3.4 Test Results and Discussions
67
3.4.4 Dynamic Increase Factor
The dynamic increase factor (DIF) is defined as the ratio of the dynamic strength
to the quasi-static strength in uniaxial tensile, which is widely used to analyze and
design concrete protective structures under intensive loadings. Tran and Kim (2014),
Su et al. (2016) and Millard et al. (2010) had experimentally investigated the dynamic
tensile properties of UHPCC by using different test methods (direct tension, splitting
tension and flexural tension). However, the corresponding strain rates were limited,
i.e. 10 ~ 30 s
−1 , 100 ~ 200 s
−1 and 0.1 ~ 10 s
−1 , and the empirical DIF formulae for
UHPCC were not derived under a wide range of strain rate. At present, based on the
spalling test, the DIFs for the dynamic tensile strength of UHPCC at the strain rate
ranging from 14.3 s
−1 to 214.8 s
−1 are listed in Table 3.3 and illustrated in Fig. 3.11.
It is well accepted that there exists a transition strain rate for the relationship
between the DIF and the logarithm of strain rate, beyond which the DIF increases
rapidly with the strain rate and the material changes from low to high strain rate
sensitivity. As shown in Fig. 3.11, the DIFs for dynamic tensile strength of UHPCC
rapidly increase with rising the strain rate and the highest DIF of 14.89 is obtained
for the UHPCC with 2.0% hooked steel fiber at the strain rate of 110.7 s
−1 .
Besides, the experimental results indicate that, (i) UHPCC with different steel
fiber contents and types has constantly higher DIF values than the plain UHPCC,
suggesting that UHPCC with various steel fiber reinforcement is more sensitive to
the strain rate than the plain UHPCC; (ii) for the hooked steel fibers, the values of
DIF for UHPCC material increase with increasing the steel fiber content from 1 to
2%; (iii) with the mixing ratio of 1.0%, the DIFs for UHPCC with hooked steel fiber
are slightly higher than those with micro-straight steel fibers within the experimental
strain rate range.
Table 3.3 DIFs for dynamic tensile strength
Test No. Strain rate
(s −1 )
DIF
Test No. Strain rate
(s −1 )
DIF
Test No. Strain rate
(s −1 )
DIF
N-0–1
14.3
2.88 N-0–2
29.2
6.09 N-0–3
33.7
5.72
N-0–4
43.0
6.09 N-0–5
46.6
7.75 N-0–6
55.5
9.43
N-0–7
102.1
9.03 N-0–8
174.2
11.09 —
—
—
S-1–1
35.7
5.57 S-1–2
43.6
7.16 S-1–3
48.7
5.80
S-1–4
57.3
7.14 S-1–5
57.7
8.50 S-1–6
82.7
12.42
S-1–7
130.7
12.59 S-1–8
182.0
12.37 S-1–9
214.8
12.17
H-1–1
24.9
4.61 H-1–2
39.4
5.95 H-1–3
44.8
8.57
H-1–4
68.0
11.06 H-1–5
89.5
12.08 H-1–6
103.9
13.07
H-2–1
18.1
4.87 H-2–2
37.0
6.52 H-2–3
48.3
10.20
H-2–4
62.2
9.16 H-2–5
69.3
10.20 H-2–6
110.7
14.89
H-2–7
141.5
14.04 H-2–8
141.6
14.50 —
—
—
67
3.4.4 Dynamic Increase Factor
The dynamic increase factor (DIF) is defined as the ratio of the dynamic strength
to the quasi-static strength in uniaxial tensile, which is widely used to analyze and
design concrete protective structures under intensive loadings. Tran and Kim (2014),
Su et al. (2016) and Millard et al. (2010) had experimentally investigated the dynamic
tensile properties of UHPCC by using different test methods (direct tension, splitting
tension and flexural tension). However, the corresponding strain rates were limited,
i.e. 10 ~ 30 s
−1 , 100 ~ 200 s
−1 and 0.1 ~ 10 s
−1 , and the empirical DIF formulae for
UHPCC were not derived under a wide range of strain rate. At present, based on the
spalling test, the DIFs for the dynamic tensile strength of UHPCC at the strain rate
ranging from 14.3 s
−1 to 214.8 s
−1 are listed in Table 3.3 and illustrated in Fig. 3.11.
It is well accepted that there exists a transition strain rate for the relationship
between the DIF and the logarithm of strain rate, beyond which the DIF increases
rapidly with the strain rate and the material changes from low to high strain rate
sensitivity. As shown in Fig. 3.11, the DIFs for dynamic tensile strength of UHPCC
rapidly increase with rising the strain rate and the highest DIF of 14.89 is obtained
for the UHPCC with 2.0% hooked steel fiber at the strain rate of 110.7 s
−1 .
Besides, the experimental results indicate that, (i) UHPCC with different steel
fiber contents and types has constantly higher DIF values than the plain UHPCC,
suggesting that UHPCC with various steel fiber reinforcement is more sensitive to
the strain rate than the plain UHPCC; (ii) for the hooked steel fibers, the values of
DIF for UHPCC material increase with increasing the steel fiber content from 1 to
2%; (iii) with the mixing ratio of 1.0%, the DIFs for UHPCC with hooked steel fiber
are slightly higher than those with micro-straight steel fibers within the experimental
strain rate range.
Table 3.3 DIFs for dynamic tensile strength
Test No. Strain rate
(s −1 )
DIF
Test No. Strain rate
(s −1 )
DIF
Test No. Strain rate
(s −1 )
DIF
N-0–1
14.3
2.88 N-0–2
29.2
6.09 N-0–3
33.7
5.72
N-0–4
43.0
6.09 N-0–5
46.6
7.75 N-0–6
55.5
9.43
N-0–7
102.1
9.03 N-0–8
174.2
11.09 —
—
—
S-1–1
35.7
5.57 S-1–2
43.6
7.16 S-1–3
48.7
5.80
S-1–4
57.3
7.14 S-1–5
57.7
8.50 S-1–6
82.7
12.42
S-1–7
130.7
12.59 S-1–8
182.0
12.37 S-1–9
214.8
12.17
H-1–1
24.9
4.61 H-1–2
39.4
5.95 H-1–3
44.8
8.57
H-1–4
68.0
11.06 H-1–5
89.5
12.08 H-1–6
103.9
13.07
H-2–1
18.1
4.87 H-2–2
37.0
6.52 H-2–3
48.3
10.20
H-2–4
62.2
9.16 H-2–5
69.3
10.20 H-2–6
110.7
14.89
H-2–7
141.5
14.04 H-2–8
141.6
14.50 —
—
—