Effect of Steel Fiber on First-Cracking Behavior of Ultra-High-Performance Concrete: New Insights from Digital Image Correlation Analysis
Abstract
1. Introduction
2. Experimental Program
2.1. Raw Materials and Mixture Proportions
2.2. Test Methods and Preparation of Specimens
2.2.1. Flowability
2.2.2. Compressive Testing
2.2.3. Direct Tensile Testing
2.3. Crack Identification by Improved DIC Technology
3. Results and Discussion
3.1. Effect of Steel Fiber on Flowability of UHPC
3.2. Effect of Steel Fiber on Compressive Strength of UHPC
3.3. Initial Crack Pattern of UHPC
3.4. Effect of Steel Fiber on First-Cracking Behavior of UHPC
3.5. Comparison of First-Cracking Strength According to Different Methods
4. Establishment of a Model for Predicting the First-Crack Strength
4.1. Background
4.2. Establishment and Verification of Formula
5. Conclusions
- DIC analysis reveals distinctions between the first-cracking and linear limit points during DTT. Employing DIC technology reduces the uncertainty in manually pinpointing initial cracks or linear limit points, thus enabling objective determination of the initial cracking strength. Adopting the linear limit point as the benchmark for initial cracking leads to a more conservative design methodology for UHPC.
- The length, volume fraction, diameter, and shape of steel fibers each contribute to the enhancement of the initial cracking strength, with improvements ranging from 26.07% to 121.31%. Among these parameters, fiber length and volume fraction exhibit a more pronounced influence, while the effects of diameter and shape are relatively modest.
- Steel fibers can exert both favorable and adverse effects on the compressive and first-cracking strengths of UHPC. On the one hand, they reinforce the matrix, inhibit crack propagation, and enhance compressive strength; on the other hand, the incorporation of steel fibers also introduces air, which compromises the compactness of the packing system and reduces the matrix strength.
- Stress concentration within steel fibers (such as corrugated or hooked-end fibers) affects both the first-cracking strength and the morphology of the resulting cracks. UHPC reinforced with corrugated fibers, which have more stress concentration points compared to straight and hooked-end fibers, exhibits a discontinuous crack pattern and the lowest initial cracking strength.
- For strain-softening UHPC, the linear elastic limit point method can be used to determine the first-cracking strength. For strain-hardening UHPC, the intersection point method can serve as a simplified approach to determine the first-cracking strength, though it tends to slightly overestimate the actual cracking strength.
- Considering that previous studies did not account for the adverse effects of steel fibers, this research proposes an updated formula that can predict the initial cracking strength of UHPC with reasonable accuracy, evidenced by a mean ratio of 1.07 and a standard deviation of 0.15.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Cement | Silica Fume | Fly Ash | Quartz Sand | Quartz Flour | Superplasticizer | Water |
---|---|---|---|---|---|---|
772.1 | 154.2 | 77.1 | 848.4 | 154.2 | 20.1 | 180.5 |
Notation | Fiber Type | Fiber Diameter (mm) | Fiber Length (mm) | Steel Fiber Volume Fraction (%) |
---|---|---|---|---|
Matrix | / | / | / | / |
S-0.20-06-2% | Straight | 0.2 | 6 | 2 |
S-0.20-10-2% | Straight | 0.2 | 10 | 2 |
S-0.20-13-2% | Straight | 0.2 | 13 | 2 |
S-0.20-16-2% | Straight | 0.2 | 16 | 2 |
S-0.20-20-2% | Straight | 0.2 | 20 | 2 |
S-0.20-25-2% | Straight | 0.2 | 25 | 2 |
S-0.20-13-1% | Straight | 0.20 | 13 | 1 |
S-0.20-13-3% | Straight | 0.20 | 13 | 3 |
S-0.20-13-4% | Straight | 0.20 | 13 | 4 |
S-0.25-16-2% | Straight | 0.25 | 16 | 2 |
S-0.30-16-2% | Straight | 0.30 | 16 | 2 |
H-0.20-13-2% | Hooked | 0.20 | 13 | 2 |
C-0.20-13-2% | Corrugated | 0.20 | 13 | 2 |
Notation | First-Crack Strength (MPa) | First-Crack Strain (με) | ||||||
---|---|---|---|---|---|---|---|---|
Specimen 1 | Specimen 2 | Specimen 3 | Mean (Sd) | Specimen 1 | Specimen 2 | Specimen 3 | Mean (Sd) | |
Matrix | 5.96 | 6.12 | 6.21 | 6.10 (0.10) | 138 | 140 | 141 | 140 (1.25) |
S-0.20-06-2% | 7.87 | 7.59 | 7.60 | 7.69 (0.13) | 202 | 215 | 216 | 211 (6.38) |
S-0.20-10-2% | 9.39 | 9.12 | 8.67 | 9.06 (0.30) | 249 | 224 | 219 | 231 (13.12) |
S-0.20-13-2% | 10.07 | 10.40 | 10.08 | 10.18 (0.15) | 266 | 272 | 284 | 274 (7.48) |
S-0.20-16-2% | 10.06 | 10.25 | 10.16 | 10.16 (0.08) | 273 | 253 | 252 | 259 (9.67) |
S-0.20-20-2% | 9.56 | 9.68 | 9.77 | 9.67 (0.09) | 262 | 247 | 240 | 250 (9.18) |
S-0.20-25-2% | 9.84 | 9.45 | 9.46 | 9.58 (0.18) | 236 | 258 | 233 | 242 (11.15) |
S-0.20-13-1% | 7.81 | 7.70 | 7.91 | 7.81 (0.08) | 256 | 254 | 228 | 246 (12.75) |
S-0.20-13-2% | 10.07 | 10.40 | 10.08 | 10.18 (0.15) | 266 | 272 | 284 | 274 (7.48) |
S-0.20-13-3% | 12.52 | 12.52 | 12.12 | 12.39 (0.19) | 278 | 284 | 276 | 279 (3.40) |
S-0.20-13-4% | 13.02 | 13.56 | 13.90 | 13.50 (0.36) | 311 | 313 | 323 | 316 (5.25) |
S-0.20-16-2% | 10.06 | 10.25 | 10.16 | 10.16 (0.08) | 273 | 253 | 252 | 259 (9.67) |
S-0.25-16-2% | 9.66 | 9.52 | 9.65 | 9.61 (0.06) | 249 | 234 | 232 | 238 (7.59) |
S-030-16-2% | 8.89 | 8.43 | 9.12 | 8.82 (0.29) | 243 | 223 | 249 | 238 (11.12) |
S-0.20-13-2% | 10.07 | 10.40 | 10.08 | 10.18 (0.15) | 266 | 272 | 284 | 274 (7.48) |
H-0.20-13-2% | 8.96 | 9.65 | 9.25 | 9.29 (0.28) | 247 | 236 | 252 | 245 (6.68) |
C-0.20-13-2% | 8.59 | 9.18 | 9.15 | 8.97 (0.27) | 235 | 228 | 232 | 232 (2.87) |
Resource | Notation | σm | df | lf | Vf | τ | Δf | σc,3 | σcc | σc,3/σcc |
---|---|---|---|---|---|---|---|---|---|---|
MPa | mm | mm | % | MPa | mm | MPa | MPa | |||
This paper | S-0.20-06-2% | 6.10 | 0.20 | 6 | 2 | 6.80 | 16 | 6.94 | 7.69 | 0.90 |
S-0.20-10-2% | 6.10 | 0.20 | 10 | 2 | 6.80 | 18 | 8.95 | 9.06 | 0.99 | |
S-0.20-13-2% | 6.10 | 0.20 | 13 | 2 | 6.80 | 22 | 10.19 | 10.18 | 1.00 | |
S-0.20-16-2% | 6.10 | 0.20 | 16 | 2 | 6.80 | 31 | 10.87 | 10.16 | 1.07 | |
S-0.20-20-2% | 6.10 | 0.20 | 20 | 2 | 6.80 | 58 | 10.13 | 9.67 | 1.05 | |
S-0.20-25-2% | 6.10 | 0.20 | 25 | 2 | 6.80 | 88 | 9.62 | 9.58 | 1.00 | |
S-0.20-13-1% | 6.10 | 0.20 | 13 | 1 | 6.80 | 8 | 8.16 | 7.39 | 1.11 | |
S-0.20-13-3% | 6.10 | 0.20 | 13 | 3 | 6.80 | 28 | 13.09 | 12.39 | 1.06 | |
S-0.20-13-4% | 6.10 | 0.20 | 13 | 4 | 6.80 | 58 | 13.35 | 13.50 | 0.99 | |
S-0.25-16-2% | 6.10 | 0.25 | 16 | 2 | 6.80 | 29 | 9.42 | 9.61 | 0.98 | |
S-0.30-16-2% | 6.10 | 0.30 | 16 | 2 | 6.80 | 30 | 8.00 | 8.82 | 0.91 | |
H-0.20-13-2% | 6.10 | 0.20 | 13 | 2 | 6.80 | 27 | 9.64 | 9.29 | 1.04 | |
C-0.20-13-2% | 6.10 | 0.20 | 13 | 2 | 6.80 | 31 | 9.20 | 8.97 | 1.02 | |
Bian [43] | High strain-hardening UHPFRC | 7.60 | 0.20 | 16 | 2 | 6.80 | 31 | 12.34 | 9.14 | 1.35 |
Low strain-hardening UHPFRC | 7.60 | 0.20 | 13 | 2 | 6.80 | 22 | 11.66 | 11.25 | 1.04 | |
Strain-softening UHPFRC | 7.60 | 0.20 | 16 | 1 | 6.80 | 22 | 8.94 | 11.29 | 0.79 | |
Wang [44] | High strain-hardening UHPFRC | 7.70 | 0.20 | 13 | 2.5 | 6.80 | 25 | 13.20 | 10.40 | 1.27 |
Low strain-hardening UHPFRC | 7.70 | 0.20 | 13 | 2 | 6.80 | 22 | 11.75 | 8.70 | 1.35 | |
Strain-softening UHPFRC | 7.70 | 0.20 | 13 | 1.5 | 6.80 | 15 | 10.75 | 7.70 | 1.40 | |
Ouyang [52] | S-1-0.16 | 6.42 | 0.22 | 13 | 1 | 6.80 | 8 | 8.15 | 7.44 | 1.10 |
S-2-0.16 | 6.42 | 0.22 | 13 | 2 | 6.80 | 22 | 9.84 | 8.02 | 1.23 |
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Lu, X.; Tu, L.; Tan, C.; Zhao, H. Effect of Steel Fiber on First-Cracking Behavior of Ultra-High-Performance Concrete: New Insights from Digital Image Correlation Analysis. Buildings 2025, 15, 1727. https://doi.org/10.3390/buildings15101727
Lu X, Tu L, Tan C, Zhao H. Effect of Steel Fiber on First-Cracking Behavior of Ultra-High-Performance Concrete: New Insights from Digital Image Correlation Analysis. Buildings. 2025; 15(10):1727. https://doi.org/10.3390/buildings15101727
Chicago/Turabian StyleLu, Xing, Lei Tu, Chengjun Tan, and Hua Zhao. 2025. "Effect of Steel Fiber on First-Cracking Behavior of Ultra-High-Performance Concrete: New Insights from Digital Image Correlation Analysis" Buildings 15, no. 10: 1727. https://doi.org/10.3390/buildings15101727
APA StyleLu, X., Tu, L., Tan, C., & Zhao, H. (2025). Effect of Steel Fiber on First-Cracking Behavior of Ultra-High-Performance Concrete: New Insights from Digital Image Correlation Analysis. Buildings, 15(10), 1727. https://doi.org/10.3390/buildings15101727