Seismic Performance Indicators

Lateral Strength

The skeleton curve is an important basis for determining the characteristic points of the restoring force model of the component. The skeleton curve and three characteristic points of Specimen H45-1 are shown in Fig. 11. Divide the load and lateral displacement of each point on the skeleton curve by the yield load and yield displacement of the specimen, respectively, to obtain a dimensionless normalized skeleton curve, that is, the P/Py-Δ/Δy curve. Lateral strength is an important indicator of reinforced concrete members and an important characteristic point on the skeleton curve, including the yield load, maximum load, and ultimate load, as shown in Fig. 15.

Fig. 15
figure 15

Skeleton curve and characteristic points of specimen H45-1.

Displacement Ductility

Ductility is also an important index for reinforced concrete members, reflecting the ability of specimens to deform without a significant decrease in strength. The displacement ductility coefficient is

$$mu { = }{{Delta_{{text{u}}} } mathord{left/ {vphantom {{Delta_{{text{u}}} } {Delta_{{text{y}}} }}} right. kern-nulldelimiterspace} {Delta_{{text{y}}} }}$$

(1)

Energy Dissipation Capacity

The normalized cumulative hysteretic energy coefficient EN was used in this study as the indexes to evaluate the energy dissipated capacity of the specimens. EN reflects the growth of the total energy absorbed by the component under the repeated action of the earthquake. EN, m is the cumulative hysteretic energy consumption coefficient of the component at the end of the mth loading cycle (Li et al., 2019), the formula of it was given as

$$E_{N, m} = frac{1}{{{text{P}}_{y} Delta_{y} }}sumlimits_{i = 1}^{m} {S_{i} }$$

(2)

where Si is the area surrounded by the ith hysteresis loop (that is, the area of the shaded part in Fig. 16).

Fig. 16
figure 16

Schematic of the area enclosed by the ith hysteresis loop.

Stiffness Degradation

The stiffness degradation, which is caused by cracking, yielding of reinforcements, bond-slipping between steel and concrete, is an important index to reflect the level of damage of the columns. In low-cycle repeated tests, the loop stiffness K can be used to measure the overall stiffness of all cycles under the same amplitude. To facilitate comparison, the loop stiffness of the forward and reverse loops at the same displacement was averaged. Kj is the stiffness of the loop under the jth displacement amplitude (Li et al., 2019) and its formula is

$${text{K}}_{j} = frac{{sumlimits_{i = 1}^{n} {P_{j}^{i} } }}{{sumlimits_{i = 1}^{n} {Delta_{j}^{i} } }}$$

(3)

where (P_{j}^{i}) and (Delta_{j}^{i}) are the maximum horizontal load and displacement amplitude of the ith cycle under the jth displacement amplitude; n is the total number of loading cycles of the jth displacement amplitude.

Strength Degradation

In the quasi-static test, with the increase of the loading displacement amplitude increased, the column gradually entered the elasto-plastic phase from the elastic phase, and its stiffness and strength also deteriorated. The strength degradation can be expressed by the strength degradation coefficient λ, as shown in Formula (4):

$${uplambda }_{i}^{j} = frac{{P_{j}^{i} }}{{P_{j}^{1} }}$$

(4)

where ({uplambda }_{i}^{j}) is the strength degradation coefficient of the ith cycle under the jth displacement amplitude.

Effect of Axial Load Ratio

Fig. 17 gives the normalized skeleton curves of specimens in group I. It could be seen from that the influence of the axial load ratio was mainly reflected in the descending section of the curve. Before the yield displacement, the P/Py-Δ/Δy curves of each specimen almost overlapped. After reaching the maximum load, the P/Py-Δ/Δy curve of the specimen with the axial load ratio of 0.25 decreased faster and reached the ultimate load quickly.

Fig. 17
figure 17

Normalized skeleton curves of specimens in group I.

The lateral strength and displacement ductility coefficient for specimens with different axial load ratio are shown in Table 6. After the axial load ratio was increased from 0.1 to 0.25, the yield load, maximum load, and failure load were increased by about 37% of specimens (H45-1 and H45-2) with HRB400 reinforcements. For specimens (H45-3 and H45-4) with HTRB630 reinforcements, the lateral strength were increased more greatly, reaching about 48%, indicating that increasing the axial load ratio in a certain range was beneficial to the lateral strength of concrete columns. Compared with specimens H45-1 and H45-2, the diameter of longitudinal reinforcements of specimen T45-3 was smaller and the spacing of stirrups was larger; compared with specimens T45-3, the axial load of specimen T45-3 was smaller, so the strength of specimen T45-3 was lower. The yield displacement did not change much, the maximum displacement was increased by about 15%, and the failure displacement was decreased by about 28%. The displacement ductility coefficient μ of the four specimens were all above 3. The displacement ductility coefficient μ of the specimens with HRB400 reinforcements and the specimens with HTRB630 reinforcements were decreased by 22.2% and 32.9%, respectively, indicating that the increase of the axial load ratio significantly reduced the ductility of specimens.

Table 6 Lateral strength and displacement ductility coefficient of specimens in group I.

Fig. 18a gives the cumulative hysteretic energy coefficient EN curves of specimens in group I. Before approaching the limit displacement, the cumulative energy dissipation of the specimen with high axial load ratio was larger than that of the specimen with lower axial load ratio at the same displacement ductility. However, the difference between the two kinds of specimens gradually decreased with the increase of the displacement ductility.

Fig. 18
figure 18

Seismic performance of specimens in group I.

Fig. 18b gives the average loop stiffness K curves of specimens in group I. The energy dissipation capacity and stiffness of specimens with high axial load ratio at the same displacement ductility were obviously improved, but after the maximum load, the stiffness decreases rapidly.

Table 7 shows the strength degradation coefficients of the four specimens in control group I. The strength degradation coefficient of each specimen was greater than 0.95. The strength of the specimen degraded slightly (< 5%) with the increase of the number of cycles at the same displacement amplitude. Therefore, the effect of the axial load ratio on the strength degradation coefficient was not obvious.

Table 7 Strength degradation coefficient of specimens in control group I

Effect of Concrete Grade

Fig. 19 gives the normalized skeleton curves of specimens in group II. The influence of concrete grade was mainly reflected in the descending section after reaching the maximum point. Before the yield displacement, the P/Py-Δ/Δy curves of each specimen were similar. In the descending section after the maximum load, the P/Py-Δ/Δy curve of the high-strength concrete column decreased faster and reached the ultimate load quickly, which reflected the brittleness of the high-strength concrete material.

Fig. 19
figure 19

Normalized skeleton curves of specimens in group II.

The lateral strength and displacement ductility coefficient of specimens in group II are shown in Table 8. Increasing the concrete grade from C45 to C60, the yield load, maximum load and ultimate load of specimens H45-2 and H60-1 were increased by about 13% ~ 19%; the yield displacement was reduced by about 16–19% except for specimen T60-3, the maximum displacement was reduced by about 10–26%, and the ultimate displacement was reduced by about 6–34%. Except specimen T60-3, the displacement ductility coefficients μ of the other three specimens with C60 concrete were all above 3.

Table 8 Lateral strength and displacement ductility of specimens in group II.

Fig. 20a gives the cumulative hysteretic energy coefficient EN curves of specimens in group II. Except for specimens T45-5 and T60-3, the cumulative hysteresis energy dissipation of high-strength concrete specimens was much lower than that of common concrete specimens with the same displacement ductility.

Fig. 20
figure 20

Seismic performance of specimens in group II.

Fig. 20b gives the average loop stiffness K curves of specimens in group II. With the same displacement ductility, the loop stiffness of the C60 concrete specimens was greater than that of C45 concrete specimens. The stiffness degradation rate of C60 concrete columns was faster than that of C45 concrete columns.

Table 9 shows the strength degradation coefficients of specimens in control group II. The strength degradation coefficient of each specimen was greater than 0.95. The strength of the specimen degraded slightly (< 5%) with the increase of the number of cycles at the same displacement amplitude. Therefore, the effect of the concrete grade on the strength degradation coefficient was not obvious.

Table 9 Strength degradation coefficient of specimens in control group II.

Effect of Equal Strength Substitution of Longitudinal Reinforcements

Fig. 21 gives the normalized skeleton curves of specimens in group III. The influence of equal strength substitution of longitudinal reinforcements was mainly reflected in the descending section. Before the yield displacement, the P/Py-Δ/Δy curves of the specimens were similar. In the descending section after the maximum load, the specimens with HTRB630 longitudinal reinforcement descended slowly, which was more obvious in the positive direction of loading.

Fig. 21
figure 21

Normalized skeleton curves of specimens in group III.

The lateral strength and displacement ductility coefficient of specimens in group III are shown in Table 10. The equal strength replacement of longitudinal reinforcements has little effect on the lateral strength of the specimens. The displacement ductility coefficients μ of the four specimens were all above 3, indicating that whether it was common concrete C45 or high-strength concrete C60, HTRB630 high-strength reinforcements could work well. The displacement ductility coefficients of C45 concrete specimens and high-strength concrete C60 specimens were increased by 15.41% and 19.68%, respectively, indicating that the specimens with high-strength reinforcements had better displacement ductility when used in conjunction with C60 high-strength concrete.

Table 10 Lateral strength and displacement ductility of specimens in group III.

Fig. 22a gives the cumulative hysteretic energy coefficient EN curves of specimens in group III. In the initial stage of displacement loading, there was little difference in the cumulative energy dissipation of specimens before and after the equal strength substitution of longitudinal reinforcements. When the displacement increased to a certain degree, HRB400 steel bar gradually entered yield, and the energy dissipation capacity of the specimen was significantly enhanced. Replacing HRB400 reinforcements with HTRB630 reinforcements, the total accumulated energy dissipation of C45 concrete specimens was increased by 25.27%, and that of the C60 concrete specimens was decreased by 7.09%.

Fig. 22
figure 22

Seismic performance of specimens in group III.

Fig. 22b gives the average loop stiffness K curves of specimens in group III. Equal strength substitution of longitudinal reinforcements had little effect on the stiffness of specimens. The degradation trends of the specimens were exactly the same, and the stiffness was similar. The errors of the average loop stiffness of those specimens were within 10%.

Fig. 22c shows the rebar strain envelop curves of specimens in group III. In Fig. 17c, yield strains of HRB400 and HTRB630 reinforcements were marked with horizontal lines; the yield and ultimate displacements of specimens H45-2 and T45-2 were marked with a vertical line; “LO” represents longitudinal reinforcements; “TR” represents transverse reinforcements. The strain of HRB400 longitudinal reinforcements was increased with the increase of the loading displacement, and it entered yielding at about 2Δy, and the strain reached about 7300με when the specimen failed. The strain of HTRB630 longitudinal reinforcements was below 1400με, and the longitudinal reinforcements had not yet yielded at the time of failure. Under the condition of repeated loading, the HTRB630 longitudinal reinforcements could the yield point of steel bars, the concrete was crushed, and the HTRB630 longitudinal reinforcements and the concrete reached the failure state at the same time, giving full play to the seismic capacity of the reinforced concrete column.

Table 11 shows the strength degradation coefficients of specimens in control group III. The strength degradation coefficient of each specimen was greater than 0.94. The strength of the specimen degraded slightly (< 6%) with the increase of the number of cycles at the same displacement amplitude. Therefore, the effect of equal strength substitution of longitudinal reinforcements on the strength degradation coefficient was not obvious.。

Table 11 Strength degradation coefficient of specimens in control group III.

Effect of Equal Strength Substitution of Stirrups

Fig. 23 gives the normalized skeleton curves of specimens in group IV. The effect of equal strength substitution of stirrups was different due to the different grades of concrete. For C45 concrete specimens, the normalized skeleton curves of the two specimens almost completely overlap. For C60 concrete specimens, the part of the normalized skeleton curve before the maximum point was almost the same, and the drop rate of the high-strength stirrup specimen after the maximum point was faster.

Fig. 23
figure 23

Normalized skeleton curves of specimens in group IV.

The lateral strength and displacement ductility coefficient of specimens in group IV are shown in Table 12. Equal strength substitution of stirrups had little effect on the lateral strength of specimens. The displacement ductility coefficient μ of the four specimens were all above 3, indicating that whether it was C45 concrete or C60 concrete, HTRB630 high-strength stirrups could play an effective confinement role. The effect of equal-strength substitution of stirrups on the ductility of the specimen was related to the “efficiency” of the confinement of the stirrups. The practice of equal strength substitution of the stirrups by increasing the spacing of the stirrups reduces the confining effect of the stirrups to a certain extent.

Table 12 Lateral strength and displacement ductility of specimens in group IV.

Fig. 24a gives the cumulative hysteretic energy coefficient EN curves of specimens in group IV. In the initial stage of displacement loading, the equal strength substitution of stirrups had little effect on the cumulative energy dissipation of specimens. In the middle and late stage of displacement loading, the cumulative energy dissipation capacity of the specimens at the same displacement ductility was improved, but the increase was related to the concrete grades. After the common stirrups were replaced with high-strength stirrups, the total energy dissipation of high-strength concrete specimens was decreased by 26.79%.

Fig. 24
figure 24

Seismic performance of specimens in group IV.

Fig. 24b gives the average loop stiffness K curves of specimens in group IV. The stiffness of the specimen decreased after equal strong substitution of stirrups. The degradation trend of the curves of the two specimens in the two groups was exactly the same. The spacing of stirrups of specimen T45-2 was larger than that of specimen T45-1, and the spacing of stirrups of specimen T60-2 was larger than that of specimen T60-1, so the average loop stiffness of the specimens with high-strength stirrups was slightly lower than that of the specimens with common stirrups at the same displacement ductility.

Fig. 24c shows the rebar strain envelop curves of specimens in group IV. The strain gauges of longitudinal reinforcements of specimen T45-4 were damaged when they were close to failure, and the strain of the last level in the figure was recorded as 0. In the early stage of displacement loading, the longitudinal reinforcements and stirrup strains of the specimens with high-strength stirrups were smaller than those of the specimens with common stirrups, which could explain ξeq of specimens with HTRB630 stirrups were lower when the displacement was small. When the specimens were damaged, the stirrup of the specimen T45-2 was close to yield, and the stirrup strain of the specimen T45-4 was less than half of the yield strain, indicating that the high-strength stirrup still had a large strength reserve and safety degree when the specimen was damaged.

Table 13 shows the strength degradation coefficients of specimens in control group IV. The strength degradation coefficient of each specimen was greater than 0.96. The strength of the specimen degraded slightly (< 4%) with the increase of the number of cycles at the same displacement amplitude. Therefore, the effect of equal strength substitution of stirrups on the strength degradation coefficient was not obvious.

Table 13 Strength degradation coefficient of specimens in control group IV.

Effect of Equal Volume Substitution of Stirrups

Fig. 25 gives the normalized skeleton curves of specimens in group V. The effect of equal volume substitution of stirrups was mainly reflected in the load drop section. When the maximum load point was reached, the ratio of the maximum load to the yield load of the specimen with HTRB630 stirrups was higher. In the descending section of the load, the load drop rate of the specimen with HTRB630 stirrups was significantly smaller than that of the specimen with HRB400 stirrups.

Fig. 25
figure 25

Normalized skeleton curves of specimens in group V.

The lateral strength and displacement ductility coefficient of specimens in group V are shown in Table 14. After the equal volume substitution of stirrups, the lateral strength of specimens was slightly decreased. Theoretically, after the HRB400 stirrups were replaced with HTRB630 stirrups, the strength and the ductility of specimens would not decrease significantly. Therefore, there were problems with the experimental data of specimen T60-3. After the equal volume substitution of stirrups, the elastic modulus of common steel bars and high-strength steel bars were not much different, so the passive restraint stresses of stirrups caused by the same lateral deformation of concrete were not much different. For the case that the stirrups still did not yield when the specimen was damaged, the high-strength stirrup provided greater strength reserve and redundancy. For the case that the stirrup was close to yield before the failure of specimens, the high-strength stirrups could give full play to the characteristics of high-strength and provide greater lateral restraint stress to slow down the decline of the lateral strength of specimens. The test results of specimen T45-5 supported the theoretical analysis, but the results of specimen T60-3 did not meet the theoretical analysis. Whether it was caused by the quality of the specimen production or another reason needs further testing and comparison.

Table 14 Lateral strength and displacement ductility of specimens in group V.

Fig. 26a gives the cumulative hysteretic energy coefficient EN curves of specimens in group V. In the initial stage of displacement loading, equal volume substitution of stirrups had little effect on the cumulative dissipation of specimens. After the displacement is increased to 2.0Δy, the accumulated energy dissipation capacity of specimens with high-strength stirrups was stronger than that of the specimen with common stirrups at the same displacement ductility, and the difference between the two increased as the loading displacement increased.

Fig. 26
figure 26

Seismic performance of specimens in group V.

Fig. 26b gives the average loop stiffness K curves of specimens in group V. The stiffness of the specimen was reduced to a certain extent after equal volume substitution of stirrups. At the same displacement ductility, the stiffness of specimens with high-strength stirrups was significantly lower than that of specimens with common stirrups. The stiffness deterioration rate of specimens was decreased after equal volume substitution of stirrups.

Table 15 shows the strength degradation coefficients of specimens in control group V. The strength degradation coefficient of each specimen was greater than 0.96. The strength of the specimen degraded slightly (< 4%) with the increase of the number of cycles at the same displacement amplitude. Therefore, the effect of equal volume substitution of stirrups on the strength degradation coefficient was not obvious.

Table 15 Strength degradation coefficient of specimens in control group V.

Effect of Equal Strength Substitution of Confined Stirrups

Fig. 27 gives the normalized skeleton curves of specimens in group VI. At about 1.0Δy, the specimen of high-strength stirrups had obvious secondary strengthening points, and the rate of descending section was slow. In the elastic stage, the stiffness of the specimen with HTRb630 stirrups was also slightly larger than that of the specimen with HRB400 stirrups.

Fig. 27
figure 27

Normalized skeleton curves of specimens in group VI.

The lateral strength and displacement ductility of specimens in group VI are shown in Table 16. The carrying capacity was slightly improved. The displacement ductility coefficient of specimen T60-5 was 18.61% larger than that of specimen T60-4. In Sect. 4.5, the displacement ductility coefficient of specimens with high-strength concrete was decreased significantly after equal strength substitution of stirrups. This difference further illustrated that the effects of equal strength substitution of stirrups were based on similar constraints. Only under the premise of ensuring confining effect of stirrups, can the purpose of saving steel bars be avoided without affecting the seismic performance of specimens.

Table 16 Lateral strength and displacement ductility of specimens in group VI.

Fig. 28a gives the cumulative hysteretic energy coefficient EN curves specimens in group VI. With the increase of the displacement, the cumulative energy dissipation capacity of the specimen with high-strength confined stirrups was significantly improved than that of the specimen with common constrained stirrups. The total accumulated energy dissipation of specimens with high-strength confined stirrups was increased significantly by 46.09%.

Fig. 28
figure 28

Seismic performance of specimens in group VI.

Fig. 28b gives the average loop stiffness K curves of specimens in group VI. The trend of the loop stiffness degradation curve of the two specimens was exactly the same. Equal strength of confined stirrups would not affect the stiffness of specimens.

Fig. 28c shows the rebar strain envelop curves of specimens in group VI. When the yield displacement was reached, the strain of the longitudinal steel bars of the two specimens did not reach the yield. When the specimens were damaged, the longitudinal reinforcements and stirrups of the two specimens had yielded. The rebar strain of the specimen with confined stirrups was significantly larger than that of the first 11 specimens, which indicated that confined stirrups could not only enhance the ductility of specimens, but also make full use of the strength of high-strength longitudinal reinforcements and high-strength stirrups.

Table 17 shows the strength degradation coefficients of specimens in control group VI. The cyclic strength degradation of specimen T60-5 at displacement ductility of 4.65 was slightly faster, the strength degradation of other cycles was relatively slight. The strength degradation coefficient of each specimen was greater than 0.95. The strength of the specimen degraded slightly (< 5%) with the increase of the number of cycles at the same displacement amplitude. Therefore, the effect of equal strength substitution of confined stirrups on the strength degradation coefficient was not obvious.

Table 17 Strength degradation coefficient of specimens in control group VI.

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