46
2 Dynamic Compressive Mechanical Properties of UHPCC
DIF =
0.0235log ˙
ε + 1.070.0235log ˙
ε + 1.07
for ˙
ε ≤ 266.0s
−1
0.882(log ˙
ε)
3
− 4.48(log ˙
ε)
2
+ 7.22log ˙
ε − 2.64 for ˙
ε > 266.0s
−1
(2.5)
Based on the numerical results of SHPB test on mortar, Li and Meng (2003)
formulated a relationship between DIF and the logarithm of strain rate as
DIF =
1 + 0.03438(log ˙
ε + 3)
for ˙
ε ≤ 10
2 s
−1
1.729(log ˙
ε)
2
− 7.1372log ˙
ε + 8.5303 for ˙
ε > 10
2 s
−1
(2.6)
Zhou and Hao (2008) further proposed a DIF formula based on the existing SHPB
test results of rock materials as
DIF =
0.0225log ˙
ε + 1.12
for ˙
ε ≤ 10.0s
−1
0.2713(log ˙
ε)
2
− 0.3563log ˙
ε + 1.2275 for ˙
ε > 10.0s
−1
(2.7)
The above five formulae are also plotted in Fig. 2.13, it indicates that, these
formulae could not well describe the evolution of the DIF for UHPCC material and
generally overestimate or underestimate the dynamic compressive strength.
Since there is no test data of UHPCC under quasi-dynamic loadings, it is difficult
to determine the transition strain rate ˙
ε T R exactly. As shown in Eq. (2.8), an empirical
formula is proposed to describe the strain rate sensitivity of UHPCC, where the fib
Model Code 2010 (2013) is adopted for the strain rates below the transition strain
rate.
DIF =
(˙ ε/˙ ε ts )
0.014
for ˙
ε ≤ ˙
ε T R
A f · (log˙ ε)
2
+ B f · log ˙
ε + C f for ˙
ε > ˙
ε T R
(2.8)
where A f , B f and C f are the coefficients. By fitting the test data, the values of A f , B f ,
C f and ˙
ε T R for UHPCC are confirmed and given in Table 2.4, and the corresponding
empirical DIF relations are shown in Fig. 2.14. These empirical formulae can be used
to estimate the DIF in the numerical prediction of UHPCC structure responses under
high strain rate loadings. It should be noted that, Eq. (2.8) is derived from test data
Table 2.4 Coefficients in proposed DIF formula for UHPCC
Test No.
A f
B f
C f
˙
ε T R (s −1 )
N-0
0.3714
−0.5622
1.2471
28
S-1
0.5835
−1.5905
2.1988
63
S-2
0.5103
−1.2301
1.6804
92
H-1
0.5065
−0.7046
0.7684
75
H-2
0.8152
−2.3884
2.8389
75
2 Dynamic Compressive Mechanical Properties of UHPCC
DIF =
0.0235log ˙
ε + 1.070.0235log ˙
ε + 1.07
for ˙
ε ≤ 266.0s
−1
0.882(log ˙
ε)
3
− 4.48(log ˙
ε)
2
+ 7.22log ˙
ε − 2.64 for ˙
ε > 266.0s
−1
(2.5)
Based on the numerical results of SHPB test on mortar, Li and Meng (2003)
formulated a relationship between DIF and the logarithm of strain rate as
DIF =
1 + 0.03438(log ˙
ε + 3)
for ˙
ε ≤ 10
2 s
−1
1.729(log ˙
ε)
2
− 7.1372log ˙
ε + 8.5303 for ˙
ε > 10
2 s
−1
(2.6)
Zhou and Hao (2008) further proposed a DIF formula based on the existing SHPB
test results of rock materials as
DIF =
0.0225log ˙
ε + 1.12
for ˙
ε ≤ 10.0s
−1
0.2713(log ˙
ε)
2
− 0.3563log ˙
ε + 1.2275 for ˙
ε > 10.0s
−1
(2.7)
The above five formulae are also plotted in Fig. 2.13, it indicates that, these
formulae could not well describe the evolution of the DIF for UHPCC material and
generally overestimate or underestimate the dynamic compressive strength.
Since there is no test data of UHPCC under quasi-dynamic loadings, it is difficult
to determine the transition strain rate ˙
ε T R exactly. As shown in Eq. (2.8), an empirical
formula is proposed to describe the strain rate sensitivity of UHPCC, where the fib
Model Code 2010 (2013) is adopted for the strain rates below the transition strain
rate.
DIF =
(˙ ε/˙ ε ts )
0.014
for ˙
ε ≤ ˙
ε T R
A f · (log˙ ε)
2
+ B f · log ˙
ε + C f for ˙
ε > ˙
ε T R
(2.8)
where A f , B f and C f are the coefficients. By fitting the test data, the values of A f , B f ,
C f and ˙
ε T R for UHPCC are confirmed and given in Table 2.4, and the corresponding
empirical DIF relations are shown in Fig. 2.14. These empirical formulae can be used
to estimate the DIF in the numerical prediction of UHPCC structure responses under
high strain rate loadings. It should be noted that, Eq. (2.8) is derived from test data
Table 2.4 Coefficients in proposed DIF formula for UHPCC
Test No.
A f
B f
C f
˙
ε T R (s −1 )
N-0
0.3714
−0.5622
1.2471
28
S-1
0.5835
−1.5905
2.1988
63
S-2
0.5103
−1.2301
1.6804
92
H-1
0.5065
−0.7046
0.7684
75
H-2
0.8152
−2.3884
2.8389
75