transitions concrete behavior from linear to nonlinear Additionally, it utilizes the failure criteria proposed by Willam and Warnke to effectively simulate the fracture and compression failure of concrete subjected to three-dimensional compressive and tensile stresses.

Fig 2 9 Stress-deformation relationship of reinforcement and concrete [55]

Fig 2 10 The destructive side of concrete follows Willam and Warnke model [56]

The Willam and Warnke model can effectively predict concrete material failure by considering both cracking and compression failures Essential to this model are the compressive and unilateral tensile strengths, which help identify the destructive surface of concrete under varying spatial stress states In scenarios where the primary stresses in the x and y directions are negative while the main stress in the z direction is positive, cracking failure is likely to occur perpendicular to the main stress direction Conversely, if the main stress in the z direction is zero or negative, the concrete is prone to crushing failure.

In this study choose SOLID65 element for concrete materials with the following properties:

The SOLID65 element is designed for 3D modeling of solids, accommodating both concrete and reinforcing bars (rebar) It effectively simulates cracking under tension and crushing under compression, making it suitable for various applications, including reinforced composites like fiberglass and geological materials such as rock This element is characterized by eight nodes, each with three degrees of freedom for translations in the x, y, and z directions, and allows for the definition of up to three different rebar specifications.

Concrete elements function as three-dimensional structural solids, enhanced with unique cracking and crushing properties A key feature is their nonlinear material behavior, allowing for cracking in three orthogonal directions, as well as crushing, plastic deformation, and creep Additionally, rebar within these structures can handle tension and compression, though not shear, and also exhibit plastic deformation and creep characteristics.

The SOLID65 element, depicted in Fig 2.11, is designed to handle tension and compression while excluding shear forces It also accommodates plastic deformation and creep behaviors For additional information about this element, refer to the Mechanical APDL Theory Reference.

To simplify the simulation calculation process, the reinforcement modeled by the LINK180 element has the following structure:

LINK180 is a versatile 3-D spar element designed for various engineering applications, including modeling trusses, sagging cables, links, and springs This uniaxial tension-compression element features three degrees of freedom at each node, allowing translations in the x, y, and z directions It supports tension-only (cable) and compression-only (gap) options, while also ignoring bending, akin to pin-jointed structures Additionally, LINK180 incorporates capabilities for plasticity, creep, rotation, large deflection, and large strain, making it a comprehensive choice for engineers.

LINK180 inherently incorporates stress-stiffness terms in analyses involving large-deflection effects, supporting various material models such as elasticity, isotropic hardening plasticity, kinematic hardening plasticity, Hill anisotropic plasticity, Chaboche nonlinear hardening plasticity, and creep To effectively simulate tension/compression-only scenarios, a nonlinear iterative solution method is required Additionally, the element offers features for added mass, hydrodynamic added mass and loading, as well as buoyant loading options.

Fig 2 12 Model of steel material

See LINK180 ( Fig 2.13) for more information about this element

Experimental model was built with the correct size to show the correctness of the simulation (Fig 2.14)

Fig 2 14 Experimental model in ANSYS software 2.3.6 Material declaration

For linear materials, the following parameters will be added: Young elastic module, Poisson's coefficient

Regarding nonlinear materials, the stress – deformation relationship will be considered based on the Multilinear Isotropic Hardening model (Fig 2.15)

Fig 2 15 Destructive patterns of concrete

For the destruction part of concrete, apply William - Warnke model by giving four

Table 2 1 Destructive parameters of concrete

C1 Coefficients represent open crack due to shear C2 Coefficients represent closed cracks due to shear

When the head of the reinforcement experiences an outward pull, the bonding force between the reinforcement and the concrete prevents slippage, necessitating a thorough analysis of the behavior in this area.

The largest slide displacement will be recorded in the experiment Simulate, thereby achieving comparison chart between simulation and experiment

M ATERIALS

The cement used to be Porland PCB 40 (Fig 3.1) cement according to ASTM C150 – 15 [57] PCB40 cement is a popular type of cement in the market

Fig 3 1 Cement is used in experiment [57]

The experimental concrete utilizes large aggregate macadam sourced from basalt at the Tan My quarry in Tan Uyen, Binh Duong The crushed stone is sieved and categorized based on the size ranges outlined in ASTM C136-01, followed by re-mixing to achieve the grain composition required by ASTM C33M-03.

Fig 3 2 Material: sand, crushed stone after sieving based on ASTM C136-01 [58]

Fig 3 3 Graph of grain distribution of coarse aggregate

Select the grading composition of rocks with D max mm to fabricate the strength with strength level B20; 30; 40B B The composition of the selected aggregate is shown in (Table 3.1 and Fig 3.3)

Table 3 1 The grading composition of rock after blending according to ASTM

Quantity passed through the sieve (%) 100,00 95,00 40,00 5,00 0,00

Small aggregate, specifically raw yellow sand sourced from the Dong Nai River, is utilized in concrete experiments The sand undergoes screening for grain composition analysis in accordance with ASTM C136-01 standards The findings of the grain composition analysis are detailed in Table 3.2 and illustrated in Figure 3.4.

Fig 3 4 Graph of grain distribution of fine aggregate

Table 3 2 The grading composition of sand after mixing is according ASTM

Separate amount of leftove (%) 0,0 0,0 10,0 15,0 27,0 21,0 21,0 Accumulated amount 0,0 0,0 10,0 25,0 52,0 73,0 94,0 Quantity passed through the sieve (%) 100 100 90,0 75,0 48,0 27,0 6,0

Water used to mix concrete is determined according to TCVN 4506 -2012

[60] The water used in the experiment is tap water

As tested by Abrams, Richart and Scofield both bond and compressive strength decreased in the same manner as the water ratio was increased

The tensile experiment is carried out with CB400-V ribbed steel with diameter ( 12; 16; 20D D D mm) in accordance with TCVN 1651-2:2008 ( Fig 3.5) [61] with yield limit 400MPa, strength limit 570 MPa and relative elongation 14%, respectively

Fig 3 5 Steel used in the experiment

This study focuses on evaluating the corrosion resistance of steel in a 3.5% NaCl solution, as previous research indicates that chloride (Cl−) and sulfate (SO4²−) ions significantly influence corrosion processes By utilizing this specific electrolytic medium, the experiment aims to accelerate the assessment of steel's durability against corrosion.

S AMPLE MANUFACTURING

Experimental samples are fabricated with geometric dimensions as shown in

Steel bars are placed through the center of the cube mold The bonding ability between concrete and reinforcement was determined by sample size according to

The ends of the steel sample in contact with the mold are covered by two PVC pipes

The bond length between concrete and reinforcement is influenced by the diameter of the steel bar, with the recommended anchor length being Lb = 5D according to RILEM RC6 guidelines The inclusion of two pipe segments minimizes this bond length, effectively preventing concrete failure before the reinforcement is extracted and reducing the risk of localized corrosion.

Fig 3 6 Geometry of pull-out test specimen

Table 3 3 Number of experiment specimens

The experiment is divided into 3 parts:

Part 1: Testing the bearing capacity of reinforcement in concrete when corroded

Part 2: Test to determine adhesion ability when corroded (3 samples)

Part 3: Test to determine bonded ability of specimens corroded when reinforced with FRP composite material (3 samples)

Total number of specimens presented in (Table 3.3)

E XPERIMENTAL METHOD

The experimental setup, depicted in Fig 3.7, involves connecting samples to the terminals of a transformer in a parallel circuit configuration The transformer's negative pole is linked to a copper rod immersed in a 3.5% NaCl solution (35 g/l), which simulates the salinity of seawater found in Vietnam and globally, serving as the electrolyte in the experiment.

Fig 3 7 Diagram illustrating electrode corrosion acceleration experiment

Fig 3 8 Use DC power supply to electrolysis speed up corrosion

Transformer allows to convert alternating current to direct current (Fig 3.8),

In this test, a fixed amperage of 0.05 A is applied to nine non-corrosive concrete specimens, all connected simultaneously to a single transformer Each specimen receives the same voltage, ensuring consistent testing conditions across different concrete types.

This study proposed an electroelecbraive corrosion acceleration experiment process for reinforced concrete structure consisting of 6 basic steps (Fig 3.9) :

Step 1: At the time the concrete reaches 28 days of age, the specimens are put into the solution tank The minimum immersion time is 3 days for all samples to be in the same state of complete water saturation, while also creating conditions for chloride ions to diffuse inside the concrete environment

Step 2: Connect the rebars of the samples to the transformer according to the parallel circuit diagram

Step 3: Conduct rebar corrosion acceleration experiment by electroelesification method During the experiment, the amperage was adjusted and recorded every 12 hours

Step 4: The corrosion acceleration test of the reinforcement is stopped when the reinforcement in the test sample is corroded to the desired state Experimental time is predicted by Faraday's law

Step 5: The corroded steel sample is cleaned, blown concrete dust, rusted to determine the actual length of corrosion Conduct steel bar mass weighing to determine the volume of metal lost due to corrosion Continue to determine the depth and width caused by corrosion to the steel bar

Step 6: Carry out the next experiment and collect results from the experiment to complete the research

Fig 3 9 Experiment process for reinforced concrete structure

The theoretical mass of rust generated per unit surface area of the bar from applied current over a specified duration can be calculated using an expression derived from Faraday's law The electrolysis duration in the solution is initially estimated, as detailed in Table 3.4.

Table 3 4 Electrolysis time is roughly predicted according to Faraday's law

Steel type l ( mm ) M th ( ) g T ( hours ) c c ( ) %

Theoretical rust mass per unit surface area of the bar (M) is expressed in grams, while the equivalent weight of steel (W) is calculated as the atomic weight of iron divided by its valency, approximately 27.925 grams The applied current density (I app) is measured in Amperes, and the duration of induced corrosion (T) is represented in seconds Faraday's constant (F) is valued at 96,487 Ampere-seconds, providing a crucial relationship in the electrochemical processes involved in corrosion.

C ONCRETE MIX DESIGN

At the Structural Construction Laboratory of Ho Chi Minh City University of Technology and Education, experimental samples of concrete with compressive strengths of 25 MPa, 35 MPa, and 45 MPa were prepared Each concrete type features a specific aggregate composition, and the compressive strength was evaluated at 28 days.

Fig 3 10 Sample compression test old are presented in (Table 3.5) Compression tests to determine standard gradation were performed on cylindrical nests 15 30cm  The compressive strength of the

Table 3 5 Concrete mix proportions ( 8  2 ( ) cm )

Compressive strength at 28 days (MPa)

Tensile strength of concrete (MPa)

51 exercise performed according to ACI 318(2019) [64] is the average value of a sample group with 3 members

(ii)Wooden mold casting pattern 20  20  20cm

(iii) The reinforcing bars are cut to the designed dimensions

Fig 3 11 Prepare experimental concrete casting with different steel bars

After casting the test pieces are immersed in the corrosion acceleration in solution NaCl 3,5% (Fig 3.14) for a pre – determined time to achieve corrosion value different level

(i) Specimens were soaked for 7 days in solutionNaCl 3,5% before electrolysing

(ii) Electrolysis process accelerates corrosion

(iii) The amperage is recorded and adjusted every 12 hours

Fig 3 14 : Test Samples when corrosive with salt electrolyses NaCl 3,5%

T HE EXPERIMENT TO DETERMINE BOND STRESS OF REINFORCEMENT TO CONCRETE WHEN

Samples are positioned on a millet plate with holes twice the diameter of the steel bar, allowing the bar to be threaded through and placed on a tractor Traction is applied at the longer end of the sample, while slippage displacement is measured at the shorter end, following regulatory standards The specified loading speed is Vp = 0.56d², in accordance with EN 10080:1995 The experimental setup involves arranging samples as illustrated in Figure 3.15, utilizing five strain gauges to monitor crack formation in critical areas and three LVDTs to measure displacement Data is recorded using the TDS630 digital data logger, which is connected to a computer, with a loading speed set at 100 N/m.

Fig 3 15 Layout of test samples on tractors and support device

Fig 3 16 Data Logger TDS630 digital measurement

Table 3 6 The loading speed of the sample

The relationship between bonded stress and shear displacement of steel bars is outlined in the CEB fib MC2010 model (2013), illustrated in Figure 3.16 Bond strength is assessed after the steel bar experiences sliding in the concrete, transitioning from position s1 to s2.

For low to medium strength concrete, the bond strength value is set at s l = 1 mm This study focuses on measuring the destructive force to assess adhesion stress while monitoring the shear displacement of steel reinforcing bars within the experimental sample range of s s 1 to 2 The bond stress between the reinforcement and concrete is calculated accordingly.

In which  : average bond stress( MPa ) ; F : external applied load ( ) kN ; d : the diameter of rebar( ) mm ; l : the anchorage length( ) mm

Maximum bond strength in good condition according to European CEB fib MC2010

(2013) is calculated as follows [51]: max 2,5 f c

In which: f c :concrete compressive strength (MPa)

Results of experimental bond stress calculation and maximum value of bond strength calculated according to CEB-FIP are presented in (Table 3.7 – Table 3.9)

Fig 3 17 Bond stress relationship model - steel shear displacement CEB fib

3.5.2.1 Results of bond strength with further corroded specimens

Fig 3 18 Photograph of steel bar after artificial corrosion and pull-out test

Table 3 7 Results determination bond stress of concrete and reinforcement D12

3.5.2.2 Crack opening after artificial corrosion

Fig 3 19 (a) Photograph of steel bar after artificial corrosion and pull-out test;

(b) Splitting of concrete due to corrosion

Fig 3 20 Corrosion-induced cracks of reinforcement D12

The experiment revealed two distinct failure modes, with pull-out failure observed in 12mm diameter specimens and non-corrosion 16mm diameter control specimens, characterized by spalled concrete around the steel bar without crack propagation to the edge In contrast, splitting failure mode occurred in corroded 16mm diameter specimens and all 20mm diameter specimens, marked by splitting cracks emanating from the steel bar to the edge of the concrete block Notably, the diameter and compressive strength of the steel bar appeared to influence the extent of crack generation, with larger diameters and higher strengths resulting in more pronounced cracking.

This is because the concrete cube specimen had sufficient concrete cover depth

(200 mm), which is greater than five times the reinforcing bar diameter to provide confinement of the steel bar during the pull-out testing to result in pull-out failure

All corroded specimens exhibited similar failure modes influenced by corrosion levels, with D16 and D20 bars experiencing a shift from ductile to brittle failure characterized by splitting rather than slipping This change is attributed to the accumulation of corrosion products on the steel surface, resulting in longitudinal cracks and concrete damage, which hindered the effective transfer of forces between the steel and concrete.

Fig 3 23 Relation of bond stress - sliping displacement with reinforcement D12

The relationship between bond stress and slip displacement of steel bars in concrete pull-out tests is illustrated in Figures 3.23 to 3.25 It was found that the bond stress is significantly influenced by the diameter of the steel bar and the compressive strength of the concrete; specifically, bond stress increases with higher compressive strength The average bond strengths recorded for specimens with compressive strengths of 24.6 MPa, 35.1 MPa, and 44.1 MPa were 17.98 MPa, 22.13 MPa, and 25.88 MPa, respectively Notably, the bond strength observed in this experiment exceeded the predictions made by the CEB fib MC2010 guidelines.

(2013) The bond strength predicted from CEB fib MC2010 (2013) Based on Eq

(3-3) was 12.4MPa, 14.8MPa, and 16.6MPa, respectively When steel was corroded, bond strength was reduced

The relationship between bond stress and slip in concrete is significantly influenced by the diameter of the steel bar and the compressive strength of the concrete Notably, the experimental results showed that the slip values, s1 and s2, deviated from the proposed values of 1mm and 2mm, respectively, by the CEB-FIP bond-slip model for pull-out failure mode Specifically, for a 12mm steel bar diameter, the s1 and s2 values were lower than the CEB-FIP suggested values, whereas for 16mm and 20mm diameters, they were larger Furthermore, the range of s1 and s2 was found to be less than 1mm, and this range decreased as the compressive strength of the concrete increased.

3.6 The experiment to evaluate the characteristics and tensile strength of reinforcement when being corroded

Three sample nests of each concrete type were exposed to electrochemical corrosion for varying durations to achieve different corrosion levels Figure 3.25 illustrates the reinforcement samples post-corrosion: (a) shows the test sample with rust products, while (b) displays the reinforcement samples after rust removal Notably, the sample nest subjected to electric current for the longest duration exhibited the highest degree of corrosion.

Coefficients  are calculated by ratios based on parameters of volume ( ) w i , depth

( ) d i , surface width ( ) r i , he results are presented from (Table 3.10 - Table 3.15) The value of the coefficient  will change with the strength of the concrete from 25 – 45

According to Faraday's law and the relevant coefficient, it is possible to accurately estimate the duration of current application on a test structure to achieve the desired level of corrosion when the amperage is predetermined.

(a) Steel reinforcement is corroded (b) Steel reinforcement after rust removal

Fig 3 26 Shape of reinforcement when corroded over time

Fig 3 27 Electrochemical corrosion products of reinforcing bars

3.6.2.1 Coefficient of corrosion grade rating is based on d and r

Fig 3 28 a) steel bar has been cleaned rust; b) Measure the diameter of reinforcing steel that is corroded

Fig 3 29 The figure depicts the parameters of the corroded reinforcement hole

Fig 3 30 Cross section of the reinforcement section linked to the concrete

Based on the experimental results, we can propose the following:

Table 3 10 Result of the determine r d i , i D12 bar

Table 3 11 Result of the determine r d i , i D16 bar Specimens C.strength

Table 3 12 Result of the determine r d i , i D20 bar

Fig 3 32 Relationship between steel bar diameter and bond stress

The relationship between bond strength and corrosion levels is evident, showing an initial increase in durability that later declines At low corrosion levels, rust formation expands and applies pressure on the surrounding concrete, causing it to act like a thick cylinder under internal pressure This radial pressure effectively confines the concrete around the steel bar, thereby enhancing the bond strength.

High-strength concrete exhibits superior bond pressure compared to low-strength concrete when not subjected to corrosive conditions This improvement is largely due to differences in permeability, influenced by the concrete's microstructure and porosity Specifically, control mixes tend to be more permeable, while higher-strength concrete, such as those with 45 MPa, have significantly lower capillary porosity and fewer pores than those with 35 MPa or 25 MPa, which reduces the potential for corrosion penetration.

Corrosion of reinforcement leads to a significant deterioration in the bond strength of reinforced concrete At the same level of corrosion, high-strength concrete samples experience a more rapid decline in bond force compared to low-strength concrete.

This proves that buildings using high-strength concrete when the reinforcement in the concrete is corroded is very dangerous, the quality will be severely reduced

With low standard deviation and almost absolute accuracy this proves that the experiment has very high reliability

3.6.2.2 Coefficient of corrosion mass rating is based on w

1 Determine the weight w 0 of the original 5D steel reinforcement section that has not been corroded => Electronic Scales

3 Rebalance the reinforced segment associated with corrosive concrete over time

Based on the experimental results, we can propose the following:

Fig 3 33 The steel bar section is electronically balanced

Table 3 13 Results of pull-out tests for the D12 bar

Fig 3 34 The law of current variation in reinforcing bars

The results of the recording of the intensity of the current on the reinforcement bars are introduced on the charts (Fig 3.34) for the samples of each type of concrete

In this study, the electrolyzed corrosion duration was from 51.14 to 1185.33 hours, corresponding to samples with a concrete strength of 25 - 45 MPa (Table 3.13 – 3.15)

In low-strength concrete, the oscillation amplitude of the current is significantly higher, leading to increased current flow Initially, the amperage remains stable; however, as corrosive products accumulate on both the brine solution surface and the sample surface, the amperage decreases This decline occurs despite constant voltage, as the resistance rises due to the buildup of these corrosive materials.

Fig 3 35 Normalised bond stress versus corresponding corrosion level for different concrete types

The experimental results indicated that bond strength varied with different levels of concrete compressive strength, demonstrating a clear relationship where bond strength increased alongside compressive strength In instances of consistent compressive strength, the correlation between bond strength and corrosion levels was linear, with a coefficient of determination nearing 1 Moreover, the findings revealed that bond stress degradation accelerated as corrosion levels rose, particularly when concrete compressive strength was elevated It is essential for concrete compressive strength to be at least 35 MPa in corrosive environments to maintain optimal bond performance.

[64] In the case of concrete compressive strength of 35.1MPa and 44.1 MPa, the

Corrosion significantly impacts the bond strength between steel bars and concrete, with a reduction of up to 50% observed at corrosion levels of 18% and 11% This decline in bond stress compromises the overall capacity of concrete structures Notably, in structures with higher compressive strength, the degradation of corroded reinforced concrete (RC) occurs more rapidly as corrosion levels rise Conversely, in concrete with greater strength, even lower corrosion levels in steel bars correspond to a higher capacity of the corroded structure.

3.6.3 Bearing capacity of reinforcement when corrosive

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