1 Introduction
2 Test Program
2.1 Material Properties
2.1.1 UHPFRC and Steel Fibers
W/B | Relative weight ratios to cement | Steel fiber* | |||||
---|---|---|---|---|---|---|---|
Water | Cement | Silica fume | Silica sand | Silica flour | Superplasticizer | ||
0.2 | 0.227 | 1.0 | 0.25 | 1.1 | 0.3 | 0.16 | 2% |
Test | Fresh concrete | Hardened concrete | ||
---|---|---|---|---|
Air content (%) | Flow (mm) | Compressive strength (MPa) | Flexural strength (MPa) | |
1st | 2.0 | 170.0 | 192.6 | 34.7 |
2nd | 1.6 | 170.0 | 179.6 | 29.5 |
3rd | 1.0 | 160.0 | 177.7 | 15.9 |
Average | 1.5 | 166.7 | 183.3 | 26.7 |
STDEV | 0.5 | 5.8 | 8.1 | 9.7 |
2.1.2 Prestressing Strands
Nom. diameter (mm) | Nom. area (mm2) | Tensile load (kN) | Yield load (kN) | Weight (kg/1000 m) | Modulus of elasticity (GPa) | Elongation (%) | Relaxation (%) |
---|---|---|---|---|---|---|---|
12.7 | 98.7 | 184 | 157 | 780 | 185–205 | 3.5 | 2.5 |
15.2 | 140.0 | 261 | 222 | 1100 | 185–205 | 3.5 | 2.5 |
2.2 Test Specimen, Setup and Procedure
2.2.1 Bond Strength
Specimen | Strand diameter (mm) | Prestressing force (× f
py
) | Embedment length (n × d
b
) | Cover depth (n × d
b
) |
---|---|---|---|---|
13-a-11 | 12.7 | 0.8 f
py
| 1 d
s
| 1 d
s
|
13-a-12 | 1 d
s
| 2 d
s
| ||
13-a-22 | 2 d
s
| 2 d
s
| ||
13-a-2C | 2 d
s
| 5.4 d
s
| ||
13-b-11 | 0.9 f
py
| 1 d
s
| 1 d
s
| |
13-b-12 | 1 d
s
| 2 d
s
| ||
13-b-22 | 2 d
s
| 2 d
s
| ||
15-a-11 | 15.2 | 0.8 f
py
| 1 d
s
| 1 d
s
|
15-a-12 | 1 d
s
| 2 d
s
| ||
15-a-22 | 2 d
s
| 2 d
s
| ||
15-a-2C | 2 d
s
| 4.4 d
s
| ||
15-b-11 | 0.9 f
py
| 1 d
s
| 1 d
s
| |
15-b-12 | 1 d
s
| 2 d
s
| ||
15-b-22 | 2 d
s
| 2 d
s
|
2.2.2 Transfer Length
Specimen* | Test variables | Transfer length results | |||
---|---|---|---|---|---|
Strand diameter (mm) | Prestressing force (× f
py
) | Cover depth (n × d
b
) | Live end (mm) | Dead end (mm) | |
13-1d
b
| 12.7 | 0.9f
py
| 1 d
b
| 237 | 54 |
13-2d
b
| 2 d
b
| 235 | 165 | ||
13-3d
b
| 3 d
b
| 250 | 242 | ||
15-1d
b
| 15.2 | 0.9f
py
| 1 d
b
| 380 | 265 |
15-2d
b
| 2 d
b
| 311 | 265 | ||
15-3d
b
| 3 d
b
| 375 | 246 |
3 Bond Strengths of Pretensioned Strand in UHPFRC
3.1 Effect of Prestressing Strand Diameter
3.2 Effect of Cover Depth to Diameter Ratio (c/d b )
3.3 Effect of Embedment Length
3.4 Effect of Initial Prestressing Force
3.5 Probabilistic Data Analysis
4 Transfer Length
Spec.* | Exp. result (mm) | Predictive values (mm) | Pred./exp. | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Live end (1) | ACI 318 (2) | AASHTO LRFD (3) | Russell and Burns (4) | Mitchell et al. (5) | Euro-code 2 (6) | Martí-Vargas et al. (7) | Dang et al. (8) | (2)/(1) | (3)/(1) | (4)/(1) | (5)/(1) | (6)/(1) | (7)/(1) | (8)/(1) | |
13-1d
b
| 237 | 635 | 762 | 952 | 291 | 240 | 205 | 239 | 2.68 | 3.22 | 4.02 | 1.23 | 1.01 | 0.86 | 1.01 |
13-2d
b
| 235 | 2.70 | 3.24 | 4.05 | 1.24 | 1.02 | 0.87 | 1.02 | |||||||
13-3d
b
| 250 | 2.54 | 3.05 | 3.81 | 1.16 | 0.96 | 0.82 | 0.96 | |||||||
15-1d
b
| 380 | 760 | 912 | 1140 | 347 | 286 | 242 | 286 | 2.00 | 2.40 | 3.00 | 0.91 | 0.75 | 0.64 | 0.75 |
15-2d
b
| 311 | 2.44 | 2.93 | 3.67 | 1.12 | 0.92 | 0.78 | 0.92 | |||||||
15-3d
b
| 375 | 2.03 | 2.43 | 3.04 | 0.93 | 0.76 | 0.65 | 0.76 | |||||||
Average | 2.40 | 2.88 | 3.60 | 1.10 | 0.90 | 0.77 | 0.90 | ||||||||
Standard deviation | 0.31 | 0.38 | 0.47 | 0.15 | 0.12 | 0.10 | 0.12 |
5 Conclusions
-
The average bond strength of prestressing strands embedded in UHPFRC decreased with increasing strand diameter. The bond strength of strands prestressed by 80 and 90% of the yield strength was higher than that of a round steel rebar, but lower than that of the deformed steel rebar. In addition, the bond strength of the prestressing strand in UHPFRC was approximately 2.8 times higher than that in HSC (f c ′ of 55.4 MPa).
-
Based on the calculated p-value, only the parameters of bar diameter and embedment length significantly affected the bond strength of strands in UHPFRC.
-
A higher average bond strength of the strand in UHPFRC was obtained with smaller bar diameter and embedment length. For the smaller-sized strand, the bond strength was more significantly influenced by the embedment length.
-
The average bond strength of the strands was insignificantly affected by the initial prestressing force that ranged from 80 to 90% at short embedment lengths of 1d b and 2d b .
-
The transfer length of the prestressing strand was shorter at the dead end than at the live end. UHPFRC exhibited much shorter transfer lengths than HSC, and the ACI 318 and AASHTO LRFD codes significantly overestimated the transfer length of a strand embedded in UHPFRC. Based on a design perspective, the model proposed by Mitchell et al. (1993) was considered to be most proper for predicting the transfer length of steel strands in UHPFRCC.