Experimental Study on Bond and Force Transmission Properties of Steel Reinforcement in Non-Contact Lap Splice Encased in Calcium Sulphoaluminate Cement-Based Micro Steel Fiber Concrete

Abstract

CSMSFC (Calcium Sulphoaluminate Cement-based Micro Steel Fiber Concrete) possesses the advantages of early strength, high strength, exceptional toughness, minimal shrinkage, and excellent bond performance with bars. When applied to NLSB (Non-contact Lap Splice of Bars) in prefabricated structures, CSMSFC enhances mechanical performance while preventing shrinkage cracking and reducing seismic damage. Additionally, it shortens construction periods for prefabricated structures and achieves a comprehensive improvement in seismic performance and construction efficiency. However, there is a lack of systematic testing of factors influencing the bond strength between CSMSFC and NLSB and the effect of CSMSFC on the force transfer performance between NLSB. Therefore, the axial tensile tests of NLSB were conducted on 51 non-contact lapping specimens to investigate the bond properties and force transfer mechanism between lapping bars and CSMSFC. The effects of lapping length, volume fraction of steel fibers, spacing of bars, and concrete cover thickness on the lapping characteristics were examined, and the comparison with OPMSFC (Ordinary Portland Cement-based Micro Steel Fiber Concrete) was also considered. The experimental results demonstrate that the bond strength between bars and CSMSFC increased by 36.8%, 42.3%, and 43.3% respectively, with volume fractions of steel fiber at 1.5%, 3%, and 4.5% compared to the absence of steel fiber. The bonding effect between CSMSFC and bars is similar to that of OPMSFC and bars. The bond strength between CSMSFC and the bars improved by 4.3% and 6.6% with the increases of the spacing of bars from 0 to 20 mm and the concrete cover thickness from 10 to 30 mm. Conversely, with the increases of the lapping length from 50 mm to 100 mm, 200 mm, and 300 mm, the bond strength decreased by 46.8%, 72.2%, and 82.0%, respectively. Finally, based on the force transmission mechanism of the non-contact lapping bars, a calculation model is proposed for determining the lapping length while considering the reinforcing effect of steel fiber “stirrups.” A formula is derived from the model to calculate the minimum lapping length of HRB400 bars in CSMSFC, considering the volume fraction of steel fibers, which can assist in designing the minimum lap length of NLSB in practical applications.

1. Introduction

Prefabricated reinforcement concrete (PRC) structures have been applied worldwide in construction projects owing to the advantages of high efficiency, greenness, labor savings, and economic benefits in contrast to traditional cast-in situ structures [1,2,3]. The quality of PRC buildings relies heavily on the performance of the connections between prefabricated components, which are essential to transfer loads and guarantee stiffness, ductility, and stability in earthquakes [4,5]. A great deal of investigation has been conducted on different kinds of connections; the seismic performance of post-cast monolithic assemblies closely resembles that of cast-in situ assemblies. Thus, the previous studies related to the connections of PRC structures were mainly focused on the bonding performance between bars and concrete.

The effective force transmission between the bars in a post-cast monolithic connection depends on the bonding force between the grout and the bars or sleeve [6], which can be achieved through three main forms: sleeve grout connection, restrained grout anchor lapping connection, and non-contact lapping connection [7,8]. Compared with the other two methods, the utilization of non-contact lapping is prevalent in the construction of prefabricated piers, fully prefabricated or superimposed shear walls, columns, and plates due to its inherent advantages of simple design, efficient implementation, and great quality management [9,10,11]. Previous research has demonstrated that spliced length, spacing of lapped bars, concrete cover thickness, and lateral restraint are the primary factors influencing the performance of NLSB (Non-contact Lap Splice of Bars) [12,13,14,15,16,17]. Lu et al. [16] investigated the impact of concrete cover thickness on bond performance and found that increasing the concrete cover thickness contributes to enhancing interface bond strength. They also proposed that a critical concrete cover thickness is approximately three times the diameter of bars. Kehinde et al. [17] conducted experiments to examine the influence of different stirrups on reinforcement bond strength and discovered that augmenting transverse constraint significantly enhances longitudinal reinforcement bond strength. To enhance the lateral restraint capacity of the lapped joint, conventional OPC (Ordinary Portland Concrete) or UHPC (Ultra-High-Performance Concrete) is commonly employed [18], while augmenting the stirrup reinforcement ratio of the joint [18]. The utilization of UHPC in the NLSB, studied by Haibo [19], achieved enhanced flexural capacity. However, poor toughness and a weak bond between ordinary concrete and bars may lead to problems such as long lengths of lapped reinforcement, low bearing capacity, and brittle failure [19]. The self-shrinking deformation of UHPC exhibits significant magnitude [20], thereby resulting in compromised volume stability of the joint and consequently leading to premature concrete cracking. On the contrary, both types of concrete exhibit an extended curing period, thereby impeding the construction efficiency of prefabricated structures. Additionally, an increase in the stirrup ratio results in a significant escalation of project costs. Augmenting the type and quantity of bars may lead to uneven stress distribution at the joint, posing challenges in controlling bar deformation. The concrete in the post-cast area of the prefabricated structure should therefore possess sufficient toughness, bearing capacity, bonding properties, and adequate lateral constraints.

The sulphoaluminate cement exhibits early strength, high strength, and slight expansion [21,22], which are suitable for the rapid assembly of prefabricated components. However, a lack of ductility and toughness makes it prone to brittle failure [23]. The steel fibers have the advantage of increasing the toughness of concrete [24], and the incorporation of MSF (Micro Steel Fiber) into CCSAC (Calcium Sulphoaluminate Cement) results in the formation of a novel cementitious composite material, namely CSMSFC (Calcium Sulphoaluminate Cement-based Micro Steel Fiber Concrete), which possesses superior early strength and toughness. Li et al. [25] investigated the impact of steel fibers, polypropylene fibers, and basalt fibers on the shrinkage performance of concrete. The findings revealed that steel fibers exhibited superior shrinkage inhibition properties, with a reduction in shrinkage rate of 30.6% achieved with a dosage of 0.6% steel fibers. Furthermore, steel fibers demonstrated the ability to mitigate concrete cracking, enhance resistance against splitting and bending toughness, effectively improve lateral constraints at lapped joints, and prevent brittle damages [26]. The study conducted by Feng et al. [26] demonstrated a significant improvement in the bending toughness of CSMSFC with an increase in the volume fraction of steel fibers from 0% to 2%, while the ductility showed a slight increase. Current research has indicated that incorporating an appropriate amount of steel fibers into concrete can effectively improve the bond strength between concrete and reinforcement [27,28,29]. The bonding property of steel fiber sulphoaluminate cement mortar was investigated by Feng et al. [30,31]. The result displayed that the bonding strength at 1-day age reached 85% of that at 28-day age and exhibited an increasing trend with the increase of the volume fraction of steel fibers, satisfying the requirements for efficient assembly and construction of prefabricated components during a short construction period.

Additionally, in order to determine the minimum lapped length of the NLSB, it is imperative to research the force transfer mechanism of CSMSFC within the NLSB. Robinson [32] postulated that the inclined compression bar formed subsequent to concrete cracking between bonded bars serves as the primary mode for transmitting forces among non-contact bonded bars. The mechanism of force transmission between lapped bars through concrete compression bars was verified by Sagan et al. [33]. Accordingly, they proposed that when the influence of bar spacing cannot be ignored, the actual force transmission length of bars should be calculated based on the effective lapped length. Based on this, it is necessary to establish a specific functional relationship between the minimum lapped length of bars and the basic mechanical properties of CSMSFC, component size, and other parameters in order to provide a theoretical calculation method for practical engineering components while reducing the difficulty of practical application.

The present study investigates the influence of volume fraction of steel fibers (0%, 1.5%, 3%, 4.5%), concrete type (CSMSFC, OPMSFC), lapped length of bars (50 mm, 100 mm, 200 mm, 300 mm), spacing of bars (0 mm, 5 mm, 10 mm, 20 mm), and concrete cover thickness (10 mm, 20 mm, and 30 mm) on the bonding properties at NLSB through conducting axial tensile tests on seventeen groups of specimens. The force transfer mechanism of the non-contact lapping bars is utilized to derive a formula for calculating the minimum lapped length, taking into account the inner circumferential constraint of CSMSFC. This provides a design basis for determining the minimum lapped length of the non-contact lapped bars in CSMSFC.

2. Materials and Methods

2.1. Specimen Design and Manufacture

The design of the axial tensile test specimen is based on NLSB. The test specimens are cuboid with a cross-section size of 150 mm × 150 mm. The concrete cover provides lateral restraint for the unbonded bars, ensuring their stability. The two lapped reinforcement bars serve different purposes: one is designed to bear the load, while the other functions as an anchor. Specifically, the loading reinforcement has a loading end and a free end, whereas the anchoring reinforcement has a fixed end and a free end. They represent the longitudinal bars on the same side of the two prefabricated members, and are used to simulate the bonding of a single set of non-contact lap bars in a post-cast CSMSF. According to the drawing device requirements for this test, the length of the fixed end for the loading reinforcement is set at 450 mm, while the length of the fixed end for the anchoring reinforcement is set at 360 mm. A reserve measuring 100 mm in length is provided at both of the free ends.

Both sides of the bars are equipped with PVC pipes that extend 20 mm into the concrete, serving to mitigate concentrated stress at both ends and prevent potential damage to the concrete. Displacement meters are positioned 80 mm away from the concrete surface on either end of the bars to measure its elongation. The specific dimensions of the specimen for which unit is in mm can be seen in Figure 1. A total of 51 tensile specimens (17 groups, each containing 3 specimens) were examined to investigate the influence of volume fraction of steel fibers, type of concrete, lapped length, bar spacing, and concrete cover thickness on the lapping properties of bars. The classification and key parameters for each group are presented in

Table 1. Main parameters of tensile specimens.

Specimen Number	Bar Diameter (mm)	Type of Concrete	Volume Fraction of Steel Fibers	Lap of Splice (mm)	Spacing of Bars (mm)	Concrete Cover Thickness (mm)	Specimen Length (mm)
0%-100	12	CSAC	0%	100	10	20	140
0%-200				200	10	20	240
0%-300				300	10	20	340
1.5%-100			1.5%	100	10	20	140
3%-50			3%	50	10	20	140
3%-100-CSAC				100	10	20	140
3%-200-0				200	0	20	240
3%-200-5					5	20	240
3%-200-10-10					10	10	240
3%-200-10-20-CSAC						20	240
3%-200-10-30						30	240
3%-200-20					20	20	240
3%-300-CSAC				300	10	20	340
4.5%-100			4.5%	100	10	20	140
3%-100-OPC		OPC	3%	100	10	20	140
3%-200-OPC				200	10	20	240
3%-200-OPC				300	10	20	340

Note: The group number represents the following parameters from left to right: volume fraction of steel fibers (0%, 1.5%, 3%, 4.5%), reinforcement lapped length (100 mm, 200 mm, 300 mm), reinforcement bar spacing (0 mm, 5 mm, 10 mm, 20 mm), concrete cover thickness (10 mm, 20 mm, 30 mm), and concrete type (CSAC, OPC). If not specified on the label, the default values are a spacing of 10 mm for reinforcement bars, a thickness of the concrete protective layer of 20 mm, and CSAC as the concrete type.

.

The specimen was molded using a wooden mold, which was then placed in a standard curing room for 28 days before the removal of the mold and subsequent axial tensile testing. Figure 2 illustrates the wooden mold used. Additionally, six concrete test blocks measuring 150 mm × 150 mm × 150 mm should be reserved for each group of specimens, with consistent curing methods and durations as those employed for the tensile specimens. Compressive strength and splitting tensile strength tests should be conducted in accordance with Chinese standard GB/T 50081-2009 [34].

2.2. Proportions of Concrete Mix

Specimens were made of CSAC, CSMSFC, and OPMSFC, among which CSAC-0% was not mixed with steel fibers, CSMSFC-1.5%, CSMSFC-3%, and CSMSFC-4.5% represented three volume fractions of steel fibers (1.5%, 3%, and 4.5%), respectively, and OPMSFC-3% was mixed with steel fibers of 3% volume fraction, as shown in

Table 2. Proportions of concrete mix.

Concrete Type	Material Component/(kg/m3)
	Cement	River Sand	Gravel (5–10 mm)	Water	Steel Fiber	Superplasticizers
CSAC-0%	849.58	546.16	667.53	254.87	0	1.7
CSMSFC-1.5%	836.84	537.97	657.51	251.05	117	1.67
CSMSFC-3%	824.12	529.79	647.53	247.24	234	1.65
CSMSFC-4.5%	811.36	521.59	637.49	243.41	351	1.62
OPMSFC-3%	824.12	529.79	647.53	247.24	234	1.65

. In order to guarantee that the coarse aggregates could completely pass through the gap of the lapped bars, the coarse aggregates adopted continuous graded gravel with a particle size of 5~10 mm.

2.3. Properties of Raw Materials

2.3.1. Cement

The CSMSFC and CSAC systems both employed low-alkalinity sulphoaluminate cement (grade L.CSAC 42.5), whereas the OPMSFC system utilizes P·O 42.5 ordinary Portland cement.

Table 3. Physical and mechanical parameters of sulphoaluminate cement.

Grade	Specific Surface Area (m2/kg)	Initial Setting Time (min)	Final Setting Time (min)	PH Value	Cubic Compressive Strength (MPa)		Flexural Strength (MPa)
					1 Day	7 Days	1 Day	7 Days
42.5	425	12	15	9.9	≥30	≥42.5	≥4.0	≥5.5

presents the mechanical and physical parameters of sulphoaluminate cement.

2.3.2. Steel Fiber

Both CSMSFC and OPMSFC adopted copper-coated micro steel fibers with a length of 13 mm, diameter of 0.20 mm, a length to diameter ratio of 65, and a tensile strength of 2960 MPa, as shown in Figure 3.

2.3.3. Bars

All specimens were made of HRB400 bars with a diameter of 12 mm. According to Chinese standard GB/T 228.1-2010 [35], three samples of bars were subjected to a tensile test, and their average mechanical properties are shown in

Table 4. Mechanical properties of HRB400 bar.

Bars	Diameter (mm)	Tensile Yield Strength (MPa)	Ultimate Tensile Strength (MPa)	Tensile Yield Strain (με)	Elasticity Modulus (GPa)	Percentage Elongation after Fracture (%)
HRB400	12	443	606	2289	210	27.1

.

2.3.4. Sand and Stones

The three types of concrete are all composed of river sands with a fineness modulus of 2.7 and continuous graded gravel with a particle size ranging from 5 to 10 mm.

2.3.5. Water and Water Reducing Agent

The water used for concrete is exclusively sourced from the tap water in Zhengzhou. The water-reducing agent employed is a solid polycarboxylic acid powder, capable of achieving a maximum reduction rate of 30%.

2.4. Basic Mechanical Properties of Concrete

According to the Chinese standard GB/T 50081-2019 [34], reserved concrete cubes measuring 150 mm × 150 mm × 150 mm were prepared, and the compressive strength and splitting tensile strength of the cubes were measured, respectively. The cubic compressive strength and splitting tensile strength of the three types of concrete at 28 days are presented in

Table 5. Mechanical properties of concrete.

Concrete Type	28 Days
	fcu	fts
CSAC-0%	65.9	4.41
CSMSFC-1.5%	76.2	7.62
CSMSFC-3%	96.5	8.55
CSMSFC-4.5%	108.5	9.59
OPMSFC-3%	97.4	9.11

Note: The terms “f_cu” and “f_ts” represent the compressive strength and splitting tensile strength of concrete, respectively, measured in MPa.

.

2.5. Testing Apparatus

Two 30-ton through-core hydraulic jacks, with strokes of 89 mm and 178 mm, respectively, were utilized for the tensile test loading, as depicted in Figure 4a. At the free end of the bar, two displacement meters with a measuring range of 20 mm are positioned, while at the loading end and fixed end of the bars, two displacement meters with a measuring range of 50 mm are installed, as shown in Figure 4b. Force measurement is conducted using spoke-type force sensor clamping bars with specialized anchors on both sides of the reaction frame and jack.

The reaction frame is composed of two 20 mm-thick steel plates and four 8.8 grade M30 full-tooth screws. The inner and outer parts of the steel plates are fixed with 12.9 grade M30 hexagon nuts, as shown in Figure 5.

2.6. Loading Regime

According to Chinese standard GB/T 50152-2012 [36], graded loading is conducted. Firstly, a preload of 1 kN is applied to ensure proper contact between the anchoring end and the steel plate, while keeping the specimen horizontal to prevent deflection of the lapped bars. Subsequently, a controlled loading speed of 2 kN/min is maintained during each hierarchical load increment, with continuous data reading. The load value, slip at both free ends, and slip at the loading end are manually recorded at each stage until specimen failure occurs. The failure load and mode of failure are also documented.

3. Test Results and Analysis

3.1. Specimen Failure Mode

The failure modes of specimens in this test are categorized into four types: split failure, split-pull failure, pull-out failure, and bar tensile failure. The specimens with a volume fraction of steel fiber content of 0% exhibit insufficient lateral constraint on the concrete, resulting in a relatively large bond strength. The tensile stress inside the concrete pointing outward exceeds its splitting tensile strength, leading to concrete splitting failure, as depicted in Figure 6a. The specimens with a volume fraction of steel fibers of 3% and a lapped length of 50 mm exhibit pull-out failure due to the inadequate bonding force between the bars and CSMSFC because the lapped length is shorter than the minimum anchorage requirement. In this case, the lateral constraint provided by the concrete itself is sufficient, resulting in intact concrete but dislodged bars, as depicted in Figure 6b. The concrete specimens with a volume fraction of steel fiber content of 1.5% and a lapped length of 100 mm exhibit initial cracking when subjected to loads approaching the ultimate tensile strength of HRB400 reinforcement, owing to the high bond strength between the bars and concrete as well as the inadequate tensile strength of concrete itself. However, the presence of steel fibers effectively restricts further crack propagation, thereby maintaining or even enhancing interface bonding force stability. The weak interface of the bars ultimately fails, resulting in the splitting and fracturing of the specimen, as depicted in Figure 6c. The concrete splitting tensile strength and ultimate bond strength are significantly enhanced for specimens containing 3% or more steel fibers and lapped lengths of at least 100 mm. In this case, the concrete remains intact without any obvious cracks, while the bars at the loading end experience tensile failure by being pulled off, as illustrated in Figure 6d.

3.2. Bonding Strength

The essence of NLSB lies in the anchoring of two bars in CSMSFC, while the force transferring between the bars is achieved through the bonding effect between each bar and concrete, respectively. Therefore, the calculation method for its bond strength aligns with that of the interface bond strength of a single bar in axial pull-out specimens mentioned above, which can be computed as follows:

$${\tau }_u={\displaystyle \frac{P_u}{\pi d{l}_s}}$$

(1)

The variable “τ_u” represents the bond strength of the specimen, measured in MPa; the measured diameter of the HRB400 bar is denoted as d, in mm; the variable “l_s” denotes the lapping length of the reinforcement, measured in mm; while “P_u” represents the peak load applied to the specimen, measured in N. The test results of 51 pull-out specimens in 17 groups are summarized in

Table 6. Summary of test results.

Specimen Number	fcu/MPa	P/kN	τm/MPa	Relative Slip (mm)	Displacement of Loading Bar (mm)	Anchorage Reinforcement Displacement (mm)	Failure Mode
0%-100	65.9	47.52	12.61	0	2.50	2.28	Concrete splitting
0%-200	65.9	58.35	7.74	0	12.85	6.53	Concrete splitting
0%-300	65.9	59.02	3.55	0	14.39	7.87	Concrete splitting
1.5%-100	76.2	65	17.25	0	24.77	20.12	Splitting- fracture
3%-50	96.5	63.56	33.74	7.1	22.60	19.50	Pull out
3%-100-CSAC	96.5	67.25	17.94	0	31.58	14.50	Bars fracture
3%-200-0	96.5	66.61	8.84	0	29.14	22.56	Bars fracture
3%-200-5	96.5	67.5	8.96	0	23.04	21.01	Bars fracture
3%-200-10-10	96.5	66.41	8.81	0	23.26	18.12	Bars fracture
3%-200-10-20-CSAC	96.5	68.20	9.05	0	22.59	20.25	Bars fracture
3%-200-10-30	96.5	70.79	9.39	0	23.03	22.03	Bars fracture
3%-200-20	96.5	69.51	9.22	0	28.47	20.18	Bars fracture
3%-300-CSAC	96.5	68.59	6.07	0	26.54	20.54	Bars fracture
4.5%-100	108.5	68.09	17.25	0	28.64	17.38	Bars fracture
3%-100-OPC	97.4	66.7	17.70	0	21.76	20.66	Bars fracture
3%-200-OPC	97.4	68.36	9.07	0	22.28	19.66	Bars fracture
3%-300-OPC	97.4	68.76	6.08	0	31.51	21.70	Bars fracture

during the experiments.

3.3. Trial Curve

To determine the relative slip S of the free end of the two lapping bars under different loads in the axial tensile test, the slip amount of the free end of the two bars relative to the concrete specimen (S¹, S²) should be measured, and the relative slip of the free end can be obtained by adding the two together. The formula is as follows:

$$S=S^1+S^2$$

(2)

where S represents the relative slip of the free end, measured in mm; S¹ denotes the slip at the free end of the loading bar (unit: mm); and S² indicates the amount of the slip occurring at the free end of the anchorage reinforcement, also in mm.

In order to determine the amount of slip at the loading end under different loads, it is necessary to measure the displacement of the measuring point at the loading end and calculate the difference between this displacement and the elongation of the bars within range L, which extends from the unsticking section of PVC pipe to the concrete surface, as shown in Figure 7.

The bond–slip curves at the loading end and the free ends of the tensile specimen can be obtained by analyzing the interface bond strength τ, the amount of the slip at the loading end, and the amount of the relative slip S at the two free ends under different loads.

The bars commonly yield and fracture during this test, which means that the elongation of the bars at the loading end includes both elastic and plastic deformation, making it difficult to accurately determine the sliding distance of the bars at the loading end. Moreover, only specimens of 3%-50 exhibited sliding bars. Therefore, this paper solely presents the load–displacement curve at the loading end of the bars. Additionally, as the failure modes of the specimens primarily manifested as bar strain rupture and concrete splitting, significant data variations were observed after the ultimate load. Consequently, only the ascending section of the load–displacement curve was obtained for specimens without bars.

In the axial tensile test, the load–displacement curves of the bars and CSMSFC are categorized into four distinct failure forms based on the specimens’ behavior, as illustrated in Figure 8. The presence of an evident inflection point, namely the yield point of the tensile bars, can be readily observed in the curve, indicating the initiation of plastic deformation in the bars. The failure specimens can be classified into two categories: elastic stage splitting failure and post-yield splitting failure. In the former case, the curve exhibits a linear rise and terminates prior to reaching the yield point, whereas in the latter case, the curve extends beyond plastic deformation. The split-pull failure specimens demonstrated an initial linear increase in the curve, surpassing the yield point. Subsequently, following concrete cracking, the slope of the curve initially decreased; however, it subsequently increased again due to the timely constraining effect of steel fibers on crack propagation in concrete. The pull-out failure specimen exhibits a distinct decrease in its curve after reaching the yield point, indicating the occurrence of bar slip. The tensile failure specimen exhibits a distinct secondary slope lifting section following the yield point, indicating the transition of the bars into a strengthening stage.

The load–displacement curve of the loaded reinforcement and anchor reinforcement after tension is depicted in Figure 9. It can be observed from Figure 9a–c that the ultimate load and displacement gradually increase with an increment in lapped length, while the volume fraction of steel fibers and concrete type does not influence the impact of lapped length on ultimate load and displacement. For the specimens with a lap length of 100 mm and a 0% volume fraction of steel fibers, splitting failure occurred during the elastic stage of the bars. However, when the lap length was increased to 200 mm and 300 mm, fracture of the specimens took place after yielding of the bars. This could be attributed to variations in concrete lengths among specimens with different lap lengths. The ultimate load of the specimen increases with the gradual increase in volume fraction of steel fibers, as depicted in Figure 9d. However, the rate of increase gradually diminishes. This phenomenon can be attributed to the fact that when the lap length reaches 100 mm, the bars in specimens containing 1.5% and above volume fractions of steel fibers start to separate; however, their ultimate load upon separation does not reach the ultimate bond strength of the specimens. The results depicted in Figure 9e,f demonstrate that by increasing the spacing of reinforcement bars and the thickness of the concrete protective layer, a slight enhancement in the ultimate load capacity of the specimen can be achieved. Furthermore, as illustrated in Figure 9g–I, when the bond length ranges from 100 mm to 300 mm, it is observed that the ultimate load of CSMSFC specimens approaches that of OPMSFC specimens, indicating a comparable bond strength to HRB400 bars.

In addition, during the elastic stage, the displacement of loading bars and anchorage bars is closely aligned, with both experiencing equal forces. During the consolidation stage, there is a noticeable discrepancy in displacement between the bar at the loading end and that at the fixed end, resulting in a higher force exerted on the bar at the loading end. This observation indicates a 100% efficiency in force transfer during elastic deformation. As reinforcement enters into the plastic deformation stage, however, there is a gradual decrease in transfer efficiency from loading reinforcement to anchorage reinforcement.

3.4. Analysis of Influencing Factors of Bond Strength

3.4.1. Volume Fraction of Steel Fiber Content

The variation in bond strength between HRB400 bars and concrete specimens with different volume contents of steel fibers is illustrated in Figure 10, indicating a gradual increase in bond strength with the rise in volume fraction of steel fibers.

Table 7. Change of bond strength with volume of steel fiber.

Volume Fraction of Steel Fibers	0%	1.5%	3%	4.5%
Bonding strength/MPa	12.61	17.25	17.94	18.07
Rate of increase	0	36.80%	42.27%	43.30%

presents the bond strength values for non-contact lapping specimens prepared using CSAC, where the variables include lapped length of 100 mm, concrete cover thickness of 20 mm, and varying volume fraction of steel fibers contents of 0%, 1.5%, 3%, and 4.5%.

The results demonstrate a significant increase in bond strength of the specimen by 36.80% after increasing the volume fractions of steel fiber to 1.5%. On one hand, this is attributed to the fact that the specimen with a 0% volume fraction of steel fibers experienced splitting failure during testing, resulting in a bond strength lower than the failure limit value. Additionally, incorporating steel fibers enhances the splitting tensile strength of the concrete, delaying crack propagation and preventing specimen breakage. On the other hand, the steel fibers are uniformly distributed within the concrete, resulting in a higher compressive strength at the ribs of the bars. This enhances the mechanical interlocking between the bars and concrete, thereby improving the bond strength of the specimen. Furthermore, as the volume fraction of steel fibers increases from 0% to 4.5%, there is a corresponding increase in bond strength; however, this growth trend gradually diminishes due to diminishing returns caused by the excessive the volume fraction of steel fibers on enhancing concrete compressive strength. The volume fraction of steel fibers was increased from 3% to 4.5%, resulting in a marginal increase of only 1.03% in bond strength. This indicates that the impact of increasing the volume fraction of steel fibers on bond strength at 3% is approaching saturation point. Considering economic factors and concrete fluidity requirement, a volume fraction of steel fibers of 3% was chosen for further experimentation.

3.4.2. Concrete Type

The bond strength variation between HRB400 bars and concrete specimens of different concrete types is presented in

Table 8. Bond strength of specimens of different concrete types.

Splicing Length/mm		CSMSFC	OPMSFC
100	Bonding strength/MPa	17.94	17.70
	Rate of increase	0	−1.34%
200	Bonding strength/MPa	9.05	9.07
	Rate of increase	0	0.22%
300	Bonding strength/MPa	6.07	6.08
	Rate of increase	0	0.16%

and Figure 11, revealing a similarity in the bond strength between CSMSFC, OPMSFC, and HRB400 bars. Table 8 displays the bond strength of CSMSFC and OPMSFC specimens with a concrete protective layer thickness of 20 mm at lapped lengths of 100 mm, 200 mm, and 300 mm.

Through the test results, it can be observed that the maximum bond strength of both types of concrete is closely comparable, with a maximum difference not exceeding 2%. As depicted in Table 4, the compressive strength of CSMSFC containing 3% steel fibers at an age of 28 days exhibits similarity to that of OPMSFC, measuring 96.5 MPa and 97.4 MPa, respectively. This indicates that the failure load at the rib of the bars for mechanically occluded concrete is analogous between these two types, implying a similar mechanical interlocking force between each concrete and HRB400 bars. Additionally, due to the comparable maximum bond strength between the two types of concrete at various lapped lengths, the chemical bonding force and frictional force with HRB400 bars are also approximately equivalent. The data above indicate that both CSMSFC and OPMSFC have similar bearing capacities. However, CSMSFC exhibits superior early-stage bonding performance, making it more suitable for the rapid assembly process of prefabricated components.

3.4.3. Splicing Length

The variation in bond strength between reinforcement and concrete for specimens with different lapped lengths is illustrated in Figure 12.

Table 9. The bond strength varies with the length of the bond (CSAC-0%).

Concrete Type	Splicing Length/mm	100	200	300
CSAC-0%	Bonding strength/MPa	12.61	7.74	3.55
	Reduction rate	0	38.62%	71.85%

,

Table 10. The bond strength varies with the length of the bond (CSAC-3%).

Concrete Type	Splicing Length/mm	50	100	200	300
CSAC-3%	Bonding strength/MPa	33.74	17.94	9.39	6.07
	Reduction rate	0	46.83%	72.17%	82.01%

and

Table 11. The bond strength varies with the length of the bond (OPC-3%).

Concrete Type	Splicing Length/mm	100	200	300
OPC-3%	Bonding strength/MPa	17.70	9.07	6.08
	Reduction rate	0	48.76%	65.65%

present the maximum bond strength of specimens with volume fractions of steel fibers of 0% and 3% for various types of concrete, as well as bar spacing of 10 mm and a concrete cover thickness of 20 mm, respectively. It can be observed that the bond strength decreases as the lapped length increases.

The uneven distribution of bond stress between reinforcement and concrete along the entire bond length is one reason for this phenomenon. Moreover, as the bond length increases, the disparity in bond stress distribution becomes more pronounced, leading to lower average bond strength when bond failure occurs. Additionally, an increase in the overlapping length of bars results in a larger bonding area between bars and concrete, thereby decreasing the average bonding strength [18].

For specimens with a 0% volume fraction of steel fibers, the decline in bond strength is similar due to all specimens experiencing split failure. The bond strength during failure is lower than the limit value for bond failure, which depends on the splitting tensile strength of concrete itself. Compared to the specimen at 50 mm lapped length, when the bond length is increased to 100 mm, there is a significant decrease in bond strength for CSMSFC with a 3% volume fraction of steel fibers. On one hand, apart from experiencing bond failure like the specimen with a 50 mm lapped length, all specimens with a lapped length of 100 mm or more and containing 3% steel fibers exhibit tensile failure. The bond strength at failure corresponds to the ultimate tensile strength of the bars and is lower than the ultimate bond strength at failure. On the other hand, the bond stress distribution within the lapped length range is more uniform for the tensile failure specimen and remains relatively unaffected by an increase in lapped length. Consequently, there is a significant decrease in bond strength for specimens with a lapped length of 100 mm, but this decline gradually diminishes as the lapped length continues to increase. In addition, the data in Table 9, Table 10 and Table 11 demonstrate that the variation range of the reduction rate remains consistent at 9.84% to 48.76% when there are changes in the volume fraction of steel fibers and concrete type, owing to different failure forms observed in the specimens. However, it is noteworthy that the relationship between bond strength and bond length remains unchanged.

3.4.4. Spacing of Bars

The bond strength variation between reinforcement and concrete specimens with different bar spacings is presented in

Table 12. The change of bond strength with the spacing of bars.

Spacing of Bars/mm	0	5	10	20
Bonding strength/MPa	8.84	8.96	9.05	9.22
Rate of increase	0	1.36%	2.38%	4.30%

and Figure 13. The chart illustrates the maximum bond strength of CSMSFC specimens with a volume fraction of steel fibers of 3%, lapped length of 200 mm, and concrete cover thickness of 20 mm for bar spacing ranging from 0 mm to 20 mm at intervals of 5 mm. It can be observed that the bond strength exhibits a gradual increase as the bar spacing increases.

The bar spacing ranges from 0 to 20 mm, and the bond strength exhibits a gradual increase without significant variation. On one hand, the failure load did not reach the threshold for bond failure due to tensile failure in all specimens, resulting in a narrow range of test results. On the other hand, previous research by Sagan et al. [33] has demonstrated that the impact of non-contact lapping bars under monotonic loading can be disregarded when the bar spacing is less than 12 d (144 mm). In this experiment, even with a maximum bar spacing of 30 mm, it can be concluded that changes in bar spacing have minimal influence on bond strength.

In addition, in the axial tensile test, the force transfer between the two non-contact lapping bars primarily relies on concrete compression [33]. When the spacing between bars is too narrow, there is less concrete present between them, resulting in a lower load capacity for concrete compression failure and poor force transfer between the bars. Consequently, this leads to a decline in bond strength. Therefore, maintaining a small range of bar spacing will gradually enhance the bond strength between concrete and bars as it increases.

3.4.5. Concrete Cover Thickness

The bond strength between the reinforcement bar and CSMSFC is depicted in Figure 14 and

Table 13. Change of bond strength with concrete cover thickness.

Concrete Cover Thickness/mm	10	20	30
Bonding strength/MPa	8.81	9.05	9.39
Rate of increase	0	2.72%	6.58%

for specimens with varying thicknesses of the concrete cover. It can be observed that there is a slight increase in bond strength as the thickness of the concrete cover increases, which aligns with the findings reported by Ke Lu et al. [16]. Table 13 presents the maximum bond strength of CSMSFC samples containing a 3% volume fraction of steel fibers, considering a lapped length of 200 mm, bar spacing of 10 mm, and different thicknesses (10 mm, 20 mm, and 30 mm) of the concrete cover.

The thickness of the concrete protective layer varies from 10 mm to 30 mm, resulting in a gradual increase in bond strength, albeit with marginal improvements. Upon analysis, it is evident that the increased thickness primarily enhances the lateral restraint capacity of the concrete surrounding HRB400 bars and delays crack propagation within the concrete, thereby enhancing the bond strength between the bars and concrete. However, when considering CSMSFC with a volume fraction of steel fibers of 3%, it exhibits higher splitting tensile strength at a thickness of 10 mm. Consequently, augmenting anti-splitting ability has a limited impact on bond strength. Furthermore, all CSMSFC specimens with a bond length of 200 mm experienced tensile failure without reaching the limit value for bond failure load, which further restricted potential increases in bond strength.

3.5. Reinforcement Force Transfer Mechanism and Minimum Anchorage Length Design

The experimental results demonstrate that the use of CSMSFC reinforced by MSF can effectively provide ample lateral constraints, significantly restrict bar slip, and reduce the required lapped length in design. However, currently there is a lack of design and calculation methods for determining the strength of CSMSFC at lap joints between bars. Therefore, it is necessary to investigate the specific relationship between the compressive strength of CSMSFC and various parameters within the non-contact lapping zone of bars based on theoretical models. The force transfer model of non-contact lapping joints is utilized to propose a calculation method for determining the minimum anchorage length.

The schematic diagram of the force transfer model for the non-contact lapping truss of bars is illustrated in Figure 15, where l_s represents the effective lapped length of the bars. It has been experimentally confirmed that the effective lapped length l_s in this study is equal to the total lapped length l, which aligns with the research findings by Sagan et al. [33]. Initially proposed by Robinson [32], this model suggests that oblique compression bars formed after concrete cracking between bonded bars serve as the primary means of force transmission for non-contact bonded bars. By observing concrete cracking angles in plate tensile tests, Segan et al. [33] determined that α, representing the inclination of concrete baroclinic rods, could be 50°. Building upon a truss force transmission model, Mclean and Smith [37] introduced a two-dimensional theoretical model considering transverse reinforcement effects for the first time. They assumed an inclination angle of 45° for mitre bars (as shown in Figure 16) and proposed a relationship between stirrup yield strength and lap reinforcement yield strength using the following formula:

$$f_{\mathrm{yt}}={\displaystyle \frac{A_{\mathrm{s}}{f}_{\mathrm{y}}{s}_{\mathrm{t}}}{A_{\mathrm{t}}{l}_{\mathrm{s}}}}$$

(3)

In the formula, the cross-sectional area of the stirrups, denoted as A_t, and the cross-sectional area of the lapped bars, denoted as A_s, are key parameters in this context. Additionally, f_yt and f_y represent the yield strength of the stirrup and lapped bar, respectively. However, it should be noted that this model is only applicable for a single pair of bars in a lapping configuration. To address this limitation, Mclean and Smith developed a three-dimensional force transfer model based on the initial two-dimensional model to determine the required stirrup specifications in non-contact lapping areas between bars within circular section piers (refer to Figure 17 and Figure 18). The demand for annular stirrups in these lapping areas can be calculated using the following formula. Monotonic and reciprocating loading tests have demonstrated that stirrups designed according to this formula effectively restrict crack propagation.

$$f_{\mathrm{yt}}={\displaystyle \frac{s_{\mathrm{t}}{A}_{\mathrm{s}}{f}_{\mathrm{y}}}{2\pi A_{\mathrm{t}}{l}_{\mathrm{s}}}}$$

(4)

The CSMSFC utilized in this test possesses both high compressive and tensile strength, which is equivalent to the utilization of high-strength concrete between the overlapping bars. Additionally, a lateral restraint whose effects are similar to stirrups is incorporated, CSMSFC plays a “stirrup-like” role. Consequently, the transverse confinement of CSMSFC should be analogous to that caused by stirrups. Expanding upon the three-dimensional force transfer model for circular sections, its application scope extends to rectangular column sections, as depicted in Figure 19. The tension side section of the column is selected for establishing the force model. When the inclination angle of the concrete pressure rod reaches 45°, it is imperative that the component of internal force p_c exerted by said rod within the radial plane aligns with longitudinal bond stress, then:

$$p_{\mathrm{c}}h=N_{\mathrm{s}}·{\displaystyle \frac{{\sigma }_{\mathrm{s}}d}{4l_{\mathrm{s}}}}·\pi d$$

(5)

In the formula, the tensile stress of the lapped bars (σ_s) is determined by the number of tensile longitudinal bars in the section of a rectangular column (N_s) and the diameter of the lapped bars (d). Additionally, based on force analysis, the inward transverse binding force in CSMSFC can be compared to the transverse constraint provided by stirrups, as shown by the dotted line in Figure 19. This binding force is equivalent to the internal force exerted on concrete compression rods.

$$p_{\mathrm{c}}h{l}_{\mathrm{s}}=n_{\mathrm{t}}{\sigma }_{\mathrm{t}}{A}_{\mathrm{t}}=f_{\mathrm{t}}h{l}_{\mathrm{s}}$$

(6)

The tensile strength of CSMSFC, denoted as f_t, is the parameter representing the maximum stress that can be withstood by the material. σ_t refers to the stress experienced by a single stirrup, while n_t represents the total number of limbs in each stirrup. The formula for calculating the minimum lapped length of the non-contact lapping area of the rectangular section column and reinforcement can be obtained by substituting Formula (5) into Formula (6).

$$l_{\mathrm{s}}={\displaystyle \frac{\pi N_{\mathrm{s}}{\sigma }_{\mathrm{s}}{d}^2}{4h{f}_{\mathrm{t}}}}$$

(7)

The lapped length l_s, as calculated by Equation (7), is directly proportional to the tensile strength of the lapping area CSMSFC. As the lapped length decreases, there is a corresponding increase in the demand for higher tensile strength in CSMSFC.

The conversion relationship between the axial tensile strength f_ft and the splitting tensile strength f_fts of steel fiber concrete was proposed by Han Rong et al. [38] when the characteristic parameter of steel fiber content is within the range of 0 < λ_f ≤ 1.2.

$${\displaystyle \frac{f_{\mathrm{ft}}}{f_{\mathrm{fts}}}}=\eta \left(1-{\alpha }_{\mathrm{ts}}{\lambda }_{\mathrm{f}}\right)$$

(8)

Among them, f_fts represents the splitting tensile strength of steel fiber reinforced concrete, with a recommended value of α_ts of 0.27. η represents the coefficient for converting ordinary concrete’s splitting tensile strength into axial tensile strength, which is 0.9. The functional relationship between the splitting tensile strength and the minimum lapped length can be derived.

$$l_{\mathrm{s}}={\displaystyle \frac{\pi N_{\mathrm{s}}{\sigma }_{\mathrm{s}}{d}^2}{4h\eta f_{\mathrm{fts}}\left(1-{\alpha }_{\mathrm{ts}}{\lambda }_{\mathrm{f}}\right)}}$$

(9)

The conversion relationship between the splitting tensile strength and compressive strength of steel fiber reinforced concrete was investigated by Gao Danying et al. [39]. The study examined the relationship between the splitting tensile strength and compressive strength of steel fiber reinforced concrete as well as high-strength concrete, yielding the following findings:

$$f_{\mathrm{fts}}=f_{\mathrm{ts}}\left(1+{\alpha }_{\mathrm{s}}{\lambda }_{\mathrm{f}}\right)$$

(10)

$$f_{ts}=0.34f_{\mathrm{cu}}^{0.61}$$

(11)

The formula incorporates the splitting tensile strength (f_ts) and compressive strength (f_cu) of high-strength concrete, with α_s representing the influence coefficient of steel fiber on the splitting tensile strength. For milling steel fiber, α_s is 0.96; for cut bow steel fiber, α_s is 0.90; and for shear corrugated steel fiber, α_s is 0.52. Consequently, the relationship between the minimum lapped length and the compressive strength of concrete can be established.

$$l_{\mathrm{s}}={\displaystyle \frac{\pi N_{\mathrm{s}}{\sigma }_{\mathrm{s}}{d}^2}{1.224h{f}_{\mathrm{cu}}^{0.61}\left(1-0.27{\lambda }_{\mathrm{f}}\right)\left(1+{\alpha }_{\mathrm{s}}{\lambda }_{\mathrm{f}}\right)}}$$

(12)

Test piece parameters were substituted into Formula (12) for verification, and the results were shown in

Table 14. Minimum lap length calculation.

Steel Fiber Content	fcu (MPa)	Length of Lap When the Bars Yield (mm)	Length of Lap When the Bars Fracture (mm)
0.0%	65.9	84.8	116.0
1.5%	76.2	54.4	74.4
3.0%	96.5	49.4	67.6
4.5%	108.5	78.1	106.9

:

For specimens without any steel fibers present, lower splitting tensile strength causes premature concrete splitting before reaching maximum bond strength and consequently fails prematurely compared to calculated results. The lap length calculation results of the steel bar in Table 14 are inconsistent with the performance observed at a steel fiber content of 4.5%. This discrepancy arises from λ_f exceeding the upper limit of 1.2 for this particular steel fiber content, rendering Equations (9) and (12) inapplicable. However, it can still be calculated with Formula (7). When the steel fiber content is 3% and the lap length is set to 50 mm, the calculated lap length falls within the range of 49.4 to 67.6 mm, resulting in premature pullout failure after yielding, which aligns with actual observations. Similarly, for specimens with a steel fiber content of 3%, when the lap length exceeds or equals to 100 mm, complete pullout failure occurs as predicted by calculations. Moreover, for specimens containing only 1.5% steel fibers, insufficient splitting tensile strength leads to concrete splitting but ultimately still results in pullout failure of the steel bar. Therefore, this calculation method provides a more effective approach to designing the lap length of HRB400 steel bars in CSMSF by referring to Formulas (7), (9) and (12).

4. Conclusions

The failure mode, bond strength, and load-displacement curves of 17 groups of non-contact lapping specimens were investigated. The effects of volume fraction of steel fibers, bond length, concrete type, spacing of bars, and concrete cover thickness on the bond properties of non-contact lapping bars were analyzed. Furthermore, a calculation model for the lapped length of non-contact lapping bars considering the “stirrup-like” role of steel fibers was proposed based on the force transfer model. Through this calculation model, a formula for determining the minimum lap length of HRB400 bars in CSMSFC was derived. The following conclusions can be drawn:

(1)

In the absence of steel fiber addition, the concrete lacks sufficient inner circumferential stress, resulting in split failure. When the volume fraction of steel fibers is increased to 1.5%, although the inner circumferential confinement of concrete improves, it remains insufficient and leads to split-pull failure. However, when the volume fraction of steel fibers reaches 3%, the specimen exhibits sufficient inner circumferential constraint without any splitting failure occurrence. Furthermore, with a lap length of 100 mm, the ultimate bond strength of the specimen with a volume fraction of steel fibers of 3% surpasses the ultimate tensile strength of the bars, resulting in tensile failure.

(2)

With the increase in volume fraction of steel fibers, the slope of the upward section of the displacement–load curve of the specimen gradually increases. Moreover, during the elastic deformation stage of the bars, there is a close resemblance between the displacement–load curves at both ends (the loading end and the fixed end), resulting in a stress transfer efficiency reaching 100%. However, during the plastic deformation stage, there is a greater displacement observed at the loading end compared to that at the fixed end, leading to a gradual decrease in stress transfer efficiency between both bars.

(3)

The bond strength significantly increases with the increase in volume fraction of steel fibers; however, when the fiber volume reaches 3%, its impact on the bond strength is noticeably diminished. Moreover, for bar spacing ranging from 0 to 20 mm and a concrete protective layer thickness of 10 to 30 mm, the bond strength improves as both bar spacing and concrete protective layer thickness increase. Additionally, the bonding properties between CSMSFC and OPMSFC are similar to those with bars.

(4)

Based on the analysis of the force transmission mechanism of non-contact lapping reinforcement, a calculation model for determining the anchoring length considering the “hoop-like” effect of steel fiber is proposed. After verification, this model effectively captures the influence of CSMSFC mechanical properties, bar diameter, section width, and other parameters on the lapping length, as demonstrated in Formulas (7), (9) and (12).