Study on the influence of ribs on the bonding performance between ultra-high performance concrete and normal concrete

Abstract

This study investigated the bonding performance of the interface treated by ribs between Ultra-High Performance Concrete (UHPC) and Normal Concrete (NC) through double shear tests and finite element analysis. Besides, according to existing research results, the calculation methods for the shear capacity of the interface between UHPC and NC were discussed. The results show that specimens with a rib width of less than 20 mm were predominantly susceptible to rib shear failure, whereas those with a rib width exceeding 20 mm primarily exhibited NC fractures failure. The impact of rib height and rib spacing on the interface failure mode was complex and should be assessed based on the rib width. When the rib width was less than 20 mm, with an increase in rib spacing, the shear bearing capacity of the interface remained nearly constant. Nevertheless, when the rib width was 30 mm, the bearing capacity gradually decreased with an increase in rib spacing. Additionally, the bearing capacity initially increased and then decreased with an increase in rib height for specimens with a rib width exceeding 10 mm. The current calculation methods neglected the bearing capacity provided by the ribs, resulting in significant discrepancies between calculated results and experimental values.

Keywords

ultra-high performance concrete-normal concrete interface double-sided shear test failure modes shear bearing capacity finite element calculation methods

Introduction

Due to its high strength, good durability and superior toughness, UHPC had been widely implemented in practical engineering applications (Shafieifar et al., 2017; Wang et al., 2020; Yang et al., 2020). In recent years, UHPC had been innovatively employed as thin plates, serving as a durable and effective permanent formwork. On the one hand, UHPC formwork adeptly satisfied the demands of construction formwork. On the other hand, The UHPC formwork did not require removal upon completion of component curing. Moreover, the UHPC formwork was capable of bearing the load during the service stage of the structures. Existing research indicated that UHPC formwork could retard the development of cracks, enhanced the damage resistance of reinforced concrete structures, and improved the bearing capacity of reinforced concrete structures (Liang et al., 2020a, 2020b; Wang et al., 2021, 2024; Zhang et al., 2021). This observation indicated the stay-in-place UHPC formwork possessed significant potential for practical implementation in engineering projects. Currently, scholars have found that the interface bonding performance between prefabricated UHPC formwork and cast-in-place concrete had a vital influence on the mechanical properties of the members with UHPC formwork. Insufficient bonding strength may result in the interface separation between UHPC formwork and ordinary concrete. Consequently, to mitigate the risk of UHPC formwork detachment, appropriate measures should be implemented to augment the bonding strength between the UHPC formwork and normal concrete.

In recent decades, scholars have extensively researched the mechanical performance of the interface between UHPC and NC. It had been observed that factors influencing the properties of the UHPC-NC interface primarily included concrete strength, roughness of bonding surface and curing temperature of UHPC (Feng et al., 2020; Ju et al., 2020; Valikhani et al., 2020; Wang et al., 2018). Hussen et al. (2016, 2017) conducted experimental research to investigate the influence of interface roughness on the bonding performance of the interface between UHPC and NC. Feng et al. (2022) investigated the effect of steel fiber content on the performance of the UHPC to NC interface. The results revealed that with an increase in steel fiber content, the shear bearing capacity of the interface gradually increased. Furthermore, Kim et al. (2018) and Gopal et al. (2020) investigated the influence of lateral pressure on the UHPC-NC interface load-carrying capacity, and the findings revealed a notable increase in shear strength with the increase of lateral stress.

Prior investigations have already demonstrated that the roughness of the surface significantly affects the shear bearing capacity of the interface between UHPC and NC. The applications of bonded rebar, roughening, and ribs had been demonstrated to substantially enhance the interface bonding strength. (Bu et al., 2018; Jiang et al., 2016; Jiang et al., 2021; Liu et al., 2019; Semendary et al., 2020; Tian et al., 2022). Tayeh et al. (2013) found that the shear strength was enhanced by more than 100% for the UHPC-NC interface treated by sandblasting. Zhang et al. (2020a) conducted a double-sided shear test to investigate the influence of surface treatment methods on interfacial bonding strength between UHPC and NC. The test results revealed the roughening treatments such as scarification, drilling, and reinforcing could significantly enhance the interfacial shear capacity. Zhou et al. (2021a) further examined the impact of various surface treatment methods on the mechanical performance between UHPC and NC. The relevant results indicated surface treatment methods had a relatively minor impact on shear stiffness but exerted a significant influence on shear strength. Zhou et al. (2021b), Jiang et al. (2020), Guan et al. (2021) and Zeng et al. (2024) studied the shear performance of ribbed interfaces between UHPC and NC. The results indicated that the shear strength of the ribbed UHPC-NC interface was significantly higher than that of the non-ribbed UHPC-NC interface. Additionally, due to variations in rib dimensions or shapes, there were distinct differences in the failure modes of the interface.

The mechanical properties of the interface between UHPC and NC were influenced by various factors, and increasing surface roughness could significantly enhance the shear strength of the UHPC-NC interface. Among the prevalent surface treatment methods, the rib structure was straightforward to implement, and the shear bearing capacity of the ribbed interface was higher than that of the interface treated with roughening, drilling holes, and similar methods. At present, scholars had not conducted thorough research on interfaces treated with ribs, only demonstrating its superiority over other treatment methods. The specific impact of ribs on interface bond strength and the patterns of failure remained unclear. Hence, this study investigated the shear performance of the ribbed interface between UHPC and NC through double-side shear tests. The influence of rib sizes and rib spacing on the interface bearing capacity and failure modes was analyzed. Additionally, a finite element model was established, and parameter analysis was conducted. Finally, the formulas for calculating the shear capacity of UHPC-NC interface were discussed.

Experimental programme

Specimens

Table 1 provides the detailed parameters of the specimens, with a total of six groups with sixteen double-shear specimens. Figure 1 illustrates the detailed size of the specimens; the left and right of the specimens was UHPC prism with a size of 100 mm × 100 mm × 300 mm. The central portion consisted of an NC prism with dimensions of 120 mm × 100 mm × 300 mm. The areas of both interfaces of the specimen were 250 mm × 100 mm. Moreover, the rib widths (w) included 15 mm, 25 mm, and 35 mm. The rib heights (h) included 15 mm, 20 mm, and 25 mm. The rib spacing (d) included 25 mm, 40 mm, and 55 mm.

Table 1.

Design scheme of specimens.

Group	Specimen	Rib width w (mm)	Rib height h (mm)	Rib spacing d (mm)
Group1	UN-15-20-55	15	20	55
	UN-25-20-55	25	20	55
	UN-35-20-55	35	20	55
Group 2	UN-15-15-55	15	15	55
	UN-25-15-55	25	15	55
	UN-35-15-55	35	15	55
Group 3	UN-25-15-40	25	15	40
	UN-25-20-40	25	20	40
	UN-25-25-40	25	25	40
Group 4	UN-35-15-25	35	15	25
	UN-35-20-25	35	20	25
	UN-35-25-25	35	25	25
Group 5	UN-35-20-25	35	20	25
	UN-35-20-40	35	20	40
	UN-35-20-55	35	20	55
Group 6	UN-15-25-25	15	25	25
	UN-15-25-40	15	25	40
	UN-15-25-55	15	25	55

Figure 1.

The size of specimen.

The specimen fabrication process, as illustrated in Figure 2, primarily involved mold preparation, pouring and curing of UHPC, and casting of ordinary concrete. The finalized specimens are depicted in Figure 2(c).

Figure 2.

Manufacture of specimens: (a) Mold; (b) Firstly cured part of specimen; (c) Completely cured specimen.

Material properties

The mix proportions of the UHPC used in this study are presented in Table 2. When pouring the UHPC-NC specimens, 100 mm × 100 mm × 100 mm UHPC cubes samples and NC cubes samples were poured to test their compressive strength. Furthermore, bone shaped specimens were prepared to test the tensile strength of UHPC, with its dimensions outlined in Figure 3. The mechanical properties of UHPC and NC were measured according to Chinese standard (GB/T 50,081-2002), and the results are shown in Table 3. Where f_c,m represents the average compressive strength of cubic specimens. The elastic modulus and the tensile strength of NC are obtained through computation, and the relevant calculation methods are detailed in reference Chinese standard (GB/T 50081-2002, 2002).

Table 2.

Mix proportion for UHPC (kg/m³).

UHPC premix	Steel fiber (2.0% by volume )	Water-reducing admixture	Water
2398	242	25	242

Figure 3.

The size of the UHPC tensile specimen.

Table 3.

Mechanical properties of UHPC and NC.

Concrete type	Modulus of elasticity (GPa)	Compression strength f_c,m (MPa)	Tensile strength f_t (MPa)
UHPC	43	141.1	10.4
NC	35	53	3.5

Testing procedure

The test loading device is shown in Figure 4(a), an electro-hydraulic servo pressure tester with a capacity of 2000 kN was used to apply vertical pressure. Two steel rods were placed at the bottom of the specimen to reduce the contact area, thereby reducing the effects of unevenness at the bottom of the specimen. Laser level was used to proofread the position of the specimens to ensure that the center of the specimens coincides with the center of the loading plate. Preloading was conducted on each specimen with a preload force of 5 kN before formal loading. Subsequently, the entire loading process was conducted using displacement control, and the loading rate was 0.2 mm/min.

Figure 4.

Loading and testing apparatus: (a) Double shear test; (b) DIC equipment.

Digital Image Correlation (DIC) technology was used to collect the slip of the interface, and the relevant testing equipment is depicted in Figure 4(b). DIC was a measurement technique that integrates digital image processing with binocular stereoscopic vision. With this system, displacement could be measured by tracking speckle patterns in images.

Results and discussions

Failure modes

Figure 5 illustrates the failure modes of all specimens. It can be found that there were three failure modes, and the mainly failure characteristics were as follows: Type I: Pure UHPC-NC interfaces experienced separation, with the UHPC ribs in the specimen shearing off, while the NC exhibited no apparent damage. Type II: In this type, the UHPC ribs near the bottom of the specimen were sheared off, and the NC fractured near the interface. Type III: The surface of the UHPC ribs were crushed, but the UHPC ribs were not sheared off. The NC near the interface occurred fracture.

Figure 5.

Failure modes of specimens: (a) Group1; (b) Group2; (c) Group3; (d) Group4; (e) Group5; (f) Group6.

Figure 5(a) and (b) depict the influence of rib width on the failure modes. As can be seen from Figure 5(a), with the increase in rib widths, the failure modes transitioned from type I to type III. The UHPC ribs were completely severed for specimen UN-15-20-55, while the ribs near the bottom of the specimen exhibited breakage for specimen UN-25-20-55. In contrast, specimen UN-35-20-55 primarily exhibited NC fracture failure, with no discernible damage to the UHPC ribs. In Figure 5(b), the failure mode of all three specimens was Type III. Overall, with larger rib widths, the mainly failure of the specimens was characterized by the fracture of NC.

In Figure 5(c), all specimens exhibited Type II failures, with the UHPC ribs near the bottom being sheared off. In Figure 5(d), the failure of specimens was mainly NC fracture, and the rib at the bottom of specimen UN-35-25-55 was fractured. It can be seen that, within the same group of specimens, the impact of varying rib height on the failure mode was not conspicuous. Furthermore, the distinct rib spacing in specimens from Group 3 and Group 4 resulted in marked differences in the failure modes of the specimens in the two groups. Thus, in investigating the impact of rib height on failure mode, it was imperative to comprehensively consider the influence exerted by rib spacing.

Figure 5(e) and (f) show the failure modes of specimens with various rib spacing. In Figure 5(e), three specimens exhibited Type III failures. In Figure 5(f), it was apparent that all specimens exhibited UHPC-NC interface separation failures, with at least one interface occurred complete fracture of UHPC ribs. For the specimens in these two groups, the variation in rib spacing had a negligible effect on the failure mode. The width of the ribs determined the failure modes of the specimens in the both groups. For specimens with rib width of 15 mm, the shear resistance of the ribs was relatively weak, resulting in nearly all ribs shearing off. Conversely, when the rib width was 35 mm, the larger rib width contributed to stronger shear resistance.

The effect of rib sizes and spacing on the failure modes of the interface was complicated. However, in conclusion, it was evident that rib width played a decisive role in determining the failure mode of the interface. When rib width varies, there may be differences in the impact patterns of rib spacing and height on the failure modes.

Load-slip curves

The slip value of the interface is determined by averaging the relative slip values between points A and B, and points C and D, as shown in Figure 6

Figure 6.

Slip region selection.

Figure 7 presents the load-slip curves of the specimens. Apparently, the load-slip curves could be divided into three types, and the first type of curve was composed of elastic, yielding, and descending stages. In this category, when specimens reached the peak load, the interface did not undergo complete failure, retaining a certain level of bearing capacity. The second type of curve could be classified into two branches: elastic stage and descending stage. The failure of these specimens was between ductile failure and brittle failure. The third type of curve had elastic stage and yielding stage, but there was no descending stage or the slip value in descending stage was very small. When loaded to the peak load, the specimens were almost instantly failure, showing obvious brittle failure. For specimens in which ribs experienced fracture, the load-slip curves generally undergo a yielding stage. Moreover, compared to specimens that the NC occurred fracture failures, those with ribs fractures exhibited a larger peak slip. This also indicated a substantial impact of UHPC ribs in enhancing the deformation ability of the interface

Figure 7.

Load- interfacial slip curves of specimens: (a) Group1; (b) Group2; (c) Group3; (d) Group4; (e) Group5; (f) Group6.

The load-slip curve was analyzed by taking the first group of specimens as an example. As depicted in Figure 7(a), the load-slip curve of specimen UN-15-20-55 was composed of elastic, yielding, and descending segments. During the initial loading stage, the curve was in the elastic segment, and the curve transitioned to the yielding stage as the load increased to approximately 127 kN. During this stage, the increase magnitude of slip was significantly greater than that of load. At failure, the UHPC ribs were sheared off. There was a significant improvement in slip values of the interface duo to the high toughness of the UHPC ribs. It showed that the specimen UN-15-20-55 had good plastic deformability. Before reached to the peak load, the curve of the specimen UN-25-20-55 went through only elastic stage, while the curve of the specimen UN-35-20-55 underwent elastic stage and yielding stage. However, it was noteworthy that the slip values corresponding to the peak load for these two specimens were essentially identical. Furthermore, it could be observed that there was no obviously descending stage of the curves for these two specimens. At failure, the NC of the two specimens was fractured suddenly. Duo to the quasi-brittleness characteristic of NC, the specimens exhibited a distinguishing brittle failure.

Ultimate bearing capacity

The ultimate shear bearing capacities of the specimens are presented in Table 4. For the specimens with failure modes of type I, at failure, the UHPC ribs experienced fracture, while the NC showed no signs of damage. The shear bearing capacity of these specimens was primarily determined by the shear strength of the UHPC ribs. For the specimens with failure modes of type II, significant damage was observed in both the NC and ribs. The shear bearing capacity of these specimens was determined by the shear strength of both ribs and NC. When the specimen undergoes the type III failure, the NC embedded between the UHPC ribs experienced fracture, while the UHPC ribs showed no significant damage. The shear bearing capacity of these specimens was determined by the shear bearing capacity of the NC. Furthermore, the shear bearing capacity also depended on the extent of damage sustained by the two interfaces of specimens.

Table 4.

Interfacial Bearing Capacity and Slip.

Number	Specimen	Rib width (mm)	Rib height (mm)	Rib spacing (mm)	Peak load (kN)	Peak slip (mm)	Failure mode
Group1	UN-15-20-55	15	20	55	299.4	0.47	I
	UN-25-20-55	25	20	55	436.5	0.26	II
	UN-35-20-55	35	20	55	419.8	0.28	III
Group 2	UN-15-15-55	15	15	55	313.9	0.28	III
	UN-25-15-55	25	15	55	331.3	0.35	III
	UN-35-15-55	35	15	55	332.1	0.31	III
Group 3	UN-25-15-40	25	15	40	405.7	0.49	II
	UN-25-20-40	25	20	40	297.9	0.22	II
	UN-25-25-40	25	25	40	345.4	0.37	II
Group 4	UN-35-15-25	35	15	25	213.5	0.23	III
	UN-35-20-25	35	20	25	246	0.66	III
	UN-35-25-25	35	25	25	349.6	0.14	II
Group 5	UN-35-20-25	35	20	25	246	0.66	III
	UN-35-20-40	35	20	40	377.2	0.36	III
	UN-35-20-55	35	20	55	419.8	0.28	III
Group 6	UN-15-25-25	15	25	25	294.7	0.37	II
	UN-15-25-40	15	25	40	422.8	0.53	II
	UN-15-25-55	15	25	55	270.2	0.22	I

A comparison of the load capacities of specimens in Group 1 revealed that the specimens with lager rib width (w = 25 mm and 35 mm) exhibited significantly higher bearing capacities than those with a 15 mm rib width. However, the load capacities of the two specimens with 25 mm and 35 mm rib widths were essentially the same. This discrepancy could be attributed to the predominant failure mode being NC fracture when the rib width was larger. In such cases, the load-bearing capacity was primarily contingent on the shear strength of the NC. The failure mode of specimen UN35-15-55, specimen UN35-20-55, and specimen UN35-25-55 was the same, with a similar degree of damage on both interfaces. Comparing their bearing capacities, it was evident that, when the rib width was 35 mm, the load capacities of the specimens initially rise and then decreased with the increase in rib height. Regarding the effect of rib spacing, as the rib spacing increased, there was a higher propensity for separation to occur at the interface between ribs, ultimately leading to a reduction in the shear bearing capacity of the specimens.

Finite element analysis

Materials modeling

The nonlinear behavior of UHPC and NC under compression and tension conditions was simulated using the Concrete Damaged Plasticity (CDP) model in ABAQUS. The constitutive model provided by the Chinese standard (GB 50010-2010, 2015) was employed to model the mechanical behavior of NC. The constitutive model proposed by Guo et al. (2017) and Hu et al. (2018) were respectively utilized to simulate the compressive and tensile behavior of UHPC. In addition, the damage parameters of the UHPC and the NC under compression and uniaxial tension are calculated by equation (1).

d_{c} (d_{t}) = 1 - \sqrt{\frac{σ}{E ε}}

(1)

Where, d_c and d_t are concrete compression and uniaxial tension damage parameter, respectively; σ represents the concrete stress; ε denotes the concrete strain; E represents the concrete elastic modulus.

Contact relationship

The behavior of the interface between UHPC and NC was simulated by the traction-separation model and“hard”contact with friction penalty. As shown in Figure 8, the behavior of horizontal contact surfaces was modeled by“hard”contact with friction penalty, and the behavior of vertical contact surfaces was simulated by traction-separation model. The constitutive property of traction-separation model used in the paper is shown in Figure 9. K represents uncouple stiffness coefficient, including normal stiffness K_n and tangential stiffness K_s, K_t. In addition, t denotes the contact stress, including the normal stress t_n and other two shear stress t_s, t_t. Jang et al. (2017, 2018) and Farouk et al. (2022) employed the traction-separation model to simulate the behavior of the interface between UHPC and NC, providing the values of relevant parameters in the model. Thus, based on the parameter values provided by relevant scholars, this study determined the values of these parameters, as shown in Table 5. The interaction between NC and top end plate was modeled by “tie” contact. The interaction between steel rods and bottom end plate was simulated using friction penalty with a friction coefficient of 0.4 (Zhang et al., 2020).

Figure 8.

Finite element model.

Figure 9.

Uniaxial stress-displacement curve of the interface.

Table 5.

The Values of Main Parameters (Jiang et al., 2018; Farouk et al., 2022).

Parameters	Values
K_n, K_s and K_t (MPa.mm⁻¹)	980
t_n, t_s and t_t (MPa)	2.5
Plastic displacement $δ_{m}^{f}$ (mm)	1.4
Stabilization	0.0001
Friction coefficient	0.6

Mesh and boundary condition

In the paper, all parts of the UHPC-NC specimen were modeled using solid elements (C3D8R). Moreover, in the finite element model, the accuracy of the calculation results improves as the mesh size decreases. However, this reduction in mesh size also leads to an increase in computational cost and time. Considering the rib size of the specimen, the author determined that a mesh size of 5 mm was optimal after conducting several trial calculations. The top of specimen could translate along z axis, but other degrees of freedom were restrained. For the bottom end plate, the translate and rotate in the three directions of x, y and z were restrained.

Verification

Table 6 presents the bearing capacity results obtained through FEA for the specimen with complete destruction of both interface. Figure 10 provides a comparison of the load-slip curves for some specimens. It can be observed that the finite element simulation results aligned well with the experimental results, with error values within 11%. Moreover, the curves obtained from the finite element model were essentially consistent with the experimental curves.

Table 6.

Comparison of the FEA results to the test results.

Specimen	V _t	V _s	V_s/V_t
UN-15-20-55	299.4	265.9	0.89
UN-35-20-40	377.2	358.5	0.95
UN-35-15-55	332.1	353.3	1.06
UN-25-25-40	345.4	321.2	0.93
UN-35-25-25	349.6	351.0	1.00
UN-15-25-25	294.7	287.9	0.98
UN-15-25-55	270.2	263.8	0.98

Note:V_t denotes the test result; versus represents the FEA results.

Figure 10.

Comparison of the load-slip curves: (a) Specimen UN-35-20-40; (b) Specimen UN-35-25-25.

In order to further validate the accuracy of the model, the failure modes of specimens UN-35-20-40 and UN-35-25-25 are compared in Figure 11. It can be observed that there were distinct shear cracks near both interfaces, and the NC embedded between the UHPC ribs experienced fracture. The established finite element model was capable of effectively simulating the failure of the specimens. All the above results showed that the FEA model established had certain degree accuracy and could be used for parameters analysis below.

Figure 11.

Comparison of failure modes of the specimens: (a) Specimen UN-35-20-40; (b) Specimen UN-35-25-25.

Parametric analysis

The effect of rib size, rib spacing, and rib number on the interface load-carrying capacity was further investigated by using the established finite element model. Figure 12 shows the sizes of finite element model, the size and the interface areas of the specimens in the finite element model were the same as those of the test specimens.

Figure 12.

The dimension of FEA model: (a) Specimens with various ribs size; (b) Specimens with various rib distance.

Effect of rib size

Figure 13 presents the shear bearing capacity of specimens with various rib sizes. The plotted results showed that when the rib width was 10 mm, the load-bearing capacity of the specimens remained essentially unchanged with the increase in rib height. As detailed in Section 3.1, small ribs width (w = 15 mm) were prone to fracture. Consequently, for specimens with a rib width of 10 mm, the likelihood of rib breakage was higher, and the bearing capacity was depend on the ribs shear strength. For specimens with rib widths of 20 mm and 30 mm, the bearing capacity initially rise and then decreased with the increase of rib height. Figure 14 depicts the plastic strain nephogram of the finite element model with a rib width of 20 mm and a rib height of 20 mm and 25 mm respectively. It can be observed that the compression failure area of NC under the rib of the specimen with a rib height of 20 mm was obviously higher than that of the specimen with a rib height of 25 mm. This observation indicated a higher bearing capacity of NC in the specimen with a 20 mm rib height, thus contributing to an overall greater bearing capacity of the specimen. In conclusion, it was recommended that the rib height should not exceed 20 mm.

Figure 13.

Effect of rib size.

Figure 14.

The plastic strain nephogram of specimens with different rib size.

Effect of rib spacing

Figure 15 shows the bearing capacity of specimens with different rib spacing. It can be seen that, for specimens with rib width of 10 mm or 20 mm, the load-bearing capacity remained essentially unchanged with an increase in rib spacing. Conversely, for specimens with a rib width of 30 mm, the load-bearing capacity gradually decreased with an increase in rib spacing. For specimens with rib widths of 10 mm and 20 mm, the ribs experienced fracture, and thus, the bearing capacity depended on the shear strength of UHPC ribs. Figure 16 shows the plastic strain nephogram of the finite element model with various rib spacing. It can be observed that an increase in rib spacing resulted in the plastic strain region approaching the interface. This indicated that with the increase in rib distance, the interface between the ribs was more likely to separate, thereby resulting in a gradual decline in the bearing capacity of the specimens.

Figure 15.

Effect of the rib distance.

Figure 16.

The plastic strain nephogram of specimens with different rib distance: (a) w = 30 mm, d = 70 mm; (b) w = 30 mm, d = 90 mm; (c) w = 30 mm, d = 110 mm.

Effect of rib number

Figure 17 presents the influence of the rib numbers on the shear bearing capacity. It can be seen that the shear capacity increased gradually with the increase of the rib numbers. When the rib width was 10 mm, increasing the number of ribs from one to three resulted in only a 5% increase in shear bearing capacity. However, when the rib width was 25 mm, the load-bearing capacity of the specimen with three ribs was increased by 21.8% compared with the specimen with one rib. It showed that the specimens with relatively more rib had better shear bearing capacity. In addition, as the increase of the rib numbers, the shear bearing capacity did not increase proportionally. The fact showed that although increasing the number of ribs could enhance the load-carrying capacity of the interface, the improvement effect on shear capacity gradually decreased. In practice, the number of rib should be determined according to the area of interface and the size of rib.

Figure 17.

Effect of the rib number.

Discussion on calculation methods

Currently, scholars have proposed many calculation methods for calculating the shear load-carrying capacity of the interface between UHPC and NC based on theoretical analysis and experimental verification. This paper presented five calculation methods utilized for assessing the bearing capacity of the interface between UHPC and NC, as shown in Table 7. Additionally, a thorough evaluation of the accuracy of each calculation method was conducted.

Table 7.

Calculation Methods of Shear Bearing Capacity of UHPC-NC Surface.

Source	Equation	Number
AASHTO (2003)	$V_{u} = A_{ku} \sqrt{f_{c}} (0.9961 + 0.2048 σ_{n}) + 0.6 A_{b} σ_{n}$	(2)
Zhang et al. (2020b)	$V_{u} = β τ_{c} A_{b} + α A_{ku} \sqrt{f_{u, c}}$	(3)
Zhang (2020)	$τ_{u} = c f_{t} + μ ρ κ_{1} f_{y} + κ_{2} ρ \sqrt{f_{y} f_{c} / α_{E}}$	(4)
Wang (2016)	$V_{u} = 0.5 ξ_{1} ξ_{2} \sqrt{ξ_{3} ξ_{4} f_{c} f_{t}} A_{p} + 0.5 ξ_{1} \sqrt{f_{u, c} f_{u, t}} A_{u} + τ_{z} A_{z}$	(5)
Sun (2022)	$τ_{u} = ({1.659 - 1.406 (ρ / m)}^{- 0.116}) f_{cu}^{0.55}$	(6)

Note: Where V_u and τ_u represent shear load-carrying capacity and shear strength respectively; A_ku is the sum of the cross-sectional areas of the UHPC ribs; f_c is the compressive strength of normal concrete cylinder; $σ_{n}$ is the compressive stress perpendicular to the interface; A_b is the joint surface area except the cross section of the ribs; $β$ is the interface roughness coefficient; $τ_{c}$ is the shear strength of normal concrete; $α$ is the ribs coefficient, $α = 0.996$ ; $f_{u, c}$ is the compressive strength of UHPC cylinder; c is the interfacial bonding coefficient; f_t is the split tensile strength of normal concrete; $μ$ is the friction factor; $ρ$ is the effective ribs ratio; $κ_{1}$ , $κ_{2}$ is the interaction coefficient; $f_{y}$ is the yield strength of reinforcement; $α_{E}$ is the ratio of elastic modulus of steel bar to UHPC elastic modulus; $ξ_{1}$ , $ξ_{2}$ , $ξ_{3}$ , $ξ_{4}$ are the correlation coefficient; A_p is the area from the end of the interface to the rib; A_u is the area between two ribs; A_z is the sectional area of studs; $f_{u, t}$ is the tensile strength of UHPC; $τ_{z}$ is the shear strength of stud; m is the shear key length ratio; $f_{cu}$ is the cube compressive strength of NC.

The above formulas were used to calculate the shear load-carrying capacity of the experimental specimens. Table 8 provides the calculation results, and Figure 18 presents the comparison between the calculated values and the experimental values. It was apparent that the calculation results obtained by AASHTO were obviously less than the test results, and the average ratio of the calculated results to the experimental results was 0.52. The main reason was that the impact of lateral pressure on shear bearing capacity was considered in AASHTO code, but the lateral pressure was not provided in test. This resulted in that the calculated values were smaller than the experimental values.

Table 8.

The Calculated Results of the Shear Bearing Capacity.

Specimen	V_t /kN	V₂/kN	V₃/kN	V₄/kN	V₅/kN	V₆ /kN	V₂ /V_t	V₃ /V_t	V₄ /V_t	V₅ /V_t	V₆/V_t
UN-15-20-55	299.38	97.03	176.9	358.1	266.6	226.76	0.32	0.59	1.20	0.89	0.76
UN-25-20-55	436.52	161.7	229.9	459.6	325.7	261.27	0.37	0.53	1.05	0.75	0.60
UN-35-20-55	419.80	226.4	282.9	561.1	384.8	285.71	0.54	0.67	1.34	0.92	0.68
UN-15-15-55	314.66	97.03	176.9	358.1	266.6	209.47	0.31	0.56	1.14	0.85	0.67
UN-25-15-55	331.34	161.7	229.9	459.6	325.7	245.14	0.49	0.69	1.39	0.98	0.74
UN-35-15-55	332.10	226.4	282.9	561.1	384.8	270.41	0.68	0.85	1.69	1.16	0.81
UN-25-15-40	405.70	161.7	229.9	459.6	325.7	251.86	0.40	0.57	1.13	0.80	0.62
UN-25-20-40	297.94	161.7	229.9	459.6	325.7	267.76	0.54	0.77	1.54	1.09	0.90
UN-25-25-40	345.44	161.7	229.9	459.6	325.7	279.74	0.47	0.67	1.33	0.94	0.81
UN-35-15-25	213.50	226.4	282.9	561.1	384.8	284.75	1.06	1.33	2.63	1.80	1.33
UN-35-25-25	349.64	226.4	282.9	561.1	384.8	310.74	0.65	0.81	1.60	1.10	0.89
UN-35-20-25	246.00	226.4	282.9	561.1	384.8	299.58	0.92	1.15	2.28	1.56	1.22
UN-35-20-40	377.16	226.4	282.9	561.1	384.8	291.77	0.60	0.75	1.49	1.02	0.58
UN-15-25-25	294.66	97.03	176.9	358.1	266.6	251.86	0.33	0.60	1.22	0.90	0.85
UN-15-25-40	422.84	97.03	176.9	358.1	266.6	245.14	0.23	0.42	0.85	0.63	0.58
UN-15-25-55	270.16	97.03	176.9	358.1	266.6	239.79	0.36	0.65	1.33	0.99	0.89
Average ratio							0.52	0.73	1.45	1.02	0.81
Standard deviation							0.05	0.06	0.11	0.07	0.05

Note: V_t represents test result. V₂, V₃, V₄, V₅ and V₆ denote the results calculated by equation (2), equation (3), equation (4), equation (5) and equation (6), respectively.

Figure 18.

Comparison of the calculated results to the test results.

In the equation (3), the shear bearing capacity was obtained by combining the bond strength of the interface and the shear strength of the UHPC ribs. The results showed that the calculated valued obtained by equation (3) was smaller than the test values. The average ratio was 0.73, with a standard deviation of 0.06.

Equation (4) was the calculation formula for the shear load-carrying capacity of the UHPC-NC interface with bonded rebar. From Figure 18, it can be observed that the calculated values given by equation (4) were significantly higher than the test values, and the average ratio was 1.45. Equation (5) was obtained by introducing the corresponding coefficient on the basis of the formula for calculating the shear strength of normal concrete. The average ratio of the calculated values to the test values was 1.02, and the standard deviation was 0.07. The effect of rib size, spacing, and the strength of NC was taken into account in equation (6). Nevertheless, the contribution of UHPC ribs was not incorporated, resulting in calculated values generally undershooting the corresponding experimental results.

Through a comparison of the bearing capacity for specimens with both interfaces fracture, it becomes apparent that the calculated results from equation (5) closely align with the experimental values. In contrast, other computed values significantly deviate from the experimental findings. In summary, existing calculation methods exhibited limited accuracy in predicting the shear load-carrying capacity of the ribbed interface between UHPC and NC.

Conclusions

Sixteen double-sided shear specimens of UHPC-NC were designed and cast. Through a series of push-out tests, the influence of rib size and rib spacing on the bond performance of the interface between UHPC and NC was investigated. A finite element model was established to analyze the influence of various parameters on the shear load-carrying capacity of the interface. Finally, the accuracy of the existing calculation methods for the shear load-carrying capacity of the UHPC-NC interface were discussed, the main conclusions were as follows:

(1) The failure modes of the specimens exhibited distinct variations influenced by the rib width, rib height, and rib spacing. Among these factors, the rib width emerged as the most influential in determining the failure mode. The UHPC rib was prone to fracture when rib width is 15 mm, while for specimens with a rib width of 25 mm and 35 mm, the failure was mainly NC fracture.

(2) As the width and number of ribs increase, the shear bearing capacity increased gradually. When rib width was less than 20 mm, changing the rib spacing had no impact on the bearing capacity. However, when rib width was 30 mm, the load-bearing capacity of the specimens gradually decreased with the increase in rib spacing. Besides, for specimens with a rib width exceeding 10 mm, the bearing capacity increased first and then decreases with the increase of the rib height from 10 mm to 25 mm, and the bearing capacity was the highest when the rib height was 20 mm.

(3) There were great differences in the shear bearing capacity values calculated by different calculation methods. The current calculation methods overlooked the contribution of UHPC ribs to the interface load-bearing capacity, resulting in significant discrepancies between calculated results and experimental values. In general, the calculated value was smaller than the experimental value.

Due to the limited number of specimens, the influence of concrete strength was not considered in this paper. When the concrete strength was different, the optimal rib size and rib spacing may be different. Therefore, it was necessary to further study the NC strength on bonding performance and failure mode of the ribbed interface between UHPC and NC.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is supported by the National Natural Science Foundation of China grant numbers (52178159), (52108171), (52178505), the Scientific Research Plan Projects of Education Department of Shaanxi Provincial Government (23JY040).

ORCID iDs

Xue-hui You

Yi Tao

Data availability statement

All data, models, or code generated or used during the study are available from the corresponding author by request.*

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