The composition of the UHPC reads as Table 1 [2]. Experimental results have demonstrated the notable mechanical properties of the UHPC formulated with this specific mixture. Its compressive strength (fc) reaches the magnitude of 145 MPa, and its tensile strength (ft) of 8.5 MPa. Furthermore, the UHPC exhibits an elastic modulus (Ec) of 45,000 MPa and a Poisson’s ratio (vc) of 0.2, as listed in Table 2.

Regarding the steel plates employed in this study, they were fabricated from Q345D steel, per the specifications in GB/T 714 [31], which is equivalent to S355D steel as stipulated in ISO 630 [32]. Following the standard testing, the mechanical properties of the steel plates were determined as follows. The yielding strength (fy) reads as 345 MPa, the ultimate strength (fs,u) as 550 MPa, the elastic modulus (Es) as 206,000 MPa, and the Poisson’s ratio (vs) as 0.3.

Two types of non-mechanical steel-UHPC interfaces were considered, each involving bonding without shear studs. The first type involved a sandblasting treatment of the steel plate’s surface. A shot blasting machine propelled steel shots onto the smooth steel plate, creating a rough surface with an average depth of approximately 100 μm. This interfacial treatment is called the sandblasted interface, referred to as the SB interface, as shown in Fig. 1a. The second type involved the application of 0.7 kg/m² of epoxy resin adhesive to the steel plate’s surface, followed by the sprinkling of basalt particles with a size range of 3–5 mm. This process resulted in the formation of an epoxy adhesive interface with sprinkled basalt aggregate, referred to as the EA interface, as shown in Fig. 1b.

The mechanical performance of the SB and EA interfaces, under pure tensile and shear stress, was experimentally studied using pull-off and push-out tests, respectively. For each interface, six sets of pull-off tests and three sets of push-out tests were conducted. All specimens were cured for 28 days, with their surfaces kept moist by water sprinkling.

The testing setup for the pull-off tests is illustrated in Fig. 2, consisting of a 40 mm-thick UHPC layer and a 20 mm-thick steel plate. Six specimens, each with a diameter of 55 mm and a depth of 40 mm, were carefully extracted from the steel-UHPC composite plate after the SB and EA treatments of the interfaces. To ensure a strong connection between the samples and the loading instrument, a steel drawing disk with a diameter of 50 mm was securely attached to the upper surface of each drilled core sample with epoxy adhesive, as seen in Fig. 2. Tensile loading was applied at a constant rate of 40 kPa/s to the specimen until failure occurred. The ultimate load was then recorded for analysis.

The testing setup for the push-out tests is illustrated in Fig. 3, consisting of an I-steel beam and two UHPC layers. The I-beam had a width of 150 mm and a height of 320 mm. The UHPC layers on both sides of the beam were 60 mm thick, 290 mm wide, and 320 mm high. At the midpoint of the top surface of the I-beam, a 30-ton electro-hydraulic servo test system applied a pressure load. The loading process used a displacement loading control method, preloading and loading the specimen at a constant rate of 0.5 mm/min until failure. The relative slip between the steel member and UHPC was measured by four linear variable differential transformers (LVDTs), labeled D1-D4, strategically positioned on the specimen’s surface, as shown in Fig. 3. Throughout the loading process, the load and displacement were recorded at a frequency of 10 Hz.

During the pull-off test, failure can occur either at the drilled UHPC core sample or at the steel-UHPC interface. If the tensile strength of the interface is higher than that of the UHPC, failure will occur at the drilled UHPC core sample and vice versa. The results indicated that the failure mode for both interface treatments primarily occurs at the steel-UHPC interface, representing the most vulnerable component within the steel-UHPC composite structure. The nominal bond strength or interfacial cohesion, σ, can be calculated as follows: (1)σ=PpullAt

where Ppull and At are the maximum applied load and the cross-sectional area of the drilled core sample. The average tensile strengths of the SB-treated and EA-treated interfaces in the steel-UHPC composite are 3.48 and 1.78 MPa, respectively, as shown in Table 3.

The load-slip curves for the steel-UHPC interface, derived from push-out tests, are depicted in Fig. 4. These experimental results reveal distinct behaviors between the SB and EA-treated interfaces. Specifically, the SB interface exhibits a brittle failure mode, characterized by a rapid decrease in load capacity after reaching its peak, with a relatively small interface slip. In contrast, the EA interface exhibits a ductile failure mode, characterized by significant slip at the interface upon failure. As loading progresses, the EA interface experiences gradual and slow slip. After reaching the maximum load, the slip continues to develop while the load capacity gradually decreases until ultimate failure. The average shearing strength, τ, can be calculated as follows: (2)τ=Ppush2As

where Ppush and As are the maximum applied load and the contact area between a UHPC slab and the I-steel. The average shear strength of the SB-treated and EA-treated interface of the steel-UHPC composite amounts to 0.79 and 2.1 MPa, respectively, see Table 3.

The results from the pull-off and push-out tests aid in establishing the constitutive relations for the SB and EA interfaces. The traction-separation model, which includes bilinear, exponential, trapezoidal, and other types, is commonly used to describe interface fractures [33,34]. Reflecting on the characteristics of the load-slip curves for the SB and EA interfaces, they are modeled by a bilinear and a trapezoidal traction-separation model, respectively, as depicted in Fig. 5.

Regarding the SB interface, an increasing load leads to a relatively small slip between the steel and UHPC interfaces, as indicated by the steep linear rise of the load-slip curve in Fig. 5a. Upon reaching the peak, the load quickly decreases with increasing slip. Thus, the constitutive behavior of the SB interface can be divided into two phases: the elastic phase and the failure phase. During the elastic phase, the interface remains intact, but it swiftly transitions to the failure phase after reaching the ultimate load, significantly reducing load-bearing capacity. The following constitutive model describes this behavior. (3)σn/s={σn/s0δ0δ=Kn/sδ,δ≤δ0δ−δfδ0−δfσn/s0,δ0<δ≤δf

where σn/s and σn/s0 are the normal/shear tractions and the corresponding ultimate values of the interface, respectively. δ is the interface slip with δ0 and δf are for the corresponding value when the interface reaches its ultimate strength, and the maximum value allows for interface continuity. The stiffness of the interface, denoted as Kn/s, can be quantified as σn/s/δ0. Herein, the subscript n and s refer to the normal and tangential direction along the interface, respectively.

The test results clearly indicate the EA interface’s ductile mechanical behavior. Upon reaching the maximum load, the interface does not fail abruptly but continues slipping and gradually reduces its load-carrying capacity until final failure. Therefore, the constitutive behavior of the EA interface can be described by a trapezoidal traction-separation model consisting of the elastic, plastic, and failure phases. The plastic phase ensures the interface does not immediately enter the failure phase upon reaching its maximum load-bearing capacity. The constitutive model is expressed as follows: (4)σn/s={σn/s0δ0δ=Kn/sδ,δ≤δ0σn/s0,δ0<δ≤δ0+r∗δf(δ−δf)σn/s0(δ0+r∗δf)−δf,δ0+r∗δf<δ≤δf

where δu=δ0+r∗δf is the ultimate slip value in the undamaged phase of the interface, with the trapezoidal shape parameter, r, indicating the ratio of the upper base to the lower base of the trapezoid. All the other parameters follow the definition in Eq. (3).

In the traction-separation model, the ultimate tractions of the interface, σn/s0, represent the maximum stress that the interface can sustain in a specific direction. For the vertical direction, this corresponds to the tensile strength of the interface, and for the horizontal direction, it corresponds to the shear strength of the interface [35]. These were determined by the pull-off and push-out tests of the UHPC-steel composites, respectively, as indicated in Table 4.

The trapezoidal shape parameter, r, which calibrates the shape of the trapezoidal traction-separation model, is quantified as the ratio between the upper and lower bases of the trapezoid. Extensive investigations have shown that this parameter, ranging between [0.1–0.35], has an insignificant influence on numerical simulations compared to that of the maximum separation distance δf [36–38]. Therefore, the trapezoidal shape parameter is assumed to be 0.1 for the EA interface’s trapezoidal traction-separation model.

The stiffness Kn/s and the maximum separation distance δf of the interface cannot be directly obtained from experimental measurements. Therefore, finite element simulations of the push-out tests were conducted to identify these parameters, as shown in Fig. 6. The ultimate strength σn/s0 and the trapezoidal shape parameter r of the interfaces were employed. By replicating the load-displacement curves of the push-out tests, as depicted in Fig. 7, the values of Kn/s and δf were determined for both the SB interface and the EA interface, as indicated in Table 5.

In three-point bending tests, composite plates with SB and EA interfaces exhibit a similar mode of longitudinal shear failure along the interface. The applied load leads to gradual sliding and separation of the UHPC overlay from the steel plate. At the stage of ultimate failure, the collaborative action between the UHPC and steel plates is lost, resulting in significant bending deformation and bending failure.

However, the load-deflection curves of these two composite plates differ, as shown in Fig. 10. For the SB specimens, the deflection increases linearly with the applied load, and interfacial sliding is insignificant before the final failure. Correspondingly, no evident signs of damage manifest during this stage. As the peak load approaches, minor interfacial dislocations appear within the range of 1/4 to 3/4 of the plate span, followed by slight bending cracks. Simultaneously, interface fracture emerges, leading to an abrupt loss of bearing capacity, accompanied by a significant sound. The average ultimate load of the composite plate using the SB interface is 53.31 kN. For the EA specimens, the load-deflection curve is almost linear during the initial stage. Upon reaching the ultimate stage, interfacial dislocations and obliquely oriented bending-shear cracks arise at around 3/8 span of the specimen. These cracks propagate from the bottom to the top of the UHPC layer, decreasing specimen stiffness. As the ultimate load stage is reached, the specimen loses its load-bearing capacity and eventually fails. The average ultimate load-bearing capacity of components using the EA interface is 46.70 kN.

During the simulation of the steel-UHPC interface, the experimentally derived interface pure shear strength was used as the value for the interface model σs.

The experimentally measured pure shear strength was taken as the ultimate shear traction of the interface in the numerical simulations, that is σs,SB = 0.79 and σs,EA = 2.10 MPa. The results of the numerical simulations exhibit a similar pattern to the experimental results in terms of the load-slip curves, as seen in Fig. 10. However, the load capacity of the composite plate was clearly underestimated. Specifically, the maximum simulated plate load with the SB interface is only around 34.33% of the average of the experimental results. The numerical simulation of the EA interface is slightly lower, around 87.45% of the average of the experimental results, as shown in Table 7 for comparison. This discrepancy provides motivation to refine the numerical simulations by updating the model.

The results of the preceding section indicate that taking the experimentally measured pure shear strength as the ultimate shear traction of the interface underestimates the bearing capacity of the steel-UHPC composite plate. This discrepancy is attributed to the normal stresses acting on the interface during the three-point bending test, which leads to an improvement in the ultimate shear strength of the interface [43–45], as indicated by an increase in the shear strength of the polymer-modified asphalt interface by 2–3.5 times due to the contribution of normal stress [46]. The Mohr-Coulomb strength theory is recalled for the quantitative determination of this improvement [47,48]. (20)σs=c+σn,maxtan⁡φ

where σs is the ultimate shear traction of the interface, depending on the applied maximum normal stress σn,max, as well as the internal angle of friction φ and the normal cohesion c of the interface. The latter is considered equal to the pure shear strength measured from the pull-off tests [49]. Regarding the internal friction angle, Zanotti et al. [49] and Ziraba et al. [50] reported tangent values of 1.31 and 0.53 for the SB and EA interfaces, respectively. However, the applied normal stress was typically unknown in the case of the three-point bending tests.

An iterative method, combined with the Mohr-Coulomb strength theory, was established to determine the improved shear strength of the interface subjected to complex stress states and, thus, the bearing capacity of the composite plates, as shown in Fig. 11. The experimentally measured pure shear strength, i.e., the normal cohesion c, was initially set as the ultimate shear traction σsi=0=c for the FE simulation of the steel-UHPC plate. The maximum value of the applied load PFE,maxi and the corresponding maximum normal stress at the interface σn,maxi were numerically quantified. The latter serves as input for the determination of the improved ultimate shear traction σsi+1 by applying the Mohr-Coulomb strength theory. The iteration stopped when the maximum applied load of the subsequent simulation converged, i.e., |PFE,maxi−PFE,maxi−1|<εerr.

In this investigation, the critical error was set to εerr=0.5 kN, and the iterative process is detailed in Table 8. After the iterative calculation, the values of the ultimate shear traction of the SB and EA interfaces were improved to approximately 3.95 and 1.19 times their pure shear strength, recording values of 3.12 and 2.50 MPa, respectively. The simulated load-deflection curves agreed well with the experimental measurements for the three-point bending specimens (SB-1,2,3 and EA-1,2,3), as shown in Figs. 12a and 12b. The average values of the experimentally measured ultimate loads of the composite plates with both SB and EA interfaces were very close to the simulated results, as shown in Table 9, exhibiting deviations of 3.66% and 5.05%, respectively. The final failure patterns of the steel-UHPC plate are illustrated in Fig. 13.