Experimental Study and Numerical Simulation of Precast Shear Wall with Rabbet-Unbonded Horizontal Connection

Compared with a low-shear wall and mid-high-shear wall, a high-shear wall has the most applications. Therefore, the specimens in this paper were designed as high-shear walls, and the main role of the rabbets was preventing the wall from slipping. Three full-scale shear walls, denoted as Z-1, Z-2, and BW-1, were constructed and tested under quasi-static cycle loading to comprehensively study the seismic behaviour of an RHC shear wall. Each specimen was composed of a wall and base, as shown in Fig. 2. The wall had a height, width, and thickness of 3.4 m, 1.7 m, and 0.2 m, respectively. At the top of the wall, a loading beam was cast with the wall for the purpose of loading. The base had a length, width, and height of 2.3 m, 0.69 m, and 0.82 m, respectively. The grouting region was located at the lower part of the wall. The unbonded segments at the longitudinal rebars were located in the base. According to the FE simulation results for the specimens before the test, the unbonded length was taken as 300 mm (265 mm under rabbet). The horizontal connection was located between the wall and base. Eight vertical rebars at each edge were provided with special confining rebar in the form of stirrups, which constituted the boundary element with the concrete edge. Considering the longitudinal rebar intensity of the boundary constraint element and convenient construction of metal bellows, seven rabbets were set up symmetrically at the connection, whose sizes are shown in Fig. 2. High-performance mortar was grouted in these metal bellows and connection. The three specimens had identical wall designs, but they differed from each other in their axial compression ratios and unbonded levels, as shown in Table 1 and Fig. 3.

All of the materials (concrete, steel, and mortar) employed in the tests were from China’s ‘Code for design of concrete structures (GB 50010-2010, 2010)’. The concrete grade was C35, which denoted that the ultimate compressive strength of the cubic concrete specimens (15 cm × 15 cm × 15 cm) cured under standard conditions was 35 MPa, and their Poisson’s ratio was 0.2. Here, six cubic concrete specimens were tested.

The grade of steel in the tests was HRB400, where HRB denotes hot-rolled ribbed-steel bar, and the number 400 denotes the yield strength. Its elastic modulus was 200 GPa, and its Poisson’s ratio was 0.3. Three sets of steel with different diameters (d = 10 mm, 12 mm, and 16 mm) were tested.

The high-performance mortar tested (160 mm × 40 mm × 40 mm) was the H-80 type, which had an early strength, a high strength, no shrinkage, and a high fluidity behaviour.

The mechanical parameters of all the materials are showed in Tables 2, 3 and 4.

Quasi-static cyclic tests of the specimens were performed. The axial load was applied by tensioning pre-stressed rebar strands, and the lateral load was applied on the loading beam by a 150 t hydraulic actuator that was mounted on a reaction wall. Moreover, four lateral steel supports were symmetrically employed on both sides of the wall to prevent out-of-plane movement and distortion during the testing. The lateral supports did not have any mechanical connection to the specimen because no restraining movement of the specimens occurred inside the loading plane. The test setup is shown in Fig. 4.

As seen in Fig. 4, LVDT 1 and LVDT 2 were installed to measure the lateral displacement at the top of the shear wall, LVDT 3 and LVDT 4 were installed to measure the lateral displacement at the middle of the shear wall, and LVDT 5 and LVDT 6 were installed to measure the lateral displacement at the bottom of the shear wall. Furthermore, an additional displacement transducer (LVDT 7) was installed on the base to monitor any rigid-body rotation of the whole specimen. The above final lateral displacement of the wall adopted the average value of two displacements at the same wall height after subtracting the base displacement.

The protocol employed in the paper was the standard protocol suggested by the China’s ‘Standard methods for testing of concrete structures (GB50152-2012, 2012)’, as shown in Fig. 5, which consisted of a load control procedure and displacement control procedure. There was one cycle for each target load in the load control procedure. The target load was started from 30 kN with a level difference of 30 kN. The load control procedure lasted until the specimen yielded, at which time the displacement control procedure was started. The yield state of the specimen was defined as the point when the load–displacement curve started to become nonlinear, and the corresponding load and displacement were the yield load and yield displacement, respectively. There were three cycles for each lateral target displacement in the displacement control procedure. The lateral target displacement was started from the yield displacement captured from the load control procedure, with a level difference equal to the yield displacement. The loading lasted until the lateral resistance degenerated to 85% of the peak load, defined as the failure of the specimen, which was the ultimate state, and the corresponding load and displacement were the ultimate load and ultimate displacement, respectively.

(1) Specimen Z-1

For Specimen Z-1, the axial compression ratio was 0.1, and the unbonded level was 1. The first crack observed at 210 kN was a horizontal crack at the bottom of the wall on the tension side. The crack on the top interface of the rabbets was generated at 240 kN when the specimen was pushed. With an increase in the lateral load, several new cracks appeared, while the existing cracks developed continuously. When the load increased to 330 kN, a major inclined crack occurred. The response of Specimen Z-1 was found to be almost linear during the load control procedure of testing with loads up to 330 kN. At this moment, the load–displacement curve started to be nonlinear, with 18.30 mm of yield displacement, and the displacement control procedure started. The displacement increase extended the existing horizontal cracks into inclined cracks and caused the initiation of vertical cracks. The crack on the top interface of the rabbets cut through the wall at 3Δ when the specimen was pushed, and concrete began to spall in the bottom compression zone. In addition, the cracks in the centre of the test specimen propagated to the compression zone, and the crack width increased. When the displacement reached 7Δ, concrete started crushing in a large area in the bottom compression zone. At the same time, buckling of the longitudinal rebars within the boundary element of the wall panel occurred, exposing the horizontal rebars. Finally, the tensile longitudinal rebars yielded and the compressive concrete was crushed, which showed a typical flexural failure. The final crack pattern and failure mode are presented in Fig. 6a.

(2) Specimen Z-2

For Specimen Z-2, the axial compression ratio was 0.2, and the unbonded level was 1. The general test phenomena of Z-2 were largely similar to those of Z-1. The specimen successively experienced the following response stages: concrete cracking in the tensile zone, yielding of the specimen, cracking and spalling of the concrete in the compression zone, and final failure of the specimen. However, the difference was that the first crack in Z-2 was observed at 270 kN at the bottom of the wall when the specimen was pushed. In addition, the crack on the top interface of the rabbets was generated at 300 kN when the specimen was pushed. Moreover, the load–displacement curve started to be nonlinear at 450 kN with 13.60 mm of yield displacement, and the displacement control procedure started. In addition, when the displacement reached 6Δ, the specimen failed. Finally, the tensile longitudinal rebars yielded, and the compressive concrete was crushed, which showed a typical flexural failure. The final crack pattern and failure mode are presented in Fig. 6b.

However, from Fig. 6b, we find that the failure mode was not symmetric. This might have been because the push force and pull force of the hydraulic actuator during the test were not symmetric, but this had little influence on the results.

(3) Specimen BW-1

For Specimen BW-1, the axial compression ratio was 0.2, and the unbonded level was 0.57, In general, its behaviour and damage pattern were similar to those of the previous two specimens. However, the difference was that the first crack in BW-1 was observed at 300 kN at the bottom of the wall when the specimen was pushed. In addition, the crack on the top interface of the rabbets was generated at 360 kN when the specimen was pulled. Moreover, the load–displacement curve started to be nonlinear at 420 kN with 12.47 mm of yield displacement, and the displacement control procedure started. When the displacement reached 6Δ, the specimen failed. Finally, the tensile longitudinal rebars yielded, and the compressive concrete was crushed, which showed a typical flexural failure. The final crack pattern and failure mode are presented in Fig. 6c.

However, from Fig. 6c, it can be noted that the spalling material at the middle of the bottom wall was mortar not concrete. This was because the mortar overflowed during grouting, which meant the material outside of the bottom wall was mortar. Moreover, the mortar was brittle, which made it easy to spall during loading.

Based on the results for the three specimens, it was noted that the crack load of Z-1 was smaller than that of Z-2 because the axial compression ratio of Z-1 was smaller than that of Z-2. Moreover, the crack load of Z-2 was smaller than that of BW-1 because the cohesive force between the rebar and concrete in the unbonded region of Z-2 was less than that of BW-1.

Figure 7 presents the load–displacement curves of the three specimens obtained from the tests. These hysteresis curves reveal that during the load control procedure, the load–displacement curve exhibits a linear behaviour, whereas during the displacement control procedure, its exhibits the nonlinear behaviour with a large energy dissipation. However, all of the specimens have stable hysteretic behaviour in the inelastic regions. In addition, the hysteresis curve of Z-1 with a smaller axial compression ratio is richer with a larger loop number than those of Z-2 and BW-1. The hysteresis curve of Z-2 with a larger unbonded level is richer than that of BW-1.

The three skeleton curves tend to be flat with an increase in the load before the peak load and decline slowly after the peak load. The trend of the Z-2 and BW-1 skeleton curves is almost consistent with a large initial stiffness. However, Z-1 has a relative small initial stiffness because of the small axial compression ratio.

Several points representing the key response stages are identified in the curves. It is revealed that for the first cracking of the concrete, first yielding of the tension steel, and first crushing of the concrete, Z-2 is earlier than BW-1. The first visible bending cracking of the concrete occurred at top displacements of approximately 12 mm (Z-1), 6 mm (Z-2), and 5 mm (BW-1). The first yielding in the tensile steel occurred when the top displacement reached approximately 17 mm (Z-1), 14 mm (Z-2), and 12 mm (BW-1). The concrete began to spall at top displacements of approximately 52 mm (Z-1), 21 mm (Z-2), and 19 mm (BW-1).

Based on the test results, we obtained the crack load F_cr, yield load F_y, peak load F_m, and ultimate load F_u, as listed in Table 5.

Table 5 shows that the bearing capacity of Z-1 is smaller than those of Z-2 and BW-1 because the axial compression ratio of Z-1 is smaller than those of Z-2 and BW-1. The bearing capacity of Z-2 is slightly smaller than that of BW-1, although the unbonded level of Z-2 is larger than that of BW-1.

In essence, the ductility reflects the inelastic deformation capacity of a structure, which ensures that its strength and stiffness do not fall sharply because of inelastic deformation (Choi et al. 2019). The ductility can be denoted by a ductility factor, which is defined as where Δ_u is the ultimate displacement, and Δ_y is the yield displacement. Table 6 lists the values for the yield displacement Δ_y, yield drift angle θ_y, ultimate displacement Δ_u, ultimate drift angle θ_u, and ductility factor μ of the three specimens.

Table 6 shows that all of the displacements and ductility factors of Z-1 are larger than those of Z-2 and BW-1 because the axial compression ratio of Z-1 is smaller than those of Z-2 and BW-1. All of the displacements and ductility factors of Z-2 are larger than those of BW-1 because the unbonded level of Z-2 is larger than that of BW-1. This is because there is no cohesive force between the unbonded rebar and concrete, which allows the unbonded rebar to deform freely along the longitudinal direction.

On the whole, the ductility factors of the three specimens are larger than 5, which shows that they have better ductility. Moreover, the ultimate drift angles of the three specimens are larger than 1/120, which shows that they have better deformability.

The enclosed area of the hysteresis loop reflects the energy-dissipating capacity, with a greater area showing a greater energy-dissipating capacity. However, an energy dissipation evaluation using only the area is not comprehensive. Therefore, here, the energy dissipation coefficient E and equivalent viscous damping coefficient h_e are used to evaluate the energy dissipation (Han et al. 2019). The energy dissipation coefficient E is expressed by Eq. 1. where S_ABCD represents the enclosed shaded area ABCD of the hysteresis loop (Fig. 8a), S_ΔOBE represents the enclosed area of triangle OBE, and S_ΔODF represents the enclosed area of triangle ODF.

A structure resisting cycle loading develops damping in the inelastic region, which increases as the displacement increases. The complex damping analysis can be expressed by h_e, and its calculation equation is shown in Eq. (2). Based on Eq. (2), h_e curves for the three specimens are shown in Fig. 8b.

Figure 8b shows that the energy dissipation of Z-1 is obviously larger than that of Z-2 because the axial compression ratio of Z-1 is smaller than that of Z-2. The energy dissipation of Z-2 is larger than that of BW-1. This is because the unbonded level of Z-2 is larger than that of BW-1, and unbonded rebars increase the shear wall’s horizontal displacement but slightly decrease the bearing capacity, as shown in Sect. 4.3.

The stiffness degradation shows that the structural stiffness behaviour decreases with an increase in the cyclic loading times and a constant displacement amplitude (Lu et al. 2019). Generally, the secant stiffness is used to evaluate the stiffness degradation, and its calculation formula is shown in Eq. (3).where P_i and − P_i represent the positive and negative loads of peak point i, respectively, and Δ_i and − Δ_i represent the positive and negative displacements of peak point i, respectively.

The stiffness degradation curves of the three specimens were obtained using Eq. (3), as shown in Fig. 9. Figure 10 shows that the degradation curve of Z-1 declines relatively more slowly compared with those of Z-2 and BW-1 because of the smaller axial compression ratio. Moreover, in the initial stage, the Z-2 stiffness is smaller than that of BW-1, and in the last stage, the Z-2 stiffness is close to that of BW-1. In addition, the stiffness values of Z-2 and BW-1 degenerate rapidly in the initial loading stage and then slowly after a fracture develops in the structure. On the whole, all of the specimens’ seismic performances were good.

In addition, Table 7 lists the absolute values of tangent stiffness for different feature points of the skeleton curve. It is seen that the tangent stiffness of Z-1 is smaller than that of Z-2 because of the smaller axial compression ratio. Moreover, the tangent stiffness of Z-2 is smaller before the peak point and larger after the peak point compared to that of BW-1 because of the larger unbonded level.

(1) Connection Simulation and Boundary Conditions

In order to further study the RHC shear wall, a parameter analysis was performed using the ABAQUS software. The key to the FE model was modelling the rabbets and unbonded segment. For the rabbets, in order to conveniently build the model, a flat interface was used for the connection interface, and the contribution of the rabbets to the connection’s shear capacity was reflected by the frictional coefficient in the tangential direction. A shear-friction theory model was adopted by assigning a certain frictional coefficient of 0.3, as shown in Fig. 10. When a shear force acts on the interface, a relative slip occurs in the interface. If the interface is rough and irregular, a relative separation occurs along with the slip, and thus a tensile force occurs in the steel through the interface, and a corresponding compressive force acts on the interface as a reaction (Xiong et al. 2018). The frictional coefficient of 0.3 is not large because the effect of the rabbets on the shear capacity of the high-shear wall’s connection is small. A ‘hard’ contact is applied in the normal direction, which allows the two contact surfaces to separate from but not to penetrate into each other.

For the unbonded segment, all of the rebars are embedded in the concrete except the unbonded rebar segments. The two endpoints of the unbonded rebar segment are tied to the concrete. In the range of the unbonded segment length, at two normal directions of the rebar length, some large stiffness (ten times the steel elasticity modulus) springs with 50 mm spacing are set up to reflect the interaction between the concrete and rebars during loading. At the tangential direction of the rebar length, the rebars deform freely with no springs.

The bottom of the base foundation is restrained in all degrees of freedom. The constant vertical load on the loading beam is applied prior to the lateral load for each specimen.

(2) Material Modelling

(3) Element Types and Sizes

The concrete and high-performance mortar are modelled using solid elements (C3D8R, three-dimensional eight-node continuum elements with reduced integration). In order to reduce the complexity of the FE modelling, the vertical rebar in the upper wall and corresponding inserted rebar in the base are regarded as rebars that neglect the strengthening of grouting on the wall. Moreover, because it is subjected to an axial force and a shear force at the connection, it is modelled using beam elements (B31). The other rebars are modelled using two-node truss elements (T3D2).

The element sizes of the concrete in the wall and high-performance mortar are 100 and 50 mm, respectively. Because springs are set with a 50 mm spacing along the unbonded rebar length, and the setting points need to correspond with those in the surrounding concrete, the element size of the concrete in base is 50 mm. Figure 12 shows the FE model of Specimen Z-1. The FE models of the other two specimens are similar to that of Z-1.

Figure 13 compares the experimental with the simulated results of lateral load–displacement curves for the three specimens. It should be noted that the simulated stiffness is larger than the experimental stiffness. There are two reasons for this. During the simulation, the bonded rebars are embedded in the concrete with no slippage, whereas, in the actual testing, a small slippage inevitably exists between the rebars and concrete. Another reason is that there may have been some slippage between the loading end and the specimen during testing, which led to a smaller experimental stiffness. In addition, it is observed that the experimental peak load is larger than the simulated peak load. However, on the whole, the comparison demonstrates generally good agreement between the experimental and simulated results.

Only two parameters, namely the unbonded level and axial compression ratio, were considered in the tests. In order to comprehensively study the influence of the unbonded length, unbonded level, and axial compression ratio on the seismic performance of the RHC shear wall, FE models with different parameters were built according to the modelling method in Sect. 5.1, and the results were analysed.

(1) Unbonded Length

Setting the axial compression ratio to 0.2 and the unbonded level to 1 as an example, the unbonded length ranged from 200 to 500 mm, with a 50 mm spacing, as listed in Table 9. Fig 14 shows the influence of the unbonded length on the ductility and energy dissipation of the RHC shear wall.

From Fig. 14, it can be observed that when the axial compression ratio and unbonded level are invariant, the ductility and energy dissipation increase with the unbonded length.

(2) Unbonded Level

Setting the axial compression ratio to 0.2 and the unbonded length to 300 mm as an example, the correspondence of the unbonded rebar distribution in the cross-section and unbonded level (Table 10) are shown in Fig. 15a, b and c shows the influence of the unbonded level on the ductility and energy dissipation of the RHC shear wall.

From Fig. 15, it can be observed that the ductility and energy dissipation of the specimen increase with the unbonded level. However, this increasing trend tends to level off. This is because the ductility and energy dissipation are mainly provided by boundary elements. The effect of the edge rebars is the largest, with the effect of the rebars gradually decreasing from the cross-section’s edge to the middle. Moreover, the increase in the unbonded level represents a gradual increase in the unbonded rebar number from the cross-section’s edge to the middle, as shown in Fig. 15a. Thus, the unbonded level increases, the ductility and energy dissipation increase, but the increasing amplitude decreases.

(3) Axial Compression Ratio

Setting the unbonded length to 300 mm and the unbonded level to 1 as an example, the axial compression ratio ranges from 0.1 to 0.4, with a spacing of 0.05, as listed in Table 11. Fig 16 shows the influence of the axial compression ratio on the bearing capacity of the RHC shear wall.

From Fig. 16, it is showed that when the axial compression ratio increases, the peak load increases. However, the load–displacement curve declines more obviously. This is because there is no cohesive force between the unbonded rebars and concrete, which allows the unbonded rebars’ deformation to increase and the load–displacement curve to rapidly decline under high pressure. Therefore, it is deduced that the unbonded length and unbonded level should not be too large under high pressure.

As the unbonded length and unbonded level obviously also have impacts on the storey drift and drift angle, the design suggestions for the RHC in this paper need to comprehensively consider the effects of the previously discussed factors, which require further study.