3.3.2. Effects of Vibration Frequency on the Flexural Properties of NP-ECC-BRs under the Operating Conditions for Var. 2

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 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 (δ<sup>c</sup> 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 (δ<sup>c</sup> 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 δ<sup>c</sup> 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 δ<sup>c</sup> of the vibrated specimens increased by 44% over the control group under the vibration frequency of 4 Hz.

## *3.4. Explanations and Recommendations*

Regarding the reduction of load-bearing capacity of NP-ECC-BRs under operating conditions for Var. 1 and 2, the following explanations can be made: before the initial set, continuous TRVs will lead to some extent of bleeding to the cement mixture [10], and the stronger the magnitudes of vibration frequency, the greater the amount of bleeding this would lead to; after the initial set, low-density C-S-H gels in the cement matrix gradually are transferred to high-density C-S-H gels and agglomerate into larger C-S-H particles [11,12], which gradually form the solid skeleton of the cement matrix, and TRVs during this period are likely to disturb the connection of the solid skeleton in the cement matrix or even damage the bond of C-S-H particles and C-S-H gels [13]; these above effects demonstrate a great potential for decreasing the cracking and extreme flexural load-bearing capacity of the cement matrix. According to the fiber-bridge constitutive law of engineered cementitious composites (ECCs) and its design principle [35,36], relatively lower cracking strength is beneficial for ECCs to express their bridging effect between PVA fibers and cement matrix and to exhibit larger deformation [37,38]. Therefore, TRVs could result in a negative effect on the load-bearing capacity of NP-ECC-BRs while resulting in a positive effect on the flexural deformation capacity of NP-ECC-BRs.

With regard of the reduction of load-bearing capacity of NP-ECC-BRs under operating conditions for Var. 1 and 2, the authors recommend that (a) in the design of PVA-ECC bridge repairs, engineers should try to improve the design strength of PVA-ECCs, especially its early-age strengths, such as adding an appropriate amount of silica fume and early-strength agents, adopting well-graded silicon sand and high-strength cement; and (b) during the repairing of concrete bridge using PVA-ECCs, constructors should restrict the traffic of heavy-duty trucks and medium-size vehicles in large- and medium-spans of concrete bridges, especially during the period between the initial and final set of PVA-ECC repairs.

### **4. Conclusions**


vibrated groups in this investigation. By contrast, the effects were significantly positive (above 20% growth) on the extreme flexural deformation of newly placed PVA-ECC bridge repairs. Moreover, the longer the durations of vibration, the higher the extreme flexural deformation capacity of newly placed PVA-ECC bridge repairs, generally.


**Author Contributions:** Conceptualization, S.L. and C.Y.; Methodology, X.Z., X.W., and H.W.; Project administration, X.W. and C.Y.; Writing—original draft preparation, X.Z.; Writing—review and editing, S.L. and X.W.

**Funding:** This research was funded by the National Natural Science Foundation of China, grant numbers 51768051 and 51968056, Natural Science Foundation of Inner Mongolia, grant number 2017MS0505, and the Science and Technology Innovation Guidance Project of Inner Mongolia, grant number KCBJ2018016.

**Acknowledgments:** The authors are grateful to Yue Y. and Xiumei G. for their help and suggestions in the editing and revision of figures in this article.

**Conflicts of Interest:** The authors declare no conflict of interest.
