Effects of Steel Fiber Content on Compressive Properties and Constitutive Relation of Ultra-High Performance Shotcrete (UHPSC)

Abstract

Shotcrete is widely used in civil engineering as a supporting structure. In this paper, the compressive behavior of ultra-high-performance shotcrete (UHPSC) with different steel fiber content by volume (0, 0.5%, 0.75%, 1%, 1.25%, 1.5%) was investigated. The results showed that the failure pattern of UHPSC was changed from brittle failure to ductile failure with the increase in steel fiber content. The compressive strength, peak strain and compressive toughness of UHPSC increased with the increase in steel fiber content, but the elastic modulus and Poisson’s ratio did not change significantly. With content of 1.5% steel fibers, its axial compressive strength, peak strain and compressive strain energy were 122.7 MPa, 3749 με and 0.269 MPa, respectively, increased by 14%, 23.5% and 55.5% compared with those without steel fiber. The peak strain and compressive toughness were higher than that of ultra-high-performance concrete (UHPC), while the elastic modulus of UHPSC was lower than that of UHPC. Based on the experimental data, the relationship between compressive strength, peak strain, compressive toughness and the change in the characteristic value of steel fiber content (λ_f) were revealed. The uniaxial compressive constitutive model of UHPSC with different steel fiber content was established and reflected the change rule of the shape parameter of α (constitutive model ascending section) and β (constitutive model descending section) with λ_f. The experimental results were in good agreement with the model calculation results, which can provide theoretical support for the structural design of UHPSC.

1. Introduction

Shotcrete is conveyed under pressure through a pneumatic hose or pipe and applied to the target surface by spraying it at high speed [1]. It has the advantages of simple process, good bonding performance, efficient construction, economic cost and strong adaptability, and has been widely used in underground engineering, water conservancy engineering, slope support, tunnel engineering, restoration and reinforcement engineering and other fields [2,3,4,5,6]. Shotcrete can be directly formed based on the spray surface, so belongs to the category of additive manufacturing (AM) technology and is also a kind of 3D-printing concrete molding technology [7,8,9]. Therefore, shotcrete has a broad prospect of application.

In the construction process of shotcrete, it is often necessary to add a certain amount of accelerator to accelerate the concrete setting and hardening [10,11]. However, the existing research results show that the accelerators inevitably change the microstructure of cement-based materials and increase porosity [12,13,14]. The accelerators improve the early strength of concrete, but the later strength is lower than that of the poured concrete with the same ratio, and there is later strength loss and shrinkage [13,14,15,16,17]. In order to improve the performance of shotcrete, steel fibers are applied to shotcrete, forming steel fiber-reinforced shotcrete. In recent years, with the development of ultra-high-performance concrete (UHPC), some scholars have begun to carry out research on ultra-high-performance shotcrete (UHPSC). Takeda H et al. developed a new bonding material and developed a wet-sprayed ultra-high strength shotcrete with a 28-day compressive strength of 95 MPa [5]. Cui et al. [18,19,20] developed a UHPSC with suitable sprayed thickness due to the addition of a viscosity-enhancing agent based on the designed UHPC, and its compressive strength was 109.2 MPa.

By adjusting the type and content of the accelerator, water-reducing agent and steel fiber based on the designed UHPC, UHPSC with suitable spray-forming thickness is formed [20]. It has the high compressive strength, durability and toughness of UHPC [21,22]. UHPSC is mainly used in compressive components, and its compressive performance and compressive constitutive relationship are very important and are the basis of component design, calculation and finite element analysis. Some scholars have carried out some research on the constitutive relationship of shotcrete. Yang et al. [23] conducted an experimental study on the stress–strain curve of carbon nano-tube shotcrete under uniaxial compression and determined the constitutive relationship of carbon nanotube shotcrete. Guan et al. [24] established a three-parameter Weibull distribution statistical damage constitutive equation by analyzing the stress–strain test curves of ordinary concrete and shotcrete under uniaxial compression. Bai et al. [25] used the positioning results of acoustic emission (AE) specimens to quantitatively analyze the relationship between damage variables and strain and established a constitutive model of damage variables of dry and wet shotcrete. Wang et al. [26] used the accelerating freeze–thaw method to study the uniaxial compression stress–strain curve. The stress–strain curve of specimens under damage was calculated by fitting the relationship between parameters and the number of freeze–thaw cycles. Based on the damage mechanics theory, a segmental damage constitutive model was established, which defined the elastic modulus as the damage variable and considered the loading rate [27]. These studies were aimed at ordinary shotcrete with a strength lower than C50, and there are few studies on the constitutive relationship of UHPSC.

Recently, many scholars have carried out research on the influence of steel fiber type, content [28,29,30,31,32,33], curing condition [34] and water-binder ratio [35,36] on the compressive stress–strain relationship of UHPC, and proposed various forms of uniaxial compressive constitutive equations. Wakjira et al. [37,38,39] used advanced machine learning and multi-objective optimization techniques to establish a prediction model for compressive stress–strain constitutive modeling of confined UHPC, which provided a new and effective way to study the stress–strain relationship of UHPSC. However, in the process of spraying, steel fiber can easily cause pipe blockage. When the steel fiber content is greater than 1.5% (by volume), the pipe blockage is serious, even meaning it is unable to be constructed. Therefore, the steel fiber content of UHPSC is generally within 1.5% [19]. However, the steel fiber content of UHPC is generally greater than 1.5% [40]. In addition, most of the steel fibers in the steel fiber reinforced shotcrete were basically parallel to the shotcrete surface and approximately distributed in two dimensions [41,42], while the steel fibers in the poured UHPC were approximately three-dimensional random uniform distribution. The orientation of steel fiber has a significant effect on the mechanical properties of concrete [43]. So, whether the research results of UHPC are suitable for UHPSC needs to be verified by experiments.

In this paper, uniaxial compression tests of UHPSC under different steel fiber contents were carried out to reveal the variation rules of compressive strength, peak strain, elastic modulus, compressive toughness and stress–strain relationship of UHPSC, and the constitutive model of UHPSC was constructed. The results of the study can provide a theoretical basis for the engineering application of UHPSC.

2. Materials and Methods

2.1. Materials and Mix of UHPSC

The cement used in UHPSC was P•‖52.5 Shuangfeng-Hailuo Portland cement and complied with the Chinese Standards GB175-2007 [44]. The mineral admixture was silica fume (SF) and fly ash (FA). Quartz sand (QS) with a maximum particle size of 4.75 mm was used as fine aggregate, and there was no coarse aggregate. The aggregate grading curve is shown in Figure 1. The particle size was divided according to the Chinese standard JG/T 568-2019 [45]. A polycarboxylic acid-based superplasticizer was used. A Viscosity-Enhancing agent (VE) [18] was added in order to improve the bonding strength during spraying. Straight steel fibers with a tensile strength of 2000 MPa were used. They have a length of 13 mm and a diameter of 0.2 mm. The mix proportion is shown in

Table 1. Mix proportion of ultra-high-performance shotcrete (UHPSC).

No.	Steel Fiber (%)	Water	Cement	SF	FA	QS	Superplasticizer	VE
SC	0	0.295	1.0	0.128	0.103	1.282	0.005	0.077
FSC0.5	0.5	0.295	1.0	0.128	0.103	1.266	0.005	0.077
FSC0.75	0.75	0.295	1.0	0.128	0.103	1.259	0.005	0.077
FSC1.0	1.0	0.295	1.0	0.128	0.103	1.251	0.005	0.077
FSC1.25	1.25	0.295	1.0	0.128	0.103	1.243	0.005	0.077
FSC1.5	1.5	0.295	1.0	0.128	0.103	1.235	0.005	0.077

Notes: steel fiber was the volume ratio, and the others were the weight relative to the cement.

.

2.2. Preparation of Concrete Specimens

The UHPSC specimens used in this paper were prepared in accordance with Chinese standard JGJ/T 372-2016 [1]. The size of the formworks was 450 mm × 450 mm × 120 mm. The distance between the nozzle and the sprayed surface ranged from 0.6 m to 1.0 m, and the angle between the formwork and the ground was about 80°. After 1 day of sprinkling water curing, the slabs were demolded from the formworks and moved to the standard curing room (20 ± 2 °C and 95% humidity) for 7 days. Lastly, the UHPSC slabs were cut into cubes of 100 × 100 × 100 mm³ and prisms of 100 × 100 × 300 mm³ by a cutting machine, and then the specimens were continued to be cured under standard curing conditions until 28 days of age.

2.3. Mechanical Property Test

The cube compressive strength was performed with cube specimens (100 × 100 × 100 mm³) at 28 days under a loading rate of 1.0 MPa/s conforming to Chinese Standard JGJ/T 372-2016 [1]. The loading direction should be perpendicular to the spray-forming direction of the large plate.

The axial compression test was performed with prism specimens (100 × 100 × 300 mm³) at 28 days conforming to Chinese Standard CECS13-2009 [46]. Firstly, the loading speed of force control was 0.5 MPa/s. When the stress reached about 100 MPa, it was adjusted to displacement control, 0.2 mm/min. To measure the transverse and longitudinal deformation of the specimen during axial compression, 2 transverse strain gauges were pasted on different surfaces in the middle of the specimen, and a longitudinal deformation measurement bracket with two displacement sensors was installed in the middle of the specimen (the calibration distance was 200 mm). An auxiliary rigid frame was designed to improve the stiffness of the testing machine. A spherical hinge was installed at the lower part of the specimen to make the specimen in the axial compression state to the greatest extent. Figure 2 illustrates the schematic of the stress–strain test.

3. Results and Discussion

3.1. Failure Pattern

The failure pattern of the cube specimens without steel fiber (SC) was similar to the ordinary concrete cube specimen, showing a typical “pyramid” shape, but the appearance was severely damaged, as shown in Figure 3a. For the cubic specimens with steel fibers (FSC), the occurrence and development of concrete cracks were hindered by the bridging effect of steel fibers at the cracks [32]. It finally showed the failure pattern of multiple oblique cracks, and the main crack was arc shaped. The failure surface was perpendicular to the spraying direction. The concrete shape between the failure surface was similar to “wedge” shape, but the test block was not broken in the end, showing a complete form of “crack but not broken”.

The final failure pattern of the prism is shown in Figure 3b. With the increase in steel fiber content, the number of cracks became less, but the width tended to increase. The critical failure surfaces were all perpendicular to the spraying direction. The reason for this phenomenon may be the quasi-two-dimensional distribution of steel fibers in shotcrete [42]. For the prismatic specimens without steel fiber (SC), when the vertical pressure reached the peak, the failure occurred very soon, accompanied by a loud explosion sound, and the specimen fragments scattered around. After collecting and assembling the main fragments, it was found that there was an obvious vertical main crack, which belonged to the typical splitting failure and had a brittle failure feature. For the prism specimens containing steel fiber (FSC), when the vertical pressure was close to the peak, it made a “sizzle” sound. After the peak, it changed to a continuous “crackling” sound, and then a loud “boom” sound, and the specimen was damaged. A small amount of debris was scattered around the specimen. The shape of the specimen was complete, which belonged to ductile failure, and the specimen was penetrated by a main oblique crack to form a critical failure surface. It was a typical shear slip failure.

3.2. Compressive Strength

Figure 4a shows the cubic compressive strength f_cu and the axial compressive strength f_c of the UHPSC with different steel fiber contents. It can be seen that with the increase in steel fiber content, the cubic compressive strength and the axial compressive strength both tended to increase, and the axial compressive strength increased more obviously. Compared with the group without steel fiber, the cubic compressive strength of the group with 1.5% steel fiber was increased by 1.09 times, and the axial compressive strength was increased by 1.14 times. The ratio of cubic compressive strength to axial compressive strength was between 0.841 and 0.911, which was close to that of UHPC (0.88) [40], but higher than that of ordinary concrete (0.76 to 0.82) [47]. In addition, the ratio increased first and then decreased, and reached the maximum value of 0.911 when the steel fiber content was 1%.

In this paper, to study the influence of steel fiber content on the strength of concrete, the characteristic value of steel fiber content ${\lambda }_{\mathrm{f}}={\rho }_{\mathrm{f}}{l}_{\mathrm{f}}/d_{\mathrm{f}}$ in the Chinese Standards JGJ/T 465-2019 [48] was used as the independent variable, which comprehensively considered the length (l_f), diameter (d_f) and volume ratio (ρ_f) of steel fiber. Figure 4b shows the ratio of the compressive strength f_cu,λ (f_c,λ) at different fiber contents to the compressive strength f_cu,0 (f_c,0) without fiber. The growth rate of cubic compressive strength and axial compressive strength of UHPSC were lower than that of UHPC [32]. The main reason was that most of the steel fibers in the shotcrete were basically parallel to the sprayed surface, showing quasi-two-dimensional distribution, while the steel fibers in the poured UHPC were approximately three-dimensional random uniform distribution. By fitting the data, the relationship between the compressive strength of UHPSC and the characteristic value of steel fiber content was obtained, and the fitting formula was as follows:

$$\frac{f_{\mathrm{cu},\mathsf{\lambda }}}{f_{\mathrm{cu},0}}=1.0+0.054{\lambda }_{\mathrm{f}}+0.040{{\lambda }_{\mathrm{f}}}^2{\mathrm{R}}^2=0.9855$$

(1)

$$\frac{f_{\mathrm{c},\mathsf{\lambda }}}{f_{\mathrm{c},0}}=1.0+0.155{\lambda }_{\mathrm{f}}{\mathrm{R}}^2=0.9698$$

(2)

3.3. Peak Strain

Figure 5 showed the uniaxial compressive stress–strain curves of UHPSC prismatic specimens with different fiber contents, where A, B and C represented the three specimens of each group. Under axial load, the strain corresponding to the peak stress was called peak strain ε_c, which gradually increased with the increase in fiber content, as shown in Figure 6. Its value was significantly higher than the recommended value of 2779–2895 × 10⁻⁶ε in the relevant standards of UHPC [40,49]. The peak strain of UHPSC without steel fiber was 3035 × 10⁻⁶ε. When the fiber content increased from 0.5% to 1.5%, the peak strain increased by 11.3%, 16.9%, 19.1%, 20.3% and 23.5%, respectively. The increasing trend of peak strain was similar to that of UHPC [33]. Because the distribution of steel fibers in shotcrete was quasi-two-dimensional, similar to the compressive strength, the growth rate was lower than that of UHPC. At the same time, due to the influence of the spraying process, the higher the steel fiber content was, the easier it was to agglomerate, the steel fiber reinforcement would be weakened, and the peak strain may have a maximum value and then decrease. By fitting the test data, the relationship between the peak strain and the characteristic value of steel fiber content was obtained, and the formula was as follows:

$$\frac{{\epsilon }_{\mathrm{c},\mathsf{\lambda }}}{{\epsilon }_{\mathrm{c},0}}=1.0+0.418{\lambda }_{\mathrm{f}}-0.189{{\lambda }_{\mathrm{f}}}^2 {\mathrm{R}}^2=0.9896$$

(3)

where ε_c,λ was the peak strain under the characteristic value of fiber content and ε_c,0 was peak strain without fibers.

3.4. Elastic Modulus and Poisson’s Ratio

The elastic modulus E_c and Poisson’s ratio ν_c are the key indexes for the evaluation of material deformation properties. The elastic modulus of the specimen in this paper was taken as the secant modulus corresponding to the stress of 0.5 times the axial compressive strength [50], and the ratio of the corresponding lateral strain to the vertical strain was ν_c. The results of the elastic modulus and Poisson ratio are shown in Figure 7. The Poisson’s ratio had no obvious change with different steel fiber content, and the distribution was between 0.204 and 0.217. It was close to the Poisson’s ratio of ordinary concrete and UHPC. Without steel fiber, the elastic modulus of UHPSC was 3.846 × 10⁴ MPa. When the fiber content increased from 0.5% to 1.5%, the elastic modulus increased by 0.3%, 0.5%, 1.2%, 2.8% and 3.3%, respectively. It indicated that the steel fiber has little effect on the elastic modulus. But the elastic modulus of UHPSC was significantly lower than the recommended value of 4.2–4.5 × 10⁴ MPa in the relevant standards of UHPSC [40,49].

3.5. Compressive Toughness

The toughness of a material is closely related to the deformation and energy dissipation of its components and structures. This study assessed the toughness of UHPSC by analyzing the peak strain point [32,51]. The compressive strain energy W_c was defined as the total mechanical energy consumed per unit volume of UHPSC from loading to the peak strain ε_c using Formula (4). The larger W_c, the more energy dissipation capacity. The compressive toughness index R_e was calculated as the compressive strain energy divided by the product of peak strain ε_c and peak stress σ_c, which is shown in Formula (5). The higher the compressive ductility index, the stronger the relative energy dissipation capacity of the material.

$$W_{\mathrm{c}}={\int }_0^{{\epsilon }_{\mathrm{c}}}\mathsf{\sigma }\mathrm{d}\mathsf{\epsilon }$$

(4)

$$R_{\mathrm{e}}=W_{\mathrm{c}}/({\sigma }_{\mathrm{c}}{\epsilon }_{\mathrm{c}})$$

(5)

Table 2. Characterization of compressive toughness of UHPSC.

No.	λf	Wc (MPa)		Re		Wc,λ/Wc,0	Re,λ/Re,0
		Result	Average	Result	Average
SC-A	0	0.158	0.173	0.528	0.529	1.000	1.000
SC-B		0.180		0.533
SC-C		0.181		0.527
FSC0.5-A	0.325	0.195	0.195 *	0.540	0.548	1.127	1.035
FSC0.5-B		0.242		0.560
FSC0.5-C		0.188		0.544
FSC0.75-A	0.4875	0.245	0.227	0.587	0.557	1.310	1.052
FSC0.75-B		0.210		0.545
FSC0.75-C		0.225		0.538
FSC1.0-A	0.65	0.226	0.249	0.556	0.567	1.439	1.071
FSC1.0-B		0.277		0.558
FSC1.0-C		0.244		0.586
FSC1.25-A	0.8125	0.239	0.256	0.613	0.580	1.480	1.095
FSC1.25-B		0.281		0.568
FSC1.25-C		0.248		0.558
FSC1.5-A	0.975	0.240	0.259 *	0.594	0.584	1.497	1.103
FSC1.5-B		0.308		0.586
FSC1.5-C		0.259		0.571

* Note: when the difference between one of the maximum or minimum values and the middle value exceeds 15% of the middle value, the maximum and minimum values should be removed and the middle value should be taken.

shows the relationship between the compression energy dissipation and the characteristic value of steel fiber content. It can be seen that with the increase in the characteristic value of fiber content, the compression energy dissipation and compression ductility index of UPHSC were increasing. When the characteristic value of fiber content increased from 0.325 to 0.975, the compressive strain energy of UPHSC increases by 12.7%, 31.0%, 43.9%, 48.0% and 49.7%, respectively, compared to the without fiber specimens. The compression toughness index of UPHSC increased by 3.5%, 5.2%, 7.1%, 9.5% and 10.3% respectively. The compression energy dissipation and compression ductility index were higher, but the growth rate was lower, compared with UHPC [32]. By fitting the data, the relationship between the compressive strain energy and compression toughness index and the characteristic value of steel fiber content were obtained, and the formula is as follows:

$$\frac{W_{\mathrm{c},\mathsf{\lambda }}}{W_{\mathrm{c},0}}=1.0+0.685{\lambda }_{\mathrm{f}}-0.146{{\lambda }_{\mathrm{f}}}^2 {\mathrm{R}}^2=0.9884$$

(6)

$$\frac{R_{\mathrm{e},\mathsf{\lambda }}}{R_{\mathrm{e},0}}=1.0+0.110{\lambda }_{\mathrm{f}} {\mathrm{R}}^2=0.9982$$

(7)

where W_c,λ, R_e,λ were the compressive strain energy and compression toughness index under the characteristic value of fiber content. W_c,0 and R_e,0 were the compressive strain energy and compression toughness index without fibers.

3.6. Uniaxial Compressive Constitutive Model

The mathematical model of the constitutive relationship of ordinary concrete has been perfected, and many scholars have recently carried out relevant research on the constitutive relationship of UHPC. However, there are few studies on the constitutive relationship of UHPSC, especially on the constitutive relationship of concrete with low fiber content under uniaxial compression. Therefore, the constitutive model suitable for UHPSC would be constructed by referring to the constitutive model suggested in the concrete structure design code [47]. The formula is as follows:

$$\frac{\sigma }{f_{\mathrm{c}}}=\left\{\begin{array}{ll}\frac{\alpha (\epsilon /{\epsilon }_{\mathrm{c}})}{\alpha -1+{(\epsilon /{\epsilon }_{\mathrm{c}})}^{\alpha }}& \epsilon /{\epsilon }_{\mathrm{c}}\le 1\\ \frac{\epsilon /{\epsilon }_{\mathrm{c}}}{\beta {(\epsilon /{\epsilon }_{\mathrm{c}}-1)}^2+\epsilon /{\epsilon }_{\mathrm{c}}}& \epsilon /{\epsilon }_{\mathrm{c}}>1\end{array}\right.$$

(8)

$$x=\frac{\epsilon }{{\epsilon }_{\mathrm{c}}};y=\frac{\sigma }{f_{\mathrm{c}}}$$

(9)

$$y=\left\{\begin{array}{cc}\frac{\alpha x}{\alpha -1+x^{\alpha }}\hfill & \hfill 0\le x\le 1\\ \frac{x}{\beta {(x-1)}^2+x}\hfill & \hfill x>1\end{array}\right.$$

(10)

where σ and ε are the stress and strain of UHPSC, respectively, f_c and ε_c are the peak stress and corresponding strain value of UHPSC under uniaxial compression, α is the shape parameter of the model’s ascending section and β is the shape parameter of the model’s descending section.

The derivative of x = 0 is obtained by taking the first-order derivative of the model’s ascending section in Equations (8) and (9), and the calculation is as follows:

$${\left.\frac{\mathrm{d}y}{\mathrm{d}x}\right|}_{x=0}={\left.\frac{\mathrm{d}\sigma /f_{\mathrm{c}}}{\mathrm{d}\epsilon /{\epsilon }_{\mathrm{c}}}\right|}_{x=0}=\frac{{\left.\mathrm{d}\sigma /\mathrm{d}\epsilon \right|}_{x=0}}{f_{\mathrm{c}}/{\epsilon }_{\mathrm{c}}}=\frac{E_0}{E_{\mathrm{P}}}=\frac{\alpha }{\alpha -1}$$

(11)

where E₀ is the initial elastic modulus and E_p is the peak secant modulus. The parameter α has a clear physical meaning, and the larger its value is, the closer the material initial modulus is to the peak secant modulus.

In the above formula, only α and β are the parameters to be determined. In order to study the influence of steel fiber content on the compressive stress–strain curve of UHPSC, the characteristic value of steel fiber content was introduced into the shape parameters of the model. The stress–strain curves in Figure 8 were normalized and then the shape parameters at the corresponding characteristic value of steel fiber content were calculated by fitting. The corresponding parameters were summarized in

Table 3. Fitting parameters of α and β.

No.	λf	α	β
SC	0	19.92	15.08
FSC0.5	0.325	9.44	8.24
FSC0.75	0.4875	9.04	5.44
FSC1.0	0.65	6.47	4.29
FSC1.25	0.8125	6.68	3.61
FSC1.5	0.975	7.03	3.45

. Under different characteristic values of steel fiber content, the range of the shape parameter α in the ascending section was 6.68 ≤ α ≤ 19.92, and the range of the shape parameter β in the descending section was 3.45 ≤ β ≤ 15.08. Then, the relationship between α and β with the characteristic value of steel fiber content was obtained by regression analysis, and the specific formula was as follows:

$$\left\{\begin{array}{cc}\alpha =17.53-25.82{\lambda }_{\mathrm{f}}+15.72{{\lambda }_{\mathrm{f}}}^2& {\mathrm{R}}^2=0.9333\\ \beta =15.09-26.50{\lambda }_{\mathrm{f}}+15.01{{\lambda }_{\mathrm{f}}}^2& {\mathrm{R}}^2=0.8975\end{array}\right.$$

(12)

According to Figure 8 and the fitting results of Equation (12), within the scope of this study, the parameters α and β, first decreased rapidly, then decreased slowly, and finally increased slightly, but the amplitude was very small, and the overall trend was decreasing. Without steel fiber, the values of parameters α and β were large, and the straight segment of the ascending section of the stress–strain curve was long. After reaching the peak stress, the specimen quickly failed and the curve dropped sharply. With the increase in steel fiber, the deformation ability of the material was strengthened, and the yield phenomenon was obvious before and after the peak stress, especially since the decline of the curve became more gradual.

The α and β obtained from Equation (12) were substituted into Equation (10), and the stress–strain curves under different steel fiber content were obtained after finishing. The calculated stress–strain curves of UHPSC under uniaxial compression were compared with those measured in the test, as shown in Figure 8. It can be seen that the constitutive model of UHPSC constructed in this paper can better reflect the development process of stress and strain of the specimen under uniaxial stress state, which was in good agreement with the test results. Due to the influence of complex factors such as test method, equipment and specimen construction deviation, the fitting results of the descending section of the model were not as good as that of the ascending section. Compared with UHPC [32], the variation of the stress–strain curve of UHPSC in the ascending section was similar, but the difference of the descending section was relatively large. The decrease rate of UHPC was significantly greater than that of UHPSC. This may be related to the distribution direction of steel fiber in UHPSC, which needs further study.

4. Conclusions

UHPC has been widely concerned because of its ultra-high mechanical properties and durability, but there are few studies on UHPSC, especially on the constitutive relationship of UHPSC. However, the constitutive model is very important for the modeling and design of UHPSC. Around this problem, 6 groups of 18 cubic specimens and 18 prismatic specimens were used to study the compressive behavior of UHPSC with different steel fiber content. The following conclusions can be drawn:

(1)

Before the failure of UHPSC without steel fiber, there was no obvious sign, which belonged to brittle failure. The failure pattern of UHPSC with steel fibers showed the ductile failure characteristics of multiple oblique cracks, showing a complete form of “crack but not broken”. The critical failure surfaces of the prism were all perpendicular to the spraying direction.

(2)

The compressive strength, peak strain, and compressive toughness of UHPSC increased with the increase in steel fiber content, but the elastic modulus and Poisson’s ratio did not change significantly. With content of 1.5% steel fibers, its axial compressive strength, peak strain and compressive strain energy were 122.7 MPa, 3749 με and 0.269 MPa, respectively, increased by 14%, 23.5% and 55.5% compared with those without steel fiber.

(3)

The peak strain and compressive toughness were higher than that of UHPC, while the elastic modulus of UHPSC was lower than that of UHPC. Based on the experimental data, the relationship between compressive strength, peak strain, compressive toughness and the change in the characteristic value of steel fiber content (λ_f) were revealed.

(4)

Based on the experimental results, the uniaxial compressive constitutive model of UHPSC with different steel fiber content was established, and the variation of the shape coefficients α and β with λ_f was revealed. The experimental results were in good agreement with the model calculation results.

Due to the limitation of the spraying process, the steel fiber content of the UHPSC in this paper does not exceed 1.5%. The increased speed of compressive strength, peak strain and compressive toughness of UHPSC with the increase in steel fiber content is obviously lower than that of UHPC. At the same time, the decline phase of the constitutive model of UHPSC is gentler than that of UHPC. All these require further collection of test data to continuously verify and improve the relevant formulas in this paper. In addition, the steel fiber orientation has a significant effect on the mechanical properties of UHPSC, which needs to be further studied.