Steel Fiber Reinforced Concrete Segments for Shield Tunnels: A Comprehensive Review of Mechanical Performance, Design Methods and Future Directions

Abstract

Steel fiber reinforced concrete (SFRC) has become a feasible alternative material for traditional reinforced concrete (RC) segments in shield tunnel engineering due to its excellent crack resistance, toughness, and durability. However, its design parameters have not yet been standardized, and research at the material and structural scales remains relatively fragmented, lacking a unified design framework, which limits the widespread application of SFRC segments. This paper provides a comprehensive review of the mechanical performance and design methods of SFRC segments, focusing on four aspects: (1) research methods for mechanical performance, including experimental analysis, numerical simulation, and artificial intelligence algorithms; (2) theoretical calculation methods for flexural and shear bearing capacity and crack width; (3) mechanical response characteristics, including deformation modes and crack propagation patterns; (4) key influencing factors, such as matrix strength, steel fiber types, dosages, and aspect ratios. The study systematically reviews relevant research methods on the mechanical performance of SFRC segments, evaluates the applicability and limitations of existing theoretical calculation methods, and ranks the factors affecting the mechanical performance of SFRC segments from the perspective of material composition. Finally, based on the review, future research directions for SFRC segments are proposed, providing a systematic reference for the development of design standards, improvement of mechanical performance, and full-lifecycle reliability assurance of SFRC segments.

1. Introduction

The global urban subway network continues to develop rapidly. By 2024, 44,730.14 km of operating lines have been built in 562 cities [1]. China is particularly prominent in the construction of underground rail transit. At present, the operating mileage has been close to 11,949.7 km, and is expected to exceed 12,000 km in the near future [2]. In this context, shield tunneling has become the mainstream tunnel construction method with its safety, high efficiency, and good adaptability to complex geological conditions [3].

However, the traditional reinforced concrete (RC) segment has gradually exposed the problem of insufficient durability in the process of production, construction, and service, such as cracking, spalling, and performance degradation caused by corrosion [4]. In order to meet the above challenges, steel fiber reinforced concrete (SFRC) came into being. It improves the tensile performance, crack resistance, and durability of concrete by adding steel fibers, while simplifying the construction process and reducing costs. At present, SFRC has been successfully applied in nearly 100 tunnel projects around the world [5,6,7,8], which has significantly improved the freeze–thaw resistance [9], crack bridging capacity [10,11,12,13,14], impact resistance [15], seismic performance [16,17], and fire resistance [18]. In addition, compared with the conventional reinforcement method, the addition of steel fiber helps to reduce carbon emissions. This is mainly due to the fact that steel fiber improves the tensile and crack resistance of concrete, which can partially or completely replace the traditional steel rebar, directly reducing the use of high carbon emission steel rebar. At the same time, the improvement of material properties means that the unit material can achieve higher mechanical performance, thus having better carbon efficiency on the basis of unit strength [19]. Therefore, although the steel fiber itself also contains carbon emissions, the overall carbon footprint of SFRC segments is still lower than that of traditional RC segments [20].

Although the research on the mechanical performance of SFRC segments has made significant progress, there are still some key problems to be solved in the research system, which restrict the theoretical deepening and engineering application of the technology. Specifically, first of all, the existing research methods are lacking systematic integration, and related research efforts focus on a single method or a specific scale, while the collaborative relationships and comparative analyses of experimental, numerical simulation, and theoretical calculation methods are insufficient, so it is difficult to establish an effective multi-method collaborative research paradigm. Secondly, the existing research has not yet formed a systematic understanding of the cross-scale correlation mechanism from material parameters, member behavior to the overall performance of the structure, especially the synergistic effects of key parameters such as steel fiber characteristics (types, dosages, aspect ratios), and matrix strength on the macro-mechanical performance of SFRC segments and the primary and secondary relationships still need to be further discussed. In addition, the applicability of existing design methods under complex working conditions still needs to be improved, and its calculation model still faces challenges in boundary condition changes and accuracy control.

In order to meet the above challenges, the mechanical performance and design methods of SFRC segments are comprehensively reviewed in this paper. Through the systematic integration and analysis of existing results, this study clarifies the advantages, limitations, and complementary relationships of different research methods, aiming to promote the establishment of a multi-method collaborative research model. On this basis, the key calculation theories such as the bearing capacity of normal sections and inclined sections, crack widths, and so on are comprehensively reviewed, and the applicability and limitations of the existing design methods are analyzed. Furthermore, the internal mechanisms of mechanical response from material to structural scale are systematically revealed, and the influences of key design parameters on the macro-mechanical performance of SFRC segments are clarified. Finally, combined with the development trend of SFRC segments, this paper looks forward to future key research directions such as AI-aided design and durability improvement. Through the above work, this paper constructs a comprehensive research framework covering “performance characterization—theoretical modeling—frontier exploration”, in order to provide a solid theoretical basis and systematic reference for the scientific design, optimization, and application of SFRC segments in tunnel engineering.

2. Research Methods for the Mechanical Performance of SFRC Segments

In the study of mechanical performance of SFRC segments, experimental analysis, numerical simulation, and artificial intelligence algorithms constitute the key research methodologies. As a fundamental approach, experimental analysis can obtain accurate mechanical parameters and provide a verification basis for theoretical models; numerical simulation techniques can efficiently simulate complex boundary conditions and long-term service performance; artificial intelligence algorithms enable performance prediction and design optimization through intelligent data analysis. The three approaches have their own characteristics and complementary advantages. By systematically comparing the application conditions, technical advantages, and research limitations of the three methodologies, this paper aims to promote collaborative innovation among different methods and provide a more comprehensive framework for the study of mechanical performance of SFRC segments.

2.1. Experimental Analysis

Experimental analysis is a direct means to obtain the key parameters of segment strength, toughness, and crack control, and can clearly reveal its deformation and failure mechanisms. At present, the experimental research efforts on the mechanical performance of SFRC segments mainly includes single segment tests, ring tests, and joint tests. Table 1 summarizes the mechanical performance of SFRC segments with single segments or integral ring segments as the main objects. Meng et al. [21] developed a biaxial loading system (Figure 1b) that can simultaneously apply vertical and horizontal loads on the basis of the traditional uniaxial loading test (Figure 1a), which more truly simulated the actual stress state of the structure and the effect of groundwater. Another researcher [22] studied the crack control capacity and bearing capacity of single-layer reinforced-steel fiber reinforced concrete (R-SFRC) segments with different reinforcement ratios through full-scale bending tests. Abbas et al. [23] simulated the expansion behavior of rock mass during tunnel excavation through the punching test of full-scale segments. As the joint performance has a key impact on the overall safety of the tunnel [24], the mechanical behavior of segment joints has also become an important research direction [25,26,27,28,29]. Typical full-scale joint tests often use a monotonic loading method to evaluate their ultimate bearing capacity, in which the joint specimen is simplified as a flat plate structure (Figure 2), and a biaxial loading test is carried out on it, which can realize the real loading simulation of axial force and bending moment on the premise of accurately maintaining the joint structure [25,26,28,29].

In terms of ring tests of SFRC segments, Zhang et al. [30] applied radial loads through 24 horizontal actuators to simulate external water and soil pressure, and staged unloading was carried out at the waist of the segment to simulate lateral stress release. Similarly, relevant studies [31,32,33] also analyzed the deformation modes, crack development, and deflection changes in the segments through the ring tests. Due to the large sizes of segments used in the actual projects, it is difficult to transport and hoist them. At the same time, the full-scale tests have high requirements for space and heavy equipment, and the test costs are high. In order to facilitate laboratory research, the researchers developed simplified test methods considering the effects of curvature, bending moment, and axial force. Using the “replacing curved segments with straight test beams” method, the segment was simplified as a test beam, including the simply supported beam tests under axial compression (Figure 3a) [34] and the symmetrical inclined beam tests (Figure 3b) [35]. In the experimental observations, advanced monitoring technologies such as digital image correlation (DIC) and acoustic emission (AE) are widely used to capture the processes of crack propagation and damage evolution. Among them, DIC can provide full field deformation measurement and directly visualize and quantitatively describe the local changes in strain and crack development under bending or shear so as to accurately capture the evolution of complex strain fields and the bridging effect of steel fibers [36,37,38,39]. In addition, AE can effectively characterize the damage development of SFRC segments during the stress process. By analyzing the signal characteristics such as amplitude, frequency, and energy, AE can identify different failure modes such as matrix cracking, steel fiber debonding, and pull-out [38,39,40,41,42].

Table 1. Summary of the existing literature on the mechanical performance testing of SFRC segments.

Experiment Subject	Test Type/Method	AE	DIC	Researcher
Single SFRC segment	Settlement response test/Punching test			Abbas et al. [23]
	Crack test			Zhang et al. [43]
	Thrust load test			Nehdi et al. [44]
	Biaxial loading method			Meng et al. [21]
SFRC segment joints	Biaxial loading joint bending test			Feng et al. [25]
	Biaxial loading joint bending test			Gong et al. [26]
	Biaxial loading joint bending test			Yan et al. [28]
	Biaxial loading joint bending test			Zhou et al. [29]
	Radial joint test			Caratelli et al. [27]
Full ring SFRC segment	Full-scale loading test			Zhang et al. [30]
SFRC beam	Four-point bending test	√		Aggelis et al. [42]
	Four-point bending test	√		Li et al. [45]
	Four-point bending test		√	Cardoso et al. [36]
	Four-point bending test			Li et al. [46]
	Four-point bending test			Venkateshwaran et al. [47]
	Four-point bending test	√	√	Zhou et al. [38]
	Four-point bending test			Zhang et al. [48]
	Three-point bending test	√	√	Ashraf et al. [37]
	Three-point bending test	√		Yue et al. [49]
	Three-point bending test	√		Yue et al. [50]
	Axially loaded simply supported beam method			Xu et al. [34]
	Symmetric-inclination beam loading method			Ding et al. [35]

Annotation: √ = has been investigated.

Table 1. Summary of the existing literature on the mechanical performance testing of SFRC segments.

Experiment Subject	Test Type/Method	AE	DIC	Researcher
Single SFRC segment	Settlement response test/Punching test			Abbas et al. [23]
	Crack test			Zhang et al. [43]
	Thrust load test			Nehdi et al. [44]
	Biaxial loading method			Meng et al. [21]
SFRC segment joints	Biaxial loading joint bending test			Feng et al. [25]
	Biaxial loading joint bending test			Gong et al. [26]
	Biaxial loading joint bending test			Yan et al. [28]
	Biaxial loading joint bending test			Zhou et al. [29]
	Radial joint test			Caratelli et al. [27]
Full ring SFRC segment	Full-scale loading test			Zhang et al. [30]
SFRC beam	Four-point bending test	√		Aggelis et al. [42]
	Four-point bending test	√		Li et al. [45]
	Four-point bending test		√	Cardoso et al. [36]
	Four-point bending test			Li et al. [46]
	Four-point bending test			Venkateshwaran et al. [47]
	Four-point bending test	√	√	Zhou et al. [38]
	Four-point bending test			Zhang et al. [48]
	Three-point bending test	√	√	Ashraf et al. [37]
	Three-point bending test	√		Yue et al. [49]
	Three-point bending test	√		Yue et al. [50]
	Axially loaded simply supported beam method			Xu et al. [34]
	Symmetric-inclination beam loading method			Ding et al. [35]

Annotation: √ = has been investigated.

By improving the loading modes (such as biaxial loading, punching test) and optimizing the specimen designs (such as flat plate joints, integral ring loading), the test analysis methods can more truly simulate the mechanical behavior of SFRC segments under actual working conditions. At the same time, advanced monitoring technologies (DIC, AE) provide a reliable basis for damage mechanism analysis and further reveal the mechanical performance, crack propagation law, and failure mode of SFRC segments.

2.2. Numerical Methods

Due to the complexity of geological conditions and external factors, the actual stress state of SFRC segments is difficult to be fully characterized only by test methods, and test research is greatly limited by costs and conditions. In contrast, numerical simulation methods have significant advantages in economy, whole process analysis, multi-condition simulation, and meso-mechanical behavior research. At present, the commonly used numerical methods include the finite element method, the boundary element method, the numerical manifold method, the extended finite element method, and the discrete element method, and each method has specific applicability and advantages. Therefore, this paper focuses on the numerical methods widely used in the study of mechanical performance of SFRC segments.

2.2.1. Finite Element Method

Table 2 summarizes the representative work of using the finite element method (FEM) to study the mechanical performance of SFRC segments, in which ABAQUS is the widely used numerical simulation software. In terms of the mechanical response analysis of the segment pushing process, researchers [51,52,53] established an analysis model based on the direct constraint algorithm (Figure 4), which imposed axial constraints on the segment away from the jack, and set radial constraints on the outer surface of the segment to simulate the surrounding rock resistance. The model usually includes ten ring segments, which is mainly based on the considerations that the influence range of jacking force is concentrated in the first eight rings. In terms of joint performance research, Zhang et al. [54] established a refined model of tunnel lining including three ring segments through ABAQUS. Qi et al. [55] constructed a three-dimensional fine model of large-diameter segments under bolted and bolt-free conditions, and systematically studied the joint surface opening, bending stiffness, bolt stress changes, and the corresponding damage mechanism.

Many studies [17,51,52,54] use ABAQUS to simulate SFRC integral ring segments. Avanaki et al. [17] established a two-dimensional plane strain model, used nonlinear continuous elements and a concrete damage plastic (CDP) model, and combined with the constitutive relationship of SFRC to analyze the seismic performance of segments. At the same time, the constraint convergence method is used to simulate the stress state after tunnel excavation before the seismic load is applied. Zhang et al. [54] built a three-dimensional refined model of geological strata and tunnel structure, and effectively simulated radiation damping and elastic foundation effect by setting the viscoelastic artificial boundary composed of spring dampers. These studies reflect the advantages of ABAQUS in dealing with the nonlinear behavior of SFRC segments.

In the application of other FE software, Yang et al. [56] used the modified Maekawa concrete model to simulate the crushing and cracking behavior of segments based on DIANA 9.4.4 platform. The embedded steel rebar elements in the software allow the steel rebar to be flexibly arranged without independent nodes, which not only simplifies the modeling process, but also improves the accuracy of stiffness characterization. Mo et al. [57] successfully simulated the cracking load, stress distribution, and crack morphology of SFRC segments and joints by using the concrete model in ADINA to describe the compressive softening, tensile cracking and post failure behavior of concrete through a failure envelope, and effectively evaluated the improvement effect of steel fiber on local mechanical performance during jacking.

Table 2. Summary of the relevant literature on the mechanical performance of SFRC segments by the FEM.

Researcher	Finite Element Software					Research Object
	ABAQUS	MIDAS GTS	FLAC 3D	DIANA 9.4.4	ADINA	Single Segment	Segment Joints	Full Ring Segment
Yang et al. [12]	√					√
Nogales et al. [16]	√					√
Avanaki et al. [17]	√							√
Yan et al. [52]	√					√		√
Liao et al. [51]	√					√		√
Zhang et al. [53]	√					√
Zhang et al. [54]	√							√
Qi et al. [55]	√						√
Mo et al. [57]					√	√	√
Yang et al. [56]				√		√	√	√
Xu et al. [58]			√					√
Deng et al. [59]		√				√

Annotation: √ = has been investigated.

Table 2. Summary of the relevant literature on the mechanical performance of SFRC segments by the FEM.

Researcher	Finite Element Software					Research Object
	ABAQUS	MIDAS GTS	FLAC 3D	DIANA 9.4.4	ADINA	Single Segment	Segment Joints	Full Ring Segment
Yang et al. [12]	√					√
Nogales et al. [16]	√					√
Avanaki et al. [17]	√							√
Yan et al. [52]	√					√		√
Liao et al. [51]	√					√		√
Zhang et al. [53]	√					√
Zhang et al. [54]	√							√
Qi et al. [55]	√						√
Mo et al. [57]					√	√	√
Yang et al. [56]				√		√	√	√
Xu et al. [58]			√					√
Deng et al. [59]		√				√

Annotation: √ = has been investigated.

The FEM (especially ABAQUS) has significant advantages in the study of mechanical performance of SFRC segments: it can not only effectively deal with complex problems such as material nonlinearity and contact behavior, but also flexibly build diversified models from local joints to integral ring structures, which is suitable for the analysis of various working conditions such as incremental launching and earthquake. At the same time, the combination of the accurate modeling ability of the method (such as viscoelastic artificial boundary simulation of semi-infinite foundation effect) and advanced material constitutive models (such as CDP model describing concrete damage) significantly improves the reliability of numerical simulation.

2.2.2. Extended Finite Element Method

Compared with the traditional FEM, the extended finite element method (XFEM) can simulate discontinuous problems (such as crack propagation, material interface, etc.) without re-meshing. The FEM needs to continuously refine the mesh at the crack, while the XFEM allows the crack to expand freely in the element through enhanced shape functions and level set methods, which significantly reduces the mesh dependency and improves the computational efficiency.

In the study of using the XFEM to analyze the mechanical performance of SFRC segments, Liu et al. [60] regarded the fiber–matrix interface as a bimaterial system, and explored the failure process of SFRC segments from a micro perspective. By combining the cohesive zone model, the problems of grid conformal constraints are avoided, and the cohesive element is introduced to simulate the interface debonding, which realizes the numerical analysis of the fiber–matrix interface behavior. Zhang et al. [43] proposed an improved XFEM to simulate the crack evolution process under the coupling effect of mechanical load and steel rebar corrosion by introducing a new fracture energy conversion equation and using a high-order crack growth function, the calculation flow is shown in Figure 5. The model accurately captures the effect of cracking on the deflection of the segment, and the prediction deviation is less than 9%, and the calculation efficiency is 26–35% higher than that of the traditional method.

2.2.3. Discrete Element Method

Compared with the FEM and XFEM, the discrete element method (DEM) can break through the continuum hypothesis and accurately simulate the mechanical behavior of discontinuous media through particle size modeling. This method is especially suitable for analyzing the dynamic response, large deformation, and failure process of granular materials, and has unique value in the field of composite micromechanics.

The DEM has been applied to study the mechanical behavior of SFRC segments. Based on this method, Zhou et al. [61] explored the influence of steel fiber dosages on the mechanical performance and crack development of hybrid fiber-reinforced concrete (HFRC) at the mesoscale. Figure 6 shows the meso-simulation calculation framework under different hybrid fiber dosages, in which the interface transition zones (ITZ) between coarse aggregate, mortar, polypropylene fiber, steel fiber, and each component are carefully considered. The mechanical performance of the coarse aggregate–polypropylene fiber reinforced mortar (PFRM) interface, steel fiber–PFRM interface, and the uniaxial compression properties of HFRC were measured by combining experimental tests and the DEM. Zhao [62,63] determined the meso strength parameters of segment concrete considering the internal deformation and anisotropy characteristics through the meso uniaxial test, and established the discrete element model for segment bending test based on PFC 2D, and then revealed the deformation mechanism, force chain transmission, and crack evolution law of the component during the loading process. In order to overcome the limitations of the FEM in simulating discrete geological media, Zhou et al. [64] further developed the block-based discrete element model to simulate the shield tunneling process in sandy gravel stratum and systematically analyzed the response characteristics of rock block displacement and segment mechanical performance under this condition.

Although numerical simulation methods show great advantages in studying the mechanical performance of SFRC segments, current research still has some inherent limitations. Firstly, the calculation accuracy of the FEM, XFEM, or DEM depends heavily on the material constitutive models. At present, the widely used models (such as the CDP model in ABAQUS) simplify the complex interfacial bond–slip behaviors between steel fibers and concrete matrix to a considerable extent, which makes it difficult to accurately simulate the pull-out processes of steel fibers after cracking and their contributions to material toughness. Secondly, these methods are computationally expensive when simulating the complete processes of structures from local damage to overall failure, particularly for nonlinear dynamic analyses of integral segment models with joints. In addition, most existing numerical studies focus on short-term mechanical performance, and there is still a lack of reliable and efficient numerical approaches for predicting the durability evolution of SFRC segments under the coupling effects of long-term loads, wet-dry cycles, and corrosive environments. These limitations constitute the main gap between current numerical research and practical applications, and also represent directions that need to be addressed in future research.

2.3. Application of Artificial Intelligence

With the progress of computer science, artificial intelligence (AI) technology has promoted the intelligent development of shield tunnel construction. Artificial neural networks (ANNs) and deep learning (DL) are widely used in SFRC segment research because of their powerful learning ability [65].

A variety of AI algorithms have been applied to the study of SFRC materials and segment performance, and the relevant results are summarized in

Table 3. Application summary of artificial intelligence in SFRC materials and SFRC segments.

Researcher	Method	Research Direction
		SFRC Material	SFRC Mechanical Performance	Tunnel Segment
Zhang et al. [66]	Hybrid model	√
Buttignol et al. [70]	Pull-out analytical model	√
Sun et al. [67]	Back propagation neural network	√	√
Farhangi et al. [71]	AI-based model		√
Zafarani et al. [68]	Hybrid model		√
Chaabene et al. [72]	Genetic-programming-based symbolic regression model		√
Wang et al. [73]	Bayesian model updating		√
Olalusi et al. [74]	Hybrid model		√
Yassir M. Abbas et al. [75]	Hybrid model		√
Almasabha et al. [76]	Extreme gradient boosting		√
	Light gradient boosting machine
	Gene expression programming
Zhao et al. [69]	Mask-region-based hybrid attention convolutional neural network			√

Annotation: √ = has been investigated.

. Zhang et al. [66] developed a non-destructive knocking detection technology combined with a one-dimensional convolutional neural network bidirectional long-term and short-term memory hybrid DL model, which can accurately classify the steel fiber dosage in SFRC segments based on sound signals, and the test accuracy rate is 98%. In the aspect of mix proportion design, Sun et al. [67] combined the back propagation neural network with the multi-objective particle swarm optimization algorithm to establish the nonlinear relationship model between SFRC mix proportion parameters and uniaxial compressive strength, which effectively improved the design efficiency and multivariable optimization ability. For structural performance evaluation, Zafarani et al. [68] proposed using a particle swarm optimization artificial neural network model to predict the shear capacity of unreinforced SFRC beams, as shown in Figure 7, which provides a reference method based on machine learning for segment design. In addition to material characterization, Zhao et al. [69] used the method of combining the mask R-CNN algorithm with a meso bonding model to extract the geometric characteristics of cracks and analyze the mechanical behavior of cracked segments and joints, showing the potential of DL to predict structural performance based on visual inspection data.

In summary, AI algorithms show significant advantages in SFRC segment research, including high-precision classification (such as steel fiber dosage detection), multi-objective optimization (such as mix design), and complex mechanical performance prediction (such as bearing capacity and crack damage correlation analysis). Its core value is to improve the accuracy and efficiency of the results by replacing traditional empirical methods with data-driven models. However, it needs to rely on sufficient experimental data to support model training. In the future, it needs to further tap its potential and optimize its application.

3. Calculation Methods for SFRC Segment Structures

3.1. Bearing Capacity Calculation

Accurately evaluating the bearing capacity of SFRC segments is the key to ensuring the structural integrity of tunnels. The addition of steel fiber significantly enhances the tensile contribution of concrete in the cracking zone, so the reinforcement effect must be fully considered in the calculation of bearing capacity. However, the bearing capacity calculation of SFRC segments has not yet formed a unified standard [77]. Therefore, many researchers use calculation models applicable to SFRC beams for reference and apply them to segment analysis after modification. This paper summarizes the relevant standards and reference calculation methods for the bearing capacity of normal and inclined sections of SFRC segments in Appendix A

Table A1. Calculation methods for the bearing capacity of SFRC segments in normal sections.

Ref.	Computing Formula	Explanation
GB 50010-2010 [79]	N = α1 fc b x + fy′ As′ − fy As N e = α1 fc b x (h0 − x/2) + fy’ As’ (h0 − as’)	fc is the axial compressive design value of concrete. fy’ is the design value of compressive strength of ordinary steel rebar. fy is the design value of tensile strength of ordinary steel rebar. As is the cross-sectional area of the longitudinal ordinary steel rebar in the tension zone. As’ is the cross-sectional area of longitudinal ordinary steel rebar in compression zone. αs’ is the distance from the resultant force point of the longitudinal ordinary steel rebar in the compression zone to the compression edge of the section.
JGJ/T 465-2019 [78]	Nfu = ffc b x + fy’ As’ − fy As − fftu b xt Nfu e = ffc b x (h0 − x/2) + fy’ As’ (h0 − as’) − fftu b x (hx/2 − as)	Nfu is the design value of axial compressive bearing capacity of SFRC segments. ffc is the design value of axial compressive strength of SFRC. fftu is the tensile strength of equivalent rectangular stress pattern of SFRC in tension zone. xt is the height of the tension zone of the component. αs is the distance from the resultant point of longitudinal tensile non-prestressed steel rebar to the near side of the section.
Model code 2010 [81]	Nfu = η ffc λ x b/2 − ffc (h − x) b Mfu = ηffc λ x b/2 (h/2 − λx/2) + ffts (h − x) b (x/2)	Nfu is the design value of axial compression bearing capacity. η is a coefficient, when the concrete strength grade ≤ C50, take 0.8. ffc is the design value of axial compressive strength of SFRC. λ is a coefficient, when the concrete strength grade ≤ C50, take 1.0. Mfu is the design value of bending moment bearing capacity. ffts is slenderness ratio.
ACI 318R-14 [80]	Nfu = ϕ Nn = 0.7 [0.85 ffc x b/2 − σp xt b] Mfu = ϕ Mn = 0.7 [0.85 ffc (x/2) (h/2 − x/3) b + σp xt b (h − xt)/2]	ϕ is the influence coefficient considering the size effect and the uneven material of the component. Nn is the nominal of axial compression of SFRC. Mn is the nominal resistance of SFRC. σp is the ultimate tensile strength of SFRC bearing capacity limit state.
Xu et al. [34]	Nfu ≤ α ffc b x/2 − ffts b xt Nfu (e1 + h/2 − xt) ≤ α1 ffc b x (x/β1 − x/2) + ffts b xt (xt/2) ei = e0 + ea	ffc is the standard value of axial compressive strength of SFRC. ffts is the tensile strength characteristic value of SFRC segments under ultimate bearing capacity state. xt is the height of the tension zone of the component. ei is initial eccentricity. e0 is the distance from the point of axial force to the center of gravity of the section. ea is the additional eccentricity, which should be selected according to 6.2.5 of GB 50010-2010.
Li et al. [138]	Nu = α1 ffc b xc − σsf b xft + 0.87 fy’ As’ − fy As Nu e = α1 ffc b xc (h0 − x/2) + 0.87 fy’ As’ (h0 − as’) − αsf b xft (xft/2 − as) xft = (h − xc)/β1 e = ηns,u e0 + h/2 − as	α1 is the coefficient influenced by the compressive strength. fy’ is yield strength of the compressive steel rebar. xc is the depth of the compressive zone of concrete. xft is the depth of the tensile zone of concrete. β1 is the coefficient related to the depth of compression.
Zhou et al. [139]	Nfu ≤ fc b x/2 − σ3 b xt/2 Nfu (ei − h/2 + x) ≤ fc b x2/3 + σ3 b xt2/3 fc = Esc Ɛftu (x/xt)	fc is the actual compressive stress of concrete in compression zone. Esc is the elastic modulus of SFRC. Ɛftu is the ultimate state of bearing capacity under tension.

and

Table A2. Calculation methods for the bearing capacity of SFRC segments in inclined sections.

Ref.	Computing Formula	Explanation
GB 50010-2010 [79]	Vfcs = Vfc + Vsv + 0.07 N Vfc = Vc (1 + βcw λf) Vc = 0.7 ft b h	Vfc is the design value of shear bearing capacity of SFRC. Vc is the shear bearing capacity of matrix concrete. Vsv is the design value of shear bearing capacity related to stirrups. βcw is the influence coefficient of steel fiber on the shear bearing capacity of concrete, the recommended value is 0.668.
JGJ/T 465-2019 [78]	Vfcs = Vfc + Vsv Vfc = Vc (1 + βv λf)	Vc is the design value of shear bearing capacity related to concrete. Vsv is the design value of shear bearing capacity mainly related to stirrups. Vfc is the design value of shear bearing capacity related to SFRC considering the influence of steel fiber. βv is the influence coefficient of steel fiber on the shear bearing capacity related to concrete on the inclined plane of SFRC segments. λf is the characteristic value of steel fiber dosage.
Model code 2010 [81]	VRk,4 = Vcd + Vfd + Vvd Vcd = (0.12 k (100 r1 fck)1/3 + 0.15 scp) (b h0) Vfd = 0.7 kf k τfd b h0 Vvd = 0.9 fyv h0 (Asv/s)	VRk,4 is the standard value of residual flexural tensile strength corresponding to the notch displacement of 3.5 mm SFRC. Vcd is the design value of the shear bearing capacity of ordinary reinforced concrete members without considering the effect of steel fiber and shear steel rebar. Vvd is the increased shear capacity of the section under the action of stirrups. ρ1 is the reinforcement ratio of steel rebars in the tensile zone. σcp is equivalent compressive stress of concrete. kf is the influence coefficient of the cross-section shape, and the rectangular cross-section takes 1. k is the influence coefficient of section height. τfd is the design shear strength of SFRC.
Gandomi et al. [140]	Vfcs = ((2/λ) (ρ fc + 0.41 τ F) + (1/2λ) (ρ/(288 ρ − 11)4) + 2) (b h0)	ρ is the reinforcement ratio in the tensile zone. τ is average steel fiber matrix interfacial bond stress, taken as 4.15 MPa. F is steel fiber factor.
Bi et al. [141]	Vu = Vc + Vf + Va + Vd	Vc is the shear bearing capacity provided by the concrete in the compression zone. Vf is the shear bearing capacity provided by the oblique crack section steel fiber. Va is the shear bearing capacity provided by aggregate bite force. Vd is the shear bearing capacity provided by the dowel action of longitudinal steel rebar.
Yakoub [142]	Vfcs = 2.5 β (fc’)1/2 (1 + 0.70 Vf (Lf/Df) Rg) (dv/a), for a/dv ≤ 2.5 Vfcs = β (fc’)1/2 (1+ 0.70 Vf (Lf/Df) Rg), for a/dv > 2.5	fc’ is cylinder compressive strength; Vf is volume fraction of steel fiber. Lf/Df is aspect ratio of the steel fiber. dv is beam effective depth. a is shear span.
Zhang et al. [48]	V = Vcc + Vsv + Vfrc	V is the shear bearing capacity of flexural members with web steel rebar. Vcc is the shear bearing capacity of the compression zone of the member. Vsv is the shear capacity provided by stirrups. Vfrc is the shear bearing capacity provided by steel fiber.

.

3.1.1. Calculation Method of Normal Section Bearing Capacity

Appendix A Table A1 summarizes the relevant standards and methods for calculating the flexural capacity of SFRC segments. At present, the calculation methods for the normal section bearing capacity of SFRC segments can be divided into two categories: the equivalent strengthened method based on modifications of the traditional RC model, and the mechanistic model method based on the post-cracking constitutive relationship of materials.

The equivalent strengthened method is represented by JGJ/T 465-2019 [78]. In this method, the equivalent tensile strength f_ftu is determined by the characteristic value of steel fiber dosage λ_f and the empirical coefficient β_tu to reflect the tensile contribution of steel fibers, and rectangular stress diagram blocks are used for simplified calculation. This method essentially follows the design concept of ordinary concrete in GB 50010-2010 [79] and only replaces the tensile strength of concrete with SFRC tensile strength. Its advantages include simple calculation, high compatibility with current design codes, and ease of engineering application. However, it fails to fully reflect the residual tensile stresses provided by steel fibers after cracking, with insufficient consideration of post-cracking ductility and bearing capacity. The prediction results tend to be conservative under high steel fiber dosage or complex stress conditions. ACI 318R-14 [80] also adopts a simplified approach, which assumes a triangular stress distribution for the concrete compression zone and introduces a reduction coefficient φ to account for material variability, thereby ensuring structural safety and reliability.

The reinforcement effect of steel fibers can be more accurately characterized by constitutive models. For example, Model Code 2010 [81] divides the tensile constitutive response of SFRC into rigid plastic and linear elastic types, with the latter further subdivided into hardening and softening models, and provides corresponding calculation formulae for equivalent tensile strength, improving calculation accuracy through the introduced constitutive relationship. Meng et al. [82] proposed a beam bearing capacity model using an equivalent rectangular compression stress diagram block combined with a four-linear tensile constitutive model, which completely describes the four continuous stress stages of the member from pre-cracking, cracking, crack propagation to failure, and explicitly considers the post-cracking strength contribution provided by steel fibers. Li et al. [83] based on the post-cracking linear softening model (Equations (1) and (2)), converted the elastic flexural tensile residual strength measured in notched beam tests to the plastic axial tensile strength, thereby accurately predicting the axial bearing capacity of SFRC segments and effectively reflecting the toughening mechanism of steel fibers.

f_Ftuk = 0.45 f_R1 − (0.45 f_R1 − 0.5 f_R3 + 0.2 f_R1) (w_u/CMOD₃)

(1)

f_Ftud = f_Ftuk/γ_m

(2)

where f_R1 and f_R3 are correspond to the elastic flexural residual strength values at CMOD₁ = 0.5 mm and CMOD₃ = 2.5 mm in the three-point bending test of notched beams, respectively. f_Ftuk is the standard value of axial tensile residual strength. f_Ftud is the design value of axial tensile residual strength. γ_m is the partial coefficient of steel fiber concrete material, with a value of 1.5.

In general, the constitutive model method relies on the tensile stress–crack width relationship of SFRC, which can more accurately describe the complete process from cracking to failure, particularly in reasonably reflecting the bridging effect of steel fibers after cracking, with high theoretical accuracy. However, its application is constrained by significant computational complexity and dependence on characteristic parameters obtained from notched beam tests, leading to issues of high material testing costs and design difficulties, which limit its promotion in conventional engineering. Therefore, enhancing the method’s practicality and usability while ensuring computational accuracy remains a key problem to be solved in future research.

3.1.2. Calculation Method of Inclined Section Bearing Capacity

Appendix A Table A2 summarizes the calculation methods for the shear bearing capacity of SFRC segments. At present, the core issue in calculating the inclined section bearing capacity of SFRC segments is how to accurately quantify the contribution of steel fibers. The existing methods mainly present two approaches: one is the overall correction method based on traditional reinforced concrete specifications, and the other is the component superposition method.

The overall correction method based on traditional RC specifications (such as GB 50010-2010 [79] and JGJ/T 465-2019 [78]) mainly determines the shear bearing capacity based on the strength of concrete and the cross-sectional dimensions of components. Although the influence of axial compression and reinforcement ratio is considered in the framework of GB 50010-2010, it does not directly include the shear contribution of steel fibers. Its characteristic is to indirectly reflect the effect of steel fibers by multiplying the concrete term by a comprehensive coefficient, which simplifies calculation. However, it fails to reflect the bridging effects of steel fibers on diagonal cracks from a mechanical perspective, and the predicted results are usually conservative.

The component superposition method (represented by Model Code 2010 [81]) explicitly decomposes the shear bearing capacity into the sum of the contributions of concrete (V_cd), stirrups (V_sv), and steel fibers (V_fd). The concept is clear and can independently evaluate the effect of steel fibers. Due to the reasonable consideration of the influence of steel fibers and crack width effects, this method has become a commonly used basis for the design of R-SFRC segments [84,85]. However, its key parameters (such as design shear strength) rely on complex experiments to determine, and the sensitivity to the distribution and orientation of steel fibers is not adequately considered.

To further clarify the contribution of steel fibers in the shear model, researchers have also proposed calculation methods for SFRC beams with and without web steel rebar. Kang et al. [86] established a shear design model for steel fiber lightweight aggregate concrete beams without web steel rebar by introducing a correction factor for lightweight aggregates. Zhang et al. [48] systematically constructed a shear bearing capacity calculation model for steel fiber self-compacting concrete beams with web steel rebar (Equation (3), Figure 8), taking into account the joint contributions of stirrups and steel fibers. The ultimate tensile residual strength f_Ftu was used to incorporate the bending toughness parameters into the shear design.

V = V_cc + V_sv + V_frc

(3)

where V is the shear bearing capacity of flexural members with stirrups. V_cc is the shear bearing capacity of the compressed area of the component. V_sv is the shear bearing capacity provided by stirrups. V_frc is the shear bearing capacity provided by steel fibers.

Overall, to overcome the limitations of existing methods, numerous research models have attempted to describe the shear effect of steel fibers in a more mechanically representative manner by introducing steel fiber characteristic parameters or directly utilizing material residual strength. These models show good prediction accuracy on beam specimens, but the model forms are not yet unified, and their applicability and reliability in simulating the complex confining pressure states of SFRC segments still need to be systematically verified. Therefore, future research should focus on establishing more applicable shear models to accurately predict the shear bearing capacity of SFRC segments under complex stress conditions.

3.2. Calculation of Crack Width

Appendix A 

Table A3. Calculation methods for the crack width of SFRC segments.

Ref.	Computing Formula	Explanation
GB 50010-2010 [79]	wmax = αcr ψ (σsk/Es) (1.9 Cs + 0.08 (deq/ρte))	αcr is the force characteristic coefficient of the component. ψ is the strain in homogeneity coefficient of longitudinal tensile steel rebar between cracks. σsk is the equivalent stress of longitudinal tensile steel rebar of prestressed concrete members. Es is the elastic modulus of steel rebar. Cs is the distance from the outer edge of the outermost longitudinal tensile steel rebar to the bottom of the tensile zone. deq is the equivalent diameter of longitudinal steel rebar in tension zone. ρte is the reinforcement ratio of longitudinal tensile steel rebar calculated according to the effective tensile concrete cross-sectional area.
JGJ/T 465-2019 [78]	wfmax = wmax (1 − βcw λf)	wfmax is the maximum crack width of SFRC segments. wmax is the maximum crack width of ordinary reinforced concrete members. βcw is the influence coefficient of steel fiber on crack width. λf is the characteristic value of steel fiber dosage.
Model Code 2010 [81]	wf = 2 ls,max (εsm − εcm − εcs)	wf is the crack width of SFRC under serviceability limit state. ls,max is the area where the relative slip between steel rebar and concrete is the largest. εsm is the average strain of steel rebar in the maximum slip region. εcm is the average strain of concrete in the maximum slip region. εcs is the strain caused by the shrinkage of concrete.
DafStb Technical Rule on Steel Fiber Reinforced Concrete [87]	wk = Sr,max (εfsm − εcm)	wk is the characteristic crack width of the tensile zone of steel fiber structure. Sr,max is the maximum crack spacing in the tensile zone of steel fiber structure. εfsm is the average strain of steel rebar in the range of concrete crack spacing under the condition of related load combination. εcm is the average strain in the range of concrete crack spacing.
Gao et al. [89]	wnfmax = ν (a + b lgN) wmax (1 − βcw λf)	wnfmax is the maximum crack width of SFRC beam under fatigue load. v is the comprehensive correction coefficient of crack width of SFRC segments under fatigue load, v = 1.4, a = −1.2518, b = 0.5458. wmax is the maximum crack width is calculated according to GB 50010-2010 without considering the influence of steel fiber. λf is the characteristic parameter of steel fiber. βcw is the crack width influence coefficient of R-SFRC specimen.
Wang et al. [90]	wfmax = wmax (1 − βcw λf)	wfmax is the maximum crack width of SFRC flexural members. wmax is the maximum crack width of SFRC member. βcw is the influence coefficient of SFRC crack width. λf is the characteristic value of steel fiber dosage.
Ning et al. [91]	wmax = 1.66 wm	wmax is the maximum crack width of steel fiber reinforced self-compacting concrete beams. wm is the average crack width of steel fiber reinforced self-compacting concrete beams.

summarizes the relevant standards and methods for predicting the crack width of SFRC segments. Currently, the computational models in this field generally acknowledge that the bridging effect of steel fibers is the core mechanism for suppressing crack development, though significant differences exist in the modeling strategies for quantifying this effect.

Among the main standard approaches, JGJ/T 465-2019 [78] considers the crack-limiting effect of fibers by introducing the steel fiber influence coefficient β_cw; Model Code 2010 [81] largely follows the calculation method for ordinary RC segments but incorporates the residual tensile strength of SFRC in the effective tensile zone; the DAfStb SFRC technical specification [87] simultaneously considers the dual effects of steel fibers on crack spacing and the strain difference between steel bars and concrete. Research [21] has shown that the tensile contribution of steel fibers can effectively reduce steel stress and increase the average tensile strain of concrete, thereby significantly suppressing crack propagation.

Researchers have conducted in-depth investigations into this mechanism. Bi et al. [88] established a bending moment–crack width calculation model (Equation (4)) based on fracture mechanics theory, considering effective crack widths, steel fiber pull-out angles, and fiber mechanical contributions. Gao et al. [89] proposed a formula for calculating the crack width of SFRC segments under fatigue loads, accounting for parameters such as steel fiber volume fraction, types, and distribution layer thickness. Wang et al. [90] studied the bending performance of notched SFRC beams through experiments and numerical simulations, quantified the crack width influence coefficient (Figure 9) and its correlation with crack size, and ultimately determined the β_cw for SFRC segments to be 0.42, thereby revising the recommended value of 0.35 in JGJ/T 465-2019. Based on four-point bending tests, Ning et al. [91] further considered the randomness of fiber distribution and its stress transfer mechanism, establishing a formula for calculating the maximum crack width of reinforced steel fiber self-compacting concrete beams (Equation (5)), with calculated results showing good agreement with experimental data.

w_nfmax = ν (a + b lgN) w_max (1 − β_cw λ_f)

(4)

where w_nfmax is the maximum crack width of steel fiber high-strength concrete beams under fatigue load. ν is the comprehensive correction coefficient for the crack width of SFRC segments under fatigue load, with ν = 1.4, a = −1.2518, b = 0.5458. w_max is the maximum crack width calculated according to GB50010-2010 without considering the influence of steel fibers. λ_f is the characteristic parameter of steel fibers. β_cw is the crack width influence coefficient of R-SFRC specimens.

w_max = 1.66 w_m

(5)

where w_max is the maximum crack width of steel fiber reinforced self-compacting concrete beams. w_m is the average crack width of reinforced steel fiber self-compacting concrete beams.

Existing calculation methods primarily follow three theoretical modeling approaches: the first is the macro empirical coefficient method (e.g., JGJ/T 465-2019 [78]), which modifies traditional formulas by introducing steel fiber influence coefficients. While convenient for engineering applications, empirical coefficients struggle to sensitively reflect complex factors such as fiber types and distribution randomness. The second is the constitutive model method based on residual strength (e.g., Model Code 2010 [81] and DAfStb regulations [87]), which incorporates the residual tensile strength of materials into strain analyses or crack spacing models. This approach is theoretically more rigorous but highly sensitive to the accuracy of input parameters. The third comprises specialized models designed for specific loads or material types, which achieve good accuracy under specific conditions but have limited universality.

Overall, these methods face a core challenge: how to accurately quantify the random distribution of steel fibers on crack sections and the statistical laws of the bridging stresses they provide. Revealing this micromechanical mechanism is a key direction for overcoming the limitations of existing models and developing high-precision crack width prediction theories.

4. Mechanical Performance Characteristics of SFRC Segments

The deformation and failure modes of SFRC segments are strongly correlated with their applied loads, geological environments, and other factors. However, these factors are generally complex. Therefore, when studying the stress behavior of SFRC segments, researchers simplify the calculation model of segments and transform the geological structural model under complex loads into a load structural model. The simplified SFRC segment mechanical model only bears the combined effects of horizontal and vertical loads, which is also a prerequisite for the deformation and failure modes and crack development characteristics of SFRC segments discussed in this section.

4.1. Deformation and Failure Modes

Studying the mechanical performance of SFRC under cyclic loading is of great significance for accurately predicting the deformation and failure modes of SFRC segments. Under uniaxial cyclic loading, SFRC exhibits superior hysteresis energy dissipation capacity compared to ordinary concrete. Due to the addition of steel fibers reducing plastic strain and increasing elastic stiffness, the failure modes of ordinary concrete have shifted from tensile failure to shear failure [92].

Under the combined action of vertical and horizontal loads, R-SFRC segments exhibit failure modes dominated by bending. Among them, steel fibers bear part of the loads, effectively reducing the stress level of longitudinal steel rebars. As the loads approach the ultimate state, under the synergistic effect of steel rebars and steel fibers, the structural failure modes gradually shift from brittle shear failure to ductile bending failure (Figure 10), and the overall stiffness, toughness, bearing capacity, energy absorption capacity, and ductility are significantly improved [21,35,58].

For SFRC segment joints, full-scale tests have shown that under bending compression composite stress, their failure behaviors are mainly dominated by compression bending mechanism and accompanied by significant rotational deformations. The failure of the joints begins with the yielding of the connecting bolts, followed by the contact of the pressure bearing surfaces and ultimately the collapse of the concrete at the outer edges of the joints, leading to joint failure. Throughout the entire loading process, the joints exhibited excellent toughness performance, and the diagonal bolts remained in a reliable working state [29,93].

Zhang et al. [30] conducted full-scale tests on the staggered assembly of SFRC segments, simulating external water and soil pressure by applying radial loads to 24 horizontal actuators. As shown in Figure 11, deformation and failure begin in critical areas of the full-ring segment (0°, 90°, 180°, 270°). Under the action of radial loads, cracks first appear in the main areas, and the structural state transitions from the elastic stage to the elastoplastic stage. As the concrete in critical areas fractures, the mechanical performance further develops into a plastic state. After the concrete in the main bearing areas collapses, three plastic hinges are formed successively, and the structural system changes from hyperstatic to statically determinate. The final stage of failure is characterized by the yielding of steel rebars, concrete crushing, and the formation of a fourth plastic hinge, thus forming the mechanism of structural failure.

Overall, the failure of SFRC segments goes through three stages: elastic stage, local failure stage, and overall instability [31,32]. The elastic stage has the longest and most critical duration, and the maximum bending moment of the segment usually occurs during this stage [33]. Under the action of soil and water pressure, SFRC segments mainly undergo bending deformation, and cracks gradually appear and propagate on the tensile side, resulting in continuous attenuation of bearing capacity. When the joint is subjected to adverse loads, its tensile side joint opens and the compressive side joint closes. When the bending moment continues to increase, the compression side of the joint is gradually compressed, causing cracks until it collapses, resulting in a gradual decrease in the bearing performance of the joint [77]. In the full-ring segment, the joint is often a relatively weak component [56,94], and its mechanical performance has an important impact on the stability and safety of the full-ring SFRC segments.

4.2. Crack Development Characteristics

The crack development patterns of SFRC segments are closely related to the load conditions. In the three-point bending tests, the failure process usually goes through four stages: elastic stage, stable crack propagation, unstable propagation, and final failure [49]. Some studies have also divided it into five phase zones: non-cracking, microcrack development, macroscopic crack propagation, failure, and residual stress [95]. During the process, acoustic emission monitoring showed that the rapid decrease in b and ib values before peak load indicates the intensification of local damage and the imminent formation of macroscopic cracks, while the subsequent increase in b value reflects the distributed microcrack system formed by steel fibers promoting the transformation of a single crack in the mid span into multiple parallel cracks extending towards the ends [12,37]. Increasing the reinforcement ratio can also achieve similar crack control effects [96].

In the four-point bending tests, cracks in the SFRC segments were concentrated in the pure bending section. As the loads increase, the spacing between cracks decreases and the width increases, until the cracks penetrate and cause the components to fail [97]. Similar crack evolution patterns were also observed in the three-point bending tests: initial bending cracks usually form and expand upwards in the load range of 90–120 kN, and new cracks continue to emerge until they penetrate, ultimately forming critical main cracks at mid span [98].

For the full-ring SFRC segment structure, initial cracks often appear on the upstream face and develop from both ends towards the center, eventually forming through cracks [33] (Figure 12). In the Figure 12, the full-ring segment consists of a cap block (represented by F, center angle = 20°), two adjacent blocks (represented by L₁ and L₂, respectively, with a center angle = 68.75°), and three standard blocks (represented by B₁, B₂ and B₃, respectively, with a center angle = 67.5°). The circle and arrow markings indicate the specific cracking location and actual cracking situation. The position of the cap block has a significant impact on the distribution of cracks: when it is located near the arch top, two microcrack concentration areas will appear, but the overall distribution is relatively uniform. If it is set in the shoulder or waist areas, local microcrack concentration will occur during specific loading stages [32].

As described in Section 2.1, the use of the “replacing curved segments with straight test beams” test method, which replaces full-scale SFRC segments with SFRC beams for testing, can effectively avoid lifting difficulties while maintaining the effectiveness of the test. Under pure bending, SFRC beams exhibit delayed crack initiation, prolonged stable propagation stages, reduced crack widths, and limited heights, ultimately leading to typical bending failure in the pure bending zone [99]. Under eccentric compression, SFRC beams will simultaneously form multiple fine cracks, with one to two main cracks developing rapidly in width and length. Studies [34,100] have shown that load eccentricity (usually ranging from 0 to 0.15 m) is a key factor affecting crack behavior: when the axial force is constant, an increase in eccentricity accelerates the crack propagation process and is an important parameter for controlling the cracking characteristics of SFRC segments.

Comprehensive analysis shows that the addition of steel fibers systematically optimizes the damage evolution mode and failure mechanism of SFRC segments. At the macro level, the failure mode of SFRC segments has undergone a fundamental transition from brittle shear to ductile bending [21,35,58]. The overall structure exhibits a complete evolution path from elastic stage, through local plastic hinge development, and ultimately to overall instability [30,31,32]. This progressive failure mechanism significantly enhances the safety reserve of the structure. At the microscopic level, steel fibers promote the transformation of crack morphology from a single main crack to a distributed microcrack system through their bridging effect, effectively improving the post crack performance and durability of SFRC segments [12,37]. It should be pointed out that in the full-ring segment, the joint is still a relatively weak component [56,94], and its complex mechanical performance mechanism has not been fully characterized in existing computational models. At the same time, based on the experimental method of “replacing curved segments with straight test beams” [34,99,100], the conclusions drawn still need to consider the influence of three-dimensional boundary conditions such as circumferential constraints and assembly effects when evaluating its engineering applicability with actual SFRC segments. Therefore, establishing a refined analysis and design theory that can uniformly describe the nonlinear and discontinuous characteristics of SFRC materials and the full-ring segment mechanical performance is a key direction for future research.

5. Factors Influencing Mechanical Performance

The mechanical performance of SFRC segments is comprehensively affected by load conditions, geological environments, matrix strength, steel fiber characteristics, and other inherent properties of materials. Studies [6,9,10,12,101,102] show that the matrix strength, steel fiber types, dosages, and aspect ratios have significant effects on their deformation failure modes, load–displacement relationships, and toughness characteristics. The relevant research summarized in

Table 4. Summary of the research literature on SFRC segment materials.

Researcher	Fiber Shape	Variables Investigated	Fiber Geometry			Mechanical Performance
			l (mm)	d (mm)	l/d	CS	ATS	FS	EM	BS
Yang et al. [103]	Hooked-end/ Straight	SFAR, SFT, COS, W/C	30/ 32/ 32/ 30.31	0.54/ 0.94/ 0.58/ 0.67	55.56/ 34.04/ 55.17/ 45.24		√
Güneyisi et al. [104]	Hooked-end	APS, AT, COS, SFAR, W/B	60/ 30	0.75/ 0.75	80/ 40	√	√
Ayan et al. [105]	Straight	APS, ATA, SFVF	6	0.16	37.5	√
Zhao et al. [101]	Hooked-end/ Corrugated/ Big head straight/ Indentation belt end	COS, W/C, SFV, SFAR, SFT	32/ 31/ 31/ 31	0.77/ 0.82/ 0.78/ 0.82	41.5/ 38.5/ 39.7/ 37.7			√
Wu et al. [106]	Straight/ Corrugated/ Hooked-end	APS, AT, SFAR, W/B, SFT	13	0.2	65	√		√
Abu-Lebdeh et al. [107]	Hooked-end/ Flattened-end/ Helix/ Hooked-end	COS, APS, AT, SFAR, W/B, SFT	30/ 50/ 25/ 30	0.56/ 1.17/ 0.49/ 0.38	53.57/ 42.74/ 51.02/ 78.95					√
Zhang et al. [108]	Hooked-end	COS, AZ, AT, SFAR, W/B, SFVF	30/ 35	0.6/ 0.45	50/ 77.78	√		√	√
Tian et al. [109]	Hooked-end/ Straight	COS, SAR, SFVF	35/ 33.71	0.5/ 1.08	70/ 31.21					√
Ran et al. [110]	Corrugated	APS, COS, SFVF, SFAR, SFT	36.44	1.04	35.04	√	√		√
Cao et al. [111]	Smooth straight/ Hooked-end/ Corrugated	SFAR, SFT	13/ 22/ 35	0.22/ 0.3/ 0.8	59.09/ 73.33/ 43.75		√
Li et al. [45]	Straight/ Hooked-end/ Corrugated	SFVF, SFAR, SFT	12/ 30/ 45/ 60	0.2/ 0.5/ 0.75/ 0.75	40/ 60/ 80/ 80			√
Shi et al. [112]	Straight/ Hooked-end	SFAR, SFT	13/ 33	0.2/ 0.55	65/ 60	√	√		√

Annotation: W/C = water–cement ratio, W/B = water–binder ratio, SFVF = steel fiber volume fraction, SFAR = steel fiber aspect ratio, SFT = steel fiber type, APS = aggregate particle size, AT = aggregate type, COS = concrete strength, CS = compressive strength, ATS = applying tensile strength, FS = flexural strength, EM = elastic modulus, BS = bond strength, √ = has been investigated.

shows that the current research efforts on SFRC segment materials mainly focus on the above parameters. Based on this, this paper will focus on the influence of matrix strengths, steel fiber types, dosages, and aspect ratios on the mechanical performance of SFRC segments.

5.1. Matrix Strength

Steel fiber improves the mechanical performance of segments by optimizing the crack bridging effect, which mainly depends on the bond strength between steel fiber and matrix, which is closely related to the strength of matrix [108]. The research shows that with the increase in matrix strength, the ultimate pull-out load, and total pull-out energy consumption of steel fibers increase significantly, which is particularly obvious in hooked steel fibers [103,107,109,113]. By observing the pulled-out end-hook steel fiber, it is found that the end-hook at the embedded end is almost completely straightened, and the higher the strength of the matrix, the greater the degree of end hook straightening. If the strength of the matrix is low, the matrix will be damaged before the end hook of the steel fiber is completely straightened, which will reduce the mechanical bite force between the steel fiber and the matrix and the end hook straightening force, and then affect the interface bond strength, the initial crack strain, and the peak strain of the segment.

In addition, in view of the unavoidable pore defects in the segments, it is necessary to optimize the cementitious materials for improvement. Silica fume, fly ash, and slag powder are commonly used admixtures, but their effects are significantly different: compared with fly ash, silica fume can increase the 7-day and 28-day compressive strength by 54%, and the 90-day compressive strength by 30%. The compressive strength of slag powder at the corresponding age is 53.8 MPa, 64.4 MPa, and 84.1 MPa, respectively [105]. When the silica fume dosage is 15–25%, it can refine the structure of the ITZ around the steel fiber by adding hydration products, so as to simultaneously enhance the matrix strength and bonding performance [114]. Metakaolin can also effectively optimize the pore structure and improve the steel fiber matrix interface, making it a feasible choice to optimize the matrix strength of SFRC segments [104]. At the same time, the latest research [115] shows that, as a low-carbon cementitious material, engineering muck (EM)-based polymer can not only further improve the matrix reaction efficiency and compactness through particle size optimization but also reduce 60–69% of CO₂ emissions and 18–36% of energy consumption, highlighting its potential in the application of sustainable SFRC segments.

5.2. Steel Fibers

5.2.1. Steel Fiber Type

The types of steel fibers are the key factors affecting the mechanical performance of SFRC segments. With excellent thermal compatibility, long service life, and high temperature corrosion resistance, stainless steel fibers are widely used in building structures with strict requirements for fire resistance [116]. When steel fibers with elastic modulus significantly higher than that of concrete matrix are used, the creep of concrete can be effectively inhibited. For example, adding 2% (volume fraction) of steel fibers can reduce the creep by 25.1% compared with plain concrete [117].

To systematically analyze the influence laws of steel fiber types, SFRC beams are often taken as the research object for tests. The acoustic emission monitoring in the four-point bending tests shows that the number of acoustic emission events, shear cracks, and scattering points generated by the end-hook steel fiber specimens are the most significant, and its comprehensive performance in improving the shear bearing capacity, inhibiting crack propagation and controlling deformation is better than that of corrugated and straight steel fibers [45,111,118]. The double fiber pull-out tests further verified that the end-hook steel fibers have higher pull-out work and bond strengths than the straight steel fibers by virtue of their end anchoring effects [119,120]. It is worth noting that the corrugated steel fibers have particularly prominent effects on improving the tensile performance of concrete due to the mechanical bite effects of the interface enhanced by the surface corrugated structures [110].

The comprehensive analysis shows that the current research is increasingly focused on the configuration optimization and application exploration of profiled steel fibers. For example, by integrating the anchoring advantages of the end-hook steel fibers and the surface bite characteristics of the corrugated steel fibers, building a synergistic reinforced hybrid steel fiber system will become an important research direction to improve the mechanical performance and engineering applicability of SFRC segments.

5.2.2. Steel Fiber Dosage

The steel fiber dosage has an important influence on the mechanical performance of SFRC segments. Research shows that the dosage of steel fiber is positively correlated with the peak load after cracking, toughness index, secant modulus, and ultimate bearing capacity [96,121]. With the increase in the dosage, the contribution of steel fiber bridging to the bearing capacity becomes more and more significant, which is particularly obvious in the post-peak stage of the load–displacement curve [122]. Especially under the condition of large deformation, the toughening effect of steel fiber is more prominent [123].

However, excessive steel fiber dosage (volume dosage more than 1.5%) will significantly reduce the workability of fresh concrete and cause steel fiber agglomeration. This effect is particularly significant when using straight steel fibers, which will ultimately weaken the reinforcement and toughening effects of steel fibers [106,112,124]. The study also found that the optimal steel fiber dosage has strain rate sensitivity: with the increase in strain rate, the optimal volume dosage gradually decreases from 2.0%, and when the volume dosage is 1.0%, the steel fiber–matrix interface bonding performance reaches the optimum [125,126]. Based on the evaluation of bending toughness, Zhou et al. [127] determined that the optimal steel fiber dosage was about 36 kg/m³ through the established linear relationship (Equation (6)), which was highly consistent with the 35.5 kg/m³ proposed by Zhao et al. [128].

y = −0.000147 x³ + 0.0142 x² − 0.421333 x + 4.64

(6)

where y is the bending toughness ratio of the SFRC notched beam. x is the steel fiber dosage.

In conclusion, although increasing the dosage of steel fibers can significantly improve the bending performance and crack resistance of segments, there is a clear upper limit for its dosage. For unreinforced SFRC segments, the optimal fiber dosage range is 35.5 kg/m³ to 36 kg/m³. However, for R-SFRC segments, when the synergistic effects of steel rebars and steel fibers need to be comprehensively considered, how to determine the optimal ratio between reinforcement ratio and steel fiber dosage still lacks a unified conclusion, which needs further discussion.

5.2.3. Steel Fiber Aspect Ratio

As one of the important characteristic parameters, the steel fiber aspect ratio will also affect the mechanical performance of segments to a certain extent. The finding [44] show that shorter steel fibers contribute to the formation of multiple microcracks and exhibit strain hardening characteristics, but lead to a significant decrease in the post-peak bearing capacity. The longer steel fibers can provide more stable post-peak softening response and smoother bearing capacity attenuation process. In addition, increasing the steel fiber aspect ratio can effectively inhibit the autogenous shrinkage and total shrinkage of concrete so as to reduce the risk of cracking and improve the flexural strength [129].

Similarly to the steel fiber dosage, the steel fiber aspect ratio has an optimal range based on the matrix strength. After exceeding the critical value, increasing the aspect ratio can only improve the ductility of the material, but it has limited effect on the strength and elastic modulus of the material [130,131]. Liu et al. [132] determined through systematic research that the optimal steel fiber aspect ratio is 50. At this time, the bond strength between steel fibers and matrix interface reaches the peak, which can effectively inhibit the crack initiation and propagation of segments.

In summary, from the perspective of material composition, the mechanical performance of SFRC segments is the result of the synergistic effect of matrix strength and steel fiber characteristics, and there is a clear hierarchical relationship between various parameters. Among them, the strength of the matrix constitutes a prerequisite for steel fibers to exhibit reinforcement and toughening effects [103,107,108]. In the steel fiber parameter system, although the steel fiber dosage has a significant regulatory effect on mechanical performance, the type, and aspect ratio of steel fibers have a more critical impact on the efficiency of improving material properties through dominant load transfer mechanisms (end anchoring or surface biting) [45,110,118] and post-crack response behavior [44]. It is worth noting that there is a clear optimal range for the steel fiber dosage [127,128], and exceeding this range will cause steel fiber agglomeration, which will weaken its reinforcement effect [106,112]. Based on this, the priority order of the impact of various influencing factors on the mechanical performance of SFRC segments can be established as follows: matrix strength > steel fiber type > steel fiber aspect ratio > steel fiber dosage. This priority order provides a key basis for the material mix design and mechanical performance optimization of SFRC segments. Future research should focus on revealing the collaborative working mechanism between steel rebars and steel fibers with different characteristics in R-SFRC segments, in order to establish more accurate composite reinforcement design criteria [96].

6. Conclusions and Future Research Trends

6.1. Conclusions

This paper systematically reviews the mechanical performance and design methods of SFRC segments, and the main conclusions are as follows:

(1)

Experiments, numerical simulations, and artificial intelligence methods each have their own advantages and complement each other. The combination of advanced monitoring technologies such as DIC and AE in experiments can accurately capture the mechanisms of segment damage. Numerical methods are suitable for simulating multiple working conditions such as material nonlinearity and crack propagation, with both economy and flexibility. AI methods have achieved efficient and high-precision performance prediction and material design. The collaboration of the three has constructed a systematic research system from micro mechanisms to macro performance.

(2)

Compared with traditional RC segments, SFRC segments (especially R-SFRC segments) change their failure mode from brittle shear to ductile bending under the synergistic effect of steel rebars and steel fibers, significantly improving their bearing capacity, deformation capacity, and energy dissipation performance. The failure of the full-ring segments follows the three-stage evolution law of “elastic stage local plastic hinge formation overall mechanism development”. The bridging effect of steel fibers effectively suppresses the development of crack width and promotes the transformation of crack morphology from a single main crack to a distributed microcrack system.

(3)

Among the existing design methods, the coefficient correction method based on specifications (e.g., JGJ/T 465-2019) is simple to calculate but tends to be conservative. The mechanical modeling method based on material constitutive theory (e.g., Model Code 2010) is theoretically rigorous and can better reflect the contribution of steel fibers after cracking, but the parameters are complex and the computational cost is high. The current core challenge is how to develop a practical design model that integrates the random distribution of steel fibers and bridging effects while ensuring accuracy.

(4)

Matrix strength and steel fiber characteristics (type, dosage, aspect ratio) jointly affect the mechanical performance of SFRC segments, with the order of influence being matrix strength > steel fiber type > steel fiber aspect ratio > steel fiber dosage. The end-hook and corrugated steel fibers exhibit excellent performance in shear resistance, crack control, and toughening. There is a reasonable range for the dosage and aspect ratio, and excessive dosage can easily lead to steel fiber aggregation and weaken the reinforcement effect.

6.2. Future Research Trends

With the continuous development of urban rail transit, the advantages of speed, safety, and convenience have made the application of the shield tunneling method increasingly widespread. It can be foreseen that in order to alleviate the enormous pressure faced by urban ground traffic congestion, a large number of urban subway tunnels will be constructed in the future. The complexity and diversity of structural cross-section forms, as well as the complexity of geological conditions and engineering overview, will be a major challenge for future tunnel construction. Although SFRC segments have not been widely used, their engineering application potential deserves further exploration. Future research and practice should focus on the following key areas:

(1)

Research on corrosion resistance and high durability of SFRC segments should be systematically advanced. SFRC segments exhibit better chloride and carbonation resistance than ordinary RC segments in an uncracked state, thanks to the inhibitory effect of three-dimensional discrete distribution of steel fibers on macroscopic battery corrosion, as well as the higher critical chloride ion threshold given to them by cold drawing process [133]. Experimental studies [134] have shown that even when high concentration NaCl solutions (such as 9%) are used during the preparation process, SFRC specimens can still maintain their basic mechanical and corrosion resistance performance. The recent research [135] on the performance of steel fiber reinforced materials in corrosive environments also provides a reference for the long-term performance evaluation of SFRC segments in harsh environments. In the future, the long-term performance of SFRC segments in corrosive environments should be systematically evaluated to promote their application in tunnel engineering in highly corrosive formations.

(2)

SFRC-based repair and reinforcement technology for existing tunnel segments warrants focused development. SFRC materials have good crack control and toughness recovery capabilities, making them suitable for the repair and reinforcement of existing tunnel segments. Research has shown that using steel fiber reinforced cement-based materials to reinforce concrete components can effectively change their failure modes and significantly improve their bearing capacity [136]. The advantages of fiber-reinforced self-compacting concrete in terms of repair layer performance and interface bonding [137] also provide technical references for the application of SFRC materials in segment repair. In the future, the focus should be on studying the interface behavior, collaborative working mechanism, and long-term service performance between SFRC repair materials and existing concrete segments, and developing SFRC materials and construction processes suitable for tunnel segment repair.

(3)

Intelligent design and performance prediction methods for SFRC segments need to be established. Machine learning and artificial intelligence technologies provide a new approach for the refined design and performance prediction of SFRC segments. At present, AI methods such as artificial neural networks and deep learning have demonstrated advantages in SFRC material design, performance prediction, and damage identification [65,66,67,69]. In particular, the intelligent recognition technology based on sound signals and visual data [66,69] provides innovative solutions for non-destructive testing and performance evaluation of SFRC segments. In the future, an intelligent design system specifically designed for SFRC segments should be developed, and a performance prediction model that integrates multi-scale mechanisms should be established to accurately predict the long-term behavior of SFRC segments under complex load and environmental coupling effects, promoting the development of SFRC segments segment design towards intelligence and refinement.