Seismic Performance of Recycled-Aggregate-Concrete-Based Shear Walls with Concealed Bracing

Abstract

Relatively few studies have been conducted on the seismic performance of recycled aggregate concrete (RAC) shear walls with concealed bracing. To promote the development of high-performance green building structures and the application of RAC in structural components, the seismic performance of RAC shear walls under different influencing factors was tested, and low-cycle reversed loading tests were performed on ten RAC shear walls with different shear-to-span ratios. The test parameters included the recycled coarse aggregate (RCA) replacement ratio, the recycled fine aggregate (RFA) replacement ratio, the axial compression ratio, the shear span ratio and whether to set up the concealed bracing. The influence of the above variables on the seismic performance was then assessed. The results revealed that the bearing capacity, ductility, stiffness and energy dissipation capacity of the RAC shear walls decreased in line with an increase in the replacement ratio of the RFA. However, the bearing capacity, energy consumption and stiffness of the RAC shear walls decreased within 10% and the ductility decreased within 15%. The RAC shear walls were able to meet the seismic requirements of the building structure after reasonable design and use. As the axial compression ratio increased, the bearing capacity of the RAC shear walls improved, but their elastic–plastic deformation capacity was reduced. Setting the concealed bracing significantly improved the seismic performance of the RAC shear walls, such that they achieved a seismic performance close to that of the natural aggregate concrete (NAC) shear wall. After setting up the concealed bracing, the load carrying capacity of the RAC shear walls increased by up to 15%, the ductility increased by up to 20% and the energy consumption capacity increased by up to 50%. A mechanical calculation model of the RAC shear wall was then established by considering the effect of recycled aggregate, the calculated results of which were a good match with the test results.

1. Introduction

With the developing trend toward industrial construction, reinforced concrete structures have become the main forms of building structure. However, the sand and gravel required for concrete have been extracted in large quantities, causing destruction to the ecological system, while the demolition of existing buildings produces a substantial amount of building debris, giving rise to the issue of waste disposal. The reuse of waste concrete can effectively alleviate these problems, while research on this issue has become popular in the academic and engineering fields. Recycled aggregate concrete (RAC) is a type of concrete containing aggregate made by crushing and sieving waste concrete after building demolition to produce coarse aggregates and fine aggregates, thereby replacing the coarse aggregates and fine aggregates in natural aggregate concrete (NAC) according to different percentages [1]. The research into and application of RAC have occurred in tandem with the green transformation and low-carbon development of the construction industry, which have recently been advocated and are also conducive to promoting the resourcefulness and efficient use of building debris. Recently, applications of RAC components and structures have been increasing, strongly promoting the research into and development of RAC structures.

Numerous scholars have studied various aspects of RAC and RAC components, including macro performance [2,3,4,5], different study variables [6,7,8,9], and theoretical analyses based on the mechanical properties of RAC components [10,11,12,13,14,15,16]. These have yielded important results, including findings relating to RAC shear walls. Studies have, for example, revealed that the main difference between natural aggregate and recycled aggregate is that the former has loose and porous old mortar attached to its surface; hence, RAC has more complex interfacial weaknesses than NAC under the same conditions. In addition, the elastic modulus and strength of RAC under the same ratio are generally lower than those of NAC, while these factors account for the difference in performance between RAC components and NAC components [17,18,19]. For instance, Fathifazl [20], Sato [21], and Mahdi [22] reported that the bending and shear capacity of RAC beams decreases significantly as the replacement ratio of RCA increases, and that the capacity decreases by up to 45%. Lorena [23] tested the bending performance of RAC slabs with different replacement rates of RCA and found that when the replacement ratio of RCA increases, the damage process of RAC slabs is essentially the same as that of NAC slabs, but the cracking load and ultimate load are reduced, whereas the ultimate load decreases more obviously. Ajdukiewicz [24] found that the cracks in RAC columns appear earlier than those in NAC columns but exhibit no obvious signs. Furthermore, the bearing capacity of the column is reduced and the deformation increases significantly. Chen [25] reported that the seismic behavior of shear walls with all RCAs decreases compared with that of NAC shear walls, but the elastic–plastic deformation capacity remains strong. Jiang [26] studied three kinds of RAC insulated concrete shear wall specimens with shear span ratios of 2.2, 1.62 and 1.2, the results of which revealed that the stiffness and bearing capacity of shear walls increases as the shear span ratio decreases. The high shear wall exhibited the best ductility and energy dissipation capacity, while there was a small difference between the ductility levels of the medium-high and low walls, although the low shear wall was more prone to brittle damage, which should be avoided as much as possible in a project. Furthermore, recycled aggregates have a relatively high degree of randomness and variability in their properties due to their different sources, leading to differences in the properties of RAC compared to NAC, which has been confirmed by numerous studies [27,28,29,30]. Consequently, RAC has often been initially used in non-structural components.

However, the difference in performance between RAC and NAC members can be solved by reasonable optimization means, such as controlling the replacement rate of RCAs and RFAs, using additives or by adding certain constructional measures. Etxeberria [31] found that the shear performance of RAC beams is hardly affected when the replacement rate of RCA is controlled within 25%. Zhang [32] reported that mixing silica powder and some fibers improves not only the bending performance of RAC beams, but also their cracking resistance and ultimate load. Noridah [33] and Cao [34] reported that the setting of reinforced trusses in RAC slabs can inhibit crack development and improve the ultimate load, late stiffness and ductility. Zhang [35] investigated the performance of RAC columns in axial compression and found that appropriately encrypting the hoop reinforcement can improve the ductility and load carrying capacity of RAC columns significantly. Finally, Chen [36] demonstrated that the ultimate value of the axial compression ratio needs to be set reasonably in order to apply an RAC shear wall in a project.

To summarize, because the efficient utilization of building debris has become a major demand for sustainable development, and with increasing research related to RAC, promoting the application of RAC shear walls in building structures has better feasibility and engineering value. When concealed bracing is provided in a shear wall, enhanced seismic performance can be ensured, with only a very small increase in the amount of steel used. Studies have revealed that the stiffness of shear walls with concealed bracing decays slowly, that performance is stable in the later stage and that the bearing capacity, ductility and energy-consuming capacity are significantly higher than those of normal shear walls. The application of concealed bracing to RAC shear walls can effectively compensate for the deteriorating properties of RAC but, to date, only relatively few studies have been investigated on the seismic performance of RAC shear walls with concealed bracing [37,38,39].

To study the seismic performance of RAC shear walls with concealed bracing, ten RAC shear wall specimens were tested in low-cycle reversed loading. The test parameters of the specimens included the replacement rate of the RCA and RFA, axial compression ratio, shear span ratio and whether to set up the concealed bracing. The influence of the study variables on the seismic performance of the specimens was discussed by studying the hysteresis curves and performance indexes of the specimens. Following this, a mechanical calculation model of an RAC shear wall was then established by considering the effect of the RAC, based on which the bearing capacity of the RAC concrete shear walls was calculated.

2. Experimental Investigation

2.1. Test Specimens

Ten RAC shear walls with different shear span ratios were manufactured in accordance with the standards of GB 50010-2010 [40], while the specimens were numbered RCSW1 to RCSW10. RCSW1 was a concrete shear wall with only natural aggregates, while RCSW2 to RCSW10 were concrete shear walls in which RCAs were used for all coarse aggregates. RCSW2 to RCSW4 were three specimens using different RFA replacement ratios, which were used to compare the effects of different replacement ratios of RFA on the seismic performance of RAC shear walls. RCSW5 and RCSW2 had the same reinforcement and recycled aggregate replacement ratio, but their axial compression ratios were different. RCSW6 had the same reinforcement and recycled aggregate replacement ratio as RCSW2 but, unlike RCSW2, it had a concealed bracing. RCSW7, RCSW9 and RCSW2 had the same reinforcement and recycled aggregate replacement ratios, but the shear span ratios of the three specimens differed. RCSW8 and RCSW10 were set with concealed bracing on the basis of RCSW7 and RCSW9, respectively. The thickness of specimens was 160 mm, the width was 1000 mm, and the heights varied because the shear span ratio of each specimen differed. The specific design parameters of all specimens are detailed in

Table 1. Number and design parameters of each specimen.

Specimen	Replacement Rate of RCA (%)	Replacement Rate of RFA (%)	Reinforcement Ratio of Distribution Bars (%)	Aspect Ratio	Axial Compression Ratio	Transverse Reinforcement	Longitudinal Reinforcement Arrangement for Concealed Bracing
RCSW1	0	0	0.3	1.5	0.2	D6@140
RCSW2	100	0	0.3	1.5	0.2	D6@140
RCSW3	100	50	0.3	1.5	0.2	D6@140
RCSW4	100	100	0.3	1.5	0.2	D6@140
RCSW5	100	100	0.3	1.5	0.4	D6@140
RCSW6	100	100	0.3	1.5	0.2	D6@140	4D8
RCSW7	100	100	0.3	1.0	0.2	D6@140
RCSW8	100	100	0.3	1.0	0.2	D6@140	4D8
RCSW9	100	100	0.3	2.0	0.2	D4@60
RCSW10	100	100	0.3	2.0	0.2	D4@60	4D8 4D10

, and the dimensions and steel bar arrangement of specimens are depicted in Figure 1.

2.2. Materials

2.2.1. Concrete

Photographs of natural aggregates and recycled aggregates used in the test are depicted in Figure 2. The recycled aggregates were obtained from a concrete structure in Beijing. After building demolition, aggregates were sieved into RCA and RFA. Aggregates with particle sizes of 5–25 mm were used as RCA, while particle sizes of 0.16–5 mm were used as RFA. In accordance with the standards of GB/T 14684-2011 [41], GB/T 14685-2011 [42], GB/T 25176-2010 [43] and GB/T 25177-2010 [44], the basic physical properties of NCA, NFA, RCA and RFA are listed in

Table 2. Basic physical properties of aggregates used in the test.

Aggregate	Size (mm)	Bulk Density (kg/m3)	Apparent Density (kg/m3)	Crushing Index (%)	Water Absorption (%)	Dust Content (%)
NCA	5–25	1580.21	2760.23	9.70	0.23	0.40
NFA	0.16–5	1560.37	2670.02	7.32	0.46	1.50
RCA	5–25	1252.80	2575.49	13.10	4.70	2.25
RFA	0.16–5	1307.46	2455.02	17.00	11.32	3.50

. The particle size distribution test results for recycled aggregates are presented in Figure 3.

The cement used in the test was ordinary Portland cement (P.O.42.5), and mineral powder and fly ash were used instead of cement as cementitious materials to improve its fluidity and durability. The quality indexes of the ordinary Portland cement, mineral powder and fly ash were in line with standards GB 175-2007 [45], GB/T 18046-2008 [46] and GB/T 1596-2005 [47], respectively.

2.2.2. Steel

The mechanical properties of the steel bars of the specimen are shown in

Table 3. Mechanical properties of reinforcements.

Diameter D (mm)	Yield Strength fy (MPa)	Ultimate Strength fu (MPa)	Young’s Modulus Es (×105 MPa)
4	683.5	804.1	2.01
6	535.8	654.5	2.06
8	338.2	492.9	1.99
10	427.8	527.1	2.03

. The experimental results were in line with standards GB/T 28900-2012 [48].

2.3. Mix Proportion

The mix proportions of NAC and RAC are detailed in

Table 4. Concrete mix proportion.

ρc (%)	ρf (%)	NCA (kg/m3)	RCA (kg/m3)	NFA (kg/m3)	RFA (kg/m3)	Cement (kg/m3)	Mineral Powder (kg/m3)	Fly Ash (kg/m3)	Water (kg/m3)	fcu (MPa)	Ec (×105 MPa)
0	0	910	0	910	0	227	75	75	195	34.8	3.13
100	0	0	820	1000	0	227	75	75	195	32.3	3.07
100	50	0	820	500	500	227	75	75	195	32.7	2.56
100	100	0	730	0	1090	227	75	75	195	32.0	2.35

. All the mix proportions were in accordance with JGJ 55-2011 [49]. The replacement ratios for RCA were 0% and 100%, respectively, and the replacement ratios for RFA were 0%, 50% and 100%, respectively. Cubic specimens with dimensions of 150 mm × 150 mm × 150 mm were casted in the same batch with shear walls, and then tested in accordance with GB50010-2010 to obtain the concrete strength and the Young’s modulus of the concrete. In the table, ρ_c denotes the replacement ratio of RCA, ρ_f represents the replacement ratio of RFA, and f_cu and E_c denote the cubic compressive strength and the Young’s modulus, respectively.

2.4. Test Setup

The test was conducted using the loading method of low circumferential repeated loads. Firstly, a vertical load was applied to the specimen and kept constant during the test, following which a horizontal low circumferential repetitive load was applied at the loading height. The test was conducted in two stages: the elastic stage, which adopted the method of loading and displacement-joint-control loading, and the elastic–plastic stage, which employed the method of displacement-control loading. The arrangement of the loading device and instrumentation for the test is depicted in Figure 4.

3. Experimental Results

3.1. Damage Mode

The ultimate damage mode and crack patterns at failure of the specimens are presented in Figure 5 and Figure 6.

From Figure 5 and Figure 6, the following can be seen:

(1) Bending-based failure occurred in all the specimens, except for specimen RCSW7 (Figure 5g), which experienced shear-based failure, and RCSW8 (Figure 5h), which experienced bending-shear-based failure. The results revealed that as the shear-to-span ratio increased, the form of damage to each shear wall gradually changed from shear-based failure to bending-based failure.

(2) Increasing the replacement rate of the recycled aggregate aggravated the shear wall damage. For comparison, in specimens RCSW1 to RCSW4 (Figure 5a–d), the RAC shear walls cracked earlier and at the same angle of displacement, but were damaged more than the NAC shear walls. This is because the recycled aggregate contained a large number of microcracks and pores, and the crushing index was larger than that of the natural aggregate, compression damage occurred more easily in the compression zone of the specimen, and, ultimately, the formation of a crushing and spalling zone, with a loss of load-bearing capacity.

(3) The comparison of two specimens with different axial compression ratios, RCSW2 and RCSW5 (Figure 5b,e), showed that the specimen’s initial stiffness increased and the load capacity significantly improved at larger axial compression ratios. However, the shear wall was seriously damaged in the later stage by the second-order effect of the bending moment, with large-scale concrete crushing in the compression zone of the wall, outward bulging of the concrete on the side, obvious flexure of the reinforcement and a crack width of close to 20 mm at the root of the wall. This reveals that at larger axial compression ratios, the later damage to the shear wall was more serious, demonstrating proneness to localized damage and instability, as well as deterioration of the ductility.

(4) From Figure 5e–g, it can be seen that the crack distribution of the specimen with concealed bracing was relatively uniform; the main crack, which appeared later, developed more slowly and tended to approach the concealed bracing. For specimen RCSW8 (Figure 5h) with concealed bracing in particular, the concealed bracing improved the shear capacity of the specimen and thus avoided shear damage. This reveals that the installation of the concealed bracing significantly restrained the progression of diagonal cracks in the wall and enhanced its deformation capacity, giving full play to the energy-consuming capacity of the shear wall.

3.2. Hysteresis Behavior

The hysteretic curves and skeleton curves of the ten specimens are shown in Figure 7 and Figure 8.

The hysteretic behavior of shear walls under different influencing factors can be summarized as follows:

(1) The shape of the hysteresis curve was basically the same; the hysteresis curve as a whole was relatively full, while the wall exhibited better energy dissipation capacity.

(2) In Figure 7a–d, specimens RCSW2 to RCSW4 display a more obvious pinching phenomenon in the hysteresis curve than specimen RCSW1; their energy dissipation capacity was reduced and the replacement ratio of the recycled aggregate had less influence on the energy dissipation capacity of the shear walls.

(3) According to Figure 7e and Figure 8b, at a higher axial compression ratio, the initial stiffness of specimen RCSW5 increased, the load carrying capacity obviously increased and the energy dissipation capacity improved. However, due to the second-order effect of the bending moment, the stiffness of the specimen degraded more quickly and the pinching phenomenon of the hysteresis loop was serious. The shear-to-span ratio affected the force state and damage pattern of the specimen, whereas for the specimen with a larger shear-to-span ratio, the horizontal peak load decreased, but its ductility was better (from Figure 8c).

(4) As shown in Figure 7b,f–g and Figure 8c, the hysteresis loop of the specimen with concealed bracing was relatively full, and the stiffness degradation of the specimen was well suppressed, while the load carrying capacity, ductility and energy-consuming capacity improved significantly.

3.3. Load-Bearing Capacity

The cracking load F_cr, yield load F_y and ultimate load F_u for each specimen are presented in

Table 5. Characteristic loads of specimens.

Specimen	Fcr(kN)	n	Fy(kN)	n	Fu(kN)	n
RCSW-1	94.51	1.00	203.33	1.00	237.80	1.00
RCSW-2	92.97	0.98	202.60	0.99	233.27	0.98
RCSW-3	92.43	0.98	197.78	0.97	232.27	0.97
RCSW-4	91.03	0.96	193.57	0.95	221.95	0.93
RCSW-5	142.59	1.51	302.36	1.49	336.84	1.42
RCSW-6	91.03	0.96	230.18	1.13	245.24	1.03
RCSW-7	132.50	1.00	300.46	1.00	326.99	1.00
RCSW-8	136.54	1.03	334.95	1.11	372.47	1.14
RCSW-9	68.23	1.00	147.51	1.00	176.18	1.00
RCSW-10	78.23	1.15	166.38	1.13	193.45	1.10

, where the yield point of the specimen is determined using the energy equivalence method. In the table, n denotes the ratio of specimen load to comparative specimen load.

In the table, the following can be seen:

(1) Compared with the NAC shear wall, the bearing capacity of the RAC shear walls at the same axial compression ratio was slightly lower, with decreases ranging from 2% to 7%. This shows that an RAC shear wall can achieve basically the same bearing capacity as an NAC shear wall with similar concrete strength.

(2) Compared with specimens RCSW2 to RCSW4, the cracking load, yield load and ultimate load slightly increased as the RFA replacement rates decreased. This indicates that the bearing capacity of the RAC shear wall decreased as the RFA admixture increased, but the overall effect was small (within 5%).

(3) Compared with specimen RCSW2, the cracking load, yield load and ultimate load of specimen RCSW5 increased by 56.6%, 56.2% and 51.8%, respectively. This demonstrates that under the constraint of a large axial compression ratio, the specimen’s stiffness increased and the horizontal bearing capacity improved, but the peak post-attenuation decay of the specimen’s capacity was faster and its ductility became worse.

(4) With an increase in the shear-to-span ratio, the damage form of the shear wall gradually changed from bending-shear damage to bending damage, the peak load of the specimens obviously reduced, while the bearing capacities of the specimens with respective shear span ratios of 1.5 and 2.0 were only 67.9% and 53.9% that of the specimen with a shear-to-span ratio of 1.0.

(5) The comparison of specimens RCSW6 and RCSW2 reveals that the installation of concealed bracing can improve the load-bearing capacity of RAC shear walls effectively. Under three different shear-to-span ratios, from low to high, the bearing capacity of the specimens set up with concealed bracing increased by 10.5%, 13.9% and 9.8%, respectively, compared with that of the specimens without concealed bracing.

3.4. Ductility

The corresponding displacements U_cr, U_y and U_u for the specimens under each characteristic load are presented in

Table 6. Characteristic displacements of specimens.

Specimen	Ucr/mm	Uy/mm	Uu/mm	θd	μ
RCSW-1	0.84	6.09	42.74	1/35	7.02
RCSW-2	1.05	6.07	41.02	1/37	6.76
RCSW-3	1.06	6.46	41.82	1/36	6.47
RCSW-4	1.08	6.63	41.89	1/36	6.32
RCSW-5	0.83	5.13	31.11	1/48	6.06
RCSW-6	0.88	6.30	47.03	1/32	7.47
RCSW-7	0.64	4.21	27.28	1/37	6.48
RCSW-8	0.58	3.97	31.00	1/32	7.81
RCSW-9	1.05	5.50	40.50	1/49	7.36
RCSW-10	1.01	6.25	54.90	1/36	8.79

. In the table, U_cr denotes the horizontal displacement at the time of cracking; U_y represents the horizontal displacement at the yield and U_u is the ultimate displacement, all of which are averaged in the positive and negative directions; and μ denotes the displacement ductility coefficient, μ = U_u/U_y. The ductility coefficient of each specimen is shown in Figure 9.

In Table 6 and Figure 9, the following can be seen:

(1) The displacement ductility coefficient of each specimen was greater than 6, and the ultimate displacement angle was 1/49~1/32—much larger than the limit value of 1/120 of the elastic–plastic interlayer displacement angle of shear wall structures under rare earthquakes required by the standard GB 50010-2011 [50].

(2) Compared with specimens RCSW1 to RCSW4, the ductility coefficient of the RAC shear wall was smaller than that of the NAC shear wall specimens, with the difference being within 10% (from Figure 9b). The ductility of the RAC shear wall exhibited a certain decrease compared with that of the NAC shear wall; nevertheless, it can meet the requirements of structural design. The ductility of the RAC shear wall decreased as the RFA mixing increased. Compared with the three specimens, RCSW2 to RCSW4, the µ decreased sequentially as the RFA replacement rate increased.

(3) As shown in Figure 9c, the ductility coefficient of specimen RCSW5, with a higher axial compression ratio, decreased by 10.4% compared with specimen RCSW2, which had a lower axial compression ratio, indicating that the elastic ductility of the RAC shear wall decreased as the axial compression ratio increased.

(4) The shear span ratio of the RAC shear wall exerted an effect on the ductility in that the larger the shear-to-span ratio, the better the ductility. The maximum difference between the ductility coefficient of the specimen with a shear-to-span ratio of 2.0 and the specimen with a shear-to-span ratio of 1.0 was 13.6%.

(5) In Figure 9d, the ductility coefficient of RCSW6 was significantly increased compared with that of RCSW2, indicating that the setting of concealed bracing can effectively improve the ductility of shear walls. Specifically, the ductility coefficient of specimens with concealed bracing increased by 20.5%, 10.5%, and 19.4% compared with those without concealed bracing for three kinds of axial-span ratio, ranging from low to high, respectively.

3.5. Stiffness and Degradation

The initial stiffness K₀, cracking stiffness K_cr and yielding stiffness K_y of the specimens are shown in

Table 7. Measured stiffness of specimens.

Specimen	K0/(kN/mm)	Kcr/(kN/mm)	Ky/(kN/mm)	βc0	βyc	βy0
RCSW1	300.0	112.5	33.4	0.375	0.297	0.111
RCSW2	296.6	88.5	33.4	0.298	0.377	0.113
RCSW3	295.4	87.2	30.6	0.295	0.351	0.104
RCSW4	292.1	84.3	28.9	0.289	0.343	0.099
RCSW5	292.1	171.8	58.9	0.588	0.343	0.202
RCSW6	292.1	82.0	32.2	0.281	0.393	0.110
RCSW7	773.3	207.0	71.4	0.268	0.345	0.092
RCSW8	789.9	233.8	84.5	0.296	0.361	0.107
RCSW9	136.0	65.0	26.8	0.478	0.412	0.197
RCSW10	136.5	77.5	26.6	0.568	0.343	0.195

, while the stiffness degradation curves of each specimen from cracking to damage are depicted in Figure 10. β_c0 denotes the ratio of the cracking stiffness to the initial stiffness, reflecting the stiffness decay of the specimen from the elastic stage to the concrete cracking process. β_yc represents the ratio of the yield stiffness to the cracking stiffness, reflecting the stiffness decay of the specimen from concrete cracking to the yielding process. β_y0 denotes the ratio of the yield stiffness to the initial stiffness, reflecting the stiffness decay of the specimen from the elastic stage to the yielding process.

In Table 7 and Figure 10, the following can be seen:

(1) The stiffness degradation pattern was similar in that it was faster at the beginning of the loading and then became slower in line with the increase in displacement and the constant development of plastic deformation. The stiffness degradation of each specimen was relatively uniform, without any obvious sudden change in stiffness.

(2) As shown in Figure 10a, the stiffness degradation rates of specimens with different RFA replacement ratios were close, and the effect of the RFA replacement ratio on the regularity of the stiffness degradation of the RAC shear walls was not obvious.

(3) The initial stiffness of specimen RCSW5 was close to that of RCSW2, but the cracking stiffness and yield stiffness increased by 94.1% and 76.3%, respectively. This indicates that the late stiffness of the shear wall significantly improved under the constraints of a larger axial compression ratio.

(4) The shear-to-span ratio had a considerable influence on the initial stiffness; the specimens with a small shear-to-span ratio had large initial stiffness, and the stiffness degradation also slowed to a certain extent.

(5) At three different shear-to-span ratios, the stiffness degradation rate of the specimens with concealed bracing was somewhat slower than that of the specimens without concealed bracing (from Figure 10c).

3.6. Energy Consumption Capacity

The area of the hysteresis loop surrounded by the “horizontal load-displacement curve” of each level of cyclic loading is defined as the energy consumption of the specimen. The cumulative energy consumption of the specimen was obtained by adding the cyclic energy dissipation of each level to obtain the cumulative energy consumption of the specimen E_p, which was used as a measure of the energy consumption capacity of the specimen. The total cumulative energy consumption E_p of each specimen is presented in

Table 8. Cumulative energy consumption.

Specimen	Ep/(kN/mm)	n
RCSW1	15,998	1.000
RCSW2	15,020	0.939
RCSW3	14,636	0.915
RCSW4	14,454	0.904
RCSW5	15,520	0.970
RCSW6	17,412	1.088
RCSW7	16,821	1.000
RCSW8	19,207	1.142
RCSW9	12,570	1.000
RCSW10	18,717	1.489

, where the relative energy consumption n denotes the ratio of the cumulative energy consumption of each specimen to that of the comparison specimen with the same shear-to-span ratio.

In the table, the following can be seen:

(1) The energy consumption capacity of the RAC shear wall was slightly worse than that of the NAC shear wall, RCSW1. The three specimens, RCSW2 to RCSW4, displayed a decreasing trend in energy consumption capacity as the RFA replacement rate increased in comparison with specimen RCSW1, decreasing by 6.1%, 8.5% and 9.7%, respectively.

(2) The cumulative energy consumption of specimen RCSW5, with a higher axial compression ratio, was higher than that of specimen RCSW2, with a lower axial compression ratio. This is because a specimen with a higher axial compression ratio has a larger bearing capacity, which correspondingly increases the energy consumption capacity.

(3) The energy dissipation capacity of the RAC shear walls decreased when the shear-to-span ratio was reduced as a whole.

(4) At three different shear-span ratios, ranging from low to high, the energy consumption capacity of the specimens with concealed bracing increased by 20.5%, 14.2% and 48.9%, respectively, when compared with those without concealed bracing. This indicates that the concealed bracing significantly increased the energy consumption capacity of the RAC shear walls.

4. Calculation of Bearing Capacity

To simplify the calculation, the following hypotheses were made:

(1) When the section limit state is reached, the section still satisfies the flat section assumption.

(2) The tensile action of concrete in the tension zone is not considered.

(3) The tensile reinforcement in the tensile zone of the specimen is only considered within the range of h_w–1.5x.

4.1. Calculation of Bearing Capacity of Shear Walls in the Positive Section

4.1.1. Shear Walls without Concealed Bracing

For a shear wall without concealed bracing, the bearing capacity can be calculated on the basis of the mechanical model in Figure 11a.

According to the results of this study, the incorporation of the recycled aggregate caused a small reduction in the bearing capacity of the RAC shear walls. Therefore, to correct this effect, a recycled aggregate correction factor ${\alpha }_{\mathrm{RAC}}$ was introduced by combining the results of this test and referring to the test results for other RAC shear walls. The formula for ${\alpha }_{\mathrm{RAC}}$ was determined as follows:

$${\alpha }_{\mathrm{RAC}}={\alpha }_{\mathrm{RCA}}·{\alpha }_{\mathrm{RFA}}$$

(1)

$${\alpha }_{\mathrm{RCA}}=\left\{\begin{array}{l}1.0({\rho }_{\mathrm{RCA}}<30\%)\hfill \\ 1.0-0.14{\rho }_{\mathrm{RCA}}(30\%<{\rho }_{\mathrm{RCA}}\le 100\%)\hfill \end{array}\right.$$

(2)

$${\alpha }_{\mathrm{RFA}}=1.0-0.19{\rho }_{\mathrm{RFA}}$$

(3)

where ${\alpha }_{\mathrm{RCA}}$ and ${\alpha }_{\mathrm{RFA}}$ denote the strength influence coefficients of RCA and RFA for the RAC shear wall, respectively; and ${\rho }_{\mathrm{RCA}}$ and ${\rho }_{\mathrm{RFA}}$ represent the replacement rates of RCA and RFA, respectively, and are values between 0 and 1. The 0% replacement ratio takes the value of 0, and the 100% replacement ratio takes the value of 1.0, with linear interpolation between the two.

The following equations were obtained from the balance conditions and were used to calculate the ultimate bending moment M_p:

$$N=N_{\mathrm{c},\mathrm{RAC}}+N_{\mathrm{s}}^{\prime }-N_{\mathrm{s}}-N_{\mathrm{sw}}$$

(4)

$$N_{\mathrm{c},\mathrm{RAC}}=\alpha f_{\mathrm{c}}{b}_{\mathrm{w}}\beta x{\alpha }_{\mathrm{RAC}}$$

(5)

$$N_{\mathrm{sw}}=f_{\mathrm{yw}}{\rho }_{\mathrm{sw}}{b}_{\mathrm{w}}\left(h_{\mathrm{w}}-h_{\mathrm{f}}-1.5x\right)$$

(6)

$$N_{\mathrm{s}}^{\prime }=E_{\mathrm{s}}\left[{\epsilon }_{\mathrm{c}}\left(x-a_{\mathrm{s}}^{\prime }\right)/x\right]A_{\mathrm{s}}^{\prime }\le f_{\mathrm{sy}}{A}_{\mathrm{s}}^{\prime }$$

(7)

$$N_{\mathrm{s}}=E_{\mathrm{s}}\left[{\epsilon }_{\mathrm{c}}\left(h_{\mathrm{w}}-x-a_{\mathrm{s}}\right)/x\right]A_{\mathrm{s}}\le f_{\mathrm{sy}}{A}_{\mathrm{s}}$$

(8)

$$M_{\mathrm{p}}=0.5N_{\mathrm{c},\mathrm{RAC}}\left(h_{\mathrm{w}}-\beta x\right)+N_{\mathrm{s}}^{\prime }\left(0.5h_{\mathrm{w}}-a_{\mathrm{s}}^{\prime }\right)+N_{\mathrm{s}}\left(0.5h_{\mathrm{w}}-a_{\mathrm{s}}\right)+N_{\mathrm{sw}}\left(0.75x-0.5h_f\right)$$

(9)

where N denotes the axial pressure of the test; $N_{\mathrm{c},\mathrm{RAC}}$ represents the pressure on the concrete in the compression area, taking into consideration the strength reduction of recycled aggregates; N_s′ denotes the pressure on the longitudinal reinforcement in the dark column at the edge of the compression area; N_s represents the tension on the longitudinal reinforcement in the dark column at the edge of the tensile zone; N_sw denotes the tension on the vertically distributed reinforcement of the wall web; x denotes the height of the concrete in the compression zone; f_c represents the axial compressive strength of the concrete; ρ_sw represents the reinforcing rate of the vertically distributed reinforcing bars in the wall web; f_sw and f_sy denote the yield strength of vertically distributed reinforcement in the wall web and the yield strength of longitudinal reinforcement in the dark column at the edge, respectively; b_w, h_w and h_f represent the cross-sectional width of the wall, the cross-sectional height and the height of the concealed columns at the edges, respectively; a_s and a_s′ denote the distance from the combined point of longitudinal tension and compression reinforcement to the edge of the wall, respectively; A_s and A_s′ represent the cross-sectional areas of tension and compression reinforcement in the edge dark columns, respectively; and A_xv and A’_xv represent the cross-sectional areas of tension dark support and tension dark support reinforcement, respectively.

4.1.2. Shear Walls with Concealed Bracing

For shear walls with concealed bracing, the bearing capacity can be calculated on the basis of the mechanical model in Figure 11b.

The following equations were obtained from the balance conditions and were used to calculate the ultimate bending moment M_p:

$$N=N_{\mathrm{c},\mathrm{RAC}}+N_{\mathrm{s}}^{\prime }-N_{\mathrm{s}}-N_{\mathrm{sw}}-N_{\mathrm{xv}}+N_{\mathrm{xv}}^{\prime }=E_{\mathrm{s}}\left[{\epsilon }_{\mathrm{c}}\left(x-a_{\mathrm{xv}}^{\prime }\right)/x\right]A_{\mathrm{xv}}\sin \phi$$

(10)

$$N_{\mathrm{xv}}=E_{\mathrm{s}}\left[{\epsilon }_{\mathrm{c}}\left(h_{\mathrm{w}}-x-a_{\mathrm{xv}}\right)/x\right]A_{\mathrm{xv}}\sin \phi$$

(11)

$$\begin{array}{l}{M}_{\mathrm{p}}=0.5N_{\mathrm{c},\mathrm{RAC}}\left(h_{\mathrm{w}}-\beta x\right)+N_{\mathrm{s}}^{\prime }\left(0.5h_{\mathrm{w}}-a_{\mathrm{s}}^{\prime }\right)+N_{\mathrm{s}}\left(0.5h_{\mathrm{w}}-a_{\mathrm{s}}\right)+N_{\mathrm{sw}}\left(0.75x-0.5h_f\right)\\ +N_{\mathrm{xv}}\left(0.5h_{\mathrm{w}}-a_{\mathrm{xv}}\right)+N_{\mathrm{xv}}^{\prime }\left(0.5h_{\mathrm{w}}-a_{\mathrm{xv}}^{\prime }\right)\end{array}$$

(12)

where $N_{\mathrm{c},\mathrm{RAC}}$ denotes the pressure on the concrete in the compression area, taking into consideration the strength reduction of the recycled aggregates; N_xv and N’_xv represent the vertical direction component forces of the tensile and compressive concealed bracing, respectively; φ denotes the angle between the concealed bracing and the horizontal direction; and a_xv and a’_xv represent the distances from the combined point of the tensile and compressive dark support reinforcement to the edge of the wall, respectively.

After obtaining M_p, the horizontal bearing capacity of each specimen was obtained according to Equation (13),

$$F={\displaystyle \frac{M_{\mathrm{p}}}{H}}$$

(13)

where H denotes the distance from the horizontal force loading point to the top of the wall foundation.

4.2. Calculation of the Bearing Capacity of an Inclined Section

The calculation model of the diagonal section bearing capacity of a shear wall is depicted in Figure 12. The shear bearing capacity of the shear wall in the inclined section consists of three parts: the shear force in the concrete shear compression area, taking into consideration the contribution of axial pressure; the value for the contribution of the horizontal distributed reinforcement intersecting with the inclined crack to the shear bearing capacity; and the value for the contribution of the concealed bracing intersecting with the inclined crack to the shear bearing capacity.

When eccentric compression occurs in a shear wall, the bearing capacity in the diagonal section can be calculated according to Equation (14).

$$V_{\mathrm{w}}=V_{\mathrm{c},\mathrm{RAC}}+V_{\mathrm{s}}+V_{\mathrm{s}\mathrm{b}}$$

(14)

Equation (15) calculates the contribution of the concrete shear zone to the shear bearing capacity, taking into consideration the axial pressure contribution V_c,RAC. The tensile strength of concrete in the formula takes into consideration the strength reduction of recycled aggregates.

$$V_{\mathrm{c},\mathrm{RAC}}={\displaystyle \frac{1}{\lambda -0.5}}\left(0.5f_{\mathrm{t}}{\alpha }_{\mathrm{RAC}}{b}_{\mathrm{w}}{h}_{\mathrm{w}0}+0.13N{\displaystyle \frac{A_{\mathrm{w}}}{A}}\right)$$

(15)

Equation (16) calculates the contribution of the horizontally distributed reinforcement intersecting the diagonal crack to the shear bearing capacity V_s.

$$V_{\mathrm{s}}=f_{\mathrm{y}\mathrm{h}}{\displaystyle \frac{A_{\mathrm{s}\mathrm{h}}}{s}}{h}_{\mathrm{w}0}$$

(16)

Equation (17) calculates the contribution of the concealed bracing intersecting the diagonal crack to the shear bearing capacity V_sb.

$$V_{\mathrm{s}\mathrm{b}}=f_{\mathrm{y}\mathrm{b}}{A}_{\mathrm{s}\mathrm{b}}\cos \alpha$$

(17)

Therefore, the bearing capacity of the shear wall in the inclined section is

$$V_{\mathrm{w}}={\displaystyle \frac{1}{\lambda -0.5}}\left(0.5f_{\mathrm{t}}{\alpha }_{\mathrm{RAC}}{b}_{\mathrm{w}}{h}_{\mathrm{w}0}+0.13N{\displaystyle \frac{A_{\mathrm{w}}}{A}}\right)+f_{\mathrm{y}\mathrm{h}}{\displaystyle \frac{A_{\mathrm{s}\mathrm{h}}}{s}}{h}_{\mathrm{w}0}+f_{\mathrm{y}\mathrm{b}}{A}_{\mathrm{s}\mathrm{b}}\cos \alpha$$

(18)

where b_w denotes the section width of the wall; h_w represents the section height of the wall; h_w0 denotes the effective height of the section of the wall; A and A_w represent the zone of the section and the zone of the web plate section, respectively; N denotes the axial pressure; f_yh represents the tensile yield strength of the limb horizontal distribution of the reinforcement; A_sh denotes the full cross-sectional area of the horizontally distributed reinforcement in the same horizontal section; s represents the spacing of the horizontal distribution of the reinforcement; and λ denotes the shear-to-span ratio—when λ < 1.5, λ = 1.5 and when λ > 2.2, λ = 2.2.

4.3. Comparison of the Calculated Bearing Capacity with Measured Values

The calculated results of the bearing capacity were taken as the smaller of the calculated values of the bearing capacity of the normal section and the inclined section. A comparison of the calculated results of the bearing capacity F_cal of each specimen with the measured values F_exp is presented in

Table 9. Calculated and measured values of bearing capacity.

Specimen	Fcal/kN	Fexp/kN	Fcal/Fexp
RCSW1	225.36	237.80	0.948
RCSW2	223.10	233.27	0.976
RCSW3	222.74	232.27	0.999
RCSW4	215.81	221.95	1.046
RCSW5	347.53	336.84	1.053
RCSW6	240.19	245.24	0.999
RCSW7	335.72	326.99	1.048
RCSW8	384.56	372.47	1.054
RCSW9	168.58	176.18	0.976
RCSW10	183.05	193.45	0.966

. From this table, it can be seen that the relative error between the calculated result F_cal and the measured result F_exp is 0.1% to 5.4%, and the predicted standard deviation is 3.84%. The calculated result and the measured value conform well.

5. Conclusions

In this study, the seismic performance of RAC shear walls was investigated under different replacement ratios of recycled aggregates, different axial compression ratios and different shear-to-span ratios, and with or without concealed bracing. Based on the results of the study, the following conclusions can be drawn:

(1) Compared with an NAC shear wall, the bearing capacity, ductility, stiffness and energy consumption capacity of an RAC shear wall were slightly lower. However, the bearing capacity, stiffness and energy consumption of the RAC shear walls with different shear span ratios decreased within 10% and the ductility decreased within 15%, which meets the requirements of structural design through reasonable design and use.

(2) With an increase in the axial compression ratio, the load carrying capacity of RAC shear walls increased dramatically and the increase in each characteristic load was greater than 50%. Concomitantly, the elastic–plastic deformation capacity of the shear wall decreased and the displacement ductility coefficient decreased by more than 10%. Based on this, it is recommended that RAC shear walls be used in multi-storey building structures or high-rise building superstructures, where the axial pressure is relatively small.

(3) After setting up the concealed bracing, the load carrying capacity, ductility and energy consumption capacity of the RAC shear walls improved significantly. Specifically, the load carrying capacity of the RAC shear walls with different shear-to-span ratios increased by approximately 10 to 15%, the ductility increased by about 10 to 20% and the energy consumption capacity increased by approximately 20 to 50%. These results demonstrate that the reasonable setting of concealed bracing can improve the seismic performance of RAC shear walls significantly, to a level comparable with that of NAC shear walls.

(4) By adopting the correction coefficient of recycled aggregate ${\alpha }_{\mathrm{RAC}}$, a calculation model of the RAC shear wall-bearing capacity was established that conformed well with the measured results, while the overall error was within 5.5%. The model can therefore be used to calculate the bearing capacity of RAC shear walls.