Numerical Designing of Fiber Reinforced Concrete Eco-Constructions
Abstract
:1. Introduction
2. Numerical Models for Cracking in FRC
2.1. Diffused Cracking Models
- The shape of the post-peak (this means after the linear elastic part of the tensile behavior of the FRC) behavior of the tensile stress-strain curve.
- The post-peak energy dissipation related to the tensile stress-strain curve. This dissipation energy is very often called Gf.
2.2. Explicit Cracking Models
2.2.1. The Cohesive Crack Models
2.2.2. The Probabilistic Explicit Cracking Model
- The material being considered is heterogeneous and its local mechanical characteristics are randomly distributed.
- These mechanical characteristics are scale effect dependent. This means that they depend on the volume of the material considered [18].
- Each volume element of the mesh represents a volume of the heterogeneous material.
- Cracks are simulated by using non-linear interface elements (quadratic elements). Failure criteria of Rankin in tension and Tresca in shear are used. Once one of these failure criteria is reached, the interface element is considered as opened, simulating a crack’s creation. The tensile and shear strengths, as well as the normal and tangential stiffness values of the element, are then set equal to zero.
- The normal and tangential stresses in the interface element linearly increase with the normal and tangential displacements to simulate the elastic bridging action.
- This elastic action of the fibers exists until a threshold value related to the normal displacement is reached. From this threshold value, the normal stress linearly decreases with the normal displacement. This is to consider the damage of the bond between the concrete and the fiber. This decreasing evolution is considered through a damage model.
- Finally, when the normal displacement reaches a second threshold, the action of the fibers is considered negligible, and so, the interface element is considered definitively broken. Its normal and tangential rigidities are then set to zero.
- The post-cracking energy, dissipated during all of the bridging action of the fibers, is randomly distributed over the finite element mesh. This random distribution is a log-normal distribution function with a mean value independent of the mesh elements’ size and a standard deviation that increases as the mesh elements’ size decreases. This choice is in perfect agreement with the experimental results [20].
- The mean value is determined from the experimental results related to the uniaxial tensile tests on notched specimens (see at the beginning of Section 2).
- The standard deviation is determined by an inverse analysis approach. As the mean value of the post-cracking energy is known, the inverse approach consists of simulating the uniaxial tests with different element mesh sizes. For each element mesh size, several numerical simulations are performed. The standard deviation related to each mesh size is the one that best fits the experimental results (from the uniaxial tensile tests). This inverse approach allows for the determination of the relationship between the standard deviation and the finite element mesh size.
- The two threshold parameters, evocated above, are also obtained by performing an inverse approach. This consists of fitting the post-cracking behavior of the uniaxial tensile tests by using the simplified triangular stress-displacement curve of the model.
3. Design Optimization of an FRC Track Slab
Carbon Footprint Evaluations
4. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Technical Solution Number | Concrete Slab Thickness (cm) | Steel Reinforcement (%) | Fiber Content (kg/m3) |
---|---|---|---|
1 | 15 | 2.2 | 72 |
2 | 15 | 6.61 | 80 |
3 | 17 | 5.29 | 56 |
4 | 19.5 | 0 | 56 |
5 | 19.5 | 2.2 | 48 |
6 | 19.5 | 8.81 | 40 |
7 | 22 | 7.93 | 76 |
8 | 24 | 4.41 | 48 |
9 | 24 | 4.41 | 64 |
10 | 17 | 4.41 | 68 |
11 | 17 | 2.64 | 64 |
12 | 19.5 | 7.05 | 60 |
13 | 22 | 6.17 | 56 |
14 | 22 | 5.29 | 64 |
15 | 22 | 5.29 | 76 |
16 | 22 | 7.93 | 64 |
17 | 19.5 | 5.29 | 76 |
18 | 19.5 | 7.93 | 64 |
19 | 24 | 8.81 | 80 |
20 | 15 | 17.6 | 72 |
Tech. Sol. Num. | Left Part | Central Part | Right Part | ||||||
---|---|---|---|---|---|---|---|---|---|
Crack Opening (µm) | Crack Number (Mean) | Crack Opening (µm) | Crack Number (Mean) | Crack Opening (µm) | Crack Number (Mean) | ||||
Average | Standard Deviation | Average | Standard Deviation | Average | Standard Deviation | ||||
7 | 16.5 | 3.4 | 8.5 | 31.6 | 9.3 | 0.9 | 21.7 | 5.4 | 2.8 |
9 | 17.9 | 4.8 | 7.5 | 44.5 | 27.5 | 1.8 | 44.2 | 7.1 | 1 |
14 | 17.6 | 5.2 | 3.4 | 56.3 | 16.2 | 1.1 | 21.6 | 8.2 | 2.6 |
15 | 15.5 | 4.4 | 5.8 | 34.3 | 8.6 | 1.1 | 18.9 | 7.8 | 2.8 |
16 | 17.1 | 4.5 | 4.6 | 49.8 | 13.7 | 1.0 | 22.9 | 8.4 | 2.3 |
19 | 16.0 | 3.9 | 3 | 45.8 | 13.7 | 1.2 | 27.1 | 7.1 | 1.4 |
20 | 13.5 | 2.4 | 6.4 | 16.0 | 2.6 | 0.3 | 0 | 0 | 0 |
Concrete | Fibers | Steel Reinforcement |
---|---|---|
250 kg/m3 | 2.425 kg/t | 1.932 kg/t |
Technical Solution Number | 7 | 9 | 14 | 15 | 16 | 19 | 20 |
---|---|---|---|---|---|---|---|
CO2 (t) | 57.8 | 63 | 57.7 | 57.8 | 57.7 | 63.0 | 39.4 |
Gain (%) | −8 | 0 | −8 | −8 | −8 | 0 | −37 |
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Rossi, P. Numerical Designing of Fiber Reinforced Concrete Eco-Constructions. Materials 2023, 16, 2576. https://doi.org/10.3390/ma16072576
Rossi P. Numerical Designing of Fiber Reinforced Concrete Eco-Constructions. Materials. 2023; 16(7):2576. https://doi.org/10.3390/ma16072576
Chicago/Turabian StyleRossi, Pierre. 2023. "Numerical Designing of Fiber Reinforced Concrete Eco-Constructions" Materials 16, no. 7: 2576. https://doi.org/10.3390/ma16072576