Study on Flexural Capacity of UHPC-NC Composite Slab with Reinforced Truss in the Normal Section

Abstract

Ultra-high-performance concrete (UHPC) exhibits significantly higher tensile strength compared to normal concrete (NC). In this paper, the application of UHPC to the precast base plate of composite slabs was proposed, leading to the development of a reinforced truss UHPC-NC composite slab. This approach effectively enhanced the crack resistance of the slab. A finite element model (FEM) for the reinforced truss UHPC-NC composite slab was developed based on the ABAQUS (2016) platform, using appropriate material constitutive relationships for UHPC, NC, and steel reinforcement. The validity of the model was verified through comparison with relevant test results. Subsequently, the effects of parameters such as the cross-sectional area of the upper and lower truss chords, the reinforcement ratio of the precast base plate, the strength grade of the UHPC base plate, and the thickness of the UHPC base plate on the flexural capacity of the UHPC-NC composite slab were investigated. Finally, the equations for calculating the flexural capacity of the UHPC-NC composite slab were proposed. It was found that increasing the cross-sectional area of the lower truss chord improved the flexural capacity and stiffness of such slabs to some extent, though ductility was slightly reduced. On the other hand, increasing the upper chord cross-sectional area had limited impact on the flexural performance. Increasing the reinforcement ratio of the longitudinal reinforcement in the precast base plate significantly enhanced the load-bearing capacity and stiffness but similarly reduced ductility. As the UHPC grade of the precast base plate increased, the cracking load, yield load, and ultimate load of the slab also increased. However, when the UHPC grade exceeded C120, the improvement in flexural capacity became less significant. With an increase in thickness of the precast UHPC base plate, cracking, yield, and ultimate loads also rose, but ductility decreased. When the thickness of UHPC exceeded 60 mm, the increase in flexural capacity became modest. The proposed equations for calculating the flexural capacity of the reinforced truss UHPC-NC composite slab in the normal section agreed well with simulation results, providing theoretical and numerical support for the design and analysis of UHPC-NC composite slabs.

1. Introduction

Composite slabs used in prefabricated structures, consisting of a precast base plate and a cast-in-place layer, are widely applied in the floors of residential, public, and industrial buildings [1]. This construction method, which combines factory production with rapid on-site assembly [2], effectively improves construction efficiency and quality, reduces environmental pollution, and lowers project costs. However, practical challenges persist in the daily use of composite slabs with reinforced trusses. In particular, the relatively low tensile strength of normal concrete (NC) increases the risk of cracking in the slab during regular use, which can lead to durability issues.

Ultra-high-performance concrete (UHPC) is a fiber-reinforced composite material that exhibits exceptional crack resistance, tensile and compressive strength, and improved bonding properties due to the inclusion of steel fibers [3,4]. To address the aforementioned issues, the use of UHPC for the precast base plate was proposed, while NC is employed for the cast-in-place layer, forming a reinforced truss UHPC-NC composite slab, as shown in Figure 1. The exceptional tensile strength of UHPC effectively prevents cracking during transportation and construction. UHPC also enhances the cracking load during regular use, thereby extending the expected service life of the structure [5].

Currently, significant progress has been made in studying the mechanical properties of reinforced UHPC slabs. Meng et al. [6] examined the flexural behavior of FRP-fabric-reinforced UHPC panels, and the findings indicated that FRP reinforcement significantly improves crack resistance and flexural properties, making the composite panels suitable for high-performance permanent formwork. Zeng et al. [7] analyzed the flexural behavior of FRP-grid-reinforced UHPC plates with different fibers and found that polyethylene fibers provide a cost-effective solution, and the FRP grid enhanced flexural strength while preventing load deterioration. Wu et al. [8] investigated the flexural behavior of GFRP grid framework-UHPC composite plates without steel rebar. The results showed significant improvement in flexural capacity and stiffness, with GFRP grids enhancing the cohesion between UHPC and reinforcement. Dogu et al. [9] developed a model to predict the punching shear capacity of post-tensioned UHPC plates, integrating finite element analysis with empirical equations to assess resistance under various conditions. Mészöly et al. [10] found that combining steel fibers and textile reinforcement in UHPC plates markedly improves load-bearing capacity and crack resistance, outperforming plates with single reinforcement.

Due to the high compressive strength of UHPC, the mechanical properties of composite slabs combining precast NC and cast-in-place UHPC have garnered significant attention. Wang et al. [11] investigated the static and fatigue flexural performance of UHPC slabs. The results showed that UHRC significantly enhances the crack resistance and fatigue life of slabs, enabling thinner and lighter bridge decks without compromising structural performance. Sun et al. [12] demonstrated that increasing the UHPC layer thickness and reinforcement ratio significantly enhances the flexural capacity of UHPC-NC composite slabs, with their proposed formula accurately predicting slab strength. Yin et al. [13] conducted an experimental study on RC slabs strengthened with UHPC in various configurations and found that UHPC enhanced ductility and energy absorption, with increased layer thickness shifting the failure mode from brittle shear to ductile flexure. Yan et al. [14] conducted full-scale experimental tests on UHPC-RC composite slab culverts and found that these composite slabs exhibit superior crack resistance, flexural stiffness, and load-bearing capacity compared to traditional RC slabs, demonstrating their feasibility for practical applications. Zhu et al. [15] developed a finite element model to investigate the flexural behavior of damaged RC slabs strengthened with a UHPC layer. The study concluded that accurately modeling the bond strength and existing cracks is crucial for predicting the flexural capacity and optimizing strengthening strategies. Hoang et al. [16] proposed a new method for retrofitting RC slabs using UHPC in the compressive zone and fiber-reinforced polymer (FRP) in the tension zone. The results showed a substantial increase in flexural capacity and reduced deflection, demonstrating the effectiveness of the combined use of UHPC and FRP for strengthening RC structures.

In summary, although research on UHPC applications has extended to UHPC-NC composite slabs, studies on UHPC-NC composite slabs incorporating reinforced trusses remain scarce. Furthermore, most current studies focus on the composite slabs with precast NC and cast-in-place UHPC. However, it is well known that precast NC poses challenges such as difficulties in transportation and installation, susceptibility to leakage at joints, poor seismic performance, and vulnerability to erosion. Using UHPC as the precast base layer and NC as the cast-in-place layer can effectively address these issues.

Moreover, research on the factors influencing the mechanical performance of the proposed composite slabs lacks comprehensiveness and systematic analysis. To address this gap, a finite element model (FEM) for the reinforced truss UHPC-NC composite slab was established and validated through comparison with relevant test results. The effects of various parameters, including the cross-sectional area of the upper and lower truss chords, the reinforcement ratio of the precast base plate, the strength grade of the UHPC base plate, and the thickness of the UHPC base plate, on the flexural performance of the composite slab were investigated. A full-process analysis of the mechanical behavior of the composite slab under loading was conducted. Finally, a formula for calculating the flexural capacity of the reinforced truss UHPC-NC composite slab in the normal section was proposed.

2. Numerical Model of the Cross-Shaped-Steel-Reinforced RPC Column

In this study, the general finite element (FE) software ABAQUS (2016, University of California, Berkeley, CA, the U.S.) was used to establish a numerical model of the reinforced truss UHPC-NC composite slab [17], providing a numerical analysis foundation for calculating the flexural capacity of such composite slabs.

2.1. Constitutive Relationship of Materials

The plastic damage model (concrete damaged plasticity, CDP) provided by ABAQUS was used for both UHPC and NC. The uniaxial compressive stress–strain (σ_Uc − ε_Uc) relationship and the uniaxial tensile stress–strain (σ_Ut − ε_Ut) relationship for UHPC were based on the constitutive model proposed by Zheng [18], as shown in Equations (1) and (2). In these equations, f_Uc and ε_Uc0 represent the uniaxial compressive strength of UHPC and the corresponding strain, while f_Ut and ε_Ut0 represent the uniaxial tensile strength of UHPC and the corresponding strain.

$${\sigma }_{\mathrm{Uc}}/f_{\mathrm{Uc}}=\left\{\begin{array}{ll}1.55\left({\epsilon }_{\mathrm{Uc}}/{\epsilon }_{\mathrm{Uc}0}\right)-1.20{\left({\epsilon }_{\mathrm{Uc}}/{\epsilon }_{\mathrm{Uc}0}\right)}^4+0.65{\left({\epsilon }_{\mathrm{Uc}}/{\epsilon }_{\mathrm{Uc}0}\right)}^5& \hfill 0\le {\epsilon }_{\mathrm{Uc}}/{\epsilon }_{\mathrm{Uc}0}<1\\ \left({\epsilon }_{\mathrm{Uc}}/{\epsilon }_{\mathrm{Uc}0}\right)/\left[6{\left({\epsilon }_{\mathrm{Uc}}/{\epsilon }_{\mathrm{Uc}0}-1\right)}^2+\left({\epsilon }_{\mathrm{Uc}}/{\epsilon }_{\mathrm{Uc}0}\right)\right]& \hfill {\epsilon }_{\mathrm{Uc}}/{\epsilon }_{\mathrm{Uc}0}\ge 1\end{array}\right.$$

(1)

$${\sigma }_{\mathrm{Ut}}/f_{\mathrm{Ut}}=\left\{\begin{array}{ll}1.17\left({\epsilon }_{\mathrm{Ut}}/{\epsilon }_{\mathrm{Ut}0}\right)+0.65{\left({\epsilon }_{\mathrm{Ut}}/{\epsilon }_{\mathrm{Ut}0}\right)}^2-0.83{\left({\epsilon }_{\mathrm{Ut}}/{\epsilon }_{\mathrm{Ut}0}\right)}^3& \hfill 0\le {\epsilon }_{\mathrm{Ut}}/{\epsilon }_{\mathrm{Ut}0}<1\\ \left({\epsilon }_{\mathrm{Ut}}/{\epsilon }_{\mathrm{Ut}0}\right)/\left[5.5{\left({\epsilon }_{\mathrm{Ut}}/{\epsilon }_{\mathrm{Ut}0}-1\right)}^{2.2}+\left({\epsilon }_{\mathrm{Ut}}/{\epsilon }_{\mathrm{Ut}0}\right)\right]& \hfill {\epsilon }_{\mathrm{Ut}}/{\epsilon }_{\mathrm{Ut}0}\ge 1\end{array}\right.$$

(2)

The constitutive model for NC was based on the double-parameter model proposed by Guo [19]. The uniaxial compressive stress–strain (σ_c − ε_c) relationship and the uniaxial tensile stress–strain (σ_t − ε_t) relationship are provided in Equations (3) and (4), where f_c and ε₀ represent the compressive strength of the concrete prism and the corresponding strain, respectively. The parameters α and β denote the coefficients of the ascending and descending branch of the uniaxial compressive curve. f_t and ε_t0 represent the uniaxial tensile strengths of the concrete and the corresponding strain, and γ is the coefficient for the descending branch of the uniaxial tensile curve.

$${\sigma }_{\mathrm{c}}/f_{\mathrm{c}}=\left\{\begin{array}{ll}\alpha \left({\epsilon }_{\mathrm{c}}/{\epsilon }_0\right)+(3-2\alpha ){\left({\epsilon }_{\mathrm{c}}/{\epsilon }_0\right)}^2+(\alpha -2){\left({\epsilon }_{\mathrm{c}}/{\epsilon }_0\right)}^3& {\epsilon }_{\mathrm{c}}<{\epsilon }_0\\ \left({\epsilon }_{\mathrm{c}}/{\epsilon }_0\right)/\left[\beta {\left({\epsilon }_{\mathrm{c}}/{\epsilon }_0-1\right)}^2+\left({\epsilon }_{\mathrm{c}}/{\epsilon }_0\right)\right]& {\epsilon }_{\mathrm{c}}\ge {\epsilon }_0\end{array}\right.$$

(3)

$${\sigma }_{\mathrm{t}}/f_{\mathrm{t}}=\left\{\begin{array}{ll}1.2\left({\epsilon }_{\mathrm{t}}/{\epsilon }_{\mathrm{t}0}\right)-0.2{\left({\epsilon }_{\mathrm{t}}/{\epsilon }_{\mathrm{t}0}\right)}^6& {\epsilon }_{\mathrm{t}}<{\epsilon }_{\mathrm{t}0}\\ \left({\epsilon }_{\mathrm{t}}/{\epsilon }_{\mathrm{t}0}\right)/\left[\beta {\left({\epsilon }_{\mathrm{t}}/{\epsilon }_{\mathrm{t}0}-1\right)}^{1.7}+\left({\epsilon }_{\mathrm{t}}/{\epsilon }_{\mathrm{t}0}\right)\right]& {\epsilon }_{\mathrm{t}}\ge {\epsilon }_{\mathrm{t}0}\end{array}\right.$$

(4)

The stress–strain (σ_s − ε_s) relationship for the reinforcement was modeled using a bilinear model, as shown in Equation (5). In this equation, E_s represents the elastic modulus of the reinforcement, while f_y and ε_y denote the yield strength and yield strain of the steel, respectively. The parameter k represents the slope of the hardening segment in the stress–strain curve.

$${\sigma }_{\mathrm{s}}=\left\{\begin{array}{ll}{E}_{\mathrm{s}}{\epsilon }_{\mathrm{s}}& {\epsilon }_{\mathrm{s}}\le {\epsilon }_{\mathrm{y}}\\ f_{\mathrm{y}}+k\left({\epsilon }_{\mathrm{s}}-{\epsilon }_{\mathrm{y}}\right)& {\epsilon }_{\mathrm{s}}\ge {\epsilon }_{\mathrm{y}}\end{array}\right.$$

(5)

The parameters for the plastic damage models of UHPC and NC were assigned as follows: the dilation angle ψ was set to 30°, the flow potential eccentricity ζ was taken as 0.1, and the ratio of biaxial compressive strength to uniaxial compressive strength f_b0/f_c0 was set to 1.16. The ratio of the tensile meridian stress to the compressive meridian stress K was set to 0.6667, and the viscosity parameter μ was taken as 0.005.

2.2. Establishment of the Numerical Model

The FEM of the reinforced truss UHPC-NC composite slab is shown in Figure 2. UHPC and NC were modeled using 3D solid elements (C3D8R). The C3D8R element provides high accuracy in simulating the nonlinear behavior of brittle materials like concrete, effectively capturing stress concentration and failure modes. That makes C3D8R suitable for composite plate structures under bending loads. The reinforcement was modeled using 3D truss elements (T3D2). The T3D2 element is ideal for simulating the tensile and compressive properties of the reinforcement, accurately describing the stress distribution within the composite slab while reducing computational complexity. For the interface between the NC layer and the UHPC layer, hard contact was applied in the normal direction. In the tangential direction, the bond-slip effect was considered, with a friction coefficient of 0.3 applied to simulate interfacial frictional slip. A global element size of 50 mm was used to mesh the precast UHPC base plate, the cast-in-place NC layer, and the reinforced truss. This mesh size maintains computational accuracy while controlling the model’s scale, making it suitable for simulating the overall mechanical behavior of the composite slab under four-point bending loads.

The composite slab was subjected to a four-point bending load. A fixed hinge support was applied on the left side of the slab, while a hinge support, which allowed sliding in the x-direction, was placed on the right side. To avoid stress concentration, rigid pads were placed above the loading points and beneath the supports. A tie constraint was applied between the rigid pads and the composite slab, neglecting bond-slip effects.

3. Verification of the FEM

To verify the validity of the established model, FE analyses were conducted on reinforced truss NC composite slabs, reinforced truss high-strength concrete composite slabs, and reinforced truss UHPC composite slabs. The validity of the previously developed FEM for the UHPC-NC composite slab was verified through comparison with corresponding test results.

3.1. Reinforced Truss NC Composite Slab

Tests on flexural behavior of unidirectional reinforced truss NC composite slabs were conducted in reference [20]. In this study, specimen LS-1 was used for FE validation. The dimensions and reinforcement details of specimen LS-1 are shown in Figure 3. The specimen had a total length of 2840 mm, a width of 2220 mm, and a calculated span length of 2740 mm. Four-point bending was applied to the specimen. The precast base plate of specimen LS-1 had a thickness of 60 mm, while the cast-in-place layer was also 60 mm thick. The height of the reinforced truss was 80 mm, with a width of 150 mm, and the bottom of the diagonal members of adjacent trusses was spaced 150 mm apart along the longitudinal direction of the slab. The truss chords and diagonals were made of HRB400 steel bars with a diameter of 8 mm. The strength grade of the longitudinal and transverse reinforcement in the precast base plate was HRB400, with a diameter of 8 mm and a spacing of 150 mm. The strength grade of the longitudinal and transverse reinforcement in the cast-in-place layer was HPB235, with a diameter of 6 mm and a spacing of 200 mm. Both the precast base plate and the cast-in-place layer of specimen LS-1 were made of C30 NC. The average measured compressive strength f_cu of the NC cubes was 40.6 MPa, with an elastic modulus E_c of 3.27 × 10⁴ MPa. The measured yield strength of the 8 mm steel bars was 416 MPa, and their elastic modulus E_s was 2.00 × 10⁵ MPa. The constitutive relationships for the NC and steel reinforcement in the FEM were consistent with those described in Section 2.1.

Figure 4 presents the comparison between the mid-span deflection–load (P-Δ) curves obtained from the FE simulation and the test results. The measured yield load P_y^t and ultimate load P_u^t were 34.28 kN and 50.16 kN, respectively, while the simulated yield load P_y^FE and ultimate load P_u^FE were 37.42 kN and 52.17 kN, respectively. The ratio of the P_y^t to the P_y^FE was 0.92, and the ratio of the P_u^t to the P_u^FE was 0.96. The comparison shows that the simulated P-Δ curve closely matches the test results, indicating that the established FEM is reliable.

3.2. Reinforced Truss UHPC Composite Slab

Tests on the flexural behavior of reinforced truss UHPC composite slabs were conducted in reference [14], and in this study, specimen DB-2 was used for FE validation. The geometry and reinforcement details of specimen DB-2 are shown in Figure 5. The specimen had dimensions of 3020 mm × 600 mm × 130 mm, with an effective span of 2700 mm. Three-point bending was applied to the specimen. The precast base plate had a thickness of 70 mm, and the cast-in-place layer had a thickness of 60 mm. The height and width of the reinforced truss were both 80 mm. The reinforcement strength grade was HRB400. The longitudinal reinforcement in both the precast base plate and the cast-in-place layer consisted of 12 mm diameter bars, while the transverse reinforcement consisted of 8 mm diameter bars. The upper and lower chords of the truss were made of 10 mm diameter bars, and the diagonal web bars were 6mm in diameter. Both the precast base plate and the cast-in-place layer were made of UHPC, with the measured cubic compressive strength f_cu of 135.71 MPa. The yield strengths f_y of the steel bars with diameters of 6 mm, 8 mm, 10 mm, and 12 mm were 478 MPa, 468 MPa, 542 MPa, and 403 MPa, respectively, with an elastic modulus E_s of 2.00 × 10⁵ MPa for all bars.

Figure 6 presents the comparison between the mid-span deflection–load (P-Δ) curves obtained from the FE simulation and the test results. The measured yield load P_y^t and ultimate load P_u^t were 30.95 kN and 41.84 kN, respectively, while the simulated yield load P_y^FE and ultimate load P_u^FE were 31.36 kN and 41.44 kN, respectively. The ratio of the P_y^t to the P_y^FE was 0.99, and the ratio of the P_u^t to the P_u^FE was 1.01. The comparison results demonstrate a good agreement between the FE simulation and the test data.

The comparison between the test yield and ultimate loads (P_y^t and P_u^t) and the simulated yield and ultimate loads (P_y^FE and P_u^FE) is shown in

Table 1. Comparison between test results and FE analysis results.

No.	Pyt/kN	PyFE/kN	Pyt/PyFE	Pyt/kN	PuFE/kN	Put/PuFE
LS-1	34.28	37.42	0.92	50.16	52.17	0.96
DB-2	30.95	31.36	0.99	41.84	41.44	1.01

. The average ratio of the test values to the simulated values was 0.97, with a mean square error of 0.034 and a coefficient of variation of 0.035. This indicates that the developed model has a certain level of reliability.

4. FE Analysis of Reinforced Truss UHPC-NC Composite Slab

4.1. Scheme of the FEM

A total of 11 FEMs of reinforced truss UHPC-NC composite slabs and 1 reinforced truss NC composite slab were designed. The effects of the cross-sectional area of the upper and lower truss chords, the reinforcement ratio of the precast base plate, the UHPC strength grade of the base plate, and the thickness of the UHPC base plate on the flexural performance of the composite slabs were investigated. The composite slab had a length of 2520 mm, a width of 1200 mm, and a calculated span of 2420 mm. The total thickness of the slab was 130 mm. The base plate was reinforced with 13 transverse steel bars (6 mm in diameter) and 8 longitudinal bars (8 mm in diameter). The transverse bars were placed at the outermost layer with a concrete cover thickness of 15 mm. In the precast base plate, the transverse reinforcement bars were placed 60 mm from the concrete edge, with a spacing of 200 mm. The diameters of the upper and lower chord reinforcement in the reinforced truss were 8 mm, and the diameter of the web reinforcement was 6 mm. The design of the composite slabs is shown in Figure 7, and the basic parameters of the slab models are detailed in

Table 2. Basic design parameters of the composite slab models.

No.	Lower Chord of the Reinforced Truss	Upper Chord of the Reinforced Truss	Longitudinal Reinforcement in the Precast Base Plate	The Strength Grade of UHPC Base Plate/Mpa	The Thickness of the UHPC Base Plate/mm
S-1	8	8	88	120	60
S-2	10	8	88	120	60
S-3	12	8	88	120	60
S-4	8	10	88	120	60
S-5	8	12	88	120	60
S-6	8	8	810	120	60
S-7	8	8	812	120	60
S-8	8	8	88	140	60
S-9	8	8	88	100	60
S-10	8	8	88	30	60
S-11	8	8	88	120	40
S-12	8	8	88	120	80

. Here, represents the reinforcement strength grade of HRB400.

In the FE analysis, the axial compressive and tensile strengths of UHPC and NC, as well as the yield strength of the steel reinforcement, were taken as standard values. The material properties of UHPC and NC are shown in

Table 3. Mechanical properties of concrete.

Type	Cube Compressive Strength fcu (N/mm2)	Axial Compressive Strength fc (N/mm2)	Axial Tensile Strength ft (N/mm2)	Modulus of Elasticity Ec (×104 N/mm2)
NC	30.0	14.3	1.4	3.0
UHPC	100.0	88.1	7.3	3.8
	120	105.7	9.2	4.1
	140	123.3	11.0	4.3

[21]. The diagonal bars of the truss were made of HPB300 steel, while all other reinforcement bars used HRB400 steel. The elastic modulus of the steel was set at 2 × 10⁵ MPa.

In this section, the constitutive relationships for the reinforcement, NC, and UHPC are as outlined in Section 2.1. The element types, mesh division, boundary conditions, and loading methods for the FEM are as described in Section 2.2.

4.2. Mid-Span Deflection–Load Curve

The mid-span deflection–load (P-Δ) curves obtained from the FE simulations of the 12 specimens are shown in Figure 8. The cracking load, yield load, peak load, ultimate load, and corresponding displacements are provided in

Table 4. FE simulation results.

No.	Cracking Load/kN	Cracking Displacement/mm	Yield Load/kN	Yield Displacement/mm	Peak Load/kN	Peak Displacement/mm	Ultimate Load/kN	Ultimate Displacement/mm
S-1	48.93	3.89	64.62	16.25	74.54	62.76	71.65	111.21
S-2	49.14	6.43	70.83	17.14	81.01	43.17	79.33	91.42
S-3	49.82	3.94	77.31	17.95	88.53	48.32	85.93	78.19
S-4	48.58	3.93	66.44	17.32	74.42	63.11	72.59	107.22
S-5	48.62	3.94	66.07	17.13	74.75	51.42	72.89	104.37
S-6	49.75	3.93	74.63	17.34	87.17	46.55	85.61	77.70
S-7	50.53	3.37	86.46	18.51	100.50	44.71	98.66	60.69
S-8	65.25	5.39	66.11	16.88	77.03	56.55	75.79	99.75
S-9	45.60	3.41	58.02	15.39	68.87	51.83	65.85	124.75
S-10	29.77	3.12	51.90	16.63	58.46	140.71	58.36	145.38
S-11	44.65	3.10	59.21	15.42	69.06	46.74	64.88	145.47
S-12	48.85	3.88	64.59	15.74	76.91	45.81	75.77	67.71

.

4.3. Analysis of Different Parameters

4.3.1. Cross-Sectional Area of the Lower Chord Reinforcement

As shown in Figure 8a, a comparison of the load–deflection curves for S-1, S-2, and S-3 indicates that increasing the cross-sectional area of the lower truss reinforcement resulted in no significant change in the cracking load, but both the yield load and ultimate load increased significantly. The yield loads of specimens S-2 and S-3 were 9.61% and 19.64% higher than that of specimen S-1, respectively. Similarly, the ultimate loads of S-2 and S-3 were 10.72% and 19.93% higher than that of S-1. The ratios of the lower chord reinforcement area to the total tensile reinforcement area for S-1, S-2, and S-3 were 33.3%, 43.8%, and 52.9%, respectively. Meanwhile, the flexural capacity to total tensile reinforcement area ratios for S-1, S-2, and S-3 were 0.123, 0.113, and 0.104, respectively. This suggests that increasing the cross-sectional area of the lower chord reinforcement is an effective method to enhance structural performance. Furthermore, as the lower chord reinforcement area increased, the stress per unit area in the tensile reinforcement decreased, although it remained above 0.1, indicating that the composite slab within this range maintained a high economic efficiency.

4.3.2. Cross-Sectional Area of the Upper Chord Reinforcement

The comparison of the mid-span deflection-load curves for composite slabs with different upper chord reinforcement areas (S-1, S-4, and S-5) is shown in Figure 8b. It can be observed that increasing the upper reinforcement area from 100.53 mm² to 157.08 mm² and 226.19 mm² had little effect on the cracking load of the slabs. Furthermore, the improvements in yield load and ultimate load were also relatively limited. Compared to S-1, the yield loads of S-4 and S-5 increased by 2.82% and 2.24%, respectively, while the ultimate loads increased by 1.31% and 1.73%, respectively. Therefore, increasing the diameter of the upper truss reinforcement has a relatively minor effect on enhancing the structural performance of the composite slabs.

4.3.3. Reinforcement Ratio of Longitudinal Reinforcement in the Precast Base Plate

As shown in Figure 8c, the mid-span deflection–load curves for composite slabs with different longitudinal reinforcement ratios in the precast base plate (S-1, S-6, and S-7) were compared. It can be observed that as the reinforcement ratio of the prefabricated base plate increased, the flexural capacity of the composite slab also increased [22]. When the longitudinal reinforcement ratio of the precast base plate increased from 0.32% to 0.50% and 0.73%, the impact on the cracking load was minimal, but both the yield load and ultimate load increased significantly. The yield loads of S-6 and S-7 were 15.49% and 33.80% higher than that of S-1, respectively, while the ultimate loads were 19.48% and 37.70% higher. Compared to increasing the diameter of the lower truss reinforcement, increasing the reinforcement ratio of the precast base plate resulted in more significant performance improvements, with higher overall benefits.

4.3.4. Concrete Strength Grade of the Precast Base Plate

As shown in Figure 8d, S-8 and S-9 utilized UHPC with strength grades of C140 and C100, respectively, while S-10 used C30 NC. By comparing the load–deflection curves of S-1, S-8, S-9, and S-10, it is evident that as the concrete strength of the precast base plate increased, the cracking load, yield load, and ultimate load of the composite slabs all significantly improved. Compared to S-10, the cracking loads of S-9, S-1, and S-8 increased by 53.17%, 64.36%, and 119.18%, respectively. Similarly, the yield loads increased by 11.79%, 24.51%, and 27.38%, while the ultimate loads increased by 12.83%, 22.77%, and 29.87%, respectively. Considering the complexity and high cost of producing UHPC, increasing the UHPC strength grade offers relatively low cost-effectiveness.

4.3.5. Thickness of the Precast UHPC Base Plate

The comparison of mid-span deflection–load curves for composite slabs with different thicknesses of prefabricated UHPC base plates (S-1, S-11, and S-12) is shown in Figure 8e. It is observed that as the thickness of the prefabricated base slab increased from 40 mm to 60 mm, the cracking load, yield load, and ultimate load of the composite slab all increased significantly. When the thickness increased from 60 mm to 80 mm, there was only a slight improvement in ultimate load. Compared to S-11, the cracking loads of S-1 and S-12 increased by 9.59% and 9.41%, respectively; the yield loads increased by 9.14% and 9.09%, respectively; and the ultimate loads increased by 10.43% and 16.78%, respectively. It can be observed that increasing the thickness of the prefabricated UHPC base plate is an effective method to enhance the flexural performance of the composite slab [23]. Considering the production cost of UHPC, a prefabricated UHPC base plate thickness of 60 mm was deemed the most suitable for the composite slab design in this study.

4.4. Full Process Analysis of Load-Bearing Behavior

Based on the P-Δ curve of specimen S-1, the curve can be divided into four stages: (1) Initial Stage to Pre-cracking: The composite slab experienced minor deformation under external forces, with no visible cracks. The stress–strain relationship remained linear, and the stiffness was relatively high. (2) From Cracking to Steel Yielding: Concrete carried tensile stress until it reached its tensile strength limit, at which point cracks appeared. The curve briefly declined, indicating a reduction in stiffness. However, it quickly rose as the steel reinforcement began to bear more of the tensile stress. (3) From Steel Yielding to Peak Load: Although the stiffness of the composite slab decreased and deformation became more pronounced, the overall load-bearing capacity continued to increase, reaching its maximum value. (4) Post-Peak Load Decline: After reaching the maximum load, the compressed concrete in the composite slab began to fail, causing the structure to lose stability and load-bearing capacity, with a sharp decrease in stiffness.

4.4.1. Cracking of UHPC

In the post-processing module of ABAQUS, the variable DAMAGET specifically refers to tensile damage. When the value of DAMAGET exceeds 0.75, it indicates that the UHPC in the tensile zone has begun to crack. As the loading process continues, the increase in the damage value can be regarded as an indication of the development of concrete cracks [24]. Figure 9a shows that cracks appeared in the mid-span region on the bottom surface of the UHPC precast base plate. According to Figure 10a, the stress borne by the reinforcement at this time was relatively low, with the maximum stress occurring in the mid-span region, reaching a value of 67.02 MPa.

4.4.2. Yielding of Longitudinal Reinforcement

The equivalent plastic strain (PEEQ) of the reinforcement is a key parameter that reflects the yielding condition of the steel. When PEEQ exceeds 0, it indicates that the material has yielded. During the displacement loading process, the increase in load can be monitored by observing PEEQ to determine if the reinforcement has yielded.

Figure 10b shows the distribution of the PEEQ in the reinforcement. When the PEEQ value exceeded 0, the longitudinal tensile reinforcement at the edges of the mid-span in the precast slab began to yield, corresponding to a load of 64.62 kN.

By analyzing the strain E11 along the long edge of the specimen, it was found that the compressive strain in the cast-in-place layer of the composite slab was much lower than the ultimate compressive strain. This indicates that, at this stage, the concrete in the compression zone of the cast-in-place layer had not yet failed, as shown in Figure 9b.

4.4.3. Peak Load

When the mid-span displacement reached 62.76 mm, the load rose to a peak of 74.54 kN. At this point, the compressive strain in the concrete of the compression zone was 1.6790 × 10⁻³, indicating that the concrete had not been crushed, as shown in Figure 9c. Meanwhile, the PEEQ in the steel reinforcement is presented in Figure 10c. The tensile reinforcement in the mid-span region reached a stress value of 410.5 MPa, which exceeded the standard yield strength of the reinforcement.

4.4.4. Ultimate Load

According to the formula for the ultimate compressive strain in the Code GB 50010 [25], the ultimate compressive strain for NC can be derived as 0.0033. As the mid-span displacement increased to 111.21 mm, the NC in the compression zone reached its ultimate compressive strain, as shown in Figure 9d. At this point, the NC was crushed, marking the failure of the composite slab, with the ultimate load recorded as 71.65 kN. The PEEQ in the steel reinforcement at this stage is shown in Figure 10d, indicating an expanded yield range in the tensile reinforcement.

5. Calculation of Flexural Capacity of the Normal Section

5.1. Basic Assumptions

The flexural capacity of the normal section is calculated based on the following assumptions: (1) Plane sections remain plane after deformation. (2) There is a strong bond between the steel reinforcement and UHPC, with no relative slip. (3) UHPC and NC are tied together using connectors, and bond-slip effects are neglected. (4) The contribution of the UHPC section in tension is considered. (5) The stress–strain relationships for UHPC and steel reinforcement are as outlined in Section 2.1.

5.2. Calculation Formula for Flexural Capacity of the Normal Section

Due to the tensile effect of steel fibers in UHPC, the tensile stress contribution of UHPC in the tension zone must be considered when calculating the flexural capacity of the composite slab. Under the ultimate bending load, the actual stress distribution in the tension zone is curved. To simplify the calculation, this curved tensile stress distribution is approximated as a rectangular distribution, as shown in Figure 11.

In this figure, α₁ represents the equivalent rectangular stress coefficient for the compression zone, and k and β are coefficients for the equivalent rectangular stress distribution in the tension and compression zones, respectively. b is the width of the composite slab section, and x is the height of the equivalent compression zone. ${\sigma }_{\mathrm{hy} }^{\prime }$ is the stress in the upper chord reinforcement of the truss, and $A_{\mathrm{hy} }^{\prime }$ is the cross-sectional area of the upper chord reinforcement of the truss. Similarly, f_hy and A_hy represent the standard yield strength and cross-sectional area of the lower chord reinforcement of the truss. f_y denotes the standard yield strength of the longitudinal tensile reinforcement in the precast base plate, while A_s is its cross-sectional area. The term a_s is the distance from the centroid of the tensile reinforcement to the edge of the tension zone, and h₀ is the effective depth, or the distance from the centroid of the tensile reinforcement to the edge of the compression zone. Finally, $a_s^{\prime }$ is the distance from the centroid of the compression reinforcement to the edge of the compression zone.

Considering the enhancement of flexural capacity due to the contribution of the inclined web members of the steel truss [26], along with the contribution of UHPC in the tensile zone, the static equilibrium equations based on the balance of axial forces and bending moments were established, as shown in Equations (6) and (7). In these equations, λ is an amplification factor accounting for the influence of the truss web reinforcement, and ε_cu is the ultimate compressive strain of the concrete. k was taken as 0.25. According to the Code (GB 50010-2010) [25], α₁ is taken as 1.0, β as 0.8, and ε_cu as 0.0033.

The stress in the upper chord reinforcement of the truss is calculated by Equation (8), where $E_s^{\prime }$ is the elastic modulus of the upper chord reinforcement. Based on the results of the FE analysis, the value of λ ranged from 1.18 to 1.30, and the average value of λ was taken as 1.28.

$${\alpha }_1{f}_{\mathrm{c}}\mathit{bx}+{\sigma }_{\mathrm{hy} }^{\prime }{A}_{\mathrm{hy} }^{\prime }=k{f}_{\mathrm{t}}b\left(h-{\displaystyle \frac{x}{\beta }}\right)+f_{\mathrm{y}}{A}_{\mathrm{s}}+f_{\mathrm{hy}}{A}_{\mathrm{hy}}$$

(6)

$$M_{\mathrm{u}}=\lambda \left\{{\alpha }_1{f}_{\mathrm{c}}\mathrm{bx}\left(h_0-0.5x\right)+{\sigma }_{\mathrm{hy}}^{\prime }{A}_{\mathrm{hy}}^{\prime }\left(h_0-a_{\mathrm{s}}^{\prime }\right)-k{f}_{\mathrm{t}}b\left(h-{\displaystyle \frac{x}{\beta }}\right)\left[0.5\left(h-{\displaystyle \frac{x}{\beta }}\right)-a_{\mathrm{s}}\right]\right\}$$

(7)

$${\sigma }_{\mathrm{hy}}^{\prime }=E_{\mathrm{s}}^{\prime }{\epsilon }_{\mathrm{cu}}\left({\displaystyle \frac{\beta a_{\mathrm{s}}^{\prime }}{x}}-1\right)$$

(8)

5.3. Comparison of Results

According to Equation (7), the flexural capacity M_u^p of 11 specimens with different cross-sectional dimensions and reinforcement areas was calculated. Additionally, the ultimate load P_u^FE was obtained through FE simulation, from which the simulated flexural capacity M_u^FE was derived. Finally, the calculated values were compared with the simulation results, as shown in Figure 12. To assess the agreement between the two, the ratio t = M_u^FE/M_u^p was calculated, with an average value of 1.005, a mean square deviation of 0.0521, and a coefficient of variation of 0.0518. The analysis results indicate a high consistency between the simulated and calculated flexural capacities of the UHPC-NC composite slabs with reinforced trusses.

6. Discussion

Comparing the UHPC-NC reinforced truss composite slab (S-1) with the cast-in-place NC reinforced composite slab (S-10) reveals that the UHPC-NC truss composite slab achieved increases in cracking load, peak load, and ultimate load of 64.36%, 27.51%, and 22.77%, respectively, compared to the cast-in-place NC composite slab. This demonstrates that using a prefabricated UHPC slab as the base of the composite slab can significantly enhance the load-bearing capacity. Additionally, using prefabricated UHPC slabs addresses issues associated with precast NC, such as transportation and installation difficulties, susceptibility to leakage at joints, poor seismic performance, and vulnerability to erosion.

However, it is worth noting that the study was based on existing literature, with a FE model established and its feasibility and validity verified. Nonlinear parametric analysis was subsequently conducted. While the results are considered reliable to some extent, further experimental validation is required.

7. Conclusions

Based on three-dimensional units, the numerical model of UHPC-NC composite slab with reinforced truss was established by ABAQUS software. The flexural capacity of such composite slabs in the normal section was studied, and the following conclusions are drawn:

1.

FE analyses were conducted to validate the flexural performance of UHPC-NC composite slabs with reinforced trusses. The results showed strong agreement between simulated and experimental values, confirming the reliability of the model.

2.

Increasing the area of lower chord reinforcement and the longitudinal reinforcement ratio significantly enhanced both yield and ultimate loads. Specifically, increasing the lower chord reinforcement diameter from 8 mm to 10 mm and 12 mm raised the yield load by 9.61% and 19.64%, and the ultimate load by 10.72% and 19.93%. Similarly, increasing the longitudinal reinforcement ratio in the precast bottom slab from 0.32% to 0.50% and 0.73% improved the yield load by 15.49% and 33.80%, as well as the ultimate load by 19.48% and 37.70%. In contrast, the effect of upper chord reinforcement area was limited.

3.

As the concrete strength grade of the precast base plate increased, the cracking, yield, and ultimate loads of the composite slab were significantly enhanced. Specifically, when the concrete strength grade increased from C30 to C100, C120, and C140, the cracking load increased by 53.17%, 64.36%, and 73.97%, respectively. The yield load increased by 11.79%, 24.51%, and 27.38%, while the ultimate load increased by 12.83%, 22.77%, and 29.87%.

4.

When the thickness of the UHPC base plate increased from 40 mm to 60 mm and 80 mm, the cracking load increased by 9.59% and 9.41%, respectively; the yield load increased by 9.14% and 9.09%, respectively; and the ultimate load increased by 10.43% and 16.78%, respectively.

5.

A calculation formula for the flexural capacity of UHPC-NC composite slabs was proposed. The ratio of calculated to simulated values averaged 1.005, with a mean square deviation of 0.0521 and a coefficient of variation of 0.0518, indicating good reliability. This formula provides a theoretical basis for the design of such slabs.