Experimental study on the triaxial mechanical properties of hybrid steel fiber–reinforced self-compacting concrete

In this study, the triaxial mechanical properties of hybrid steel fiber–reinforced self-compacting concrete (HSFRSCC) were investigated. Based on previous research, a mixture of HSFRSCC that satisfies the requirements of compression and workability performance was determined. Conventional triaxial compression tests were performed at confining pressures of 0, 4, 8, 12, and 16 MPa. The results showed that all the specimens had excellent deformation ability, and both the steel fibers and confining pressure improved the ductility of HSFRSCC. With an increase in the confining pressure, the triaxial peak stress and strain of concrete were increased. The differences in the damage characteristics of HSFRSCC and plain concrete were compared based on scanning electron microscopy test results. Finally, the applicability of the Mohr–Coulomb criterion with that of the Willam–Warnke (W–W) criteria to HSFRSCC was compared. the results showed that the nonlinear W–W criterion had a better fitting effect. Hence, the relationship between triaxial peak stress, peak strain, and confining pressure was established, and the triaxial compression meridian formula for HSFRSCC was obtained.


Introduction
Shield tunnels primarily use densely and bulky reinforced concrete segments.It is difficult to vibrate and compact concrete in areas with dense reinforcement, which reduces the pouring quality of concrete segments [1][2][3].During the construction stage, under the action of a large jack eccentricity, the segment is in a complex three-dimensional stress state.Complications, such as cracking, damage, and collapsing of the segment, are prone to occur, significantly influencing the normal use and safe bearing capacity of the tunnel structure [4].In addition, dense steel bars may result in poor pouring and vibration qualities of concrete at the joints, corners, and near the joint box [5,6].Unfortunately, these parts bear complex loads, resulting in the cracking of concrete segments and reducing the bearing capacity.
In view of the above compact pouring defects of the shield segment structure in the manufacturing stage as well as cracking problems in the construction and operation stages, the emergence of selfcompacting concrete (SCC) and fiber-reinforced concrete (FRC) provides a new solution for avoiding the poor pouring quality of segment concrete and controlling segment cracking and damage [7,8].SCC 1333 (2024) 012020 IOP Publishing doi:10.1088/1755-1315/1333/1/012020 2 depends only on self-gravity without an additional mechanical vibrating force and has an excellent filling ability, clearance passing capacity, and segregation resistance.Hence, SCC is suitable for the high-quality pouring of densely reinforced concrete members [9].FRC is a type of composite material to which fibers are added to improve its deformation performance.The fibers can bear the initial external load through the bond stress between the fiber and the concrete matrix, thereby preventing the expansion of microcracks and improving the response ability of the concrete matrix to external loads, resulting in better crack resistance [10].Hybrid FRC (HFRC) is mixed with two or more different fibers (usually a mixture of micro-and macrofibers) to combine the characteristics of different fibers, and its performance is better than that with a single fiber.Generally, the engineering problems described above can be effectively solved using HSFRSCC as the matrix material of a shield tunnel segment [11].
HSFRSCC materials applied to shield tunnel segments are usually in a complex stress state under biaxial or multiaxial forces [12,13].When designing or verifying the bearing capacity of shield segment structures, if only the mechanical properties of uniaxial tension and compression are considered, the strength of concrete under biaxial or triaxial compression may be overestimated, resulting in material waste.Furthermore, the strength of concrete under multiaxial tensile and compressive stresses may be underestimated, resulting in safety hazards [14].Hence, this study explored the mechanical properties of HSFRSCC under multiaxial stress and the effects of steel fiber type, content, and hybrid degree on its multiaxial mechanical properties.Moreover, using scanning electron microscopy (SEM), the differences in damage characteristics between HSFRSCC and plain concrete were compared.On this basis, the triaxial strength failure criterion and constitutive curves were analyzed, and a triaxial failure criterion was established.The research results are significant for the design and analysis of concrete structures and engineering practices of shield tunnel segments using hybrid steel fiber-reinforced SCC (HSFRSCC).

Experiment design
The concrete prepared in this study was an HSFRSCC with a C50 strength requirement.Based on the existing HSFRSCC trial mixing experience [15][16][17], the adopted mix ratios are listed in Table 1.P.O 52.5 Portland cement was used in combination with first-class fly ash, in line with the GB/T1596 standard.The graded compositions of the aggregates are listed in Table 1.The 0213 straight microfiber with a diameter of 0.22 mm and a length of 13 mm, and a 0535 end-hooked macrofiber with a diameter of 0.55 mm and length of 35 mm were used.The superplasticizer adopted a polycarboxylic acid superplasticizer mother liquor, thus achieving the standard for self-leveling.From the compression and flowability performance tests shown in Figure 1, we verified that the concrete mix parameters presented in Table 2 satisfy the dual requirements of C50 strength and self-compaction.Subsequently, four 150× 150 × 150-mm concrete cube specimens were prepared, and 15 groups of φ50*100-mm cylinder specimens were obtained from the cube specimen after curing for 28 d.Conventional triaxial compression tests were performed on each cylinder specimen under a confining pressure of 0, 4, 8, 12, and 16 MPa, and three repeated tests were performed for each confining pressure.The test instrument was an MTS 815 triaxial mechanical test system, as shown in Figure 2.

Triaxial constitutive curves
The stress-strain curves of conventional triaxial compression specimens are shown in Figure 3.As shown in Figure 3, with an increase in the confining pressure, both the peak stress and strain of the specimens significantly increased.For example, the peak stress increased from 50 to 80 MPa, and the peak strain increased from 0.002 to 0.006.The confining pressure had a significant effect on the compressive strength of HSFRSCC, which is consistent with the existing research [12][13][14].In addition, each specimen had an obvious post-peak stage, which was caused by the positive synergistic effect of the confining pressure and steel fibers.The confining pressure can improve the axial bearing capacity of concrete by restraining its transverse expansion, which causes the concrete to change from brittle failure to ductile failure.Moreover, steel fibers, especially hybrid steel fibers, can disperse the internal failure stress to each part of the concrete matrix and inhibit the development of macro-and microcracks by bridging, anchoring, and friction effects.Combined with the above effects, the HSFRSCC presents an excellent post-peak response stage.

Analysis of SEM test results
The failure surface of the HSFRSCC cylindrical specimen was characterized using SEM, as shown in Figure 4(a).We found that, under the synergistic effect of confining pressure and hybrid steel fibers, no excessive cracks were observed in concrete and no obvious separation was observed between the damaged matrixes of HSFRSCC.Compared with the plain concrete shown in Figure 4 (b), HSFRSCC showed better fracture characteristics.Chemical adhesion, dynamic friction, and static friction between the steel fiber and the matrix, as well as the bridging effect of end-hooked steel fibers on macrocracks and straight microfibers on microcracks, are the primary factors associated with the breaking of without cracking [18,19].

Triaxial failure criterion
By calculating the ratio of triaxial strength to uniaxial strength (σ1/fc) and the ratio of confining pressure to uniaxial strength (σ3/fc) of each specimen shown in Figure 3, the relationship curves between triaxial strength and confining pressure were drawn, as shown in Figure 5. Similarly, Figure 6 shows the relationship between the ratio of triaxial peak strain to uniaxial peak strain (εcc/εc) and confining pressure.Figures 5 and 6 show that the linear Mohr-Coulomb (M-C) criterion is not suitable for simulating the triaxial mechanical law of HSFRSCC in this study.Therefore, based on the research of Noori et al. [20], the power function was used to fit the triaxial peak stress and strain, and the relationship in equations 1-2 was obtained.By calculating equations 3-4, the multiaxial stress of each specimen was transformed into an octahedral coordinate system [21], as shown in Figure 7.As shown in Figure 7, compared with the linear M-C criterion (R 2 =0.79), the nonlinear Willam-Warnke (W-W) criterion has better applicability (R 2 =0.99) for HSFRSCC; thus, the pressure meridian formula of HSFRSCC was obtained as shown in equation 5.

Conclusion
To explore the multiaxial mechanical properties of HSFRSCC, in this study, we conducted 15 sets of conventional triaxial compression tests on HSFRSCC.Based on the existing research results, HSFRSCC satisfying the requirements of compression strength and flowability performance was designed, and repeated conventional triaxial compression tests at 0, 4, 8, 12, and 16 MPa were performed.Using the test results, the triaxial stress-strain curves under low and high confining pressures were obtained.The effect of confining pressure and hybrid steel fibers on the deformation performance of HSFRSCC was demonstrated, and the relevant analysis and discussion were verified via SEM tests.For the scattered points of the relationship between triaxial peak stress, peak strain, and confining pressure, as well as the scattered points of the octahedral stress distribution, the M-C and W-W criteria were used for fitting and comparison.The results showed that the nonlinear W-W criterion had a better fitting effect; thus, triaxial peak stress, peak strain, and triaxial pressure meridian formulas were established.

Figure 1 .
Performance verification test of HSFRSCC: (a) Compressive performance test and (b) flowability test.

Figure 6 .
Figure 6.Relationship between triaxial peak strain and confining pressure.

Table 2 .
Composition and grading of aggregates.