Experimental investigation and analytical modeling of shear behavior at UHPC-NC interfaces in wet joints of precast assembly piers

Abstract

This study investigates the shear properties of ultrahigh performance concrete (UHPC) wet joints through direct shear tests on UHPC flat joint specimens. Four sets of specimens were designed with varying levels of constrained normal stress. The results showed that all specimens exhibited brittle shear damage near the UHPC-NC interface. The application of 1 MPa, 2 MPa and 3 MPa constrained normal stress increased the shear strength by 103.4%, 184.4%, and 272.3%, respectively, compared to the unconstrained specimen. An analytical model is proposed to quantitatively describe the shear stress-slip behavior of the UHPC-NC interface under various levels of constrained normal stress, accompanied by a calculation formula for its characteristic points. The model links normal stress, stiffness, roughness, and defines shear curve descent., allowing for reliable prediction of the shear stress-slip relationship of the UHPC-NC interface. Furthermore, a validated finite element model using ABAQUS software was developed, which aligned with analytical results and further strengthened the reliability of the proposed model. The results suggest that the shear strength of the UHPC-NC interface can be enhanced by adjusting the constrained normal stress, given its high sensitivity as an impact factor. The shear bearing capacity can be described using the proposed model, which consists of a linear ascending segment, a peak point, and a declining damage segment with an exponential evolution pattern, with a recommended damage index parameter of 4.68.

Keywords

precast assembly pier ultrahigh-performance concrete wet joint shear behavior

Introduction

Over time, precast assembly bridges have become increasingly important in bridge engineering due to their efficient and environmentally friendly construction methods as well as their minimal disruption to road traffic (Xu, 2021; Wang, 2022; Shen, 2021). One commonly used method to connect precast assembly piers is the cast-in-place wet joint, which allows for simple construction operations and provides a well-defined force transfer path, as shown in Figure 1. The cast-in-place wet joint has been successfully utilized in various precast assembly bridge projects, including the Donghai Bridge (Shen, 2005), Hangzhou Bay Cross-Sea Bridge (Zeng, 2005), Shanghai Yangtze River Bridge (Ye, 2007) and Jintang Bridge (Zhou, 2008), as shown in Figure 2. These bridges showcase the effectiveness of this type of joint. The bridge pier, as a critical support element in the bridge structure, is susceptible to bending damage, shear damage, and bending-shear damage during seismic events. Joints are typically the weakest parts of assembled piers when subjected to loads. It is crucial to evaluate not only the flexural capacity but also the shear capacity of joints when assessing the seismic performance of bridge piers (French, 2017; Zhou, 2005; Jiang, 2018; Shamass, 2015).

Figure 1.

Wet joint connection diagram of precast assembly pier.

Figure 2.

Pier construction of Shanghai Yangtze River Bridge.

In recent years, there has been a growing trend towards utilizing high-performance materials to improve the load-bearing capacity of structures (Brühwiler, 2013; Habel, 2007; Oesterlee, 2010; Noshiravani, 2013; Prem, 2015; Nunes, 2016; Safdar, 2016; Zhang, 2017). Ultrahigh performance concrete (UHPC) is one such material that has gained a lot of attention due to its strong bonding action, high toughness, good fatigue resistance and durability (Richard, 1995; Brühwiler, 2005). Researchers have been exploring the use of UHPC in wet joints between precast concrete structures (Hamoda, 2023a; Abadel, 2022; Hamoda, 2023b; Hamoda, 2024), as it has the potential to enhance joint strength and accelerate construction speed in precast assembly structures. However, for prefabricated piers with UHPC wet joint under seismic action, the shear properties of the interface between UHPC and normal concrete (NC) are crucial in evaluating the efficacy of this connection.

Tian et al. (2022) conducted slanting shear tests and double-sided shear tests to investigate the shear bearing mechanism at the UHPC-NC interface. They developed a calculation formula for interfacial cohesion by considering the strength of NC and the density of interfacial grooves. Yu et al. (2022) utilized a multiscale analysis method to simulate the mechanical behavior of the NC-UHPC interface and obtained an effective traction-separation law (TSL) for the interface, which enabled them to understand the tensile and shear separation mechanisms at the NC-UHPC interface. They were able to evaluate the influence of interfacial roughness and strength on the macroscopic shear and tensile strength. Hussein et al. (2017) performed a finite element analysis to study the bonding behavior at the joint interface between UHPC and high-strength concrete (HSC). Interfacial parameters were proposed from this numerical model and validated through indoor model tests with good agreement. Zhang et al. (2020) evaluated and discussed the shear performance of different interfacial treatments through interfacial shear push-out tests on UHPC-NC specimens. They proposed a comprehensive method for calculating interfacial shear strength, considering factors such as interfacial cohesion, mechanical interlocking between concrete and rebars, UHPC grooved joints, and the dowel action of UHPC. Feng et al. (2022) performed direct shear push-out tests on 17 UHPC specimens, considering the effects of key-joint shape and lateral stresses on the damage modes, crack development, straight shear strengths, and shear slip properties of UHPC key-wet-joints. They established a unified formula for calculating the direct shear capacity, considering the previous test results of monolithic UHPC specimens and specimens with UHPC flat (wet) joint (Feng, 2021). This formula can be applied to the monolithic interface of UHPC without shear-resistant reinforcement, the interface of flat-wet joints, and the interface of key-wet joints. Zhang et al. (2021) conducted seven sets of shear push-out tests on UHPC-NC specimens to evaluate the shear performance and failure modes of interfaces treated with smoothing, chiseling, and rebar exposing. Results showed that either complete NC substrate failure or partial interface + partial NC failure were the failure modes. Surface roughness of the NC was found to be the major factor affecting interfacial shear strength, and NC wettability was found to be positively correlated with interfacial shear strength. Kim et al. (2018) conducted direct shear push-out tests on UHPC dry joints, UHPC glued joints, and UHPC wet joints with untreated interfaces, considering the effects of the number and height of shear keys and lateral compressive strength on the shear performance of the interface. Results showed that the wet joint type with UHPC filler was approximately three times stronger than the concrete or mortar filler type, indicating that if the joints maintain an equivalent strength to that of the main body, the structural efficiency of a UHPC structure made of precast segments can be ensured. Jiang et al. (2021) conducted push-off tests of UHPC grooved wet joints with different groove depths and found that the peak shear strength of the UHPC wet joint reached 86.4% of the monolithic specimen at a groove depth of 30 mm, whereas it could only reach 67.2% at a groove depth of 20 mm. The peak straight shear strength of the UHPC grooved wet joints specimens was increased by 163% compared to the UHPC smooth flat joint specimens with steel reinforcement. While these studies contribute to the understanding of the UHPC-NC interface, few scholars have proposed formulae for the calculation of shear capacity at the interface. Further research is needed to develop mathematical models for the interfacial shear stress-slip curve to calculate shear capacity and describe the behavior of the UHPC-NC interface under shear loading.

This paper investigates the shear performance of UHPC wet joints between precast assembly pier segments, with a particular focus on designing UHPC flat wet joint specimens that align with the structural characteristics of these segments. Direct shear experiments were conducted to analyze the damage morphology and shear stress-slip behavior of these joints. The influence of restrained normal stress on the shear capacity of UHPC wet joints is also examined. Based on the experimental data, an analytical model is proposed to quantitatively describe the shear stress-slip behavior of the UHPC-NC interface under various levels of constrained normal stress, accompanied by a calculation formula for its characteristic points. The model links normal stress, stiffness, roughness, and defines shear curve descent. A finite element model is then developed to validate the analytical model. The satisfactory agreement between experimental, analytical, and numerical results demonstrates the robustness of the proposed model and supports its effectiveness in predicting the mechanical performance of UHPC-NC interfaces. This study improves the understanding of shear resistance in UHPC wet joints, facilitating the optimization of design and construction practices for precast assembly piers. The findings underscore the importance of considering constrained normal stress to enhance the shear performance of UHPC wet joints.

Direct shear tests

Experimental design

To replicate the wet joint connection of an assembled bridge abutment, a UHPC wet joint direct shear specimen was designed as a five-section structure, consisting of three precast NC segments (left, middle, and right) and two UHPC wet joint segments with flat interfaces. The specimens were grouped into four categories: SP-0 MPa, SP-1 MPa, SP-2 MPa, and SP-3 MPa, with each group containing one specimen. The prefix “SP” denotes a specimen with a flat joint, and the subsequent strength value represents the level of constrained normal stress. The specimen’s overall dimensions are 520 mm in length and 350 mm in height. The UHPC segment has a width of 60 mm and a height of 150 mm, while the middle NC segment has a square cross-section with a side length of 150 mm. The left and right NC segments extend 75 mm outward to accommodate four high-strength screws with a 14 mm diameter. The flange design increases the specimen’s overall deadweight, ensuring stable boundary conditions at the wet joints. Notably, the bottom of the wet joint area (including the UHPC wet joint segments and the middle NC segment) is elevated relative to the side NC segments. This design not only provides space for load application but also limits the rotation of the wet joint area during loading, thereby minimizing the effects of bending moments. The constrained normal stress is controlled by tightening the high-strength screws. Both hoop and structural reinforcements with a diameter of 6 mm were incorporated into the NC segments to enhance the specimen’s overall integrity and prevent premature failure. The specimen’s design parameters are presented in Figure 3 and Table 1.

Figure 3.

Design of the direct shear test specimen (unit: mm). (a) Front view of the specimen. (b) Top view of the specimen. (c) Top view of reinforcement arrangement. (e) Front view of reinforcement arrangement.

Table 1.

Design Parameters for direct Shear test Specimen.

Specimen number	Material of the substrate	Material of the wet joint	Thickness of the joint (mm)	Interface treatment	Constrained normal stress (MPa)
SP-0 MPa	C40	UHPC	60	Grooved	0
SP-1 MPa	C40	UHPC	60	Grooved	1
SP-2 MPa	C40	UHPC	60	Grooved	2
SP-3 MPa	C40	UHPC	60	Grooved	3

Material properties and fabrication process

The test specimens in this study comprised two types of concrete: C40 concrete for the NC segments and UHPC mixture for the UHPC segments. The UHPC mixture primarily consisted of cement, silica fume, quartz sand, a high-efficiency water-reducing agent, and steel fibers. The steel fibers used in the UHPC had a volume fraction of 2.5%, a diameter of 0.2 mm, a length of 13 mm, and a tensile strength of 2850 MPa. The UHPC mixture proportions are presented in Table 2. For both NC and UHPC, six cubic compressive specimens, each measuring 100 mm × 100 mm × 100 mm, were prepared. Material property tests were conducted on these specimens in accordance with the GB/T 50081-2019 (2019) “Standard for Test Methods of Concrete Physical and Mechanical Properties” The results of the 28-day compressive strength tests for each material are shown in Table 3.

Table 2.

Mix Proportions for UHPC.

Constituent	Cement	Silica fume	Quartz sand	Water reducer	Water	Steel fiber
Amount (kg/m³)	955	229	1051	13	153	191
Mix proportion	1	0.24	1.1	0.0136	0.1623	0.2

Table 3.

Measured Mechanical Properties of NC and UHPC.

Concrete type	Compressive strength (MPa)	Modulus of elasticity (MPa)	Tensile splitting strength (MPa)
NC (C40)	43.3	32500	2.41
UHPC	134.9	44130	7.48

In the preparation of the test specimens, three NC segments were first prefabricated, and the interfaces of the segmental joints were grooved at 1 cm intervals using a chisel, resulting in an average groove depth of 2 mm. This created a rough interface to enhance bonding. The procedure to control the roughness was as follows: the ordinary concrete surface was surrounded by a plastic plate, with the surface flush to the highest point of the bonding surface’s convex part. Fine standard sand was then filled between the bonding surface and the top of the plastic plate, and the volume was measured. By comparing the volume with the cross-sectional area, the average depth was calculated, reflecting the roughness of the bonding surface. High-tensile screws were inserted through pre-drilled holes in the left and right NC segments for secondary support. Afterward, the UHPC wet joint segments were poured and maintained. The production process of the test specimens with flat joints is illustrated in Figure 4.

Figure 4.

Fabrication process of direct shear specimens. (a) Prefabrication of NC segments. (b) Chiseling of interfaces. (c) Secondary molding and support. (d) Maintenance of UHPC segments.

Testing procedure

Figure 5 illustrates the sensor arrangement for the flat-joint direct shear specimen. Two strain gauges were placed on each of the two UHPC wet joint segments to measure their deformations, and a dial indicator was positioned on the middle NC segment to measure its vertical displacement. The relative displacement caused by shear stress was calculated by subtracting the strain gauge data from the displacement data obtained from the dial indicator. Strain and displacement data were collected using the TDS-530 data collector.

Figure 5.

Schematic diagram of sensor arrangement for direct shear specimen.

To apply the constrained normal stress, the nuts on the high-strength screws were tightened diagonally in a graded manner. The pressure sensor readings were monitored in real-time to control the target value. Loading was performed using an electro-hydraulic servo universal testing machine with a load capacity of 200 tons. Before the main loading, a preload test was conducted at a rate of 0.1 kN/s, incrementally increasing by 10 kN steps up to 30 kN to ensure proper fixation and connection of the pressure transducer, per cm m, and strain gauges. The official loading was then carried out step by step, increasing by 50 kN at a rate of 0.2 kN/s. If cracks appeared in the specimen, the loading continued incrementally by 20 kN, with the loading rate remaining constant until failure. Figure 6 shows the overall arrangement of the direct shear specimens during field testing.

Figure 6.

Overall arrangement of direct shear specimens loaded in the field.

Results and discussions

Failure mode

During the initial stage of testing, no significant cracking was observed in any of the specimens. However, as the load increased, cracks began to form in the SP-0 MPa, SP-1 MPa, SP-2 MPa, and SP-3 MPa specimens at load values of 70 kN, 140 kN, 230 kN, and 280 kN, respectively. These cracks primarily appeared at the bottom of the middle NC segment near the UHPC wet joint. As loading continued, the cracks widened and extended vertically, eventually leading to failure at load values of 152 kN, 308 kN, 431 kN, and 566 kN, respectively. At this point, large vertical displacements occurred in the middle NC segment, and shear failure at the interface was observed, indicating a brittle failure mode. The load corresponding to this point represents the ultimate bearing capacity of each specimen. As loading continued, the displacement of the middle NC segment increased while the load value decreased rapidly. The final bearing capacity of each specimen stabilized at approximately 15 kN, 35 kN, 50 kN, and 100 kN, respectively. Figure 7 provides a visual representation of the final failure morphology of each specimen.

Figure 7.

Failure modes of each direct shear specimen. (a) Schematic diagram of the failure of specimen SP-0MPa. (b) On-site picture of the failure of specimen SP-0MPa. (c) Schematic diagram of the failure of specimen SP-1MPa. (d) On-site picture of the failure of specimen SP-1MPa. (e) Schematic diagram of the failure of specimen SP-2MPa. (f) On-site picture of the failure of specimen SP-2MPa.

As shown in Figure 7, two types of damage were observed: shear failure in the NC segment and shear failure at the UHPC-NC interface. The shear damage in the NC segment can be attributed to the bonding characteristics between the UHPC and NC interface, which result from the interaction between the old and new concrete. According to the interfacial bonding mechanism, a transition layer forms near the bonding surface, and failure typically occurs within this transition layer rather than at the surface itself (He, 2017; Muslim, 2020; Xie, 2003). For the UHPC-NC interface, the transition layer consists of UHPC, the bonding surface, and NC. Since UHPC is significantly stronger and tougher than NC, the damage tends to occur in the weaker NC segment, leading to shear failure in the NC. However, when the bond strength at the interface is weaker than the NC, shear failure may occur at the UHPC-NC interface. This phenomenon may be influenced by the curing conditions, which can affect the strength of the specimens.

It is important to note that in specimens SP-1 MPa, SP-2 MPa, and SP-3 MPa, several cracks formed at the bottom of the middle NC segment due to bending. This is attributed to the externally applied constrained normal stress, which enhances the bond strength at the UHPC-NC interface, resulting in a greater strength disparity between the interface and the middle NC segment. Consequently, with both sides of the middle NC segment subjected to bonding forces in the same direction from the UHPC-NC interface, bending damage at the bottom of the middle NC segment became inevitable.

Shear stress-slip curve

The shear stress-slip curves for direct-shear specimens with flat joints between UHPC and NC under varying normal stress constraints are presented. As shown in Figure 8, the curves exhibit similar trends for all specimens. Initially, the shear stress at the interface increases rapidly, while the slip increases gradually. This linear-elastic relationship between shear stress and slip suggests that the shear strength of the interface is primarily attributed to the chemical bond between UHPC and NC. At the cracking load, the curve slope decreases slightly. At this stage, the shear strength is provided by both the chemical bond and the interlocking forces from the aggregate in the concrete. The interface reaches its peak shear strength at the ultimate load, marking the point of brittle failure. Beyond this point, the shear strength declines rapidly, while slip increases at an accelerated rate, resulting in a concave shape in the descending section of the shear stress-slip curve. Once this state is reached, the interface has fully cracked and the resistance to external loads relies entirely on the occlusal force of the aggregate until complete failure occurs. Table 4 summarizes the cracking load, failure load, displacement at failure, and residual load for each specimen during testing.

Figure 8.

Test results of shear stress-slip curves of each specimen.

Table 4.

Characteristic Values of Testing Load for Each direct Shear Specimen.

Specimen number (MPa)	Cracking load (kN)	Failure load (kN)	Displacement at failure (mm)	Residual load (kN)	Failure mode
SP-0	70	152	0.84	15	Shear damage of NC
SP-1	120	308	1.33	35	Shear damage of NC
SP-2	230	431	1.46	50	Shear damage at UHPC-NC interface
SP-3	280	565	1.53	100	Shear damage of NC

Influence of constrained normal stress

The results presented in Figure 8 illustrate the behavior of the UHPC-NC interface under different levels of constrained normal stress. As the normal stress increases, the interface undergoes elastic-plastic deformation and reaches its peak shear stress. The cracking loads for the specimens with constrained normal stresses of 1 MPa, 2 MPa, and 3 MPa increased by 71.4%, 228.6%, and 300%, respectively, compared to the specimen without constrained normal stress (SP-0 MPa). Similarly, the failure loads for these specimens increased by 103.4%, 184.4%, and 272.3%, respectively. Moreover, the corresponding peak slip values increased by 58.8%, 73.81%, and 82.38% for specimens SP-1 MPa, SP-2 MPa, and SP-3 MPa, respectively. The influence of normal stress on peak slip was relatively minor, yet it led to a significant increase in shear stiffness, as observed in the stress-slip curves for each specimen before reaching the peak shear stress. For the specimen without constrained normal stress, the shear capacity gradually decreased during the residual stage and tended toward zero. In contrast, for specimens SP-1 MPa, SP-2 MPa, and SP-3 MPa, the sliding friction between the interfaces remained critical for load-bearing, maintaining residual shear capacities of approximately 15 kN, 35 kN, 50 kN, and 100 kN, respectively. The effect of constrained normal stress on residual load was smaller compared to its influence on failure load. In conclusion, the application of constrained normal stress significantly enhances the shear strength, shear stiffness, and residual shear capacity of the UHPC-NC interface. The variation of cracking load, failure load, and residual load with changing constrained normal stress for each specimen is shown in Figure 9.

Figure 9.

Comparison of cracking, failure and residual load under different constrained normal stress.

Analytical model of the shear stress-slip relationship

Typical dimensionless shear stress-slip curve

The shear stress-slip curve at the UHPC-NC interface is derived from experimental results, and the mathematical expressions for its characteristic points are obtained through analytical derivation. To facilitate comparison and data analysis, the shear stress-slip curves for specimens with different joint parameters are transformed using dimensionless coordinates. Analytical derivation is then conducted based on this transformation. Let:

x = \frac{s}{s_{u}}, y = \frac{τ}{τ_{u}}

(1)

where

s

is the interfacial slip,

τ

is the interfacial shear stress,

s_{u}

is the peak slip and

τ_{u}

is the peak shear stress.

The shape of the shear stress-slip curve in a flat joint specimen is determined by its shear deformation and damage progression. The typical dimensionless shear stress-slip curve obtained from the transformed test data is shown in Figure 10.

Figure 10.

Typical dimensionless shear stress-slip curve. Note: $τ_{u}$ and $s_{u}$ denote the residual shear stress and its corresponding residual displacement; point O represents the starting point of the shear stress-slip curve; point A denotes the peak shear stress point, corresponding to the maximum shear strength; point B indicates the inflection point in the descending section, where the rate of decrease in shear stress changes; point C represents the stabilization point of the residual shear stress after failure.

The typical dimensionless shear stress-slip curve exhibits distinct segmental nodes, which divide it into two segments: an ascending segment (Segment I) and a descending segment (Segment II). To construct the model, the curve is represented by the following segmental expression:

y = {\begin{cases} a_{1} x + b_{1} & 0 \leq x \leq 1 \\ a_{2} x^{- b_{2}} & x \geq 1 \end{cases}

(2)

where

a_{1}

and

b_{1}

are the parameters for the ascending segment, and

a_{2}

and

b_{2}

are the parameters for the descending segment.

Substituting point O (where $y = 0$ at $x = 0$ ) into the ascending section expression of equation (2) from the typical curve (Figure 8) yields $b_{1} = 0$ . For $0 \leq x \leq 1$ , the derivative $\frac{dy}{d x} = 1$ , meaning that the modulus of the linearly elastic segment in this range is equal to the peak secant modulus. Therefore $a_{1} = 0$ , and the ascending curve can be expressed as:

y = \begin{array}{l} x & (0 \leq x \leq 1) \end{array}

(3)

Substituting point A (where $y = 1$ at $x = 1$ ) into the expression for the descending section of equation (2) results in $a_{2} = 1$ . From the characteristics of the descending section of the curve, it is observed that the curvature $κ$ is maximized at point B, with coordinates $x_{B} (x_{B} \geq 1)$ .The expression for the curvature $κ$ is given by:

κ = \frac{y^{″}}{{[1 + {(y^{'})}^{2}]}^{3 / 2}}

(4)

When the curvature reaches its maximum value,

κ^{'} = 0

, which gives the following equation:

κ^{'} = \frac{y^{‴} \cdot {[1 + (y^{'})]}^{3 / 2} - 3 \cdot {(y^{″})}^{2} \cdot y^{'} \cdot {[1 + {(y^{'})}^{2}]}^{1 / 2}}{{[1 + {(y^{'})}^{2}]}^{3}} = 0

(5)

Hence, the value of $x$ is given by:

x = {(\frac{2 {b_{2}}^{3} + {b_{2}}^{2}}{b_{2} + 2})}^{\frac{1}{2 b_{2} + 2}}

(6)

Since $x \geq 1$ in the descending section of the curve, solving the equation yields $b_{2} \geq 1$ . To determine the appropriate range for the parameter $b_{2}$ in the descending segment, calculations were performed by varying $b_{2}$ from 1.2 to 1.6 in increments of 0.1. The resulting analytical curve for the descending segment was then compared with the experimental curve for each specimen. The comparison results are shown in Figure 11.

Figure 11.

Comparison of descending section between analytical curves at different values of $b_{2}$ and test curves.

The comparison shown in Figure 11 indicates a good agreement between the experimental curve and the analytical curve when the parameter $b_{2}$ is within the range of 1.2 to 1.6. Based on this observation, the following mathematical expression for a typical shear stress-slip curve is established:

y = {\begin{cases} x & 0 \leq x \leq 1 \\ x^{- b_{2}} & x \geq 1, 1.2 \leq b_{2} \leq 1.6 \end{cases}

(7)

Figure 12 shows the comparison between the calculated dimensionless analytical curve (for $b_{2} = 1.262$ ) and the dimensionless experimental curve obtained through the aforementioned transformation. The results indicate strong agreement between the analytical and experimental curves.

Figure 12.

Analytical and experimental shear stress-slip curves (dimensionless).

Mathematical equation for peak shear stress and slip

Once the mathematical expressions for the ascending and descending segments of the dimensionless analytical curve are derived, it is essential to identify the characteristic points, specifically the peak points (( $s_{u}$ , $τ_{u}$ ). To achieve this, the shear stiffness $K$ of the ascending section plays a key role.

The ascending segments of the shear stress-slip curves for each specimen are simplified to a linear relationship, allowing for the calculation of the shear stiffness values $K$ for the ascending segments, which are 1.9661 N/m, 3.1914 N/m, 4.0949 N/m, and 5.1838 N/m, respectively. Notably, shear stiffness $K$ is the only variable in the test that is influenced by the constrained normal stress. By fitting the shear stiffness $K$ to the corresponding constrained normal stresses $σ_{n}$ , the following relationship can be established:

K = 0.914 σ_{n} + 2.33

(8)

While significant progress has been made in understanding the shear bearing capacity of the UHPC-NC interface, further research is required to refine predictive models and address specific challenges, such as the impact of interface conditions and varying material properties. In this study, the expression for shear bearing capacity $V_{b v}$ proposed by Zhang (2020) was adopted as a reference.

V_{b v} = β τ_{c} A_{b}

(9)

τ_{c} = 0.75 \sqrt{0.8 f_{c u} f_{c t}}

(10)

where

τ_{c}

is the direct shear strength of the NC.

f_{c u}

is the cubic compressive strength of NC and

f_{c t}

is the tensile strength of NC.

A_{b}

represents the bonding area between UHPC and NC.

β

is the influence coefficient of interfacial roughness on shear strength. It is defined as the ratio of the average shear stress

τ

between the interfaces to the shear stress

τ_{c}

of NC:

β = \frac{τ}{τ_{c}}

(11)

Using the values of $τ_{u}$ and the corresponding $s_{u}$ for each specimen obtained in this study, along with the selected type of normal strength concrete, the corresponding $β$ values for each specimen were calculated as 0.308, 0.627, 0.877 and 1.148, respectively.

Based on the conclusions from Zhang (2020), it was determined that for the specimen without constrained normal stress, the value of $β$ should be taken as 0.353. This value aligns closely with the $β$ calculated for the SP-0 MPa specimen in this study. However, for the SP-1 MPa, SP-2 MPa, and SP-3 MPa specimens, the values of $β$ show a progressive and significant increase, as shown in Figure 13. This variation can be attributed to the fact that $β$ represents the effect of interfacial roughness on interfacial shear strength, and the application of constrained normal stress enhances this effect. Consequently, $β$ changes as the constrained normal stress varies. Based on the available data, the relationship between $β$ and the constrained normal stress $σ_{n}$ can be linearly fitted as follows:

β = 0.265 σ_{n} + β_{0}

(12)

where

β_{0}

represents the

β

values corresponding to different roughness levels when no constrained normal stress is applied. The correlation coefficient

R

-Square (COD) of this linear fitting is 0.99745, which represents a satisfied accuracy of the fitting. According to Zhang’s research, interfacial roughness can be classified into three categories—smooth, low roughness, and high roughness—corresponding to

β

values of 0.2268, 0.353 and 0.4388, respectively.

Figure 13.

Relationship between the interfacial roughness coefficient and constrained normal stress.

By summarizing the equations above, the expressions for the peak shear stress $τ_{u}$ and the corresponding peak slip $s_{u}$ considering constrained normal stress can be derived as:

τ_{u} = (0.178 σ_{n} + 0.671 β_{0}) \sqrt{f_{c u} f_{c t}}

(13)

s_{u} = 0.195 \sqrt{f_{c u} f_{c t}} (1 + \frac{3.77 β_{0} - 2.55}{σ_{n} + 2.55})

(14)

Experimental verification

To obtain the analytical shear stress-slip curves for each specimen, the calculated peak shear stress and corresponding peak slip (using the above formulas) are multiplied by the dimensionless curve. The comparison between these analytical curves and the experimentally obtained shear stress-slip curves is shown in Figure 14.

Figure 14.

Comparison of analytical and experimental shear stress-slip curves.

To assess the accuracy of the analytical calculations, we compared the peak shear stress and corresponding peak slip values obtained from the analytical calculations with those from the tests. The error statistics for these values are presented in Table 5.

Table 5.

Comparison of analytical and Experimental Values of Peak Points.

Specimen number (MPa)	Analytical value of $τ_{u}$ (MPa)	Test value of $τ_{u}$ (MPa)	Error in $τ_{u}$	Analytical value of $s_{u}$ (mm)	Test value of $s_{u}$ (mm)	Error in $s_{u}$
SP-0	2.32	2.02	14.48%	0.99	0.84	18.3%
SP-1	4.05	4.12	1.48%	1.25	1.33	6.32%
SP-2	5.79	5.75	0.68%	1.39	1.46	4.6%
SP-3	7.53	7.53	0.003%	1.49	1.53	3.1%

Based on observations in Figure 14 and Table 5, the analytical model proposed in this study for the shear stress-slip behavior at the UHPC-NC interface exhibits maximum errors of up to 20% for both peak shear stress $τ_{u}$ and corresponding peak slip $s_{u}$ . Furthermore, the shear stress-slip curves from the analytical model closely align with the experimental data.

To further assess the applicability of the proposed model, recent studies on direct shear tests at the UHPC-NC interface were reviewed. The applicability of the analytical model proposed in this study and its comparison with existing standards (CEB-FIP, 1990; Eurocode, 2004; AASHTO LRFD, 2010; AFGC, 2013; as shown in Table 6) are shown in Figure 15.

Table 6.

Typical Calculating Models for the interfacial Shear Capacity.

Number	Codes	Formulas
1	CEB-FIP, 1990	$τ = c f_{t} + μ (σ_{n} + ρ f_{y})$
2	Eurocode, 2004	$τ = c f_{t} + μ σ_{n} + ρ f_{y} (μ \sin α + \cos α)$
3	AASHTO LRFD, 2010	$V = c A_{cv} + μ (A_{vf} f_{y} + P_{c})$
4	AFGCm 2013	$τ = \begin{array}{l} c_{U} \frac{f_{ctk, el}}{γ_{c}} + ρ f_{y} & Smooth surface \\ c_{U} \frac{f_{ctk, el}}{γ_{c}} + ρ f_{y} + (0.35 μ_{U} + 0.3) \frac{f_{ctfk}}{γ_{cf} K} & Intented surface \end{array}$

Nomenclature: $τ$ and $V$ : Interface shear capacity and shear strength; $c$ and $μ$ : Interface roughness factor for NC; $c_{U}$ and $μ_{U}$ : Interface roughness factor for UHPC; $f_{t}$ : Design tensile strength for NC; $ρ f_{y}$ : Contribution of the reinforcement to the shear strength of the interface; $σ_{n}$ : Constrained normal stress; $α$ : Angle between the shear reinforcement and the shear plane; $A_{cv}$ : Area of concrete at the shear interface; $A_{vf}$ : Area of shear reinforcement; $f_{ctk, el}$ : Characteristic limit of elasticity under tension; $f_{ctfk}$ : Characteristic maximal post-cracking stress; $γ_{c}$ : Partial factors for materials for ultimate limit states; $γ_{cf}$ : Partial safety factors for materials for ultimate limit states; $K$ : Fiber orientation factor in the indented area.

Figure 15.

Applicability analysis of the proposed analytical model and comparison with existing standards. (a) Tian (2022), (b) Valikhani (2020). (c) Zhao (2023) (d) Zhang (2023). (e) Al-Osta (2022). (f) Zhang (2020). (g) Jiang (2021) (h) Li (2022). (i) Banta (2005). (j) Haber (2018). (k) Farzad (2019). (l) Jafarinejad (2019)

Figure 15 presents a total of 94 data points from 12 literatures. The vertical axis in the figure represents the ratio of analytical values to experimental values. Material parameters in theses literatures were used in these analytical models. The grey dashed line indicates perfect agreement between the analytical and experimental values, while the degree of deviation of each data point from the grey dashed line reflects the discrepancy between the analytical and corresponding experimental values. Data points closer to the grey dashed line (i.e., a ratio of 1) indicate higher accuracy, whereas points further away signify lower accuracy.

From Figure 15(a)–(l), it can be observed that the analytical model proposed in this study demonstrates higher precision compared to other standards. It provides a more accurate representation of the shear strength at the interface between UHPC and NC. The Eurocode follows in terms of accuracy, while the CEB-FIP, AASHTO LRFD, and AFGC standards exhibit poorer performance, with larger errors in the calculated shear strength. This superior performance of the proposed model is attributed to its consideration of not only the compressive and tensile strengths of NC but also the relationship between constrained normal stress and surface roughness. Consequently, the model provides a more precise depiction of the shear capacity of the UHPC-NC interface under different interface treatment methods and varying NC strengths.

FE model of the direct shear specimens

Modelling details

Figure 16 presents a detailed representation of the 3D finite element model used for the direct shear specimen. The model incorporated various element types to accurately simulate the structural behavior. For the NC and UHPC wet joint segments, an 8-node linear brick element with reduced integration and hourglass control (C3D8R) was used. This choice ensured enhanced numerical stability and accuracy. To model the reinforcement, a 2-node linear displacement element (T3D2) was employed, enabling a realistic representation of the reinforcement. Embedded connections were used to simulate the interaction between the reinforcement and the NC segments, allowing for an accurate analysis of the bond between the reinforcement and surrounding material. The interface between the UHPC wet joint and NC segments was modeled using a cohesion model based on the traction-separation law, effectively capturing the interface behavior under loading conditions. The bottom surface of the specimen was fully constrained to simulate realistic boundary conditions. Additionally, a reference point was placed at the center of the top surface of the middle NC segment and coupled to the model, enabling the application of a displacement-controlled vertical load. Constrained normal stress is considered uniformly distributed on the outside surface of the left and right NC segment. Through these modeling techniques, the finite element model provided a comprehensive representation of the direct shear specimen, facilitating an accurate analysis of its behavior under specified loading conditions.

Figure 16.

Schematic of the FE 3D model of the direct shear specimen.

To account for the non-linear behavior of the materials used in this study, the Concrete Damage Plasticity (CDP) model in ABAQUS software was employed to simulate both UHPC and C40 concrete. Material properties of UHPC and NC are considered homogeneous and isotropic. The constitutive relationship for C40 concrete was based on the guidelines outlined in the Code for Design of Concrete Structures GB 50010-2010 (2015). The uniaxial stress-strain relationship for C40 concrete is provided by equations (15) to (20). The uniaxial compressive stress-strain relationship for UHPC, derived from Ma’s research (2006), is given by equation (21), while the uniaxial tensile stress-strain relationship for UHPC, based on Zhang’s research (2009), is provided in equation (22). The constitutive curves for NC and UHPC are shown in Figure 16. For the reinforcement material, an ideal elastic-plastic model was used, with a yield strength of 400 MPa and an ultimate tensile strength of 540 MPa.

σ_{C} = {\begin{cases} \frac{ρ_{C} n}{n - 1 + x^{n}} \cdot E_{C} ε_{C} & x \leq 1 \\ \frac{ρ_{C}}{α_{C} {(x - 1)}^{2} + x} \cdot E_{C} ε_{C} & x > 1 \end{cases}

(15)

ρ_{C} = \frac{f_{C r}}{E_{C} ε_{C r}}

(16)

n = \frac{E_{C} ε_{C r}}{E_{C} ε_{C r} - f_{C r}}

(17)

x = \frac{ε_{C}}{ε_{C r}} o r \frac{ε_{t}}{ε_{t r}}

(18)

σ_{t} = {\begin{cases} ρ_{t} (1.2 - 0.2 x^{5}) \cdot E_{C} ε_{t} & x \leq 1 \\ \frac{ρ_{t}}{α_{t} {(x - 1)}^{1.7} + x} & x > 1 \end{cases}

(19)

ρ_{t} = \frac{f_{t r}}{E_{C} ε_{t r}}

(20)

where

σ_{C}

and

σ_{t}

are the compressive strength and tensile strength of NC, respectively.

ε_{C}

and

ε_{t}

are the compressive strain and tensile strain of NC, respectively.

E_{C}

is the elastic modulus of NC.

α_{C}

and

α_{t}

are the descending parameters of NC uniaxial compressive and uniaxial tensile stress-strain curve, respectively.

f_{C r}

and

f_{t r}

are the representative value of uniaxial compressive strength and uniaxial tensile strength of NC, respectively.

ε_{C r}

and

ε_{t r}

are the peak compressive strain and peak tensile strain of NC, respectively.

y = {\begin{cases} a x + (5 - 4 a) x^{4} + (3 a - 4) x^{5} & 0 \leq x \leq 1 \\ \frac{x}{b {(x - 1)}^{2} + x} & x > 1 \end{cases}

(21)

σ = {\begin{cases} \frac{f_{c t}}{ε_{c a}} ε & 0 < ε \leq ε_{c a} \\ f_{c t} & ε_{c a} < ε \leq ε_{p c} \\ f_{c t} \frac{1}{{(1 + ω / w_{p})}^{p}} & ε_{c p} < ε (ω_{c p} < ω) \end{cases}

(22)

where

x = \frac{ε}{ε_{p}}

y = \frac{σ}{f_{p}}

. The preferred ranges of

a

and

b

are 1.1 to 1.4 and 0 to 10, respectively.

f_{p}

and

ε_{p}

are the prismatic compressive strength and the corresponding peak compressive strain of UHPC, respectively.

f_{c t}

is the uniaxial tensile strength of UHPC.

ε_{c a}

is the tensile strain at initial cracking.

ε_{p c}

is the ultimate tensile strain.

In equation (21), the definition of $x$ in terms of $ε_{p}$ was proposed by Guo (2017), who derived the formula by summarizing and analyzing experimental results from various sources. The expression for $ε_{p}$ is given as follows:

ε_{p} = (6.7264 f_{p} + 2460.9) \times 10^{- 6} 80 M P a \leq f_{p} \leq 150 M P a

(23)

In the CDP model, the compressive damage variable

d_{c}

and the tensile damage variable

d_{t}

for both NC and UHPC materials are calculated using the following formula:

d_{c} = 1 - \frac{σ_{C}}{E_{C} (ε_{C} - {ε_{C}}^{p l})}

(24)

d_{t} = 1 - \frac{σ_{t}}{E_{C} (ε_{t} - {ε_{t}}^{p l})}

(25)

where

{ε_{c}}^{p l}

and

{ε_{t}}^{p l}

are compressive and tensile plastic strains, respectively;

E

is the initial (undamaged) elastic stiffness of the material.

The parameters determining the shape of this yield function and non-associated plastic flow rule are the dilation angle $ψ$ , the biaxial strength-to-uniaxial strength ratio $f_{b 0} / f_{c 0}$ , the eccentricity of the plastic potential surface $ε$ , and the shape factor $K$ . These parameters were derived from previous studies by Jang (2018) and are assigned the following values: 20, 1.16, 0.1 and 0.6667, respectively.

Damage evolution pattern at the UHPC-NC interface

This study employs a cohesive contact model based on the traction-separation bilinear constitutive law to simulate the interaction between UHPC wet joint segments and NC segments. The model accounts for slip in the horizontal direction and stress in the vertical direction. The slope of the linear elastic phase represents the stiffness $K_{n n} (K_{s s}, K_{t t})$ , while the area under the triangle corresponds to the energy released upon material failure. The contact model captures the linear elastic behavior until the interfacial bond strength $τ_{n} (τ_{s}, τ_{t})$ reaches its maximum value $τ_{n}^{0} (τ_{s}^{0}, τ_{t}^{0})$ within the displacement range $0 \leq δ \leq δ_{n}^{0} (δ_{s}^{0}, δ_{t}^{0})$ . Once the strength limit is reached, the model simulates the stiffness-softening phase for displacements $δ_{n}^{0} (δ_{s}^{0}, δ_{t}^{0}) \leq δ \leq δ_{n}^{f} (δ_{s}^{f}, δ_{t}^{f})$ , during which the material experiences a reduction in stiffness. $K_{n n} {, K}_{s s}, K_{t t}$ represent the stiffness values in the normal ( $n n$ ) and tangential ( $s s, t t$ ) directions, respectively. These parameters define the initial slope of the linear elastic phase in the traction-separation law, indicating the resistance to deformation in the respective directions. $τ_{n}, τ_{s}, τ_{t}$ denote the interfacial bond strengths in the normal ( $n$ ) and tangential ( $s, t$ ) directions, respectively. These values indicate the traction forces at the interface before failure begins. $τ_{n}^{0}, τ_{s}^{0}, τ_{t}^{0}$ represent the maximum interfacial bond strengths in the normal ( $n$ ) and tangential ( $s, t$ ) directions. These are the peak values of traction that the interface can withstand before softening occurs. $δ_{n}^{0}, δ_{s}^{0}, δ_{t}^{0}$ denote the displacement values corresponding to the peak bond strengths $(τ_{n}^{0}, τ_{s}^{0}, τ_{t}^{0})$ in the normal ( $n$ ) and tangential ( $s, t$ ) directions. These mark the transition point from the elastic phase to the softening phase. $δ_{n}^{f}, δ_{s}^{f}, δ_{t}^{f}$ represent the final displacement values at which the interfacial bond strength is fully degraded to zero in the respective directions. These indicate the completion of the softening phase, where the interface has lost its load-bearing capacity.

It is observed that once the shear stress reaches its peak, damage initiates at the interface between UHPC and NC, marked by a degradation in bond stiffness governed by a specific damage evolution law. During this stage, the decline in bond stiffness is represented by the damage variable $D$ , which starts at 0. After the peak shear stress, interfacial damage develops, either linearly or nonlinearly, in conjunction with slip, until the interface is fully degraded, as indicated by the damage variable $D$ reaching 1. Based on the experimental shear stress-slip curves for each specimen, it was found that the damage variable $D$ follows an exponential variation. This relationship is quantified using equation (26) (Fernández-Cañadas, 2016), which calculates $D$ as a function of the plastic displacement $δ$ for each specimen. The results are presented in Figure 17.

D = 1 - {\frac{δ_{m}^{0}}{δ_{m}^{\max}}} {1 - \frac{1 - \exp (- α (\frac{δ_{m}^{\max} - δ_{m}^{0}}{δ_{m}^{f} - δ_{m}^{0}}))}{1 - \exp (- α)}}

(26)

where

α

is a dimensionless parameter that defines the rate of damage evolution. It is associated with specific material properties and follows a linear relationship when equals to 0.

δ_{m}^{0}

represents the effective separation at damage initiation.

δ_{m}^{\max}

refers to the maximum effective separation attained during the loading history.

δ_{m}^{f}

denotes the effective separation at complete failure.

Figure 17.

Damage variable-plastic displacement curves.

The exponential evolution of the damage variable $D$ for the SP-0 MPa, SP-1 MPa, SP-2 MPa, and SP-3 MPa specimens follows a similar pattern, as indicated by the fitting of the damage variable-plastic displacement curves. The exponent $α$ for each specimen were 4.68, 4.67, 4.69 and 4.68, respectively, with an average value of 4.68. The differences observed in the curves presented in Figure 17 can be attributed to variation in the peak loads of the specimens.

Simulation results

In this study, four models were analyzed with identical parameters except for the constrained normal stress. The results demonstrate that the failure processes of all models exhibit highly similar characteristics, including the sequence of damage initiation, crack propagation patterns, and ultimate failure modes. This consistency suggests that the variation in the constrained normal stress does not significantly alter the fundamental failure mechanisms. Therefore, to avoid redundancy and enhance clarity, we present the detailed failure process of one representative model (SP-1 MPa) as a reference. This selected model typifies the overall behavior observed across all cases, ensuring that the findings remain generalizable and scientifically robust.

By comparing Figure 18(d) with Figure 18(b) or Figure 18(c), the damage patterns and strain propagation in the simulation closely resemble those observed in the experiments, both exhibiting shear failure in the joint region. However, the failure mode in the simulation is symmetric, whereas the experimental results display an asymmetric damage pattern. This discrepancy arises because the constrained loads applied in the finite element model are ideally symmetrical in real-time, while in the experiments, the constrained loads require manual adjustments. During the experimental loading process, deformation of the specimen leads to variations in the constrained forces on both sides, which cannot be consistently maintained at the designed values. Consequently, manual adjustments of the threaded rods are required, introducing delays and asymmetry in the constrained forces. This lag and asymmetry in the experimental setup are the primary reasons for the asymmetric failure observed in the test results.

Figure 18.

Failure state of SP-1 MPa model and its comparison with the test specimen. (a) Initial state of damage. (b) Final state of damage. (c) Equivalent plastic strain contour. (d) Failure state of SP-1MPa specimen during the test.

Figure 19 compares the results from the finite element model with those obtained from the analytical analysis and direct shear test. In the ascending portion of the curve, the simulation results closely match the analytical analysis, with a maximum error of only 9.3% for peak shear stress and 12.2% for the corresponding peak slip. In the descending portion of the curve, both the simulation and analytical results exhibit a similar decreasing trend; however, there is some disparity in the rate of interface stiffness degradation. This discrepancy is primarily due to the assumption in the finite element model that the interface experiences complete failure when the damage variable $D$ reaches 1, leading to a reduction in interfacial bond stiffness to zero. Nonetheless, the error between the simulation and analytical results remains within an acceptable range, further validating the reliability of the proposed analytical model for finite element analysis.

Figure 19.

Comparison between analytical results, experimental results and simulation results of shear stress-slip curves and peak points of each specimen.

The influence of mesh size on the accuracy of the numerical simulation has been investigated with three different sizes of mesh, including 10 mm, 20 mm and 30 mm. The simulation results are shown as Figure 20.

Figure 20.

Comparison of FE results under different mesh sizes.

It can be observed from the figure that the mesh size has minimal impact on the simulation results. This is likely because all components of the model are of regular geometric shapes, and the hexahedral elements used for meshing have dimensions with an aspect ratio close to 1, ensuring uniformity. These factors play a dominant role in governing the simulation outcomes, and this control effect is not easily altered by changes in mesh size.

Conclusions

This paper investigates the shear behavior of UHPC wet joints between precast assembly pier segments. Direct shear tests were performed to examine the shear behavior at the UHPC-NC interface. An analytical model describing the shear stress-slip curve was developed, along with a calculation formula for its characteristic points. A finite element model was also established to further validate the accuracy of the analytical model. The main conclusions are as follows:

(1) The damage pattern observed in the UHPC flat joint specimens is characterized by brittle shear failure in the concrete. The shear capacity of the UHPC-NC interface is initially governed by adhesive forces and friction, resulting in a linear shear stress-slip relationship. Once interfacial bonding fails, load resistance is sustained by surface friction and aggregate interlocking, leading to a concave descending segment in the shear stress-slip curve.

(2) Increasing the constrained normal stress from 0 MPa to 3 MPa significantly improves the cracking load, failure load, residual load, and relative displacement at failure of the NC segment. Among these, the failure load exhibits the greatest sensitivity to changes in normal stress, followed by the cracking and residual loads.

(3) To characterize the behavior of the UHPC-NC interface, dimensionless shear stress-slip curves were developed, and corresponding mathematical models were proposed. Formulas to predict peak shear stress and peak slip considering constrained normal stress were derived. The analytical model exhibited a maximum error of 20% compared to experimental results and closely replicated the experimental shear stress-slip behavior.

(4) After reaching the peak shear stress, interface damage evolves exponentially as plastic displacement increases. This pattern was consistent across specimens subjected to varying normal stresses. An index parameter of 4.68 was recommended for the damage variable.

(5) A 3D finite element analysis results closely aligned with both analytical predictions and experimental data, thereby confirming the accuracy and reliability of the proposed model. These findings provide a robust framework for predicting the mechanical behavior of the UHPC-NC interface under shear loading.

For prefabricated assembled bridge piers connected by wet joints, the longitudinal reinforcement typically passes through the joint area. The impact of this reinforcement penetration on the shear mechanism at the UHPC-NC interface must be considered. Consequently, future research will focus on developing a shear behavior model for the UHPC-NC interface that accounts for the effects of reinforcement penetration, the connection of longitudinal reinforcement at joints, and the longitudinal reinforcement ratio.

Footnotes

Author contributions

Shujun Yin: Conceptualization, Writing –original draft, Investigation, Validation, Data curation.

Mi Zhou: Supervision, Funding acquisition, Writing - review & editing.

Xiaonan Zhao: Investigation, Data curation, Writing – review & editing.

Lei Ma: Investigation, Writing –original draft.

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 was supported by “the National Natural Science Foundation of China (51978062)”, “Natural Science Basic Research Program of Shaanxi -Joint Fund Program (Program No.2021JLM-47)”, “the Fundamental Research Funds for the Central Universities, CHD (300102212209)”, “Shanxi Province Transportation Science and Technology Project (2021-02-03)”, “Natural Science Basic Research Program of Shaanxi (2022JC-23)”, “Innovation Capability Support Program of Shaanxi (2023-CX-TD-38)”.

ORCID iD

Shujun Yin

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