4.2 A Review of the Existing Works on Triaxial Behavior of Concrete
75
Correspondingly, Lu and Hsu (2006) compared the triaxial compressive stress–
strain relations and failure criteria of HSC and steel fiber reinforced HSC (SFHSC),
and also found the slight reinforcing effect on the uniaxial and triaxial strengths of
100 × 150 mm cylindrical specimens, in which the unconfined compressive strengths
of HSC and SFHSC were 67 and 69 MPa, and the maximum confinement ratios
were 0.74 and 1, respectively. Xie et al. (1995) experimentally confirmed the threeparameter parabolic relationships between the confined pressure and the maximum as
well as residual strengths of HSC containing silica fume specimens (55.5 × 110 mm
cylinder), the variation ranges of unconfined compressive strengths and confinement
ratio were 60.2 ~ 119 MPa and 0 ~ 0.504, respectively. Ansair and Li (1998), Li and
Ansair (1997, 2010) experimentally studied the triaxial constitutive relationships of
100 × 200 mm and 75 × 150 mm cylindrical concrete specimens, with the uniaxial
compressive strengths ranging from 47.7 MPa (maximum confinement ratio of 0.878)
to 107.3 MPa (maximum confinement ratio of 0.7792). The less pronounced effect
of confining pressure on the failure strength of HSC than NSC, and the distinct effect
of confining pressure on the failure strain were found. Also the specimen size of
HSC has slight effect on the triaxial compressive failure strength and failure surface.
Furthermore, the empirical failure criterion based on Ottosen constitutive model
(Ottosen 1977) was established for HSC. Attard and Setunge (1996) and Candappa
et al. (2001) investigated the stress–strain relationships of concrete specimens (100
× 200 mm cylinders) with the unconfined compressive strength ranging from 60 ~
130 MPa and 41.9 ~ 103.3 MPa, respectively. The empirical model for full triaxial
stress–strain relationship was developed and the parameters for Ottosen constitutive
model (Ottosen 1977) were suggested. By comprehensively assessing the validities
of the existing nine empirical formulae for triaxial ultimate compressive strength
of HSC, Girgin et al. (2007) proposed a new relationship to predict the ultimate
strength of concrete with the unconfined strength ranging from 60 to 132 MPa.
Sovják et al. (2013) experimentally studied the triaxial cylinder (100 × 200 mm)
and cubic (100mm
3 ) compressive strengths of ultra high performance concrete, of
which the unconfined compressive strengths were 123 MPa and 148 MPa and the
confined ratio increased up to 0.25 and 0.6, respectively.
Additionally, Imran and Pantazopoulou (1996), Farnam et al. (2010), Vu et al.
(2011) and Piotrowska et al. (2014) have systematically studied the influences of
moisture content, loading path, steel fiber volumes, size, shape and composition of
coarse aggregates as well as the cement paste volume on the triaxial compressive
behavior of concrete.
However, for the widely applications of UHPCC in the on-site constructions
of protective structures against projectile impact, limited works were concentrated
on the composition optimization based on the balances of anti-strike ability and
costs, preparation of optimal UHPCC under ordinary procedure, triaxial compressive
behavior of optimal UHPCC as well as its applications in the projectile penetration
or perforation analyses. The present chapter is aiming to fill in the above gaps.
75
Correspondingly, Lu and Hsu (2006) compared the triaxial compressive stress–
strain relations and failure criteria of HSC and steel fiber reinforced HSC (SFHSC),
and also found the slight reinforcing effect on the uniaxial and triaxial strengths of
100 × 150 mm cylindrical specimens, in which the unconfined compressive strengths
of HSC and SFHSC were 67 and 69 MPa, and the maximum confinement ratios
were 0.74 and 1, respectively. Xie et al. (1995) experimentally confirmed the threeparameter parabolic relationships between the confined pressure and the maximum as
well as residual strengths of HSC containing silica fume specimens (55.5 × 110 mm
cylinder), the variation ranges of unconfined compressive strengths and confinement
ratio were 60.2 ~ 119 MPa and 0 ~ 0.504, respectively. Ansair and Li (1998), Li and
Ansair (1997, 2010) experimentally studied the triaxial constitutive relationships of
100 × 200 mm and 75 × 150 mm cylindrical concrete specimens, with the uniaxial
compressive strengths ranging from 47.7 MPa (maximum confinement ratio of 0.878)
to 107.3 MPa (maximum confinement ratio of 0.7792). The less pronounced effect
of confining pressure on the failure strength of HSC than NSC, and the distinct effect
of confining pressure on the failure strain were found. Also the specimen size of
HSC has slight effect on the triaxial compressive failure strength and failure surface.
Furthermore, the empirical failure criterion based on Ottosen constitutive model
(Ottosen 1977) was established for HSC. Attard and Setunge (1996) and Candappa
et al. (2001) investigated the stress–strain relationships of concrete specimens (100
× 200 mm cylinders) with the unconfined compressive strength ranging from 60 ~
130 MPa and 41.9 ~ 103.3 MPa, respectively. The empirical model for full triaxial
stress–strain relationship was developed and the parameters for Ottosen constitutive
model (Ottosen 1977) were suggested. By comprehensively assessing the validities
of the existing nine empirical formulae for triaxial ultimate compressive strength
of HSC, Girgin et al. (2007) proposed a new relationship to predict the ultimate
strength of concrete with the unconfined strength ranging from 60 to 132 MPa.
Sovják et al. (2013) experimentally studied the triaxial cylinder (100 × 200 mm)
and cubic (100mm
3 ) compressive strengths of ultra high performance concrete, of
which the unconfined compressive strengths were 123 MPa and 148 MPa and the
confined ratio increased up to 0.25 and 0.6, respectively.
Additionally, Imran and Pantazopoulou (1996), Farnam et al. (2010), Vu et al.
(2011) and Piotrowska et al. (2014) have systematically studied the influences of
moisture content, loading path, steel fiber volumes, size, shape and composition of
coarse aggregates as well as the cement paste volume on the triaxial compressive
behavior of concrete.
However, for the widely applications of UHPCC in the on-site constructions
of protective structures against projectile impact, limited works were concentrated
on the composition optimization based on the balances of anti-strike ability and
costs, preparation of optimal UHPCC under ordinary procedure, triaxial compressive
behavior of optimal UHPCC as well as its applications in the projectile penetration
or perforation analyses. The present chapter is aiming to fill in the above gaps.