2.2.5. Data Analysis

To minimize the variance of the data measured in this study, the winsorized mean of the measured data for each group of specimens was taken as the representative value of the corresponding group. Additionally, for the one specimen in each group whose maximum mid-span deflection was the closest to the winsorized mean of the group, its load versus mid-span deflection (P–δ) curve would be taken as the representative P–δ curve of its group.

## **3. Results and Discussion**

The results of calculated winsorized means of the cracking load (Pc) and the corresponding mid-span deflection (δc), extreme flexural load (Pu) and the corresponding mid-span deflection (δu) of the specimens are shown in Table 9.

**Table 9.** Winsorized means of the cracking load (Pc), mid-span deflection (δc), extreme flexural load (Pu), and mid-span deflection (δu) of all 37 groups of polyvinyl alcohol fiber reinforced engineering cementitious composite (PVA-ECC) specimens.



span deflection (δc), extreme flexural load (Pu) and the corresponding mid-span deflection (δu) of the

**Table 9.** *Cont*.

Strictly speaking, it should be pointed out that P<sup>c</sup> and δ<sup>c</sup> correspond to the load and deflection when the first crack appeared on the specimen. In this study, the end point of the elasticity region in the P–δ curve was defined as the cracking point, as shown in Figure 4, point A. For convenience, the corresponding load and deflection at the cracking point were taken as the P<sup>c</sup> and δ<sup>c</sup> of the specimen. Similarly, the corresponding load and deflection at the peak point in the P–δ curve were taken as the P<sup>u</sup> and δ<sup>u</sup> of specimens, as shown in Figure 4, point B. specimens are shown in Table 9. Strictly speaking, it should be pointed out that Pc and δc correspond to the load and deflection when the first crack appeared on the specimen. In this study, the end point of the elasticity region in the P–δ curve was defined as the cracking point, as shown in Figure 4, point A. For convenience, the corresponding load and deflection at the cracking point were taken as the Pc and δc of the specimen. Similarly, the corresponding load and deflection at the peak point in the P–δ curve were taken as the Pu and δu of specimens, as shown in Figure 4, point B.

**Figure 4**. Representative load versus mid-span deflection (P–δ) curve of the control specimen, showing the classical strain-hardening and super-toughness characteristics of polyvinyl alcohol fiber reinforced engineering cementitious composites (PVA-ECCs). **Figure 4.** Representative load versus mid-span deflection (P–δ) curve of the control specimen, showing the classical strain-hardening and super-toughness characteristics of polyvinyl alcohol fiber reinforced engineering cementitious composites (PVA-ECCs).

### *3.1. Effects of AWV on the Flexural Properties of NP-ECC-BRs 3.1. E*ff*ects of AWV on the Flexural Properties of NP-ECC-BRs*

In this section, to determine the effects of AWV on the flexural properties of NP-ECC-BRs, a total of 216 (24 groups, and nine specimens in each group) thin-plate PVA-ECC specimens were tested by a four-point flexural test after the specimens were vibrated under the operating conditions for Var. 1. In this section, to determine the effects of AWV on the flexural properties of NP-ECC-BRs, a total of 216 (24 groups, and nine specimens in each group) thin-plate PVA-ECC specimens were tested by a four-point flexural test after the specimens were vibrated under the operating conditions for Var. 1.

### 3.1.1. Effects of AWV on the P–δ curves of NP-ECC-BRs

3.1.1. Effects of AWV on the P–δ curves of NP-ECC-BRs In a typical P–δ curve of a thin-plate PVA-ECC s specimen, the flexural loads will fluctuate and increase slowly with the increase in deflection after the first crack appears during loading, as shown in Figure 4. Through extensive experimental observation, it was found that the volatility (frequency and value of fluctuation) characteristics of the P–δ curve generally reflected the formation and propagation processes of cracking. That is to say that the number of downward fluctuations of the load at the P–δ curve approximately reflects the number of cracks forming in the specimens, and the levels of load reduction approximately reflect the instantaneous and unstable propagation degree of In a typical P–δ curve of a thin-plate PVA-ECC s specimen, the flexural loads will fluctuate and increase slowly with the increase in deflection after the first crack appears during loading, as shown in Figure 4. Through extensive experimental observation, it was found that the volatility (frequency and value of fluctuation) characteristics of the P–δ curve generally reflected the formation and propagation processes of cracking. That is to say that the number of downward fluctuations of the load at the P–δ curve approximately reflects the number of cracks forming in the specimens, and the levels of load reduction approximately reflect the instantaneous and unstable propagation degree of cracks during the process of cracks from their appearance to maintaining stability.

cracks during the process of cracks from their appearance to maintaining stability. According to the collected data, the P–δ curves of all the 24 groups of PVA-ECC specimens were According to the collected data, the P–δ curves of all the 24 groups of PVA-ECC specimens were obtained, as shown in Figure 5.

obtained, as shown in Figure 5. It can be seen in Figure 5 that the volatility of the P–δ curves of most of the vibrated groups was not as obvious as that of the control group, indicating that the TRVs that occurred during setting It can be seen in Figure 5 that the volatility of the P–δ curves of most of the vibrated groups was not as obvious as that of the control group, indicating that the TRVs that occurred during setting

periods affected the multi-cracking characteristics of NP-ECC-BRs to some extent. It can also be seen in Figure 5 that significant hardening segments appeared in the P–δ curves of all the specimens under

significant deformation-hardening or strain-hardening characteristics, indicating that vibrations that occurred during different setting periods have no significantly negative impact on the inherent strainperiods affected the multi-cracking characteristics of NP-ECC-BRs to some extent. It can also be seen in Figure 5 that significant hardening segments appeared in the P–δ curves of all the specimens under the operating conditions for Var. 1. In the hardening segments, the flexural loads of the specimens increased slowly with the increase in the corresponding deflection, and the segments presented significant deformation-hardening or strain-hardening characteristics, indicating that vibrations that occurred during different setting periods have no significantly negative impact on the inherent strain-hardening behavior of PVA-ECCs under the operating conditions for Var. 1.The above results are consistent with the tensile stress–strain curves of NP-ECC-BRs that were obtained under the same experimental and parametric conditions in [29]. *Materials* **2019**, *12*, x FOR PEER REVIEW 10 of 19 hardening behavior of PVA-ECCs under the operating conditions for Var. 1.The above results are consistent with the tensile stress–strain curves of NP-ECC-BRs that were obtained under the same

**Figure 5.** P–δ curves of all the 24 groups of specimens under the operating conditions for Var. 1 with frequencies of (**a**) 2 Hz, (**b**) 3 Hz, (**c**) 4 Hz, and (**d**) 5 Hz and that of the control group. **Figure 5.** P–δ curves of all the 24 groups of specimens under the operating conditions for Var. 1 with frequencies of (**a**) 2 Hz, (**b**) 3 Hz, (**c**) 4 Hz, and (**d**) 5 Hz and that of the control group.

### 3.1.2. Effects of AWV on the Flexural Properties of NP-ECC-BRs 3.1.2. Effects of AWV on the Flexural Properties of NP-ECC-BRs

Pc under the same vibration frequency (2−5 Hz).

lines).

experimental and parametric conditions in [29].

In this subsection, the question of to what extent the TRVs that occurred during different setting periods affected the Pc, δc, Pu, and δu of NP-ECC-BRs was investigated and determined quantitively. The rates of the Pc, δc, Pu, and δu of the groups that were vibrated under the operating conditions for Var. 1 over the corresponding control winsorized means are shown in Figure 6. In this subsection, the question of to what extent the TRVs that occurred during different setting periods affected the Pc, δc, Pu, and δ<sup>u</sup> of NP-ECC-BRs was investigated and determined quantitively. The rates of the Pc, δc, Pu, and δ<sup>u</sup> of the groups that were vibrated under the operating conditions for Var. 1 over the corresponding control winsorized means are shown in Figure 6.

Effects of AWV on the cracking load (Pc) of NP-ECC-BRs. It can be seen in Figure 6a–d (black lines) that the Pc of each group of specimens decreased by 2%–71% over the control average under the operating conditions for Var. 1, indicating that the effects of AWV on the Pc of NP-ECC-BRs are significantly negative throughout the three setting periods. Furthermore, when the specimens were subjected to frequencies of 2 and 5 Hz, the AWV that resulted in the most negative effects for Pc occurred at ages of 8, 15, or 23 h which were within the setting period (the period between the initial and final set), as shown in Figure 6a,d. However, when the specimens were subjected to the frequencies of 3 and 4 Hz, the AWV that resulted in the most negative effects for Pc occurred at the ages of 36 or 48 h which were after the final set, as shown in Figure 6b,c. Effects of AWV on the cracking load (Pc) of NP-ECC-BRs. It can be seen in Figure 6a–d (black lines) that the P<sup>c</sup> of each group of specimens decreased by 2%–71% over the control average under the operating conditions for Var. 1, indicating that the effects of AWV on the P<sup>c</sup> of NP-ECC-BRs are significantly negative throughout the three setting periods. Furthermore, when the specimens were subjected to frequencies of 2 and 5 Hz, the AWV that resulted in the most negative effects for P<sup>c</sup> occurred at ages of 8, 15, or 23 h which were within the setting period (the period between the initial and final set), as shown in Figure 6a,d. However, when the specimens were subjected to the frequencies of 3 and 4 Hz, the AWV that resulted in the most negative effects for P<sup>c</sup> occurred at the ages of 36 or 48 h which were after the final set, as shown in Figure 6b,c.

Effects of AWV on the extreme flexural load (Pu) of NP-ECC-BRs. It can be seen in Figure 6 that the Pu (blue lines) of NP-ECC-BRs specimens decreased by 1%–39% over the control average under the operating conditions for Var. 1, which shows a similar impact trend of to that of Pc. Moreover, it also can be seen in Figure 6 that the rates of Pu and Pc increase or decrease in harmony with the Effects of AWV on the extreme flexural load (Pu) of NP-ECC-BRs. It can be seen in Figure 6 that the P<sup>u</sup> (blue lines) of NP-ECC-BRs specimens decreased by 1%–39% over the control average under the operating conditions for Var. 1, which shows a similar impact trend of to that of Pc. Moreover, it also can be seen in Figure 6 that the rates of P<sup>u</sup> and P<sup>c</sup> increase or decrease in harmony with the increase in

the group F3–23–5, which decreased by 2% and can be ignored) tended to be insignificantly positive, and for most of them, the positive impact degrees were within 20%, as shown in Figure 6a–d (green

Effects of AWV on the extreme flexural deformation (δu) of NP-ECC-BRs. The effects of AWV on

increase in the AWV, and the most negative effect for Pu also occurred at the same AWV as those of

the AWV, and the most negative effect for P<sup>u</sup> also occurred at the same AWV as those of P<sup>c</sup> under the same vibration frequency (2−5 Hz).

Effects of AWV on the extreme flexural deformation (δu) of NP-ECC-BRs. The effects of AWV on the extreme deformation of NP-ECC-BRs specimens were very different to that of the load-bearing properties (Pc, Pu). The effects of the AWV on the δ<sup>u</sup> of almost all the NP-ECC-BR groups (except for the group F3–23–5, which decreased by 2% and can be ignored) tended to be insignificantly positive, and for most of them, the positive impact degrees were within 20%, as shown in Figure 6a–d (green lines). *Materials* **2019**, *12*, x FOR PEER REVIEW 11 of 19

Effects of AWV on the cracking deformation (δc) of NP-ECC-BRs. Before the initial set and under relatively lower magnitudes of vibration frequency (2 and 3 Hz), it can be seen in Figure 6a,b (red lines) that the effects of AWV on the δ<sup>c</sup> of all the NP-ECC-BR groups tended to be insignificantly negative (within 20% reduction). On the contrary, the effects were significantly positive (more than 20% growth) on the δ<sup>c</sup> of most of the vibrated groups under a relatively higher vibration frequency (4 and 5 Hz) during the same setting period, as shown in Figure 6c,d. Effects of AWV on the cracking deformation (δc) of NP-ECC-BRs. Before the initial set and under relatively lower magnitudes of vibration frequency (2 and 3 Hz), it can be seen in Figure 6a,b (red lines) that the effects of AWV on the δc of all the NP-ECC-BR groups tended to be insignificantly negative (within 20% reduction). On the contrary, the effects were significantly positive (more than 20% growth) on the δ<sup>c</sup> of most of the vibrated groups under a relatively higher vibration frequency

(4 and 5 Hz) during the same setting period, as shown in Figure 6c,d.

**Figure 6.** Rates of Pc, δc, Pu, and δu for the 24 groups of specimens over the corresponding control averages under the operating conditions for Var. 1 with frequencies of (a) 2 Hz, (b) 3 Hz, (c) 4 Hz, and (d) 5 Hz. **Figure 6.** Rates of Pc, δc, Pu, and δ<sup>u</sup> for the 24 groups of specimens over the corresponding control averages under the operating conditions for Var. 1 with frequencies of (**a**) 2 Hz, (**b**) 3 Hz, (**c**) 4 Hz, and (**d**) 5 Hz.

In summary, these above results indicate that the effects of TRVs that occurred during different setting periods on the cracking and extreme load-bearing capacity of NP-ECC-BRs tend to be significantly negative under the combination of different frequencies ranging from 2 to 5 Hz and a constant duration of 5 h. On the contrary, the effects of AWV on the extreme flexural deformation of NP-ECC-BRs generally tended to be insignificantly positive. In addition, the effects of AWV on the cracking deformation of newly placed PVA-ECCs varied according to the corresponding vibration frequency that the specimens suffered when TRVs occurred before the initial set. In summary, these above results indicate that the effects of TRVs that occurred during different setting periods on the cracking and extreme load-bearing capacity of NP-ECC-BRs tend to be significantly negative under the combination of different frequencies ranging from 2 to 5 Hz and a constant duration of 5 h. On the contrary, the effects of AWV on the extreme flexural deformation of NP-ECC-BRs generally tended to be insignificantly positive. In addition, the effects of AWV on the cracking deformation of newly placed PVA-ECCs varied according to the corresponding vibration frequency that the specimens suffered when TRVs occurred before the initial set.

### *3.2. Effects of Duration of Vibration (DV) on the Flexural Properties of NP-ECC-BRs 3.2. E*ff*ects of Duration of Vibration (DV) on the Flexural Properties of NP-ECC-BRs*

under the operating conditions for Var. 2.

obtained, as shown in Figure 7.

In this section, to determine the effects of DV on the flexural properties of NP-ECC-BRs when vibrations only occurred during the setting period (the period between the initial and final set, where the penetration resistance was within the scope of 3.5 to 28 MPa), a total of 144 (16 groups) thin-plate In this section, to determine the effects of DV on the flexural properties of NP-ECC-BRs when vibrations only occurred during the setting period (the period between the initial and final set, where the penetration resistance was within the scope of 3.5 to 28 MPa), a total of 144 (16 groups) thin-plate

PVA-ECC specimens were tested by a four-point flexural test after the specimens were vibrated

According to the collected data, the P–δ curves of all the 16 groups of PVA-ECC specimens were

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

PVA-ECC specimens were tested by a four-point flexural test after the specimens were vibrated under the operating conditions for Var. 2.
