## Design and Analysis of Fiber Reinforced Concrete Structure for Transportation Infrastructures

##### Abstract

Concrete is one of the most popular materials in superstructures (buildings), substructures (foundation) and infrastructure facilities (bridges, pavements, and tunnels). However, concrete is a brittle material that cracks easily under tension.
Fiber may be used as reinforcement to impede the concrete from cracking as well as to increase the concrete flexural strength. Nevertheless, current design codes do not include this design enhancement. Furthermore, there are discrepancies in the design methodology concerning the inclusion of discrete fibers in concrete structures. Therefore; there is a need to develop new analysis methodology and design methodology for fiber reinforced concrete (FRC) and fiber reinforced cement composite (FRCC).
The aim of this study is to deepen the knowledge to analyze and design the fiber-reinforced concrete by developing a novel method to predict the stress compression and tension blocks at the design ultimate limit state. To accomplish this, an experimental program was developed to characterize FRC and FRCC using common test methods. Three group of fibers were investigated: steel, PVA, and synthetic fiber with volume fractions ranging from 0 to 2%. The experimental program consisted of compression tests, flexural tests, and direct tensile tests which were used to assess the fibers’ usefulness as reinforcement components and to compare to the assumptions of current design methods. Experimental results of this research, combined with an additional 1,120 data points obtained from other researchers, were statistically analyzed to develop a new model to predict the design stress block of FRC and FRCC so that their design. This dissertation is divided into four parts:1) development of stress block in compression, 2) development of stress block in tension, 3) development of analysis, and 4) development of design of the new FRC and FRCC components.
First, the development of stress block in compression requires the yield and ultimate strains to be know.
A new equation for yield strain was developed by modifying the American Concrete Institute (ACI) Committee 544, fiber reinforced concrete and Rilem equations that depend on the compressive strength. An ultimate strain of 0.0035 and 0.005 at the extreme concrete compression fiber for the volume fraction of less than 1% and for a volume fraction of more than or equal to 1%, respectively, are proposed. New parameters are also introduced to account for different fiber types. Steel, PVA, basalt and synthetic fibers, two compresive stress block shapes are proposed. The two shapes consist of a rectangular stress block commonly used in regular concrete and a tapezoid stress block.
For the rectangular compressive stress block, two constants, 𝐾1and 𝐾2, are proposed. These constants are affected by the volume fraction (Vf) of FRC and FRCC. For 𝑉𝑓≥1%, 𝐾1 and 𝐾2 are constant value of 0.75 and 0.375 for FRC and FRCC, respectively, while for 𝑉𝑓<1%, they depend on the concrete compressive strength of FRC and FRCC. To this end, there are two additional parameters, 𝛽 and ∝, which depend on the strain at the elastic, yield, and the ultimate stages. For the ultimate stage, Ξ², which is also affected by the volume fraction of fiber, is proposed to be the same as the ACI 318 Code value for 𝑉𝑓<1%. While for 𝑉𝑓≥1%, 𝛽 depends on the FRC and FRCC concrete compressive strength. On the other hand, ∝ depends on the FRC and FRCC concrete compressive strength for 𝑉𝑓<1%. While for 𝑉𝑓≥1%, it may be observed that it becomes approximately a constant value of 1.0.
For the trapezoid stress block in compression, an idealized constitutive model which is a bilinear, elastic-perfectly plastic stress-strain response, has been a proposed. It is ssumed in compression that the linear portion of the response terminates at a yield point (∝fc',𝜀𝑐𝑦) and remains perfectly plastic at the compressive yield stress until the ultimate compressive strain 𝜀𝑈𝑙𝑡.. ∝ of fiber-reinforced concrete for ultimate design is taken to be 0.85, which is the same as the ∝ of ACI 318 for volume fraction less than 1%, and 1 for 𝑓𝑐′≥69 𝑀𝑝𝑎, ∝=1. The proposed models were compared to six design codes using 250 data points obtained from previous studies.
The evaluation for an area of the database which used the other codes more than twice underestimated the lower bond of the database. Therefore, the other codes do not give a valid evaluation for compressive strength due to neglecting the effect of fiber. For volume fraction of fiber more than 1, the rectangular and trapezoid area of stress blocks are almost matches. While for volume fraction less than 1 and compressive strength more than 40 MPa, there is a small difference between the rectangular and trapezoid stress blocks. For 𝐾2 value, the rectangular of stress block is in the lower bond of the database, while the trapezoid stress block model is near to the average of the database. As a result, the rectangular stress block is underestimated by the database and also is easy for a designer to use. Therefore, it will be used in the new design and analysis proposal model.
Second, determining tension stress block by knowing the first crack strength, first crack strain, elastic modulus, and ultimate strain in tension is necessary. More than 250 points of data are used to evaluate the first crack strength. The new empirical relations developed ACI 318 equation by multiple factor 𝜆. Factor 𝜆 depends on the length of the fiber. In this dissertation, factor 𝜆 is determined by the average and lower bond of the database.
Third, analysis of the new model for the ultimate stage is assumed to have a rectangular stress block with an average uniform stress. Also, this model adopts ∅ equal to 0.75 because of safe.
Comparing the proposal model with a moment of ACI 544 model shows that the proposed model is safer and more accurate than the ACI 544 model because the ACI 544 model has overestimated moment value for more than 3.5 Kn.m.
Finally, in the design of the new model for the ultimate stage, the majority of the design volume fraction for a proposal is more than the measurement volume fraction for the database. According to the database, this model works for volume fraction ≤2. It is necessary for the designer to know what kind of behavior is appropriate for each design. Through that, it is possible to precisely estimate the volume fraction of the requirement of each behavior as will be explained below. The volume fraction of fiber is critical for the response of strain-softening (hardening deflection). In the case of the strain of softening, the internal moment provided by FRC and FRCC is to resist the external moment more than the first crack moment. In addition to that, the volume fraction of fiber is critical for the response of strain-hardening. In the case of the strain hardening for FRC and FRCC, the strength of tension is defined for the stress block model as a constant value. FRC and FRCC strengths in tension are more than the first crack strength.
In conclusion of this dissertation, twelve equations were evaluated:
1. yield strain in compression,
2. ultimte strain in compression,
3. first crack strength in tension,
4. first crack strain in tension,
5. the elastic modulus in tension,
6. neutral axis for the elastic stage in tension,
7. ultimate strain in tension,
8. moment capacity for analysis and design model,
9. tensile strength for analysis and design model,
10. volume fraction equation of fiber for the design model,
11. volume fraction equation as a minimum requirement for deflection- hardening, and
12. volume fraction equation as a minimum requirement for strain-hardening.
In addition, there were the five parameters, in which 𝐾1𝑎𝑛𝑑 𝐾2 factor for stress block in compression and 𝛽 factor for rectangular stress block in compression and Ξ± factor for rectangular and trapezoid stress block in compression. In summary, this dissertation proposes new design and analysis for fiber-reinforced concrete and fiber-reinforced cement in order to increase safety and to provide an easier process method for the designer.