Research Article  Open Access
Wei Guo, Zhipeng Zhai, Zhiwu Yu, Feng Chen, Yongzhi Gong, Tao Tan, "Experimental and Numerical Analysis of the Bolt Connections in a LowRise Precast Wall Panel Structure System", Advances in Civil Engineering, vol. 2019, Article ID 7594132, 22 pages, 2019. https://doi.org/10.1155/2019/7594132
Experimental and Numerical Analysis of the Bolt Connections in a LowRise Precast Wall Panel Structure System
Abstract
This paper develops a novel dry connection utilizing highstrength bolts and introduces the corresponding lowrise precast wall panel structure system. To investigate the seismic performance of the structure system with full bolt connections, monotonic loading tests of the connection joint and cyclic lateral loading tests of three fullscaled precast shear walls are both conducted. Based on the test data, axial and shear mechanical models of the connection are given. Meanwhile, experimental results show that the failure mode of the connection is dominated by anchored rebar ductile rupture, and the precast structure system presents a stable energy dissipation capacity and a good seismic ductility. The numerical model of the precast shear wall is then developed and validated by the cyclic loading test. Also a simplified calculation method to predict the lateral strength of the precast shear wall is proposed. According to the calculation results, the distance between the center of the connection and the edge of the shear wall is suggested to be 150 mm, while the wall thickness is recommended to be 120 mm or 150 mm. Finally, a threestory precast wall panel structure is employed to assess the collapse performance of the proposed precast structure system by using the presented numerical model. The results indicate that the proposed structure system with full bolt connections has high stiffness and high seismic resistance against collapse.
1. Introduction
Precast concrete structure has been widely used because of the distinct advantages of high quality, high industrialization level, fast construction speed, low labor intensity, and green construction [1–8]. Over the last decades, many countries and regions, such as the United States, Japan, China, and Europe, have been increasingly advocating the precast concrete structure system for residential and industrial buildings [3, 4]. Especially, the lowrise precast structures, most of which adopt the precast wall panel structure system [2, 3, 9, 10], have a wide application in building construction [2, 3]. Meanwhile, previous studies have shown that the structure system adopting precast reinforced concrete shear wall as the main lateral resistance component exhibits a good seismic performance [11–13]. At present, many lowrise precast wall panel structure systems have been reported. Xu et al. [1] has conducted quasistatic test to verify the validity of sleeve connection to be used in the precast shear wall. The maximum interstory drift angle of the precast specimen approached 1/56. And the results showed that the precast specimen behaved similarly to the castinsitu specimen with respect to failure mode, interstory drift angle, ultimate force, ductility, stiffness degradation, and energy dissipation capacity. Brunesi and Nascimbene [3] proposed a new type of lightly reinforced concrete precast shear wall structure for lowrise residential building, which is connected by using threaded anchors and bolts. The seismic performance and damage pattern of the shear wall were studied by the pseudostatic test, and it showed that there is large residual deformation in the connection joints. Lim et al. [10] presented a type of precast concrete Twall structural system with Cshaped steel plate connected, and the seismic performance and connection’s reliability were verified by the quasistatic test. Gavridou [14] carried out a shaking table test of a fullscale posttensioned concrete wall building, and under strong earthquake excitation, the structural damage was repairable and no prestress loss was found despite the interface grout crushed partially.
The seismic performance of the precast wall panel structure system generally depends on the behavior of connection. The connection type not only affects the manufacture and installation process of precast components but also determines the overall structural performance. Great efforts have been made to investigate the mechanical performance of various connection types of precast wall panel structures, such as types of sleeve [1], emulative [5], hybrid [6], bolted [10], grouted [11, 15], and friction connection [16, 17]. In the previous research, the dry connection presented great advantages for lowrise precast buildings, in terms of quick erection, maintenance, and reuse [18]. Steel plate and bolts are commonly used to create dry connections. Lago et al. [16] and Bora et al. [19] proposed a connection consisting of steel plates, brass plates, and bolts. The well hysteresis behavior and energy dissipation capacity of the connection were demonstrated by quasistatic load tests. Guo et al. [17] developed a friction device composing of two steel angles and one T steel, which were bolted in the connection joint of the column and wall. And lowcyclic load test had shown that the friction device provided good energy dissipation and was controllable and readily replaceable. Bournas et al. [18] carried out the monotonic load test for one type of dry connection, which used bolts and two thick steel plates to connect the longitudinal rebar of the wall joints. The results revealed that this connection has good ductility, and its failure mode is the break of longitudinal rebar. Sun et al. [20] presented a Hshaped horizontal connector welded by a web plate and two flange plates, and two identical wallconnector assembly specimens were tested under monotonic loading and cyclic loading. The results showed that the performance of the shear walls was satisfactory in terms of ensuring the shear wall strength and ductility.
Since 21st century, the world has entered a seismicprone period. More challenges are raised for the development of precast buildings. Especially the countries like China where high seismic intensity areas are widely distributed and facing the problem of reconstruction in disaster areas and urbanization construction. In such circumstances, the developmental potential of the lowrise shear wall structure is gradually highlighted. Dry connection has been proven to be effective for the lowrise precast wall panel structure system in previous studies. However, more fast development and effective assembly connection are significant for reconstruction of disaster areas. In this paper, a new type of dry connection, which is more convenient for installation and composed of steel plates and highstrength bolts, is developed. Also the corresponding lowrise precast wall panel structure system with full bolt connections is introduced. The static loading test of the connection is conducted to investigate the joint performance. Then three fullscaled specimen of the precast concrete wall with bolt connections is cyclically tested. In order to describe the nonlinear behavior of the precast shear wall and evaluate the overall performance of the precast lowrise building, a finite element model (FEM) modified by the test data is developed. And a simplified method to calculate the lateral strength of the precast shear wall is derived. Considering the failure of connection is usually the main cause of collapse [21], the adjusted collapse margin ratio of a threestory precast wall panel structure is assessed based on pushover analysis.
2. Description of the Novel Dry Connection
The proposed novel dry connection in this paper consists of anchored steel plate and highstrength bolt. Figure 1 depicts the details of the connection. The steel plate adopts the Q345 steel with the nominal yield strength of 345 MPa and is anchored by using the HRB400 rebar with a nominal yield strength of 400 MPa. Grade 10.9 highstrength bolts with the nominal yield strength of 900 MPa are used to install the walls. Figure 2 describes the details of the vertical connection joint, and the horizontal joint is similar. As the reinforcement in the precast wall panels are discontinuous, all precast components can be erected conveniently. To ensure the performance of the connection, the anchored steel plate should be carefully designed to avoid the early failure, such as pullout of the anchored steel plate and bending of the steel plate. Current design codes, such as GB 500112010 [22] and ASCE [23], can be adopted to design the dry connection. The basic configuration of the lowrise precast wall panel structure system is displayed in Figure 3. Thickness of the walls is 150 mm, and all the precast wall panels are connected by the dry connections. The concrete walls work as a tube to transfer the gravity load and lateral load. This precast structure system has a rapid assembly advantage, and the main structure can be constructed at site within one day. It has been employed in practical engineering [24].
3. Experiment of the Connection Joint
To investigate the static behavior and obtain the axial and shear forcedisplacement models of the bolt connection joint, monotonic tensile and shear test are performed in this section. The axial and shear forcedisplacement models are used for establishing numerical model of precast shear walls in Section 5. Therefore, the designing parameters of the specimens in the monotonic test are the same as the precast wall. In order to avoid randomness and unreliability, three same specimens are constructed for tensile test, as well as the shear test.
3.1. Tensile Test
3.1.1. Test Specimens and Setup
The specimens for the axial tensile test consist of connection described in Section 2 and C30 concrete (nominal compressive strength f_{cu} equals to 30 MPa) block. Its dimensions are 1200 mm high, 400 mm wide, and 150 mm thick, as shown in Figure 4(a), where represents the HRB400 steel bar. Figure 4(b) depicts the details of embedded connection. The steel plate with dimensions of 180 mm (height) × 130 mm (width) × 14 mm (thickness) is anchored by four steel bars. And the length of the steel bars is 420 mm. Diameters of the steel bars and grade 10.9 highstrength bolts are 12 mm and 22 mm, respectively.
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Three same specimens marked as T1, T2, and T3 were tested by monotonic axial loading. Before test loading, the 550 N·m torque was applied to fasten the highstrength bolt according to the Code for design of steel structures [25], which can be calculated by the following expression:where T is the torque; P is the pretightening force, which equals to 190 kN based on the code [25]; d is the diameter of the highstrength bolt, which is 22 mm; k is the torque coefficient, which adopts 0.13 [25]. The monotonic loading process adopted force and displacement double control. During the force control stage, each load step was increased by 10 kN until the load reached 70 kN. Then each step was increased by 5 kN till the specimens cracked. After that, displacement loading was implemented till the specimen fails. During the test, one displacement sensor (DS) was used to monitor the connection behavior, as shown in Figure 5. According to the Chinese code, specification of testing methods for earthquakeresistant building [26], when the peak load of a loading cycle dropped to less than 85% of the maximum load, the specimen is defined to be destroyed and the test is terminated.
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3.1.2. Test Results
Damage of the specimens was observed during the test. Before the axial loading, transverse fine crack was induced by the applied torque. It propagated slightly at the end of the test. Figure 6 shows the finial failure mode of each specimen. In general, the three specimens failed with the similar mode. The failure process of the specimen can be described as (a) before the load was lower than 80 kN, no visible damage was observed, and the specimens were elastic; (b) while the load increased to 80 kN, the anchored rebar began to slip, it then caused the concrete to crack at the load of 120 kN, and the steel plate started to yield and bend; and (c) when the displacement control load started, concrete spalled gradually and the steel plate bent seriously. Subsequently, the connection failure that was characterized by the rupture of the anchored rebar in the weld point occurred when the displacement approached to 22 mm. In summary, the failure mode in the connection joint can be described in the following sequence: anchored rebar slipped, concrete cracked, steel plate bent, and anchored rebar ruptured. It should be noted that the failure, including steel plate bending and rebar rupture, exhibited good ductile behavior.
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Figure 7 gives the axial loaddisplacement curve of the three specimens. The specimens have large initial stiffness. The stiffness decreases obviously at the load of about 80 kN and 120 kN due to the anchored rebar slipping and steel plate bending. For establishing a numerical model in the later section, the axial mechanical model representing the axial forcedisplacement relationship is obtained by adopting the mean value of load and displacement at the critical loading points, such as cracking and yielding points. Because the lateral load drops rapidly as a result of connection failure at the displacement of about 22 mm, a sudden drop is defined for the axial mechanical model to reflect the connection failure. Moreover, the load and displacement values for different loading phase of the three specimens are provided in Table 1.

3.2. Shear Test
Three identical specimens, marked as S1, S2, and S3, were constructed to be tested in the monotonic shear loading. The design parameters were the same as the tensile test specimens. The monotonic shear loading was applied by using a hydraulic jack. Two displacement sensors (DSs) were used, and the relative location of the two DSs is shown in Figure 8. And their relative displacement would be measured as the shear displacement of the connection joint.
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Figure 9 compares the shear failure modes of the three test specimens. It can be observed that the failure mode of each specimen was similar. The failure process can be depicted as follows: (a) at the beginning of the test, the applied loading was smaller than the friction. The displacement was proportional to the shear load, and the specimens were elastic. (b) With the load near 80 kN, the connecting bolt began to slip as the shear force was larger than the friction. Then, the sliding stopped around the load of 110 kN due to the contact of the screw rod and steel plate. (c) At the load of 170 kN, concrete began to crack and spall, which was induced by the bondslip effect of the anchored rebar. When the load neared 220 kN, the anchored rebar of S1 and S3 fractured, while S2 lost bearing capacity due to the serious bending of the anchored rebar. In summary, sequence of the shear failure of the connection joint can be listed as follows: the bolt slipped, concrete cracked, and anchored rebar ruptured. Figure 10 shows the shear loaddisplacement curves of the three specimens. The dramatic degradation of the shear stiffness at load about 80 kN is caused by the bolt slipping. And contact of the screw rod and steel plate leads to the significant stiffness hardening at a load of about 110 kN. For establishing the numerical model in the later section, the shear mechanical model representing the axial forcedisplacement relationship is also obtained by the test data. In addition, the load and displacement values for different loading phase are provided in Table 2.
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4. Experiment of Precast Shear Wall
4.1. Wall Specimen
Three fullscaled precast shear wall specimens with different axial compressive ratios are constructed to investigate the seismic performance of the proposed wall system. The three specimens are named SW1, SW2, and SW3 here, corresponding to the axial compressive ratios of 0, 0.1, and 0.2, respectively. Designing parameters of these specimens are the same. The wall height is 3000 mm, the width is 1550 mm, and the thickness is 150 mm. Configuration and reinforcement details of the test specimens are drawn in Figure 11. The wall longitudinal and transverse reinforcement adopts the HRB400 steel bar with the diameter of 6 mm, and the C30 concrete is used. As shown in Figure 11, the longitudinal reinforcement is discontinuous, and the precast shear wall is connected to the rigid foundation beam by two dry connections. Dimensions of the foundation beam are 2500 mm × 800 mm × 600 mm. Design parameters and construction details of the connections are the same as static tests above. The installing holes are filled by using C35 fine aggregate concrete with 35 MPa nominal compressive strength. The interface between the wall and foundation beam is filled by ceramic tile adhesive. The distance between center of the connection and edge of the shear wall, marking as d, is 100 mm.
4.2. Test Setup and Loading History
The details of the test setup are shown in Figure 12. The specimens are fixed to the strong floor through six anchored bolts. Reversed cyclic lateral loads are applied to the specimen by using a 1000 kN hydraulic actuator that is mounted to a reaction wall. The distance from the center of the actuator to the bottom of the shear wall is 2750 mm. Thus, the shearspan ratio for the bottom section of the wall can be calculated as 1.77. A steel girder is installed on the top of the shear wall to distribute the vertical load, while the vertical load is simulated by using a hydraulic jack placed on the steel girder. The reaction force of the hydraulic jack is transferred to the strong floor by using the four thread steel bars mounted around the shear wall. Four displacement sensors are instrumented in the lateral direction to monitor the shear wall behavior. The relative displacement between DS1 and DS4 is measured as the shear wall displacement.
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First step of the test is to impose the axial load. For these specimens, the applied axial loads are 0 kN, 332 kN, and 664 kN, corresponding to the precast walls SW1, SW2, and SW3, respectively. The cyclic lateral loads applied by using the actuator are in accordance with the test loading history, as shown in Figure 13. The force and displacement double control loading are employed during the test. In the process of the force control stage, each load level is maintained for one cycle till the specimen yield. Then the displacement control is implemented, and each load level increases by one yield displacement. Meanwhile, each level is implemented for two cycles till to the specimen failure. During the cyclic lateral test, there are 6 load levels, 10 load levels, and 10 load levels for SW1, SW2, and SW3, respectively. When the peak load of a loading cycle dropped to less than 85% of the maximum load, the specimen is defined to be destroyed, and the test is terminated [26].
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4.3. Test Results
4.3.1. Failure Mode
An identical failure mode for the specimens was observed during the test. All the specimens failed as the result of connection rupturing and presented similar damage evolution. Due to failure behavior of the three specimens are similar, the damage evolution of typical wall SW2 is described here in detail. Figure 14 depicts the damage pattern of the test specimen SW2. The initial tension crack on the filled interface between the wall and foundation occurred at the load of 100 kN, as shown in Figure 14(a). When the load approached to 170 kN, which corresponds to the displacement of 11.27 mm, vertical compression crack in the wall corner appeared, as shown in Figure 14(b). As the load increased continuously, concrete in the compression zone spalled and crushed gradually, and anchored steel bars of the connection were bent by compressive stress. Meanwhile, bending deformation of the steel plate in the tension zone occurred. After reaching the ultimate load, corresponding to the displacement of 26.45 mm in the positive direction and 29.28 mm in the negative direction, the lateral load degraded dramatically due to the failure of anchored steel bar rupturing. During the cyclic loading test, no shear cracks on the wall were observed, and damages were concentrated on the connection joints. The failure mode of the test specimen is shown in Figure 14(c). In summary, the failure mode of the specimens is presented as the concrete crushing and connection rupturing, which is mainly induced by the flexural tensile stress.
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4.3.2. Hysteretic Behavior and Energy Dissipation
The hysteretic and backbone curves of the specimens are drawn in Figure 15. At the initial loading stages, the specimen performed elastic basically. At the displacement control loading stages, the stiffness decreased obviously and the energy dissipation increased gradually as a result of nonlinear plastic behavior and damage of the specimen. It can be observed that axial compressive ratio has significant influence on the energy dissipation and bearing capacity. Increasing the axial compressive ratio, the lateral strength and area of hysteresis loop increase significantly. Pinching effect can be observed in the plastic stage, especially for SW2 and SW3, indicating wall displacement was influenced by shear deformation or wall sliding. Moreover, it can be observed that the test specimen had a long yielding platform.
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In the loading cycles, residual displacement may generate. The residual displacement and maximum displacement in each load level are compared in Figure 16. The residual displacement for each loading cycle is defined as the relative displacement to the wall initial position after unloading. It can be found that residual and maximum displacement increase gradually with the load level, and residual displacement is positively correlated with the maximum displacement of the cycle. Residual displacement of the wall SW1 is obviously larger than those of the walls SW2 and SW3, demonstrating the damage of SW1 develops faster. For SW2 and SW3, the residual displacements are relatively small due to the restriction of axial compressive force. At the early loading stage, residual displacement is very small, with 0.03 mm and 0.07 mm in the negative and positive directions, respectively, for SW2. And they are 0.01 mm and 0.09 mm for SW3. Then they increase to 2.68 mm and 6.22 mm, respectively, in the last load level for SW2 and increase to 0.65 mm and 4.54 mm for SW3. Residual displacement ratios that are defined as the ratio of residual displacement to maximum displacement are 0.15 and 0.21 for SW2 and SW3, respectively, in the finial loading cycle. These illustrate that overall residual displacements of the walls SW2 and SW3 are small and also indicate that sliding friction effect on the connecting interface is slight, otherwise the large residual displacements will be caused due to the friction sliding.
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Two important indexes, cumulative dissipated energy and equivalent viscous damping ratio, are adopted to assess the energy dissipation capacity of the test specimen. According to the area of the hysteretic loop in each loading cycle, the energy dissipation of the specimens can be calculated, as shown in Figure 17. The equivalent viscous damping ratio is expressed as [27]where E_{D} is the dissipated energy in one hysteresis loop and E_{S0} is the strain energy of an equivalent linear elastic system at maximum displacement. The equivalent viscous damping ratio of the specimen is shown in Figure 18. Because the positive and negative displacements in a given cycle are not identical, the average value of them is adopted to represent the horizontal ordinate in Figures 17 and 18. As observed from the figure, energy dissipation and equivalent damping ratio increase obviously with the increasing load level. The equivalent damping ratio increases from 0.056 to 0.195 for SW1, from 0.047 to 0.142 for SW2, and from 0.073 to 0.125 for SW3. Because the wall SW1 without axial compressive force applied has a smaller bearing capacity and faster damage evolution, it presents a much smaller cumulative energy dissipation and a larger damping ratio. With the increment of axial compressive ratio, the dissipative energy of the wall increase obviously. In general, the walls SW2 and SW3 exhibit a stable energy dissipation capacity.
4.3.3. Ductility and Damage Factor
During the cyclic test, no obvious yielding of longitudinal reinforcements of the wall specimen was observed. Therefore, the yielding point is defined by the principle shown in Figure 19. The ductility is a significant factor to evaluate the seismic performance of structure and component. The ductility factor μ is defined as the ratio of the ultimate displacement Δ_{u} to the yielding displacement Δ_{y}. Through calculation, the final results are listed in Table 3. Although the ductility factor has an obvious difference in the negative direction and positive direction, the average ductility factors for walls SW1, SW2, and SW3 are 4.97, 5.03, and 6.09, respectively. That is, the test specimen possessed a good seismic ductility. The stiffness degradation usually determines the damages of structure and component. Hence, a damage factor is also defined in this paper, which is represented by the change of secant stiffness. It can be expressed as [28]where D_{i} is the damage factor of ith load level, K_{i} is the secant stiffness of ith load level, and K_{0} is the initial secant stiffness. It is clear that the lager damage factor indicates more serious damage. The damage factors of the test specimens are depicted in Figure 20. At the early loading stage, the damage factors in the negative direction are larger than those in the positive direction. However, there is only a little discrepancy after the specimen yielding. At the peak point, the damage factors range from 0.89 to 0.92. At the ultimate point, the damage factors range from 0.94 to 0.96. The stable variation of damage factors after the specimen yielding is the result of the identical failure mode of the specimens. To ensure seismic safety, a conservative value of damage factor, 0.9, is suggested for the performance state of collapse prevention.
 
V_{cr} and Δ_{cr} represent the cracking load and displacement; V_{y} and Δ_{y} represent the yielding load and displacement; V_{p} and Δ_{p} represent the peak load and displacement; V_{u} and Δ_{u} represent the ultimate load and displacement; μ represents the ductility factor; μ′ represents the average ductility factor. 
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5. Numerical Analysis
5.1. Modeling
An effective approach to numerically simulate shear wall component is proposed to adopt the multilayer shell element [29]. To predict the nonlinear behavior, a finite element model (FEM) of the tested precast shear wall is established, as shown in Figure 21. The software ETABS is adopted. The precast shear wall is modeled by using the multilayer shell element, which contains one concrete layer and four steel bar layers. The stressstrain relationship of concrete and steel bar is given in Figure 22, in which the concrete strength adopts 0.88f_{cu} according to the Chinese code [30], and steel strength adopts measured yield strength 400 MPa and ultimate strength 570 MPa. In order to simulate the dry connection joint, nonlinear zerolength element is utilized. Axial and shear mechanical models of the connections have already been obtained by monotonic loading tests, as drawn in Figures 7 and 10. Interface contact effect between foundation and wall is also a vital factor needed to be considered. The friction isolator element, employing a high vertical stiffness and friction coefficient of 0.6, is implemented to simulate the contact effect.
Here, the specimen SW2 is numerically simulated to verify the modeling approach. Figure 23 shows the stress distribution of FEM in the failure state, and it is in accordance with the damage state observed at the end of the test (Figure 14). The numerical analysis indicates that the wall is destroyed as a result of connection rupturing, the same failure mode as the test specimen. The backbone curve and damage factor of FEM and experiment are compared in Figure 24, which shows that simulation results match well with the experimental results. The methodology of the proposed FEM is validated.
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5.2. FEM Modification
The axial and shear behaviors of the connections are considered uncoupled in Section 5.1, making the connections more ductile. Hence, the FEM failed to capture the breakdown performance, as shown in Figure 24(a). In order to give more accurate simulation, axial loaddisplacement behavior of the connections is modified until a satisfactory match was achieved between the FEM and the experimental results. Figure 25 compares the backbone curves and damage factors of modified FEMs (MFEMs) and test specimens, while the critical deformation and load value are listed in Table 4. Although there are some differences with regard to the backbone curves between the MFEM and the tests, especially for SW3, the initial stiffness, peak load, and ultimate displacement of MFEM match well with those of the experimental results. And the MFEMs can capture the breakdown performance. Damage factors of MFEMs are slightly greater than that of the experiment, but they are still in good accordance with experiment on the whole, illustrating that the damage evolution can be simulated by the MFEMs. In general, the simulation results are in good agreement with the experimental results. The differences between the MFEMs and the test maybe mainly caused by the following reasons: (a) coupling effect of axial and shear behaviors of the connections is not fully considered in the MFEMs; (b) interfacial friction coefficient, adopted as 0.6, may have difference from the actual component; (c) the connections are simulated by using the macroscopic element (link element) based on the static test result, which do not consider the bonding slip behavior between the connection and the wall fully.
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D_{y}, D_{p}, and D_{u} represent the corresponding damage factors. 
Figure 26 plots the internal force of the dry connection in MFEMSW2, shear force of which is larger than MFEMSW1 and SW3. As the displacement reached 22.79 mm, the connection is ruptured by axial tensile force. Then the lateral load drops rapidly due to the failure of the connection. The shear force 79.46 kN is slightly larger than tangential slipping force 78.3 kN (Table 2), demonstrating that the wall slid slightly. The analysis on the above indicates that the MFEMs can predict the nonlinear responses of the precast wall panels, and it can be used to study the overall mechanical performance of the precast lowrise structure with bolt connection.
5.3. Effect of d
As mentioned above, d is defined as the distance between center of the connection and edge of the shear wall. To investigate the effect of d on the wall performance, MFEMs with various d, including d = 100 mm, d = 150 mm, d = 200 mm, d = 300 mm, and d = 400 mm, are established and analyzed. The axial compressive ratios are set as 0.1. Figure 27 compares the results of different models. When d increases to 150 mm, the peak load increases to 181.85 kN and ductility factor increases to 7.12. As d increases continually, the peak load decreases to 176.24 kN, 163.98 kN, and 161.10 kN, respectively, while the corresponding ductility factors are 7.43, 8.3, and 7.0, respectively. The effect of d on the damage factors is slight. At the initial and finial stages, the damage factor curves basically coincide with each other. However, the damage factor of the model with d = 150 mm is slightly smaller than other curves at the middle stages. Based on the results, d = 150 mm is suggested for the practical use.
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6. Simplified Calculation of Lateral Strength
In this section, a simplified calculation method to predict the lateral strength of the precast shear wall is derived for engineering application. According to the failure mode of test specimens, the following assumptions are made to determine the lateral strength of the wall: (a) the failure mode is dominant by axial tension fracture of the connection, and the axial force of connection, T, reaches the axial ultimate load; (b) the contribution of shear deformation of connection to the lateral strength is not taken into account, as well as the interfacial friction; (c) the discrete longitudinal steel bars in the wall are treated as continuum, and the compression zone width is assumed to be the same as that of the concrete compression zone. Therefore, the area of steel bars in the compression zone can be calculated by using equation (4), and the calculation diagram can be simplified and shown in Figure 28. According to the balance of vertical force and bending moment, equations (5) and (6) can be obtained. Then, the lateral strength of the wall, V, can be calculated by solving the equations:where A represents the total area of the longitudinal steel bars in the precast wall, x is the width of the compression zone, l is the width of the precast wall, T is the axial strength of connection which can be assumed as 150 kN based on the static test, N represents the axial load, f_{c} is the compressive strength of concrete, f_{y} is the yield strength of the steel bars, b is the wall thickness, h is the height of the lateral force, d is the distance between the center of the connection and edge of the shear wall, and V is the lateral strength of the precast wall.
The lateral strength values of walls SW1, SW2, and SW3 are calculated as 78.09 kN, 162.18 kN, and 236.55 kN, respectively. These values well match with the experimental results which are 78.9 kN, 178.6 kN, and 249.8 kN, respectively. To further verify the validation of the simplified method, MFEMs in Section 5.3 is adopted for comparison. The lateral strength ratio which is defined as the ratio of calculation strength V to simulation strength V_{m} of MFEMs in Section 5.3 is provided in Figure 29. The lateral strength ratios are about 0.9, indicating the accuracy of simplified calculation method again. The calculated strength is more conservative due to the negligence of connection shear deformation and interfacial friction.
Based on the simplified calculation method, the bearing capacity of shear walls under different parameters can be calculated, as listed in Table 5. It can be found that the lateral strength of shear wall increases gradually with the increase of wall thickness, axial compression ratio, and axial strength of connections. In general, the connection strength and axial compression ratio have a greater influence on the lateral strength, while the influence of wall thickness is small. The main reason for this is that the failure mode of precast wall is dominated by connection rupture, not by the complete crushing of concrete. Hence, the wall thickness is recommended to adopt 120 mm or 150 mm in practical engineering applications.

7. Adjusted Collapse Margin Ratio Assessment
Extensive collapse of structure caused by the failure of welded and poorly constructed connection had been reported in the previous studies [21]. It is necessary to evaluate the collapse prevention performance of the lowrise precast wall panel structure system proposed in this paper. Accuracy of the MFEM has been verified on the above. By using the MFEM, an actual threestory structure is numerically established here. The adjusted collapse margin ratio (ACMR) defined in FEMA P695 [31] is used to assess the structural collapse resistance [32]. However, methodology in FEMA P695 needs to perform massive calculation of nonlinear incremental dynamic analysis (IDA), and it is timeconsuming. Considering the lowrise precast wall panel structure is firstmodedominated structure, the ACMR is assessed in this section by using a fast method based on the pushover analysis [33, 34]. This method is essentially a modified version of FEMA P695. It calculates the seismic demand (displacement response here) of earthquake records by the capacity spectrum method, instead of nonlinear timehistory analysis.
The threestory precast wall panel structure with dimensions of 9.6 m (length) × 5.1 m (width) × 9 m (height) is simulated. Each story height is 3 m, and the thickness of wall panels is 150 mm. All wall panels are connected by dry connections which have the same design parameters of the cyclic loaded tested specimen in Section 4. Also, the concrete adopts grade C30, and the steel bar adopts HRB400. In total, there are 78 horizontal connections and 48 vertical connections used for the precast wall assembly. The characteristic period of the site is 0.4 s. Peak ground accelerations (PGAs) for the service level earthquake (SLE), designbased earthquake (DBE), and maximum considered earthquake (MCE) are 0.07 g, 0.20 g, and 0.40 g, respectively. The precast shear wall is modeled by using the multilayer shell element. The dry connection is simulated by using the nonlinear zerolength element. Interface contact effect between foundation and wall adopts the friction isolator element. By using the same modeling approach and parameters as the MFEM in Section 5.2, the numerical model of the precast structure is established, as shown in Figure 30.
The first step for the collapse assessment is to perform pushover analysis. The inverted triangle lateral load pattern is applied during the pushover procedure. Figure 31 plots the structure pushover curve and the corresponding idealized bilinear curve. The structure ductility can be calculated as μ = 2.58 according to the bilinear curve. The stiffness hardening after a lateral displacement about 18 mm is caused by the bolt connections because some of which change from the compressive state to the tension state. The fundamental period of the structure is T_{1} = 0.05 s. The equivalent damping ratio for the elastic design spectrum of Chinese code [22] is adopted approximately as 5% according to the analysis in Section 4.3.2. Then, the elastoplastic demand spectrum for SLE, DBE, and MCE can be given by the elastic design spectrum of Chinese code [20] and Vidic–Fajfar–Fischinger model [35], as shown in Figure 32. It can be observed that seismic capacity can meet the demand of code [22], and the stiffness of the structure is very large. Meanwhile, Figure 33 provides the relationship between roof drift and spectral displacement S_{d}. The results show that 1.33 can be used as the coefficient to modify the spectral displacement of equivalent linear single degreeoffreedom (ELSDOF) system to roof drift of multiple DOF system. It verifies rationality of ASCE/SEI 4106 [36] which suggested the modified coefficient as 1.3.
The next step is to obtain the structural performance curves based on the pushover results. Firstly, 16 ground motions are selected, as listed in Table 6, and the comparison of response spectra is plotted in Figure 34. Secondly, the intensity of each record is scaled incrementally from 50% to 1200% of the MCE intensity. And the elastoplastic demand spectrum of each record should be calculated using the method mentioned above. Thirdly, the target S_{d} can be obtained from the intersection point between the capacity spectrum of the structure and elastoplastic demand spectrum of the records. Then target S_{d} is multiplied by 1.33 to get the roof drift of the precast wall panel structure (Figure 33). Taking this calculation process for different intensities of each seismic record, the performance curves can be obtained then, as drawn in Figure 35.

The third step is to develop collapse fragility curve based on performance curves. The development employs the fitting technique proposed by Porter [34]. In Section 4.3.3, the damage factor, 0.90, is suggested for collapse prevention. Moreover, the damage factor at the peak load point of the pushover curve (Figure 32) is calculated as 0.9. Thus, for each individual performance curve, spectral acceleration at which the damage factor exceeds 0.9 is defined as the state of structural collapse. According to the secant stiffness of each performance curve and equation (3), the spectral acceleration of each record corresponding to structural collapse can be obtained, as listed in Table 7. According to Porter [37], the fragility parameters can be computed aswhere N is the number of records, r_{i} is the spectral acceleration at which the structural is collapsed in ith records, and β_{u} equals to 0.25 due to all specimens were under the same configuration [37]. The developed collapse fragility curve is shown in Figure 36. The median collapse spectral acceleration S_{CT} can be obtained from the curve as 4.28 g. At the structural fundamental period, the median MCE, S_{MT}, is 0.65 g. Hence, the collapse margin ratio (CMR), which is defined as the ratio of S_{CT} to S_{MT}, is calculated as 6.58 for the precast wall panel structure.

The final step is to determine the structural ACMR by adjusting the CMR with a spectral shape factor (SSF). It can be expressed as
The SSF in this case can be calculated to be 1.17 based on the structural fundamental period and ductility [27]. Hence, ACMR for the proposed precast wall panel structure is computed as 7.70. For ACMR assessment, it needs to determine the acceptable value of ACMR based on the total system collapse uncertainty β_{TOT}. This uncertainty is due to the recordtorecord variability in the ground motions β_{RTR}, the quality ratings of design requirement β_{DR}, test data β_{TD}, and numerical model β_{MDL}. β_{TOT} can be obtained as
In this case, β_{TOT} is computed to be 0.65 according to FEMA P695 [31]. And the acceptable ACMRs for a collapse probability of 10% and 20% are 2.30 and 1.73, respectively [31]. The result shows that the proposed structure with an AMCR of 7.70 has high seismic resistance against collapse during strong earthquake excitations.
8. Conclusions
A novel type of dry connection is presented and the corresponding lowrise precast wall panel structure system was introduced in this study. To assess the seismic performance of the connection and structure system, experimental work and numerical analyses are conducted. Based on the test and simulation, the following conclusions can be obtained:(1)Failure mode of the connection in axial tensile loading follows the sequence of anchored rebar slipping, concrete cracking, steel plate bending, and anchored rebar rupturing. In the shear loading, it generally follows the sequence of the bolt slipping, concrete cracking, and anchor rebar rupturing. The connection has a good ductile behavior. Moreover, axial and shear mechanical models of the connection are provided by the test results.(2)Failure mode of the precast shear wall includes the concrete crushing and connection rupturing, which is mainly induced by flexural stress. Test shows that the precast system has a stable energy dissipation capacity and a satisfactory seismic ductility with minimum average ductility factor of 4.97 and small residual displacement. Meanwhile, the damage factor, which is defined based on secant stiffness, is suggested to be 0.90 for the performance state of collapse prevention.(3)Numerical analysis modified by using the tested shear wall shows a good nonlinear behavior of the proposed wall panel system. Then, a simplified calculation method to predict the lateral strength of the precast shear wall is derived, and the accuracy is verified.(4)The distance between center of the connection and edge of the shear wall, d, is suggested to be 150 mm, and the wall thickness, b, is recommended to be 120 mm or 150 mm in practical engineering.(5)Adjusted collapse margin ratio (AMCR) of threestory precast wall panel structure systems is calculated to be 7.70, indicating the presented structure system has high seismic resistance against collapse in the strong earthquakes.
Data Availability
The data used to support the findings of this study are included within the article.
Disclosure
Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
The authors are grateful for the financial support from the Fundamental Research Funds for the Central Universities of the Central South University (project no. 502221804), National Natural Science Foundation of China (Project no. 51878674), Foundation for Key Youth Scholars in Hunan Province, and Project of Yuying Plan in Central South University.
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Copyright © 2019 Wei Guo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.