Cyclic behavior of slender and mid-rise resilient recycled aggregate concrete walls: Experiment and theoretical analysis

Abstract

Quasi-static experiments and analytical investigations of ultra-high-strength bars (UHSB) reinforced walls with two shear span ratios of 1.5 and 2.2, were conducted. The hysteretic responses of test walls in terms of damage evolution, load–displacement curves, curvature profiles, reinforcement strain, and residual drift ratio were explored. Experimental results indicated that all test walls exhibited drift-hardening behavior. Specimens achieved a maximum residual drift ratio of 0.27% before 2% drift ratio, satisfying the limit value of 0.5%. The calculation of hysteresis curves calculation of the test walls was conducted considering the weak bond behavior of UHSB and verified by the experimental results.

Graphical abstract

Keywords

resilient wall / recycled aggregate concrete / ultra-high-strength bars / seismic performance / shear span ratio

1 Introduction

Reinforced concrete walls, as the first line of defense in frame-shear wall structures, have significant lateral stiffness and bearing capacity, and bear most of the lateral force generated by earthquakes and other forces. Conventionally, the seismic design basis for reinforced concrete structures requires that the structures exhibit inelastic behavior during extremely strong earthquakes in order to prevent structure collapse. This design objective is achieved through the plastic deformation of the reinforcing steel and the concentrated damage of the concrete within the plastic hinge region of the wall. Although structures designed based on the above concept can achieve effective energy dissipation and prevent structural collapse, this comes at the cost of non-elastic deformation at the bottom. The excessive irreparable deformation generated by such structures can result in building repair costs that may even surpass the cost of demolition and reconstruction. Additionally, difficulty in repairing generally leads to prolonged downtime after earthquakes, which is also typically a major cause of casualties and economic losses after earthquakes [1]. Therefore, from the perspective of post-earthquake damage, building structures that are easy to repair are more desirable, even after experiencing an extremely strong earthquake with a probability of exceeding 2% within a 50-year period, which is known as the maximum considered earthquake (MCE) and corresponds to the drift limit value for the design objective of collapse prevention (CP) [2].

Recently, reducing post-earthquake damage to structures and developing easily repairable structures have attracted widespread interest among researchers. Initially, unbonded prestressed steel bars were primarily used in steel structure connections [3], unbonded prestressed steel bars subsequently became widely used in concrete structures or components to provide restorable moments [4–6]. Prestressed bars are basically combined with a slit at the bottom of the components to achieve self-centering [7,8]. Some researchers also add ductile materials [9,10] or energy-dissipating components [11,12] between the bottom of walls and foundations, aiming to reduce damage and improve energy dissipation capacity. Owing to the approximately hinged interface relationship between the foundation and walls, the plastic deformation of the wall is limited, while concentrating on the rotation of the contact interface. Moreover, the relatively insignificant plastic deformation of the prestressed steel bars is also one of the reasons why the concrete walls have a small residual displacement and satisfactory resilient performance.

For the purpose of avoiding excessive damage and deformation to the concrete walls, it is feasible to induce the wall to incur damage and deformation in the specific area. By concentrating damage on replaceable components [13–16], plastic deformation in replaceable components dissipates earthquake energy, protecting the main structure from severe damage or only causing minor damage. After the earthquake, only the energy-dissipating components need to be replaced to restore structural functionality. Xu et al. [17] incorporated self-centering energy dissipating braces on both sides of the steel plate shear walls, and the destructive test results demonstrated that the steel plate shear wall with self-centering energy dissipating braces maintained stable resistance to lateral forces, energy dissipation, and self-centering capacity, even at a drift ratio of 4%. Li et al. [18] achieved damage and energy dissipation concentration by arranging replaceable connected beams in the coupled concrete walls, and replaceable components were also installed at the corners of the walls to enable rapid post-earthquake structural restoration.

As materials with unique properties have emerged, they are not being employed in resilient structures. Materials like shape memory alloys (SMAs), which are able to recover the initial shape after unloading, can be used in the plastic hinge region of the walls, to reduce the irreversible displacement caused by the yielding of longitudinal reinforcement [19,20]. Apart from the superelasticity of SMAs, materials with high elasticity and high strength are also employed to control residual displacement [21–23].

Zhao et al. [22] conducted a quasi-static test on full-scale carbon fiber reinforced polymer (CFRP) strengthened shear walls to investigate their seismic performance. The research concluded that the residual displacement of the CFRP strengthened shear walls was reduced by approximately 50% compared to the conventional shear walls at the drift ratio of 1%. A fiber-reinforced concrete shear wall strengthened with fiber-reinforced polymer (FRP) was proposed in Ref. [24]. This composite system had better self-centering capability compared to conventional concrete fiber-reinforced concrete shear walls. Ghazizadeh et al. [23] performed numerical analysis and concluded that placing GFRP reinforcement at the middle-height of the wall cannot only present self-centering performance but also have higher stiffness and energy dissipation capacity.

However, the aforementioned methods have not been widely adopted due to certain limitations. Connection between concrete walls with prestressed tendons or bottom slits and foundation typically rely only on the steel bars, leading to a significant decrease in stiffness and seismic reliability of the shear wall. Therefore, the collapse-resistant performance of walls lacks reliable safeguards. SMA and FRP reinforcements have significantly lower elastic modulus. In addition, the large difference in thermal expansion coefficients between FRP materials and concrete makes the stress transfer between them more complicated, which is detrimental to long-term stable seismic performance. Therefore, steel bars with a longer elastic range have attracted the attention of researchers [25–28]. Except for higher yield strength, the remaining mechanical properties of this type of reinforcement are well-known to researchers. Sun et al. [27,29] initially proposed the use of ultra-high-strength bars (UHSB), with helical grooved grooves, capitalizing on their weak bond behavior and extended elastic performance to provide resilient moments in columns or walls [26,27,30]. The efficacy of this approach in achieving resilient structural recovery has been validated. Building upon previous research, the present study aims to further attenuate the bond behavior of UHSB and retard yielding.

Previous studies [25,31,32] have explored the use of UHSB in shear walls, primarily in slender walls. Related research [33] found that compared to traditional walls reinforced with ductile steel, walls reinforced with UHSB in the boundary elements can reduce residual displacements of specimens and enhance their recoverable performance. This paper aims to explore the reliability of UHSB in walls with different shear-span ratios. The present research also provides a detailed analysis and comparison of the hysteretic performance of the UHSB reinforced-walls with two different shear-span ratios. Test walls are expected to be constructed using recycled aggregate concrete (RAC). It is hoped that through proper design, recycled concrete can be applied to the proposed walls, thereby expanding the potential use of RAC in practical engineering projects. If such walls are implemented in engineering projects, they cannot only reduce the generation of post-earthquake construction waste but also further promote the utilization rate of construction waste resources. Experimental results have shown that properly proportioned RAC components and structures can still exhibit satisfactory seismic performance [34–37].

With the aim of ensuring the performance of RAC in the walls, reliable confinement was implemented in the stirrups of the boundary elements during the test design. Research on the post-earthquake structures [38] has found that walls with well-designed transverse steel reinforcement remain relatively intact. Furthermore, the inclusion of steel fibers can also assist in maintaining the integrity of concrete. The mechanical properties of RAC are also enhanced with the addition of steel fibers [39–41]. The steel fibers strengthen the connections between concrete matrices [42], reduce wall damage [43]. This helps alleviate the difficulty of post-earthquake repair work, and shorten the breakdown time of structures, which demonstrate the improved the repairability of components or structures. Therefore, steel fiber is also included as an experimental variable during the test. An appropriate volume fraction can prevent the formation of steel fiber bundles while ensuring a significant improvement in performance. The designed volume fraction of steel fibers was 1%.

Concrete walls with an aspect ratio ≥ 2 (AR ≥ 2) were primarily associated with flexural failure, while walls with an aspect ratio between 1 and 2 (1 ≤ AR ≤ 2) typically exhibited a response that involved a coupling of both bending and shear effects. The experiment focuses on four specimens, including two slender walls with an aspect ratio of 2.2 and two mid-rise walls with an aspect ratio of 1.5. Hysteretic response of each specimen under constant axial load and cyclic lateral force. Additionally, numerical simulation aimed to reveal the influence of different research variables, such as axial load ratio (ALR), longitudinal reinforcement ratio and stirrup ratio, on the seismic performance of the test walls. The computational model incorporated the impact of the weak bonding performance of UHSB, and comparison with experimental results and further parameter analysis were also performed.

2 Experimental program

2.1 Details of specimens

The wall featured a rectangular cross-section with dimensions of 800 mm in length and 150 mm in thickness. Slender walls with an aspect ratio of 2.2 had a height of 1600 mm, while the mid-rise walls, with an aspect ratio of 1.5, had a height of 1150 mm. The aspect ratio was chosen to ensure that the test walls predominantly experience flexural failure, allowing the UHSB to work effectively. The foundation was 1800 mm in length, 500 mm in height, and 420 mm in width, which secured the wall to the laboratory floor. The design of the loading beam, with dimensions of 1200 mm in length, 350 mm in width, and 300 mm in height, was integrally cast to ensure a certain level of safety margin against premature failure during test.

Reinforcement details for slender walls and mid-rise walls are provided in Fig.1. Within the wall panel, there are two layers of horizontally and vertically distributed reinforcement, consisting of 8 mm diameter bars with the spacing of 100 mm in both vertical and horizontal directions. The boundary elements were reinforced with four longitudinal bars with a diameter of 12.6 mm. These bars were confined by stirrups with a diameter of 8 mm, spaced at 50 mm along the height. Mechanical anchorage was employed using nuts and steel plates for anchoring the reinforcement bar ends through the threading at the ends of the UHSB. More details can be seen in Fig.2.

Tab.1 presents the experimental parameters, including the aspect ratio and the presence of steel fibers. As for the designation of the specimens in Tab.1, “S” refers to the specimens; “N” represents the plain RAC without steel fibers, and “F” represents the steel fibers reinforced RAC; the last number 1.5 or 2.2 indicates aspect ratio of test walls, which is the ratio of the calculated height (h) to the width (l) of the wall. The test walls were subjected to an axial load of 462 kN, and the actual ALRs of each specimen are provided in Tab.1. The compressive strength of the concrete used in each specimen is also provided in Tab.1.

2.2 Material properties

Two different concrete mix proportions were included: plain RAC and steel fiber reinforced concrete (SRAC). To estimate the compressive strength of the concrete, prismatic samples (dimensions 150 mm × 150 mm × 300 mm) and cube samples (dimensions 150 mm × 150 mm × 150 mm) were tested for concrete strength. Tab.2 provides the average values of concrete strength for the same type of concrete, ranging from 52.49 to 56.49 MPa. Additionally, elastic modulus of the concrete was also tested and provided.

The mechanical properties of steel reinforcement, as well as the steel plate used for anchorage, are provided in Tab.3. According to the data obtained from the coupon test, it was evident that the UHSB in the boundary elements exhibited significantly longer elastic range and higher yield strength. This characteristic delayed the occurrence of yielding under cyclic loading, thereby achieving the objective of improving the resilient performance. Fig.3 illustrates the surface configuration of the UHSB. Although different bond strengths were obtained due to variations in testing methods, including beam tests, pull-out tests, and pull-out tests under cyclic loading, all tests have reached a similar conclusion that the bond strength of UHSB is significantly lower than that of conventional deformed bars. Funato et al. [29] concluded that the bond strength of UHSB under cyclic loading was 3 MPa.

2.3 Test setup

Test setup is shown in Fig.4, where the vertical and lateral force were exerted through the reaction frame and reaction wall, respectively. A constant axial load was initially applied, followed by cyclic lateral force controlled based on drift ratio. The axial load was uniformly distributed through a horizontal steel beam on the loading beam. The cyclic lateral force was applied using a horizontal jack with a loading capacity of 2000 kN connected to the reaction wall. The specific loading history is illustrated in Fig.5. As shown in Fig.5, each target drift ratio underwent two cycles prior to the 2% drift ratio, and one cycle thereafter. The loading was stopped when the capacity was reduced by approximately 15%.

Instrumentation installed on the walls included 14 linear variable differential transformers (LVDTs) to measure horizontal displacement, curvature and sliding. Four or five regions were selected in the test walls, and each region was equipped with two vertical LVDTs to measure the curvature, as shown in Fig.6. In slender walls and mid-rise walls, the height of LVDTs extended from the surface of the foundation to a height of 1.5l or 1.0l. LVDTs near the bottom region were more densely arranged to capture the nonlinear behavior more accurately in the severely damaged areas. In addition to the external LVDTs, strain gauges were attached to the steel bars to measure the strains at different locations.

3 Experimental results and discussion

To investigate the hysteretic response of the test walls and compare with various performance-based design objectives, the experimental results were analyzed in relation to three specified performance objectives in Ref. [2]: immediate occupancy (IO), life safety (LS), and CP. Hysteretic responses of four test walls were analyzed and compared at specific drift ratios corresponding to each performance objectives

3.1 Damage evolution

The damage of different aspect ratio walls was evaluated by observing the crack propagation patterns during the loading process. Under specific drift ratios, digital sketches of crack development were created, and the crack patterns were manually tracked during the loading process. The damage state is shown in Fig.7 at three specific drift ratios corresponding to the three performance objectives, IO, LS, and CP, are 0.5%, 1.0%, and 2.0%, respectively.

Based on the crack distribution, the damage in all specimens, including mid-rise walls, is predominantly characterized by flexural damage. In general, the cracks initiate from the bottom of the wall and propagated toward the interior of the wall panel, where diagonal cracks were concentrated. Prior to a drift ratio of 0.5%, the predominant form of damage was flexural cracks. Due to the crack bridging effect of steel fibers, the development of diagonal cracks in early-stage SRAC walls was not significant. As the applied displacement increased, cracks developed continuously, including the appearance of flexural cracks and the extension of diagonal cracks. Based on the crack development at a drift ratio of 1%, it can be observed that the specimens reinforced with steel fibers exhibited a significantly denser distribution of cracks. However, the overall range of crack distribution had decreased. Meanwhile, no significant vertical cracks were observed, indicating minimal damage to the compressive concrete. The crack development pattern of the test walls had reached a relatively stable state.

When the shear walls were loaded to a drift ratio of 2%, the crack development was essentially complete, including the occurrence of vertical cracks. There was spalling in the concrete cover at the wall corner, but the concrete remained intact, especially confined concrete reinforced with stirrups. Comparing the crack distributions, it can be observed that the steel fiber-reinforced walls had denser crack distribution. During the test, it was observed that although specimens without steel fibers had fewer cracks, the crack widths were larger. Regardless of aspect ratio, the crack propagation range in the steel fibers-reinforced specimens was limited, and this phenomenon was more pronounced in slender walls.

At the end of the loading process, the walls showed no significant damage, including both the compressive concrete and the tensile reinforcement. However, the lateral resistance of the wall sharply decreased. After finishing the test, it was discovered that damage had occurred at the anchorage of the UHSB from the cut foundation. The reinforcement was unable to transfer the force to the anchorage plate, resulting in a rapid decline in the lateral resistance. It is recommended the treatment of the UHSB at the anchoring plate needs improvement, such as increasing the cross-section area at both ends or considering alternative threading methods. Alternatively, enhance the bond strength of the reinforcement within the anchorage zone to alleviate the strain penetration effect in this area.

3.2 Global response

The overall response of all specimens is summarized in Fig.8, which incorporates the envelope of the hysteresis curves for each specimen, known as the skeleton curves. The drift ratio is defined as the relative horizontal displacement divided by the calculated wall height (H = 1750 mm). Net horizontal displacement refers to the difference in horizontal displacement between the loading point and the foundation beam. The calculated wall height (H) is the distance between the top surface of the foundation and the midpoint of the loading beam. Additionally, a comparison of the skeleton curves is also provided in Fig.9.

The solid black lines in Fig.8 represent the hysteresis curves of the test walls. It can be observed that before the sudden decrease of lateral force, the hysteresis curves exhibited significant pinching. However, the lateral forces maintained continuous and stable growth as the drift ratio increased. In the elastic stage, test walls all exhibited large stiffness, leading to a rapid increase in lateral force. The formation of flexural cracks and plastic deformation of steel bars and concrete were responsible for the sharply reduced stiffness. However, the lateral force remained steadily increase due to elasticity of UHSB. In comparison, mid-rise walls exhibited a faster growth in lateral force, resulting in higher lateral resistance compared to slender walls. Regardless of the aspect ratio, it can be concluded that the hysteresis curves of test walls with steel fibers were slightly plumper. The improved toughness of SRAC led to slightly better energy dissipation performance than that of RAC walls.

Fig.9 illustrates a comparison of the skeleton curves for all specimens. All skeleton curves exhibited a consistent growth pattern, consisting of three stages, before the failure of the walls. In the first stage, the test walls were predominantly in the elastic state, and the lateral force can be approximately considered as linear elastic growth with the increase of horizontal displacement. This stage was commonly considered to occur before the appearance of flexural cracks. The second stage was characterized by a rapid decline in stiffness. With the appearance of horizontal cracks, the effective load-bearing area of the wall section decreased significantly. Coupled with the nonlinear behavior of the materials, this led to a significant degradation in stiffness. Subsequently, the wall entered the third stage, in which the effective load-bearing area of the wall underwent minimal changes. Due to the elastic state of UHSB, the lateral force resistance continued to increase steadily. Since the concrete maintained good integrity until the end of the loading, adding steel fibers had a limited impact on the hysteretic response.

Due to the weakness effect of threading treatment to the UHSB, there was a sudden drop in the lateral force at the end of the tests. However, all test walls can be loaded up to 2% drift ratio, which was a reasonable limit for performance-based design and widely adopted in many design guidelines. Therefore, this study primarily focused on the response before 2% drift ratio.

3.3 Curvature distribution

Fig.10 represents the curvature distribution along the height for different states and performance objectives with corresponding drift ratio limits specified in FEMA 356 [2], 0.1% (elastic state), 0.5% (IO), 1.0% (LS), 1.5%, and 2.0% (CP). The curvature was calculated by measuring the vertical deformation in four sections along the wall height (three sections for mid-rise walls). Since the slip of weakly bonded reinforcement was difficult to directly measure in the experiment, the bottom curvature also included the deformation resulting from the slip of UHSB.

During the initial loading stage, the curvature exhibited a nearly linear distribution along the height. As the drift ratio increased, the curvature gradually increased and showed a nonlinear distribution along the wall height. Due to concentrated damage, the curvature experienced a rapid increase at the bottom. The curvature distribution of mid-rise shear walls was concentrated at the lower part, approximately 300 mm height above the foundation, while slender walls showed a more concentrated curvature distribution around 400–600 mm above the foundation. The curvature distribution in the upper portion was more uniform for shear walls with the same aspect ratio when steel fibers were added.

3.4 Plastic hinge length

In engineering calculations, simplified plastic hinge models were commonly used to approximate the actual curvature distribution. This involved representing the nonlinear curvature distribution as a uniform distribution within the plastic hinge region, as shown in Fig.11. It was commonly held that the section rotation obtained from vertical LVDTs in walls comprised contributions from both flexural deformation and shear deformation. Therefore, section rotations can be obtained in the test at four measurement sections (three measurement sections for mid-rise walls). Under the target drift, the section rotation at a specific height can be calculated based on the given ratio of flexural deformation contribution and the plastic hinge length. The calculation can be performed using the following equations. As shown in Fig.12, the measured horizontal deformation in the test included both flexural deformation and shear deformation.

1) Assuming the ratio of horizontal displacement caused by flexural deformation (Δ_f) to total horizontal displacement (Δ) is α, and the plastic hinge length (l_p) is β times the wall length (l). Thus, the shear deformation contribution can be expressed by (1 − α) × Δ.

2) As shown in Fig.13, if the shear deformation was known, according to the Eq. (7), the angle, tanψ_si, contributed by the shear deformation in the measurement of section rotate at a specific height, h_i can be calculated.

3) For a given horizontal displacement, based on the flexural deformation and plastic hinge length, the section rotates (tanψ_fi) contributed by flexural deformation in the measurement of section rotation at a specific height (h_i) can be calculated, according to Eq. (9).

4) The calculated angle (tanψ_cal,i), the sum of the angle contributed by shear deformation and flexural deformation, was compared with the measured sectional angle (tanψ_exp,i) at different heights. The sectional rotations at heights of 200, 400, 800, and 1200 mm in slender walls (200, 400, and 800 mm for mid-rise walls) can be measured and used for above assumption verification. If the error (ξ) was within an acceptable range, it indicated that the values of α and β in the plastic hinge model were reasonable.

(1){\mathrm{\Delta }}_{\mathrm{f}}=\alpha \mathrm{\Delta },

(2){\mathrm{\Delta }}_{\mathrm{s}}=(1-\alpha )\mathrm{\Delta }.

Measured sectional rotate generated by shear deformation at height of h_i:

(3)\tan {\theta }_{\mathrm{s}}=\frac{{\mathrm{\Delta }}_{\mathrm{s}}}{H},

(4)\delta (h_i)={\mathrm{\Delta }}_{\mathrm{s}}\frac{h_i}{H},

(5)v_{\mathrm{p}\mathrm{a}\mathrm{s}\mathrm{h}}\left(h_i\right)=\left(x+\delta \left(h_i\right)\right)\tan \theta ,

(6)v_{\mathrm{p}\mathrm{a}\mathrm{l}\mathrm{l}}\left(h_i\right)=\left(x-\delta \left(h_i\right)\right)\tan \theta ,

(7)\tan {\mathrm{\Psi }}_{si}=\frac{V_{\mathrm{p}\mathrm{u}\mathrm{s}\mathrm{h}}(h_i)+V_{\mathrm{p}\mathrm{u}\mathrm{l}\mathrm{l}}(h_i)}{2x+l}.

Measured sectional rotate generated by bending deformation at height of h_i:

(8)\phi =\frac{{\mathrm{\Delta }}_f}{(H-(l_{\mathrm{p}}/2))l_{\mathrm{p}}},

(9)\tan {{\psi }_{\mathrm{f}}}_i=\{\begin{array}{ll}\phi \cdot h,& h_i⩽l_{\mathrm{p}},\\ \phi \cdot l_{\mathrm{p}},& h_i>l_{\mathrm{p}},\end{array}

(10)\tan {\mathrm{\Psi }}_{\mathrm{c}\mathrm{a}\mathrm{l},i}=\tan {\mathrm{\Psi }}_{\mathrm{f}i}+\tan {\psi }_{\mathrm{s}i},

(11)\xi =\sum _{i=1}^n(\tan {\mathrm{\Psi }}_{\mathrm{c}\mathrm{a}\mathrm{l},i}-\tan {\mathrm{\Psi }}_{\mathrm{e}\mathrm{x}\mathrm{p},i}{)}^2.

Based on the above equations, the plastic hinge length of the test walls can be determined, and the calculated plastic hinge lengths are provided in Tab.4.

3.5 Strain distribution in longitudinal bars

The development of reinforcement strain during the loading process was monitored using strain gauges. The distribution of UHSB strain along the height at different drift ratio corresponding to various performance objectives limits is shown in Fig.14. In the elastic stage, the strain distribution along the height was approximately linear. As the loading displacement increased, the strain distribution exhibited nonlinearity. Due to the slip of UHSB, the distribution pattern of tensile strain differed from that of the conventional ribbed bars. At a certain height, there was a significant change in the rate of strain variation with height, which fell within the range of 300 to 600 mm.

It can be observed from compressive strain of UHSB that strain distribution performed more uniformly along the height in the test walls reinforced with steel fibers. The compressed strain in SN-2.2 and SN-1. exhibited a more concentrated distribution at the bottom of the walls. Based on the distribution of compressive strain, it can be inferred that the curvature generated by flexural deformation was more evenly distributed along the height. This can be explained by that the presence of steel fibers suppressed cracking. Thus, the stiffness degradation of the critical section was slower, and the damage was not excessively concentrated. Similar conclusions have been obtained in other studies [37,45], where specimens with steel fibers or higher steel fiber content exhibited a more uniform distribution of curvature.

3.6 Residual deformation

Residual deformation was widely recognized as an indicator to evaluate the resilient performance, as acknowledged by many studies [46–48]. When the lateral force was unloaded to zero, it was considered to have reached the residual drift. Fig.15 illustrates the residual drift ratio of the test walls at loading level, up to target drift ratio of 2% (corresponding to the interstory drift limit for MCE). The two red dashed lines in Fig.15 correspond to the threshold value for the IO and LS performance levels specified in FEMA 356 [2], which are 0.125% and 0.5%, respectively.

It was evident that all test walls met the IO performance level before 1% target drift ratio, as the residual drift ratios were less than 0.125%. This indicated that the walls can be reoccupied immediately without necessitating any repairs. Within the 2% drift ratio, the residual drift ratios of the test walls were significantly smaller than 0.5% specified according to LS performance objectives. A residual drift ratio of 0.5% was considered to indicate significant damage to structural components, requiring repairs before re-occupancy. However, post-earthquake repairs were often deemed impractical due to the economic considerations. McCormick et al. [49] concluded that a residual drift ratio limit of 0.5% was based on economic factors. In addition, considering the damage to the specimens, the test walls exhibited minimal damage with a small area of concrete spalling and the confined concrete remained intact, which indicated satisfied resilient performance.

4 Hysteresis curves calculation

4.1 Calculation methods

Further research parameters need to be discussed, and a computational model for test walls was established based on the present specimen dimensions and reinforcement details. Due to limitations in the failure mode, the proposed computational model analyzed the hysteretic behavior of the test walls up to 2% drift ratio and compared with the experimental results. For walls reaching a 2% drift ratio, it corresponds to the threshold value specified for CP in code FEMA 356 [2], and exceeds the displacement angle limit of 1/100 for elastic-plastic interstory drift specified in GB 50011-2010 [50]. After 2% drift ratio, other structural or non-structural components will also experience obvious severe damage, significantly reducing the structural repair speed and recoverability. Therefore, focusing on the hysteretic behavior of walls before 2% drift ratio is also essential, and it is crucial for analyzing their influence on the seismic performance of the structure.

The computational model was taken SN-2.2 and SN-1.5 as reference. In the models, for columns or shear walls primarily dominated by flexure, the commonly adopted approach was based on the plastic hinge assumption. Flexural deformation was concentrated within the plastic hinge region, where the curvature was assumed to be evenly distributed. Therefore, it was reasonable to assume that the bond strength within the plastic hinge region was zero, and the concrete behavior can be characterized based on the plane section assumption. Based on the Funato model [29], Sun et al. [51] proposed a model that incorporated spring elements to consider the bond relationship between the reinforcement and concrete. This model obtained the reinforcement stress considering the allowance for UHSB slip. The schematic diagram of the calculation model is shown in Fig.16. Based on the proposed calculation model by Ref. [52] for columns reinforced with UHSB, the present research conducted calculations on the test walls and further parameters analysis. The analysis results mentioned above have indicated that the deformation of test walls was primarily due to flexural deformation. Therefore, it was reasonable to apply this model to the present research.

In this model, the specimen was divided into three sections, including the plastic hinge region at the bottom of the wall with uniformly distributed curvature, the upper part of the plastic hinge region, and the reinforcement anchorage section within the foundation. The flowchart of the calculation model is shown in Fig.17.

1) The drift ratios resulting from bending, θ_f, can be obtained based on calculated ratio, α. Then, the curvature within the plastic hinge region can be determined for a given strain at the center of section, ε_k, based on which the strain distribution that confirms to the plane section assumption can be obtained. It assumed that the UHSB inside the foundation experienced a slip displacement s_f1 at the surface of the foundation.

2) For the stress of UHSB on the surface of the foundation, an initial value, denoted as “f_f1”, was given. The boundary conditions were determined through an iterative calculation process. Subsequently, a verification procedure was conducted to ensure the accuracy and validity of these obtained boundary conditions. If the boundary conditions were not satisfied, the initial value, f_f1, would be reassumed.

3) On the basis of steel stress f_c1 and the assumed steel slip displacement s_c1, the slip displacement s_ck and reinforcement stress f_ck generated in Section III can be obtained. Similar to the calculation process in step 2, the steel reinforcement stress f_c1 can be determined.

4) If the equality f_c1 = f_f1 held true, it demonstrated that the stress and slip obtained in the aforementioned steps accurately represented the actual state of UHSB. And calculate the sum of the internal forces in concrete and steel, P. If the difference between the sum of internal forces, P, and the applied external force, N, falls within an acceptable range, the assumed strain, ε_k, is considered reasonable.

In addition, the calculation model required the following assumptions to be made.

1) The tensile stress in concrete was ignored. 2) The concrete within the same cross-section satisfied the plane section assumption. 3) Horizontal displacement was considered concentrated within the plastic hinge region. 4) The bond strength of UHSB was 3 MPa.

In Fig.17, θ represents arbitrary loading drift ratios and θ_f represents the drift ratios caused by bending; ϕ is the curvature of the plastic hinge region corresponding to the loading drift ratio θ_n. l_p is used to indicate the length of the plastic hinge region. The foundation and the upper part above the plastic hinge region are divided into m and k fiber segments. ε_ct is the calculated tensile strain of the concrete according to the plane section assumption. s_f1 and f_f1 refer to the slip and stress of the UHSB on the side near the plastic hinge region in the foundation, s_c1 and f_c1 are the slip and stress of the UHSB on the side near the plastic hinge region in the upper part of the wall panel. d represents the diameter of the longitudinal steel reinforcement. τ(s) represents the bond stress as a function of slip displacement, established based on the Funato model [29]. δ_f and δ_c represent the lengths of the fibers divided in the foundation and the upper part above the plastic hinge region, respectively. s_fi and f_fi represent the slip displacement and steel reinforcement stress, respectively, of the ith fiber in the foundation. s_cj and f_cj represent the slip displacement and steel reinforcement stress of the jth fiber in the part above the plastic hinge region. l_total refers to the overall deformation of the tensile steel reinforcement in the plastic hinge region. ε_lp is the tensile strain of UHSB in the plastic hinge region. ε_ct refers to the deformation of the tensile concrete calculated based on the plane cross-section assumption. s represents the sum of slip displacements of the steel reinforcement.

4.2 Material constitutive behavior

4.2.1 Steel constitutive behavior

The longitudinal steel reinforcement used in the wall model includes UHSB and HRB 600 steel reinforcement. Due to the lack of a distinct yield point, the Menegotto and Pinto model [53] was adopted for the calculations, as show in Eq. (12). The values of Q and ε_ch are 0.0013 and 0.0074 for UHSB. The steel reinforcement model used in the experiments is shown in Fig.18. The unloading and reloading calculation process can be obtained in Ref. [54].

(12)f_{\mathrm{s}}=E_{\mathrm{s}}{\epsilon }_{\mathrm{s}}\left\{Q+\frac{1-Q}{{\left(1+|{\epsilon }_{\mathrm{s}}/{\epsilon }_{\mathrm{c}\mathrm{h}}{|}^N\right)}^{1/N}}\right\}.

4.2.2 Concrete constitutive behavior

The concrete constitutive behavior was calculated using the Sakino−Sun model [55], as shown in Eq. (13). The constraint effect was not considered for cover concrete, in which strength enhancement factor K was taken as 1. In the boundary elements, the constraint of the concrete surrounded by stirrups was considered, and the strength enhancement factor K was calculated based on the model [55]. The cylinder compressive strength used in the constitutive model calculation was obtained by converting the cubic compressive strength measured in tests, as shown in Tab.5. The peak strain of natural aggregate concrete with same strength of RAC was determined using Guo model [56]. Then method proposed by Ref. [57] was utilized to calculated the peak strain of RAC. The peak strain of SRAC was modified based on peak strain of RAC according to Ref. [58] The specific parameters for three types of concrete are provided in Tab.5. The obtained constitutive model is presented in Fig.19.

(13)f_{\mathrm{c}}=K{f}_{\mathrm{p}}\frac{aX+(b-1)X^2}{1+(a-2)X+b{X}^2}.

4.3 Comparison with experimental results

The hysteresis curves obtained from the calculation based on the above assumptions and the material constitutive behavior were compared with the experimental curves of all test walls, as shown in Fig.20. It can be observed that, except for slightly higher initial stiffness and smaller residual displacements in the calculated results, there was a small discrepancy between the computed results and the experimental results. This indicated that the calculation method can be applied to the test walls with good accuracy. To further verify the calculated results, the strain development of the UHSB in the plastic hinge region was extracted and compared with the measured results at a position 50 mm above the foundation, shown in Fig.21. Except for the calculated compressive strain of reinforcement being slightly smaller than that of the experiment, calculated results can be brought in good agreement with the strain of UHSB.

4.4 Parametric analysis

Building upon the calculation method, detailed parameter analyses were conducted to examine the effects of various design parameters on the hysteresis response for slender walls and mid-rise walls, based on SN-2.2 and SN-1.5 configuration. The parameters investigated included ALR, longitudinal reinforcement ratio and stirrup ratio in the boundary elements.

4.4.1 Longitudinal reinforcement ratio

Longitudinal reinforcements in the boundary elements played a critical role in the resilient performance of the specimens, which captured the interest of researchers. Therefore, the following discussion primarily focuses on the influence of the reinforcement ratio of UHSB on the hysteretic performance. Fig.22 presents the hysteretic response of mid-rise walls and slender walls with varying longitudinal reinforcement ratios.

It is evident that the increasing reinforcement ratio in the boundary elements led to a significant increase of the secondary stiffness, exhibiting a more pronounced drift-hardening behavior. With an increase in longitudinal reinforcement ratio, the lateral force at 2% drift ratio clearly increased. However, it can be observed that the residual displacements of the shear walls are relatively small and similar, indicating increasing the UHSB had little impact on the residual deformation of simulated walls within the investigated range of UHSB ratio.

4.4.2 Stirrup ratio

Sufficient stirrups were arranged in the boundary elements to confine the boundary concrete, prevent premature failure, and improve the concrete toughness, which promoted the resilient performance of the wall. During loading, no significant concrete damage was observed. Therefore, in the numerical calculations, it aimed to verify the influence of stirrup ratio.

Test results were compared with calculated results designed according to the minimum stirrup ratio in the boundary elements specified in ACI-318 [59]. For slender walls and mid-rise walls, the specified transverse reinforcement ratios in the boundary elements are 1.25% and 1.5%, respectively. By comparing the development of concrete strains in the plastic hinge region shown in Fig.23, it is evident that walls with higher stirrup ratios exhibited a slower progression of compressive concrete strains. This indicated that increasing the concrete confinement can effectively delay the development of compressive strains. Concurrently, it can be observed that specimens with stronger confinement experienced faster development of tensile strains. This observation suggested a reduction of the compressed zone.

Furthermore, the results in Fig.24 showed that the reduced confinement in the boundary elements only led to a modest decrease of approximately 6% in the lateral resistance at 2% drift ratio. This can be attributed to the fact that, until 2% drift ratio, the test walls experienced minimal concrete damage in the boundary elements, with only concrete spalling observed at the wall toe. Therefore, it can be concluded that within the permissible range according to the codes ACI 318-19 [59], reducing the stirrup ratio had little effect on the hysteresis curves before 2% drift ratio.

4.4.3 Axial load ratio

The ALR is also one of the main factors influencing the seismic performance of the wall. In the analysis of the influence of ALR on the hysteresis response of the walls, the effect of ALR on the plastic hinge length was considered. The plastic hinge lengths of the calculated wall with varying ALR were adjusted using the formula proposed in Ref. [60]. The plastic hinge lengths for different ALR are listed in Tab.6.

To provide a clearer illustration, the present research shows comparisons of the skeleton curves under different ALR for slender walls and mid-rise walls in Fig.25. It was evident that increasing ALR significantly improved the stiffness and lateral resistance. Comparing specimens with different ALR, it was obvious that lateral force increased with the increase of the ALR. For lower ALR, with each incremental of 0.1 in ALR, the lateral force increased by approximately 6% at 2% drift ratio. As the ALR continued to increase, the lateral force growth rate decreased. With an excessive ALR, a declining segment in the lateral force emerged before reaching 2% drift ratio, and the peak bearing capacity gradually decreased. In consideration of the lateral force, it was recommended to limit ALR of slender walls and mid-rise walls to be controlled within 0.19 and 0.15. Exceeding the threshold values may result in more substantial damage prior to a 2% drift (corresponding to MCE), which was unfavorable for the performance-based design of resilient walls.

Fig.26 compares the residual drift ratios of calculated walls under different ALR. With the ALR equal to 0, the wall with UHSB still satisfied the limit of residual drift less than 0.5% at a 2% drift ratio. In addition, it can be observed that increasing ALR within a certain range can reduce the residual drift of the walls, thereby improving the resilient performance. However, excessive ALR led to an increase in residual drift, particularly in slender walls. For slender walls, the test ALR limit was recommended as 0.15, beyond which the residual drift increased with the increase of ALR. When ALR was greater than 0.5, the residual drift increased significantly, and at 2% drift ratio, the residual drift even almost reaches exceeded the limit of 0.5%. Similarly, a recommended threshold of 0.15 for test ALR was suggested for mid-rise walls.

5 Conclusions

The current research presented a detailed analysis of four walls consisting of UHSB, including two mid-rise walls and two slender walls, tested under cyclic lateral force and constant axial load. The experimental results were analyzed in terms of damage evolution, overall response, curvature profiles, strain of UHSB, and residual drift ratio. The analytical results presented in the present research could draw the following conclusions.

1) Regardless of aspect ratio, flexural cracks were predominant in all specimens. All test walls demonstrated satisfactory drift-hardening behavior, with the lateral force steadily increasing until the end of the loading. The mid-rise walls, due to smaller shear span, exhibited greater stiffness and could withstand higher lateral forces. All test walls were able to reach a 2% drift ratio, satisfying the drift ratio limit specified by the design code for the performance objective of CP.

2) All test walls exhibited relatively uniform curvature distribution. For the mid-rise walls, the curvature distribution was concentrated below the height of 300 mm, while for the slender walls, this concentration was found below height ranging from 400 to 600 mm. Adding steel fibers resulted in a more uniform distribution of curvature except at the bottom. Based on the curvature distribution, the calculated plastic hinge lengths ranged from 0.48l to 0.62l for slender walls, while, the plastic hinge lengths ranged from 0.36l to 0.39l for mid-rise walls.

3) Prior to 2% drift ratio, all test walls exhibited relatively small residual drift ratios, with the maximum residual drift ratio of 0.27%. The test walls were able to meet the IO performance objective with a residual drift ratio limit of 0.125% before a loading drift ratio of 1%. Furthermore, before reaching a 2% drift ratio, specimens were able to satisfy LS performance objective, of which the threshold drift ratio is 0.5%.

4) The present study employed a calculation model that considered the slip of UHSB and investigated the influence of longitudinal reinforcement ratio, stirrup ratio, and ALR on the hysteresis behavior. The decreased longitudinal reinforcement ratio significantly reduced the secondary stiffness but had less influence on residual performance before 2% drift ratio. Similarly, the stirrup ratio had a minimal impact on the hysteresis behavior before 2% drift ratio. However, excessive ALR increased residual drift ratio, therefore, it was recommended to keep the test ALR below 0.15 for the test walls.

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