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UNIVERSITY OF TRANSPORT AND COMMUNICATIONS RESEARCH ON THE MECHANICAL BEHAVIOR OF REINFORCED CONCRETE BRIDGE DECK SLAB ON BEAMS SUBJECTED TO THE STATIC EFFECT OF VEHICLE LOADS BRIEF S

UNIVERSITY OF TRANSPORT AND COMMUNICATIONS

RESEARCH ON THE MECHANICAL BEHAVIOR OF REINFORCED CONCRETE BRIDGE DECK SLAB

ON BEAMS SUBJECTED TO THE STATIC EFFECT

OF VEHICLE LOADS

BRIEF SUMMARY OF ENGINEERING DOCTORAL THESIS

Hanoi - 2022

University of Transport and Communications

Reader can find this thesis at:

- Library of University of Transport and Communications;

- Vietnam National Library

INTRODUCTION

1 Why choose the topic

The reinforced concrete bridge deck slab (BDS) on beams is commonly used in bridge constructions [6] This element is an important part of the span The BDS participates in the overall load bearing together with the supporting beams/beam ribs, local load bearing due to wheel loads, contributes with the transverse beams to distribute the live load horizontally across the bridge, and protects the underlying structure The main damage types in the bridge deck slab are cracking, breaking, peeling of concrete, and abrasion [10] Cracking of the bridge deck slab leads to water and corrosive substances penetrating into the concrete, corroding, and rusting the rebar, causing peeling of the concrete layer, and water seeping through the water gap into the supporting beams, causing loss of construction aesthetics If not remedied in time, the cracks expand and propagate, and the rebar is rusted and corroded, reducing the bearing capacity It eventually leads to a decrease in bearing capacity, reduced exploitation capacity, reduced service life, and deterioration of the building Therefore, the quality of the deck slab greatly affects the bridge construction

In Vietnam, the overloading of vehicles is relatively common The cause of the overload is due to the rapid industrialization process, the traffic infrastructure has not been able to meet the requirements Many old bridges have not been repaired and strengthened The awareness of obeying traffic laws is not high, and the need to transport a number of special machinery and equipment Due to the unfavorable factors of the hot and humid tropical environment and overloaded exploitation conditions, the deterioration of concrete deck slabs in Vietnam is relatively common The cost of maintaining and repairing the bridge deck slab is quite expensive [9]

Regarding the design cracking resistance of reinforced concrete bridge deck slab, AASHTO LRFD standard, as well as TCVN 11823:2017, only stipulate rebar spacing, while 22TCN 272-05 only considers stress limit in rebar according to state usage limits (use standard load combinations for validation) These design standards do not consider crack formation, propagation, and expansion according to the theory of concrete fracture and failure mechanics On the other hand, in the design of reinforced concrete deck slabs by some consultants, there are still many shortcomings such as the lack of a clear equivalent slab diagram, and the assumptions that simplify the problem in many cases are not consistent with reality There is no comparison and selection of concrete grade, type, and arrangement for rebar

Some studies have been studying the cracking behavior of reinforced concrete bridges, specifically, the cracking behavior of reinforced concrete deck slabs [10]; reducing slab cracking by using alternative materials [17]; cracking behavior of reinforced concrete deck slabs due to ambient temperature [20] These studies have not solved the cracking mechanism, crack distribution, and propagation in the reinforced concrete bridge deck slab caused by heavy trucks

Some Vietnamese researchers have also been studying the cracking behavior of reinforced concrete deck slabs due to heavy loads; however, the publications are still limited Trinh Van Toan (2010) [5] analyzed and evaluated the damage of the deck slab and span due to heavy trucks based on fatigue theory The author has evaluated the damage in the structure due to fatigue after each stress cycle of trucks that are many times heavier than those of trucks within the allowable limit However, the study has not specifically evaluated the formation and development

of cracks such as cracking load and crack distribution

The overloaded vehicle creates large stress in the reinforced concrete deck slab and thus causing the crack When the concrete is cracked, the tensile force

in the concrete is transferred to the rebar causing increasing stress in the rebar, and the stiffness of the BDS decreases leading the increasing deflection Obviously, this situation will be more serious if overloaded vehicles are not effectively controlled The deck slab has cracked and continues to be loaded, and the cracks continue to grow, propagate and expand, leading to more severe damage, reduced service life, loss of quality, and exploitability of construction Research on the mechanical behavior of reinforced concrete deck slabs due to heavy trucks is required The clarification of the mechanism of occurrence, propagation, and expansion of cracks in the reinforced concrete deck slab due

to overloaded vehicles will provide further improvement of structural solutions

as well as in terms of controlling vehicle weight Therefore, choosing the research topic "Research on the mechanical behavior of reinforced concrete bridge deck slab on beams subjected to the static effect of vehicle loads" is very necessary, and has scientific and practical significance

2 Subjects of research

The subject of the thesis is the slab-on-beam reinforced concrete bridge deck of a simple span In the span, the reinforced concrete deck slab is poured with the girder rib or poured in place in conjunction with the main girder

Method of analysis and synthesis of theory: research of relevant documents

to select a suitable model for simulation of cracking in reinforced concrete deck slab poured in-situ due to overloaded vehicle

Modeling method: simulate the number of cracks in the reinforced concrete deck slab poured in-situ caused by overloaded cars according to the theory of failure mechanics

Experimental method: Creating models, arranging and conducting experiments to determine the mechanical behavior of the new T-beam span or

damaged T-beam span reinforced with FRP sheet and reinforced concrete slab listed above 2 edges under the effect of static loads

5 Scopes of research

Do not consider the interaction between load and cracking factors such as shrinkage, corrosion, temperature, fatigue to cracking of the deck slab Initial damage in deck slabs is not considered

The load used in the numerical simulation is a heavy truck placed statically

on the bridge taking into account the shock coefficient

Concrete and rebar are assumed to be fully bonded

6 The scientific meaning and practical application of the thesis

Building a dataset of cracking characteristics of concrete

A computational model has been experimentally verified to analyze the cracking behavior of the deck slab

A suitable experimental model was built to analyze the cracking behavior

of the deck slab similar to reality, thereby performing BDS's cracking behavior analysis experiments

Recommend equivalent strip model when calculated according to slab structure based on numerical simulation results

Analyze the effect of reinforcing FRP sheet on the anti-cracking effect of the deck slabs by experiment

Evaluation of the solution for the structure of the reinforced concrete deck slab for the I-beam span, which is commonly used in Vietnam today, when it is subjected to overloaded vehicle loads

Investigate the structural parameters of the slab-on-beam reinforced concrete bridge deck and propose a solution for anti-cracking design

CHAPTER 1 OVERVIEW OF CRACKING IN BRIDGE DECK SLAB

AND OVERLOADED VEHICLE IN VIETNAM

1.1 Slab-on-beam reinforced concrete bridge deck

The deck slab is the part that participates in the overall load bearing, and local bearing due to the axial load, shields and protects the underlying structure and contributes to the distribution of live load in the transverse direction of the bridge The slab-on-beam reinforced concrete deck structure is commonly used

in simple span structures with I-beams, T-beams, super T-beams, and beams The deck structure depends on many factors such as the type of girder support, beam spacing, material strength, design load, design criteria, and other factors The deck slab works according to the cantilever plan, the list on 2 sides, or the list on 4 sides [2] Structural reinforced concrete slabs on beams are usually calculated according to the two-sided list diagram with the main working direction being the bridge transverse For bridges designed according

-to standard 22TCN 272-05 and TCVN 11823:2017 from 2005 onwards, simple span reinforced concrete BDS has a minimum thickness of 175 mm The common thickness of the deck slab is 175 mm  220 mm, depending on the

calculated aperture of the slab, design load, and type of girder In some bridge constructions, where the deck slab thickness is changed to create a horizontal slope, the deck thickness can be up to 300 mm at the thickest position For bridges designed according to standard 22TCN 18-79 with no specified minimum deck thickness, many bridges with BDS thickness less than 175 mm have been built Horizontal load-bearing rebar with a diameter of 12 mm  18

mm is arranged in 2 layers above and below When the distance between beams/supporting beams increases, the calculated aperture of BDS needs to increase the load-bearing rebar The longitudinal rebar with a diameter of 10

mm  12 mm is arranged in 2 layers and is usually used Regarding materials, the yield strength of rebar is 240 MPa  420 MPa, and concrete strength is 20 MPa  35 MPa and tends to increase The reinforced concrete deck slab is combined with the supporting beam through rebar or an anchoring system [8]

In Vietnam, the overloaded of vehicles is relatively common [1, 5] An overloaded vehicle is a vehicle whose total weight or axle load exceeds the road's operating load The cause of the overload is due to the rapid industrialization process that the traffic infrastructure has not been able to meet, the awareness of obeying traffic laws is not high, or the need to transport certain types of machinery and special equipment

Figures 1 1: Load distribution density of overloaded 3-axles truck [1] Due to unfavorable environmental factors and operating conditions, cracking of concrete deck slabs in Vietnam due to overloaded vehicles still occurs The bridge repair work, including the deck slab, takes place quite often and in many cases has to be replaced with a new deck

Figures 1 2: Cracks at the bottom of the deck slab - Ba Trien Bridge (Km

1482+474 National Highway No.1)

1.2 Cracking of reinforced concrete deck slab due to load

1.2.1 Causes of cracking of reinforced concrete deck slab due to overloading

Since the tensile strength of concrete is very small; in areas with high tensile stress, concrete cracks and the tensile force in reinforced concrete deck slab will be borne by the rebar When the reinforced concrete deck is subjected to a larger vehicle load than the bearing capacity, the first cracks appear at locations with high stress or locations subject to large shock loads and concentration of stress In the case of reinforced concrete members in general, under the effect of load, cracks form and develop in 3 stages:

- Stage 1: New cracks form invisible to the naked eye In the member section without change of internal force and section, the first crack is formed at the location where the concrete quality is the worst At this time, the crack width is still small

- Stage 2: The crack is open to the naked eye

- Stage 3: The crack expands to the critical value, at this time the cracks tend to

be evenly distributed over the member sections

When subjected to the concentrated load of the wheel, the slab-on-beam reinforced concrete bridge deck has an arch effect as shown in Figure 1 4 Compression film in reinforced concrete slabs occurs due to the large difference between tensile and compressive strengths of concrete The cracking of concrete causes displacement of the neutral axis, which is accompanied by the in-plane expansion of the slab at its boundaries If the expansion tendency is restrained in two dimensions, the development of the arch effect will strengthen the bearing capacity of the deck slab The cross-sectional equilibrium is maintained by a belt loop around the compression field as shown in Figure 1 5

Figure 1 4: The arch effect in the concrete deck slab [14]

Figure 1 5: Belt loop around the compression field [14]

1.2.2 Calculation of crack width

The first crack in a reinforced concrete element will appear when the maximum tensile stress reaches the tensile strength Where there is a crack, the stress in the rebar increases significantly This change in stress is directly proportional to the tensile strength of the concrete and inversely proportional to the rebar content The width of each crack is determined depending mainly on the longitudinal deformation difference between the rebar and the surrounding concrete

Gergely and Lutz (1968) proposed a formula for calculating the maximum crack width in the tensile zone of the flexural member as follows [15]:

wmax is the largest crack width,

 = (h-c)/(d-c) is the coefficient that considers the variation of strain in sectional height, h is the cross-sectional height, d is the effective height and c is the height of the compressive concrete area Normally,  = 1,2,

dc is the thickness of the protective concrete layer up to the center of gravity of the first layer of rebar,

s is the maximum strain in the rebar caused by the applied load, usually taken as 0,6y with normal structure if not specifically calculated,

c,eff

bc

A

A =

 is the area of concrete in tension divided by the number of

reinforcing bars in the tension zone Ac,eff is defined as the concrete area whose center of gravity coincides with the centroid of the tension rebar, and c is the converted number of tensile rebars

1.2.3 Permissible crack width

Cracks cause damage to reinforced concrete structures, so they need to be limited To limit the crack width in normal reinforced concrete members, we arrange the tensile longitudinal rebar in the maximum tensile concrete area The crack width depends on the tensile stress in the rebar and the arrangement

of the rebar in the tensioned concrete area

The maximum allowable crack width for a member depends on the function

of the member and the ambient contact conditions Table 1 1 gives the allowable crack width values for concrete structures under different environmental conditions specified in ACI Standard 318-05 [12] In case the calculation results are not satisfactory, it is necessary to use many small-diameter rebars or increase the rebar diameter

Table 1 1: Permissible crack width according to ACI 318-05

Environmental conditions Permissible crack width (mm) Dry or with a protective film 0,41

Sea water or sea dust; wet and dry 0,15

Water barrier structures (except for

1.3 Research situation on reinforced concrete deck slab cracking due to vehicle load in the world and in Vietnam

1.3.1 Research situation in the world

In 1996, Michael F Petrou and his colleagues conducted an experimental study conducted on a model of a composite steel girder bridge with a scale of 1/6.6 [18] The results show that the correlation results between the deck slab models from the most complex diagram that closely follows reality to the simplified diagram that is the equivalent slab strip diagram for simplicity of calculation The limitation of the study is that the miniature model is used with low accuracy and the applied loads do not accurately reflect the vehicle load acting on the bridge

In 2014, Baah presented research results on « the cracking behavior of reinforced concrete bridge deck» in his doctoral thesis [10] The thesis presented details of an experimental investigation on the cracking behavior of concrete structures

In 2016, Fareed Elgabbas and colleagues conducted a research project investigating the behavior of edge-restricted concrete deck slabs reinforced with BFRP (basalt-fiber-reinforced-polymer) bars [13]

1.3.2 Research situation in Vietnam

In Vietnam, research results on reinforced concrete cracking generally are limited Typical studies on concrete cracking are as follows:

Trinh Van Toan (2010) presented in his doctoral thesis the results of the analysis and damage assessment of deck slabs and span structural members due

to heavy trucks based on fatigue theory [5]

Nguyen Lan (2014) has evaluated and determined the allowable load to cross the bridge on the basis of the bridge test results [1]

Other research results related to the topic, such as Tran Duc Nhiem (2004) [3], Tong Tran Tung (2005, 2014) [8, 9], and Doan Minh Tam (2005) [4] The studies presented the problems of overloading vehicles, determining the load of the signboards, the damage to the road and bridge system, and the economic losses caused by the overloaded and oversized vehicles

1.4 Summary of chapter 1

The deck slab is a part of the bridge structure that is directly affected by the vehicle load through the wheel pressure; therefore the reinforced concrete deck often occurs various damages There are different types of damage, the most common of which is cracking When the deck slab has been cracked and continues to be loaded in an incomplete state, the cracks continue to grow, propagate and expand, leading to more severe damage, reduced service life, and serious injury quality and exploitability of the construction This situation will be more serious if overloaded vehicles are not effectively controlled The researches on cracks for bridge construction in the world and in Vietnam are mainly for bridge girders Studies on the cracking of concrete deck slabs are limited and focus mainly on causes due to shrinkage and corrosion Cracking of deck slab due to overloading of the vehicle is only considered as a primary cause of cracking There have not been in-depth studies on the formation mechanism, and the propagation of cracks due to overloading in an adequate way It is necessary to clarify the mechanism of occurrence, propagation, and expansion of cracks in the reinforced concrete slab of the bridge deck due to general loads and overloaded vehicles, which will have a basis for further improvement of structural solutions as well as in terms of controlling vehicle weight

CHAPTER 2 THEORETICAL CALCULATION OF REINFORCED CONCRETE BRIDGE DECK SLAB SUBJECTED TO STATISTIC

EFFECT OF VEHICLE LOADS 2.1 Behavioral models of concrete and rebar

Concrete and rebar are two basic materials constituting the main structural forms, including reinforced concrete and prestressed reinforced concrete To numerically simulate structural members, three modeling problems are required for solving: the material model of concrete, the behavior model of steel, and the interaction model between concrete and rebar [21], [23]

2.1.1 Behavioral model of concrete

The mixed behavior law has been developed by many authors in recent years to consider all the properties of concrete materials including asymmetry, brittleness, inelasticity, and compressive strength and anisotropy, whereby brittleness and plasticity are considered together to get the model closest to

experimentally observed results, two combined parts include elastic-brittle state and brittle-plastic composite

Figure 2 1: The mixed behavior law of elastic - brittle - plastic

2.1.2 Behavioral models of rebar

The behavior of the rebar is usually taken according to the absolute elastic law When higher accuracy is required, the elastic-plastic law with isotropic reinforcement can be used or the elastic-plastic law with dynamic reinforcement can be used

Figure 2 2: Elastic-plastic model with dynamic reinforcement

2.1.3 Simulation of the interaction between concrete and rebar

2.1.3.1 Geometric representation of rebars

Rebars in reinforced concrete structures can be represented discontinuously

or continuously depending on the calculation approach :

If the representation is discontinuous, the rebars are simulated by bar elements connected to the concrete continuous medium by special connections

If the representation is continuous, a group of rebars with a known orientation angle is considered as a steel strip whose thickness depends on the steel content in this direction; two possibilities of unidirectional or bidirectional behavior of the strip can be considered If the behavior is unidirectional, the rebars are stiff strips located along the direction of the rebars and evenly distributed over the element, two strips in two different directions will form a reinforcing mesh whose thickness depends on the number of rebars

in each direction If the behavior is bidirectional, the upper rebar mesh is represented by a layer of bidirectional behavior rebar having different elastic moduli Ea and Eb in each direction as for orthotropic materials [21, 23]

(2) Discontinuous representation (b) Homogenized continuous representation

Figure 2 3: Representation of the presence of rebars in concrete

For concrete structures that work mainly under bending such as structural members of bridge constructions, simulating the discontinuous representation

of rebars in concrete as the first case is the optimal choice Although the homogenization representation as the continuous case is unnecessary and complicates the calculation, it is only suitable for structures with more complex structures such as nuclear reactors…

2.1.3.2 Model of concrete-rebars connection

The concrete-steel rebar bond ensures the existence of reinforced concrete structures, allowing the effects of loads to be transmitted between them under load

The interaction between the components significantly affects the actual behavior of the sample and the simulated behavior of the sample Simulating real-world interactions is difficult because many factors influence the relationships between components In fact, there is always a relative slip between concrete and rebars, but within the scope of this thesis, to simplify calculations, the author mainly uses the assumption of the rigid connection between concrete and rebar The separation effects of these two materials are excepted in the calculation process Three types of interaction models between concrete and rebars are smeared model, the discrete model, and the embedded model These models are widely used in specialized software such as Abaqus, Ansys, and Midas FEA [19]

Figure 2 4: Interaction form between rebars and concrete [16]

2.2 The theory of concrete failure and cracking, applied in the analysis of the failure mechanism of reinforced concrete structures

2.2.1 The behavior of concrete when destroyed and cracked

To analyze the mechanism of failure and cracking in concrete, it is necessary to accept some assumptions as follows:

- Concrete is assumed to be intact while working in the elastic stage

- The concrete environment is assumed to be homogeneous until the formation of large cracks begins

- Concrete failure is initiated by the appearance of small scattered cracks in the adverse bearing areas As the load continues to increase, these microcracks tend to gather to produce visible large cracks

Figure 2 5: Stages of concrete behavior under the applied loads [7]

Figure 2 5 shows that the application scope of the theory of failure mechanics to analyze the behavior of concrete is in segment ABC, and the application scope of the theory of fracture mechanics is in the end BCD Thus, the common segment BC can simultaneously use these two theoretical bases to describe the behavior of concrete The trend of current research is to use combination theory to analyze the behavior of concrete from initial to complete destruction

2.2.2 The behavior of concrete according to the fracture model

Dispersion crack model (weak continuum cracking model)

Figure 2 6: Representation of crack development zones in distributed cracking models

The considered discontinuity is the displacement in these models Typical for this group of models is the Crack Band Model (CBM) proposed by Bazant & al (1983) when assuming the existence of a parallel discontinuous crack band with a thickness h  3dmax (dmax is the maximum diameter of aggregate particles) [33]

Bazant and Oh proposed a CBM banding model based on the assumption that there exists a crack band with wt

width around the initial crack tip The crack band appears from many very small cracks This assumption is completely consistent with the basic knowledge that the structure of concrete is a heterogeneous material The author suggests that there is an even distribution of strain f

in the crack band

2.3 Applying numerical methods in destructive mechanics

Nowadays, various numerical methods have been developed to solve destructive mechanics problems such as the finite element method, boundary