302
9 Dynamic Responses of Reinforced UHPCC Members Under …
in Figs. 9.7 and 9.9, respectively. It indicates that, the numerically simulated impact
force- and deflection-time histories are in good agreement with the test data except
for the peak value of impact force, which may be caused by the change of contact
stiffness, as well as the impact inclination of indenter. It is worthily noted that the
contact stiffness would significantly affect the peak impact force, and the contact
stiffness is sensitive to the actual impact inclination and the contact condition (Li
et al. 2019). In addition, the contact stiffness has little effect on the impact impulse
and the deformation response of specimens.
Furthermore, the comparisons between the experimental and numerical damage
of specimens are shown in Fig. 9.26. It can be drawn that, the numerical model
can capture the identical diagonal shear fractures of NSC specimens as exhibited
experimentally in Fig. 9.26a. As shown in Fig. 9.26b, the numerical results of UHPCC
specimens with the developed CSC model exhibits the same ductile bending damage
as the experimental results. The shear damage on UHPCC specimens without axial
force exaggerated generally with increasing the impact energy in the simulation.
Additionally, as shown in Fig. 9.27, the simulated instantaneous damage contour
agrees well with the experimental photograph recorded by the high-speed camera of
specimen U-3-AF0.
Generally, by comparisons of the experimental and numerically predicted damage
and dynamic response of present specimens, the validations of the calibrated CSC
model parameters for UHPCC are verified.
9.4.3.3 Discussion on Axial Force
The axial force has a great degree of inhibition to the deflection response of the
UHPCC specimens based on the above experimental and numerical analyses, which
can be attributed to the following two reasons. The first one is that the core UHPCC
is restrained by the axial force, and the pre-load axial compressive stress could
help postpone the propagation of tensile cracks to enhance the impact-resistance of
specimen. The second reason is compressive membrane action (or called arching
effect) of column under impact, which might be more important (Fan et al.2019).
From the numerical results, as shown in Fig. 9.28, the mechanism of axial force is
an energy transfer system based on compressive membrane action. As the deflection
of UHPCC specimens increasing, the axial force absorbs a part of impact energy by
doing the negative work. Comparably, the axial force provides the energy needed
for the recovery of UHPCC specimens by doing positive work during the rebound
stage of specimen. The internal energy in disc spring and mid-span deflection-time
histories are presented in Fig. 9.28. The axial compressive length of the disc spring
is 5.35 mm, which is calculated from spring internal energy.
Aiming to clearly demonstrate the mechanism of compressive membrane action,
a simplified arch model has been provided in Fig. 9.29. The h
in simplified model is
vertical distance between mid-span and supported plastic hinges, which is 140 mm in
present test. According to the geometric relation of the arch model, the axial elongation of specimen U-3-AF0.1 at the maximum deflection is 5.26 mm. The elongation
9 Dynamic Responses of Reinforced UHPCC Members Under …
in Figs. 9.7 and 9.9, respectively. It indicates that, the numerically simulated impact
force- and deflection-time histories are in good agreement with the test data except
for the peak value of impact force, which may be caused by the change of contact
stiffness, as well as the impact inclination of indenter. It is worthily noted that the
contact stiffness would significantly affect the peak impact force, and the contact
stiffness is sensitive to the actual impact inclination and the contact condition (Li
et al. 2019). In addition, the contact stiffness has little effect on the impact impulse
and the deformation response of specimens.
Furthermore, the comparisons between the experimental and numerical damage
of specimens are shown in Fig. 9.26. It can be drawn that, the numerical model
can capture the identical diagonal shear fractures of NSC specimens as exhibited
experimentally in Fig. 9.26a. As shown in Fig. 9.26b, the numerical results of UHPCC
specimens with the developed CSC model exhibits the same ductile bending damage
as the experimental results. The shear damage on UHPCC specimens without axial
force exaggerated generally with increasing the impact energy in the simulation.
Additionally, as shown in Fig. 9.27, the simulated instantaneous damage contour
agrees well with the experimental photograph recorded by the high-speed camera of
specimen U-3-AF0.
Generally, by comparisons of the experimental and numerically predicted damage
and dynamic response of present specimens, the validations of the calibrated CSC
model parameters for UHPCC are verified.
9.4.3.3 Discussion on Axial Force
The axial force has a great degree of inhibition to the deflection response of the
UHPCC specimens based on the above experimental and numerical analyses, which
can be attributed to the following two reasons. The first one is that the core UHPCC
is restrained by the axial force, and the pre-load axial compressive stress could
help postpone the propagation of tensile cracks to enhance the impact-resistance of
specimen. The second reason is compressive membrane action (or called arching
effect) of column under impact, which might be more important (Fan et al.2019).
From the numerical results, as shown in Fig. 9.28, the mechanism of axial force is
an energy transfer system based on compressive membrane action. As the deflection
of UHPCC specimens increasing, the axial force absorbs a part of impact energy by
doing the negative work. Comparably, the axial force provides the energy needed
for the recovery of UHPCC specimens by doing positive work during the rebound
stage of specimen. The internal energy in disc spring and mid-span deflection-time
histories are presented in Fig. 9.28. The axial compressive length of the disc spring
is 5.35 mm, which is calculated from spring internal energy.
Aiming to clearly demonstrate the mechanism of compressive membrane action,
a simplified arch model has been provided in Fig. 9.29. The h
in simplified model is
vertical distance between mid-span and supported plastic hinges, which is 140 mm in
present test. According to the geometric relation of the arch model, the axial elongation of specimen U-3-AF0.1 at the maximum deflection is 5.26 mm. The elongation