Cyclic Performance and Strain Characteristics of a Curved RC Shear Wall

doi:10.21203/rs.3.rs-4940347/v1

Download PDF

Research Article

Cyclic Performance and Strain Characteristics of a Curved RC Shear Wall

https://doi.org/10.21203/rs.3.rs-4940347/v1

This work is licensed under a CC BY 4.0 License

Version 1

posted

You are reading this latest preprint version

Curved reinforced concrete shear walls (CRCSWs) not only are capable of offering both the stiffness and strength in any arbitrary horizontal direction, but can also fulfill some of the aesthetic and architectural requirements. Despite these advantages, a paucity of decent and in-depth investigation does exist in the literature that have examined the cyclic response of CRCSWs. Aiming to complement the existing knowledge and to highlight some particularities inherent in the cyclic performance of CRCSWs, an experimental program is established and a new loading apparatus is designed and fabricated capable of concurrently following the in-plane and out-of-plane motions. A large number of instrumentation is employed to capture the full-field measurements. Test results including the global load-deformation, onset and progression of structural damages are delineated. The findings divulge that the tested CRCSW exhibited stable performance with no evident premature strength degradation and the induced warping torsion due to intrinsic eccentricity of the centroid and shear center is largely responsible for the failure mode of the CRCSW. Detailed reconnaissance studies regarding the performance levels, and strain characteristics of the reinforcing bars and concrete surface are presented and the collected strain gauge data confirms the mechanisms of the induced damages. The inevitable effects of the longitudinal bars are highlighted in comparison with transverse bars for the response evaluation of the tested squat CRCSW. Although, the CRCSWs are utilized in practical applications, experimental evidences are scanty and it is believed that the testing program presented herein will contribute into the seismic characterization of the CRCSWs.

Curved RC Shear Wall

Experimental Program

Cyclic Loading

Strain Profile

Performance Level

Failure Mode

Curved elements can extensively be employed in different engineering applications due to the aesthetic, architectural, and structural reasons (Abdoos et al., 2020; Abdoos et al., 2024; Foyouzat et al., 2022; Khaloo et al., 2023). Reinforced concrete shear walls (RCSWs) are effective structural elements in the earthquake-prone regions owing to their benefits including simple construction method and good seismic performance (Habibi et al., 2021; Hoult & Beyer, 2020; B. Li & Xiang, 2011; Xu et al., 2023; Zhang et al., 2019). In general, RCSWs can be categorized into two groups with: (1) rectangular or barbell-shaped cross-sections, and (2) non-rectangular sections. Of the most conventional non-rectangular sections are T-, H-, L-, U-, Y-, Z-, and C-shaped (channel-shaped) walls composed of rectangular segments aligned along two or more different directions. In addition, the structural characteristics of non-rectangular RCSWs, i.e., stiffness, strength, and ductility are essentially different depending on the loading direction (Behrouzi et al., 2020; Choi et al., 2004; Hoult et al., 2015; Wang et al., 2023).

In view of design practice, for the rectangular RCSWs, the lateral stiffness in the shorter direction is often overlooked; nevertheless, in non-rectangular RCSWs, this effect can be notable due to the geometrical configuration of the section. Furthermore, in non-rectangular flanged RCSWs, the well-known shear-lag effects may be induced due to the cross-sectional properties, which can attenuate the capacity and ductility of the section (Tabiee et al., 2023). The shear-lag influence is also aggravated for squat RCSWs, particularly, by reduction of the wall length (Abdoos et al., 2023, 2024; Hassan & El-Tawil, 2003; Pantazopoulou & Moehle, 1990). However, in the curved sections with constant thickness, especially curved RCSWs, negative impacts of the shear-lag are not basically evident.

In addition to the structural merits of CRCSWs, current architectural trends tend toward employing complex shapes such as curved elements, which allows a more continuous load transfer (Alaghmandan et al., 2014; Carpinteri et al., 2016). Therefore, these advantages can potentially introduce RCSW with curved cross-sections as a well-deserved alternative instead of the conventional non-rectangular flanged RCSWs.

The technical literature contains a wealth of specialized information on the experiments carried out to assess the cyclic performance of RCSWs with rectangular and non-rectangular cross-sections. As one of the early contributions to the subject in hand, Benjamin and Williams (Benjamin & Williams, 1957) established an experimental program on shear walls reinforced by single layer of web reinforcement. Barda et al. (Barda et al., 1972) conducted the first cyclic test on non-rectangular flanged RCSWs. Gulec et al. (Gulec et al., 2009) reviewed and categorized the results of the experimental studies performed on 434 squat RCSWs with different cross-sections (150 rectangular walls, 191 walls with barbells, and 93 walls with flanges). For further details, one can refer to the robust dataset provided by Gulec et al. (Gulec et al., 2009).

Moreover, in order to provide a dataset regarding the experimental studies on squat RCSWs, Luna et al. (Luna et al., 2015) catalogued most of the tests carried out between 2010 to 2015. Grammatikou et al. (Grammatikou et al., 2015) utilized a database of 866 reversed cyclic tests on RCSWs to propose predictive formulations for the shear strength and deformation capacity of the walls. A comprehensive database of RCSWs, known as UCLA-RC Walls (Abdullah & Wallace, 2018), was established, in which detailed information of over 200 test programs and more than 1000 walls had been addressed. A significant number of investigations have also been dedicated to experimentally delineate the overall response of non-rectangular RCSWs, of which a brief survey is presented herein. To emphasize the specific characteristics pertaining to the geometrical properties of the wall cross-section, the following materials are grouped for T-, U-, L-, H-, and C-shaped walls.

It is worthy of mention that, the cross-sectional layout of non-rectangular flanged RCSWs can essentially affect the overall performance of the walls, particularly in terms of the twisting demand as well as the torsional stiffness (Collins & Lampert, 1973; El-Hashimy et al., 2019, 2020; Hoult et al., 2015; Hoult & Beyer, 2020; Tabiee et al., 2023). Further details dealing with the structural damages due to the torsional effects have been addressed in quite a few studies (Gokdemir et al., 2013; Hart et al., 1975; Hoult, 2021). With this in view, attention should be accorded to non-rectangular RCSWs with an offset between the shear center and centroid of the section.

Oesterle et al. (Oesterle et al., 1976, 1979) explored the load-deformation characteristics of flanged and barbell-shaped RCSWs through testing under monotonic as well as reversed cyclic loading. A T-shaped RCSW at 1/3 scale was cyclically tested by Goodsir (Goodsir, 1985) and the failure mode of the specimen was due to the eccentric loading and high ductility demand of the wall. Two T-shaped walls with different design procedures and confinement reinforcements of the web toe were tested by Thomson and Wallace (Thomsen & Wallace, 1995). The failure mechanisms of the walls, TW1 and TW2, were respectively buckling of all the longitudinal reinforcements in the web toe at a drift of 1.25%, and the out-of-plane buckling of the web toe after concrete spalling at a drift ratio of 2.5%.

Choi et al. (Choi et al., 2004) investigated the effect of confining length (15% and 10% of the wall length) of T-shaped walls to evaluate their drift and displacement ductility capacity through the experiments and moment-curvature analyses. Brueggen et al. (Brueggen et al., 2017) tested two half-scale walls under reversed cyclic loading to investigate different parameters such as the shear-lag effects on the effective width of T-shaped walls beyond the original requirements of the design codes.

Ile and Reynouard (Ile & Reynouard, 2005) presented the results of experimental tests conducted on U-shaped walls under lateral uniaxial and bi-axial loadings. The findings of this research led to a number of supplementary recommendations for analysis and design of U-shaped RCSWs. Beyer et al. (Beyer et al., 2008) presented the results of quasi-static cyclic tests on two half-scale U-shaped walls. The main aim of the test was to assess the performance of U-shaped RCSWs subjected to different loading directions and the results indicated that the diagonal direction is the most critical one for which the displacement capacity is smallest. Constantin and Beyer (Constantin & Beyer, 2016) reported the findings of tests performed on two U-shaped walls due to the cyclic loading applied along the diagonal direction to outline some particularities in the characteristics of U-shaped walls.

Nakachi et al. (Nakachi et al., 1996) conducted a lateral loading test on four one-eighth scale L-shaped RCSWs. The axial load ratio and confinement details including the amount of confining reinforcements, confinement of concrete at the corner of the section, and area of the confined concrete were the test parameters to delineate the deformation capacity of core RC walls after flexural yielding. In another study, Hosaka et al. (Hosaka et al., 2008) tested four 1/6 scale L-shaped RCSWs under lateral and axial loadings to enhance the deformation capacity of L-shaped walls. Three RC L-shaped core-walls with 1/4.5 scale were constructed and statically tested by Inada et al. (Inada et al., 2008) to evaluate the seismic performance of L-shaped sections through examining the influence of loading direction and configuration of the cross-section.

Kono et al. (Kono et al., 2011) established an experimental program to address the influence of the axial loading on the seismic behavior of L-shaped RC core walls. The experiment findings indicated that the plane-section assumption did not hold true after the onset of concrete crushing. Li and Li (Li & Li, 2012) tested six 1/2 scale L-shaped walls subjected to quasi-static uni-directional loading parallel to one flange to examine the effects of wall length to thickness and axial load ratio on the seismic response of the walls.

Hasnalbant and Eyyubov (Hasnalbant & Eyyubov, 2016) tested four 1/2 scale L-shaped walls due to the constant axial loading and reversed lateral cyclic loading to investigate the effects of cross-sectional dimensions on the seismic performance of the walls. Wang et al. (Wang et al., 2022b) reported the experimental observations of a test campaign on three T-shaped and two L-shaped walls subjected to the bi-axial loading.

Two large-scale H-shaped RCSWs were tested by Kitada et al. (Kitada et al., 1997), which indicated that presence of large flanges can complicate the peak shear strength evaluation of H-shaped walls. Maruta et al. (Maruta et al., 2000) established an experimental program to examine the simultaneous effects of lateral and torsional loadings on the behavior of nine 1/12 scale specimens of H-shaped RCSWs. By variation of the loading direction as well as the ratio of torsional to bending moment at the lowest portion of the walls, they concluded that the loading direction does play a pivotal role in the overall behavior of H-shaped walls. Ma and Li (Ma & Li, 2018) tested four H-shaped squat RCSWs under concurrent gravity as well as lateral cyclic loading to evaluate the cracking pattern, failure mechanism, non-principal bending action, hysteretic response, deformation components, strain profiles, and shear strength of H-shaped walls.

As for C-shaped RCSWs, Sittipunt and Wood (Sittipunt & Wood, 1993) tested two walls with 1/4 scale due to the cyclic loading applied along the symmetric axis of the sections. Afterwards, effective stiffness of the walls was evaluated at different levels of displacement. In another experimental program, Behrouzi et al. (Behrouzi et al., 2018, 2020) tested three large-scale C-shaped walls subjected to quasi-static lateral loading to assess the impact of bi-directional loading and axial load ratio. Flexural failure of the specimens occurred due to the buckling of the boundary element longitudinal rebars followed by fracture. Further details dealing with the experimental findings of C-shaped RCSWs have been reported by Lowes et al. (Lowes et al., 2013).

As one of the main contribution of the subject in hand, Abdoos and Khaloo (Abdoos & Khaloo, 2024) conducted an state-of-the-art experimental testing program on a 1/3 scale curved RC shear wall subjected to the quasi-static lateral cyclic loading, in which the potential structural performance of CRCSWs was scrutinized. From the background introduction, one can conclude that, although the seismic performance evaluation of non-rectangular flanged RC shear walls is a well-researched topic, examining the cyclic behavior of CRCSWs is original and represents a new development. Moreover, this study builds on the recent aesthetic and architectural trend of curvilinear RCSWs, which found their applications in design practice. Therefore, aiming to complement the dearth of knowledge on the structural behavior of curved RCSWs, an experimental testing program is developed, of which the main objectives are summarized below:

An experimental testing platform is developed to evaluate the cyclic response of a CRCSW under the action of quasi-static lateral cyclic loading in the absence of axial loading,
Extensive monitoring systems and instrumentations are utilized to enable measurements of the specified target locations,
A reconnaissance investigation is made on the damage evolution mechanisms and load-displacement response of the CRCSW,
A methodology is put forward, on the strength of obtained experimental data, to establish performance levels and corresponding drift thresholds of the tested CRCSW.
Variations of the concrete surface strain profile in accordance with the localized and full-field measurements are developed and discussed in detail,
Stress and strain development originated from the strain gauges readings are captured to indicate how the longitudinal and transverse reinforcements do contribute during the loading excursions,
Finally, within the framework of the testing program, some previously unknown features and peculiarities in terms of the structural responses are delineated to provide insight regarding the application of CRCSWs in practice being currently unclear for structural design engineers.

As there is relatively no specific guideline for the structural analysis and design of CRCSWs, the findings of this study can be recognized for future validation of FE numerical simulations. Moreover, numerical models can essentially be implemented in a parametric investigation in order to elaborate an applicable analytical guidance for the response evaluation of CRCSWs.

As previously mentioned, the main focus of this research lies in examining the cyclic behavior of CRCSW in detail through establishing an state-of-the-art testing program. Thus, a one-third scale specimen was designed and fabricated and then tested subjected to the reversed lateral cyclic loading in the absence of axial loading. It should be noted that, the no axial load condition considered herein represents low-rise RCSWs in practice; although, the effects of axial loading on the performance of such squat RCSWs have been well understood in the previous researches (Hidalgo et al., 2002; Li et al., 2015; Luna et al., 2013; Moehle, 2015).

In addition, applying and maintaining even low axial loadings on the wall cross-section with an area of circa 10⁵ mm², particularly at high drift values, is extremely complicated (Luna et al., 2013). Furthermore, the absence of axial loading can further signify how the warping torsion affects the overall behavior and failure mechanisms of CRCSWs, which has not decently been addressed in the literature. Moreover, performing the quasi-static cyclic testing has been recognized in quite a few studies (El-Azizy et al., 2023; Hoult & Beyer, 2020; Wang et al., 2022a; Xu et al., 2023) and design guidelines (ACI 318, 2019; ASCE, 2017) for the seismic response identification of RCSWs.

In what follows, details dealing with the test specimen, mechanism of the loading-system apparatus, instrumentations and monitoring systems are provided. All the casting process and experiment of the specimen were conducted at the strong floor laboratory at Sharif University of Technology (SUT), Iran. Figure 1 demonstrates the main components of the testing program.

2.1 Description of the test unit

The geometrical and mechanical characteristics of the CRCSW were chosen based on the preliminary finite element (FE) simulations and limitations of the strong floor laboratory. An appropriate scaling factor was also selected and considered in each step of design process as well as detailing of the test specimen (Noor & Boswell, 1992). Figure 2 portrays the schematic outlook of a CRCSW possessing constant thickness and radius of curvature.

The CRCSW under consideration is a cantilever type with a stiff block foundation, and a heavily reinforced loading head at the top, as a rigid diaphragm. Presented in Fig. 3(a) to (f) are the geometrical dimensions as well as the reinforcement details of the test unit. The exact location of the loading head is so that the eccentricity of the induced torsional loading is in correspondence with the shear center offset from the centroid of the wall section (see Fig. 3(c) and (d)).

The block foundation was clamped down the specimen to the laboratory strong floor by means of special steel connectors and anchorage bars. The special connectors are then fixed to the strong floor to fully restrict the translational and rotational degrees of freedom. In order to ascertain that the cyclic loading is evenly applied to wall cross-section, five continuity plates have been embedded into the loading head along with double orthogonal mesh of 20mm @130mm provided at the top and bottom of loading head. The main geometrical properties of the wall panel are listed in Table 1.

Table 1

Key geometrical properties of the CRCSW (Abdoos, 2024)
Parameter	Value	Unit	Description
h_w	1200	mm	Height of the wall panel
t_w	100	mm	Thickness of the wall panel
R	1000	mm	Central radius of the cross-section
R_i	950	mm	Inner radius of cross-section
R_o	1050	mm	Outer radius of cross-section
2θ	60	degree	Central subtended angle of the wall cross-section
l_w	1000	mm	Length of the wall (l_w=2Rsinθ)
A	104720	mm²	Cross-sectional area of the wall
y_c	956	mm	Shear center of the section (see Fig. 2), $R\frac{{\sin \theta }}{\theta }\left( {1+\frac{{t_{w}^{2}}}{{12{R^2}}}} \right)$,
y_s	1028	mm	Centroid of the section (see Fig. 2), $2R\frac{{\sin \theta - \theta \cos \theta }}{{\theta - \sin \theta \cos \theta }}$,
e	72	mm	Offset of the shear center and centroid, i.e., \|y_s - y_c\|

In addition, the arrangement and key details of the steel reinforcements of the wall panel are shown in Fig. 3(d) to (h). As the wall tips are prone to additional axial deformations introduced due to the twisting and warping torsion, supplementary vertical bars have been provided at the outermost layers of longitudinal reinforcements to preclude any possible premature flexural/torsional failure of the specimen (Abdoos & Khaloo, 2024). Thus, a total of 20 reinforcing bars of 8 mm diameter are sufficiently anchored into the block foundation and loading head and are symmetrically located in the cross-section at a center to center angular distance of 8̊ from each other (see Fig. 3(f)) resulting in a longitudinal reinforcement ratio of ρ_l = 1.00%.

The confinement effect is also provided by means of two-piece stirrups of 8 mm diameter (D8) spaced at 150 mm along the height of section, resulting in a transverse reinforcement ratio of ρ_t = 0.67%. The stirrups were terminated with 135-degree hooks and extended 300 mm into the foundation at spacing of 75 mm. The D8 crossties with seismic hooks are also supplied at the level of transverse rebars to offer additional support for the vertical rebars.

As the lateral cyclic loading is imposed at the mid-height of loading head, the shear span ratio (SSR) is 1.30 and the CRCSW can be cataloged as an squat RC shear wall (ACI 318, 2019). Although the current design codes propose no specific recommendation for the analysis and design of CRCSWs, assigning the mentioned values for the longitudinal and transverse reinforcement ratios, i.e., ρ_l = 1.00%>ρ_t = 0.67%, meets the available requirement recommended by ACI 318 − 19 for conventional RCSWs. Moreover, all the frameworks employed in the construction process were designed and fabricated based on the special geometrical configurations of the test setup. A CNC cutting machine was also utilized to accurately specify the exact location of the curved cross-section for the loading head framework.

2.2 Material Properties

The CRCSW was constructed utilizing a self-compacting concrete (SCC) grade C45 for all the subassemblies of the test specimen, i.e., the foundation, wall panel, and loading head. The maximum size of the coarse and fine aggregates were respectively 9.50 mm and 4.75 mm. The workability of the SCC was attained employing filler material (passing sieve No. 200) and poly-carboxylate-based superplasticizer. For the wall panel, the average concrete compressive strength at the test day,${f^{\prime}_c}$, ranged between 44.1 MPa and 48.7 MPa, with standard deviation of 2.05 MPa and C.O.V of 4.43%. In addition, according to the performed tensile tests on five cylindrical specimens, the initial tensile cracking points were between 132 to 151 microstrain, µε, with an average of circa 145 µε, which will be considered in the succeeding sections regarding the concrete surface strain profiles (Carmona & Aguado, 2012).

Moreover, based on the conducted UTM tests (ASTM Standard A370-20. Standard Test Methods and Definitions for Mechanical Testing of Steel Products, 2020) and according to ASTM A675 (ASTM Standard-A675. Standard Specification for Steel Bars, Carbon, Hot-Wrought, Special Quality, Mechanical Properties, 2019), the mechanical properties of the steel rebars (longitudinal and transverse reinforcements as well as crossties) are specified and summarized in Table 2.

Table 2

The actual mechanical properties of 8 mm diameter steel reinforcements
Bar Designation	E_s (GPa)	f_y (MPa)	f_u (MPa)	f_u / f_y	ε_su (%)
D8	204.76	472	594	1.26	17.1
	203.69	468	592	1.26	18.9
	206.18	490	615	1.25	17.7
Average	204.88	477	600	1.26	17.9
C.O.V. (%)	0.61	2.46	2.12	0.40	5.12

2.3 Testing methodology

Due to the shear center position of a curved section, i.e., generally being outside of the cross-section, as well as any irregularities of the building plan layout (Hoult et al., 2020; Hoult & Beyer, 2021), CRCSWs can potentially twist under the applied earthquake ground motions. In order to monitor the possible out-of-plane movement of the CRCSWs due to the offset of the application line of lateral loading from cross-sectional shear center of the test specimen, a new loading system apparatus is designed and constructed to simultaneously accommodate both the in-plane as well as the out-of-plane displacement of the wall. The newly designed loading system also allows capturing the twisting/torsional behavior, which is of great interest in the response investigation of non-rectangular RCSWs, especially with curved cross-section (Abdoos & Khaloo, 2024).

The load-carrying capacity of the servo-hydraulic actuator is 280 kN with a deformation capacity of 250 mm. As shown in Fig. 4(g), two swivels are provided to offer the concurrent in-plane and out-of-plane motions linked through a special connector (SPK 2379) supported by an incompressible steel reinforced elastomeric bearing (SREB) (Maghsoudi-Barmi et al., 2021). The in-plane movement is possible employing the block carriage, labeled H35C-HIWIN, which can traverse along the linear guideway with negligible friction due to the special rolling circulation system of the block carriage. The seating of the loading system includes an H-shaped section consists of three UNP200 segments along with a manual chain block for the purpose of offering supplementary support and leveling of the actuator. Further details regarding the components and construction sequence of the loading system are provided in a recently published paper by the authors (Abdoos & Khaloo, 2024).

2.4 Testing instrumentation and monitoring systems

To the best knowledge of the authors, the current study is known as one of the first attempts to offer an insight into the cyclic response of CRCSWs. Therefore, in order to assess the seismic performance of such salient structural members, due care was given to accomplish elaborate device measurements. Furthermore, as a detailed arrangement of the instrumentations can facilitate post-test investigations on the validation and model-development process of structural elements; hence, the CRCSW specimen is heavily instrumented with the following measuring devices.

2.4.1 Strain gauges

In order to measure the contribution of reinforcing bars, strain gauges were affixed at 32 target locations, which respectively include 14 and 18 commercial strain gauges (FLA-6-11 model manufactured by Tokyo Sokki Kenkyujo (TML)) for the longitudinal and transverse reinforcements. The layout of strain gauges is shown in Fig. 3(e) to (h), in which, in all cases, the strain gauges are mounted in the centroid of the bar cross-section. Strain gauges affixed to the vertical rebars are also placed on five alignments, including L1, L7, L8, L10, and L10 (see Fig. 3(f)), at three different elevations denoted by Base (B), Middle (M), and Top (T). The strain gauges of the longitudinal rebars are labeled as: LR (Longitudinal Reinforcement) – Alignment No..

The transverse reinforcements of the CRCSW are made of two piece-wise stirrups, i.e., Inner stirrup (I) and Outer stirrup (O), elevated at the Base (B), Middle (M), and Top (T) of the wall, and each one is instrumented with symmetrically located strain gauges labeled as Left (L), Center (C), and Right (R) regarding the localized coordinated system defined in the succeeding section (see Fig. 14). The designation of the transverse reinforcement strain gauges is introduced below:

Moreover, the technical specifications of the strain gauges are as follows: 6 mm gauge length, 2.2 mm gauge width, 2.11 gauge factor, 5% strain limit, and 120 Ω resistance. It is worthy of mention that, in order to provide adequate protection for the strain gauges, SB Tape and VM Tape, as pressure-sensitive adhesive, were utilized. Adopting these butyl rubber tapes, as a coating, offered excellent resistance to moisture and water, and in turn, no malfunction of the strain gauges was observed within the data acquisition process.

In order to make possible measuring of strain distributions at the front and rear views of the wall panel, concrete surface strain gauges are employed including a set of 10 strain gauge Rosette PLR 60 − 11, consisted of three strain-sensing elements arranged at 0̊, 45̊, and 90̊, along with two pairs of PL 60 − 11 adhered at the specified locations of the wall mid-height (see Fig. 3(i-1) and (i-2)). The gauge length, gauge width, gauge factor, and strain limit of the concrete surface strain gauges are respectively 60 mm, 1 mm, 2.10, and 2%. This type of strain gauges has been designed with a resistance of 120 Ω for measuring at low or high operational temperatures ranging from − 20 ̊C to 80 ̊C. All the strain gauges have also been adhered with TML CN adhesive. In the following, the designation of the concrete surface strain gauges are defined:

in which, the strain gauges ID was previously introduced in Fig. 3(i-1) and (i-2). It is worth mentioning that, all the target locations have been nominated through conducting preliminary FE analyses of the wall under the pre-defined cyclic loading. A grid pattern of approximately 100 mm by 100 mm was drawn to make facilitate the strain gauge installation and post-processing analyses. According to the extensive number of strain gauges (66 strain gauges), two data acquisition systems were employed with sampling rates of 100 and 1000 data per second for the reinforcing bar and concrete surface strain gauges, respectively. The calibration process of the instrumentation was also executed five times in order to make ascertain that the obtained data are reliable and accurate.

2.4.2 High-resolution cameras

As full-field non-contact measurement system, seven high-resolution cameras were adopted to fully capture details of the monitoring targets, prorogation of the cracking, possible slippage at the wall-foundation interface, in-plane and out-of-plane displacements, twisting and distortion behavior, along with the localized failures of the specimen.

The schematic view of the camera locations is portrayed in Fig. 6; in which, two cameras regarding the top and long-shot views are not shown. Four cameras are also installed to capture the front, rear, east side, and top views of the specimen. Additional camera, i.e., Camera 6, is installed in the east view to further scrutinize the upper mid-height twisting of the CRCSW. From a long shot view, the loading system apparatus is captured, and Camera 2 and Camera 3 have been devoted to monitoring localized damages of the specimen.

In addition to the above-described instrumentations, vast images were captured to document details including the out-of-plane buckling and rupture of the vertical reinforcements at the wall tips, concrete cover spalling, sliding of the wall-foundation interface, and sequence of damage evolution.

2.5 Loading procedure

Figure 7 depicts complete description of the loading history for testing of the CRCSW (X. Li et al., 2020; S.-Y. M. Ma et al., 1976), which includes a pseudo-static, fully reversed, lateral cyclic loading possessing two cycles at each displacement level.

This loading protocol is controlled by displacements to indirectly simulate the influence of earthquake shaking and one mm augmentation was assigned for the lateral displacements to thoroughly apprehend all the details regarding the damage sequences. The loading pattern is imposed within the pre-defined eight phases introduced in Table 3; in which, the drift values are expressed as the normalized ratios of the displacements at mid-height of the loading head divided by the distance to the base of the wall panel. For the purpose of convenience, the maximum drift at each phase is described as the phase representative. Moreover, the lateral cyclic loading is applied at a constant rate of 5 mm/min (Hube et al., 2020).

Table 3

Loading phases
Phase No.	1	2	3	4	5	6	7	8
Target displacement (mm)	0–5	5–8	8–11	11–14	14–17	17–20	20–23	23–26
Drift (%)	0–0.38	0.38–0.62	0.62–0.85	0.85–1.08	1.08–1.31	1.31–1.54	1.54–1.77	1.77-2.00
Phase representative	0.38	0.62	0.85	1.08	1.31	1.54	1.77	2.00

3.1 Experimental observations

The CRCSW experienced several response stages up to the failure. Table 4 summarizes the highlighted details and key observations obtained during the testing process.

Table 4

Key details extracted from the cyclic testing of the CRCSW
Stage No.	Observation		Drift (%) / Excursion	Load (kN)	Description / Explanation
1	Onset of the first horizontal crack		0.23 / first	46.10	West tip of the wall following the lines of transverse reinforcements
2	The first diagonal X-shaped cracking		0.31 / second	58.60	Front and rear facades of the wall panel
3	The first sign of longitudinal rebar yielding		0.54 / first	74.85	Bottom of the vertical rebar located at L15
4	Onset of concrete cover spalling		1.15 / first	139.94	West side of the wall tip at the base level
5	Onset of sliding		1.23 / first	140.95	Wall-foundation interface
6	Maximum bearing capacity	positive	1.38 / first	141.48	-
6	Maximum bearing capacity	negative	1.00 / first	146.95	-
7	Severe concrete cover spalling		1.54 / second	138.02	West side of the wall tip at the base level
8	Concrete cover crushing and exposure of longitudinal rebar		1.77 / second	110.66	Wall tips at the base level and exposure of the longitudinal rebar located at L1, L2, L15, and L16
9	Longitudinal rebar buckling		1.85 / first	104.55	Buckling of longitudinal rebar placed at L1, L2, L15, and L16
10	Failure of the specimen due to the rupture of the longitudinal rebar		2.00 / second	57.05	Rupture of the longitudinal rebar located at the base level of L1 and L2

The onset of cracking was observed at the initial stage of loading, i.e., at the first excursion of 3 mm displacement, drift ratio of 0.23%. As displayed in Fig. 8(a) to (d), the mentioned cracks, marked in red, are evenly spaced, horizontally aligned, and follow the transverse reinforcements’ lines (≈ 150 mm$\pm$10 mm). Within the initial stages of loading, in which the specimen behaves elastically, the material discontinuity and localized inhomogeneity at the horizontal reinforcement level led to cracking. These superficial cracks, which do not penetrate to the confined part of concrete provided by transverse reinforcements, are generally induced due to the flexural/twisting combination (Aaleti et al., 2013; Arabzadeh & Galal, 2018; Chen et al., 2016).

Drift ratio of 0.31% was also suffice to make appear the first diagonal (inclined) cracking pattern. The diagonally aligned cracks formed during the later loading excursions essentially remain parallel to the main X-shaped cracking and there was no remarkable evidence of cracks rotating. By further increasing the drift amplitude, the diamond-shaped cracking pattern was developed which follows an approximately symmetrical distribution on the wall panel. Moreover, the first yielding of steel reinforcements was detected at the base level of the outermost longitudinal layer, located at L15, at a drift ratio of 0.54%. In addition, no evident sign of yielding was captured for the piece-wise stirrups.

At drift ratio of 1.23%, a visible evidence of sliding was observed at the wall-foundation interface owing to the yielding of a majority of the longitudinal reinforcing bars, and within the upcoming steps of loading, the sliding was essentially resisted through the dowel action of the longitudinal reinforcements that have not been fractured. By increasing the drift values after the onset of sliding drift, the base slippage as well as the rotation of the specimen becomes more pronounced. In low-rise RCSWs with SSR between 1.0 and 1.5, the sliding shear deformation mechanism does play a substantial role in the overall performance of the walls (Salonikios, 2002, 2007; Wei et al., 2022).

The maximum shear strength of the wall, i.e., V_n≈145 kN, has been attained at an approximately drift ratio of 1.00% and 1.38% for the negative and positive loading directions, respectively. The mentioned shear strength capacity of the CRCSW was also well predicted applying the analytical framework established by the authors (Abdoos et al., 2024). With further load cycling, as the crushed area of the wall tips at the base level enlarged, the stiffness and strength of the CRCSW slightly diminished and it is obvious that the wall tips are evidently susceptible to the out-of-plane buckling following concrete cover spalling. After the exposure of vertical rebars placed at L1, L2, L15, and L16, at drift ratio of 1.77%, the first sign of buckling was captured at drift ratio of 1.85%. Finally, at the second excursion of drift 2.00%, the CRCSW failed due to the longitudinal rebars fracture after previous buckling in the boundary region at L1 and L2.

With this in view, even though there are no restrictions, based on the design guidelines (ACI 318, 2019), on the wall’s slenderness ratio and thickness for CRCSWs, the effect of boundary elements on the overall response of CRCSWs is inevitable and the need is essential to be considered in the analysis and design of these types of structural walls. Hence, as the wall tips are vulnerable to the buckling/rupture of the outermost longitudinal reinforcing bars following the concrete cover spalling, appropriate strategy should be implemented in the boundary regions of the wall within the rehabilitation process of the specimen. Figure 9 displays localized failures of the CRCSW at the final stage of loading. For further details on the failure mechanism of the tested CRCSW, one can consult the recently published paper of the authors (Abdoos & Khaloo, 2024).

In order to better interpret the cyclic performance of the tested CRCSW, Fig. 10(a) to (h) demonstrates the hysteresis sequence of the wall within the loading phases. As shown in the curves provided in Fig. 10, the hysteresis response follows an approximately symmetrical trend in the positive and negative excursions of loading.

Presented in Fig. 11(a) is the full hysteresis response of the CRCSW, measured in terms of lateral loading versus drift ratio. This figure manifests the approximately symmetric and spindle-shaped hysteresis loops possessing large energy dissipation characteristic. A pinching effect was also exhibited due to the shear cracking, inelastic shear deformation, and slippage of the wall-foundation interface evidenced by strength deterioration and stiffness reduction of RCSWs (Lee et al., 2012; Paulay & Priestley, 1992; Siddique et al., 2023). This observation has previously been addressed for low-aspect-ratio RCSWs (Abdoos & Khaloo, 2024; Luna et al., 2013). The sudden drop in bearing capacity of the wall is coincide with the buckling followed by rupture of the longitudinal reinforcing bars at the outermost layers of the CRCSW.

In an attempt to obtain additional information regarding the trend and estimation of strength capacity of the tested wall, bearing capacity degradation coefficient is introduced capable of assessing the stability of the structure under constant amplitude cyclic loading (Mu & Yang, 2020):

$${\lambda _i}=\frac{{{F_{i+1}}}}{{{F_i}}}$$

wherein F_i+1 and F_i represent the average maximum bearing capacity corresponding to the (i + 1)^th and i^th cycles, respectively. As evident in Fig. 11(b), except the final stage of loading, the bearing capacity degradation coefficient ranged between 0.95 to 1.05, for the positive and negative loading directions, signifying stable bearing capability of the tested CRCSW with no appreciable strength degradation.

Moreover, the stiffness of RCSWs can be altered under the action of seismic loading and it generally degrades owing to the material nonlinearity, concrete cracking, and yielding of the reinforcing bars (Li & Xiang, 2011; Zhang & Li, 2018). In view of seismic response evaluation, the stiffness degradation ratio, γ_i, is of paramount importance regarding the reliability and safety of the RCSWs, which can be calculated as follows (Ni et al., 2019):

$${\gamma _i}=\frac{{{K_i}}}{{{K_I}}}$$

in which K_i and K_I are respectively the stiffness at the i^th cycle and initial stiffness of the CRCSW. As shown in Fig. 11(c), the stiffness degradation ratio of the tested CRCSW is in an approximate linear descending manner, and in turn, the stiffness reduction is essentially smooth (Abdoos & Khaloo, 2024); nevertheless, for conventional squat flanged RCSWs, the stiffness reduction is basically more evident, especially at the initial stages of loading. The mentioned discrepancy should be further corroborated through conducting complementary experimental investigations.

3.2 Performance levels of the CRCSW

What we are going to do herein is to put forward performance levels (PLs) for the tested CRCSW. Based on the Chinese code JGJ 3-2010 (Code for seismic design of buildings, 2010), five performance levels (PLs) are introduced for the structural members, including: (1) No Damage, (2) Minor Damage, (3) Light Damage, (4) Moderate Damage, and (5) Limited Sever Damage (Han et al., 2019). For the purpose of better assessing the seismic performance as well as the post-earthquake rehabilitation of damaged RC structures, six PLs, labeled as PL1 through PL6, are proposed based on the approach established by Han et al. (Han et al., 2019). The First five PLs are in accordance with those defined in the Chinese code JGJ 3-2010, and the sixth threshold, i.e., PL6, corresponds to the severe damage, beyond which the RC structural member experiences the failure condition.

In what follows, at the first place, the PLs are introduced on the basis of the force-displacement backbone curve obtained from the hysteresis response of the tested CRCSW, in which the abscissa of the backbone curve is altered from displacement value to its corresponding drift ratio to express the thresholds of deformation capacity in a non-dimensional manner. It is worthy of mention that, as there is only one tested CRCSW, the established skeleton curve originates from the average absolute values of the backbone curves attained within the negative and positive loading directions.

Thereafter, the threshold of drift ratio pertaining to each PL is determined based on the framework presented by Han et al. (Han et al., 2019). The first deformation limit of PL1, denoted by D₁, as shown in Fig. 12, is defined as the drift ratio attained employing the following guideline: horizontal projection of the intersection point of two straight lines, (1) the line extended from the origin to pass the skeleton curve at 0.70P_max, and (2) the horizontal line, parallel to the abscissa, corresponding to the P_max. The fifth deformation limit, D₅, as depicted in Fig. 12, is the drift ratio in correspondence with 20 percent loss of the lateral load bearing capacity, i.e., 0.80P_max, in descending branch of the skeleton curve. The deformation thresholds, D₂, D₃, and D₄, pertaining to PL2 through PL4 are respectively defined based on the quartiles between D₁ and D₅, as follows:

D₂ = D₁ + 0.25(D₅ - D₁)	(3.a)
D₃ = D₁ + 0.50(D₅ - D₁)	(3.b)
D₄ = D₁ + 0.75(D₅ - D₁)	(3.c)

Finally, the sixth deformation limit, D₆, represents the onset of failure in the structural element. On the strength of the above-introduced PLs, the corresponding deformation thresholds for the tested CRCSW are computed and then summarized in Table 5. It should be noted that, as the proposed performance levels are deduced based on the results of a single CRCSW; hence, it is obvious that the PLs and corresponding threshold for drift values should be exercised with caution and can be further improved employing additional test specimens.

Table 5

Threshold of the performance levels introduced for the tested CRCSW.
PL No.	PL1	PL2	PL3	PL4	PL5	PL6
Drift (%)	0.77	1.06	1.35	1.64	1.93	2.00

The performance levels of the CRCSW is schematically portrayed in Fig. 12, in which key stages regarding the damage sequences (See Table 2) observed in loading process are highlighted in the backbone curve of the wall.

3.3 Strain Characteristics

In what follows, strain gauges measurements pertaining to the longitudinal and transverse reinforcements along with those affixed to the concrete surface are derived and discussed in detail.

3.3.1 Longitudinal steel reinforcements

As displayed in Fig. 3(f) and (g), 14 strain gauges were affixed to the vertical rebars at the specified locations of interest to make sense about the trend and contribution of the longitudinal rebars on the governing failure mode along with the strength and stiffness variations of the CRCSW at different levels of drift. In this regard, the strain variation along the height of the longitudinal rebars are presented in Fig. 13, in which the maximum induced strain is reported in each stage of loading. It noteworthy to mention that, at higher drift amplitude, owing to the high strain values induced by the severe spalling and concrete cover crushing at the bottom level of the wall tips, two strain gauges have been detached, at L1 and L15 alignments. Hence, “SG debonding” in addition to its corresponding drift value, i.e., 1.07% and 1.77%, respectively, are signify to highlight this observation in Fig. 13(a) and (e). In other cases, the attachment of the strain gauges remained essentially intact and the maximum induced strain is derived at each stage of loading. In Figs. 14–15, the yielding threshold is specified by a dark red dashed line with abscissa and ordinate of 0.0023 for the longitudinal and transverse rebars, which correspond to the average yield strain of the reinforcing bars obtained from the UTM testing. The main findings are summarized below:

The first sign of the vertical rebar yielding was identified at the base of L15 corresponding to the drift ratio of 0.54% (the first excursion of 7 mm displacement). The second yielding was also experienced at the base of L1 at the drift ratio of 0.62% (second excursion of 8 mm displacement).
In general, at the base level, the strain gauges readings indicate yielding of the longitudinal rebars, especially following the onset of sliding at the wall-foundation interface. This observation does not necessarily imply that the longitudinal rebars provided elsewhere not yielding.
The vertical (axial) strains of the longitudinal reinforcements are essentially introduced due to the interaction of the flexure and warping torsion, which are higher at the wall tips (L1 and L15) as compared to those located in the central regions of the wall section, i.e., L7, L8, and L10;
A general reduction can be seen in the induced strain values from bottom to top of the wall height, expect for the vertical rebars positioned at L8 and L10, which are highly affected by development of the main diagonal cracking intersected approximately at center of the wall panel;
The strains at mid-height of L1 were introduced up to 4 times of yielding strain, due to the strong bond between the deformed bars and concrete and confinement effects provided by the stirrups.
The increasing trend of strain measurements versus drift values was highly influenced by redistribution of the internal forces stemmed from occurrence of the sliding;
At top level of the wall, the maximum induced strain ranges between 0.00090 (0.39ε_y) and 0.00145 (0.63ε_y); thus, no yielding was detected at upper half region of the wall height.
The vertical rebars were sufficiently anchored to the loading head; hence, no evident sign of cracking and slippage was observed at the wall-loading head interface in data collation process.

3.3.2 Transverse steel reinforcements

The strain variations across the transverse rebars are provided in Fig. 14(a) to (c). In the curves plotted in this figure, the abscissa is the normalized circumferential coordinate, along the inner and outer layers of transverse rebars and the ordinate is the maximum induced strain in the piece-wise stirrups. Numbers denoted by 0.25, 0.50, and 0.75 are respectively in accordance with the strain gauge locations at the Left (L), Center (C), and Right (R) of the transverse reinforcements. On the strength of the strain gauge measurements, the following observations can be drawn:

At the drift ratio of 0.23%, a debonding sign was observed for strain gauge labeled TR-B-C-O; therefore, the corresponding information was eliminated in the upcoming data analysis;
The strain values at centerline of the stirrups are larger than those at the side regions, which can be ascribed to the presence of X-shaped diagonal cracking patterns surfaced the wall panel;
Yielding of the transverse reinforcements was only observed for the center of TR-B-I at the latest excursion of drift 2.00%, due to the severe concrete cover crushing and sliding of the longitudinal rebars at the vicinity of the strain gauge designated by TR-B-I-C;
In general, except the case of TR-B-I-C, no evident sign of yielding was detected for transverse rebars, which coincides with the characteristics of a squat RC shear, as considered in this study;
The contribution of the inner and outer pieces of the transverse reinforcements was separately assessed at identical levels and no specific increasing/decreasing trend was detected. This observation can be ascribed to the fact that, the wall thickness (100 mm) and distance of the inner and outer layers (55 mm) are not large enough to obviously distinct between the mentioned layers;
The results of the strain gauges for those affixed to the top-level transverse rebars make up approximately 80 percent of the yield strain, which can be attributed to the opening width of the diagonal cracks developed during the loading excursions.
At the top elevation, a similar trend was also found for both the inner and outer layers of the stirrups. Prior to drift 0.85%, the discrepancy of the strain values is not remarkable; nonetheless, for greater drift values, the centerline strains become higher than the side values up to 40%.

Moreover, presented in Fig. 15(a) to (f) are the strain profiles at elevation view of the wall panel. The following observations have been made:

By an increase in the wall elevation (from base to top), a general decreasing trend of the induced strain/stress was observed for both the inner and outer layers of the horizontal reinforcements;
At the mid height of the wall (middle elevation), strain values are remarkably larger than the side regions, which is due to the passage of the main diagonal and diamond-shaped crackings surface at both faces of the wall panel followed by concrete cover crushing at the intersection of cracks;
The strain gauges readings also signify a decreasing inclination after drift ratio of 1.54%, which is described by the internal force redistribution due to the post-cracking behavior and development of diagonal cracking followed by the spalling at both faces of the wall panel (Hidalgo et al., 2002).

In general, readings of the strain gauges obviously indicate that the contribution of the vertical rebars is more remarkable than those of horizontal rebars, which can be attributed to the wall’s aspect ratio, i.e., the CRCSW under examination is catalogued as an squat RC shear wall. This observation is also in line with the outcomes reported beforehand by quite a few researchers (Carrillo & Alcocer, 2013; Kassem & Elsheikh, 2010; Luna et al., 2013; Massone & Melo, 2018), who have scrutinized participation of the reinforcing bars on the response evaluation of squat RCSWs. Furthermore, attentions should be focused toward the susceptibility of CRCSWs to the premature flexural/torsional failure, which essentially stems from the induced warping torsion (Abdoos & Khaloo, 2024).

3.3.3 Concrete Surface

Provided in the following are the results and discussion dealing with the readings of strain gauges mounted on the front and rear surfaces of the wall panel. At each stage of loading, according to the strain gauge orientation, it is possible to pursue how the cracks have been created and developed during the testing process, and in turn, the trend of corresponding failure pattern will be deduced.

The strain gauge measurements divulge that the horizontal cracks developed especially within the primary stages of loading due to the warping effects causes longitudinal strains to develop in the front and rear panels of the wall. To this aim, the strain profile at various directions of the wall panel along with the peak strain values measured at the specified critical locations are presented.

On account of the strain gauge measurements, the following outcomes are made:

Based on the localized damages of the wall tips at the base level, an early debonding of two strain gauges, i.e., F-B-2 and F-B-3, was observed at drift ratio of 1.08%, and the maximum measured strain of which was 180 µs and 220 µs, respectively,
The horizontally aligned crackings due to the flexural/warping torsion interaction are highly responsible for augmentation of the strain values, particularly at the initial stages of the loading,
As the lateral loading increased, the effects of diagonal X-shaped cracking patterns became more pronounced in the strain gauges measurements,
The highest measured strain value, approximately 7800 µs, was captured by R-B-5 located 300 mm from the base level on the rear face of the wall. As shown in Fig. A(i), a diagonally aligned cracking exactly passes through the center of corresponding strain gauge Rosette and is responsible for the mentioned remarkable value. The experienced values for other strain gauges placed in this target location, i.e., R-B-4 and R-B-5, are circa 6000 µs.
The main diagonal X-shaped cracking at the front view of the wall panel, particularly after drift ratio of 0.62% introduced high values of strains. Also, the average inclination angle of 47̊ to 53̊ originated from the experienced tension field during the loading excursions are essentially close to the alignment of strain-sensing element arranged at 45̊ (Abdoos & Khaloo, 2024).

Moreover, in order to quantitatively provide an insight into the subject in hand, the maximum absolute strain values at different levels of drift have been calculated and summarized in Table 6.

Table 6

The maximum absolute strain values at different levels of drift (all data are in microstrain, μs)
No.	Strain Gauge Designation	Drift (%)
No.	Strain Gauge Designation	0.38	0.62	0.85	1.08	1.31	1.54	1.77	2.00
1	F-B-1	32	99	132	389	858	243	277	342
2	F-B-2	100	154	220	-	-	-	-	-
3	F-B-3	102	119	180	-	-	-	-	-
4	F-B-4	63	104	127	421	368	327	2301	-
5	F-B-5	52	113	134	118	142	220	130	-
6	F-B-6	19	2722	2825	2867	2899	2910	2968	2944
7	F-M-7	381	3202	3281	3270	3261	3229	3154	3174
8	F-M-8	308	399	450	517	516	530	475	525
9	F-M-9	257	372	487	592	611	598	620	666
10	F-M-16	38	81	91	148	262	-	-	-
11	F-M-17	76	160	167	147	189	180	273	214
12	F-T-10	1114	3850	4926	5754	6504	6857	7079	7209
13	F-T-11	82	275	263	730	687	943	633	779
14	F-T-12	37	2722	3429	3878	4359	5026	5302	5637
15	F-T-13	140	199	210	215	205	191	199	196
16	F-T-14	216	320	408	480	489	506	524	534
17	F-T-15	426	652	788	801	628	653	776	717
18	R-B-1	120	145	292	260	235	270	-	-
19	R-B-2	110	126	145	221	247	268	360	335
20	R-B-3	43	110	135	204	212	175	125	156
21	R-B-4	2286	3835	4759	4809	4793	4852	6011	6084
22	R-B-5	3896	5815	5832	5904	5995	6092	7574	7792
23	R-B-6	3550	5596	5652	5556	5564	5612	5605	5620
24	R-M-7	113	155	180	211	237	240	329	317
25	R-M-8	69	86	103	116	140	147	242	232
26	R-M-9	86	153	164	162	157	141	140	95
27	R-M-16	61	76	183	162	305	333	394	361
28	R-M-17	47	67	183	162	1152	1063	1107	1134
29	R-T-10	70	79	2095	3110	3484	3673	3729	3733
30	R-T-11	70	95	2302	4120	4151	4171	4215	4267
31	R-T-12	93	100	1044	1503	1809	1958	1954	2270
32	R-T-13	1582	1954	2796	3298	3463	3729	3708	4181
33	R-T-14	2645	3354	4340	5204	5502	5599	5531	5668
34	R-T-15	1771	2488	3321	4018	4226	4384	4440	4611
Note: • Dash symbol, (-), indicates strain gauge debonding, • The initial tensile cracking of the concrete material is 145 µs.

According to the data presented in this table, almost all the concrete surface strain gauges captured occurrence of minor/major cracking at the vicinity of the specified target locations. Summarized details of the close-up photographs corresponding to the strain gauges affixed to the concrete surface are presented in Appendix (Fig. A(a) through (n)) to further illuminate the localized crack propagation at the specified target locations at the final stage of the loading.

In what follows, in order to better interpret how the strains have been distributed within the wall panel, the strain variations at both faces of the wall panel are presented. As depicted in Fig. 16, onset of the initial tensile cracking at concrete surface, i.e., 145 µs, is identified by a dark red dashed line. As the tensile strength of concrete is relatively low, it is expected to be vulnerable even within the initial stages of loading; hence, debonding of the concrete strain gauges can potentially be occurred at the lower drift amplitudes as compared to those mounted on the reinforcing bars. To address this point, the drift level corresponding to the strain gauge debonding is reported in the caption of Fig. 16.

Generally, owing to the limited experiments conducted on CRCSWs, this paper can potentially contribute new insights into the applicability of such salient structural elements in the future construction industry to resist against lateral loadings.

Although the conventional reinforced concrete shear walls (RCSWs) are known to be effective under lateral cyclic loadings, research examining the seismic performance of curved RC shear walls (CRCSWs) is very scarce. In that regard, the intent of the current experimental investigation was to convey insights and detailed information pertaining to the cyclic performance of CRCSWs in order to fill some of the identified knowledge gaps within this research area. Within the framework of the experimental testing, the following conclusions and observations can be drawn:

The tested CRCSW indicated stable cyclic performance with no discernable strength degradation,
Damage evolution process due to the quasi-static lateral cyclic loading indicted that, in general, a failure mode with flexural nature has taken place. This failure type, in which, yielding of the longitudinal rebars followed by the concrete crushing at bottom of the wall tips, can essentially be attributed to the dominating effect of the warping torsion induced in the CRCSW’s section,
The failure mechanism also dictated that special care should be given in adopting a well-designed boundary element at the CRCSWs’ tips in order to circumvent occurrence of the premature flexural/torsional failure in realm of practice,
On the strength of the obtained skeleton curve, an applicable framework was established for the

performance levels and deformation threshold of the tested CRCSW, which can be aided to the future performance-based seismic design evaluation of such salient structural elements,

The strain gauges successfully captured the strain values experienced by the CRCSW during the loading phases. Regarding the strain data, an estimation toward the damage evolution process was possible for the seismic performance of CRCSWS,
A concrete surface strain gauge measurement made it possible to figure out the nature of the induced cracking patterns during the loading phases and also indicated the damage sequences,
Strain gauge readings divulged yielding of the longitudinal rebars, especially at base level of the wall; however, no significant sign of yielding was detected for the transverse reinforcements,
Moreover, along the wall’s height, a general decreasing trend was observed for the induced stresses pertaining to the longitudinal and transverse reinforcements,
Strain gauges measurements also confirmed that the contribution of the longitudinal reinforcing bars is more significant as compared to those of transverse rebars, which holds true for conventional squat RC shear walls applied in practice,

The database presented in this study will serve as validation and calibration of future analytical and numerical models for RC shear walls with curved cross-section. In recognition of the problematic behavior of such salient elements, further experimental research programs should be devoted to provide insight into the analysis and design of earthquake-resistant CRCSWs.

A = cross-sectional area of the wall;
D_i = threshold of drift ratios in correspondence with the performance level (for i = 1 to 6);
e = eccentricity between the centroid and shear center of the wall section;
E_s = elastic modulus of steel reinforcements;
${f^{\prime}_c}$ = compressive strength of concrete materials;
f_u = ultimate stress of steel reinforcements;
f_y = yield stress of longitudinal and transverse reinforcements;
h_w = height of the wall;
l_w = equivalent length of the wall;
R = average radius of curvature of the wall cross-section;
R_i = inner radius of the wall cross-section;
R_o = outer radius of the wall cross-section;
t_w = wall thickness;
y_c = centroid of the wall’s cross-section;
y_s = shear center of the wall’s cross-section;
γ_i = stiffness degradation ratio;
λ_i = bearing capacity degradation coefficient;
ε_su = elongation of steel reinforcements;
θ = half angle of embrace;
ρ_l = ratio of longitudinal reinforcements;
ρ_t = ratio of transverse reinforcements;

Data Availability Statement

Some or all data that support the findings of this study are available from the corresponding author upon reasonable request

Acknowledgments

The authors highly appreciate the supports provided by the Center of Excellence in Composite Structures and Seismic Strengthening (CECSSS) at Sharif University of Technology (SUT), Iran.

Declaration of generative AI in scientific writing

The authors declare that no AI generative tool were employed AI and AI-assisted technologies in the writing process of this manuscript.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Aaleti, S., Brueggen, B. L., Johnson, B., French, C. E. & Sritharan, S. (2013). Cyclic response of reinforced concrete walls with different anchorage details: Experimental investigation. Journal of Structural Engineering, 139(7), 1181–1191.
Abdoos, H & Khaloo, A. R. (2024). Failure mechanism of a curved RC shear wall subjected to cyclic loading : Experimental findings. Engineering Structures, 304(February), 117703. https://doi.org/10.1016/j.engstruct.2024.117703
Abdoos, H, Khaloo, A. R. & Foyouzat, M. A. (2020). On the out-of-plane dynamic response of horizontally curved beams resting on elastic foundation traversed by a moving mass. Journal of Sound and Vibration, 115397.
Abdoos, Hatef. (2024). PhD Thesis: Experimental, analytical, and numerical investigation on the cycle response of curved RC shear walls. Sharif University of Technology.
Abdoos, Hatef, Khaloo, A. & Tabiee, M. (2023). Effective width estimation of L-shaped RC shear walls using EPR algorithm. Sharif Journal of Civil Engineering.
Abdoos, Hatef, Khaloo, A. & Tabiee, M. (2024). An analytical investigation into the lateral load response of curved RC shear walls. The Structural Design of Tall and Special Buildings. https://doi.org/10.1002/TAL.2097
Abdullah, S. A. & Wallace, J. W. (2018). UCLA-RCWalls Database for Reinforced Concrete Structural Walls. Proceedings of the 11th National Conference in Earthquake Engineering.
ACI 318. (2019). Building code requirements for structural concrete (ACI 318-19) and commentary.
Alaghmandan, M., Bahrami, P. & Elnimeiri, M. (2014). The future trend of architectural form and structural system in high-rise buildings. Architecture Research, 4(3), 55–62.
Arabzadeh, H. & Galal, K. (2018). Seismic-response analysis of RC C-shaped core walls subjected to combined flexure, shear, and torsion. Journal of Structural Engineering, 144(10), 4018165.
ASCE. (2017). ASCE/SEI 41-17. Seismic evaluation and retrofit of existing buildings.
ASTM Standard-A675. Standard Specification for Steel Bars, Carbon, Hot-Wrought, Special Quality, Mechanical Properties,. (2019).
ASTM Standard A370-20. Standard Test Methods and Definitions for Mechanical Testing of Steel Products,. (2020).
Barda, F. (1972). Shear strength of low-rise walls with boundary elements. Lehigh University.
Behrouzi, A. A., Mock, A., Lehman, D., Lowes, L. & Kuchma, D. (2018). Seismic Performance of Slender C-Shaped Walls Subjected to UniI-and Bi-Directional Loading. Eleventh US National Conference on Earthquake Engineering Proceedings.
Behrouzi, A. A., Mock, A. W., Lehman, D. E., Lowes, L. N. & Kuchma, D. A. (2020). Impact of bi-directional loading on the seismic performance of C-shaped piers of core walls. Engineering Structures, 225, 111289.
Benjamin, J. R. & Williams, H. A. (1957). The behavior of one-story reinforced concrete shear walls. Journal of the Structural Division, 83(3), 1–49.
Beyer, K., Dazio, A. & Priestley, M. J. N. (2008). Quasi-static cyclic tests of two U-shaped reinforced concrete walls. Journal of Earthquake Engineering, 12(7), 1023–1053.
Brueggen, B. L., French, C. E. & Sritharan, S. (2017). T-shaped RC structural walls subjected to multidirectional loading: test results and design recommendations. Journal of Structural Engineering, 143(7), 4017040.
Carmona, S. & Aguado, A. (2012). New model for the indirect determination of the tensile stress–strain curve of concrete by means of the Brazilian test. Materials and Structures, 45, 1473–1485.
Carpinteri, A., Lacidogna, G. & Nitti, G. (2016). Open and closed shear-walls in high-rise structural systems: Static and dynamic analysis. Curved and Layered Structures, 3(1).
Carrillo, J. & Alcocer, S. M. (2013). Shear strength of reinforced concrete walls for seismic design of low-rise housing. ACI Structural Journal, 110(3), 415.
Chen, S., Diao, B., Guo, Q., Cheng, S. & Ye, Y. (2016). Experiments and calculation of U-shaped thin-walled RC members under pure torsion. Engineering Structures, 106, 1–14.
Choi, C.-S., Ha, S.-S., Lee, L.-H., Oh, Y.-H. & Yun, H.-D. (2004). Evaluation of deformation capacity for RC T-shaped cantilever walls. Journal of Earthquake Engineering, 8(03), 397–414.
Collins, M. P. & Lampert, P. (1973). Redistribution of moments at cracking-the key to simpler torsion design? Special Publication, 35, 343–384.
Constantin, R. & Beyer, K. (2016). Behaviour of U-shaped RC walls under quasi-static cyclic diagonal loading. Engineering Structures, 106, 36–52.
El-Azizy, O. A., Ezzeldin, M. & El-Dakhakhni, W. (2023). Analysis of Reinforced Concrete Shear Walls with Different End Configurations for Seismic Design. Journal of Structural Engineering, 149(6), 4023056.
El-Hashimy, T., Ezzeldin, M., El-Dakhakhni, W. & Tait, M. (2020). Behavior of seismically detailed reinforced concrete block shear walls with boundary elements under out-of-plane loading. Journal of Structural Engineering, 146(3), 4020005.
El-Hashimy, T., Ezzeldin, M., Tait, M. & El-Dakhakhni, W. (2019). Out-of-plane performance of reinforced masonry shear walls constructed with boundary elements. Journal of Structural Engineering, 145(8), 4019073.
Foyouzat, M. A., Abdoos, H., Khaloo, A. R. & Mofid, M. (2022). In-plane vibration analysis of horizontally curved beams resting on visco-elastic foundation subjected to a moving mass. Mechanical Systems and Signal Processing, 172, 109013.
Gokdemir, H., Ozbasaran, H., Dogan, M., Unluoglu, E. & Albayrak, U. (2013). Effects of torsional irregularity to structures during earthquakes. Engineering Failure Analysis, 35, 713–717.
Goodsir, W. J. (1985). The design of coupled frame-wall structures for seismic actions.
Grammatikou, S., Biskinis, D. & Fardis, M. N. (2015). Strength, deformation capacity and failure modes of RC walls under cyclic loading. Bulletin of Earthquake Engineering, 13(11), 3277–3300.
Gulec, C. K., Whittaker, A. S. & Stojadinovic, B. (2009). Peak shear strength of squat reinforced concrete walls with boundary barbells or flanges. ACI Structural Journal, 106(3), 368.
Habibi, O., Khaloo, A. & Abdoos, H. (2021). Seismic behavior comparison of RC shear walls strengthened using FRP composites and steel elements. Scientia Iranica, 28(3), 1167–1181.
Han, X., Chen, B., Ji, J., Xie, S. & Lu, H. (2019). Deformation limits of L‐shaped reinforced concrete shear walls: Experiment and evaluation. The Structural Design of Tall and Special Buildings, 28(13), e1627.
Hart, G. C., DiJulio Jr, R. M. & Lew, M. (1975). Torsional response of high-rise buildings. Journal of the Structural Division, 101(2), 397–416.
Hasnalbant, M. & Eyyubov, C. (2016). The Effects of Cross Sectional Dimensions on the Behavior of L-Shaped RC Structural Members. Journal of Civil Engineering and Architecture, 10, 1355–1363.
Hassan, M. & El-Tawil, S. (2003). Tension flange effective width in reinforced concrete shear walls. Structural Journal, 100(3), 349–356.
Hidalgo, P. A., Ledezma, C. A. & Jordan, R. M. (2002). Seismic behavior of squat reinforced concrete shear walls. Earthquake Spectra, 18(2), 287–308.
Hosaka, G., Funaki, H., Hosoya, H. & Imai, H. (2008). Experimental study on structural performance of RC shear wall with L shaped section. Proceedings, 14th World Conference on Earthquake Engineering, Beijing, China.
Hoult, R. (2021). Torsional capacity of reinforced concrete U-shaped walls. Structures, 31, 190–204.
Hoult, R., Appelle, A., Almeida, J. & Beyer, K. (2020). Seismic performance of slender RC U-shaped walls with a single-layer of reinforcement. Engineering Structures, 225, 111257.
Hoult, R. & Beyer, K. (2021). RC U-shaped walls subjected to in-plane, diagonal, and torsional loading: New experimental findings. Engineering Structures, 233, 111873.
Hoult, R. D. & Beyer, K. (2020). Decay of Torsional Stiffness of RC U-shaped Walls When Subjected Simultaneously to In-plane Translational Displacements. J Struct Eng, 146(9).
Hoult, R. D., Lumantarna, E. & Goldsworthy, H. M. (2015). Torsional displacement for asymmetric low-rise buildings with RC C-shaped cores. Proceedings of the Tenth Pacific Conference on Earthquake Engineering, Sydney, Australia.
Hube, M. A., María, H. S., Arroyo, O., Vargas, A., Almeida, J. & López, M. (2020). Seismic performance of squat thin reinforced concrete walls for low-rise constructions. Earthquake Spectra, 36(3), 1074–1095.
Ile, N. & Reynouard, J. M. (2005). Behaviour of U-shaped walls subjected to uniaxial and biaxial cyclic lateral loading. Journal of Earthquake Engineering, 9(1), 67–94.
Inada, K., Chosa, K., Sato, H., Kono, S. & Watanabe, F. (2008). Seismic performance of RC L-shaped core structural walls. The 14th World Conference on Earthquake Engineering, In.
Kassem, W. & Elsheikh, A. (2010). Estimation of shear strength of structural shear walls. Journal of Structural Engineering, 136(10), 1215–1224.
Khaloo, A. R., Foyouzat, M. A., Abdoos, H. & Mofid, M. (2023). Axial force contribution to the out-of-plane response of horizontally curved beams under a moving mass excitation. Applied Mathematical Modelling, 115, 148–172. https://doi.org/10.1016/j.apm.2022.10.047
Kitada, Y., Akino, K., Terada, K., Aoyama, H. & Miller, A. (1997). Report on seismic shear wall international standard problem organized by OECD/NEA/CSNI.
Kono, S., Sakamoto, K. & Sakashita, M. (2011). Simulation of seismic load resistance of core-walls for tall buildings. Applied Mechanics and Materials, 82, 386–391.
Lee, J.-Y., Mansour, M. Y. & Park, J. (2012). Structural behavior of RC membranes having inclined steel bars. Engineering Structures, 41, 146–156.
Li, B., Pan, Z. & Zhao, Y. (2015). Seismic behaviour of lightly reinforced concrete structural walls with openings. Magazine of Concrete Research, 67(15), 843–854.
Li, B. & Xiang, W. (2011). Effective stiffness of squat structural walls. Journal of Structural Engineering, 137(12), 1470–1479.
Li, W. & Li, Q. (2012). Seismic performance of l‐shaped rc shear wall subjected to cyclic loading. The Structural Design of Tall and Special Buildings, 21(12), 855–866.
Li, X., Zhang, J. & Cao, W. (2020). Hysteretic behavior of high-strength concrete shear walls with high-strength steel bars: Experimental study and modelling. Engineering Structures, 214, 110600.
Lowes, L., Lehman, D., Kuchma, D., Mock, A. & Behrouzi, A. (2013). Large scale tests of C-shaped reinforced concrete walls. Summary Report from NEES Project Warehouse. Available at Https://Nees. Org/Warehouse/Project/104.
Luna, B., Rivera, J. & Whittaker, A. (2015). Seismic Behavior of Low-Aspect-Ratio Reinforced Concrete Shear Walls. Aci Structural Journal, 112, 593–604. https://doi.org/10.14359/51687709
Luna, B., Whittaker, A. & Rivera, J. (2013). Seismic behavior of low aspect ratio reinforced concrete shear walls.
Ma, J. & Li, B. (2018). Experimental and Analytical Studies on H-Shaped Reinforced Concrete Squat Walls. ACI Structural Journal, 115(2).
Ma, S.-Y. M., Bertero, V. V & Popov, E. P. (1976). Experimental and analytical studies on the hysteretic behavior of reinforced concrete rectangular and T-beams. Earthquake Engineering Research Center, College of Engineering, University of California.
Maghsoudi-Barmi, A., Khaloo, A. & Moeini, M. E. (2021). Experimental investigation of unbonded ordinary steel reinforced elastomeric bearings as an isolation system in bridges. Structures, 32, 604–616.
Maruta, M., Suzuki, N., Miyashita, T. & Nishioka, T. (2000). Structural capacities of H-shaped RC core wall subjected to lateral load and torsion. Proceedings of the 12th WCEE. New Zealand: The New Zealand Society for Earthquake Engineering, 1028.
Massone, L. M. & Melo, F. (2018). General solution for shear strength estimate of RC elements based on panel response. Engineering Structures, 172, 239–252.
Moehle, J. P. (2015). Seismic design of reinforced concrete buildings (Vol. 814). McGraw-Hill Education New York.
Mu, Z. & Yang, Y. (2020). Experimental and numerical study on seismic behavior of obliquely stiffened steel plate shear walls with openings. Thin-Walled Structures, 146, 106457.
Nakachi, T., Toda, T. & Tabata, K. (1996). Experimental study on deformation capacity of reinforced concrete core walls after flexural yielding. Young, 52, 71–79.
Ni, X., Cao, S., Li, Y. & Liang, S. (2019). Stiffness degradation of shear walls under cyclic loading: experimental study and modelling. Bulletin of Earthquake Engineering, 17, 5183–5216.
Noor, F. A. & Boswell, L. F. (1992). Small scale modelling of concrete structures. CRC Press.
Oesterle, R. G., Aristizabal-Ochoa, J. D., Fiorato, A. E., Russell, H. G. & Corley, W. G. (1979). Earthquake resistant structural walls-tests of isolated walls-phase II. Construction Technology Laboratories, Portland Cement Association.
Oesterle, R. G., Fiorato, A. E., Johal, L. S., Carpenter, J. E., Russell, H. G. & Corley, W. G. (1976). Earthquake resistant structural walls-tests of isolated walls. Research and Development Construction Technology Laboratories, Portland Cement Association.
Pantazopoulou, S. J. & Moehle, J. P. (1990). Identification of effect of slabs on flexural behavior of beams. Journal of Engineering Mechanics, 116(1), 91–106.
Paulay, T. & Priestley, M. J. N. (1992). Seismic design of reinforced concrete and masonry buildings (Vol. 768). Wiley New York.
Press, C. A. & B. (2010). Code for seismic design of buildings.
Salonikios, T. N. (2002). Shear strength and deformation patterns of R/C walls with aspect ratio 1.0 and 1.5 designed to Eurocode 8 (EC8). Engineering Structures, 24(1), 39–49.
Salonikios, T. N. (2007). Analytical prediction of the inelastic response of RC walls with low aspect ratio. Journal of Structural Engineering, 133(6), 844–854.
Siddique, A., Mehmood, T., Qazi, S., Khan, S., Nawaz, A. & Tufail, R. F. (2023). Seismic performance evaluation of code compliant and non-compliant RC walls. Australian Journal of Structural Engineering, 24(2), 120–135.
Sittipunt, C. & Wood, S. L. (1993). Finite element analysis of reinforced concrete shear walls. Civil Engineering Studies SRS-584.
Tabiee, M., Abdoos, H. & Khaloo, A. (2023). Concurrent effects of the shear-lag and warping torsion on the performance of non-rectangular RC shear walls. Archives of Civil and Mechanical Engineering, 23(2), 138.
Tabiee, M., Abdoos, H., Khaloo, A. & Kavei, S. (2023). Effective width estimation of flanged reinforced concrete shear walls. The Structural Design of Tall and Special Buildings. https://doi.org/10.1002/TAL.2057
Thomsen, J. H. & Wallace, J. W. (1995). Displacement-based design of RC structural walls: an experimental investigation of walls with rectangular and T-shaped cross-sections. Clarkson University, Department of Civil Engineering.
Wang, B., Wu, M.-Z., Shi, Q.-X. & Cai, W.-Z. (2022a). Effects of biaxial loading path on seismic behavior of T-shaped RC walls. Engineering Structures, 273, 115080.
Wang, B., Wu, M.-Z., Shi, Q.-X. & Cai, W.-Z. (2022b). Seismic performance of flanged RC walls under biaxial cyclic loading. Journal of Building Engineering, 105632.
Wang, B., Wu, M.-Z., Zhang, L.-P., Cai, W.-Z. & Shi, Q.-X. (2023). Seismic behavior and shear capacity of shear-dominated T-shaped RC walls under cyclic loading. Structures, 55, 557–569.
Wei, F., Chen, H. & Xie, Y. (2022). Experimental study on seismic behavior of reinforced concrete shear walls with low shear span ratio. Journal of Building Engineering, 45, 103602.
Xu, G., Zheng, L., Zhou, W., Zhai, C. & Wang, D. (2023). Quasi-static tests of squat reinforced concrete shear walls with openings. Engineering Structures, 293, 116666.
Zhang, J.-W., Zheng, W.-B., Cao, W.-L., Dong, H.-Y. & Li, W.-D. (2019). Seismic Behavior of Low-rise Concrete Shear Wall with Single Layer of Web Reinforcement and Inclined Rebars: Restoring Force Model. KSCE Journal of Civil Engineering, 23(3), 1302–1319.
Zhang, Z. & Li, B. (2018). Effective stiffness of non-rectangular reinforced concrete structural walls. Journal of Earthquake Engineering, 22(3), 382–403.

Appendix.docx

Download PDF

Version 1

posted

You are reading this latest preprint version

Cyclic Performance and Strain Characteristics of a Curved RC Shear Wall

Status:

Version 1

Abstract

Figures

1 Introduction

2 Experimental program

2.1 Description of the test unit

2.2 Material Properties

2.3 Testing methodology

2.4 Testing instrumentation and monitoring systems

2.4.1 Strain gauges

2.4.2 High-resolution cameras

2.5 Loading procedure

3 Test results and discussion

3.1 Experimental observations

3.2 Performance levels of the CRCSW

3.3 Strain Characteristics

3.3.1 Longitudinal steel reinforcements

3.3.2 Transverse steel reinforcements

3.3.3 Concrete Surface

4 Summary and conclusions

Nomenclature

Declarations

References

Supplementary Files

Status:

Version 1