The envelope curves of HFRC can be approximately divided into two branches: ascending branch and descending branch.
Moreover, a stiffness ratio [R.sub.s] is defined and used to characterize the damage of HFRC:
The stiffness degradation process of HFRC under cyclic compression is shown in Figure 8.
The stiffness degradation process of HFRC under cyclic tension is shown in Figure 9.
In order to evaluate the energy dissipated capacity of HFRC, the dissipated energy [W.sub.pl] and [SIGMA] [W.sub.pl] are defined  and presented in Figure 10.
It should be noted that due to the small hysteretic loop between the reloading and unloading paths and the low energy dissipated capacity of concrete under cyclic tension, the energy dissipation capacity of HFRC is not evaluated and discussed in this study.
As previously discussed, significant stiffness degradation is observed for HFRC under both cyclic compression and tension, which is induced by the damage accumulation during the loading process.
Using the suggested equation, the fitting results of the damage evolution curves of HFRC for different fiber parameters are shown Figures 12 and 13.
where [[epsilon].sub.co] is the elastic limit of the compressive strain, which is defined as the strain where the stress is 30% of the peak strength of HFRC.
It is found from Figure 9 that the effect of PF on the damage evolution of HFRC is insignificant accounted that PF mainly affects the prepeak stage of the stress-strain curves of concrete.
Therefore, in order to precisely predict the behavior of HFRC structures subjected to external loads, the two aspects of damage and plastic strain should be considered.
The modification of the five additional parameters for HFRC has been conducted by the authors' previous studies.