Effects of horizontal web reinforcement on cyclic behavior of RC squat walls

This paper evaluates the effects of horizontal web reinforcement on cyclic behaviour of RC squat wall using test results of three pairs of specimens. One specimen was tested by the authors while the other five were adopted from the existing researches. Each specimen pair was designed with approximately the same design parameters, except that uniformly distributed horizontal web reinforcement was provided in one specimen only. Shear stress demand, evaluated based on the shear associated with the development of flexural strength at the base, was approximately 3.5√f c ' (psi), 6.0√f c ' (psi), and 8.0√f c ' (psi), respectively, for each specimen pair. Test results show that specimen with uniformly distributed horizontal web reinforcement exhibited larger deformation capacity compared to specimens without it. Specimen peak strengths, on the other hand, appear to be similar with and without uniformly distributed horizontal reinforcement and can be satisfactorily predicted by nominal flexural strength.


Introduction
Reinforced concrete (RC) shear wall not only provides lateral strength but also keeps lateral deformation within acceptable limits due to its large in-plane stiffness. According to Moehle et al. [1], RC shear walls are often more cost-effective than RC moment-resisting frames for low-to-medium-rise structures. A RC squat wall typically refers to a structural wall having an aspect ratio (h w ℓ ⁄ ) of 2.0 or less, where h w is the wall height, measured from center of the load application to the base of the wall and ℓ is the wall length.
Researches on effects of horizontal reinforcement on load-deformation responses of RC squat walls have been conducted previously [2,3]. Maier [2] tested a total of 10 squat wall specimens with h w ℓ ⁄ of around 1.10. Two specimens, specimens S4 and S9, were designed identically except that no horizontal reinforcement was provided in specimen S9. Under approximately 0.08Agfc' axial force and monotonically increased lateral displacement, test results showed that two specimens exhibited similar peak lateral strength but slightly different deformation capacity. Specimen S4 achieved larger deformation capacity of 1.11% compared to 0.93% from specimen S9. Similar findings were reported by Greifenhagen and Lestuzzi [3]  With two pair of specimens collected from Maier [2] and Greifenhagen and Lestuzzi [3], one specimen, H60_V, was designed identically with specimen H60 tested by Cheng et al. [4], except that no horizontal reinforcement is provided. A test matrix that illustrates the key test parameters in specimens H60 and H60_V is summarized in Table 1. Unfortunately, design parameters in specimens S4, S9, M1, and M2 are not available because specified material strength was not reported, and thus only test results of those specimens are presented. In Table 1, V mn and V mpr is the shear assocated with the development of nominal flexural strength, Mn, and probable flexural strength, Mpr, at the wall base, respectively. That is, Vmn= Mn/hw and Vmpr = Mpr/hw, where Mpr is determined using 1.25 steel specified yield strength. As can be seen from v mpr /√f c ' , specimen H60 and H60_V were designed with shear stress demand close to 10A cv √f c ' (psi).
V n1 and V n2 is the nominal shear capacity determined based on Eq. 1, and Eq. 2, respectively, per ACI 318-14 [5], A cv is the wall cross section area determined by wall width ( b w ) times the wall length ( ℓ w ), and ρ t is the horizontal web reinforcement ratio.
In addition to the code design equations, another three shear strength prediction models are also used to evaluate specimen peak strength later. Equation (3), which has a form similar to Eq. (2), was proposed by Wood [6] based on a database consisting of 143 RC squat wall specimens. In which, A vf is the area of total vertical reinforcement in the wall (sum of areas of vertical web reinforcement and longitudinal reinforcement in the special boundary element).
Another model, known as simplified softened strut-andtie (SSST) model by Hwang and Lee [7], was developed assuming that shear resisted by the wall is transferred through three mechanisms including diagonal struts, horizontal ties, and vertical ties. The shear strength (V n4 ) per SSST model can be determined using Eq. (4), where K h and K v is the reinforcement index for horizontal and vertical reinforcement, respectively.  is the concrete softening coefficient, A str is the diagonal strut area and  is the angle of inclination.
Gulec and Whittaker [8] used an extensive database consisting of 148 specimens and proposed an empirical shear strength prediction model as shown in Eq. (5). This empirical relation was proposed to evaluate the mean shear resistance of the rectangular RC squat walls with aspect ratios of 1.0 or less.
where A cv is the wall area that can be determined as the product of wall thickness (t w ) and wall length (ℓ w ), f c ' is the concrete compressive strength of concrete, F vw is the force attributed to vertical web reinforcement, F vbe is the force attributed to boundary element reinforcement, N is the axial force applied to the wall, h w is the wall height, and ℓ is the wall length.

Experimental Setup and Instrumentation
The experimental setup for both specimen H60 and H60_V is shown in Fig. 2. This setup intends to impose in-plane single-curvature deformation to the test specimens with negligible axial force. Due to length limitation, experimental layouts for the other 4 specimens can be found elsewhere [2,3].

Overall Response
Based on test result from Cheng et al. [4], specimen H60 exhibited extensive deterioration along the base of the wall at the final state, as can be seen in Fig. 3(a). For specimen H60_V, inclined and horizontal cracks developed in test specimens during the 1 st cycle at 0.25% target drift level. More cracks developed as the target drift increased from 0.25% to 0.75%. As the specimen was pushed to the target drift of 1.00%, widths of some inclined cracks grew wider and spall-off of concrete cover was observed at center of the wall where the two major inclined cracks intersected. Before reaching the target drift of 1.00%, a major inclined crack propagated from upper left corner to the lower right corner suddenly opened and lateral resistance started to drop after that. As the specimen was loaded to 1.50% target drift, the major inclined crack widths grew even wider and the lateral resistance dropped more than 50% from the peak in both loading directions at peaks of the 1 st cycle of 1.50% target drift. Test terminated after completion of the 1.50% target drift cycles. Final state of the test specimen is presented in Fig. 3(b).
For specimen S4, based on visual observation of Fig. 3(c), in addition to have several inclined cracks at bottom half of the wall, several damage including spall-off of the concrete cover and buckling of the vertical reinforcement appears to localize at lower corner of the wall. Final state of specimen S9 shows similar failure mode but with a few inclined cracks that opened more widely.
Specimen M1 and M2 [4] show similar failure mode as well, Fig. 3(e) and 3(f). Cracks and concrete spall-off were primarily observed along the wall base and within a narrow height. The outmost vertical reinforcement ruptured as specimen M1 was loaded to 3.00%, while the outmost vertical reinforcement in specimen M2 buckled at the end of the test. According to the authors, sliding movement of the two specimens contributed substantially to the top lateral displacement in the last few drift cycles.  (c) S4 [2] (d) S9 [2] (e) M1 [3] (f) M2 [3]

Test Results
Concrete cylinder strength was 6.4, 6.7, 4.8, 4.2, 7.3 and 7.4 ksi (44, 46, 33, 29, 50, and 51 MPa) for specimen H60 [4], H60_V, S4 [2], S9 [2], M1 [3] and M2 [3] respectively. Steel coupon test results are listed in Table  3. Load-deformation responses of the six specimens are presented in Fig. 4. As shown in Fig. 4, the peak strength of specimens reinforced with/without horizontal web reinforcement were similar but there were differences in the deformation of the specimens. Specimens with horizontal web reinforcement had greater deformation than specimens without horizontal web reinforcement. Some key test results of the six specimens are summarized in Table 4. Ultimate drift ratio du is defined at the point when one of the following two criteria is first met: 1) the drift where the load drops 20% from the peak on the envelope curve; or 2) the drift where the load drops more than 20% in the repeated cycles and the load in the 1 st cycle of the next drift level is lower than the load in the 3 rd cycle of this drift level. The loading direction in which du is determined is consistent with that of Vpeak, the larger peak strengths from the two loading directions.  (c) S4 [2] (d) S9 [2] (e) M1 [3] (f) M2 [3] Fig. 4. Load -deformation relationship

Strength
As can be seen from Table 5, the Vpeak/Vmn ratios indicate that peak strengths of all test specimens appear to be satisfactorily estimated by Vmn, the shear demand associated with development of the nominal flexural strength (Mn) at the wall base, i.e. Vmn = Mn/hw. Despite of this, shear capacity, particularly for specimens without horizontally distributed web reinforcement, appears to be exhausted simultaneously as the specimen achieved its peak strength, as can be seen in the load -deformation relationship and observation during the test. As a result, specimen peak strength is further evaluated using the aforementioned shear strength models. It should be noted that Vn1 and Vn4 are associated with the web shear failure mode, while Vn2 and Vn3 are associated with the friction shear failure mode. The shear strength model proposed by Gulec and Whittaker [8], Vn5, is derived using regression analysis without associating with any specific failure modes. Among Vn1, Vn4, and Vn5, based on results shown in Table 5, it appears Vn4 provides the closest estimation for specimens H60_V, S4 and S9 that appears to fail in web shear.
For specimens that appear to fail in sliding shear, specimens H60, M1 and M2, neither Vn2, Vn3, and Vn5 are able to provide consistent estimation. However, Vn3 provides the most conservative results.

Deformation
The normalized peak shear stress versus ultimate drift ratio (du) of all test specimens is presented in Fig. 5. Previous research indicates that the wall deformation capacity increase when the horizontal web reinforcement is used (Maier [2] and Greifenhagen and Lestuzzi [3]). It appears that the test results of specimen H60 and H60_V with shear stress close to 10 A cv √f c ' (psi) support the previous findings. Despite of using different test setups and reinforcement detailing (with/without special boundary element), the trend in Fig. 5 shows that specimen deformation capacity tends to increase as the specimen normalized shear stress decreases.

Conclusion
This study extends the work from Maier [2], Greifenhagen and Lestuzzi [3] and Cheng et al. [4] to evaluate effects of uniformly distributed horizontal web reinforcement on cyclic behavior of RC squat walls. Among the six specimens (three pairs) discussed in this study, one specimen was tested by the authors. Shear stress demand for each specimen pair is 3.5 √f c ' (psi), 6.0 √f c ' (psi), and 8.0 √f c ' (psi), respectively. Based on limite test results, the following conclusions are drawn: 1) Regardless of the presence of unifomly distributed web reinforcement, the peak strength of each specimen pair is similar and can be satisfactorily estimated by the nominal flexural strength. 2) Specimen deformation capacity, however, increases when the horizontal web reinforcement is used.