## 4 Discussion of Results
### Toughness in Compression  
The energy dissipated during the fracture process in compression, also designated as the work of fracture in compression [59, 60], can be obtained by dividing the area under the stress vs. displacement response into two parts; see Figure 13. The area indicated as \(A_{prc}\) represents the energy dissipated in compression before the peak and \(A_{post}\) the energy dissipated after the peak. Since the post-cracking portion of the experimental response tends to extend over large deformations, it is important to define a reference residual stress, \(\sigma_{0}\), common to all specimens, up to which the energy dissipated during the fracture process in compression is computed. Therefore, the \(A_{post}\) value was measured up to a deflection in the post-peak phase corresponding to \(\sigma/\sigma_{0}\) = 0.33. The results obtained for both curing conditions are shown in Figure 14, where it is visible that the energy dissipated during the fracture process in compression increased with the fibre fraction. However, in the case of the specimens cured at 85% of RH, the value of the pre-peak energy dissipated remained approximately constant for mortars with different fibre contents. Probably, the curing environment with a higher RH favoured the curing of the NHL-based matrix, therefore leading to increased energy required to induce the same level of damage. The toughness ratio in compression (\(TR_{c}\)) can be used to identify the capacity of the materials to absorb energy and plastically deform before failure. Considering that one of the main aims of this study is to develop FRMs that maximise the capacity of masonry elements to dissipate energy when used as strengthening overlays, this ratio was computed following the procedure adopted by other authors [56, 61, 62]. As described by Equations (4) and (5) and represented in Figure 15, \(TR_{c}\) represents the ratio between the area limited by the stress vs. strain response up to a predefined level of strain, \(\varepsilon\), and the area given by \(f_{c}\times\varepsilon\), with \(f_{c}\) being the compressive strength, as shown in Figure 15. The predefined strain values,  
Figure 13: Method to calculate the work of fracture in compression [59, 60]. \(\varepsilon\), were assumed as 0.0105 and 0.0175, which represent three and five times the concrete ultimate strain (\(TR_{c,3}\) and \(TR_{c,5}\)), assuming that this strain was 0.0035 according to EN 1992-1-1:2010 (EC2) [63], and following the methodology adopted in [56]. \[TR_{c,3}=\frac{Area\,OABC}{f_{c}\times 0.0105}\times 100\% \tag{4}\]  
\[TR_{c,5}=\frac{Area\,OABC}{f_{c}\times 0.0175}\times 100\% \tag{5}\]  
The \(TR_{c}\) values obtained when considering lower predefined strains \(\varepsilon\), \(TR_{c,3}\), show an increase of around 25% when compared to the reference mixture without fibres, with the mixtures containing 0.75% and 1.00% of PAN fibres; see Figure 16a. However, when higher values of the predefined strain \(\varepsilon\) are considered, \(TR_{c,5}\), this increase tendency is considerably higher, reaching around 100% for the specimens cured in 85% RH; see Figure 16b. This  
Figure 14: Compression fracture energy for different curing conditions: (**a**) RH 60; (**b**) RH 85. Figure 15: Definition of compressive toughness ratio [61; 62]. variation of the \(TR_{c}\) values reveals the significant contribution of the fibre reinforcement to the improvement in the post-peak behaviour of the mixtures while subjected to compression loading. The relation between compressive strength and toughness ratios for lower and higher deformation levels, \(TR_{c,3}\) and \(TR_{c,5}\), is shown in Figure 17, considering both curing conditions, RH60 and RH85. For RH60, when lower levels of deformation were used as a reference, \(TR_{c,3}\), lower variations in this ratio were obtained, changing from 60% to 85%, while more expressive increments, from 40% to 85%, were obtained when higher deformations were considered, \(TR_{c,5}\).