Numerical Modeling of Concrete Deep Beams Made with Recycled Aggregates and Steel Fibers
Abstract
:1. Introduction
2. Research Objectives
- Establish tensile softening laws (tension functions) that can describe the post-cracking behavior of concrete made with RCAs and different steel fiber volume fractions.
- Develop numerical simulation models capable of predicting the shear behavior of steel fiber-reinforced recycled aggregates concrete deep beams.
- Validate the prediction of the numerical models through a comparative analysis with published experimental data.
- Investigate the effect of varying a/h, vf, and presence of a web opening on the shear capacity and strength gain caused by the addition of steel fibers.
3. Methodology and Material Characteristics
3.1. Properties of Concrete Mixtures
3.2. Tensile Softening Laws of Concrete Mixtures
3.3. Large-Scale Deep Beam Numerical Models
4. Numerical Results and Validation of FE Deep Beam Models
4.1. Solid Deep Beam Models
4.1.1. Shear Load–Deflection Response
4.1.2. Crack Patterns
4.1.3. Stirrup Strains
4.1.4. Tensile Steel Strains
4.2. Deep Beam Models with Openings
4.2.1. Shear Load–deflection Response
4.2.2. Crack Patterns
4.2.3. Stirrup Strains
4.2.4. Tensile Steel Strains
5. Parametric Study and Discussion
5.1. Effect of Shear Span-to-Depth Ratio
5.2. Effect of Web Openings
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Property | Standard | Sample Type and Dimensions (mm) | Characterization Test Results * | ||||
---|---|---|---|---|---|---|---|
R0-SF0 | R100-SF0 | R100-SF1 | R100-SF2 | R100-SF3 | |||
f’c (MPa) | ASTM C39 [52] | Cylinder, 150 × 300 | 36.4 (1.5) | 23.6 (0.4) | 25.8 (0.3) | 25.6 (1.4) | 25.0 (0.8) |
fcu (MPa) | BS 12390-3 [53] | Cube, 150 | 40.5 (1.8) | 24.7 (1.0) | 32.2 (0.6) | 30.0 (1.0) | 28.3 (0.7) |
fr (MPa) | ASTM C1609 [54] | Prism, 100 × 100 × 500 | 3.4 (0.2) | 2.4 (0.5) | 4.1 (0.4) | 5.4 (0.4) | 6.1 (0.7) |
Ec (GPa) | ASTM C469 [55] | Cylinder, 150 × 300 | 34.7 (1.8) | 19.8 (2.4) | 21.5 (2.9) | 20.7 (2.5) | 21.1 (1.6) |
Group | Model Designation | a/h | RCA (%) | vf (%) | Presence of Traditional Shear Reinforcement | Presence of Openings |
---|---|---|---|---|---|---|
S | SR0-SF0 | 1.6 | - | - | - | - |
SR0-SF0-S | 1.6 | - | - | √ | - | |
SR100-SF0 | 1.6 | 100 | - | - | - | |
SR100-SF0-S | 1.6 | 100 | - | √ | - | |
SR100-SF1 | 1.6 | 100 | 1 | - | - | |
SR100-SF2 | 1.6 | 100 | 2 | - | - | |
SR100-SF3 | 1.6 | 100 | 3 | - | - | |
N | NR0-SF0 | 0.8 | - | - | - | √ |
NR0-SF0-S | 0.8 | - | - | √ | √ | |
NR100-SF0 | 0.8 | 100 | - | - | √ | |
NR100-SF0-S | 0.8 | 100 | - | √ | √ | |
NR100-SF1 | 0.8 | 100 | 1 | - | √ | |
NR100-SF2 | 0.8 | 100 | 2 | - | √ | |
NR100-SF3 | 0.8 | 100 | 3 | - | √ |
Model | Shear Capacity | Deflection Capacity | VFE/VEXP | ΔFE/ΔEXP | ||
---|---|---|---|---|---|---|
VEXP (kN) | VFE (kN) | ΔEXP (mm) | ΔFE (mm) | |||
SR0-SF0 | 203 | 198 | 7.3 | 7.1 | 0.98 | 0.97 |
SR0-SF0-S | 309 | 280 | 10.3 | 8.0 | 0.91 | 0.78 |
SR100-SF0 | 193 | 181 | 9.0 | 6.2 | 0.94 | 0.69 |
SR100-SF0-S | 300 | 270 | 10.7 | 8.2 | 0.90 | 0.77 |
SR100-SF1 | 235 | 251 | 8.3 | 7.9 | 1.07 | 0.95 |
SR100-SF2 | 271 | 296 | 10.4 | 9.5 | 1.09 | 0.91 |
SR100-SF3 | 401 | 387 | 15.8 | 12.0 | 0.97 | 0.77 |
Average | 0.98 | 0.83 | ||||
Std Dev | 0.07 | 0.10 | ||||
COV (%) | 7.03 | 11.95 |
Model | Shear Capacity | Deflection Capacity | VFE/VEXP | ΔFE/ΔEXP | ||
---|---|---|---|---|---|---|
VEXP (kN) | VFE (kN) | ΔEXP (mm) | ΔFE (mm) | |||
NR0-SF0 | 273 | 273 | 4.7 | 2.9 | 1.00 | 0.62 |
NR0-SF0-S | 341 | 327 | 4.8 | 3.0 | 0.96 | 0.63 |
NR100-SF0 | 237 | 211 | 4.9 | 2.6 | 0.89 | 0.53 |
NR100-SF0-S | 279 | 255 | 5.3 | 2.7 | 0.91 | 0.51 |
NR100-SF1 | 329 | 306 | 5.6 | 5.4 | 0.93 | 0.96 |
NR100-SF2 | 362 | 326 | 6.0 | 5.9 | 0.90 | 0.98 |
NR100-SF3 | 435 | 358 | 7.4 | 6.0 | 0.82 | 0.81 |
Average | 0.92 | 0.72 | ||||
Std dev | 0.05 | 0.18 | ||||
COV (%) | 5.74 | 25.26 |
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Kachouh, N.; El-Maaddawy, T.; El-Hassan, H.; El-Ariss, B. Numerical Modeling of Concrete Deep Beams Made with Recycled Aggregates and Steel Fibers. Buildings 2022, 12, 529. https://doi.org/10.3390/buildings12050529
Kachouh N, El-Maaddawy T, El-Hassan H, El-Ariss B. Numerical Modeling of Concrete Deep Beams Made with Recycled Aggregates and Steel Fibers. Buildings. 2022; 12(5):529. https://doi.org/10.3390/buildings12050529
Chicago/Turabian StyleKachouh, Nancy, Tamer El-Maaddawy, Hilal El-Hassan, and Bilal El-Ariss. 2022. "Numerical Modeling of Concrete Deep Beams Made with Recycled Aggregates and Steel Fibers" Buildings 12, no. 5: 529. https://doi.org/10.3390/buildings12050529