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MINISTRY OF EDUCATION AND TRAINING 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 This thesis was completed at: University of Transport and Communications Supervisors: Reviewer 1: Reviewer 2: Reviewer 3: The thesis is defended in front of the University-Graded Committee of thesis evaluation according to Decision # ./QĐ-ĐHGTVT, on date 2022 signed by the Rector of University of Transport and Communications on date………………… 2022 Reader can find this thesis at: - Library of University of Transport and Communications; - Vietnam National Library INTRODUCTION 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 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 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 Purpose of research Determining the mechanism of occurrence, propagation, expansion of cracks along with stress, and deflection of slab-reinforced concrete bridge slab on cast-in-place beams subjected to the static effect of vehicle loads Research methodology Methods of investigation: to collect, survey and evaluate the current state of cracks in the reinforced concrete bridge deck poured in place 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 edges under the effect of static loads 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 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 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 sides, or the list on 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 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 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: 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 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 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 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 Figure 4: The arch effect in the concrete deck slab [14] Figure 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]: w max = 2, 2s d c A (1 1) Where: 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, A= A c,eff  bc 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 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 smalldiameter rebars or increase the rebar diameter Table 1: Permissible crack width according to ACI 318-05 Environmental conditions Permissible crack width (mm) Dry or with a protective film 0,41 Moist, air or moist soil 0,30 Descaling chemicals 0,18 Sea water or sea dust; wet and dry 0,15 Water barrier structures (except for non0,10 pressurized pipes) 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 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 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 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 1: The mixed behavior law of elastic - brittle - plastic 11 Figure 5: Stages of concrete behavior under the applied loads [7] Figure 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 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 w there exists a crack band with t 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  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 f 12 element method, extended finite element method, and finite element method combined with modified boundary element method, non-grid method, … 2.4 Summary of chapter Chapter presented numerical methods in failure mechanics applied to reinforced concrete structures, the behavioral models of concrete and rebar; determine the suitable model for nonlinear analysis of reinforced concrete structure cracks In this thesis, the author chooses a distributed crack model (Weak Continuous Cracking Model) for cracking analysis of reinforced concrete deck slabs For concrete, in addition to the normal physical and mechanical criteria as in the linear analysis model, it is necessary to determine the failure characteristics of the concrete to meet the input parameters for the nonlinear fracture analysis model CHAPTER EXPERIMENTAL RESEARCH TO DETERMINE MECHANICAL AND DETERMINATELY CHARACTERISTICS OF CONCRETE AND MECHANICAL BEHAVIOR OF REINFORCED CONCRETE BRIDGE DECK SLAB 3.1 Experiment to determine the physical and mechanical properties of materials Purpose of the experiment: Testing materials to determine the physicomechanical parameters for a grade of concrete used in bridge construction, supplementing the data set on the physical and mechanical parameters of concrete and the cracking parameters Determine the input parameters of concrete materials in numerical simulation Testing to determine cracking characteristics The cracking characteristics of concrete to be determined include the ultimate stress strength KC, the ultimate cracking energy GC, the total cracking energy GF, and the incomplete cracking energy Gf [2] Cylindrical test specimens of size 15 x 30 (cm) were used to determine the compressive strength of concrete f’c Test specimens of 15 x 15 x 60 (cm) flexural beams were used to determine the tensile strength of concrete f’t Thin beam test specimens with primer cracking are used to determine the cracking parameters of concrete The total number of test beam samples is x x = 16 samples Figure 1: Three-point bending test with primer cracks 13 Total cracking energy value GF can be inferred from Gf using the approximate formulas GF = 2,5Gf [11] Calculation results: Gf = 148,75J/m2 and GF = 371,87J/m2 3.2 Test of T-beam structure under static load – Test Purpose of the experiment: Experiment with a model of a reinforced concrete deck slab with large dimensions similar to reality to determine the mechanical behavior of a composite slab reinforced concrete deck with beams under the influence of concentrated loads, which simulates the wheel load The test for checking the accuracy of numerical simulation results 3.2.1 Test set-up Figure 2: Experimental test with T beam - Test The testing process for T-beam: Loading from for each load level of Tons until the sample is damaged 3.2.2 Test resutls 3.2.2.1 Measurement results of crack expansion and crack distribution Figure 3: Development of crack width in slab bottom under each load level Figure 4: Crack distribution at slab bottom – Test 14 Side crack – View direction Side crack – View direction Side crack – View direction Side crack – View direction Figure 5: Crack distribution and crack width at the side faces 3.2.2.2 Result of deflection Layout diagram of deflection measurement points as shown in Figure 6: Figure 6: Layout diagram of deflection measurement point and measurement results – Test 3.3 Test of severely damaged T-beam structure repaired by gluing FRP sheet under static load – Test Purpose of the experiment: To determine the mechanical behavior of reinforced concrete deck slabs with reinforced beams after being severely damaged under the influence of concentrated loads simulating wheel loads 15 Analyze and evaluate the effectiveness of the reinforcement solution for BDS by the gluing FRP sheet 3.3.1 Test setup Figure 8: Reinforcing the FRP sheet and the test setup of the reinforced concrete deck slab – Test 3.3.2 Experiment results Figure 23: Crack distribution and crack width at the side faces – Test Figure 26: Compare the deflection at the slab bottom on the longitudinal centerline between the original structure and after repair for the same load levels 16 3.4 Test of 2-sided list deck slab under static load – Test Purpose of the experiment: Experiment with a model of a reinforced concrete deck slab with large dimensions similar to reality to determine the mechanical behavior of a reinforced concrete deck slab that is not associated with the girder or that rotates freely with the lower girder under the effect of a concentrated load of wheel load 3.4.1 Test setup Figure 8: Conduct test of reinforced concrete deck slab – Test 3.4.2 Experiment results Figure 9: Crack distribution at the bottom of the slab after the end of test CHAPTER NUMERICAL INVESTIGATING BEHAVIOR OF REINFORCED CONCRETE BRIDGE DECK SLAB SUBJECTED THE CONCENTRATED LOAD 4.1 Compare simulation results with nonlinear cracking experimental results Model the reinforced concrete bridge deck slab according to the 3D diagram with the actual size of the experimental model 1- 3D model and analysis results of T-beam using ANSYS 17 2- 3D model and analysis results of T-beam using MIDAS FEA Figure 1: 3D model and crack analysis results of T beam Figure 2: 3D model of 2-sided list reinforced concrete bridge deck slab in ANSYS Compare the results of the crack nonlinear analysis with the experimental results of the T-beam structural model and the 2-sided list under static loads Figure 3: Comparison of the deflection at the center of the deck slab (V3) between the numerical and experimental results The deflection curve of the numerical simulation closely matches the experimental curve 18 The results of measuring cracks in the experiment and simulating crack distribution in the simulation are presented as shown in Figure 4 and Figure 5: 1- Experiment results 2- ANSYS results Figure 4: Comparison of crack distribution between numerical simulation results by ANSYS with experimental results of the T-beam model 1- Experiment results 2- MIDAS FEA results Figure 5: Comparison of crack distribution between numerical simulation results by MIDAS FEA with experimental results of the T-beam model In this thesis, both ANSYS and MIDAS FEA software are used simultaneously, suitable for each specific problem to be analyzed 4.2 Structural analysis of T-beam spans subjected to the static effect of heavy trucks 4.2.1 Analytical model 1350 250kN 175kn 8700 150 1900 250 625 625 658 1250 398 625 250 4500 1250 250 625 150 3300 250kN 4500 4500 Figure 6: Schematic of 3-axle truck on the span 19 4.2.2 The analysis results of the span subjected to the static effect of trucks Figure 7: Stress distribution of deck slab bottom with axial load levels Figure 8: Crack distribution at 25 tons axial load levels Under 25 ton axial load of a heavy truck, the span is cracked in BDS, longitudinal beams, and transverse beams The deflection, stress in rebar, and crack expansion in BDS are still within the allowable limits 4.3 Determine the equivalent deck slab strip diagram when bearing the load of a heavy truck The 3D models of the surveyed reinforced concrete strip subjected to the wheel load in the center of the slab, as shown in Figure Compare the results of the survey models with the 3D model of span in Section 4.2 to determine the equivalent strip model Figure 9: Model of the strip subjected to the wheel load 20 Figure 10: Stress distribution at slab bottom - Linear analysis When the girder ribs or supporting beams with high flexural stiffness are combined with transverse beams, the equivalent slab strip is a slab strip with two clamped edges in the longitudinal direction of the bridge and two free edges in the transverse direction of the bridge The calculated aperture of the slab is calculated according to the formula Stt = S - tw/2, where, S is the distance between the centers of the girder ribs/longitudinal beams, tw is the thickness of the girder/longitudinal beams The width of the strip is taken according to the bridge design standard TCVN 11823:2017 4.4 Mechanical behavior of reinforced concrete deck slab of prestressed reinforced concrete I girder span under the static effect of trucks 4.4.1 Analytical model Table 1: Structural parameters of reinforced concrete deck slab of typical prestressed reinforced concrete I girder Type of Design S bw ts Horizontal Longitudinal Stt E span load (mm) (mm) (mm) rebar rebar (mm) (mm) Type 1: D14 D10 I12.5m pre- HL93 1500 140 175 1430 1485 a=0,15m a=0,2m tension Type 2: D14 D10 I33m pre- HL93 1750 160 180 1670 1623 a=0,15m a=0,2m tension Type 3: D12 D10 I25.7m post- HL93 2400 200 200 2300 1980 a=0,1m a=0,2m tension Note: S-distance between centers of longitudinal beams; bw -thickness of girder rib; ts-thickness of deck slab; D-diameter of rebar; a-step rebar; Stt – the calculated aperture of the equivalent strip; E - equivalent strip width 4.4.2 Analysis results 21 Figure 11: Maximum deflection of deck slab according to load levels Type Type Type Figure 12: Crack distribution corresponding to 25 tons level The deflection, stress in rebars, and crack extension of the survey models are within the allowable limits Cracks are concentrated below the loading zone 4.5 Research of parameters affecting mechanical behavior of reinforced concrete deck slab on beams subjected to the static effect of vehicle loads 4.5.1 Parameter survey of material Figure 13: Mechanical behavior of reinforced concrete BDS according to concrete strength levels As the concrete strength increases, the crack area at the bottom of the slab and the jaws narrow gradually When the compressive strength of concrete is higher than 50 MPa, the bottom of the slab does not appear crack The deflection, the stress in rebar, and the crack extension are all much smaller than the allowable limit even for the low strength class of 20 MPa, as 22 shown in Figure 13 The values of these behaviors decrease rapidly when the concrete strength increases from 20 MPa to 45 MPa, then they decrease slowly, with strength grades from 55 MPa to 70 MPa The increasing concrete strength did not provide much additional anti-cracking effect 4.5.2 Parameter survey of slab thickness Figure 14: Mechanical behavior of reinforced concrete BDS according to slab thickness The curves presented the relationship between the stress in rebar, deflection, the extension of crack, and the slab thickness are divided into two branches; the branch has a steep slope corresponding to a thickness of less than 190 mm However, the difference between the two branches is not clear, and both branches decrease almost linearly with the slab thickness Crack distribution area, large cracks, the stress in rebar, and crack expansion decrease rapidly with increasing BDS thickness The increasing thickness provides a high anti-cracking effect 4.5.3 Parameter survey of rebar Table 2: Summary of survey results on the mechanical behavior of reinforced concrete BDS according to slab thickness Crack fsmax wmax max Sample distribution (Mpa) (mm) (mm) Sample 1, diameter 10 mm, distance 75 mm 58,20 0,2875 0,0716 Sample 5, diameter 18 mm, distance 245 mm 51,88 0,2792 0,0898 Note: fsmax – Maximum stress in rebar; max – Maximum deflection; wmax – Maximum crack expansion 23 Changing the rebar diameter while keeping the rebar content does not bring about a synchronous anti-cracking effect for BMC Using the small diameter rebar for small crack expansion and wide crack area The rebar with a diameter from 12 to 16 mm can limit the crack area and reduce deflection 4.5.4 Proposing a solution to reinforced concrete deck slab on beams subjected to heavy trucks Table 3: Proposed reinforced concrete BDS subjected to heavy trucks Proposed BDS Compressive Diameter – a strength of concrete distance of rebar Beam distance Slab thickness (mm) (mm) (MPa) (mm) Sample 1250 175 35 12 - 150 Sample 1500 185 35 14 - 150 Sample 1750 195 40 14 - 150 Sample 2000 205 40 14 - 150 Sample 2250 205 45 16 - 150 Sample 2500 210 45 16 - 150 Sample 2750 215 50 18 - 150 Sample 3000 220 50 18 - 150 CONCLUSIONS AND FUTURE RESEARCH Conclusion New contributions of the thesis: Provide data set on mechanical properties of concrete used in bridge construction, such as compressive strength, tensile strength, crack energy, and ultimate cracking strength etc, which are necessary for computational simulation of bridge structure behavior Some experiments have been built to analyze the mechanical behavior of the reinforced concrete deck slab subjected to the static effect of vehicle loads and measurements Provide data on the formation and development of cracks, deflection, and crack widening in BDS and the effectiveness of reinforcing FRP sheets for the cracked reinforced concrete slabs 24 A computational model was built to analyze the mechanical behavior of the reinforced concrete deck slab on the girder under the impact of static loads Analyze and evaluate the mechanical behavior of the T-beam span subjected to the static effect of vehicle load Propose an equivalent strip to calculate and design reinforced concrete deck slabs On that basis, analyze and evaluate the behavior of reinforced concrete bridge deck slab with prestressed reinforced concrete I girder span; propose a reasonable structure of reinforced concrete deck slab, considering concrete grade, slab thickness, and arrangement of rebar to control the cracks due to overload of the vehicle Future research Research on cracking behavior of the deck slab subjected to dynamic loads Research on the cracking behavior of the old deck slab, considering reducing material properties, the reduction of rebar cross-section, and the deterioration of adhesion between the rebar and the concrete Research on the development of cracks under repeated load Research on the mechanical behavior of the bridge deck structure using high strength and ultra high strength concrete under the effect of vehicle load Combination of finite element method and artificial intelligence to analyze the mechanical behavior of deck slab Research on cracking of reinforced concrete deck slabs, considering orrosive and temperature factors LIST OF PUBLICATION Nguyen Duc Hieu, Pham Van Hung, Tran The Truyen (2017), Simulation of mechanical behavior of reinforced concrete deck slabs subjected to overloaded vehicles, National Mechanics Conference Xth, pp 351-358 Nguyen Duc Hieu (2018), Determining the causes and solutions to overcome longitudinal cracks for wide slab bridges with prestressed reinforced concrete poured in-situ, Proceedings of the National Scientific Conference on Solids Mechanics XIV, pp 244-251 Nguyen Duc Hieu, Tran The Truyen, Bui Thanh Tung (2018), “Fracture analysis of reinforced concrete bridge deck under overload vehicles”, 2018 International Conference on Sustainability in Civil Engineering, pp.345-350 Nguyen Duc Hieu, Ngo Chau Phuong (2018), Initial assessment of the current situation of structural cracking of the bridge span due to overloaded vehicles in the southern region and proposed solutions to overcome Scientific Conference 21st, University of Transport and Communications, campus in Ho Chi Minh, pp 178-188 Nguyen Duc Hieu, Ngo Chau Phuong, Tran The Truyen (2019), Analysis of the behavior of reinforced concrete deck slab of I-beam span subjected to overloaded vehicles", Journal of Transport, Issue 3/2019, pp 34-38 Nguyen Duc Hieu, Tran The Truyen, Bui Thanh Tung, Doan Bao Quoc (2019), Cracking analysis of reinforced concrete bridge deck subjected to overload vehicle, In: The 5th International Conference on Engineering Mechanics and Automation, pp 161-168 Nguyen Duc Hieu, Tran The Truyen (2020), "Effect of overloaded vehicle loads on the crack distribution on reinforced concrete bridge span structures", Journal of Transport, No 5/2020, pp 43-46 Duc Hieu Nguyen, The Truyen Tran, Thanh Tung Bui, Minh Cuong Le, Ngoc Trinh Vu (2021), Analysis of crack characteristics of reinforced concrete bridge deck under the effect of static wheel load, In: CIGOS 2021, Emerging Technologies and Applications for Green Infrastructure Springer, Singapore, pp 69-77