Seismic performance of a new type of RC shear walls con�ned with high-strength rectangular spiral reinforcements

. To improve the seismic performance of structures, a new type of reinforced concrete (RC) shear walls confined with high-strength rectangular spiral reinforcements (HRSRs) is proposed. Pseudo-static tests were conducted on four 1/2-scale HRSR shear walls possessing different parameters. The influence of HRSR on the bearing capacity, ductility, and failure modes of the shear walls was systematically studied. The test results clearly indicate that using HRSR as hoops and transverse reinforcements can effectively restrain the deformation and capacity-decline stage of the high-strength concrete shear walls, improving their bearing capacity and ductility. Particularly, the seismic performance of the RC shear walls with a high axial-compression ratio can be significantly improved by applying HRSR. A simplified model was proposed for the ultimate flexural capacity of the HRSR shear walls, which precisely agreed with the experimental results. These results provide a new strategy for seismic-performance design of RC shear walls in engineering structures.


Introduction
Reinforced concrete (RC) shear walls at the bottom of high-rise buildings are subjected to large axial forces, bending moments, and shearing forces.Under strong earthquakes, shear compression and crushing failure often occur in shear walls with high axial-compression ratios, causing a significant decline in component strength and energy dissipation.Consequently, recovery from an earthquake is difficult.Therefore, developing suitable methods for improving the seismic performance of shear walls is critical in the seismic design of high-rise buildings.
RC shear walls are commonly used in high-rise buildings owing to their large in-plane stiffness  Corresponding author, Ph.D, E-mail: zhaohj@xauat.edu.cn and strength [1].Liang et al. [2] experimentally investigated the seismic performance of high-strength concrete (HSC) shear walls.Their results indicated that the deformation capacity of shear walls can be effectively improved by adopting several high-strength stirrups along confined boundary elements in the potential plastic-hinge regions of a shear wall.Fang et al. [3] performed cyclic loading tests on HSC shear walls with various span-to-depth ratios and reinforcement ratios of confined boundary elements.The failure modes, deformation ability, and energy-dissipation capacity of specimens were compared and analysed.They suggested that HSC shear walls exhibit superior ductility and energy-dissipation capacity for high axial-compression ratios when adopting small-spacing, high-strength stirrups; confined boundary elements with high reinforcement ratios; and horizontal-and vertical-distribution rebars with appropriately high reinforcement ratios.
Scholars have conducted research on the mechanism of confined concrete [4][5][6][7].The test showed that a quick failure occurred for unconfined columns once the ultimate bearing capacity had been reached, and the columns exhibited an obvious brittle characteristic.However, the confined columns could continue to bear load and further undergo deformation, due to the confinement effect after the load reached the peak strength of unconfined columns.
The application of continuous spiral reinforcement has been extended to RC elements with rectangular cross sections [8][9][10].RC beam-column joints, columns and frames with rectangular members, and rectangular spiral reinforcement (RSR) used as shear reinforcements have been tested under cyclic loading.
Chalioris and Karayannis [11] experimentally investigated the behaviour of RC shear-critical beams with transverse reinforcement replaced by continuous RSR under monotonous loading.Their results demonstrated that continuous RSR improved the bearing capacity and shear performance of shear-critical beams.Additionally, the same authors [12] experimentally investigated the behaviour of RC beams with rectangular cross sections and continuous RSR as transverse reinforcement under pure torsion.Woutert et al. [13] investigated the use of spiral shear reinforcement through a static four-point bending test of 24 RC beams.The results indicate that spiral shear reinforcement is a valid alternative with applicability to international codes.Their experimental program, consisting of 11 beams, clearly indicated that RSR provided enhanced torsion capacity and improved post-peak performance in the examined beams.Yang et al. [14] experimentally investigated 10 HSC columns confined with high-strength stirrups, which were effective for preventing a sharp decline in the stress-strain curve of HSC.High-strength stirrups can continuously provide large constraining forces after the peak load, improving the ductility of confined concrete and the structure's seismic performance.
Lonnie et al. [15] and Jonathan et al. [16] investigated the axial behaviour and analytical compressive stress-strain model of HSC confined with multiple spirals.Karayannis et al. [17] experimentally examined RC beam-column joints with continuous RSR as shear reinforcement.
Zhao et al. [18] investigated 5 HSC shear-wall specimens confined with high-strength RSR (HRSR) possessing different parameters; the reinforcement significantly improved the load-carrying capacity and ductility.Fan et al. [19] studied two concrete-filled steel tube (CFST) composite-shear-wall specimens and one RC shear-wall specimen; the load-carrying capacity of the spirally reinforced shear-wall specimens was greater than that of the CFST composite shear walls with the equivalent reinforcement ratio.Furthermore, the spirally reinforced shear wall had better energy-dissipation capacity than the RC shear wall.
According to the above studies, specimens with RSR exhibited a better response in terms of the developing failure mechanisms, maximum loads, hysteretic energy absorption, and seismic capacity compared to specimens with stirrups.The results of various tests [20][21][22][23][24][25][26][27] revealed that the application of RSRs in various components, such as beams, columns, and beam-column joints, improved the overall seismic performance of the examined specimens compared with conventionally reinforced sub-assemblages.Since spiral reinforcement can be positively and quickly tied into place, the replacement of individual stirrups by a continuous spiral can reduce the labour cost for production of the reinforcement cage.
Most existing experimental research was conducted to investigate the behaviour of RC elements with RSR.In the present study, by using a high-strength spiral stirrup to replace conventional stirrups in confined boundary elements and high-strength spiral reinforcement to replace the horizontal-distribution reinforcement in the wall, pseudo-static tests were performed on 4 shear-wall specimens confined with HRSR having various parameters.We investigated the effects of the axial-compression ratio, stirrup characteristic value, stirrup configuration, and stirrup spacing on the bearing capacity, ductility, and failure modes of the shear walls.A simplified model was proposed for the ultimate flexural capacity of an HRSR shear wall, which was validated by experimental results from the 4 HRSR shear walls.

Specimen design
Four shear walls confined with 1/2-scale HRSR were designed and labelled HCRCW-01 to HCRCW-04.The concrete strength grade was C50.The cross-sectional dimensions of the shear wall was 100×1000 mm 2 , the height of the wall was 1400 mm, and the span-to-depth ratio was 1.5.The testing axial-compression ratio and vertical load of HCRCW-01 were 0.31 and 1155 kN, respectively, while those of HCRCW-02 to HCRCW-04 were 0.22 and 809 kN, respectively.An RC loading beam was set on the wall top to apply a reversed horizontal load 100 mm away from the wall top.A 400×500×1800 mm 3 rigid-grade beam was set on the wall bottom and cast with the entire shear wall.
Embedded columns were set within 200 mm on both sides of the wall cross section, and longitudinal bars were densely configured in the embedded-column regions on both sides of the wallboard to simulate the stirrup configuration of a confined boundary element of the shear wall.To improve the confinement of concrete reinforcement, ductility of the HSC shear wall, and shearbearing capacity of the shear wall, the following three measures were taken for all 4 specimens.1) A closed high-strength rectangular spiral stirrup with 5-mm diameter and 1120 MPa tensile strength was adopted in the confined boundary elements on both sides of the shear wall.
2) The horizontal-distribution reinforcement bar in the shear wall was replaced by closed HRSR with 5-mm diameter.A common high-strength reinforcement bar with 5-mm diameter was used as the vertical-distribution reinforcement bar.
3) HRSR was adopted with a piece-confining configuration such as a chain.The confining range of the spiral reinforcement was divided into multiple independent confining segments; the concrete in each segment was separately confined.The HRSR in each segment was connected at the joint with vertical steel bars.Horizontal spiral reinforcement bars were mutually nested at locations where vertical reinforcement bars were configured.To adequately study shear walls with HRSR, specimens HPCSW-03 and HPCSW-04 [2] were employed for comparison.Fig. 1 shows the specimen dimensions and reinforcement configuration.Specimen details are listed in Table 1, and the measured material indexes of the reinforcement and concrete are listed in Tables 2 and 3, respectively.
where c1  is the ratio of prism strength to cube strength.For C50 and below, c1 0.76  = . is the shear span ratio; n is the testing axial-compression ratio; l  and s  are the longitudinal-steel-bar ratio and volume-stirrup ratio of the confined boundary elements, respectively; w  is the horizontal-distribution reinforcement ratio of the wall.

Loading equipment and loading mechanism
The experiment was conducted in the Key Lab of Structure Engineering and Earthquake Resistance of the Ministry of Education at Xi'an University of Architecture and Technology.Fig. 2 shows pseudo-static loading equipment.Horizontal loads were provided by a reciprocating actuator with the loading point at the centre of the loading beam on the wall top.The push and pull directions of the actuator were specified as the positive and negative directions, respectively.
In this test, by using the midpoint loading method, an oil jack applied a vertical load, which was uniformly transmitted to the loading beam on the specimen top through a rigid bearing beam.
The vertical load was increased to the predetermined axial pressure and was maintained constant by a load-regulating device.Subsequently, a horizontal cyclic load was applied.A loading mechanism and load-displacement control were adopted according to the JGJ 101-2015 Specification of Testing Methods for Earthquake Resistance Building.Before the specimens yielded, load control was utilized to exert a load at increments of 50 kN, and each load grade underwent one cycle.The yielding load and yielding displacement were determined by comprehensive observation of the loaded outermost longitudinal bars in the shear wall and distinctive deviations in the loaddisplacement curves.After the specimen yielded, displacement control was adopted for the load.
The load was cyclically exerted in multiples of yield displacement y  , and the cycle was applied thrice for each yield displacement until specimen failure, unavailable loading, or the decrease of load to approximately 85% of the maximum.

Test content and measuring-point arrangement
The test content primarily includes 1) cyclic horizontal load and the corresponding displacement of each grade cycle at the horizontal loading point of the wall top; 2) bending deformation, shearing deformation, rebar sliding deformation, and the total horizontal displacement of the wall above the plastic hinge region; 3) rigid displacement of the grade beam; 4) stress of the longitudinal steel bars in the plastic hinge region of the wall, stirrup stress, and stress of horizontally and vertically distributed reinforcement bars; 5) load-displacement hysteresis loop of the specimen under repeated cyclic loading.Fig. 3 shows the arrangement of displacement metres.

HCRCW-01
When the horizontal thrust reached 250 kN, the apex displacement of HCRCW-01 was 1.56 mm, and multiple tiny cracks occurred in the tensile region.At 550 kN, the apex displacement was Owing to large axial pressure, when HCRCW-01 was damaged, fracture and buckling occurred in the longitudinal bars, and severe buckling occurred in the vertical steel bars.Under a large vertical load, concrete in the plastic hinge region of the wall bottom was crushed in the entire cross section.
Slight buckling occurred on the horizontally distributed reinforcement bars in the wall.However, the confining stirrups and horizontally distributed steel were not broken.

HCRCW-02 to HCRCW-04
Compared with HCRCW-01, HCRCW-02 to HCRCW-04 had low axial pressure, and the failure pattern at each stage was similar; however, failure properties differed.Cracking appeared at an early stage in the specimens.When the wall yielded, load and displacement were small.After yielding, load cycling was conducted in multiples of y  .When the peak load was attained, crumbling occurred at a late stage on the protective layer in the compression region of the wall.
When the specimens were damaged, no reinforcement bar was broken, and cracks were more regularly distributed on the wall.The longitudinal steel bars were compressed to buckle in each specimen, and concrete was crushed with compressive flexure as the failure mode.
Compared with HCRCW-01, HCRCW-02 had a smaller spacing between the horizontaldistribution rebars in the wall, and dense, uniform cracks appeared in the wall.The plastic hinge region on the bottom was small, and the horizontally distributed reinforcement bars were intact during failure.
Compared with HCRCW-02, the distributed reinforcement ratio of the wall was smaller for HCRCW-03.When the specimen was damaged, the distributed reinforcement suffered significant buckling, and the bearing capacity rapidly decreased.
For HCRCW-04, high-strength spiral stirrups with dense spacing were employed in the confined boundary elements, and the volume-stirrup ratio was high.The high-strength spiral stirrup formed an effective constraint on the core concrete, and flexural deformation of the longitudinal steel bars was confined.When the specimen was damaged, slight buckling was observed on the longitudinal steel bars, but no fracture occurred.Fig. 4 shows the failure patterns and cracks of the four specimens.

HPCSW-03 and HPCSW-04
The confined boundary elements of HPCSW-03 and HPCSW-04 were ordinary stirrups and a wall of horizontally and vertically distributed reinforcements with a common form.Under cyclic loading, shear force was relatively large, and crack development was insufficient for failure.The distributed reinforcement yielded at an early stage, and the concrete in the wall bottom was crushed in the entire cross section.The failure pattern exhibited distinct fragility.

Hysteresis loop and skeleton curve
Figs. 5 and 6 show the load-displacement hysteresis loops and skeleton curves of the four specimens, respectively.The hysteresis loops of HCRCW-01 to HCRCW-04 appeared full without pinching, and the walls exhibited satisfactory deformation ability.At the peak load, the specimens exhibited a decrease in bearing capacity, decrease in stiffness, and continuous increase in the hysteresis area, revealing a suitable plastic-deformation capacity.
Before HCRCW-01 to HCRCW-04 yielded, their skeleton curves almost coincided, demonstrating their similar elasticity and stiffness.After yielding, all skeleton curves displayed a significant decline.The specimens reached their peak loads when the displacement angle was 1%.
HCRCW-01 had a larger axial-compression ratio than HCRCW-02.The cracking load and ultimate bearing capacity improved, but the ductility decreased.The load-carrying capacity rapidly deteriorated after the peak load.
The bearing capacities of HCRCW-02 and HCRCW-03 were similar, but the decrease in bearing capacity of HCRCW-02 decelerated after the peak load, indicating that reducing the horizontaldistribution spacing of the wall body decelerated strength deterioration.
Increasing the stirrup characteristic value of the confined boundary elements can effectively improve specimen ductility.Compared with HCRCW-03, the high-strength spiral-stirrup spacing of the confined boundary elements in HCRCW-04 was smaller and the volume-stirrup ratio was larger, resulting in a fuller hysteresis loop and superior deformation ability.After the peak load, the bearing capacity of HCRCW-03 rapidly decreased, whereas HCRCW-04 showed a slow decrease, indicating that the deterioration of bearing capacity is reduced with decreasing stirrup spacing.
HPCSW-03 and HPCSW-04 had a larger shear span ratio and reinforcement compared with HCRCW-01 to HCRCW-04.However, their hysteresis loops were narrow and spindly, pinching was apparent, and the cycling time was less.Furthermore, HCPSW-03 and HPCSW-04 exhibited an inferior bearing capacity and deformability.The 135° clasp at the stirrup tip was easily broken, invalidating the concrete confinement.After the peak load, the bearing capacity rapidly decreased.
The densely distributed high-strength spiral stirrup can form closed confinement, effectively constraining the concrete in the confining zone.

Deformability
The decline in bearing capacity to 85% of the peak load was considered failure, and the corresponding displacement was considered the ultimate displacement.The displacement ductility can be determined according to the ratio of ultimate displacement to yield displacement.Table 4 lists the load and displacement of characteristic points of each specimen, and Table 5 compares characteristic parameters.
The comparison of HCRCW-01 and HCRCW-02 revealed that the axial-compression ratio (especially a high axial-compression ratio) significantly influenced the deformation of the HSC shear wall.For well-confined shear walls, the bearing capacity can be improved, and the specimen exhibits reasonable ductility and energy dissipation for high axial-compression ratios.The ductility coefficient of HCRCW-01 was 3.53, indicating suitable deformation under a high vertical load.
Adopting a densely configured, high-strength spiral bar in the confined boundary element and horizontal reinforcement of the wall can result in superior constraints on the HSC shear wall to prevent brittle failure.The maximum ductility of HCRCW-02 and HCRCW-03 was approximately 4.0.The two specimens had similar bearing capacity and ductility, but the bearing capacity of HCRCW-02 slowly decreased after the peak load.
Compared with HCRCW-03, the ductility coefficient of HCRCW-04 was 45.6% higher, indicating that densely configured, high-strength spiral reinforcements in the confined boundary element can effectively confine the wall limb, improve the concrete compression strength, and significantly enhance the shear-wall deformability.Compared with HCRCW-01 to HCRCW-04, HPCSW-03 and HPCSW-04 had a smaller bearing capacity and displacement at each stage and ductility coefficients of 2.73 and 2.6, respectively, demonstrating that using the conventional reinforcement strength and form for high axial-compression ratios cannot satisfy the ductility requirement for shear walls.
The interlayer displacement angles  of HCRCW-01 to HCRCW-04 were 1/67-1/50, indicating an improvement in specimen deformability.The interlayer displacement angles  of HPCSW-03 and HPCSW-04 were 1/76 and 1/78, respectively.These specimens had large reinforcement ratios, span-to-depth ratios, and diameter but poor deformability, indicating that high spacing for the stirrup and common horizontal-distribution reinforcement resulted in inferior confinement.
The ductility coefficient of HCRCW-04 increased by a factor of 2.17 compared with HPCSW-03, demonstrating that confinement with rectangular spiral stirrups can improve the deformability compared to shear walls with a larger quantity of commonly employed stirrups.

Energy dissipation
Energy dissipation reflects the energy-absorbing capacity of the element in cyclic loading.The hysteretic energy dissipation is an important index for demonstrating the damage accumulation and evaluating the seismic performance of shear walls.The amount of energy dissipated in each cycle was determined as the sum of the area enclosed by the hysteresis hoop.The energy dissipation coefficient E is a critical index of seismic ability that is measured using the area enclosed by the load-displacement hysteresis loop.The total energy dissipation Esum and energy-dissipation coefficient E are usually employed to measure the energy-absorbing capacity, as shown in Fig. 7.In this paper, the energy-dissipation coefficient E and the equivalent viscous damping coefficient eq  to quantify the energy dissipation capacity of the structure.
E and eq  are defined as follows: The larger the area enclosed by the hysteresis loop, the greater is the energy dissipated by the specimen and the stronger is the energy-dissipation capability.Table 6 lists the energy-dissipation coefficient E and equivalent viscous damping coefficient eq  of specimens at the cracking, yielding, peak, and failure points.HPCSW-03 [2]   HPCSW-04 [2]   ------0.69 Note：E represents energy-dissipation coefficient; eq  represents equivalent viscous damping coefficient.
As evident from Table 6, when the axial compression ratio increased, the energy dissipation capacity of shear walls were significantly improved, and the equivalent viscous damping coefficient also increased within a certain range of axial pressure.Through comparisons of specimens HCRCW-01 and HCRCW-03-HCRCW-04, the energy dissipation capacity of the shear wall was effectively improved as a decrease in the spacing between stirrups and horizontal bars in the wall.Moreover, the equivalent viscous damping coefficient was also increased effectively.
The experimental results show that shear walls confined with HRSR had an excellent energydissipation capacity for a high axial-compression ratio.When using high-strength and smalldiameter spiral stirrups, the spacing between stirrups can be smaller with the equivalent reinforcement ratio.In a hence, the energy consumption capacity of shear walls can be effectively improved, especially in the post-peak period.
The energy-dissipation coefficients at failure point of HPCSW-03 and HPCSW-04 are listed in Table 6.The values of other feature points were not calculated in Ref. [2].However, on comparing E, the shear walls confined with HRSR exhibited a considerably higher energy-dissipation capacity compared to the specimens arranged with a larger quantity of commonly stirrups.

Compressive strain
Fig. 8 shows the arrangement of the strain gauge on the longitudinal steel bars and verticaldistribution reinforcement of a typical specimen.Fig. 9 shows the axial strain of the embedded columns and wall near the embedded-column zone based on strain gauges z1 and v1, where  denotes the wall-displacement angle.The compression strain of HCRCW-01 showed a rapid increase caused by the excessively large axial-compression ratio when the displacement angle reached 0.5%.As shown in Fig. 9(a), the compression strain of the embedded-column zone of HCRCW-04 slowly increased as the higher stirrup characteristic value of the embedded column and better constraint produced a stronger bearing capacity.Compared with HCRCW-02 and HCRCW-03, the wall compression strain slowly increased under a small spacing between the horizontal-distribution rebars.Compared with HCRCW-03, the compression strain of HCRCW-04 slowly increased owing to a higher volumestirrup ratio of the confined boundary element, exhibiting superior confining axial deformation of the concrete core.

Stiffness deterioration
Under cyclic loading, stiffness can be expressed by the secant stiffness i K , which is defined as follows: where i P is the peak load of the i th circulation and i  is the peak-point displacement of the i th circulation."+" means positive cycle and "-" means negative cycle.For the same axial-compression ratio, the larger the volume-stirrup ratio and the smaller the horizontal-distribution rebar spacing, the slower is the stiffness deterioration.Furthermore, the stiffness deterioration decreased with increasing axial-compression ratio.

Ultimate flexural capacity
Liang et al. [22] proposed a method for calculating the ultimate flexural capacity of RC shear walls; however, it is not applicable to HRSR shear walls.Thus, a method for HRSR shear walls is established here.
Fig. 11 displays a peak-load-point strain-distribution diagram of HRSR shear walls by combining the test results of the four specimens in this paper and Ref. [12].The strain of confined boundary elements in the compression region significantly increased; to simplify calculation, the cross-section strain was assumed to agree with the plane-section assumption.Fig. 12 shows the calculation model of peak bearing capacity of an HRSR concrete shear wall.
When the outside of the compression-zone section reached the peak compressive strain cc  of the confined concrete, the strain at the compression-zone edge in the non-confined area was c  (under the plane-section assumption), and the shear wall reached the maximum cross-section capacity.At this time, the corresponding ultimate flexural capacity was p M .The basic features of the peak state are as follows.First, the role of tensile concrete was not considered; the compression concrete stress in the non-confined area of the compression zone reached c f , and the confined concrete stress reached the peak stress cc f [8].Second, at the peak- load condition, the longitudinal stress of both the tension-and compression-confined boundary elements had reached the ultimate tensile strength su = ff (when employed in the design calculation, s y = ff ).Third, at the peak load capacity, the vertical-distribution reinforcements in the compression zone had not yielded and were ignored.Only the vertical-distribution reinforcements in the tension compression zone were considered.
The yield strength of vertical-distribution reinforcement was high ( yw 965MPa f = ).When the load reached the peak, the stress of vertical-distribution reinforcement near the boundary constraint elements can reach yw f .The average tensile strain was 4765 × 10 -6 .The mean tensile strain near the centroid axis was 1660 × 10 -6 .According to the actual strain and distribution, the stress distribution in the tensile zone of the vertical-distribution reinforcement is triangular.
As the concrete stress in the unconstrained area was curvilinear, an equivalent rectangular stress block was employed to replace the actual compressive stress curve, and the height of the equivalent rectangular stress block is 0.8 times the actual compression-zone height [22].
The concrete stress was assumed to reach cc f in the confined zone at the peak stage.HRSR was adopted in the embedded columns and wall; thus, the stress-strain relation [8] was adopted in the confined and unconfined concrete zones.
The peak curvature of the cross section is obtained from Fig. 12 as follows: where p x is the height of the compression zone at the peak state and w0 h is the effective height of the shear wall.

1) When p c
xl  , as shown in Fig. 12 (a), the forces can be expressed as follows: Taking the moment to the mandrel, the ultimate flexural capacity of the cross section is expressed as follows: 2) When p c xl  , as shown in Fig. 12 (b), the forces can be expressed as follows: sw yw w w w c 0.5 ( 2 ) Taking the moment to the mandrel, the ultimate flexural capacity of the cross section is expressed as follows: When the specimens reached the peak load, the stress of the longitudinal steel bars reached the ultimate tensile strength; i.e., su ff = , and the peak loads were in agreement, which was consistent with the test.When designing specimens, s y ff = should be adopted, which was specified a minimum 10% guarantee rate.According to Table 7, the average ratio between the calculated and experimental values is 1.021, the standard deviation is 0.047, and the coefficient of variation is 0.046.
HRSR concrete shear walls can provide the tensile strength of longitudinal steel bars and the compressive strength of concrete to achieve a high bearing capacity.

Conclusions
This study proposed a new type of RC shear walls confined with HRSR to improve the seismic performance.Compared with the reference specimens, the seismic capacity of walls confined with HRSR was significantly improved in terms of the ultimate confinement compression and maximum strain attained.HRSR confinement is efficient for ensuring superior deformation and dissipation capacity for high axial-compression ratios.Further, vertical reinforcement with an extremely small diameter caused reinforcement buckling under a high vertical load, and excessive strength prevented yielding.Therefore, larger-diameter, lower-strength reinforcement bars are recommended.Moreover, high-strength, dense, and closed spiral reinforcement in shear walls is proven to be more beneficial for confinement effectiveness compared with other designs.This approach is not only time-saving and cost-effective but also energy-saving and emission-reducing.Finally, a calculation method for the ultimate flexural capacity of HRSR shear walls is established based on the plane-section assumption, and the calculated values agree with the test values.
(a) Spirals in the shear wall (b) Wall dimensions and reinforcement arrangements Fig. 1.Structure and reinforcements of shear walls.
f are the test average values of the steel yield strength and tensile strength, respectively; s A is the reinforced elongation.Table 3. Mechanical properties of the concrete

approximately 5 .
6 mm.A significant deviation in the load-displacement curve was observed, and the longitudinal bars in the embedded column of the shear wall yielded, indicating that the component began to yield.The assumed yield displacement y  at this moment was represented by the corresponding displacement, and the loading became controlled by the displacement.In the third cycle, the original horizontal cracks substantially widened.A vertical crack appeared near the outermost longitudinal bars in the compression zone of the wall bottom.Diagonal cracks on the higher part of the wall extended to the loading beam.In the 2 y  cycles, buckling occurred in the concrete protective layer of the tensile region, large areas subsequently fell off, and vertical cracks near the outermost longitudinal bars widened.In the 3 y  cycles, concrete on both sides of the wall bottom fell off; the area without concrete continuously spread towards the wall centre and formed a penetrating zone.With increasing displacement, a longitudinal bar on the wall edge broke, and the wall body was covered with dense cracks.When the load was decreased to 452 kN, the specimen bearing capacity declined to 74% of the maximum load, and the specimen suffered flexural failure by compression.
Compressive strain of the column (b) Compressive strain of the wall Fig.9.Compressive strain of the column and wall at different displacements.

Fig. 10 shows
Fig.10shows the stiffness deterioration curves of the specimens.As shown in Fig.10(a), the plastic deformation continuously increased and specimen stiffness gradually deteriorated with the action of cyclic horizontal load and increase in load and displacement amplitudes.Fig.10(b)shows the displacement-relative stiffness curve.The relative stiffness was defined as the ratio of measured stiffness to the initial stiffness of each specimen.The trends of all specimens were similar.From initial loading to specimen cracking, the stiffness rapidly deteriorated to 50% of the initial stiffness.From specimen cracking to yielding, the stiffness deteriorated less rapidly.Most of the cracks in the specimens occurred at this stage.After the specimens yielded, the stiffness slowly deteriorated with a few new cracks, which corresponded to the specimen-stiffness deterioration curves.

Fig. 11 .
Fig. 11.Strain-distribution diagram of the cross section at the peak point.

Fig. 12 .
Fig. 12. Stress and strain distribution of a section at the peak state.

Table 4 .
Characteristic loads and displacement of specimens

Table 5 .
Comparison of characteristic parameters

Table 6 .
Energy-dissipation coefficient and equivalent viscous damping coefficient at characteristic points

Table 7 .
Comparison of calculated and experimental values of peak loads Vtest and Vcal represent the test peak load and calculation peak load, respectively.