1.4 Test Results and Discussion
25
k β (α) =
α
1/2
(1 − α) 3/2 (1 + 3α)
p ∞ (α) +
4
β
p 4 (α) − p ∞ (α)
(1.5)
where p 4 (α) and p ∞ (α) are cubic polynomial and can be expressed as
p 4 (α) = 1.90 + 0.41α + 0.51α
2
− 0.17α
3
(1.6)
p ∞ (α) = 1.99 + 0.83α − 0.31α
2
+0.14α
3
(1.7)
Based on the Eqs. (1.3–1.7) and the three-point flexural load-CMOD curves of
UHPCC shown in Fig. 1.22, the fracture toughness of UHPCC is derived and listed
in Table 1.9. For example, “TN400-0” denotes the test No. and the capital “T”
represents the three-point flexural test. The results show that, addition of steel fibers
can significantly improve the fracture toughness of UHPCC and the steel fiber type
has relatively minor effect. The fracture toughness of UHPCC with 2.5% microstraight or hooked steel fibers (~15.8 MPa·m
1/2 ) is about 11 times compared to the
corresponding value of plain UHPCC (~1.4 MPa·m
1/2 ).
1.4.4.3 Fracture Energy
Fracture energy G F is defined as the energy required to generate unit fractured surface
area, it is generally considered as a material property and determined by the following
equation recommended by RILEM (1985).
G F =
W 0 + m 0 gδ 0
b(h − a 0 )
(1.8)
where W 0 is the area under the load–deflection curve. m 0 is the mass of specimen
including the mass of measuring device attached to the specimen. δ 0 and a 0 are the
deflection at finale fracture and the notch depth, respectively.
Based on the three-point flexural load–deflection curves of UHPCC given in
Fig. 1.23, Table 1.10 lists the fracture energy of UHPCC, where “—” denotes that
the data is not obtained or discarded due to the large deviation. Figure 1.25 further
shows the effects of steel fiber content and type on the fracture energy. As can be
seen, the fracture energy of UHPCC gradually increases with the rising of steel fiber
content. When the steel fiber content is more than 1.0%, the micro-straight steel fiber
has better effect on improving the fracture energy of UHPCC than the hooked steel
fiber. For example, the maximal fracture energy of UHPCC with 2.5% micro-straight
steel fibers (13583 N/m) can reach almost 1.2 and 3.5 times larger than the corresponding values of UHPCC with 2.5% hooked steel fibers (11308 N/m) and 0.5%
micro-straight steel fibers (3879 N/m), respectively. Furthermore, the fracture energy
of C100 plain concrete suggested by the fib Model Code 2010 (2013) is 169.6 N/m,
25
k β (α) =
α
1/2
(1 − α) 3/2 (1 + 3α)
p ∞ (α) +
4
β
p 4 (α) − p ∞ (α)
(1.5)
where p 4 (α) and p ∞ (α) are cubic polynomial and can be expressed as
p 4 (α) = 1.90 + 0.41α + 0.51α
2
− 0.17α
3
(1.6)
p ∞ (α) = 1.99 + 0.83α − 0.31α
2
+0.14α
3
(1.7)
Based on the Eqs. (1.3–1.7) and the three-point flexural load-CMOD curves of
UHPCC shown in Fig. 1.22, the fracture toughness of UHPCC is derived and listed
in Table 1.9. For example, “TN400-0” denotes the test No. and the capital “T”
represents the three-point flexural test. The results show that, addition of steel fibers
can significantly improve the fracture toughness of UHPCC and the steel fiber type
has relatively minor effect. The fracture toughness of UHPCC with 2.5% microstraight or hooked steel fibers (~15.8 MPa·m
1/2 ) is about 11 times compared to the
corresponding value of plain UHPCC (~1.4 MPa·m
1/2 ).
1.4.4.3 Fracture Energy
Fracture energy G F is defined as the energy required to generate unit fractured surface
area, it is generally considered as a material property and determined by the following
equation recommended by RILEM (1985).
G F =
W 0 + m 0 gδ 0
b(h − a 0 )
(1.8)
where W 0 is the area under the load–deflection curve. m 0 is the mass of specimen
including the mass of measuring device attached to the specimen. δ 0 and a 0 are the
deflection at finale fracture and the notch depth, respectively.
Based on the three-point flexural load–deflection curves of UHPCC given in
Fig. 1.23, Table 1.10 lists the fracture energy of UHPCC, where “—” denotes that
the data is not obtained or discarded due to the large deviation. Figure 1.25 further
shows the effects of steel fiber content and type on the fracture energy. As can be
seen, the fracture energy of UHPCC gradually increases with the rising of steel fiber
content. When the steel fiber content is more than 1.0%, the micro-straight steel fiber
has better effect on improving the fracture energy of UHPCC than the hooked steel
fiber. For example, the maximal fracture energy of UHPCC with 2.5% micro-straight
steel fibers (13583 N/m) can reach almost 1.2 and 3.5 times larger than the corresponding values of UHPCC with 2.5% hooked steel fibers (11308 N/m) and 0.5%
micro-straight steel fibers (3879 N/m), respectively. Furthermore, the fracture energy
of C100 plain concrete suggested by the fib Model Code 2010 (2013) is 169.6 N/m,