Abstract
In order to study the seismic performance of precast short-leg shear wall connected by grouting sleeves (PSSW), the three-dimensional numerical model was established by using the experiment of PSSW subjected to low cyclic loading. Based on good agreement between numerical results and experimental results, the numerical analysis models with different structural parameters of axial compression ratio and splicing position were designed in detail, and the effects of various parameters on the seismic performance of PSSW were analyzed. The results show that the PSSW exhibits wide and stable hysteresis loops, indicating a satisfactory hysteretic performance and an excellent energy consumption capacity. With the increase of the axial compression ratio, the shear capacity of horizontal splice seam is improved, but the ductility coefficient and total energy consumption decrease obviously. The most disadvantageous position of PSSW can be effectively avoided by changing the position of the post pouring seam. The bearing capacity of the specimens is basically stable, and the energy consumption increases significantly, so the post pouring seam of precast wall is recommended to be far away from the bottom section of the wall. In addition, the failure mechanism of different splicing positions was analyzed in detail.
Keywords
Introduction
In general, cast-in-place shear wall structure is widely used in civil buildings, but its construction method has many shortcomings such as environmental pollution, long construction period and high resource consumption, etc. Compared with traditional construction methods, precast shear wall structure has many advantages (Guo et al., 2014; Kang et al., 2013). Therefore, precast shear wall structure has been rapidly developed and widely used (Pavese and Bournas, 2011; Perez et al., 2013; Smith et al., 2013).
In general, the performance of the precast shear walls will be affected by the method of connection between the components, so the reliable connection has been a hot and difficult research topic in recently years. Soudki et al. (1995a, 1995b, 1996) studied the seismic behavior of precast concrete shear wall specimens with different connection modes, and the results showed that the precast concrete shear wall can have good mechanical properties. However, the cracks of the post pouring seams between precast members formed a weak region in the later loading stage. Thus researchers carried out the research of unbounded prestressing connection, which can not only reduce the cracking of the post-poured seam, but also control the residual displacement of the specimens via providing restoring forces (Bai and Zhang, 2013; Cheng, 2008; Chou and Chen, 2011; Karavasilis and Seo, 2011; Miller et al., 2012; Shim et al., 2008). The quasi-static tests of precast structure connected with prestressing tendon was carried out (Cheok and Lew, 1993), the results revealed that the ductility of precast structure was obviously better than that of monolithic structure, but its energy consumption was lower than that of monolithic structure. Smith et al. (2011) conducted monotonic horizontal load tests on a full-scale precast concrete shear walls with post tensioned horizontal connections to study their horizontal connection performance and bearing capacity. Erkmen and Schultz (2009) studied the influence of prestressing tendon arrangement, end structure of prestressed reinforcement and vertical load on the performance of unbonded post-tensioned precast concrete shear wall under seismic load. Because the precast specimens with unbounded prestressing connections have poor general economy and limit the energy consumption performance of the structures, so further promotion is limited.
Among many connection modes, the connection of grouting sleeve offers many advantages over other connection methods, the most important of which is the reduction of onsite construction time, good economy, convenient installation and easy detection, etc. It has been widely used in Europe, Asia, and the Americas (Ameil et al., 2015, 2016; Ameli and Pantelides, 2017; Haber et al., 2014; Parks et al., 2016). Adajar et al. (1993) developed a new, simple and economical technique for connecting vertical reinforcement in precast concrete shear walls, and they concluded that the ultimate strength of the joints used in the study was equal to the tensile strength. Peng et al. (2016) studied the cyclic behavior of precast concrete shear walls connected with sleeves, and it is concluded that the failure mode of precast shear wall specimen is similar to that of cast-in-place shear wall specimen, including tensile yield of longitudinal reinforcement and fracture of concrete in compression zone. Xu et al. (2017) carried out experimental research on a full-scale precast reinforced concrete shear wall endowed with single-row grout-filled sleeves connection, the results showed that the precast shear wall behaved similarly to the cast-in-situ specimen with respect to failure mode, interstory drift angle, ultimate force, ductility, stiffness degradation, and energy dissipation. Gu et al. (2019) studied the connection mode of grouting confined hole, and the seismic behaviors of four precast shear wall specimens and one cast-in-place shear wall specimen are investigated by pseudo-static test method. The results indicated that the precast concrete shear walls have good seismic behaviors and could be equivalent to the cast-in-place shear walls on the conditions of specified construction details. In addition, Belleri and Riva (2012) studied the applicability of grouting sleeves connection to precast concrete column-to-foundation, and they considered that connection of grouting sleeve can effectively prevent the buckling of longitudinal reinforcement and increase the local stiffness.
The post pouring seams between precast members will gradually crack when the specimen enters the plastic stage, which could have a serious effect on the overall performance of precast structures (Soudki et al., 1995a, 1995b, 1996). Apart from the adverse effects, the stiffness of precast specimens was strengthened by the grouted sleeve to prevent buckling of a reinforcement bar (Belleri and Riva, 2012). As a consequence, an important issue of both theoretical and practical significance is raised. How can the seismic performance of precast members connected by the grouted sleeve be affected. In addition, it is noteworthy that the splicing position of precast members is generally located at the end of the beam or the bottom of the wall, which is the most unfavorable position under stress. There are few studies on different splicing positions, and different axial loads also have obvious influence on the seismic performance of precast walls. In order to study the effect of grouted sleeve on precast members, the low-cycle repeated load test of precast short-leg shear wall connected with grouted sleeve was carried out in this paper. The finite element model which was consistent with the results of test was established. The seismic performance of specimens affected by axial compression ratio and the location of splicing seam were analyzed in detail. Furthermore, the friction of post pouring seam was also studied. After this introduction, the test model and numerical model is presented in section “Establishment and Verification of Finite Element Model.” The results and discussions are shown in section “Results and discussions.” Furthermore, the friction of post pouring seam is analyzed in section “Analysis of mechanical behavior of horizontal splicing joints.” The conclusions are drawn as section “Conclusion.”
Establishment and verification of finite element model
Test model
In order to better reflect the performance of the real structure, the size of the test piece was designed as large as possible to make full use of the bearing capacity of the test equipment. The size of the test piece should conform to the technical specification (JGJ3-2010, 2010), and the size of specimen is 2800 × 1000 × 200 mm. Figure 1 shows the detailed size and reinforcement of PSSW. In general, the short-leg shear wall can be defined when the ratio of width-thickness is between 4 and 8 (JGJ3-2010, 2010). In order to facilitate the loading of the specimen, a loading beam with the size of 300 × 1000 × 300 mm was designed on the top of the shear wall. In addition, the bottom beam of 600 × 600 × 2200 mm was designed to fix the specimen to the ground. According to the requirement of reinforcement ratio in Chinese Code (JGJ3-2010, 2010), the ratio of vertical reinforcement of concealed column and horizontal reinforcement should not be less than 1.0% and 0.25%, respectively. Meanwhile, the diameter and distance of stirrup of concealed column should not less than 6 and 200 mm, respectively. Therefore, steel bars with diameters of 10 and 16 mm were used to configure the walls horizontally and longitudinally, respectively. The ratios of longitudinal reinforcement, transverse reinforcement and volume stirrup were 1.2%, 0.79%, and 1.176%. In this study, the mixed method of force and displacement was employed, and this method was proven to be reliability (Gu et al., 2019; Xu et al., 2017). The method of force loading was used before the precast shear wall cracking, then the displacement loading was adopted until the final failure occurs.

Reinforcements detailing and dimensions (unit: mm).
The results of test
Figure 2 shows the final failure mode of PSSW. It can be seen from the graph that the specimens failed in flexural mode with plastic hinges forming at wall base, and corner concrete is characterized by spalling and crushing. The grouting sleeves remains intact without deformation. The distribution of cracks in the wall is mainly horizontal and sparse. The maximum cracking width of post-poring seam reaches 23 mm, and the main reason for the cracking distribution is that the post pouring seam forms weak zones during the later loading of the specimen.

Failure modes and crack distribution of specimens.
The response of the specimens in term of the horizontal load related to the displacement is illustrated in Figure 3. After the specimen yielded in succession, the specimen gradually enters the plastic stage. At this stage, the corresponding hysteretic hoops possess a reversed “S-shape,” as pointed out by Soudki et al. (1995a, 1995b, 1996) who found similar behavior in their investigation. It is worth mentioning that the areas covered by the hysteretic hoops become larger, which demonstrates that the energy consumption capacity of specimen increases gradually. When the peak load is reached, the loading stiffness and unloading stiffness decrease and the hysteretic curve shrinks caused by obvious slip between steel bars and surrounding concrete. The hysteretic curves of PSSW is dissipative, and the energy consumption capacity is better.

Hysteretic curve of PSSW specimens.
The numerical model
In order to better simulate the stiffness degradation of concrete under low cyclic repeated loading, the concrete damage plasticity model (CDP) was used for concrete and grouted material (Lee and Fenves, 1998; Lubliner et al., 1989). Generally speaking, the CDP model is based on five plastic parameters and two sets of basic uniaxial concrete data. The five parameters are respectively
Material properties.
Plastic demage model parameters.
In this study, the bilinear model was implemented for the simulation of the reinforcing bar, and the material properties are shown in Table 1. According to the literature (Sayadi et al., 2014), the grouting sleeve is always in an elastic state in the process of loading, so the ideal elastic model was used to simulate the constitutive relationship of grouting sleeve.
The concrete and grouted material are modelled with standard solid elements with reduced integration, and the T3D2 three-dimensional truss element was used for the reinforcing bar. The reinforcing bar was embedded in the surrounding concrete under the no-slip conditions between the steel bar and the surrounding concrete. The slipping effect of grouting sleeve, internal grouting material and external concrete were neglected based on the assumption that the connection performance of grouting sleeve is well.
In order to better simulate the bond behavior of the post pouring seam, the normal and tangential constitutive equations of the interface between the new and old concrete were established by using the non-linear spring model and Coulomb friction model, respectively. Figure 4(a) is a schematic diagram of the non-linear spring constitutive relation of the normal interface between new and old concrete, in which “

Contact interface constitutive relationship. (a) Nonlinear spring interface normal constitutive model, (b) tangential constitutive model of Kulun friction interface.
The loading procedure of the numerical model was in agreement with the test. Fixed boundary condition were simulated by restricting the whole bottom beam. Subsequently, the loading beam was subjected to axial pressure, and the cyclic loading controlled by transverse displacement applied to the top of the loading beam according to a predetermined drift rate. The finite element model loading diagram and the loading control mode are shown in Figures 5 and 6. In order to study the seismic performance of precast short-leg shear walls, the parameters of axial compression ratio and the location of post pouring seam were taken into account. The specific parameters of the specimens are shown in Table 3. The PW-0.15, PW-0.2, PW-0.4, and PW-0.6 mean that the axial compression ratios of precast walls are 0.15, 0.2, 0.4, and 0.6 respectively. PW-600 indicates that the distance of post pouring seam is 600 mm from the bottom of the wall, and the corresponding distance of PW-1200 is 1200 mm.

Finite element model loading diagram.

Displacement control process of numerical model.
Specimen parameters of precast short-leg shear wall.
Validation of numerical model
In the numerical simulation, it is observed that the concrete damaged seriously located at the bottom of specimen and the most serious and the maximum stress of the reinforced skeleton occurs at the corner, which is consistent with the experimental results, as shown in Figure 7. Furthermore, the stress behavior of grouting sleeve is in elastic state, as reported by literature (Sayadi et al., 2014). Figure 8 depicts the hysteretic curves and envelope curves. Compared with experimental results of PSSW, there is a good agreement between the numerical and the experimental results in which the general trend of the hysteresis loops from the numerical model is similar to the test results, but there is a slightly difference in the unloading stiffness between the compared results. The main reason for above observations is that a smaller

Failure mode in numerical result.

Hysteresis curves and envelope curves.
Results and discussions
Axial compression ratio
To bridge this gap of effect of the axial force on the seismic performance of precast short-leg shear walls, this paper considers the different working conditions with axial compression ratios of 0.15, 0.2, 0.4, and 0.6, respectively. The load-displacement curves of numerical models with different axial compression ratios are plotted in Figure 9. The peak bearing capacity increases with the increase of the axial compression ratio when the axial compression ratio is less than 0.4. It is should be noted that the peak bearing capacity of the specimens decreases gradually when the axial compression ratio is larger than 0.4. In addition, with the increase of the axial compression ratio, the plumpness of the hysteretic curve decreases gradually, which indicates the energy consumption capacity is reduced.

Load-displacement curves of specimens with different axial compression ratios.
Table 4 shows the major bearing capacity states, such as yield load (Fy), peak load (Fp) and ultimate load (Fμ), of specimens under different axial compression ratios. The yielding point is determined by observing the key point based on reduced stiffness equivalent elasto-plastic yield, as pointed by literature (Park, 1988). The maximum bearing capacity of each specimens is 1.36, 1.40, and 1.21 times of PW-0.15, respectively. When the axial compression ratio is less than 0.4, the maximum horizontal bearing capacity of the specimens shows an increasing trend with the increase of the axial compression ratio. However, it is worth noting that when the axial compression ratio is 0.6, its peak bearing capacity is about 3% less than PW-0.4.
Bearing capacity of characteristic points of specimens with different axial compression ratios.
a is the ratio of average peak bearing capacity of each specimen to PW-0.15.
Table 5 describes the yield displacement (
Horizontal displacement of characteristic points of specimens with different axial compression ratios.
The
Figure 10 describes the relationship curves of cumulative energy consumption and horizontal displacement of specimens under different axial compression ratios. With the increase of loading displacement, its energy consumption capacity gradually increases due to the specimen gradually enters the plastic stage. Because the ultimate displacement and bearing capacity of each specimens are different under the different axial compression ratio, so the total energy consumption of the specimens during the whole loading stage is defined to compare the energy consumption capacity of each specimens. The total energy consumption of PW-0.15, PW-0.2, PW-0.4, and PW-0.6 are 88.71, 55.49, 29.64, and 20.20 kN·m, respectively. The total energy consumption decreases significantly with the increase of axial compression ratio.

Energy consumption curve of precast specimens with different axial compression ratios.
Position of post pouring seam
The ultimate failure modes of precast shear wall specimens with different seam heights are bending failure. However, the force transfer mechanism of precast shear wall specimen changes during the whole loading process because of the different post pouring seam positions. The specific failure modes are shown in Figure 11.

Failure modes of specimens with different joint heights.
In order to account for the failure mechanism of specimens in detail, the forcing process of specimens is divided into three stages, as plotted in Figure 12. The first stage is that the bond strength of the post pouring seam is greater than the required tensile strength in the initial stage of loading. The overall performance of the whole specimen is well, and the transfer path is directly transferred to the corner of the wall by the diagonal compressive rod mechanism, which results in the stress concentration and forms the local plastic hinge. With the increase of horizontal force, the load of post pouring seam increases gradually. When the bonding strength of the post pouring seam is less than the required tensile strength, the cracking of interface occurs, which leads to weakening of the overall performance of precast wall. The path of force transmission is changed. The force of the diagonal bar is transmitted to the corner of the splicing joint and then to the corner of the wall in the form of the vertical bar. Therefore, two regions of local stress concentration and plastic hinges are formed. Because the stress at bottom section is the maximum, the larger plastic hinge is formed at the corner of the wall with the increase of the horizontal load, which makes the stress and crack width of the post pouring seam decrease. Then the force transfer mechanism of the specimen is gradually converted to baroclinic pressure, which leads to more serious stress concentration at the corner of the wall and ultimate failure. The result of this process is consistent with the stress state of precast walls.

Analysis of force transfer mechanism of precast walls with different joint heights.
Figure 13 shows the load-displacement curves of specimens with different seam heights. It can be seen that the hysteretic curve of PW-600 and PW-1200 is fuller than that of PW-0.15, the main reason is that the position of connections keep away from the maximum stress section so as to avoid coinciding with the plastic hinge regions. In addition, the bearing capacity and ductility of the specimens are basically stable despite the different post pouring seam heights.

Load-displacement curves of specimens with different joint heights.
Table 6 shows the yield load (Fy), peak load (Fp), and ultimate load (Fμ) of specimens with different seam heights. It can be seen that the different seam heights have little effect on the peak bearing capacity. Table 7 describes yield displacement (
Bearing capacity of characteristic points of specimens with different seam heights.
a is the ratio of average peak bearing capacity of each specimen to PW-0.15.
Horizontal displacement of characteristic points of specimens with different seam heights.
Figure 14 depicts the relationship between energy consumption and horizontal displacement of precast specimens with different seam heights. With the increase of loading displacement, the energy consumption of each specimen increases gradually, but the energy consumption capacity of PW-0.15 specimen shows a downward trend after reaching its peak value. When the loading displacement is less than 44 mm (drift ratio = 1.49%), the energy consumption capacity of PW-0.15, PW-600, and PW-1200 are basically the same. When the loading displacement is greater than 44 mm (drift ratio = 1.49%), the energy consumption capacity of PW-600 and PW-1200 is better than that of PW-0.15. The main reason is that the crack width of the post pouring seam has a negative effect on the energy consumption of the specimen. The crack width of the seams of PW-600 and PW-1200 decreases gradually during the later loading, while the crack width of the joints of PW-0.15 increases gradually. The variation of crack width is shown in Figure 15. Therefore, the ductility and energy consumption capacity of specimens are the lowest when the splicing position is at the bottom of the wall. Therefore, the post pouring seam of precast shear wall needs to be taken into account in design.

Energy consumption of precast specimens with different joint heights.

Cracking width of post pouring seams with different joint heights.
Analysis of mechanical behavior of horizontal splicing joints
In general, most of the methods for calculating the shear capacity of precast concrete splice interface are based on shear friction theory (Birkeland and Birkeland, 1966; Mast, 1968). When shear force acts on the interface of concrete post pouring seam, the interface will slip relatively. The tension generated in the steel bar passing through the interface exerts pressure on the concrete interface, and the shear force acting on the interface will be resisted by the interface friction mainly caused by the pressure. The shear capacity of horizontal post pouring seam comes from the direct shear resistance of interface concrete (bond, fine rough material, aggregate occlusion), shear friction of reinforcing bars, pin and bolt action of reinforcing bars, axial pressure action, and shear resistance of shear keys, etc.
Figure 16 depicts the change of friction stress between interface of post pouring seam. When the specimen is subjected to a small horizontal force, the interface of the post pouring seam has not yet slippage, and the static friction force increases with the increase of loading displacement. With the further increase of horizontal displacement, the interface will be separated after the static friction of the interface reaches its maximum value. In addition, the friction shear capacity between the splice interfaces will decrease, which is consistent with the change trend of Seible model (Seible and Latham, 1990). The average values of the frictional forces are utilized to compare the frictional forces between concrete interfaces of specimens with different axial compression ratios, as shown in Figure 17. The static friction at the interface between precast concrete increases with the increase of axial compression ratio, so the axial compression of precast specimen has a positive contribution to the shear resistance of concrete horizontal interface as depicted in table 8. The

Interface friction stress of precast shear wall.

Interfacial friction shear force of concrete with different axial compression ratios.
Interfacial frictional shear forces.
Conclusion
In this paper, the precast short-leg shear wall is designed and tested under low-cycle repeated loading. Based on the experimental model, the analysis of numerical simulation is carried out, and the factors of different axial compression ratios and different post pouring seam heights are considered to analyzed the seismic performance of precast short-leg shear wall. In addition, the frictional force of horizontal post pouring seam is analyzed. Based on the results of the experiment and finite element simulation, the conclusions are as follows:
The experimental results of precast short-leg shear wall connected by the grouting sleeves demonstrate that the connection performance of grouting sleeve is good, and the mechanical performance of the test is stable and reliable.
With the increase of the axial compression ratio of precast specimens, the total energy consumption and ductility coefficient decrease gradually. Based on the analysis of bearing capacity, ductility and energy consumption capacity, the recommended axial compression ratio of precast short-leg shear wall is 0.2 in this research.
With the increase the height of post pouring seam, the energy consumptions of the precast specimens increase gradually. It should be noted that the effect on the bearing capacity of the specimen can be neglected. In addition, the mechanism analysis of different heights of post pouring seam is analyzed.
The axial force has a noticeable effect on the friction of the horizontal post pouring seam, and the friction increases gradually with the increase of axial compression ratio.
Footnotes
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 research was supported by the National Natural Science Foundation of China (No. 51421005, 51908013), the Beijing Natural Science Foundation (No. 8204054), and the National Key Basic Research and Development Program of China (No. 2018YFC1504302).
