The push-out specimens are favored by many researchers because of their advantages such as small specimen size and low stress redistribution in studs (Cao et al., 2017; Fang et al., 2023a). In this study, there push-out specimen was used to study the shear behavior of headless studs. The specimens were designed with reference to Eurocode-4 (Anderson, 2023). The steel beam was made of two T-shaped steels made of Q345. The material of headless studs was M15, the diameter was 13 mm, and the height was 27 mm. The 12 headless studs were welded on the steel flanges on both sides of the specimen in three rows and two columns. The thickness of UHPC slab was 50 mm and the headless studs have a cover thickness of 15 mm. The reinforced steel bars in the UHPC slab were made of HRB400 and had a diameter of 10 mm. The structures of each push-out specimen were exactly the same, as shown in Figure 2. Among these three specimens, two were monotonically loaded specimens and one was cyclically loaded. They were distinguished by M and C and named DS-M1, DS-M2 and DS-C respectively.

The fabrication of push-out specimens was divided into 5 steps in total. (1) Welded the headless studs to the both sides of the steel flange according to the designated position. (2) Made formworks according to the size of the specimen and tied the steel bars. (3) Assembled the steel components and formworks. (4) Applied lubricating oil to the interface of steel plate and placed steel bars into formworks. (5) Poured UHPC. After the specimens were produced, they were watered and cured under natural conditions for 28 days. The fabrication steps of specimens are shown in Figure 3.

In this study, the selected UHPC is formulated by mixing cement, silica fume, quartz sand, quartz flour, water reducing agent, water, and steel fibers. The dry material mix ratio of UHPC is listed in Table 1.

According to GB/T31387-2015 (General Administration of Quality Supervision, 2015), the compressive strength of UHPC was determined by conducting axial compression tests on cubic specimens, while the tensile strength was measured through axial tension tests on dog-bone-shaped specimens. Following the Chinese standard (China NTMC, 2010), the mechanical properties of the steel plate (Q345) and steel bar (HRB400) were measured through tension tests using the electronic universal testing machine (CMT2503). As shown in Figure 4, on the premise of ensuring the welding quality, the steel bars with a diameter greater than the diameter of the head of stud (22 mm) were welded at each end of the studs, and then the tensile tests were performed on these components to obtain the mechanical properties of studs. The specific performance parameters of the above materials are shown in Table 2.

As shown in Figure 5A, the push-out specimens were tested in an electrohydraulic servo pressure testing machine with a capacity of 1,000 t. In order to ensure uniform force distribution on the studs on both sides of the specimen during the test, a small quantity of fine sand was placed at the bottom of the specimen and subsequently leveled using a balance ruler. The loading devices were arranged on top of the steel plate in the following order: spreading plate, circular cushion block, pressure transducer, and another circular cushion block. Six linear variable displacement transducers (LVDT) were used, as shown in Figure 5B, to measure the relative slip and relative separation between UHPC and steel plate, thereby obtaining the load-slip curve and load-separation curve. S1 and S2 in the figure are the tangential slip measuring points in the middle, while T1, T2 and B1, B2 are the normal separation measuring points at the top and bottom respectively. The thrust load during the test can be directly read from the digital display instrument on the pressure testing machine.

As shown in Figure 6, the loading procedure consists of monotonic and cyclic loading. Three preloading were performed before formal loading, and the force was set to 30% of the predicted ultimate load (P_u), the P_u here was determined through numerical simulation before loading, and its value was 720 kN. Monotonic loading means loading from zero load to failure of the specimen. Cyclic loading involves cycling between 0 P_u to 0.5 P_u and 0 P_u to 0.7 P_u ten times each and then loading beyond 0.7 P_u until failure of the specimen. During the elastic stage, loading was conducted in increments of 10 kN with a loading rate not exceeding 1 kN/s. During the elastic-plastic stage, loading was conducted in increments of 5 kN with a loading rate not exceeding 0.5 kN/s. The displacement control was utilized when the specimen entered the plastic stage or slip was observed, and a loading of 0.05 mm per level was applied.

When each specimen was loaded to failure, the final shape of the specimen was recorded. As shown in Figure 7A, all three specimens showed that one side UHPC slab fell off from the steel beam. This is because it is difficult to ensure that the stress state of headless studs on both sides of specimen is exactly the same during the test, the headless studs on both sides did not fail at the same time. Among them, the left side slab of DS-M1 and DS-M2 specimens fell off, while the right slab of DS-C specimen fell off. Figure 7B shows the details of the interface between UHPC plate and steel flange. It can be seen from Figure 7B that the failure of the three specimens was controlled by the fracture of stud shank near the root of the headless stud. The headless studs were still embedded in the UHPC and there was no obvious pull-out phenomenon. The welds on the steel flanges remain intact. In addition, except for the partial crushing at the root of headless stud, there was no damage in other areas on the inside of the UHPC slab, and there were no obvious cracks or damage on the outside. These phenomena were basically similar to the failure modes of the push-out specimens of conventional studs in UHPC (Kim et al., 2015; Cao et al., 2017; Tong et al., 2020).

Figure 8 shows the load-slip curves of all specimens, where the load represents the shear strength per headless stud (P_stud), which is calculated by dividing the shear capacity of specimen (P_u) by headless stud numbers. The interface slip is represented as the average of two vertical LVDTs (i.e., (S1+S2)/2, Figure 5B. For the DS-M1 and DS-M2 specimens under monotonic loading, the load slip curve can be divided into three stages. (1) Elastic stage (A1∼B1): The load increases linearly with slip. (2) Plastic stage (B1∼C1): As the slip increases, the UHPC under the root of headless stud was gradually crushed, the headless stud begins to undergo plastic deformation, and the load growth slows down. (3) Descending stage (After C1): After the load exceeded the ultimate bearing capacity, the headless studs were sheared off one after another, and the load dropped rapidly.

The DS-C specimen under cyclic loading can also be divided into the above three stages. When the cyclic load was 0.5 P_u, the headless studs was basically in the elastic stage (A2∼B2), the residual deformation after cyclic loading was small, and the loading and unloading curves basically coincide. After the 10th unloading of 0.5 P_u was completed, the residual slip was 0.041 mm. When the cyclic load was 0.7Pu, the headless studs had begun to undergo plastic deformation. The residual deformation after cyclic loading gradually increases with the number of loadings. The loading and unloading curves do not overlap. After the 10th 0.7 P_u unloading was completed, the residual slip reached 0.450 mm. It can be observed that the residual slip of the specimen under 0.7 P_u cyclic load is more obvious, which could be attributed to the gradual increase in cumulative deformation with the increase in the number of loadings after the headless studs yielded. However, the slip of the DS-C specimen under ultimate load was 22.15% and 19.07% higher than that of the DS-M1 and DS-M2 specimens respectively, and the ultimate bearing capacity was only 4.21% and 1.10% lower. It shows that cyclic loading has little effect on the bearing capacity of the headless studs, but it helps to improve the plastic deformation ability of the headless studs.

According to Eurocode 4 (Anderson, 2023), when the load of the connector reached the characteristic value (i.e., the load drops to 0.9 P_u), the interface slip is not less than 6 mm before it can be called a “plastic connector”. As can be seen from Figure 8, the characteristic slip of three specimens was in the range of 3.41–3.65 mm. Therefore, the headless studs in UHPC do not meet the requirements of plastic connectors.

As shown in Figure 5B, the interfacial separation between steel plate and UHPC slab was measured using four transverse LVDTs. The top separation is represented as (T1+T2)/2, while the bottom separation is represented as (B1+B2)/2. Here, two specimens under monotonic loading were used for analysis, and the load-separation curves are shown in Figure 9. It can be seen that the trends of all load-separation curves are relatively similar to the trends of the load-slip curves. During the elastic phase, the bellow separation grew faster than the upper separation. After entering the plastic stage, the separation growth accelerated as the headless stud yielded. When the ultimate load was reached, the top separation and below separation of the DS-M1 specimen was 0.483 mm and 1.367 mm respectively, and top separation and below separation of the DS-M2 specimen was 0.814 mm and 0.935 mm respectively. Obviously, the below separation part was larger than the top separation, because the inevitable friction caused the transferred load to be applied eccentrically on the UHPC slab, thus causing the lateral deformation of the UHPC slab (Xu et al., 2012). Further, for the thin UHPC bridge deck with a thickness of 55 mm, a shear span length of 1,200 mm, and a conventional stud spacing of 200 mm, the interfacial separation between steel beam and UHPC slab was 1.17 mm under ultimate load (Xu, 2022). This result is 17% smaller than the maximum interfacial separation of the UHPC slab configured with headless studs in this study. Therefore, it is suggested to use headless studs together with conventional studs in UHPC slabs to ensure sufficient anti-lifting bearing capacity.

Since there have been some studies on the shear performance of conventional studs in UHPC (Kim et al., 2015; Wang et al., 2018; Ding et al., 2021; Fang et al., 2023b), in this study, we plan to use existing research results to compare with the experimental results of this paper. To ensure that the data comparison is valuable, existing data need to be screened. The filtering principles include the following four conditions: (1) The conventional stud diameter is 13 mm; (2) The UHPC compressive strength is greater than 120 MPa; (3) The group stud effect is not considered; (4) Specimens under monotonic loading.

Figure 10 shows the comparison of the shear capacity of selected conventional studs with the test results in this paper. It can be seen from Figure 10 that the test results in this paper are close to the results of the research by Cao et al. (Cao et al., 2017), and lower than the research results of Li et al. (Li et al., 2021) and Wu et al. (Wu et al., 2022) This is because in the study by Cao et al. (Cao et al., 2017), stud fractures were mostly caused by weld fracture, and there was almost no local damage of the UHPC slab. But in other studies, it was basically the shear failure of the stud shank. On average, the shear capacity of headless studs is 16.3% lower than that of conventional studs. This may be because the headless stud loses the head restriction, and there may be a slight pull-out displacement in the normal direction, which leads to large plastic deformation at its root, an increase in stress level, and a decrease in bearing capacity.

Shear stiffness is an important indicator to measure whether the composite structure has good composite effect. The shear stiffness can be calculated based on the load-slip curve, which is defined as the slope of a secant line on the load-slip curve. Some researchers also use the slope of the secant line where the slip is 0.2 mm to express the shear stiffness (Tong et al., 2020; Zou et al., 2022). Cao et al. (Cao et al., 2017) used 3 methods to calculate the shear stiffness of conventional studs in UHPC. The results showed that the higher the point on the secant line, the lower the shear stiffness. For a single stud, the shear stiffness of stud obtained by the three methods varies between 266 and 396 kN/mm. However, since the slip of the stud in UHPC is relatively small, considering that the slip will have a greater impact on the shear stiffness, this paper adopted the method recommended in JSSC (2002) (JSSC Japan Society of Civil Engineers, 2002) to calculate the shear stiffness. JSSC (2002) (JSSC Japan Society of Civil Engineers, 2002) prefers to use points corresponding to 1/3 P_u. The shear stiffness calculated using selected data and test results is listed in Table 3. It can be seen from Table 3 that the shear stiffness of the headless studs is lower than that of the conventional studs. The average shear stiffness of conventional studs (STA-1 to UHPC-120–13) is 354.8, and the average shear stiffness of headless studs is 224.3. The average shear stiffness of headless studs is 36.8% lower than that of conventional studs. This may be attributed to the deformation of the headless studs during the elastic phase is larger than that of the conventional studs, resulting in lower shear stiffness.

The FE analysis was performed in the ABAQUS Explicit Module. The nonlinear contact as well as material damage and failure behavior can be powerfully simulated using the explicit central difference rule (Simulia, 2014; Guan et al., 2022; Xu et al., 2022). The FE models consisted of five components: H-section steel, UHPC layer, headless stud, weld, and steel bar. Considering the symmetry of geometry and loading, only a quarter of the push-out specimen was modeled to enhance computational efficiency.

As shown in Figure 11A, the UHPC layer, H-section steel, headless studs, and welds were simulated utilizing the C3D8R element type provided by the ABAQUS element library. C3D8R can prevent unexpected element shear locking, making it a suitable method for nonlinear analysis with reasonable accuracy (Mia, 2017). The steel bars were constructed via B31 elements because they primarily acted as constraints on the concrete. It is worth noting that for studs embedded in UHPC, the welds should be modeled in the analysis considering their necessary contribution to the shear strength of studs (Cao et al., 2017; Cao and Shao, 2019; Tong et al., 2020; Huang et al., 2021). In this study, the modeling method for welds was referenced from the literature (Cao and Shao, 2019), where a 1 mm × 1 mm slope was simulated at the top corner of the weld, as shown in Figure 11B. To accurately simulate the severe distortion of the headless stud and the contact behavior between UHPC layer and steel plate, a refined mesh was essential in these specific zones. Thus, the size of the element representing the root of headless studs and the surrounding UHPC material was set to 2.5 mm, and other zones were set to 8 mm.

As shown in Figure 11C, the involved contact pairs were the steel-UHPC interface and the headless stud-UHPC interface. A surface-to-surface contact was applied on the above-mentioned contact pairs. In this contact model, the normal behavior between the two surfaces was defined as “hard contact” in the normal direction. For headless stud-UHPC interface, a “penalty function method” was utilized for the tangential direction, with a friction coefficient of 0.4 (Luo et al., 2016b; Huang et al., 2021; Guan et al., 2022). While the friction coefficient was not defined for the steel-UHPC interface.

Based on the symmetry of the specimens, the symmetric boundary conditions were applied to the surface along the symmetric plane of the model. While all degree of freedoms were restricted at the bottom of UHPC layer. Steel bars were embedded into the UHPC layer through the “embedded region constraints” available in ABAQUS. In addition, the top surface of the steel beam was coupled to a point, a 6 mm displacement was applied to this point, and a smoothing analysis step was set to prevent load fluctuations.

Figure 14 shows the comparison between the FE analysis results based on the load-slip curve and the test results. It can be seen from Figure 14 that the curve trend obtained by FE calculation was close to the test results. The ultimate bearing capacity per headless stud in the FE was 62.6 kN, and the ratios to the DS-M1 and DS-M2 specimens were 0.99 and 1.02 respectively. The slip corresponding to the ultimate bearing capacity of the FE model was 2.419 mm, and the slip corresponding to the ultimate bearing capacity of the DS-M1 and DS-M2 specimens was 2.553 mm and 2.619 mm respectively, i.e., the errors were 5.2% and 3.0% respectively. These results show that the load-slip curve calculated by FE model is in good agreement with the test results.

Figure 15 shows the comparison of the failure mode between test results and FE analysis results. The compressive and tensile damage coefficients of concrete (DAMAGC and DAMAGT), along with the equivalent plastic strain (PEEQ) were used to track the UHPC and headless stud failure zones, respectively. As can be seen from Figure 15A, the damage of UHPC in the FE results appeared in a very small zone around the headless studs. The compressive damage mainly occurred at the rear of headless studs, while the tensile damage was obvious at the front of headless studs. Figure 15B shows the PEEQ of the steel components in FE results. The zones in gray represent that the PEEQ exceeds 20%, and at this threshold, the stud fracture is assumed (Xu et al., 2022). It can be observed that the gray zones appeared at the junction of stud shank and weld, indicating that the failure of headless studs is caused by the fracture at the root of stud shank. The results observed above are in good agreement with the test results.

Based on the stress slicing function in ABAQUS, the failure process of the headless stud in UHPC was observed, as shown in Figure 16. Here, q represents the resistance produced by UHPC to prevent headless stud from bending, and the red arrow corresponds to the maximum stress of headless stud and UHPC. The number of steps shown corresponds to the star markings in Figure 14. When the load was 0.3P_u, the headless stud was in the elastic stage. The bearing capacity mainly comes from the material properties of headless stud, and the bearing capacity increases rapidly. When the bearing capacity reached 0.7P_u, the headless stud begins to yield gradually, and the stress of the UHPC below the root of headless stud increased. At this time, the bearing capacity was mainly provided by UHPC, and the growth of bearing capacity was slower than before. In addition, a small amount of gap was observed at the rear end of the weld, which was caused by the downward movement of the steel beam. When the load was 0.85P_u, the stress of the local UHPC below headless stud exceeded the ultimate compressive stress, indicating that it was crushed. The plastic deformation of the headless stud becomes larger and larger. This moment the bearing capacity continued to be provided by UHPC. However, there was a slight pull-out displacement on the top of the headless stud, and a small separation occurred at the interface between the steel beam and UHPC. When the load reached 1.0P_u, the stress at the intersection between the root of headless stud and the weld was close to 530 MPa. The stress of the UHPC near headless stud continued to increase, and the bearing capacity was still mainly provided by UHPC. When the load exceeded 1.0P_u, the headless stud was sheared along its root, and the bearing capacity decreases rapidly.