Damage Progression
The damage initiation was similar for all tested columns. The damage started with a crack at nearly 500 mm from the column-foundation interface. This location coincided with the end of the dowel bar. The first sign of cracking was observed at a 1.43% drift ratio for the CO40 and CI40 specimens whereas this was noted at a 0.98% drift ratio for the CI20 specimen. The difference in the cracking load for the CO40 and CI20 was due to the different concrete strengths. On the other hand, observed cracking for the CI40 specimen at a higher drift ratio as compared to CI20 was a result of the loss of clamping force of the reaction frames on the foundation block during the application of the 0.98% drift ratio. These clamps were tightened before the application of the next drift ratio of 1.43%.
The cracks in the specimens increased with increasing drift ratios both in numbers and sizes. Concrete started to crush at a 3.86% drift ratio for all three specimens. Spalling of cover concrete was extensive for the CO40 specimen and spread over the lap spliced region of the rebars which became exposed due to spalling. Conversely, the damage region in CI20 and CO40 remained fairly confined close to the column-foundation interface. Although concrete spalling in the CI40 specimen also exposed the steel reinforcement, the extent of this spalling was less as compared to the CO40 specimen. Least spalling was observed for the CI20 specimen which was insufficient to expose the embedded reinforcing bars.
Figure 4 illustrates the damage pattern for the specimens at the end of testing at a 4.61% drift ratio. Note that Near Face and Far Face refer to the faces adjacent and opposite to the actuator, respectively (Fig. 2). It is seen in Fig. 4 that the major difference in the column damage progression is the concentration of damage near the column-foundation interface for the IMRF columns (CI20 and CI40). Contrary to this, wide cracks and heavy concrete spalling were observed near the tip of the dowel bar for the CO40 specimen which was 500 mm away from the column-foundation interface. Shear sliding in the cracks in the CO40 column was also indicated by the data of the potentiometers mounted perpendicular to the longitudinal axis during the last two drift ratios. Conversely, this behaviour was not observed for the IMRF columns. The above observations signify the effectiveness of increased confinement of the lap spliced region in the IMRF column specimens.
Cyclic Load-displacement Behaviour
The cyclic load-displacement responses of the tested columns are illustrated in Fig. 5. Considering different fc for the CO40 column compared to the other specimens (CI20 and CI40), the load and displacement axes were scaled corresponding to fc = 13 MPa for a meaningful comparison of the former specimen with the latter. This scaling of load and displacement axes was carried out by using fc and elastic modulus, respectively. Therefore, the observed load was divided by 17 MPa and multiplied by 13 MPa to proportionate it to fc = 13 MPa. Similar proportioning of the recorded displacement was carried out by using √fc. The same method has been followed for all the data presented in the forthcoming discussion in this paper. Further, the curves for the applied drift ratio of 3.86% and 4.61% are shown in red and blue, respectively, in Fig. 5 (which were the last two drift ratios) for clarity of changes in the specimen behaviour at these stages.
It is seen in Fig. 5 that the load-displacement responses of all the columns are fairly symmetrical for the negative and positive directions of the loading until the end of testing. An abrupt strength degradation can be observed for the CO40 specimen in the final stages in both the aforementioned directions of loading (red and blue curves). Conversely, strength degradation was gradual for the CI20 and CI40 specimens.
Figure 6 illustrates the capacity curves for the columns which are the envelope curves for the positive and negative directions of loading. The specimen drift ratio was determined by dividing the displacement data by Lv. It is seen in Fig. 6 that the curve of each specimen comprises several linear segments. The initial branch of the curve has a steep slope (when the concrete is uncracked) and is similar for all three specimens. The slope of the curve reduced for all the columns at a drift ratio of 0.45% and 0.20% in the positive and negative directions of loading, respectively, which signifies specimen cracking. The observed cracking load (Vcr) of these specimens corresponding to the abovementioned drift rations are given in Table 2. It is noted that although Vcr is similar for all the specimens it was 18% less for the CI40 specimen in the negative direction of loading. This was possibly influenced by the aforementioned clamping issues with this specimen.
Table 2
Observed load and displacement for tested columns at different stages
Column | Vcr | Vmax | ds | Vr | dr | Vy | dy | Vu | du | µd |
| (kN) | (kN) | (mm) | (kN) | (mm) | (kN) | (mm) | (kN) | (mm) | |
CO40 | -18.7 | -41.3 | -1.38 | -12.6 | -4.16 | -29.45 | -10.57 | -33.1 | -39.14 | 3.7 |
26.0 | 38.6 | 1.39 | 2.2 | 4.16 | 31.94 | 14.83 | 30.9 | 42.15 | 2.8 |
CI40 | -15.8 | -47.3 | -2.64 | -25.7 | -4.58 | -32.43 | -12.78 | -37.9 | -66.70 | 5.2 |
27.0 | 44.2 | 2.50 | 19.3 | 4.58 | 30.52 | 12.76 | 35.3 | 60.35 | 4.7 |
CI20 | -18.9 | -54.4 | -2.20 | -27.3 | -4.63 | -38.83 | -12.83 | -43.5 | -60.19 | 4.7 |
27.2 | 46.3 | 1.96 | 21.1 | 4.28 | 33.52 | 12.79 | 37.0 | 55.0 | 4.3 |
The observed Vcr can be compared with the estimated Vcr which is determined with the help of Eq. (2)
$${V}_{cr}=\left({f}_{r}+\frac{P}{{A}_{g}}\right)\times \frac{2\times {I}_{g}}{{L}_{v}\times h}$$
2
where P is the applied axial load; and Ig is the moment of inertia of the cross-section. The theoretical Vcr from Eq. (2) using fr = 1.43 MPa comes out to be 16.6 kN which is similar to the observed Vcr for all specimens in the negative direction of loading.
It is seen in Fig. 6 that the slope of the linear segments of the curves for the CO40 and CI40 specimens are similar after cracking until the peak applied load (Vmax) for the former specimen in the positive direction of loading. Conversely, the slope of the ascending part of the curve for the CI40 is lower after cracking as compared to the remaining two specimens in the negative direction of loading. Further, the slopes of the curves for the CO40 and CI20 specimens are similar after cracking for the negative direction of loading until a drift ratio of 0.4%. The slope of the curve for the CO40 specimen decreased rapidly thereafter until the peak load which is an indication of rapid strength degradation for this specimen.
The values of Vmax for all the specimens in both the negative and positive directions of loading are given in Table 2. It is noted that Vmax for the CI20 and CI40 specimens increased as an effect of better concrete confinement used for these specimens. For example, Vmax for the CI40 specimen was 15% higher in both the positive and negative directions of loading as compared to the CO40 specimen. Conversely, Vmax is the least for the CO40 specimen. Further, Vmax for the CI20 specimen is the highest in the negative direction of the loading, as this specimen benefitted from both the increased concrete confinement in the plastic hinge region and the larger concrete core area. Nevertheless, Vmax values for the CI20 and CI40 specimens were similar in the positive direction of loading.
The specimen drift ratios (ds) corresponding to Vmax are also given in Table 2. It is noted that ds was highest for the CI40 specimen in both the positive and negative directions of loading. Similar ds values for the CO40 specimen in the positive and negative directions of loading signify symmetrical behaviour of this specimen in these directions, although the non-symmetry was not large for the other specimens.
It is seen in Fig. 6 that the post-peak branches of the curves for all three specimens are nearly parallel to each other in both the negative and positive directions of the loading which signifies their similar strength and stiffness degradation. A summary of the residual load (Vr) and corresponding drift ratio (dr) of the specimens is given in Table 2. It is noted that specimen CO40 has the least value of Vr and dr in both the positive and negative directions of loading. A smaller value of dr for this column signifies its relatively low ductility as compared to the other columns. Further, the Vr value of the CI40 specimen was 50% and 88% higher as compared to the CO40 in negative and positive directions of loading, respectively. Conversely, Vr is similar for the CI20 and CI40 specimens in their respective directions of loading. Further, similar dr values for the CI40 specimen in the positive and negative directions of loading signify that its unsymmetrical behaviour in the pre-peak phase changes to symmetrical behaviour in these directions of loading in the post-peak phase of behaviour. On the other hand, the post-peak behaviour of the CI20 specimen was also unsymmetrical in the positive and negative directions of loading similar to its behaviour in the pre-peak phase of testing. Finally, the dr values of the CI40 and CI20 specimens are similar in the negative direction of loading, although these are different in the positive direction of loading.
Flexural Stiffness
The variations in the flexural stiffness of the column were studied with the help of secant stiffness. This stiffness was calculated by the slope of a line connecting the origin and the peak point of the hysteresis loops formed by all three cycles of excursions at a given applied drift ratio [42, 43]. Figure 7 compares the changes in the secant stiffness of the specimens at different drift ratios for both the positive and negative directions of loading. It is seen that initial stiffness is similar for the CO40 and CI20 specimens while this is considerably less for the CI40 specimen. Since the uncracked stiffness of the column is not influenced by the variables considered for all three columns, this difference could be a result of some loosening in the clamping force at the base of the column and may not be real.
The stiffness of all the columns reduced rapidly at low drift ratios. This behaviour can be attributed to the fact that the specimen Vcr was small (Table 2). It is seen in Fig. 7 that the rapid decrease in the stiffness continued until a drift ratio of 0.4% and 0.5% in the positive and negative directions of loading, respectively. The specimens exhibited a gradual decrease in stiffness beyond this point which was also nonlinear. Nevertheless, the differences in the residual stiffness of all three columns are marginal to this point although (on a relative scale) the stiffness for the CI20 specimen was the highest until the last applied drift ratio.
It is seen in Fig. 7 that the residual stiffness for the CO40 column became less compared to both the remaining columns beyond the aforementioned drift ratios. Further, although the residual stiffness of all specimens is less than 1 kN/mm in both directions of loading at the end of testing, it is largest for the CI20 specimen followed by CI40 and CO40 in the same order. The residual stiffness for the latter specimen was 3% and 4% for the positive and negative directions of loading respectively. Conversely, these were nearly 5% and 7% for the CI40 and CI20 specimens, respectively. A higher residual stiffness of the CI20 specimen compared to the CI40 specimen was a result of a larger core area of the former column.
Curvature Distribution
The variations in the curvature distribution along the specimen were studied with the help of data from potentiometers mounted along the specimen longitudinal axis (Fig. 2). Figure 8 illustrates typical curvature distribution for the tested specimens at 0.98%, 1.95%, 3.16% and 4.61% applied drift ratios. It is seen that the specimen curvature is higher at the column-foundation interface at the lower levels of drift ratios (up to 0.98%) which is typical of cantilever behaviour. In addition, the curvature is symmetric for the CO40 and CI40 specimens and un-symmetry for the CI20 specimen. This disparity can be attributed to the fact that cracking in the CI20 specimen started at this applied drift ratio contrary to the remaining two specimens which experienced cracking at the next applied drift ratio (1.43%). This also explains a higher curvature value (1.6×10− 5 mm− 1) near the column-foundation interface for CI20 as compared to the values of 1.1×10 − 5 mm− 1 and 4.9×10− 6 mm− 1 for the CI40 and CO40 specimens, respectively.
A spike in the induced curvature is seen in Fig. 8 for all specimens at the 1.95% applied drift ratio in a region of 510–680 mm from the column-foundation interface. The concentration of induced curvature within this region continued for the CO40 specimen at further higher applied drift ratios until the end of testing. The induced curvature for this specimen was highest far away from the column end as compared to any other point along the lengths. The cracks for this specimen were also seen to widen in this part of the specimen. Although the concentration of curvatures within the aforementioned region is also considerable for the CI20 specimen, the curvature at the column-foundation interface also increased and became higher at the final applied drift ratio (4.61%). Contrary to the other specimens, the behaviour of the CI40 specimen was different at all stages as its curvature remained concentrated near the column-foundation interface until the end of testing.
It can be inferred from the above that once the splice capacity to prevent a slip was exceeded it caused curvature concentration in the area around the end of dowel bars. However, the presence of higher confinement in the CI40 and CI20 specimens prevented further degradation and adequate stress transfer took place to the column-foundation interface for these columns.
Plastic hinge length (Lp) refers to a region where plasticity spreads [44–47]. Kim et al. [6] suggested that Lp could be the effective depth (d) of a column. It is noted in the above that although this may barely suffice for the CI20 and CI40 columns, this is highly non-conservative for the CO40 column. Similarly, FEMA 356 [48] (2000) suggested Lp as 0.5d which is smaller compared to Kim et al. [6] (2021) and does not apply to the tested columns.
ASCE 41 − 17 [49] has recommended Eq. (3) for the estimation of Lp.
$${L}_{p}=0.18 {L}_{v}+0.021{d}_{b}{f}_{y}$$
3
The estimated Lp from Eq. (3) is approximately 450 mm which may be sufficient for the CI40 and CI20 specimens. This length, however, is smaller as compared to the observed plasticity region for the CO40 specimen and may not apply to this specimen.
Ductility
The displacement ductility (µd) is taken as the ratio of yield displacement (dy) and ultimate displacement (du). The latter is taken as displacement corresponding to 80% residual capacity [50].
A cross-sectional analysis was performed using the Section Designer tool available in the computer programme SAP2000 [51] for estimating steel yielding in the column. The concrete stress-strain behaviour was simulated using the confined concrete model by Mander et al. [8] while elasto-plastic stress-strain behaviour was used for steel reinforcement. The moment-curvature relationships of the tested columns were determined from this analysis and were compared with experimentally obtained curvatures. This comparison indicated that yielding in the CO40 specimen started at 2.53% applied drift ratio while this happened at 1.43% applied drift ratio for both the CI40 and CI20 specimens. It is seen in Fig. 8 that the maximum curvature up to the aforementioned levels of testing concentrated in the region close to the column end which signifies that the rebar slip began after yielding which resulted in curvature concentration away from the column-foundation interface.
Table 2 summarises yielding load (Vy), dy, du and µd for all three columns in both positive and negative directions of loading. It is noted that Vy is nearly 70% of Vmax for the CI20 and CI40 specimens while although this is 70% of Vmax for the negative direction of loading it was 82% for the positive direction of loading for the CO40 specimen. Park [50] has suggested that Vy can be taken as 75% of Vmax which correlates well with that observed in this paper. Further, (except the CO40 column) similar ductility was exhibited by the columns in both the positive and negative directions of loading. Further, the ductility of both IMRF columns (CI40 and CI20) is similar and higher as compared to the CO40 column.
The obtained ductility of the tested columns can be compared with the ductility demand
for structural elements recommended by ACI 369 [52]. The structural elements with µd = 2–4 are considered as moderate ductility while µd > 4 is classified as high ductility. It is noted in Table 2 that the column CO40 exhibited moderate ductility while specimens CI20 and CI40 exhibited high ductility according to the classification of ACI 369 [52].