3.2.1. Effects of DV on the P–δ Curves of NP-ECC-BRs

compressive behaviors of NP-C-BRs [17–21].

According to the collected data, the P–δ curves of all the 16 groups of PVA-ECC specimens were obtained, as shown in Figure 7.

It can be seen in Figure 7 that the volatility of the P–δ curves of most of the vibrated groups was not so obvious compared to that of the control group, indicating that there is some extent of negative effect on the multi-cracking characteristics of NP-ECC-BR specimens when the specimens were vibrated during the setting with different DVs. Even so, it also can be seen in Figure 7 that significant hardening segments appeared in the P–δ curves of all the 16 groups of specimens when they were subjected to TRVs with a duration completely covering the setting period. In this section, the longest DV was 11 h, the TRVs began at the age of 8 h, and the time of the final set was 23.8 h. Therefore, for the series of F2,3,4,5–8–11, the duration of 11 h almost covered the whole setting period. *Materials* **2019**, *12*, x FOR PEER REVIEW 12 of 19 hardening segments appeared in the P–δ curves of all the 16 groups of specimens when they were subjected to TRVs with a duration completely covering the setting period. In this section, the longest DV was 11 h, the TRVs began at the age of 8 h, and the time of the final set was 23.8 h. Therefore, for

Combined with the results in Subsection 3.1.1 and the results of our previous work in [29], it can be further concluded that the effects of TRVs are not significant, but to some extent there are still negative effects on the strain-hardening behaviors of NP-ECC-BRs within the limits in these studies. On this point, this result was also consistent with the previously found effects of TRVs on the compressive behaviors of NP-C-BRs [17–21]. the series of F2,3,4,5–8–11, the duration of 11 h almost covered the whole setting period. Combined with the results in Subsection 3.1.1 and the results of our previous work in [29], it can be further concluded that the effects of TRVs are not significant, but to some extent there are still negative effects on the strain-hardening behaviors of NP-ECC-BRs within the limits in these studies. On this point, this result was also consistent with the previously found effects of TRVs on the

**Figure 7.** P–δ curves of all the 16 groups of specimens under the operating conditions for Var. 2 with frequencies of (**a**) 2 Hz, (**b**) 3 Hz, (**c**) 4 Hz, and (**d**) 5 Hz and that of the control group. **Figure 7.** P–δ curves of all the 16 groups of specimens under the operating conditions for Var. 2 with frequencies of (**a**) 2 Hz, (**b**) 3 Hz, (**c**) 4 Hz, and (**d**) 5 Hz and that of the control group.

### 3.2.2. Effects of DV on the Flexural Properties of NP-ECC-BRs 3.2.2. Effects of DV on the Flexural Properties of NP-ECC-BRs

when the vibration frequencies were lower than 5.0 Hz.

that of Pc in general, as shown in Figure 8a–d (blue lines).

In this subsection, we investigate and quantitively characterize the extent to which the DV during the setting period affected the Pc, δc, Pu, and δu of NP-ECC-BRs. The rates of the Pc, δc, Pu, and δu of the groups that were vibrated under the operating conditions for Var. 2 over the corresponding control winsorized means are shown in Figure 8. In this subsection, we investigate and quantitively characterize the extent to which the DV during the setting period affected the Pc, δc, Pu, and δ<sup>u</sup> of NP-ECC-BRs. The rates of the Pc, δc, Pu, and δ<sup>u</sup> of the groups that were vibrated under the operating conditions for Var. 2 over the corresponding control winsorized means are shown in Figure 8.

The effects of DV on the Pc of NP-ECC-BRs under the operating conditions for Var. 2 are examined. Similar to the Pc obtained under the operating conditions for Var. 1, the effects of DV on the Pc of all the 16 groups of NP-ECC-BRs tended to be significantly negative under the operating The effects of DV on the P<sup>c</sup> of NP-ECC-BRs under the operating conditions for Var. 2 are examined. Similar to the P<sup>c</sup> obtained under the operating conditions for Var. 1, the effects of DV on the P<sup>c</sup> of all the 16 groups of NP-ECC-BRs tended to be significantly negative under the operating conditions

conditions for Var. 2, decreasing by 19%–57% over the control average, as shown in Figure 8a–d (black lines). Furthermore, Pc did not change significantly with the increase in DV under the imposed

TRVs on the cracking load-bearing capacity of NP-ECC-BRs tended to be significantly negative, while it was not sensitive to increases in the DV when vibrations occurred during the setting period and

The effects of DV on the Pu of NP-ECC-BRs under the operating conditions for Var. 2 were examined. Likewise, a similar impact trend was presented for Pu compared to Pc under the operating conditions for Var. 2. The difference was that the impact degree of DV on Pu was less obvious than for Var. 2, decreasing by 19%–57% over the control average, as shown in Figure 8a–d (black lines). Furthermore, P<sup>c</sup> did not change significantly with the increase in DV under the imposed vibration frequencies of 2, 3, and 4 Hz, as shown in Figure 8a–c, while it presented an obvious reduction trend under the imposed vibration frequency of 5 Hz, as shown in Figure 8d. Based on these results and the results obtained in Section 3.1.2, it could be further concluded that the effects of TRVs on the cracking load-bearing capacity of NP-ECC-BRs tended to be significantly negative, while it was not sensitive to increases in the DV when vibrations occurred during the setting period and when the vibration frequencies were lower than 5.0 Hz.

The effects of DV on the P<sup>u</sup> of NP-ECC-BRs under the operating conditions for Var. 2 were examined. Likewise, a similar impact trend was presented for P<sup>u</sup> compared to P<sup>c</sup> under the operating conditions for Var. 2. The difference was that the impact degree of DV on P<sup>u</sup> was less obvious than that of P<sup>c</sup> in general, as shown in Figure 8a–d (blue lines). *Materials* **2019**, *12*, x FOR PEER REVIEW 13 of 19

The effects of DV on the δ<sup>u</sup> of NP-ECC-BRs under the operating conditions for Var. 2 were examined. However, the effects of DV on the δ<sup>u</sup> of all the 16 groups of specimens was positive, and for most of them, the positive impact degrees were above 20% under the operating conditions for Var. 2, as shown in Figure 8a–d (green lines). Moreover, δ<sup>u</sup> increased with the increasing of the DV under the imposed vibration frequencies of 2, 3, and 5 Hz, as shown in Figure 8a–c, but it decreased under the imposed vibration frequency of 4 Hz, as shown in Figure 8d. The effects of DV on the δu of NP-ECC-BRs under the operating conditions for Var. 2 were examined. However, the effects of DV on the δu of all the 16 groups of specimens was positive, and for most of them, the positive impact degrees were above 20% under the operating conditions for Var. 2, as shown in Figure 8a–d (green lines). Moreover, δu increased with the increasing of the DV under the imposed vibration frequencies of 2, 3, and 5 Hz, as shown in Figure 8a–c, but it decreased under

The effects of DV on the δ<sup>c</sup> of NP-ECC-BRs under the operating conditions for Var. 2 were examined. It can be seen in Figure 8a–d (red lines) that the effects, regardless of the impact trend, polarity, or degree of DV on the δ<sup>c</sup> of the specimens, varied according to the corresponding frequencies that the specimens were subjected to. the imposed vibration frequency of 4 Hz, as shown in Figure 8d. The effects of DV on the δc of NP-ECC-BRs under the operating conditions for Var. 2 were examined. It can be seen in Figure 8a–d (red lines) that the effects, regardless of the impact trend, polarity, or degree of DV on the δc of the specimens, varied according to the corresponding

frequencies that the specimens were subjected to.

vibration variables of AWV and DV.

some extent which should not be ignored.

**Figure 8.** Rates of the Pc, δc, Pu, and δu of the 16 groups of specimens over the corresponding control averages under the operating conditions for Var. 2 with frequencies of (**a**) 2 Hz, (**b**) 3 Hz, (**c**) 4 Hz, and (**d**) 5 Hz. **Figure 8.** Rates of the Pc, δc, Pu, and δu of the 16 groups of specimens over the corresponding control averages under the operating conditions for Var. 2 with frequencies of (**a**) 2 Hz, (**b**) 3 Hz, (**c**) 4 Hz, and (**d**) 5 Hz.

These above results indicate that the effects of DV on the cracking and extreme load-bearing capacity of NP-ECC-BRs were significantly negative (19%–57% reduction for most of them) under the operating conditions for Var. 2. By contrast, the effects of DV on the extreme flexural deformation were significantly positive, increasing by over 20% under the operating conditions for Var. 2. These above results indicate that the effects of DV on the cracking and extreme load-bearing capacity of NP-ECC-BRs were significantly negative (19%–57% reduction for most of them) under the operating conditions for Var. 2. By contrast, the effects of DV on the extreme flexural deformation were significantly positive, increasing by over 20% under the operating conditions for Var. 2. Moreover, the

Moreover, the results in Figure 8 also indicate that the longer the DVs, the higher the extreme flexural deformation capacity of NP-ECC-BRs when TRVs occurred only during the setting period.

These above results regarding the flexural load-bearing capacity obtained in this section was similar to that of the ultimate tensile strength of NP-ECC-BRs in [29], as well as the compressive strength, bond strength, splitting tensile strength, and flexural strength of NP-C-BRs when vibrations occurred only during the setting period [22–24]. The results in [22–24, 29] showed that the TRVs that occurred only during the setting periods affected the performance of NP-C-BRs or NP-ECC-BRs to

However, these above results concerning the extreme flexural deformation were just opposite to the tensile deformation properties of NP-ECC-BRs when TRVs occurred only during the setting period [29]. The result in [29] showed that the effects of DVs ranging from 2 to 11 h on the extreme

tensile deformation capacity of NP-ECC-BRs tended to be negative overall.

before the initial set.

during these periods, followed by δc or Pu, and then δu.

results in Figure 8 also indicate that the longer the DVs, the higher the extreme flexural deformation capacity of NP-ECC-BRs when TRVs occurred only during the setting period. Additionally, the effects of DV on the cracking deformation of NP-ECC-BRs seem to vary according to the corresponding vibration frequencies that the specimens experienced, regardless of the vibration variables of AWV and DV.

These above results regarding the flexural load-bearing capacity obtained in this section was similar to that of the ultimate tensile strength of NP-ECC-BRs in [29], as well as the compressive strength, bond strength, splitting tensile strength, and flexural strength of NP-C-BRs when vibrations occurred only during the setting period [22–24]. The results in [22–24,29] showed that the TRVs that occurred only during the setting periods affected the performance of NP-C-BRs or NP-ECC-BRs to some extent which should not be ignored.

However, these above results concerning the extreme flexural deformation were just opposite to the tensile deformation properties of NP-ECC-BRs when TRVs occurred only during the setting period [29]. The result in [29] showed that the effects of DVs ranging from 2 to 11 h on the extreme tensile deformation capacity of NP-ECC-BRs tended to be negative overall. *Materials* **2019**, *12*, x FOR PEER REVIEW 14 of 19 *3.3. Effects of Vibration Frequency on the Flexural Properties of NP-ECC-BRs*  The results in Sections 3.1 and 3.2 show that effects of TRVs on the flexural properties of NP-

### *3.3. E*ff*ects of Vibration Frequency on the Flexural Properties of NP-ECC-BRs* ECC-BRs are related to the corresponding vibration frequency. Accordingly, to further quantitatively

The results in Sections 3.1 and 3.2 show that effects of TRVs on the flexural properties of NP-ECC-BRs are related to the corresponding vibration frequency. Accordingly, to further quantitatively investigate the flexural properties of NP-ECC-BRs when imposing different vibration frequencies, the effects of vibration frequency on the flexural properties of NP-ECC-BRs are analyzed in this section. The rates of flexural properties of the specimens over the control averages under the operating conditions for Var. 1 and Var. 2 are shown in Figures 9 and 10, respectively. investigate the flexural properties of NP-ECC-BRs when imposing different vibration frequencies, the effects of vibration frequency on the flexural properties of NP-ECC-BRs are analyzed in this section. The rates of flexural properties of the specimens over the control averages under the operating conditions for Var. 1 and Var. 2 are shown in Figures 9 and 10, respectively. 3.3.1. Effects of Vibration Frequency on the Flexural Properties of NP-ECC-BRs under the Operating Conditions for Var. 1

**Figure 9.** The rates of flexural properties with different vibration frequencies over the control averages under the operating conditions for Var. 1 at ages of (**a**) 1.5 h, (**b**) 8 h, (**c**) 15 h, (**d**) 23 h, (**e**) 36 h, and (**f**) 48 h. **Figure 9.** The rates of flexural properties with different vibration frequencies over the control averages under the operating conditions for Var. 1 at ages of (**a**) 1.5 h, (**b**) 8 h, (**c**) 15 h, (**d**) 23 h, (**e**) 36 h, and (**f**) 48 h.

Effects of Vibration frequency on the flexural properties (Pc, δc, Pu, and δu) of NP-ECC-BRs when vibrations occurred before the initial set were examined. It can be seen in Figure 9a that the Pc of the vibrated specimens changed in an approximately linearly fashion from −2% to −24%, and −50% over the control average with an increase in vibration frequency ranging from 2 to 4 Hz, and this changed up to −2% under the vibration frequency of 5 Hz. It also can be seen in Figure 9a that δc presented a

not so obvious compared to those of the cracking properties (Pc and δc) when vibrations occurred

Effects of Vibration frequency on the flexural properties (Pc, δc, Pu and δu) of NP-ECC-BRs when vibrations began just after the initial set were examined. When the specimens were vibrated at the age of 8 h, it can be seen in Figure 9b that all the flexural properties increase or decrease in harmony and approximately linearly with the increase in vibration frequency. The differences are that the impact polarity was negative on Pu, Pc, and δc, and it was positive on δu. Additionally, the impact degree of TRVs on Pc was the largest, indicating that Pc was the most sensitive in its response to TRVs Conditions for Var. 2

within 20%).

3.3.1. Effects of Vibration Frequency on the Flexural Properties of NP-ECC-BRs under the Operating Conditions for Var. 1 As described in Figure 9b and shown in Figure 10b, the effects of imposed vibration frequency on the flexural properties (Pu, δu, Pc, and δc) of NP-ECC-BRs specimens is that they increase or

*Materials* **2019**, *12*, x FOR PEER REVIEW 15 of 19

Effects of Vibration frequency on the flexural properties (Pc, δc, Pu and δu) of NP-ECC-BRs when vibrations occurred after the middle stage of the setting period were examined. When the specimens were vibrated after the age of 15 h, it can be seen in Figure 9c–f that the effects of TRVs on the loadbearing properties (Pc and Pu) of the specimens was negative throughout the scope of imposed vibration frequencies in this study. However, it was positive on the deformation properties (δc and δu). Figure 9c–f also show that the flexural properties of most of the vibrated groups declined, in general, with the increase in imposed vibration frequency. Moreover, regarding the impact degree (regardless of polarity), the cracking properties (the Pc and δc of most of the specimens presented a reduction or growth above 20%) were more sensitive to the imposed vibration frequency than those of the extreme flexural properties (the Pu and δu of all the specimens presented a reduction or growth

Effects of Vibration frequency on the flexural properties (Pc, δc, Pu, and δu) of NP-ECC-BRs when vibrations occurred before the initial set were examined. It can be seen in Figure 9a that the P<sup>c</sup> of the vibrated specimens changed in an approximately linearly fashion from −2% to −24%, and −50% over the control average with an increase in vibration frequency ranging from 2 to 4 Hz, and this changed up to −2% under the vibration frequency of 5 Hz. It also can be seen in Figure 9a that δ<sup>c</sup> presented a roughly opposite trend compared with Pc, which changed in an approximately linearly fashion from −32% to 156% over the control average with an increase in vibration frequency ranging from 2 to 5 Hz. Moreover, the effects of vibration frequency on the extreme flexural properties (P<sup>u</sup> and δu) were not so obvious compared to those of the cracking properties (P<sup>c</sup> and δc) when vibrations occurred before the initial set. decrease in an approximately linearly fashion with the increase in vibration frequency with the constant duration of 5 h during the setting period. However, the results in Figure 10a,c,d show that when subjected to durations of 2, 8, and 11 h during the setting period, the effects of imposed vibration frequency on the deformation properties (δc and δu) of some of the vibrated groups were obviously different to those with the constant duration of 5 h. The obvious observed differences can be described as follows: (1) with a duration of 2 h, the effects of TRVs on the deformation properties (δc and δu) of the specimens were positive, and they generally increased with an increase in vibration frequency, as shown in Figure 10a; (2) with a duration of 8 h, the rate of the δc of the vibrated PVA-ECC specimens decreased approximately linearly from 40% to − 40% over the control average, as shown in Figure 10c; (3) when subjected to a duration of 11 h, the δc of the vibrated specimens increased by 44% over the control group under the vibration frequency of 4 Hz.

**Figure 10.** The effects of vibration frequency on the flexural properties of newly placed PVA-ECC bridge repairs (NP-ECC-BRs) under the operating conditions for Var. 2 with durations of (**a**) 2 h, (**b**) 5 h, (**c**) 8 h, and (**d**) 11 h. **Figure 10.** The effects of vibration frequency on the flexural properties of newly placed PVA-ECC bridge repairs (NP-ECC-BRs) under the operating conditions for Var. 2 with durations of (**a**) 2 h, (**b**) 5 h, (**c**) 8 h, and (**d**) 11 h.

Effects of Vibration frequency on the flexural properties (Pc, δc, P<sup>u</sup> and δu) of NP-ECC-BRs when vibrations began just after the initial set were examined. When the specimens were vibrated at the age of 8 h, it can be seen in Figure 9b that all the flexural properties increase or decrease in harmony and approximately linearly with the increase in vibration frequency. The differences are that the impact polarity was negative on Pu, Pc, and δc, and it was positive on δu. Additionally, the impact degree of TRVs on P<sup>c</sup> was the largest, indicating that P<sup>c</sup> was the most sensitive in its response to TRVs during these periods, followed by δ<sup>c</sup> or Pu, and then δu.

Effects of Vibration frequency on the flexural properties (Pc, δc, P<sup>u</sup> and δu) of NP-ECC-BRs when vibrations occurred after the middle stage of the setting period were examined. When the specimens were vibrated after the age of 15 h, it can be seen in Figure 9c–f that the effects of TRVs on the load-bearing properties (P<sup>c</sup> and Pu) of the specimens was negative throughout the scope of imposed vibration frequencies in this study. However, it was positive on the deformation properties (δ<sup>c</sup> and δu). Figure 9c–f also show that the flexural properties of most of the vibrated groups declined, in general, with the increase in imposed vibration frequency. Moreover, regarding the impact degree (regardless

of polarity), the cracking properties (the P<sup>c</sup> and δ<sup>c</sup> of most of the specimens presented a reduction or growth above 20%) were more sensitive to the imposed vibration frequency than those of the extreme flexural properties (the P<sup>u</sup> and δ<sup>u</sup> of all the specimens presented a reduction or growth within 20%).
