3.4 Test Results and Discussions
69
Zhou et al. (2008) further proposed a DIF formula by curve fitting the existing
experimental results of dynamic tensile tests on concrete materials (Schuler et al.
2006).
DIF =
⎧
⎨
⎩
1.0
f o r ˙
ε ≤ 10
−4 s
−1
2.06 + 0.26 log ˙
ε for 10
−4 s
−1
≤ ˙
ε ≤ 1s
−1
2.06 + 2.0 log ˙
ε for ˙
ε > 1s
−1
(3.11)
The above four formulae are also plotted in Fig. 3.11. Because these formulae are
mainly concentrated on normal strength concrete and not suitable for high strength
concrete, they could not well describe the evolution of the DIFs for UHPCC material
and generally underestimate the dynamic tensile strength.
Since the available test data of UHPCC under quasi-dynamic loadings is limited,
it is difficult to determine the transition strain rate ˙
ε T R exactly. Othman and Marzouk
(2016) experimentally obtained the DIFs for two types of fiber-reinforced cementitious composites (FRCCs) with the compressive strengths of 110.8 and 132.7 MPa
at low to medium strain rates (0.58 ~ 2.58 s
−1 ), as shown in Fig. 3.11. Due to the
good consistence with the DIF for FRCCs, the empirical formula of fib Model Code
2010 (2013) is adopted for the strain rates below the transition strain rate. Thus an
empirical formula is proposed to describe the strain rate effect of UHPCC as follows,
DIF =
(˙ ε/˙ ε 0 )
0.018
for ˙
ε ≤ ˙
ε T R
A · log˙ ε + B for ˙
ε > ˙
ε T R
(3.12)
where A and B are the coefficients. By fitting the test data, the values of A, B and ˙
ε T R
for UHPCC are determined and listed in Table 3.4. Then the corresponding empirical
DIF relations of Eq. (3.12) are given in Fig. 3.12. These empirical formulae can be
used to predict the tensile DIFs in the numerical predictions of UHPCC structure
responses under high strain rate loadings. It should be noted that Eq. (3.12) is derived
from the test data for the strain rate up to ~214.8 s
−1 , beyond which there is no
available test data to substantiate its validity.
Table 3.4 Coefficients for
the proposed DIF formula of
UHPCC
Test No.
A
B
˙
ε T R (s −1 )
N-0
7.362
−5.167
7.8
S-1
9.637
−8.814
11.5
H-1
14.338
−15.695
15.5
H-2
11.561
−10.446
10.5
69
Zhou et al. (2008) further proposed a DIF formula by curve fitting the existing
experimental results of dynamic tensile tests on concrete materials (Schuler et al.
2006).
DIF =
⎧
⎨
⎩
1.0
f o r ˙
ε ≤ 10
−4 s
−1
2.06 + 0.26 log ˙
ε for 10
−4 s
−1
≤ ˙
ε ≤ 1s
−1
2.06 + 2.0 log ˙
ε for ˙
ε > 1s
−1
(3.11)
The above four formulae are also plotted in Fig. 3.11. Because these formulae are
mainly concentrated on normal strength concrete and not suitable for high strength
concrete, they could not well describe the evolution of the DIFs for UHPCC material
and generally underestimate the dynamic tensile strength.
Since the available test data of UHPCC under quasi-dynamic loadings is limited,
it is difficult to determine the transition strain rate ˙
ε T R exactly. Othman and Marzouk
(2016) experimentally obtained the DIFs for two types of fiber-reinforced cementitious composites (FRCCs) with the compressive strengths of 110.8 and 132.7 MPa
at low to medium strain rates (0.58 ~ 2.58 s
−1 ), as shown in Fig. 3.11. Due to the
good consistence with the DIF for FRCCs, the empirical formula of fib Model Code
2010 (2013) is adopted for the strain rates below the transition strain rate. Thus an
empirical formula is proposed to describe the strain rate effect of UHPCC as follows,
DIF =
(˙ ε/˙ ε 0 )
0.018
for ˙
ε ≤ ˙
ε T R
A · log˙ ε + B for ˙
ε > ˙
ε T R
(3.12)
where A and B are the coefficients. By fitting the test data, the values of A, B and ˙
ε T R
for UHPCC are determined and listed in Table 3.4. Then the corresponding empirical
DIF relations of Eq. (3.12) are given in Fig. 3.12. These empirical formulae can be
used to predict the tensile DIFs in the numerical predictions of UHPCC structure
responses under high strain rate loadings. It should be noted that Eq. (3.12) is derived
from the test data for the strain rate up to ~214.8 s
−1 , beyond which there is no
available test data to substantiate its validity.
Table 3.4 Coefficients for
the proposed DIF formula of
UHPCC
Test No.
A
B
˙
ε T R (s −1 )
N-0
7.362
−5.167
7.8
S-1
9.637
−8.814
11.5
H-1
14.338
−15.695
15.5
H-2
11.561
−10.446
10.5