Use of shear nails connector to improve UHPC-NC interface bonding performance of functional graded concrete components in offshore structure

doi:10.21203/rs.3.rs-4954119/v1

This paper designed functional graded concrete components to meet the bearing and durability improvement subjected to marine environment, where the normal concrete (NC) core was used to bear loads and was protected by the ultra-high-performance concrete (UHPC) permanent formwork from chloride ion permeability. By inspiring of transfer printing technology and controlled permeability formwork, a new simple shear nails construction treatment on UHPC formwork was proposed for establishing a connection between UHPC formwork and NC core. In order to study shear nails construction measures on the interface bonding performance between UHPC and NC, UHPC-NC bonding specimens were subjected to double-sided shear tests using the density and distribution spacing of shear nails on the surface of UHPC formwork as experimental parameters. The results showed when the shear nail density ρ ≥ 6.4, the specimen failure transformed into axial compression failure of NC core. The shear stress on the bonding surface increases approximately parabolic with the density of shear nails. Under the same density, the shear stress on the bonding surface of specimens with larger nail spacing was enhanced by 19.04%-41.74% compared to specimens with smaller spacing. The results show that the density and the distribution spacing of shear nails have a significant impact on the shear strength of the UHPC-NC surface. The influence of shear nail density on the shear strength of UHPC-NC interface is greater than that of the distribution spacing of shear nails. Based on comparing and analyzing the existing shear strength models of UHPC-NC bonding surfaces, fully considering the failure mode of bonding surfaces, a calculation formula for the shear strength of prefabricated UHPC-NC bonding surfaces was established. The calculation results have a high degree of agreement with experimental values, which can provide reference for the interface design of UHPC-NC composite specimens.

UHPC Permanent formwork

Shear resistance performance

Interfacial bond performance

Shear nail connector

numerical formula

Along with urban sprawl and a severe shortage of land resources, marine resources have become an inevitable trend in the development. As this trend continues, there are an increasing number of coastal engineering. However, ocean engineering usually shows durability issues in harsh marine environments where dry-wet cycles, corrosive substances such as SO₄²⁻ and Cl⁻ result in the corrosion of steel bars.

Recently, functionally graded concrete (FGC) has been adopted to improve the durability of these structures. FGC is a cementitious composite that the material compositions are spatially varied by two or more mixes ^[1–2], and material properties are engineered to change locally in a controlled way to meet the actual need. Wen et al. ^[2] investigated the possibility of protecting steel reinforcement through an external layer of low-permeability concrete. FGC can be divided into layered or continuously graded concrete. The former, the layered graded concrete is further classified as fresh-on-hardened and fresh-on-fresh layered graded concrete according to the sequence of casting operations. In fresh-on-hardened layered graded concrete, new layers of fresh concrete are added when previous layers have set and hardened, while different concretes are mixed and cast simultaneously in fresh-on-fresh layered graded concrete. Fresh-on-hardened layered graded concrete is more widely adopted than fresh-on-fresh layered graded concrete to achieve functional gradation due that the production process of latter is more complicate by requiring multiple concrete mixes to be mixed at the same time ^[3].

In recent years, many scholars have proposed permanent formworks ^[4–7]. These formworks are specially designed to contain the fresh concrete, mold it to the required dimensions and remain in site throughout the service life of structures. Using permanent formworks can simplify construction processes, save the construction time, and reduce the engineering cost ^[4]. Therefore, replacing traditional construction formworks with permanent formworks is gaining its significance. If permanent formworks techniques could be utilized in graded concrete element, it allows the geometry of the layers and the location of each interface to be accurately monitored during production. Ultra-high-performance concrete (UHPC), as a new type of cement-based composite material developed in recent years, has high strength, high density, high toughness, high durability, and good ductility ^[8–9]. At the same time, it also has good bonding performance with steel bars ^[10]. UHPC, as a permanent template material, can improve the load-bearing capacity of the template, reduce the thickness and weight of the template, and has received widespread attention.

In the UHPC permanent formwork structure system, the bonding interface between the formwork and cast-in-place ordinary concrete is the weakest link in the composite structure. Therefore, domestic and foreign scholars have conducted experimental research on the interface shear performance of UHPC-NC composite components. For example, Munoz et al. ^[11] conducted oblique shear and splitting experiments, and studied the bonding performance between the two materials under different conditions such as concrete wetness and surface roughness. The experimental results show that regardless of the exposure degree of freeze-thaw cycles, the age of composite specimens, the roughness of concrete substrates, and different loading schemes, the bonding performance between UHPC and NC is sufficient for the requirements of bridge cover layer. Bassam et al. ^[12] conducted oblique shear and splitting experiments to study the adhesive strength and permeability between the two materials. The experimental results show that the bonding strength between the UHPC layer and the NC matrix is high, and the impermeability of the UHPC-NC interface are good, which can significantly improve the impermeability of the concrete matrix. Wang Xingwang^[13] conducted interface shear tests on UHPC-NC structures and studied the stress and failure modes of the reinforcement model using ANSYS numerical analysis method. Husam et al. ^[14] conducted interface direct tensile experiments and determined the cohesion between UHPC and high-strength concrete using the roughness of the material surface as a variable, and deduced the friction coefficient between the materials. Due to the smooth surface of the UHPC template, Zhang Rui et al. ^[15] uniformly distributed pits on UHPC templates and improved interface adhesion by embedding shear keys into the pits with post poured concrete. Wang Dehong et al. ^[16] set grooves on the surface of the template to improve its roughness, and established a calculation formula between keyway density and bonding surface shear stress through double-sided shear tests. However, these processing methods form ordinary concrete shear keys, exhibiting NC shear failure ^[17], and therefore the improvement is limited.

In summary, this article proposes to set up UHPC shear stubs for prefabricated templates, which can shift from NC failure to UHPC shear when subjected to loads, further improving the interfacial bonding performance of UHPC template NC core composite specimens. However, there is little research in this area. Therefore, this article conducts double-sided shear tests on UHPC-NC to study the influence of shear nail density and distribution spacing on interface failure modes and shear bonding performance, and establishes a formula for calculating the shear strength of interface bonding, in order to provide useful reference for the design and construction of UHPC-NC composite specimens.

2.1 Design and Fabrication of Specimen

To study the impacts of shear nails on interface bonding performance, density and distribution spacing of shear nails on the surface of UHPC formwork to be more specific, double-sided shear tests have been carried out, design parameters can be found in Table 1. Each specimen consists of UHPC formwork and normal concrete inner core.

Table 1

Specimen design
No.	Outer diameter of shear nail	Height of shear nail	Number of shear nail	Density of shear nail
N0	0	0	0	0
N1	50	30	1	0.533
N2	50	30	2	1.067
N3	50	30	3	1.6
N4K	50	30	4	2.133
N6K	50	30	6	3.2
N8K	50	30	8	4.267
N12K	50	30	12	6.4
N18H	50	30	18	9.6
N4M	50	30	4	2.133
N4K	50	30	4	2.133
N8M	50	30	8	4.267
N8K N12M	50 50	30 30	8 12	4.267 6.4
N: Sticking; number: number of nails applied; K: wide distance between nails; M: narrow distance between nails

UHPC was made up of Grade 52.5 ordinary Portland cement, I grade fly ash, silica fume, quartz powder, quartz sand, steel fiber, polycarboxylate superplasticizer and water. Mixture proportion of the UHPC is shown in Table 2. The volume ration of steel fibers to UHPC is 2.5%. According to GB/T 50081 − 2019, the slump-flow of UHPC was tested, and the result was 720mm. In accordance with GB/T 31387 − 2015, the compressive strength of UHPC was measured using cube specimens with 100 mm×100 mm × 100 mm size, and the result was 142.3MPa. According to GB/T 50081 − 2019, the tensile properties of UHPC were tested using dog bone-shaped specimens with a cross-section of 100 mm × 50 mm size, and the result was 8.3MPa.

Table 2

Mix proportion of UHPC
P.O 52.5 cement	Silica fume	Fly ash	Quartz sand	Quartz powder	water	Superplasticizer	Steel fiber/%
1	0.23	0.15	1.0	0.08	0.25	0.025	0.228

Table 3

Mix proportion of C30 concrete
P.O 42.5 cement	II-Fly ash	Coarse aggregate	Fine aggregate	water
1	0.43	4.92	3.14	0.71

Normal concrete with a designed compressive strength grade of C30 was used for this study. The mixture was mainly consisted of ordinary Portland cement, river sand with a fineness modulus of 2.3, II grade fly ash, gravel with maximum size of 31.5mm, naphthalene superplasticizer and water. Table 3 list the mix proportion of normal concrete in this study. The measured compressive strength of the concrete standard cubic specimen was 38.5MPa.

The computational formula for the density of shear nails$\:\:$is as follows ^[18]:

$$\:\begin{array}{c}\rho\:=\:\frac{n{V}_{u}}{S}\left(1\right)\end{array}$$

Where $\:\rho\:$ is the density of shear nails; $\:n$ is number of shear nails; $\:{V}_{u}$ is volume of single shear nail; $\:S$ is area of bonding surface.

1) Casting of UHPC formwork

By inspiring of transfer printing technology, a new simple shear nails processing method on UHPC formwork inner surface was proposed for establishing a connection between UHPC formwork shell and NC core. Moreover, in order to identify the impact of UHPC formwork's shear nails structural measures on interface bonding performance between UHPC and post-poured NC, formworks were treated in different ways at the time of UHPC pouring, as well as no treatment.

Formworks were treated as follows: the wooden mold lined with silicone sheet (there are 30mm-deep holes distributed in different positions on the sheet) were adopted to make UHPC formworks with different numbers of shear nails and placed in different positions; for specifics, see Fig. 1.

By changing the surface of silicone sheet, different shear nails structure of UHPC formwork could be realized, as shown in Fig. 2. Afterwards, fresh UHPC was stirred and poured into a prepared mold. The poured UHPC formwork was rested quietly and demolded after 24 hours, and then placed to a standard curbing box for 28 days.

2) Casting of specimen

The prefabricated UHPC formwork was installed in the prepared mold, with the UHPC formwork on both sides clinging to the inner walls of mold, and then normal concrete was poured in the middle. In order to ensure the quality of pouring, when each 1/3 concrete was poured, it was vibrated by a vibrating rod. After settling for 24h, the mold was removed, and specimen was cured in standard curing box for 28d. Process flow is shown in Fig. 2.

2.2 Test Loading Device and Measuring Point Arrangement

The testing device consists of 200t POPWIL static pressure tester, 60L concrete mixer, Donghua static collector, industrial camera, digital collector, electro-hydraulic loading system and displacement meter, as shown in Fig. 3.

The strain distribution law of UHPC formwork and concrete core can be obtained by strain sensors on the surfaces of prefabricated UHPC and concrete. The arrangement scheme for such strain gauges is as follows: ten strain sensors are separately attached to UHPC and NC near interface to obtain the strain values of UHPC slab and concrete length-wise. four sensors are arranged at each cross section, as shown in Fig. 4(a); the average value of sensors at the same cross section is taken as the strain values of UHPC and NC near interface; for instance, the strain values of UHPC and NC at 1–1 cross section near interface are denoted as U1 and C1, respectively.

Moreover, displacement meters are separately inserted on UHPC and NC to obtain the slip values of UHPC formwork and concrete core. 4 and 6 displacement meters are inserted on UHPC formwork and NC core, respectively, including 2 displacement meters on NC at opposite angles of A-A cross-section and 2 displacement meters on UHPC and NC in the centers of B-B cross-section and C-C cross-section, as shown in Fig. 4(b). Worth noticing is that the average value of displacement meters at the same cross-section is taken as the displacement values of UHPC, NC at such cross-section; for instance, the displacement values of UHPC and NC at B-B cross-section are denoted as UB and C_B, respectively.

Preloading is conducted before test; loading rate is controlled at 5KN/min; preloading ends at 5KN, while in the test round, the loading rate is controlled at 5KN/min until specimen fails.

3.1 Failure Mode

Table 4 presents the test results of the ultimate bearing capacity, interface shear stress, and failure mode of the specimens.

When the UHPC template is not equipped with nails, the interface of the UHPC-NC composite specimen experiences shear failure of the bonding surface after being sheared, and the cross-section is smooth and flat. After the shear nail construction is set on the surface of the template, its failure mode presents three types:

Table 4

Experimental results
Serial number	ultimate bearing capacity (P_u/KN)	interfacial shear stress (MPa)	failure mode
N0	100.2	1.67	Shear failure between UHPC and NC
N1	130.2	2.17	A
N2	149.4	2.49	A
N3	185.8	3.10	A
N4K	205.99	3.43	B
N6K	273.2	4.55	B
N8K	288	4.8	B
N12K	356.53	5.94	C
N18K	393.6	6.56	C
N4M	145.1	2.42	B
N4K	205.99	3.43	B
N8M	206	3.43	B
N8K	288	4.8	B
N12M	299.6	4.99	B

A type: UHPC-NC bonds and nails shear failure. In the early stage of loading, the shear performance of the composite specimen interface is mainly borne by the bonding force between UHPC-NC. Small shear cracks first appear on the bonding surface near the free end and propagate along the bonding surface until encounters shear nails. Afterwards, the interface shear performance of composite specimens is mainly provided by shear nails. Due to insufficient density of shear nails on the template, UHPC shear nails were cut along the root. Finally, shear failure occurred on the bonding surface and shear nails of the composite specimen.

B type: UHPC-NC bonding surface shear failure, UHPC shear nail shear failure or peeling off. In the early stage of loading, the shear performance of the composite specimen interface is mainly borne by the bonding force between UHPC-NC. Shear failure first occurs in the free end, and as the load increases, the force continues to propagate along the bonding surface until it encounters a group of shear nails. Afterwards, the interface shear performance of the composite specimen is mainly provided by the shear nail group. Under the action of the shear nail group, the force continues to propagate along the bonding surface until the UHPC shear nail is sheared, especially near the free end. In addition, some force develops obliquely to the NC near the shear nail and micro cracks appear. Finally, the NC adhered to the UHPC shear nail is peeled off together.

C type: Shear failure of UHPC-NC bonding surface and axial compression failure of NC cores. In the early stage of loading, the shear performance of the composite specimen interface is mainly borne by the bonding force between UHPC-NC. Shear failure first occurs near the free end, and as the load increases, the force continues to propagate along the bonding surface until it encounters the shear nail group. If the density of shear nails is large enough, under the action of shear nail group, cracks will develop diagonally to the loading point at NC, and finally exhibit NC axial compression failure.

These three typical failure modes are shown in Fig. 5, when 2.133 ≤ shear nail density ρ<6.4, the specimen undergoes a transition from A type failure to B type failure. When the shear nail density ρ ≥ 6.4, the specimen failure transformed into C type failure.

3.2 Load-strain relation curve

Figure 6 shows specimen's load-strain relation curves under different parameters.

According to Fig. 6, the development and distribution of strain on interface under different treatments are quite similar. In the initial stage of loading, only the sensors near the free end had data changes, in which case, the interfacial chemical action of UHPC formwork and NC core served to bear load, whose load-strain relation curve appeared to be linear. As load gradually increased, shear nails and aggregate on the UHPC-NC bonding surface started to act, so the difference between the free end's strain and the loading end's strain gradually increased until failure. In the whole process of loading, strain increased linearly with load. As shown by the linearity stages on the load-strain curve of UHPC-NC specimens, the slope of curve from the free end to the loading end increased, suggesting that strain was gradually delivered from the free end to the loading end; as it reached the ultimate load, specimen failure quickly occurred.

3.3 Load-slip relation curve

With displacement meters on UHPC and NC, the load-slip curve at A, B and C cross-sections in UHPC and NC's effective bonding sections are recorded as shown in Fig. 7. After it reached the peak load, shear specimen was quickly separated, so there was no descent part of the curve. The load-slip curves for various specimens prepared with different construction measures showed a same pattern. In the initial stage of loading, UHPC and NC at interface deformed synergistically, in which case, the shear force at the prefabricated UHPC-NC interface was borne by the chemical action. As load continued to increase, the mechanical meshing force between shear nails and aggregate started to play a role, so shear strength increased and slip increased with load linearly. As the mechanical meshing force between shear nails and aggregate continued playing a role until cracked, slip increased nonlinearly with load. When it reached the ultimate load, interfacial bonding failed quickly. As shown in Fig. 7, subject to the same load, compared with curves C_B and U_B, the difference in slippage of curves C_C and U_C were large, so failure at specimen interface should occur at the free end first.

The difference in slippage between UHPC and NC at cross-section C# can be used to derive the relative displacement of C# cross-section. Figure 8 showed the load-relative displacement curve of composite specimen under different constructions. As indicated by Fig. 8(a), the ultimate bearing capacity of specimen N8K was larger than that of N4K, but smaller than that of N12K. Subjected to the same load, relative displacement on the bonding surface of N8K was larger than that of N12K, but smaller than that of N4K. This showed that as the density of shear nails increased ($\:\rho\:\le\:9.6$), the bond performance at specimen's bonding surface became better. The impact of shear nail interval on the load-slip curve was shown in Fig. 8(b). As shown in the figure, when $\:\rho\:=4.267$, the ultimate bearing capacity of N8K is higher than that of N8M. N8K's relative displacement was smaller subject to the same load, so N8K had better bond performance. Likewise, specimen with density $\:(\rho\:=6.4)$ showed same pattern. The ultimate bearing capacity of N12K was larger than N12M. N12K's relative displacement was smaller subject to the same load, so N12K had better bond performance. This suggested that with same density of shear nails, increasing shear nail interval can further improve the interfacial bond performance.

3.4 Interfacial bonding shear strength

The bonding shear strength of the prefabricated UHPC-NC specimen is calculated according to Equ. (2).

$$\:\begin{array}{c}{\tau\:}_{u}=\frac{P}{2A}\left(2\right)\end{array}$$

Where, $\:{\tau\:}_{u}$ is the bonding shear strength; $\:P$ is the shear peak load; $\:A$ is the area of the bonding surface, A = 60000 mm².

The bonding shear strength of the prefabricated UHPC-NC is calculated according to Equ.(2), as shown in Fig. 9.

From Fig. 9, under the same condition, the bonding shear strength of UHPC-NC composite specimen increased with the density of shear nails, and the bonding shear strength features parabolic relation with the density of shear nails. Because as the density of shear nails at prefabricated UHPC increased, the mechanical meshing force at the bonding surface increased, thus increasing the bonding shear strength.

With the same grooving density, the bonding shear strength of prefabricated UHPC-NC and the impact of shear nail interval were further studied, with its result shown in Fig. 10.

According to Fig. 10, the bonding shear strength of prefabricated UHPC-NC increased with shear nail interval. The bonding shear strength of specimen N4K was 41.74% higher than that of N4M, and the bonding shear strength of N8K was 39.94% higher than that of N8M, and the bonding shear strength of N12K was 19.04% higher than N12M. This is because as shear nail interval increased, the interlocking mechanism of shear nails and aggregate increased and the interfacial bonding shear strength increased.

3.5 shear strength of single shear nail

Furthermore, as indicated by the results of shear strength tests of single shear nail, with different shear nail densities, the relation between the shear strength of the bonding surface and the shear nail density of prefabricated UHPC was parabolic. The bonding strength of superposed concrete structure comes from the mechanical meshing force of the bonding surface, its chemical action force and Van der Waals force ^[19–20]. The mechanical meshing force is generated by the interfacial interaction on uneven bonding surface; generally, the mechanical meshing force is the main part of interfacial bonding force. Chemical action force is generated by chemical reaction between two materials on the bonding surface. Van der Waals force is caused by the mutual attraction of molecules between crystals; crystal's intermolecular distance in concrete is so large that Van der Waals force is negligible ^[16]. Therefore, this paper assumes that the bonding force fully comes from mechanical meshing force and chemical action force.

When there was no shear nail on UHPC ($\:\rho\:=0$), its formwork surface was smooth, and upon subjected to load, interface encountered shear failure. Failure surface was relatively flat, whose interfacial bond strength fully came from chemical action. After shear nails were placed on formwork surface ($\:\rho\:＞0$), the interfacial bonding strength of specimen came from mechanical meshing and chemical action. Compared with the specimen with smooth formwork, the composite specimen with shear nail also encountered the mechanical meshing force. So, the specimen's mechanical meshing force ^[16] can be derived by discounting the corresponding shear capacity of the corresponding smooth interface from that of composite specimen’s shear capacity. The mechanical meshing force of single shear nail can be obtained by dividing the obtained mechanical meshing force by the number of shear nails, with its result shown in Table 5.

According to Table 5, as the density of shear nails increased, the shear strength of single nail gradually decreased. The causes may be as follows, (1) when the density of shear nail was excessively large, the bonding interface was dispersed, interfacial chemical bonding actions can't develop concurrently, resulting in decreasing effective bonding area, and (2) when the density of shear nails was excessively large, the interlocking mechanism between shear nails and aggregate failed to fully develop. Both causes led to a decrease in both the number of effective shear nails within interface and mechanical meshing force. Therefore, the density of shear nails on UHPC formworks shall be controlled to a reasonable level in real practice.

Table 5

The shear strength of a single shear nail
Serial number	Nail Density	Shear strength /MPa	Discounted shear strength /MPa	Shear strength of one single nail /MPa
N0	0	1.67	1.67	/
N1	0.533	2.17	0.72	0.72
N2	1.067	2.49	1.26	0.63
N3	1.6	3.10	2.09	0.70
N4K	2.133	3.43	2.63	0.66
N6K	3.2	4.55	4.19	0.70
N8K	4.267	4.8	4.88	0.61
N12K	6.4	5.94	6.89	0.57
N18K	9.6	6.56	8.82	0.49

With respect to calculation of shear strength of the bonding surface of superposed member, domestic and foreign scholars have conducted extensive research and analysis, and figured out the corresponding calculation method. As specified in the Code for Design of Concrete Structures (GB50010-2010), regarding non-reinforced superposed slab, if there is compliance with the provision relating to construction in subparagraph 10.6.15 (Roughness of Superposed Cross-section) of the Code, the shear strength of its superposed surface shall be not higher than 0.4 N/mm^2[21]. Foreign codes such as Eurocode 2, ACI 318^[22–23] consider the bonding force, aggregate interlocking effect and the role of anti-shear pins, it is stipulated as follows:

1) In Eurocode 2 (1992), the shear strength $\:{{\tau\:}}_{\text{u}}$ of concrete bonding surface can be calculated according to Equ. (3):

$$\:\begin{array}{c}{\tau\:}_{u}=c{f}_{t}+\mu\:{\sigma\:}_{n}+\rho\:{f}_{yd}\left(\mu\:sin\alpha\:+cos\alpha\:\right)\le\:0.5v{f}_{cd}\left(3\right)\end{array}$$

Where, $\:c$ and $\:\mu\:$ represent cohesion coefficient and friction coefficient relating to the superposed surface construction mode, 0.35 and 0.6 are taken for the natural bonding surface without special treatment, 0.45 and 0.7 are taken for rough bonding surface; $\:{f}_{t}$ is the lowest tensile strength of two materials; $\:\rho\:$ is reinforcement ratio of shear reinforcement on superposed surface; $\:{f}_{yd}$ is the design value of yield strength of shear reinforcement on superposed surface; $\:{\sigma\:}_{n}$ is the minimum value of normal positive pressure to which interface is subject; $\:{f}_{cd}$ is the design value of concrete compressive strength; $\:v$ is strength reduction factor, for which 0.6 is taken, if $\:{f}_{ck}\le\:60$ MPa, the requirement $\:0.9-{f}_{ck}/200\ge\:0.5$ shall be satisfied, $\:{f}_{ck}$ is the standard value of compressive strength of concrete's axial compressive strength.

2) In the Code ACI 318M-05 (2005), when the bonding surface is a natural rough surface and there is no or little shear reinforcement, the shear capacity of superposed surface is as follows:

$$\:\begin{array}{c}{V}_{nh}=0.55{b}_{v}d\left(4\right)\end{array}$$

Where, $\:{V}_{nh}$ is the shear capacity of superposed surface, $\:{b}_{v}$, $\:d$ represent the width and length of superposed surface, separately.

3) In the Code AASHTO LRFD (2005), the nominal shear capacity of superposed surface is as follows:

$$\:\begin{array}{c}{V}_{u}=c{A}_{cv}+\mu\:\left({A}_{vf}{f}_{y}+{P}_{c}\right)\le\:\text{min}\left(0.2{f}_{c}^{{\prime\:}}{A}_{cv}，5.5{A}_{cv}\right)\left(5\right)\end{array}$$

Where, when concrete is later poured onto the hardened rough concrete surface, $\:c$ =0.7, $\:\mu\:=1$; $\:{A}_{cv}$ is the area of superposed surface; $\:{A}_{vf}$ is the area of shear reinforcement; $\:{f}_{y}$ is the yield strength of shear reinforcement; $\:{P}_{c}$ is the pressure perpendicular to superposed surface; $\:{f}_{c}^{{\prime\:}}$ is concrete's compressive strength, whichever is lower.

The interfacial bonding shear strength of fabricated UHPC-NC specimen in this test was calculated according to the above codes. The tensile strength $\:{f}_{t}$ of C30 was 2.348 MPa, which was calculated according to the relationship ^[24] between compressive strength and tensile strength. NC compressive strength $\:{f}_{cu}$ in this study was the measured value of 150mm×150mm×150mm cubic specimen, which was different from the Formula's compressive strength $\:{f}_{c}^{{\prime\:}}$, $\:{f}_{c}^{{\prime\:}}=0.79{f}_{cu}$^[24].C30's compressive strength $\:{f}_{c}^{{\prime\:}}$ was taken as 30.42MPa.

Comparison between the normalized value of prefabricated UHPC-NC's bonding shear strength and experimental value were shown in Table 6.

Table 6

Experimental results
No	Measured value $\:{\tau\:}_{u}$/MPa	Eurocode 2 $\:{\tau\:}_{1}$/MPa	ACI 318M-05 $\:{\tau\:}_{2}$/MPa	AASHTO LRFD $\:{\tau\:}_{3}$/MPa	GB 50010 − 2010 $\:{\tau\:}_{4}$/MPa	$\:{\tau\:}_{u}/{\tau\:}_{1}$	$\:{\tau\:}_{u}/{\tau\:}_{2}$	$\:{\tau\:}_{u}/{\tau\:}_{3}$	$\:{\tau\:}_{u}/{\tau\:}_{4}$
N0	1.67	0.822	0.55	0.7	0.4	2.032	3.306	2.385	4.175
N1	2.17	1.057	0.55	0.7	0.4	2.053	3.945	3.1	5.425
N2	2.49	1.057	0.55	0.7	0.4	2.356	4.527	3.557	6.225
N3	3.10	1.057	0.55	0.7	0.4	2.933	5.636	4.429	7.75
N4K	3.43	1.057	0.55	0.7	0.4	3.245	6.236	4.9	8.575
N6K	4.55	1.057	0.55	0.7	0.4	4.305	8.273	6.5	11.375
N8K	4.8	1.057	0.55	0.7	0.4	4.541	8.727	6.857	12
N12K	5.94	1.057	0.55	0.7	0.4	5.620	10.8	8.486	14.85
N18K	6.56	1.057	0.55	0.7	0.4	6.206	11.927	9.371	16.4
N4M	2.42	1.057	0.55	0.7	0.4	2.289	4.4	3.457	6.05
N4K	3.43	1.057	0.55	0.7	0.4	3.245	6.236	4.9	8.575
N8M	3.43	1.057	0.55	0.7	0.4	3.245	6.236	4.9	8.575
N8K N12M N12K	4.8 4.99 5.94	1.057 1.057 1.057	0.55 0.55 0.55	0.7 0.7 0.7	0.4 0.4 0.4	4.541 4.721 5.620	8.727 9.073 10.8	6.857 7.129 8.486	12 12.475 14.85

According to data in the table, the result of Eurocode 2 formula is closest to experimental value, while results from the other three formulas greatly differ from experimental value. However, Eurocode 2 formula does not consider the impact from the density of shear nails on interfacial shear stress. When the density of shear nails is excessively high, such formula is no longer applicable.

Thus, this paper puts forward a new parameter $\:\gamma\:$, which relates to UHPC's density of shear nails, and develops the following proposed formula. This equation does not consider the interfacial normal pressure and shear reinforcement.

$$\:\begin{array}{c}{\tau\:}_{u}=\gamma\:{f}_{t}\left(6\right)\end{array}$$

Where,

$\:{\tau\:}_{u}$ = interface shear strength between UHPC formwork and NC core;

$\:\gamma\:$ = parameter relating to UHPC's density of shear nails;

$\:{f}_{t}$ = NC's tensile strength.

In real practice, Eq. (6) can be expressed in the following way based on the conversion relation between concrete's axial tension strength $\:{f}_{t}$ and cube compressive strength $\:{f}_{cu}$:

$$\:\begin{array}{c}{\tau\:}_{u}=0.395\gamma\:{f}_{cu}^{0.55}\left(7\right)\end{array}$$

According to experimental result, the relationship between $\:\gamma\:$, from Eq. (7), and the density of shear nails $\:\rho\:$ can be written as $\:\gamma\:=-0.0174{\rho\:}^{2}+0.3425\rho\:+0.5402,\rho\:\le\:9.6$, Correlation index$\:\:{R}^{2}=0.9935$, suggesting that the such formula is reliable. Combining the above equation with Eq. (7), correlation-ship between interfacial shear stress of prefabricated UHPC-NC and the density of shear nails can be arrived, as shown in Eq. (8).

$$\:\begin{array}{c}{\tau\:}_{u}=（-0.006873{\rho\:}^{2}+0.135288\rho\:+0.213379）{f}_{cu}^{0.55}\left(8\right)\end{array}$$

Where, $\:\rho\:$ is density of shear nails; $\:{f}_{cu}$ is cube compressive strength.

According to Table 7, the model built in this paper was used to calculate the interface shear strength in references [16] and references [25]. Results showed that the ratio of experimental value to calculated value was smaller than 1, but discreteness was low, for instance, experimental value/calculated value in references [16] fluctuate around 0.548, while that in references [25] it fluctuated around 0.771, correlation index R² = 0.9935.

Table 7

Calculated values of corrected model and experimental values for interface shear strength
Specimens in this paper	Calculated values (experimental value / calculated value)/MPa	Specimens in references [16]	Calculated values (experimental value / calculated value) /MPa	Specimens in references [25]	Calculated values (experimental value / calculated value) /MPa
N0	1.589(0.951)	SB3	2.911(0.436)	ZJ-Z-1-1	2.830(0.735)
N1	2.112(0.973)	SB4	3.622(0.513)	ZJ-Z-1-2	3.935(0.788)
N2	2.606(1.047)	SB5	3.988(0.512)	ZJ-Z-1-3	4.823(0.647)
N3	3.071(0.991)	SC3	4.014(0.605)	ZJ-Z-2-2	3.935(0.795)
N4K	3.506(1.022)	SC4	4.990(0.573)	ZJ-Z-2-3	4.823(0.889)
N6K	4.289(0.943)	SC5	5.499(0.556)	/	/
N8K	4.957(1.033)	SD3	5.152(0.595)	/	/
N12K	5.940(1.000)	SD4	6.124(0.581)	/	/
N18K	6.542(0.997)	SD5	6.740(0.558)	/	/
The cause for the fact that the calculated values were higher than the experimental results in references [16] and references [25] is as follows. The model built in this paper is based on the case where UHPC's shear nails on the bonding surface are sheared, while the interfacial failure mode in references [16] is that NC is sheared, and the failure mode in references [25] is UHPC-NC's composite failure (bonding interface and NC failure), thus the errors in theoretical calculation. Therefore, it is necessary to consider the failure mode on the bonding surface of UHPC-NC's composite members, and introduce correction factor a to Eq. (8). When failure mode appears to be the case where NC is sheard, the average value is 0.584, which is the experimental value/calculated value in references [16]. When failure mode is bonding surface failure, the average value is 0.832, which is the experimental value/calculated value in references [25]. When failure mode appears to be the case where UHPC is sheard, a = 1. Therefore, based on Eq. (8), considering different bonding surface failure modes, and the calculation formula for shear strength of the bonding surface of UHPC-NC's composite specimen is developed:

$$\:\begin{array}{c}{\tau\:}_{u}=（-0.006873{\rho\:}^{2}+0.135288\rho\:+0.213379）a{f}_{cu}^{0.55}\left(8\right)\end{array}$$

Where,

$\:\rho\:$ =density of shear nails;

$\:{f}_{cu}$ =cube compressive strength;

a = the parameter of bonding surface failure mode; when interface is the case where NC is sheared, a = 0.584; when interface is bonding surface and NC failure, a = 0.832; when interface is the case where UHPC's shear nails are sheared, a = 1.

Equation (8) was used to calculate shear strength in references [16] and references [20], the results and experimental value / calculated value ratio are listed in Table 8.

From Table 8, experimental-to-calculated ratio for references [16] was 1.0040, mean square error and coefficient of variation were 0.0936 and 0.0932 respectively, while experimental-to-calculated ratio for references [25] = 1.0002, mean square error and coefficient of variation were 0.1032 and 0.1032 respectively. Calculation agreed well with experiment, which suggest the theoretic model can be used to predict and evaluate the bonding shear stress of UHPC-NC interface.

Table 8

Calculated and experimental values of the modified model of shear strength of bonded surface of UHPC-NC specimens after the introduction of parameters
Specimens in this paper	Calculated values (experimental value / calculated value)/MPa	Specimens in references [11]	Calculated values (experimental value / calculated value)/MPa	Specimens in references [20]	Calculated values (experimental value / calculated value)/MPa
N0	1.589(1.051)	SB3	1.648(0.781)	ZJ-Z-1-1	2.181(0.954)
N1	2.111(1.028)	SB4	1.959(0.948)	ZJ-Z-1-2	3.033(1.022)
N2	2.606(0.955)	SB5	2.157(0.946)	ZJ-Z-1-3	3.717(0.839)
N3	3.070(1.010)	SC3	2.273(1.068)	ZJ-Z-2-2	3.033(1.032)
N4K	3.505(0.979)	SC4	2.702(1.058)	ZJ-Z-2-3	3.717(1.154)
N6K	4.289(1.061)	SC5	2.975(1.028)	/	/
N8K	4.956(0.969)	SD3	2.787(1.100)	/	/
N12K	5.940(1.000)	SD4	3.313(1.074)	/	/
N18K	6.544(1.002)	SD5	3.648(1.033)	/	/

(1) When the UHPC template is not equipped with studs, the interface of the UHPC-NC composite specimen experiences shear failure of the bonding surface after being sheared, and the cross-section is smooth and flat. After the shear nail construction is set on the surface of the template, its failure mode presents three situations. Namely, A type failure: shear failure of UHPC-NC bonds and nails; B type failure: UHPC-NC bonding surface shear failure, UHPC shear nail shear failure or peeling off; C type failure: Shear failure of UHPC-NC bonding surface and axial compression failure of NC core. when 2.133 ≤ shear nail density ρ<6.4, the specimen undergoes a transition from A type failure to B type failure. When the shear nail density ρ ≥ 6.4, the specimen failure transformed into C type failure.

(2) The interface shear strength between UHPC formwork and NC core is 1.67-6.56MPa. The shear stress between the bonding surfaces mainly comes from mechanical biting force and chemical bonding effect. Reasonably setting shear forces between precast UHPC-NC bonding surfaces can fully utilize the strength of precast UHPC and significantly increase the shear stress between bonding surfaces.

(3) The density and distribution spacing of prefabricated UHPC shear nails have a significant impact on the shear strength of prefabricated UHPC-NC bonding surface, and the influence of nail density on the shear strength of the bonding surface is greater than that of the distribution spacing. Under the same conditions, when the shear nail density is between 0 and 9.6, and the higher the shear nail density, the greater the shear strength of the prefabricated UHPC-NC bonding surface. Under the same density of shear nails, compared to specimens with smaller spacing of shear nails, the shear stress with larger spacing of shear nails can be increased by 19.04–41.74%.

(4) After comparing and analyzing the existing shear strength models of UHPC-NC bonding surfaces and the failure modes of bonding surfaces during testing, the failure mode parameters of bonding surfaces are introduced to establish a new rule to calculate the shear strength of prefabricated UHPC-NC bonding surfaces. The calculation results have a high degree of agreement with the experimental values, which can provide reference for the interface design of UHPC-NC composite specimens.

Acknowledgements

The study was supported by National Natural Science Foundation of China (No.51569305) and Ningbo Scientific and Technological Innovation Major Project in 2035 (No.2023Z148, No.2023Z017).

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Use of shear nails connector to improve UHPC-NC interface bonding performance of functional graded concrete components in offshore structure

Status:

Version 1

Abstract

Figures

1. Introduction

2. Experiment Overview