## 6 Test Results
### Dissipated Energy  
In the case of seismic loads, the imposed displacements are asymmetric, and the loops may not be closed. The dissipated energy (E\({}_{d}^{i}\)) should be evaluated appropriately for each half loop (i) during the test as the area of the ith half loop, in Equation (14) in [PERSON] et al. (2018), as indicated in Figure 13.  
\[E_{d}^{i}=\ A_{Half-Loop}^{i} \tag{14}\]  
The cumulative energies (\(\Sigma\mathrm{E}^{i}_{d}\)) calculated for the ASB and the RR columns for the negative and the positive half loops were obtained as the sum of the dissipated energy E\({}_{d}^{i}\) during the Tol part of the displacement history, and are given in Figure 14a,b.  
Figure 12: Experimental secant stiffness (k\({}^{i}_{sec}\)) measured at each cycle for the column P16B (the ASB column) and the RR columns R16-UHS and R16-UHP during the Tol and Tol \(\times\) 2 parts of the displacement history.  
Figure 13: Example of damping determination for a hysteretic force (F) displacement (D) half-cycles.  
The repair strategy improved the energy dissipation capacity of the column during the tests, both in the negative direction. The polymer fibers ensured considerable improvement but it was a little smaller than the one produced by the steel fibers in the negative direction. The polymer fiber produced a good improvement but with a greater difference with respect to the one produced by the steel fibers in the positive direction.  
The parameter \(v^{\rm i}_{\rm Ed}\) defined in Equation (15) is an estimation of the variation in the dissipated energy after column repair for each half cycle.  
\[v^{\rm i}_{\rm Ed}=\frac{E^{\rm i}_{\rm d,RR}-E^{\rm i}_{\rm d,ASB}}{E^{\rm i }_{\rm d,ASB}} \tag{15}\]  
where \(E^{\rm i}_{\rm d,RR}\) and \(E^{\rm i}_{\rm d,ASB}\) are the dissipated energy of the RR column and the ASB columns for each cycle, respectively. The parameter \(v^{\rm i}_{\rm Ed}\) was calculated for each negative and positive half loop in: (1) Figure 14 for the RR column repaired by concrete with steel fibers (UHS); and (2) Figure 14 for the RR column repaired by concrete with polymer fibers (UHP).  
The response of the columns subjected to low cycle fatigue excitation can be evaluated considering the first five cycles (Figure 7b) during the application of the Tol part of the deformation history. The mean value of \(v^{\rm i}_{\rm Ed}\) calculated during the first five cycles was, for the negative half loops, 30.5% for R16-UHS and 18.8% for column R16-UHP, and for the positive half loops, 33.7% for R16-UHS and 15.0% for the column R16-UHP. This means that the polymer and steel fibers may increase the column energy dissipation capacity, but the steel fibers were more efficient, especially in the positive direction when the mean variation in the energies obtained for the column with polymer fibers (UHP) was less of the half of that obtained for the column with steel fibers (UHS). The mean value of \(v^{\rm i}_{\rm Ed}\) calculated during the Tol part of the displacement history was, for the negative half loops, 34.8% for R16-UHS and 18.8% for column R16-UHP.  
Figure 14: Cumulative dissipated energy (\(\Sigma E^{\rm i}_{\rm d}\)) calculated during the displacement history part Tol for the ASB column (P16B) and the repaired columns (R16-UHS, R16-UHP): (**a**) For the negative (N), and (**b**) for the positive (P) half loops. Dissipated energy variation (\(v^{\rm i}_{\rm Ed}\)) for: (**c**) the column R16-UHS and (**d**) the column R16-UHP.  
and 22.8% for the column R16-UHP; and for the positive half loops, 37.8% for R16-UHS and 17.9% for R16-UHP.  
The column with either steel or polymer fiber modestly improved the energy dissipation capacity after low cycle fatigue excitation in each load direction. Similar consideration to those discussed for the low cycle fatigue response can be provided by considering the entire Tol displacement history.