Seismic Performance Analysis of the Internal Joint in the New Demountable Fabricated Concrete Frame with Prestressed Mortise–Tenon Connections

Abstract

This paper proposed a novel demountable fabricated joint in frame, which is connected by the prestressed and mortise–tenon connection. The prefabricated components of the demountable structures are designed to be reused, and the joint presented in this paper will promote the sustainable application of prefabricated components in future. The damage process and damage pattern of the internal joints under the horizontal load were analyzed using the refined numerical analysis model based on ABAQUS 6.14. Parametric analyses were conducted simultaneously for five parameters: axial compression ratio, the area and effective initial stress of unbonded prestressed strands (UPSs), the local reinforcement ratio in the core zone of the demountable joint, and the friction coefficient between the interface of concrete. The results showed that the demountable joint exhibits excellent energy dissipation potential under horizontal loads, but the damage was concentrated in the core zone. The deformation of the joint mainly consisted of the self-deformation of the prefabricated components, including bending, bearing and shear, as well as the relative slip deformation between the prefabricated components. The axial compression ratio has a more significant effect on the hysteresis performance compared to the areas of the UPSs and the reinforcement ratio. The initial effective stress of the UPS and the friction coefficient have relatively minor influence on the hysteretic performance of the joint. Finally, this paper recommends the design parameter values (axial compression ratio should not exceed 0.4, area of unbonded prestressed reinforcement should be not lower than As_n=0.₀₂ and not higher than As_n=0.₁, the initial stress of the UPS takes the value of 0.75f_pu) and outlines optimization measures.

1. Introduction

In recent years, prefabricated structures have been one of the hottest topics in civil engineering, with various projects developing towards prefabricated structures. For the prefabricated structures, the frame structures have the most applications in various building structures due to their excellent mechanical properties and functional characteristics [1,2,3]. Based on the different connection methods, the prefabricated structures can be categorized into two types: wet connection and dry connection [4,5]. In the case of wet connections, such as grouting sleeves and corrugated pipe grouting connections. Due to the equivalent connectivity of steel bars at the connection, the strength and stiffness are usually higher or emulative compared to those of the cast-in-place structures [6,7], and the connections can meet the criteria of the rigid connections.

The main connection methods for dry connections are bolts, welding, and prestressing [8,9]. The efficient utilization of prestressing provides the potential for the innovative development of structures with dry connections. In the 1990s, Priestley first proposed the prestressed prefabricated frame structures within the earthquake resistance cooperation project PRESSS (Precast Seismic Structural System) between the United States and Japan [10]. Subsequently, numerous researchers conducted extensive research on the prestressed prefabricated frames and improved their connection types. At the same time, these structures were applied in practical projects and the relevant specifications were issued [11,12,13]. For example, the United States and New Zealand have also issued relevant regulations [14,15]. At the same time, China has also introduced relevant regulations, such as Technical Specification for Prefabricated Prestressed Concrete Assembled Integral Frame Structures (JGJ224-2010) [16], Seismic Design Standard for Prestressed Concrete Structures (JGJ/T-2019) [17], and Technical Specification for Application of Prestressed Compression Assembled Concrete Frames (T/CECS992-2022) [18].

The study above demonstrates that prestressed fabricated frame structure is an assembly structural system with excellent performance and ease of construction. Due to the discontinuity of the concrete and steel reinforcement in the connections of beam–column prefabricated components within the prestressed assembled frame structure, the contact surfaces of the joints with dry connections are established. This leads to the generation of both normal bearing pressure and tangential friction between the contact surfaces. This forms a nodal force transfer pattern that relies on pressure-bearing and friction connections.

The beam–column joints exhibit a rocking state under prestressing, which relaxes the degree of the restraint between the components, demonstrating good ductility (deformation capacity) and self-resetting ability. Previous studies have shown that the prestressed connections rely solely on the pressurized and frictional forces between the components to resist external loads, resulting in low energy dissipation capacity and localized high damage. Subsequently, many researchers optimized the prestressed connection joints by adding various types of dissipative devices, such as friction dampers, metal dampers, and connecting bolts [19,20,21,22]. And at the same time, the local reinforcement measures were implemented, including the use of UHPC, ECC, and reinforcing steel plates [23,24,25,26]. The results show that the application of dissipative devices and localized enhancement measures can effectively improve the strength and energy dissipation capacity while reducing the local damage [27,28]. Nevertheless, the incorporation of energy-dissipative devices and local reinforcement measures not only increases costs and complicates construction but also affects the functionality of the building. Furthermore, the durability of various types of energy-dissipative devices often does not align with the durability of the main structure, limiting the practical application of dissipative devices in projects.

The mortise-and-tenon joints have been popular for use in traditional Chinese wood structures [29,30,31,32,33,34]. From the analysis of the force transmission mechanism, the mortise and tenon is one kind of the semi-rigid connection. Due to the inherent characteristics of wood self-structuring, the mortise and tenon connections exhibit a high percentage of energy dissipation capacity and excellent deformation capacity [35,36]. A few scholars have explored the application of mortise and tenon joints in concrete structure connections and demonstrated their capability [6,37,38]. However, the combination of the mortise-and-tenon and prestressed for the connection between precast concrete members has not been reported.

Therefore, this paper proposes a new type of fabricated frame structure, which combined the respective advantages of prestressed and mortise-and-tenon joints, as shown in Figure 1a. The joints are mainly composed of the column tenons, the column cups, one-piece beam–slabs, and the UPS in vertical load, as shown in Figure 1b. This novel frame structure proposed in the paper not only meets the requirements for prefabricated manufacturing and assembly construction but also offers a degree of demountable capability. Recognizing that there are relatively few studies on demountable assembly structures [39,40,41,42,43,44], the research presented in this paper aims to further promote the development of such structures. This advancement has the potential to facilitate the reuse of prefabricated components and contribute more effectively to low-carbon and sustainable development.

2. Proposal of the New Joint

Because there is no second casting process, the reinforcement between the prefabricated components is usually discontinuous in dry connections [42,43,44]. Furthermore, there is a unique contact property where the concrete contact interface experiences compression only but not tension [45]. As a result, the shear and energy dissipation capacities of dry connections are usually lower than those of wet connections [1]. Among the dry joints, prestressed joints are used in various types of building and bridge structures because of the excellent deformation recovery performance and lower residual deformation. The hysteresis curve of a typical prestressed-only joint is shown in Figure 2a. Based on the hysteresis curve, it can be observed that the joint exhibits minimal residual deformation but has limited energy dissipation capacity.

The mortise-and-tenon connections originated from the traditional Chinese wood structures. The joints mainly depend on the mortise and tenon socket structure and the embedded pressure between the wood materials to transfer the loads, in which the typical hysteresis curve is shown in Figure 2b. According to the hysteresis curve, the hysteresis curve of the joint has more obvious pinch-shrinkage phenomenon due to the interface slip phenomenon, and the residual displacement is larger. Due to the presence of tenons, the shear performance of the mortise and tenon joint is typically superior to the frictional shear performance of the prestressed joint, which only relies on interface contact.

Therefore, by combining the advantages of the above two methods of dry connection, the mortise–tenon connection can effectively improve the energy dissipation capacity and shear bearing capacity, while the application of prestressing can effectively reduce the residual displacement. The combination of mortise–tenon and prestressing is a reasonable method for connecting the prefabricated components in frame structures.

Based on the above analysis, this paper proposes a new type of fabricated frame structure by combining the mortise–tenon connection and prestressing connection, as shown in Figure 1a. The assembly process is as follows: (a) installing prefabricated frame columns and placing the UPS; (b) installing one-piece beam–slabs at the cup of the column; (c) installing upper columns above one-piece beam–slabs; and (d) tensioning and anchoring the UPS to form the complete structure. The internal joint of the frame is shown in Figure 1b.

3. Foundation and Validation of FEM

3.1. Foundation of FEM

3.1.1. Material Constitutive Model

The CDP (concrete damage plasticity) model was used to characterize the damage evolution of concrete under the cyclic loading. The tensile and compressive damage paths were determined based on the tensile and compressive damage factors [46], as shown in Figure 3. The CDP model is based on the material plastic damage model proposed by Lubliner J [47], which can describe the material cracking failure under tension and crushing failure under compression. The mechanisms of cracking and crushing failure are characterized by defining the damage factors and the stiffness recovery coefficients of the compressive and tensile. The tensile and compressive damage factors can be calculated by Equations (1) and (2). According to the related literature, the recommended value of η_c is in the range of 0.35 to 0.7, and η_t is between 0.5 and 0.95. The concrete stress–strain curve relationship is selected according to “the code for design of concrete structures GB50010-2010” [48]. In addition to the definition of the tensile and compressive stress–strain curve for concrete, as well as the tensile and compressive strain–damage factors, it is still necessary to define five other parameters, as shown in

Table 1. Parameters of concrete damage plasticity constitutive model.

Dilation Angle	Eccentricity	fbo/fco	k	Viscosity Parameter
38	0.1	1.16	0.6667	0.0005

f_bo: the biaxial compressive strength of the concrete, f_co: uniaxial compressive strength of the concrete, k: the influencing parameter of the yield form about the concrete.

.

$$d_c={\displaystyle \frac{(1-{\eta }_c){\overline{\epsilon }}_c^{in}{E}_0}{{\sigma }_c+(1-{\eta }_c){\overline{\epsilon }}_c^{in}{E}_0}}$$

(1)

$$d_t={\displaystyle \frac{(1-{\eta }_t){\overline{\epsilon }}_t^{in}{E}_0}{{\sigma }_c+(1-{\eta }_t){\overline{\epsilon }}_t^{in}{E}_0}}$$

(2)

The constitutive model of the UPS adopted the randomly strengthened tridiagonal model [49,50], as shown in Figure 4. The Clough model [51] was used for the steel bars, which can consider the degradation of load-carrying capacity, as shown in Figure 5.

3.1.2. Element

C3D8R elements (eight-node hexahedral linear reduced integration elements) are used for both concrete and steel anchor blocks, which can avoid the shear self-locking phenomenon of the elements under cyclic loading. The results are less affected by the quality of the mesh. And the elements have the advantages of high-convergence speed at the same time [52]. T3D2 (two-node linear three-dimensional truss elements) elements are used for both steel bars and UPSs.

3.1.3. Boundary and Load

Multiple analysis steps are set up to accomplish the modification of boundary and loading conditions in different stages. In Step 1, effective initial stresses are applied to the UPS using the temperature reduction method. In Step 2, axial forces are applied to the upper column. In Step 3, horizontal cyclic load was applied at the ends of the upper columns. The boundary conditions and load are shown in Figure 5. The horizontal loading mechanism references “the code of Seismic Testing Procedures for Buildings JGJ/T101-2015 [53]”, as shown in Figure 6.

3.1.4. Interaction and Connections

The concrete–concrete contact surfaces were normalized to hard contact. The coulomb friction model was used in a tangential direction. Based on the literature [54], the coefficient of friction between the contact surfaces of the concrete typically ranges from 0.4 to 1.0. The ordinary reinforcement bars are embedded in the concrete. The top and bottom of the columns are arranged with rigid blocks, which are connected to the columns by tie connections.

The simulation of the contact between the UPS and the concrete needs to ensure free displacement along with the axial direction of the UPS. In the two directions perpendicular to the axial direction of the prestressing bar, the UPS is constrained by the surrounding concrete, and its deformation is coordinated with the deformation of the column. Two virtual prestressed steel bars (VPS) are set up in the parallel direction of the UPS. The VPS were embedded in concrete [55,56]. The VPS and UPS were connected by rigid springs at the corresponding nodes. The spring direction was perpendicular to the axial direction of the UPS, as shown in Figure 5. A coupling connection was used between the end of the prestressing tendon and the rigid blocks to simulate the anchoring effect of the UPS.

3.2. Validation of FEM

Considering the generality of the modeling technique, the feasibility of the modeling technique used in this paper is verified by the prestressed assembled frame test in the Precast Seismic Structural System (PRESSS) project. The joint details and finite element model in the literature [10] are shown in Figure 7 and Figure 8. Also, multiple analysis steps are set up to accomplish the modification of boundary and loading conditions in different stages. In Step 1, effective initial stresses are applied to the UPS using the temperature reduction method. In Step 2, axial forces are applied to the column. In Step 3, a horizontal cyclic load was applied at the column end. The detailed modifications to the boundary conditions in each step in Figure 8.

Figure 9 and Figure 10a,b show the comparison between the test results in the literature [10] and the calculation results of the finite model established by the material constitutive model and modeling technique used in this paper, respectively. The skeleton curves of the internal joint in the test are basically consistent with the curves calculated by the FEM. The tensile damage, compressive damage, and the distribution of diagonal cracks in the core zone under cyclic horizontal loading are basically consistent between the test and the FEM. Although the yield point of the skeleton curve of the numerical results are slightly smaller than the test results, the main reason is that the selection of the concrete material in FEM cannot be completely consistent with the concrete material involved in the test, and this phenomenon is more obvious after the concrete cracks. Comprehensive analysis of the above verifies the feasibility of the finite element numerical modeling approach used in Section 3.

4. Analysis of Results

In this section, the internal joints of the frame structure proposed in this paper are analyzed numerically. The damage process and damage pattern of the internal joints under monotonic horizontal loading are investigated. The hysteresis curve and skeleton curve of the internal joints under horizontal cyclic loading are systematically investigated.

4.1. Failure Process and Failure Type

Figure 11 shows the results of concrete and reinforcement stress, as well as concrete damage distribution of the joints under ultimate loading. From the results in Figure 11, it is obvious that the stress and damage distribution in the core zone of the joint with its surroundings is much higher than that in the other parts of the specimens in the limit state. The other parts are basically in the elastic stage. The main reason for this is that the core area of the joint consists of multiple areas of prefabricated parts, with discontinuous reinforcement and dry junctions between the prefabricated parts. The result is that only pressure can be transferred between the precast parts, and not tension.

The tenon of the column varies among sections along the height direction, and it can be placed in the cup formed by the framing beam–slab and the lower framing post together. The vertical load at the top of the column is transmitted through the upper frame column tenon and the contact surface with the frame beam–slab. The beam connection zone transfers the vertical load to the lower frame column through the contact surfaces with the lower frame column cups. Horizontal loads in the upper section of the joint core are carried by the friction between the upper frame column tenon and the bottom surface of the upper frame column. Horizontal loads in the lower section of the joint core are transmitted by the compression between the mortise and tenon of the beam, the mortise and tenon of the upper frame column, and the cup of the lower column.

Under the action of horizontal cyclic loading, the prefabricated components are connected only by the connection, which releases the degree of constraint between the components in the core zone of the joint compared to the cast-in-place joint. The core zone of the joint is relatively weak compared to the prefabricated beam and column components. Simultaneously, there is frictional contact in the tangential direction between the precast parts in the core zone. Under the horizontal cyclic loading condition at the top of the column, there is relative slip deformation between the prefabricated parts. Under the condition of relative slip and the relative weakness of the joint core region, the plastic deformation of the beam–column joints under the horizontal reciprocating load mainly occurs in the core zone. The beam–column itself is mainly rigid deformation, and the elastic deformation and plastic deformation of the beam–column itself are relatively small. Comprehensive analysis shows that the damage mode of the joints proposed in this paper mainly consists of the damage of the prefabricated parts in the core zone of the joints (bending and compression are the main components) and the relative slip between the prefabricated parts.

Figure 12 and Appendix A show the monotonic horizontal load-displacesment curves of the joints and the distribution of the stress of the components (column tenons, beam–slab connection areas, and column cups) in the core zone of the joints throughout the entire process.

Based on Figure 12, the load process of internal joints under horizontal loading can be divided into four stages. Stage I is the elastic stage, in which the components of the joint form an overall bearing member under the pre-compression of the vertical UPS. As the horizontal force increases gradually, the separation between the components begins to appear, resulting in a decrease in the stiffness of the joints. Stage II is the yield stage, with the separation between the components, resulting in a decrease in the effective contact zone between the components. The stress concentration of the components in the core zone of the joint increases significantly, and the reinforcement of the prefabricated components in the core zone enters the yielding stage first. Stage III is the plastic deformation extension stage; after the yielding of the stress reinforcement of a component in the core zone, the relative deformation of this component increases, while the joint enters the load-holding stage due to the constraints imposed by the other components in the core zone. Stage IV is the destruction stage. With the increase in horizontal load, each component of the core zone of the joint enters the yielding stage. Their plastic deformation accumulates and the degree of damage gradually increases. This leads to the drop-out of concrete in some regions and yielding of steel reinforcement in surrounding regions. The relative slip between the prefabricated components continues to increase, and the joint failure duo to the horizontal bearing capacity of the joint core decreases rapidly.

Based on Appendix A, in order to further analyze the force mechanism in the core region of the joint, the whole loading process of the components in the core region is analyzed.

4.1.1. The Tenon of the Upper Column

In the simplified mechanical analysis model, the tenon of the upper column can be regarded as a cantilever member fixed to the upper column. Under the horizontal load at the top of the column, a part of the height of the tenon is separated from the surrounding frame beams and slabs on one side. The bottom region of the upper frame column tenon is subjected to both horizontal and axial reaction forces, forming a compression and bending member.

With the increase in horizontal load, the tensile side of the root of the tenon (the connection between the upper frame column and the tenon) cracks first, which corresponds to the end of Stage I. With the increase in horizontal load, the longitudinal reinforcement of the tensile side of the tenon enters the yielding stage, and the bearing capacity of the tenon characterized by compression and bending members decreases. The cracks on the tensile side of the tenon root gradually extends to the internal part of the tenon. The crack size at the root of the tenon gradually increases. The effective section at the root of the tenon decreases. Since the tenon of the upper column is a typical compression and bending short column member, its final failure mode is shear damage.

Due to the difference between the constrain of the beam end to the tenon of the upper column in the height of the beam and the constrain of the beam tenon to the tenon of the upper column in the height of the lower column cups, the tenon of the upper column could be divided into two parts. The upper and lower segments, h₁ and h₂, respectively, are shown in Figure 12.

4.1.2. Connection Region of the One-Piece Beam–Slabs

The integrated beam and slab within the core zone of the joint is called the connection zone of the one-piece beam–slabs, which relies on the friction of the interface contact between the mortise and tenon of the upper columns, the bottom surface of the columns and the cup of the lower columns to transfer the vertical and horizontal loads. From the numerical analysis results, as shown in Appendix A, the connection zone of the one-piece beam–slabs can be regarded as a semi-rigid member supported on the bottom edge of the upper column and the top surface of the cup of the lower column. The connection zone of the one-piece beam–slabs rotates around the support point under horizontal load. Due to the small size of the tenon of the one-piece beam–slabs, it is the first to undergo bending failure under combined horizontal and vertical loads.

4.1.3. Lower Frame Column Cups

Based on Appendix A, the lower column cups may be viewed as semi-rigidly attached to the combined tenon formed by the tenon of the upper column and the tenon of one-piece beam–slabs. Vertical loads are transmitted through the contact surfaces of the lower column cup and the combined tenon. Under the horizontal load, the cup of the lower column rotates relative to the combined tenon, and one side of the cup of the lower column separates from the combined tenon, while the other side extrudes on each other. When the top surface of the cup of the lower column on the compressed side reaches the ultimate compressive strain, the cup undergoes compression crushing damage.

Through the above comprehensive analysis, the whole damage limit state of the joint core zone is determined by the limit state of each component. The tenon of the upper column mainly suffered bending and shear deformation. Bending damage of the tenon and localized compression damage of beams mainly occurred in the connection zone of the one-piece beam–slabs.

4.2. Hysteretic Behavior

To further analyze the seismic performance of the joints, and considering the similarity of the hysteresis performance under each working condition, the hysteresis curve and skeleton curve of a typical working condition (n = 0.3, A_p = 280 mm², f_py = 780 N/mm², μ = 0.7) of the joints are selected for detailed analysis in this section. While n is the axial compression ratio, A_p is the area of the UPS, f_py is the effective stress of the UPS, and μ is the fraction coefficient.

The hysteresis curve and skeleton curve for the internal joint are shown in Figure 13. And the single-turn hysteresis loop curves in different stages are presented in Figure 14. Based on Figure 13 and Figure 14, it is known that the hysteresis curve of the middle joint shows an obvious shuttle shape, which indicates that the joint has a good potential in energy dissipation. The main reason for the shuttle shape of the hysteresis loop is that under the pre-compression of the UPS, the prefabricated components form an overall loading mode. The pre-compression effect is further increased by increasing the stress level of the prestressing tendons with increasing horizontal loads. The pre-compression effect is further increased by increasing the stress level of the prestressing tendons with increasing horizontal loads. The mortise–tenon of the joint in the core zone can effectively transfer the horizontal load, so the joint shows good energy dissipation potential under horizontal cyclic loading. However, due to the discontinuity in the core zone of the joint, its shear capacity is low. Therefore, the prestressed assembled tongue-and-groove joints proposed in this paper are inherently different from cast-in-place joints in terms of the force transfer mechanism in the core zones. Further improvement of the shear capacity is the direction of the optimal design of the joints.

According to Figure 13, it shows that the skeleton curve of the joints under the horizontal cyclic loading shows an obvious multilinear relationship. And based on the number of inflection points of the skeleton curve, it is divided into four stages: elastic stage (OA), yield strengthening stage (AB), plastic load-holding stage (BC), and destruction stage (CD).

Based on Figure 14, it shows that the hysteresis loop curve is close to a straight line at the early loading stage, and the hysteresis curve shows small energy consumption and residual deformation. When the drift is close to 0.6%, the components in the core zone of the joint locally enter the stage of separation, cracking and plastic deformation, the hysteresis loop area gradually increases, and the joint enters the yielding stage. Due to the presence of prestressing tendons, the hysteresis curves exhibit linear unloading characteristics in both positive and negative unloading phases. The main reason is the presence of dry connections between the prefabricated components in the core zone. The restoring force provided by the UPS dominates the unloading stiffness of the joint during the unloading phase.

When the drift exceeds 1.2%, the hysteresis loop area increases significantly, and the shape of the hysteresis loop changes from a shuttle shape to a parallelogram shape, which is mainly due to the relative slip between prefabricated components inside the core zone. When the drift exceeds 2.5%, the peak horizontal load of the hysteresis loop shows a decreasing trend, indicating that part of the components in the core region of the joint have entered the stage of the plastic deformation.

With the accumulation of the damage in the core zone, the hysteresis curve shows a significant decrease in the loading stiffness. And at the same time, there is a significant pinch-shrinkage phenomenon in the hysteresis curve during the forward and reverse unloading, which indicates that there is a significant relative slip between the prefabricated components in this stage. This is consistent with the relative deformation presented by each prefabricated component in FEM. While the drift reaches 5.6%, the ultimate load reaches 85% of the peak load, and the joint can be judged to reach the failure state in accordance with the code of Seismic Testing Procedures for Buildings JGJ/T101-2015 [53].

5. Parameter Study

In this section, to further analyze the influence of each parameter on the seismic performance of prestressed tenon-assembled frame joints and provide a reference for the optimized design of the joints, five parameters are analyzed. The parameters are axial compression ratio, prestressing tendon area, initial effective stress of prestressing tendon, equivalent reinforcement ratio in the core region, and the friction coefficient between the concrete contact interface. The specific parameter study framework is shown in Figure 15.

5.1. Axial Compression Ratio n

The axial compression ratio is one of the important factors affecting the seismic performance of structures, and it has been shown that the effect of the axial compression ratio on the ductile performance of structures is more significant [55,56]. This section focuses on the effect of the axial pressure ratio on seismic performance aspects such as hysteresis curve, skeleton curve, ductility, and energy dissipation capacity of the internal joint. Considering that the core zone of the joint is composed of the different prefabricated parts, the axial compression ratio should be limited. Therefore, this paper considers 0.1–0.5 as the variation range of the axial compression ratio.

Figure 16 and Figure 17 show the hysteresis curves and skeleton curves of the internal joints under different axial compression ratios. From Figure 16 and Figure 17, it shows that the initial stiffness and peak load of the joints tend to increase with the increase in the axial pressure ratio, but the increment of peak load shows a decreasing trend with the increase in the axial pressure ratio. Comparing the descending stage of the skeleton curve, it shows that the slope of the descending stage of the skeleton curve increases with the increase in the axial compression ratio, especially while the axial compression ratio is greater than 0.4, which indicates that the damage speed of the joint is accelerated with the increase in the axial pressure ratio in the damage stage.

Figure 18 shows the variation curves of the stress of UPS stress with the horizontal displacement in each joint with different axial compression ratios. According to Figure 18, it demonstrates that the stress of UPS under horizontal cyclic loading varies periodically with the horizontal displacement. The UPS remains in an elastic working state throughout the loading process, with minimal variation in stress values. Comparing the stress of the UPS under different axial compression ratios, it is evident that the amplitude of stress variation for the UPS decreases with the increase in the axial compression ratio. While the axial compression ratio is 0.5, the joint is severely damaged due to the relatively larger axial compression ratio in the damage phase, resulting in a significant decrease in the stress of the UPS. Comprehensive analysis suggests the axial compression ratio of the joint proposed in this paper should not exceed 0.4 in the design process.

5.2. Area of Unbonded Prestressed Reinforcement As

To investigate the influence of the area of the UPS on the seismic performance of the joint, the area of the UPS varied, with 280 mm², 420 mm², 560 mm², and 700 mm² as the parameter values of variation. The results of the hysteresis curve and the skeleton curve are shown in Figure 19 and Figure 20. According to Figure 19 and Figure 20, it was found that the increase in the area of the UPS had a small effect on the initial stiffness of the joint. After the yield stage, the peak load capacity of the joint increases with the increase in the area of the UPS. According to Figure 19, the hysteresis curve of the joint with the area of the UPS is 280 mm², showing a more significant pinching phenomenon compared to the other joints, and indicating that the increase in the UPS area can reduce the relative slip between the precast components in the destructive stage.

Figure 21 shows the curves of UPS stress with the displacement under the different parameter of the UPS area. According to Figure 21, the UPS stress shows a periodical change under the horizontal cyclic displacement. With the increase in prestressing tendon area, the magnitude of prestressing tendon stress change shows a decreasing trend, indicating that the increase in prestressing tendon area will reduce the utilizations of prestressing tendon. With the increase in the UPS area, the change amplitude of the UPS stress shows a decreasing trend, indicating that the increase in the UPS area will reduce the utilization rate of UPS.

Therefore, the total area of the UPS should be limited, considering the improvement of the strength by the prestressing tendons and the utilization of the UPS. For the object studied in this paper, it is recommended to be not lower than As_n=0.02 and not higher than As_n=0.1 (As_n=0.1 is the area of the UPS while the axial compression ratio is 0.1 only due to the combined force of the UPS).

5.3. Initial Effective Stress of Prestressed Reinforcement f_pu

To study the effect of effective initial stress of the UPS on the seismic performance of the joint, the initial stress of the UPS was designed to be 0.55f_pu, 0.63f_pu, 0.77f_pu, and 0.92f_pu (where f_pu is the design strength of UPS in tension), and the hysteresis curve and skeleton curve are shown in Figure 22 and Figure 23, respectively. From the figure, it shows that the effect of the effective stress level of UPS is basically the same as the effect of UPS area. However, in the later stages of loading, the effect of the increase in initial stresses of UPS was not as significant as the increase in UPS area in terms of limiting the relative slip between the precast components in the core regions of the joint.

Figure 24 shows the curves of UPS stresses with the displacement under different prestressing levels, and the magnitude of prestressing tendon stress variation is basically unchanged with the increase in UPS stress. Therefore, increasing the initial effective stress of prestressing tendons has limited impact on enhancing the stiffness and strength of the joint. Excessive initial stress should be avoided to ensure that the UPS operates within the elastic working stage [57,58]. According to the requirements of the tension control stress of the Code for the Design of Prestressed Concrete Structures JGJ 369-2016 [59], the initial stress of the UPS should less than 0.75f_pu. It suggests that the initial stress of the UPS takes 0.75f_pu.

5.4. Reinforcement Ratio of the Joint in Core Region ρsv

Based on the analysis in Section 4, it is evident that the seismic performance of the joint is significantly affected by each prefabricated part in the core region. Consequently, the strength and the stiffness of each prefabricated part have a significant impact on the seismic performance of the joint. Therefore, the reinforcement ratio of each prefabricated part was used as a parameter for analysis.

The reinforcement ratio mainly considers the longitudinal reinforcement ratio and hoop reinforcement ratio of the tenon of the upper column, the tenon of the one-piece beam–slab, and the cup of the lower column. Based on the equivalent cross-section a-a, the reinforcement ratio of the location of all the prefabricated parts in the core region is shown in Figure 25a. The configuration of the longitudinal and hoop reinforcement ratio of the components in the joint is shown in Figure 25b–d.

Figure 26 and Figure 27 show the hysteresis curves and skeleton curves of the internal joint under the different reinforcement ratios of the core region. The curves are named by the diameters of the longitudinal and hoop bar. For example, 10-6, representing a longitudinal bar diameter of 10 mm and a hoop bar diameter of 6 mm. Based on Figure 26 and Figure 27, it can be seen that the reinforcement ratio of the components in the core region has less effect on the initial stiffness, while the effect on the post-yield stiffness, the peak load, and the slope of the descending section of the skeleton curve is more obvious.

With the increase in reinforcement ratio of the components in the core region of the joint, the post-yield stiffness and peak load showed an increasing trend. It shows that increasing the local reinforcement ratio in the core region can improve the energy dissipation capacity. However, when the local reinforcement ratio in the core region reaches a certain degree, the descending stage of the skeleton curve becomes steeper, and the ultimate displacement of the joint shows a decreasing trend.

It shows that when the local reinforcement ratio of the core region reaches a certain degree, the increase in the local reinforcement rate improves the bearing capacity, but the local damage is more serious under the same displacement. The joint enters the destructive stage first, so it reduces the ductility of the joint. Figure 28 shows the stress curves of UPSs under different reinforcement ratios of each prefabricated part in the core region. According to the result, it shows that the UPS stress shows an increasing trend with the increase in the reinforcement ratio. It indicated that the increase in strength of the core region of the prefabricated components increases the potential for the utilization of UPSs.

Combined with the analysis above, the local reinforcement ratio of prefabricated components in the core region should be limited. The excessive local reinforcement ratio is unfavorable to the ductility of the joint. Meanwhile, the analysis results also show that it is not feasible to improve the performance of the joint by only increasing the local reinforcement ratio of the precast components in the core region. It is necessary to explore the methods to improve the local capacity and concurrently reduce local damage. Utilizing materials like steel tube confined concrete, UHPC or ECC in the core region can be considered.

5.5. Friction Coefficient μ

In this paper, the core region of the joint is composed of discontinuous prefabricated components, so the contact properties of the contact interface between the prefabricated components are crucial to the performance of the joint. The friction coefficient affects the degree of constraint between prefabricated components in the core region. Therefore, this paper utilizes 0.5, 0.6, 0.7, and 0.8 as the friction coefficients of the contact surfaces. Those values correspond to different interface treatments that can be used to either reduce or increase the friction coefficients between prefabricated components in the actual engineering.

Figure 29 and Figure 30 show the hysteresis curves and skeleton curves of the internal joints under the different friction coefficients. The friction coefficient has a certain effect on the shape of the hysteresis curve and it is more significant in the damage stage. The peak load of the internal joint increases with the higher friction coefficient. Meanwhile, under the condition of a higher friction coefficient, while the drift exceeds 4%, the hysteresis curve shows a significant pinch-shrinkage phenomenon, indicating that there is a slip between the components in the core region.

At the same time, the hysteresis curve shows negative stiffness during the damage stage, the reason may be the local damage of the prefabricated components in the core zone is accelerated under the larger friction coefficients. The components of the core region are not sufficient to resist the secondary additional moments generated by the vertical pressure. Figure 31 shows the curves of prestressing tendon stress with the horizontal cyclic displacement under different friction coefficients.

From the figure, the amplitude of stress change in the UPS shows a significant increase with the increase in the friction coefficient between the components. It indicates that the relative restraint between the components increases with the increase in the friction coefficient. The utilization of the UPS is significantly increased at the same displacement level.

In summary, it is evident that an increase in the friction coefficient can enhance the bearing capacity of the joint to some extent, but it comes at the expense of the reduced deformation capacity and accelerated the development of the damage in the core zone of the joint. This paper recommends setting the friction coefficient of the concrete interface within the range of 0.6 to 0.7.

6. Conclusions

In this paper, the seismic performance of the joint with the prestressed and mortise–tenon composite connection was studied primarily through the refined numerical analysis model. The damage evolution process and failure modes of the joint under horizontal loading were analyzed, and the parametric analysis was conducted at the same time. The main conclusions are as follows:

(1)

The novel joint combines the advantages of mortise-tenon and the UPS, resulting in the internal joint exhibits excellent energy dissipation potential under the horizontal cyclic loads. The damage process of the joint under the horizontal loading can be divided into four stages: elasticity, yielding, plastic deformation extension, and failure stage. The deformation in the core zone of the internal joint involves the local damage and plastic deformation, as well as the relative slip deformation.

(2)

The damage mode of the tenon in the upper column is bend-shear damage, while the damage mode of the cup in the lower column is crushing damage. The damage mode of the tenon in the one-piece beam-slabs is bending and shear damage, while the other parts in the connection region is localized crushing damage.

(3)

Increasing the axial compression ratio enhances the shear bearing capacity of the joint but diminishes its ductility. The effective initial stress of the UPS and the concrete friction coefficient exhibit a minor influence on the seismic performance of the joint. Appropriately increasing the area and the effective initial stress of the UPS, the local reinforcement ratio of the core region, and the friction coefficient can improve the peak capacity, but they may accelerate the local damage of the core zone. This paper suggests that the value of the axial compression ratio should not exceed 0.3, the area of the UPS is between As_n=0.02 and As_n=0.1, the effective initial stress of the UPS is lower than 0.75f_pu, and the friction coefficient of concrete interface is between 0.6 to 0.7.

(4)

This paper primarily investigates the internal joint using the refined finite element modeling. The findings require further validation through subsequent experimental research. Additionally, the overall performance of this new frame structure needs to be assessed in future work.

7. The Limitations and Challenges of the Study

The primary focus of this paper is on the finite element model, which has been validated by experimental results documented in the existing literature. While there are similarities between the experimental specimens in the existing literature and the new type of joints proposed in this paper regarding connection methods, significant differences exist in the detailed construction of the connected joints. Variations in factors such as material models, element types, mesh quality, and interaction types within the finite element model can influence the calculation results to some extent. Consequently, conclusions derived from numerical analysis models established based on these different parameters may exhibit some deviations. However, since the main emphasis of this paper is on qualitative discussions based on finite element numerical analysis results and proposing optimization measures for the joints, the impact of these factors on the relevant conclusions is relatively minor. In the future, the corresponding experimental research will be conducted on the new type of frame structure joints proposed in this paper to obtain more accurate seismic performance indicators of the joints.