Behavior of Nonconforming Flexure-Controlled RC Structural Walls Under Reversed Cyclic Lateral Loading

Abstract

Reinforced concrete (RC) structural walls are essential for ensuring adequate lateral stiffness and strength in buildings located in seismic regions. However, many older structures incorporate nonconforming walls constructed with low-strength concrete, plain longitudinal reinforcement, and insufficient boundary confinement, and experimental data on such systems remain limited. This study investigates the seismic performance of two full-scale, relatively slender nonconforming RC wall specimens representative of older construction: one with no boundary confinement (SW-NC-FF) and one with insufficient confinement (SW-IC-FF). Both specimens exhibited flexure-controlled behavior, with initial yielding of boundary longitudinal bars occurring at an approximately 0.30% drift ratio and maximum reinforcement tensile strains of 0.006 (SW-IC-FF) and 0.015 (SW-NC-FF). Rocking governed the lateral response due to progressive debonding of the plain bars along the wall height, producing pronounced pinching and self-centering behavior. Failure occurred through longitudinal bar buckling and concrete crushing, with ultimate drift ratios of 2.0% and 1.5% and displacement ductility values of 4.0 and 4.3 for SW-IC-FF and SW-NC-FF, respectively. Experimental results were compared with backbone predictions from ASCE 41:2023, NZ C5:2025, and EN 1998-3:2025. While all three guidelines captured initial stiffness and yield rotations, their rotation-capacity predictions diverged, underscoring the need for improved assessment approaches for rocking-dominated, plain-reinforced walls.

1. Introduction

The significance of reinforced concrete (RC) structural walls in design and seismic performance of multistory buildings has been well established, particularly as walls that are well-positioned in the structural system effectively resist the lateral loads induced by wind or seismic actions [1]. Compared to framed systems, RC walls provide greater lateral stiffness, thereby reducing displacement demands during frequent earthquakes. For minimizing structural damage under moderate-level earthquakes, sufficient strength can be achieved through appropriately designed longitudinal reinforcement and horizontal web reinforcement, while ductile detailing and providing confinement at wall boundaries ensures a ductile response and prevents brittle failure during severe seismic events [2].

Flexure-controlled slender walls typically exhibit one of two failure modes under lateral loading: flexural or flexural-shear. The failure mode is influenced by the wall geometry, reinforcement amount and configuration, loading conditions (e.g., shear-span-to-depth ratio), and material properties. As shown in Figure 1a, flexural behavior is defined by the yielding of longitudinal reinforcement prior to the crushing of confined concrete at the wall boundaries. Displacement (drift) capacity is reached upon core concrete crushing and buckling of longitudinal boundary reinforcement, rupture or post-buckling rupture of boundary reinforcement, or lateral instability (out-of-plane buckling) at the wall boundaries due to formation of an exceedingly thin confined core once the cover concrete has spalled, together with imperfect crack closure after yielding of longitudinal reinforcement. As will be demonstrated in this paper, rocking-type deformation of the wall, in the form of large rotations accumulating at the wall–pedestal (W–P) interface crack, which arises from debonding of longitudinal reinforcement bars from surrounding concrete (both in the pedestal and along wall height), may also contribute significantly to wall top displacements, especially when the wall incorporates plain longitudinal bars. Flexural-shear behavior, as illustrated in Figure 1b, is typically observed in walls subjected to high shear demands (i.e., with relatively low shear span-to-depth ratios), and is characterized by the development of flexural cracks and yielding of longitudinal boundary reinforcement within the wall plastic hinge region, together with (or followed by) formation of diagonal shear cracks on the wall, yielding of horizontal web reinforcement (in some cases), and eventual crushing of concrete under combined flexural (vertical) and shear (diagonal) compressive stress demands.

A considerable number of experimental studies are available in the literature on relatively slender RC walls with rectangular cross-sections. Early investigations examined the effects of openings [3], as well as load–displacement behavior, energy dissipation, ductility, and design procedures under reversed cyclic lateral loading with varying cross-sectional properties [4]. Subsequent research explored the relationship between wall shear capacity and concrete compressive strength in the compression zone [5,6,7] and assessed RC–wall behavior in mid-rise buildings designed per the Iranian seismic code [8]. The influence of axial–load ratio, shear–compression ratio, and longitudinal reinforcement type was also investigated [9]. Further studies analyzed the role of boundary transverse reinforcement on deformation capacity [10] and emphasized the need for web vertical reinforcement to prevent sliding-shear failure at negligible axial load [11]. Data were also reported for rectangular and T-shaped walls with moderate boundary confinement [12]. The effects of varying concrete compressive strength on reversed cyclic behavior were subsequently examined [13], while the combined influence of axial load ratio and confinement on the seismic response of RC structural walls was investigated under simulated loading conditions [14]. The detailing and ductility of longitudinal reinforcement were studied [15], and drift-capacity equations were proposed, along with an evaluation of the contribution of boundary transverse reinforcement [16]. The effects of aspect ratio, shear stress, and axial load on deformation capacity, as well as the shear–flexure interaction, were further explored [17]. Additional investigations assessed the applicability of the plane-sections assumption and the role of boundary regions in moment–curvature behavior [18]. The influence of high axial loads on walls with unconfined boundaries was evaluated [19], while other studies examined the impact of various design parameters—including wall thickness, aspect ratio, reinforcement detailing, and boundary detailing—typical of Chilean residential buildings [20]. Large-scale testing was also conducted on a wall dominated by flexure–shear interaction [21], and the hysteretic response of flexure-dominant RC walls detailed with minimum vertical reinforcement per New Zealand standards was evaluated [22]. The effects of lap splices and transverse reinforcement were analyzed [23], and flexure-controlled thin walls from Colombian buildings were investigated [24]. Full-scale experiments on ultra-high-performance concrete walls with varying axial–load ratios were presented [25], while additional tests on cantilever walls designed per ACI 318 under different axial loads were performed [26], and slenderness effects on lateral stability were examined [27]. Lastly, the seismic performance of previously damaged walls with unconfined boundaries was evaluated [28].

Although numerous experimental studies have examined the behavior of slender RC walls—including specimens tested with and without boundary confinement—the available literature has largely focused on walls constructed with deformed longitudinal reinforcement and relatively higher concrete strength. These configurations do not reflect the characteristic conditions frequently observed in older RC buildings, where plain longitudinal reinforcement, low concrete strength, and inadequate confinement typically coexist. The present study directly investigates this wall typology and provides full-scale experimental evidence for deformation mechanisms that have not been captured in prior research.

In contrast, experimental studies in the literature on nonconforming and substandard RC walls are limited. These walls—common in older residential buildings (Figure 2)—typically exhibit low-strength concrete, plain reinforcement, and absent or inadequate boundary confinement. For such walls, modeling parameters (e.g., plastic hinge rotations) in assessment/retrofit guidelines (e.g., ASCE 41:2023 [29], NZ C5:2025 [30], and EN 1998-3:2025 [31]) are based on limited experimental data. To address this gap, the present study investigates the lateral load responses and failure modes of such walls, providing experimental insights and comparing the results with modeling parameters recommended in current seismic assessment guidelines. The full-scale testing program was conducted within a fixed laboratory schedule, which limited the investigation to two representative wall configurations. These configurations were intentionally selected to isolate the specific influence of boundary confinement deficiency, a defining characteristic of nonconforming RC walls in older building stock.

2. Experimental Program

2.1. Description of the Wall Specimens

Two relatively slender RC wall specimens ($h_w/l_w = 3.0$; where $h_w$ and $l_w$ denote the wall height and length, respectively) were constructed and tested at Istanbul Technical University. They were intentionally detailed for a flexural failure mechanism by limiting flexural capacity to approximately one-half of shear capacity. The specimens incorporated low-strength concrete, plain reinforcing bars, and no transverse cross-ties on the web vertical reinforcement. The boundary region of one wall specimen was unconfined, while that of the other was inadequately confined. These specimens were deliberately designed to represent walls in substandard structures constructed prior to development of modern seismic codes in Türkiye (effective 1998, 2007, and 2018). The height, length, thickness, and shear span-to-depth ratio of the specimens were 3000 mm, 1000 mm, 200 mm, and 2.2, respectively. The dimensions of the foundation block (pedestal) were 600 mm × 800 mm × 1900 mm (depth × width × length). Concrete was cast in three stages: the pedestal, the test unit, and the upper section where axial and horizontal loads were applied. For preventing damage in the upper section (top 1 m), reinforcement spacing was reduced to half, and a relatively higher-strength concrete was also used. The specimen characteristics and designations are provided in

Table 1. Salient properties of the wall specimens used in the experimental program.

Specimen	Horizontal Web Reinf.		Boundary Length Ratio a (%)	${\rho }_b$ (%)	${\rho }_t$ (%)	${\rho }_v$ (%)	${\rho }_{\mathrm{con}}$ (%)
	Anchorage Pattern	Hook Angle
SW-IC-FF	straight	135°	20	1.54	0.39	0.57	0.63
SW-NC-FF	closed hoop	90°	10	2.37	0.39	0.57	NC

Note: SW: Shear Wall, IC: Inadequate Confinement, NC: No Confinement, FF: Flexural Failure. ^a Ratio of the boundary region length to the overall wall length.

. The specimens were named based on the presence of transverse reinforcement at the wall boundaries and the expected failure mode. All longitudinal reinforcement was continuous along the height of both specimens and was well-anchored within the pedestal and upper section of each specimen, as depicted in Figure 3a–c. Specimen SW-IC-FF had insufficient boundary transverse reinforcement with 90° hooks at hoop ends; its horizontal web reinforcement was anchored with 135° hooks. Specimen SW-NC-FF had no boundary transverse reinforcement; its horizontal web reinforcement formed closed hoops with 90° hooks. Boundary lengths were 20% (SW-IC-FF) and 10% (SW-NC-FF) of the wall length (Figure 4). Construction stages are shown in Figure 5. Uniaxial stress–strain curves for 150 mm × 300 mm concrete cylinders and plain reinforcement coupons are given in Figure 6 and Figure 7, respectively. Average concrete compressive strengths were 33.7 MPa (pedestal), 15.1 MPa (test unit), and 43.4 MPa (upper section), per ASTM C39/C39M-24 [33]. The corresponding average modulus of elasticity values ($E_c$) were calculated as 23.4 GPa, 16.1 GPa, and 26.4 GPa, respectively, using the formulation provided in Equation (1) [34].

$$E_c=\left({\sigma }_2-{\sigma }_1\right)/\left({\epsilon }_2-{\epsilon }_1\right)$$

(1)

In Equation (1), ${\sigma }_2$ is the stress at 40% of the ultimate load, ${\epsilon }_1 = 0.00005$, ${\sigma }_1$ is the stress at ${\epsilon }_1$, and ${\epsilon }_2$ is the longitudinal strain at ${\sigma }_2$.

Table 2. Average experimentally measured tensile properties of plain reinforcing steel bars.

Reinf. Bar	$E_s$ (GPa)	$f_y$ (MPa)	${\epsilon }_y$ (%)	${\epsilon }_h$ (%)	$f_{\max }$ (MPa)	${\epsilon }_{\max }$ (%)	${\epsilon }_{\mathrm{rup}}$ (%)
ϕ8	224.8	378	0.168	2.23	522	16.9	37.7
ϕ10	216.6	340	0.157	3.97	425	21.3	43.7
ϕ12	230.3	311	0.135	3.10	414	21.0	47.0
ϕ14	198.6	294	0.148	3.20	396	21.4	41.3

presents the average mechanical properties of plain reinforcement, obtained through direct tensile tests conducted on three samples for each diameter in accordance with ASTM A370-24 [35].

2.2. Experimental Setup and Loading History

The wall specimens were tested under quasi-static reversed cyclic lateral loading with a constant axial compressive load ($N$), corresponding to 20% of the wall cross-sectional area multiplied by concrete compressive strength (Equation (2)), where $t_w$, $l_w$, and $f_c^{\prime }$ denote wall thickness, wall length, and average concrete compressive strength, respectively.

$$N=20\%\left(t_w\times l_w\times f_c^{\prime }\right)\approx 600 \mathrm{kN}$$

(2)

The tests were conducted on isolated cantilever wall specimens subjected to single-curvature loading, using the uniquely designed testing system shown in Figure 8. After leveling of the laboratory floor, the setup was firmly anchored to the strong floor using ten high-strength rods. Roller support frames were then installed 2.7 m above the pedestal, to prevent out-of-plane (i.e., twisting) displacements during in-plane reversed cyclic lateral loading. Subsequently, each specimen’s pedestal was securely attached to the setup with fourteen additional high-strength rods. After installing strain gauges (SGs) and Linear Variable Differential Transformers (LVDTs), lateral loading was applied 2.2 m above the pedestal. The loading protocol, per ACI 374.2R-13 [36], comprised initial force-controlled cycles—gradually increased to the expected cracking load of 45.4 kN—followed by displacement-controlled cycles at drift ratios of 0.3%, 0.5%, 0.75%, 1.0%, 1.5%, 2.0%, 2.5%, 3.0%, and 4.0%. Three cycles were applied up to the yield displacement, and two cycles at each subsequent drift level (Figure 9).

2.3. Instrumentation

Throughout testing, extensive instrumentation was used to measure loads, displacements, deformations, average strain, and reinforcement strain at critical locations on the wall specimens. Horizontal LVDTs measured lateral displacements at the top and mid-height, pedestal sliding, and sliding shear at the wall–pedestal (W–P) interface. Vertically mounted LVDTs were employed to measure average relative rotations along specimen height, average vertical strains at wall base across wall length, vertical displacements resulting from debonding/slip of the wall longitudinal reinforcement (which accumulate at the W–P interface) and the associated rocking-type wall rotation, and the rigid body rotation of the pedestal. Sliding and rigid body rotation of the pedestals were measured to be negligible throughout both tests. Out-of-plane displacements were monitored using LVDTs affixed near the wall boundaries at approximately the elevation of lateral loading, and were also measured to be negligible. Shear deformations were recorded using both vertically mounted LVDTs and those arranged diagonally in an X-shaped configuration along the wall height. The overall layout of the LVDTs is illustrated in Figure 10. SGs were installed on selected longitudinal boundary reinforcement, boundary transverse reinforcement (if any), and vertical/horizontal web reinforcement within 500 mm above the W–P interface to detect yielding in potential plastic-hinge regions. To evaluate strain penetration, additional SGs were affixed to longitudinal boundary bars embedded in the pedestal, extending 300 mm below the W–P interface. In total, 34 and 28 SGs were used for SW-IC-FF and SW-NC-FF, respectively (Figure 11).

3. Experimental Results

During testing, the first hairline crack at the W–P interface was identified at the second stage of the force-controlled phase ($M_{\mathit{cr}}$) for SW-IC-FF and at the initial cycle of the displacement-controlled phase (${0.5∆}_y$) for SW-NC-FF; in both cases, the maximum crack width reached 0.1 mm during the third cycle. Initial reinforcement yielding occurred at a drift ratio of 0.30% in both specimens. Diagonal cracks were first observed on both specimens at a drift ratio of 0.50%, with a maximum crack width of 0.40 mm. At 0.75% drift, vertical cracks began to form at the wall boundaries, marking the onset of concrete cover crushing in these regions. Concrete core spalling first occurred in the boundary zones at 1.50% drift for both specimens, followed by simultaneous buckling of the two outermost ϕ14 longitudinal boundary bars in each boundary zone. With further drift to 2.5% (SW-IC-FF) and 2.0% (SW-NC-FF), concrete core crushing propagated inward along the wall base, affecting the second row of longitudinal boundary bars and causing buckling of the adjacent two ϕ14 bars. At the final drift level of 4.0%, the failure mechanism was governed by concrete core crushing and reinforcement bar buckling, collectively resulting in a flexural failure mode. At this drift level, the tests were terminated to protect the instrumentation, following lateral load degradations of 32.8% (SW-IC-FF) and 35% (SW-NC-FF). Maximum tensile strains in the longitudinal reinforcement were approximately 0.006 (SW-IC-FF) and 0.015 (SW-NC-FF). In SW-IC-FF, the horizontal web and boundary transverse reinforcement reached approximately 82% and 55% of the yield strain, respectively, whereas in SW-NC-FF, the horizontal web reinforcement attained nearly 92% of the yield strain. The 90° hooks of the boundary transverse reinforcement (SW-IC-FF) and the horizontal web bars (SW-NC-FF) remained fully intact without evidence of hook opening throughout the tests. The damage progression observed during the tests is depicted in Figure 12.

The W–P interface crack was identified as the primary crack in the specimens and was observed to widen progressively throughout the loading process. At a drift level of 1.50%, the maximum widths of the flexural cracks on the wall, flexural cracks at the W–P interface, and shear cracks on the wall were measured as 1.4 mm, 7.8 mm, and 1.9 mm, respectively, for specimen SW-IC-FF. In contrast, for specimen SW-NC-FF, which exhibited a better-distributed crack pattern, the corresponding crack widths were 1.0 mm, 7.6 mm, and 1.5 mm. For both specimens, flexural cracks at the W–P interface were significantly wider than those on the wall. This observation suggests that uplift of the wall specimens at the W–P interface, due to debonding of the plain longitudinal bars (both in the pedestal and along wall height) and the associated rocking-type rotation of the walls, contributed significantly to wall lateral displacements. The observed distribution of the cracks is illustrated in Figure 13.

The hysteretic responses of both specimens were remarkably comparable (Figure 14a,b), characterized by highly pinched loops and negligible residual displacements. These characteristics jointly affirm a self-centering, rocking-dominant mechanism. This behavior fundamentally implies that the progressive debonding of the plain longitudinal bars at the W–P interface, in conjunction with the limited reinforcement yielding observed, governed the overall seismic performance of the walls. Ultimate drift capacities were 2.0% (SW-IC-FF) and 1.50% (SW-NC-FF). Despite similar quantities of longitudinal boundary reinforcement, the more concentrated boundary layout in SW-NC-FF produced slightly higher lateral stiffness and load capacity (Figure 14c). Peak lateral loads were +211.2/−207.4 kN at ±1.50% drift for SW-IC-FF and +212.6/−209.4 kN at ±1.00% for SW-NC-FF. Post-peak degradation in both walls was governed by progressive concrete core crushing and boundary-bar buckling; the inadequately confined SW-IC-FF exhibited a slightly more gradual strength loss and a delayed buckling onset. The average yield drift (${\delta }_y$) for the idealized bilinear representation—defined using the secant stiffness at 75% of peak load [37]—was 0.50% (SW-IC-FF) and 0.35% (SW-NC-FF), while the ultimate drift (${\delta }_u$) was 2.00% and 1.50%, giving displacement ductilities μ = 4.0 and 4.3, respectively (Figure 14d).

For drift ratios up to 2.0%, average vertical concrete compressive strains along wall height, derived from the outermost vertical LVDTs installed on the boundaries (Figure 10), localized within the bottom 0–50 mm (Figure 15a,c). In addition, Figure 15b,d show the average vertical concrete strain distributions at the wall base along the wall length, including both tensile and compressive strains. For most drift levels prior to strength degradation, the depth of the compression region (neutral axis depth) remained close to 200 mm at the base of both specimens. The maximum average compressive strains measured along 50 mm of the wall base were 0.033 (SW-IC-FF) and 0.021 (SW-NC-FF). Cylinder tests on the test-unit concrete indicated an average compressive strain of approximately 0.004 at a 15% reduction from peak stress (Figure 6b). At 0.5% drift, the threshold was exceeded only in the outermost vertical LVDTs at the wall boundaries over the lower 50 mm, where compressive strains reached 0.007 and 0.004 for SW-IC-FF and SW-NC-FF, respectively. Relative rotation distributions up to 2.0% drift were also concentrated within the bottom 50 mm (Figure 16a,b). This observation corroborates the rocking-dominated response evidenced by the large W–P interface crack widths. This behavior is discussed in further detail in the following section.

Table 3. Overview of loading conditions and experimental results with ACI-318 predictions.

Specimen	ALR (%)	SSDR	$V_u$ (kN)	$V@M_{n,\mathit{ACI}}$ (kN)	$V_{n,\mathit{ACI}}$ (kN)	${\delta }_y$ (%)	${\delta }_u$ (%)	Governing Failure Mode
SW-IC-FF	20	2.2	209.3	196.5	399.4	0.3	2.0	BB/CCC
SW-NC-FF	20	2.2	211	199.8	399.4	0.3	1.5	BB/CCC

provides the test results, including drift ratios, failure modes, and calculated flexural and shear capacities, along with the corresponding loading conditions (i.e., shear span-to-depth ratio) of the wall specimens. The slightly higher drift capacity of SW-IC-FF (2.0%) can be attributed to the presence of transverse reinforcement in the boundary regions, which, although still not compliant with ACI 318, resulted in slightly improved drift capacity compared to specimen SW-NC-FF (1.5%) without any boundary confinement.

4. Discretizing of Deformation Contributions to Wall Displacements

The test data were analyzed to quantify the contributions of flexural, shear, and slip-induced (debonding-induced) rocking deformations to the overall lateral displacement of the wall specimens throughout different loading stages. Figure 17a–c illustrate these primary deformation components.

Rocking, flexural, and shear deformation components were measured and calculated using the extensive LVDT setup detailed in Figure 10 and Figure 19, following established methods. In order to measure the rocking deformation contribution to lateral displacement, vertical LVDTs 1 and 2, with gauge lengths of 50 mm, were affixed on the wall boundaries, straddling the W–P interface. Although the gauge length of these sensors was small, the measurements captured a part of the flexural deformation resulting from wall curvatures developing along that length. To isolate the deformation due solely to rocking, the average curvatures measured by LVDTs 1 and 2 were assumed to be approximately equal to the average curvatures measured by LVDTs 3 and 4, which were affixed on the walls at the same locations but along a gauge length of 250 mm. It must be noted that LVDTs 3 and 4 also straddled the W–P interface and therefore measured the rocking rotations also. Consequently, the rocking rotation at the W–P interface and its contribution to the top lateral displacement of the wall—which is the rocking rotation multiplied by the wall height—was calculated. Flexural deformation (curvature) contributions to wall top displacement were calculated using measurements from the vertically mounted LVDTs on the wall boundary regions, along wall height. For the evaluation of these measurements, the centroid of the curvature distribution was assumed to be located at two-thirds of the height of the ith instrumented segment (i.e., ${\alpha }_i = 2/3$) [38]. Shear deformations along the wall height were measured using both diagonally oriented LVDTs forming an X-shaped configuration and vertically mounted LVDTs positioned at the wall boundary regions, following the approach proposed in [38]. For both specimens, the sum of the deformation contributions calculated in this manner differed from the measured top displacements by less than ±3% across all drift ratios.

In addition to the LVDTs installed on the wall specimens, as depicted in Figure 11, SGs were affixed on the longitudinal boundary reinforcement of the walls at three elevations above the W–P interface and two below. Vertical tensile strain data obtained from these SGs—both along the wall height and within the pedestal—corresponding to increasing drift levels (up to 2.0%) on each boundary (C-side and D-side), are presented in Figure 18. Based on these data, reinforcement yielding was first recorded at a drift ratio of 0.30% in both specimens.

Figure 19. Decomposition of top lateral displacement into rocking, flexural, and shear deformation components.

Figure 19. Decomposition of top lateral displacement into rocking, flexural, and shear deformation components.

The load–displacement responses for rocking, flexure, and shear are comparatively presented in Figure 20a–f. For both specimens, shear and flexural response components were approximately linear elastic. The decomposition analysis provided quantitative evidence that slip-induced rocking was the overwhelmingly dominant deformation mechanism for both substandard walls, validating the qualitative observations discussed in the previous section.

Table 4. Comparison of experimentally obtained and ASCE 41:2023-prescribed stiffness values.

Specimen	Condition	Flexural Rigidity		Shear Rigidity
		Exp.	Pred.	Exp.	Pred.
SW-IC-FF	Uncracked	$0.62{\mathrm{E}}_{\mathrm{c}}{\mathrm{I}}_{\mathrm{g}}$	$0.80{\mathrm{E}}_{\mathrm{c}}{\mathrm{I}}_{\mathrm{g}}$	$0.35{\mathrm{E}}_{\mathrm{c}}{\mathrm{A}}_{\mathrm{w}}$	$0.30{\mathrm{E}}_{\mathrm{c}}{\mathrm{A}}_{\mathrm{w}}$
	Cracked	$0.31{\mathrm{E}}_{\mathrm{c}}{\mathrm{I}}_{\mathrm{g}}$	$0.25{\mathrm{E}}_{\mathrm{c}}{\mathrm{I}}_{\mathrm{g}}$	$0.23{\mathrm{E}}_{\mathrm{c}}{\mathrm{A}}_{\mathrm{w}}$	$0.15{\mathrm{E}}_{\mathrm{c}}{\mathrm{A}}_{\mathrm{w}}$
SW-NC-FF	Uncracked	$0.67{\mathrm{E}}_{\mathrm{c}}{\mathrm{I}}_{\mathrm{g}}$	$0.80{\mathrm{E}}_{\mathrm{c}}{\mathrm{I}}_{\mathrm{g}}$	$0.39{\mathrm{E}}_{\mathrm{c}}{\mathrm{A}}_{\mathrm{w}}$	$0.30{\mathrm{E}}_{\mathrm{c}}{\mathrm{A}}_{\mathrm{w}}$
	Cracked	$0.35{\mathrm{E}}_{\mathrm{c}}{\mathrm{I}}_{\mathrm{g}}$	$0.25{\mathrm{E}}_{\mathrm{c}}{\mathrm{I}}_{\mathrm{g}}$	$0.22{\mathrm{E}}_{\mathrm{c}}{\mathrm{A}}_{\mathrm{w}}$	$0.15{\mathrm{E}}_{\mathrm{c}}{\mathrm{A}}_{\mathrm{w}}$

Note: Modulus of elasticity for concrete ($E_c$) calculated per ACI 318.

presents the average flexural stiffness, accounting for both rocking and flexural displacements, and the shear stiffness, based solely on shear displacements, for SW-IC-FF and SW-NC-FF in the uncracked and cracked states. Flexural rigidities were computed from the pre-cracking stage and the first yielding of longitudinal reinforcement, while shear rigidities were obtained from the linear-elastic and early inelastic ranges of the behavior. ASCE 41 appreciably overestimated the uncracked flexural rigidity while underestimating the remaining parameters, including the cracked flexural and shear rigidities, compared with the experimental results.

As shown in Figure 21a, at low drift levels (up to 0.75%), flexural and rocking deformations contributed almost equally to the top lateral displacements of specimen SW-IC-FF, while flexural deformation contributions were more pronounced in specimen SW-NC-FF, as depicted in Figure 21b. Beyond 0.75% drift, the contribution of rocking deformations became substantially larger than those of flexural deformations, for both specimens. At 2.0% drift, the deformation contributions for specimen SW-IC-FF were approximately 18% from flexure, 76% from rocking, 3% from shear, and 3% from other deformation sources, which included sliding shear deformation at the W–P interface, as well as the sliding and rigid body rotation of the pedestal. For specimen SW-NC-FF, these contributions were approximately 20% from flexure, 74% from rocking, 4% from shear, and 2% from other sources.

Progressive debonding along the surfaces of plain reinforcement within both the pedestal and the wall resulted in the distribution of relatively low tensile strains over an extended region along the height of both wall specimens. Analysis of these strains (Figure 18a,b) revealed that pre-yield reinforcement strains exhibited an almost uniform distribution. This low strain level, indicated by the markedly lower SG readings compared to average concrete strains recorded by LVDTs (Figure 15b,d), confirms the reinforcement did not attain high post-yield strain values. This finding is also consistent with the pronounced pinching (self-centering behavior) observed in the cyclic load–displacement response (Figure 14a,b). Furthermore, concrete crushing developed under the combined effects of flexural crushing (induced by curvature) and toe crushing (induced by rocking), where the concrete compressive strains initially concentrated within a highly localized region along the bottom 50 mm of the wall and subsequently progressed upwards (Figure 15a,b). Overall, these findings validate the governing influence of debonding of the plain longitudinal bars and the associated rocking rotation developing at the W–P interface, on the experimentally observed response of both wall specimens.

5. Comparison of Test Results with Backbone Curves Defined in Assessment Guidelines

This section evaluates the prediction capabilities of three widely adopted international seismic performance assessment guidelines—ASCE 41:2023 [29], NZ C5:2025 (v2A) [30], and EN 1998-3:2025 [31]—for RC walls incorporating substandard detailing and exhibiting a predominantly rocking-induced response. The evaluation is based on comparison of the experimentally measured load–displacement backbone curves of the wall specimens tested and the corresponding backbone curves specified by each guideline.

A detailed evaluation of ASCE 41:2023 [29] specifications is first presented. The backbone curves were constructed by first determining the flexural yield strengths at Point B ($M_{\mathit{Cy}}$), illustrated in Figure 22, via sectional analysis, and then adopting an initial stiffness of $0.80E_c{I}_g$, corresponding to an axial load of $0.20A_g{f}_c^{\prime }$. The modeling parameters ($c_{\mathit{nl}}$, $c_{\mathit{nl}}^{\prime }$, $d_{\mathit{nl}}$, $d_{\mathit{nl}}^{\prime }$, and $e_{\mathit{nl}}$) were established for nonconforming walls in accordance with Table 7.4.1.1.1b of ASCE 41 [29]. Herein, ‘nonconforming’ denotes walls that fail to satisfy the following requirements: (i) the minimum area ratio of provided-to-required (per ACI 318-19 Section 18.10.6.4 [39]) boundary transverse reinforcement ($A_{\mathit{sh},\mathit{provided}}/A_{\mathit{sh},\mathit{provided}}\ge 0.7$) and (ii) the ratio of vertical spacing of boundary transverse reinforcement to the diameter of the smallest longitudinal reinforcement ($s/d_{b }\le 8.0$). It is noteworthy that the specimens investigated herein exhibit a more severe confinement inadequacy, as the provided-to-required boundary transverse reinforcement ratio is significantly lower (0.36 for SW-IC-FF and no confinement for SW-NC-FF) and the ratio of vertical spacing of boundary transverse reinforcement to the diameter of the smallest longitudinal reinforcement is considerably greater (14.3 for SW-IC-FF and no confinement for SW-NC-FF) than the nonconforming limits specified by ASCE 41. The parameters, summarized in

Table 5. Modeling parameters for RC wall specimens tested, per ASCE 41 Table 7.4.1.1.1b [29].

Specimen	Conditions		$d_{\mathit{nl}}$
	${\lambda }_b$	Detailing
SW-IC-FF	≤10	$A_{\mathit{sh},\mathit{provided}}/A_{\mathit{sh},\mathit{required}}=0.36$ and $s/d_b=14.3$	0.0196
SW-NC-FF	≤10	NC	0.0190
Specimen	Conditions		$c_{\mathit{nl}}$	$c_{\mathit{nl}}^{\prime }$	$d_{\mathit{nl}}^{\prime }$	$e_{\mathit{nl}}$
	${\mathit{\lambda }}_b$	$N/\left(A_g{f}_c^{\prime }\right)$
SW-IC-FF	≤10	≥0.20	0.10	1.15	0.020	0.021
SW-NC-FF	≤10	≥0.20			0.019	0.019

, were determined using a cross-sectional slenderness parameter, ${\lambda }_b=l_{w}c/b^2$, defined as the product of the slenderness of the wall section ($l_w/b$) and the slenderness of the compression zone ($c/b$), where $c$ is the depth of the neutral axis (approximately 300 mm, determined through sectional analysis), and $b$ is the width of the compression zone (200 mm). The resulting value is ${\lambda }_b=7.5$. This parameter ${\lambda }_b$ captures the combined effects of material properties, axial load, cross-sectional geometry, and the detailing of longitudinal reinforcement in both the web and boundary regions. In addition to ${\lambda }_b$, the modeling parameters are influenced by other critical design variables, including the ratio of provided-to-required boundary transverse reinforcement amounts ($A_{\mathit{sh},\mathit{provided}}/A_{\mathit{sh},\mathit{required}}$), the ratio of transverse reinforcement spacing to the diameter of the smallest longitudinal boundary bar ($s/d_b$), and the normalized axial load ($N/\left(A_g{f}_c^{\prime }\right)$). Per ASCE 41, for walls without boundary transverse reinforcement and subjected to a normalized axial load level exceeding 8%, the parameters $e_{\mathit{nl}}$ and $d_{\mathit{nl}}^{\prime }$ are taken as 0.8 of their nominal values, provided that they do not fall below $d_{\mathit{nl}}$. For specimen SW-NC-FF, the 0.8-scaled values of these parameters were lower than $d_{\mathit{nl}}$: therefore, $d_{\mathit{nl}}$, $d_{\mathit{nl}}^{\prime }$, and $e_{\mathit{nl}}$ were all assigned a value of 0.0190 rad. The resulting modeling parameters are presented in Table 5. To account for bar-slip/extension flexibility, a yield rotation (${\theta }_y$) of 0.003 rad at Point B (Figure 22) was adopted in accordance with ASCE 41.

While the ASCE 41 backbone curves capture the initial stiffness of the specimens with reasonable accuracy, they slightly underestimate peak lateral load capacities and tend to conservatively estimate the deformation capacity—particularly in the post-peak phase. This discrepancy is primarily attributed to the improved displacement capacity resulting from debonding-induced rocking response. For example, at a drift of 4.0%, the experimentally measured residual strengths—approximately 67.2% for SW-IC-FF, which contains insufficient confinement reinforcement, and 65% for SW-NC-FF, which contains no confinement reinforcement—substantially exceeded the ASCE 41 recommendations of 10% and 0%, respectively.

NZ C5:2025 (v2A) [30] outlines two complementary procedures for evaluating the deformation capacity of RC walls: the moment–curvature method and the direct rotation method. The moment–curvature approach is analytically based and typically applied to walls with deformed longitudinal reinforcement, whereas the direct rotation method—developed from a comprehensive experimental database—is used for walls with plain reinforcement. Within this framework, rocking behavior is explicitly incorporated by equating the probable inelastic rotation capacity of walls with continuous plain longitudinal reinforcement to the post-yield rocking capacity (${\theta }_p={\theta }_r$). For walls reinforced with deformed longitudinal bars, the inelastic rotation capacity is defined using the curvature ductility index $K_d$, which captures the flexural plastic deformation mechanism. Although ASCE 41 does not explicitly distinguish plain-reinforced walls, both standards derive their rotation limits from a comprehensive experimental database, meaning that bar buckling, shear deformation, and plasticity spreading are inherently reflected in the direct rotation approach without requiring explicit modeling. The sequence of capacity points adopted herein is illustrated in Figure 23. In this study, the probable capacity (Point C) was obtained through section analysis using expected material properties and the moment corresponding to a concrete compressive strain of −0.003 at the extreme fiber. The overstrength capacity (Point D) was then calculated using the same analytical framework—maintaining the −0.003 concrete compressive strain criterion—while amplifying the reinforcement stresses by the prescribed overstrength factor ($f_o ={ \phi }_o{f}_y$, ${\phi }_o= 1.25$), which captures material variability, expected strength exceedance, and strain hardening (if present). Notably, the yield rotation is defined consistently for walls with either plain or deformed longitudinal reinforcement, corresponding to the rotation at the onset of yielding in the longitudinal reinforcement. The rotations corresponding to these strength levels represent the yield rotation (or yield drift) and the rotation capacity (or probable drift capacity), as summarized in

Table 6. Comparison of guideline-based predictions and experimental results for yield rotation and rotation capacity of the tested wall specimens.

Source of Reference	Type of Bar	Yield Rotation (Rad)	Rotation Capacity (Rad)
EN 1998-3:2025 [31]	Deformed	${\theta }_{\mathrm{y}}={\phi }_{\mathrm{y}}{\displaystyle \frac{{\mathrm{h}}_{\mathrm{w}}+{\mathrm{a}}_1}{3}}+{\displaystyle \frac{{\phi }_{\mathrm{y}}{\mathrm{d}}_{\mathrm{b}}{\mathrm{f}}_{\mathrm{y}}}{8\sqrt{{\mathrm{f}}_{\mathrm{c}}^{\prime }}}}+0.0011\left(1+{\displaystyle \frac{{\mathrm{l}}_{\mathrm{w}}}{3{\mathrm{h}}_{\mathrm{w}}}}\right) \approx 0.0031$	$\left.\begin{array}{c}{\theta }_{\mathrm{u}}={ \theta }_{\mathrm{y}}+{\alpha }_{\mathrm{bars}}{\theta }_{\mathrm{u}}^{\mathrm{pl}}\\ {\alpha }_{\mathrm{bars}}=1.0; {\theta }_{\mathrm{u}0}^{\mathrm{pl}}=0.023\\ {\theta }_{\mathrm{u}}^{\mathrm{pl}}={\kappa }_{\mathrm{conform}}{\kappa }_{\mathrm{axial}}{\kappa }_{\mathrm{reinf}}{\kappa }_{\mathrm{concrete}}{\kappa }_{\mathrm{shearspan}}{\kappa }_{\mathrm{confinement}}{\theta }_{\mathrm{u}0}^{\mathrm{pl}}\\ {\kappa }_{\mathrm{conform}}=0.8; {\kappa }_{\mathrm{axial}}=0.725; {\kappa }_{\mathrm{reinf}}=1.0\\ {\kappa }_{\mathrm{concrete}}=0.951; {\kappa }_{\mathrm{shearspan}}=0.956; {\kappa }_{\mathrm{confinement}}=1.0\end{array}\right\} \approx 0.0152$
	Plain	$\left.\begin{array}{c}{\theta }_{\mathrm{y}}=2{\displaystyle \frac{{\phi }_{\mathrm{y}}{\mathrm{h}}_{\mathrm{w}}}{3}}\\ {\phi }_{\mathrm{y}}=1.44{\displaystyle \frac{{\epsilon }_{\mathrm{y}}}{{\mathrm{l}}_{\mathrm{w}}}}\end{array}\right\} \approx 0.0031$
NZ C5:2025 (v2A) [30]	Deformed	$\left.\begin{array}{c}{\theta }_{\mathrm{y}}={\beta }_{\mathrm{v}}{\displaystyle \frac{{\phi }_{\mathrm{y}}{\mathrm{h}}_{\mathrm{w}}}{3}}\\ {\phi }_{\mathrm{y}}=2{\displaystyle \frac{{\epsilon }_{\mathrm{y}}}{{\mathrm{l}}_{\mathrm{w}}}}\end{array}\right\} \approx 0.0031$	$\left.\begin{array}{c}{\theta }_{\mathrm{u}}={\theta }_{\mathrm{y}}+{\theta }_{\mathrm{p}}\\ {\theta }_{\mathrm{p}}=\left({\mathrm{K}}_{\mathrm{d}}-1\right){\phi }_{\mathrm{y}}{\mathrm{L}}_{\mathrm{p}}\\ {\mathrm{K}}_{\mathrm{d}}=15 \text{–} 20\left(\mathrm{c}/{\mathrm{l}}_{\mathrm{w}}\right)\\ {\mathrm{L}}_{\mathrm{p}}=313.3 \mathrm{m}\mathrm{m}; \mathrm{c}=300 \mathrm{m}\mathrm{m}\end{array}\right\} \approx 0.0105$
	Plain		$\left.\begin{array}{c}{\theta }_{\mathrm{u}}={\theta }_{\mathrm{y}}+{\theta }_{\mathrm{p}}\\ {\theta }_{\mathrm{p}}={\theta }_{\mathrm{r}}\\ {\theta }_{\mathrm{r}}=0.2{\mathrm{k}}_{\mathrm{r}}\alpha \\ {\mathrm{k}}_{\mathrm{r}}=0.85; \alpha =0.16\end{array}\right\} \approx 0.0303$
ASCE 41:2023 [29]	Deformed	0.0030	0.0190–0.0196 a
Experimental	Plain	0.0030	0.0250–0.0300 b

^a Predicted values correspond to the SW-NC-FF and SW-IC-FF specimens, respectively. ^b Experimentally obtained values associated with nearly a 20% reduction in strength correspond to the SW-NC-FF and SW-IC-FF specimens, respectively.

. The deformation at the onset of loss of gravity capacity (Point F) was taken equal to the drift at which lateral strength degradation (Point D or E) begins, as NZ C5 relates this limit state to the axial–load capacity defined by the wall reinforcement configuration ($\mathrm{s}/{\mathrm{t}}_{\mathrm{w}}$). The walls examined here—lacking adequate boundary confinement and subjected to an axial–load ratio of 20%—exceed the allowable axial–load limit for this configuration; therefore, the deformation corresponding to gravity–load instability (onset of loss of gravity capacity) was taken equal to the deformation at the probable drift capacity. The resulting total rotation capacity of 0.0303 rad reflects the combined influence of the wall geometry and its internal flexural response, captured through the strut angle $\alpha$, which incorporates the neutral-axis depth derived from section analysis and illustrates that the rocking rotation is governed by the interaction of geometric and intrinsic material nonlinearities rather than geometry alone.

In EN 1998-3:2025 [31], the deformation capacity of yielded members—expressed through the chord rotation—is integrated into the explicit definitions of yielding and ultimate chord rotations. The yield chord rotation is taken as twice the flexural contribution to incorporate the additional deformations arising from slippage and shear. For RC walls, the plastic part of the chord rotation is derived from a basic plastic capacity of ${\theta }_{u0}^{\mathit{pl}}=0.023$ rad, corresponding to detailing for a high ductility level (DC3), zero axial load, symmetric reinforcement, a concrete strength of 25 MPa, and a shear-span ratio $h_w/l_w = 2.5$. This basic value is subsequently refined through six modification factors that represent the actual characteristics of the wall: the ductility-class factor ${\kappa }_{\mathit{conform}}$, the axial–load factor ${\kappa }_{\mathit{axial}}$ governed by the normalized axial force, the reinforcement-asymmetry factor ${\kappa }_{\mathit{reinf}}$, the concrete-strength factor ${\kappa }_{\mathit{concrete}}$, the shear-span factor ${\kappa }_{\mathit{shearspan}}$, and the confinement factor ${\kappa }_{\mathit{confinement}}$, which reflects the influence of transverse reinforcement and confinement efficiency [40]. The resulting plastic chord capacity contributing to the ultimate rotation is then adjusted by the coefficient ${\alpha }_{\mathit{bars}}\le 1.0$, a reduction factor that accounts for the reinforcement type (ribbed or smooth) and the presence of lap splices. When the longitudinal reinforcement is continuous, EN 1998-3 assigns the same rotation capacity to plain and deformed bars; accordingly, the bar-type reduction factor is taken as ${\alpha }_{\mathit{bars}}=1.0$. The detailed formulations governing both the yield chord rotation and the plastic part of the ultimate chord rotation are provided in Table 6, from which the coefficient values used for the specimens in this study were determined based on their specific geometric, material, and reinforcement characteristics. The lateral load corresponding to the yield chord rotation is obtained from a cross-sectional analysis of the end section, where yielding is defined as the point at which either the longitudinal reinforcement yields or the concrete reaches its compressive strength limit, whichever occurs earlier. In this study, the onset of yielding of the longitudinal reinforcement was adopted as the governing criterion for identifying the yield stage. For the ultimate lateral load, both the lower-bound ultimate concrete compressive strain for unconfined concrete (0.0035) and the ultimate tensile strain of the longitudinal reinforcement, taken as 40% of ${\epsilon }_{\mathit{su},\mathit{nom}}$, were considered. Herein, for walls without or with insufficient confinement, the sectional response was consistently governed by concrete compressive strain reaching 0.0035, while the reinforcement strains remained well below their tensile limit. Accordingly, this strain threshold was adopted as the controlling parameter for establishing the ultimate lateral load.

The experimental results are compared with the predictions of ASCE 41, NZ C5, and EN 1998-3 with respect to yield rotation, ultimate rotation (rotation capacity), and lateral load– displacement response. Table 6 summarizes the yield-rotation and rotation-capacity predictions of each guideline alongside the experimental findings, and these predictions were generated for conditions where plain and/or deformed flexural reinforcements are continuous (without lap splices) and possess sufficient development length. All three procedures capture the initial stiffness and yield rotation of the specimens with commendable fidelity. The experimentally measured ultimate rotations are 0.030 rad for SW-IC-FF and 0.025 rad for SW-NC-FF. ASCE 41 predicts 0.0196 rad and 0.0190 rad, providing distinctly conservative estimates for both specimens. NZ C5, which shows the closest agreement with the experimentally observed ultimate drift ratio—owing to its explicit linkage between the probable inelastic rotation capacity of walls with continuous plain longitudinal reinforcement and their post-yield rocking response—estimates an ultimate rotation of 0.0303 rad for each specimen. This value closely matches the result for SW-IC-FF while remaining mildly unconservative for SW-NC-FF. EN 1998-3, with its uniform prediction of 0.0152 rad, offers the most conservative estimate among the three standards. Among three technical documents, ASCE 41 stands out as it makes reliable and conservative estimates for the two nonconforming walls tested during this study. Accordingly, for ultimate rotation, the hierarchy of conservatism extends from EN 1998-3 (most conservative) to ASCE 41 and then to NZ C5. ASCE 41 also provides the most conservative lateral load estimates for both specimens, while EN 1998-3 yields moderately conservative values and NZ C5 achieves the closest—though mildly unconservative—agreement with the experimental capacities. In terms of lateral load predictions, the resulting hierarchy of conservatism places ASCE 41 at the most conservative end, followed by EN 1998-3 and, finally, NZ C5. The overall comparison between the experimental and predicted backbone curves is presented in Figure 24a,b.

6. Summary and Conclusions

This paper presented results of a full-scale experimental investigation on relatively slender and flexure-controlled RC walls that are representative of outdated design and low-quality construction practice in numerous countries worldwide. The wall specimens investigated in this study were characterized by low-strength concrete, plain longitudinal reinforcement, and either absent or insufficient confinement at the wall boundary regions, failing to meet ductile detailing requirements specified in modern seismic code provisions and design standards. The test results and observations presented in this paper aim to provide valuable insight into the behavioral characteristics, deformation mechanisms, ductility attributes, strength degradation behavior, and failure modes of such nonconforming/substandard walls, as well as how these response characteristics may differ from what is typically assumed in currently employed modeling approaches and assessment strategies for seismic performance evaluation of existing structures. The principal conclusions of this experimental study can be summarized as follows:

• Both the SW-IC-FF and SW-NC-FF specimens predominantly exhibited flexural-dominated behavior. In each specimen, a principal crack initiated at the W–P interface and progressively widened as the drift ratio increased during the test. Yielding of the longitudinal boundary reinforcement was observed at approximately 0.30% drift ratio, with maximum tensile strains of 0.006 in SW-IC-FF and 0.015 in SW-NC-FF. In both specimens, the horizontal web reinforcement did not yield, as expected.
• Rocking response was identified as the predominant mechanism governing both the lateral displacements of the walls and their overall behavior. This response was primarily attributed to the progressive debonding of plain longitudinal reinforcement, occurring not only in the pedestal but also along the wall height. Large W–P interface crack widths, significant interface rotations, and higher concrete tensile strains recorded by LVDTs compared to the reinforcement strains measured by SGs collectively substantiated this mechanism. The pronounced pinching observed in the hysteresis loops further confirmed the self-centering behavior induced by reinforcement debonding and the associated rocking.
• Failure in both specimens occurred through longitudinal bar buckling accompanied by crushing of the concrete core. Ultimate drift ratios were 2.0% for SW-IC-FF and 1.50% for SW-NC-FF, corresponding to displacement ductility values of 4.0 and 4.3, respectively. The SW-IC-FF specimen, detailed with insufficient boundary transverse reinforcement, exhibited a slightly greater drift capacity. Concrete crushing in each specimen began in the form of toe crushing just above the W–P interface and subsequently propagated upward.
• All three guidelines capture the initial stiffness and yield rotation of the substandard wall specimens with commendable fidelity; however, their predictions of rotation capacity diverge significantly. NZ C5 provides the closest agreement with the experimental results, yet this arises from predicting the same rotation capacity for both specimens, which leads to a distinctly unconservative estimate for specimen SW-NC-FF. ASCE 41 is the only procedure that reflects the slight differences between the specimens, whereas EN 1998-3 remains the most conservative. These findings highlight the need for development of improved assessment procedures that explicitly incorporate the rocking-dominated deformation mechanisms governing walls reinforced with plain longitudinal bars.

Although the experiments clearly demonstrate the pivotal role of reinforcement debonding and slip-induced rocking, developing a detailed analytical framework capable of explicitly modeling bond–slip behavior, interface uplift, and their interaction with concrete crushing lies beyond the scope of this study. These aspects represent a promising and important direction for future research.