3.2.2. Shear Strength Results

3.2.2. Shear Strength Results Because of the uneven surface of the UHPC flat joint interface, the interface subjected to shear force can provide resistance through the friction between the poured aggregates at the interface. When the applied load increases, some UHPC aggregates are sheared off, which results in a decrease in shear stiffness and rapid deformation of the interface. Therefore, the shear failure of the specimen without fibers occurs directly once the aggregates are crushed. The test results of 12 WJTSs are given in Table 6.



From Table 6 as well as the shear load–slip curves of UHPC specimens with different fiber types (Figure 14), the cracking load of the specimens without fibers is very close to the failure load, and it is difficult to accurately distinguish the cracking load from the failure load. The difference is that the ratio of initial crack load to ultimate load of WJ25H16 is significantly greater than that of other conditions. Besides, the direct shear strength of WJ25H16 can reach 9.15 MPa, which is 2.47 times that of WJ-NN and 1.29 times that of WJ25S13, respectively. Thus, increasing the length of the fibers and using profiled fibers can significantly improve the interfacial bonding force. From the above analysis, it can be seen that the interface shear strength of UHPC can be significantly increased by using 16HSF. in Table 6.

**Specimen Number** 

WJ25H16

WJ25S13

WJ25H13

WJ-NN

**Initial Crack Load** *Fci* **/kN** 

**Ultimate Load** *Fcr* **/kN** 

159.7 205.60

115.9 128.4

141.2 146.9

67.2 70.2

Because of the uneven surface of the UHPC flat joint interface, the interface subjected to shear force can provide resistance through the friction between the poured aggregates at the interface. When the applied load increases, some UHPC aggregates are sheared off, which results in a decrease in shear stiffness and rapid deformation of the interface. Therefore, the shear failure of the specimen without fibers occurs directly once the aggregates are crushed. The test results of 12 WJTSs are given

**Table 6.** Direct shear test results of the WJTSs.

**Shear Strength /MPa** 

10.28

139.5 147.75 7.39 1.059

6.42

129.3 133.2 6.66 1.030

7.35

128.8 163.2 8.16 1.267

3.51

77.0 77.0 3.85 1.000

From Table 6 as well as the shear load–slip curves of UHPC specimens with different fiber types (Figure 14), the cracking load of the specimens without fibers is very close to the failure load, and it is difficult to accurately distinguish the cracking load from the failure load. The difference is that the ratio of initial crack load to ultimate load of WJ25H16 is significantly greater than that of other conditions. Besides, the direct shear strength of WJ25H16 can reach 9.15 MPa, which is 2.47 times that of WJ-NN and 1.29 times that of WJ25S13, respectively. Thus, increasing the length of the fibers and using profiled fibers can significantly improve the interfacial bonding force. From the

160.5 195.40 9.77 1.217 1.188

154.9 163.7 8.18 1.057 1.042

140.1 161.3 8.06 1.151 1.153

70.0 75.2 3.76 1.074 1.040

**Shear Strength /MPa (Average)** 

**Coefficient of Variation** 

9.15 0.139

7.09 0.110

7.86 0.046

3.71 0.039

*Fcr* **/** *Fci*

1.287

1.108

1.040

1.045

*Fcr* **/** *Fci* **(Average)** 

**Ultimate Load**  *Fcr* **/kN (Average)** 

182.9

141.8

157.1

74.1

**Figure 14.** Shear load–slip curves of UHPC specimens with different fiber types: (**a**) WJ25H16, (**b**) WJ25S13, (**c**) WJ25H13 and (**d**) WJ-NN. **Figure 14.** Shear load–slip curves of UHPC specimens with different fiber types: (**a**) WJ25H16, (**b**) WJ25S13, (**c**) WJ25H13 and (**d**) WJ-NN.

## **4. Analytical Study 4. Analytical Study**

where *mn* 

in this paper.

**Ratios of Length-Diameter** *<sup>f</sup> <sup>f</sup> l* / *d*

**Specimen Number** 

and 

### *4.1. Interaction of Compressive and Shear Strength of the MPSs*

*mn* (1

is the shear strength of the MPSs,

**Volume Fraction of Fibers** 

*f*

*4.1. Interaction of Compressive and Shear Strength of the MPSs*  The experimental results demonstrate that the influence of concrete strength should be considered when calculating the ultimate shear strength of the MPSs without pre-cracking. The experimental data are shown in the Table 7. Considering that the shear strength and shear failure characteristics of UHPC are closely related to the compressive strength of concrete and the bridging effect of steel fibers [29], the relationship between the compressive strength and shear strength of The experimental results demonstrate that the influence of concrete strength should be considered when calculating the ultimate shear strength of the MPSs without pre-cracking. The experimental data are shown in the Table 7. Considering that the shear strength and shear failure characteristics of UHPC are closely related to the compressive strength of concrete and the bridging effect of steel fibers [29], the relationship between the compressive strength and shear strength of concrete is proposed based on the test results, as shown in Equation (2).



*f f <sup>f</sup> d l* , (3) Owning to the orientation of the steel fibers inside the concrete matrix, it is affected by a number of parameters, which are essentially the geometry of the fibers and their interaction effects (fibers–aggregates–formwork), the flowability of the concrete, the means of pouring and compacting of

*f*

*<sup>f</sup>* ) *fcu* / 0.45 , (2)

*<sup>f</sup>* is the volume fraction of steel fibers, *<sup>f</sup> <sup>f</sup> l* / *d*

*<sup>f</sup>* is the characteristic coefficient of steel fibers,

**Cubic Compressive Strength** *cu f* **/MPa** 

**Shear Strength**  *cal* **/MPa** 

*exp* 

**/** *cal* 

 *cr*

**Table 7.** Tests of UHPC shear specimens.

MP20H16 80 2.0% 1.6 18.01 150.25 20.11 0.90

**Characteristic Coefficient of Steel Fibers**  *f*

*cr* is the influence coefficient of steel fiber dispersion; the experimental value of 0.1 was chosen

**Shear Strength**  *exp* **/MPa**  the concrete [12]. In addition, the distribution and orientation of fibers is, in turn, the parameter which most influences the ductility of UHPC. Hence, Equation (2) draws into the influence coefficient of steel fiber dispersion β*cr* on direct shear bearing capacity to weaken the above effects. *Materials* **2017**, *10*, x FOR PEER REVIEW 15 of 17 MP25H16 80 2.5% 2.0 21.53 159.35 22.58 0.95

$$
\tau\_{\rm mu} = \left(1 + \beta\_{\rm tr} \lambda\_f\right) \sqrt{f\_{\rm cu}/0.45} \,\tag{2}
$$

$$
\lambda\_f = \frac{\rho\_f l\_f}{d\_f},\tag{3}
$$

where τ*mn* is the shear strength of the MPSs, ρ*<sup>f</sup>* is the volume fraction of steel fibers, *l<sup>f</sup>* /*d<sup>f</sup>* stands for the ratio of length-diameter of steel fibers, λ*<sup>f</sup>* is the characteristic coefficient of steel fibers, and β*cr* is the influence coefficient of steel fiber dispersion; the experimental value of 0.1 was chosen in this paper. MP25S13 65 2.5% 1.625 23.13 165.50 22.29 1.04 As can be seen from Table 7, the variations between the calculated shear strength and the

As can be seen from Table 7, the variations between the calculated shear strength and the experimental shear strength are insignificant, in which the mean value of τ*exp*/τ*cal* is 0.986 and the difference is only 0.014. For this reason, Equation (2) can provide a reference for the design of cast-in-place UHPC structures. It is worth mentioning that the configuration of shear reinforcement is not considered in this paper. Therefore, Equation (2) is only applicable to the condition of no shear reinforcement, while other situations, including the vertical shear stress direction of steel bar arrangement, need to be further studied. experimental shear strength are insignificant, in which the mean value of *exp* **/** *cal* is 0.986 and the difference is only 0.014. For this reason, Equation (2) can provide a reference for the design of castin-place UHPC structures. It is worth mentioning that the configuration of shear reinforcement is not considered in this paper. Therefore, Equation (2) is only applicable to the condition of no shear reinforcement, while other situations, including the vertical shear stress direction of steel bar arrangement, need to be further studied.

### *4.2. Relative Reduction of Shear Strength Ratio of the WJTSs 4.2. Relative Reduction of Shear Strength Ratio of the WJTSs*

Figure 15 shows the relative reduction of the shear strength ratio with different fiber types. Compared with the MPSs, the shear strength of WJ25H16 can reach 42.5% of MP25H16, that of WJ25S13 can reach 30.6% of MP25S13, and that of WJ25H13 can reach 34.2% of MP25H13. Therefore, the maximum shear strength of the UHPC shear bond interface treated by a waterjet can reach 42.5% of the monolithic placement. It can be concluded that the shear strength at the interface of the UHPC specimens reinforced with steel fibers (because of the contribution of the aggregate biting force, interface friction force and steel fiber drawing force) can be effectively utilized under the appropriate interface treatment. What is insufficient is that the number of specimens in this study is still fewer, and the study of direct shear strength under a different fiber volume fraction has not been carried out, so the relative reduction formula of the shear strength ratio under various conditions cannot be obtained accurately. Figure 15 shows the relative reduction of the shear strength ratio with different fiber types. Compared with the MPSs, the shear strength of WJ25H16 can reach 42.5% of MP25H16, that of WJ25S13 can reach 30.6% of MP25S13, and that of WJ25H13 can reach 34.2% of MP25H13. Therefore, the maximum shear strength of the UHPC shear bond interface treated by a waterjet can reach 42.5% of the monolithic placement. It can be concluded that the shear strength at the interface of the UHPC specimens reinforced with steel fibers (because of the contribution of the aggregate biting force, interface friction force and steel fiber drawing force) can be effectively utilized under the appropriate interface treatment. What is insufficient is that the number of specimens in this study is still fewer, and the study of direct shear strength under a different fiber volume fraction has not been carried out, so the relative reduction formula of the shear strength ratio under various conditions cannot be obtained accurately.

**Figure 15.** Relative reduction of the shear strength ratio with different fiber types. **Figure 15.** Relative reduction of the shear strength ratio with different fiber types.

### **5. Conclusions 5. Conclusions**

drawn:

This study investigates the direct shear strength and failure mechanism of Z-shaped specimens through the push-off test. A total of 27 specimens with the test parameters of steel fiber shape, steel fiber volume fraction and interface treatment, were designed to test their shear strength, loadcarrying capacity and failure modes. Based on the testing results, the following conclusions can be This study investigates the direct shear strength and failure mechanism of Z-shaped specimens through the push-off test. A total of 27 specimens with the test parameters of steel fiber shape, steel fiber volume fraction and interface treatment, were designed to test their shear strength, load-carrying capacity and failure modes. Based on the testing results, the following conclusions can be drawn:

(1) Ductile characteristics of the monolithic placement specimens with appropriate steel fibers can be improved in direct shear load, and the ultimate load can reach 166.9% of the initial cracking load.

(2) Increasing the steel fiber volume fraction can significantly improve the shear strength of UHPC structure. Direct shear strength of UHPC specimens with 3.0% volume fraction can reach 24.72 MPa. In addition, the steel fiber shape has little effect on the shear strength and ductility, while increasing the length of steel fibers improves its ductility and slightly reduces the shear strength.

(3) The waterjet treatment for the interface of the adjacent segment is an effective way to improve the direct shear performance of cast-in-place segmental UHPC structures. The direct shear strength of the specimens with the waterjet treatment can reach 42.5% of the monolithic placement specimens.

(4) The formula proposed for predicting the direct shear strength of the cast-in-place UHPC structures shows good agreement with the test results.

Although the feasibility of the segmental cast-in-place UHPC structure has been validated and the influence of steel fiber on shear performance has been obtained through the experimental studies in this paper, further experimental studies are still needed, including the configuration of shear reinforcement at the interface, the type of key joints at the interface (shape, structure size), the number of key joints, the level of normal stress and the roughness of the interface.

**Author Contributions:** C.L. and R.P. planned and managed the project. Z.F. conducted the experiments, analyzed the data, and compiled the final manuscript. L.K. and J.N. contributed to the literature review for this study. Moreover, all authors reviewed the data and the final manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (NO. 51778069, NO. 51808055), Excellent Youth Project of Hunan Education Department (NO. 18B131), the Hunan Provincial Innovation Foundation for Postgraduate, China (NO. CX2018B522), the Open Fund of the Key Laboratory of Provincial and Ministerial Level of Bridge Engineering, China (NO.18KE04, No. 18KB03).

**Acknowledgments:** The authors gratefully acknowledge the financial support of the National Natural Science Foundation of China and the Hunan Provincial Innovation Foundation for Postgraduate.

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