Effect of axial load and transverse reinforcements on the seismic performance of reinforced concrete columns

Abstract

The aim of this research is to assess the seismic performance of reinforced concrete columns under different axial load and transverse reinforcement ratios. These two parameters are very important as for the ductility, strength, stiffness, and energy dissipation capacity for a given reinforced concrete column. Effects of variable axial load ratio and transverse reinforcement ratio on the seismic performance of reinforced concrete columns are thoroughly analyzed. The finite element computer program Seismo-Structure was used to perform the analysis of series of reinforced concrete columns tested by the second author and other researchers. In order to reflect the reality and grasp the actual behavior of the specimens, special attention was paid to select the models for concrete, confined concrete, and steel components. Good agreements were obtained between the experimental and the analytical results either for the lateral force-drift relationships or for the damage progress prediction at different stages of the loading.

Keywords

reinforced concrete columns / axial load / transverse reinforcement / ductility

Introduction

During the past 30 years, numerous researchers carried out several investigations on the flexural behavior of reinforced concrete columns. Many parameters, such as axial load ratio, volumetric transverse reinforcement ratio, configurations of transverse reinforcements, main reinforcement ratio, concrete strength, and yield strength of steel reinforcements, can influence the seismic performance of a reinforced concrete column.

Flexural tests were carried out on reinforced concrete columns under eccentric loading. Flexural response parameters, such as ductility and rotation capacity of reinforced concrete columns depends on the type of configurations of transverse reinforcements, spacing, and amount of transverse reinforcements. An equation integrating these parameters has been developed in order to predict the curvature ductility [¹].

Twelve flexural tests were carried out on reinforced concrete columns. The axial load ratio applied to the columns was varied in the range of 0.2–0.4. The flexural strength has been increased with axial load. There was no difference on the flexural behavior of columns having the same volumetric transverse reinforcement ratio with different transverse reinforcement spacing [²]. However, when the transverse reinforcement ratio was dropped to 50% of ACI-318 provision, the columns behaved in a less ductile manner [³].

In another context, eight full-scaled reinforced concrete columns were tested in order to investigate the flexural behavior of reinforced concrete columns with different transverse reinforcement ratios. The results showed that the shear strength of the column was not correlated to the displacement ductility demand. It has been noted also that the vertical strength was sharply reduced after the loss of the lateral resistance and columns with small amount of transverse reinforcement ratio would fail in a shear manner. On the other hand, the columns with high transverse reinforcement ratio would fail in a flexural manner with some degree of ductility [⁴].

In 1993, tests were conducted on reinforced concrete columns subjected to cyclic lateral load and high axial load. The experimental results were compared with predicted values obtained from ACI-318 [⁵]. The study revealed that the maximum strength and ductility of reinforced concrete column increased when reducing the spacing of transverse reinforcements and main reinforcements. Configurations of transverse reinforcements affect flexural behavior of reinforced concrete column. Intermediate reinforcements benefit confined core concrete to resist buckling of main reinforcements. The load capacity ratio of reinforced concrete column increased with peak strength but reduced the ductility. In addition, beam and slab provide restraint to enhance flexural strength of end section of reinforced concrete column. Flexural strength of reinforced concrete column reduces with span depth ratio.

ACI-318 did not consider the configurations of transverse reinforcement, load capacity, and stub column effect. The required volumetric ratio of transverse reinforcement may not be conservative to resist severe seismic action [⁶].

Fourteen tests were carried out to investigate cyclic behavior of reinforced concrete column. High axial load values reduced considerably the flexural capacity of the RC columns. Closely spaced transverse reinforcements were effective to restrain the main reinforcements of the column. Ductility level with a flexural capacity of reinforced concrete column can be increased by limiting the axial load. Biaxial lateral loading reduced the flexural strength of the tested reinforced concrete columns [⁷]. In 1999, four experimental tests were conducted. The tests consisted of specimens with 40% to 60% volumetric transverse reinforcement ratio as required by American Association of State Highway and Transportation Officials (AASHTO). Axial load ratio applied to the specimens was relatively small, similar to loading capacity ratio of reinforced concrete column added on bridge structures (0.1 and 0.24P/P₀) [⁸].

The transverse reinforcement ratio required in AASHTO is reserved mainly for severe seismic zone. The aim of Wehbe’s project was to propose a volumetric ratio of transverse reinforcement for elements of structures resisting moderate earthquakes. Nine tests were carried out to investigate the shear span depth ratio, the configuration of transverse reinforcements and axial load ratio effects on the seismic performance of RC columns. It was found that the drift capacity of the reinforced concrete column with reinforcement hoops having 90° end hooks was reduced to 40% compared to specimens with reinforcement hoops having 135° end hooks [⁹]. Later, 14 reinforced concrete specimens with high axial load ratio were investigated [¹⁰]. The test parameters were: configuration of transverse reinforcements, transverse reinforcement ratio, and shear span depth ratio. Increasing the axial load ratio increased the shear capacity but reduces the ductility of reinforced concrete specimens. Therefore, the authors suggested to limit the applied axial load of reinforced concrete column for a better seismic resistance.

In the present study, the effects of two significant parameters, namely the axial load ratio and the amount of transverse reinforcement, were thoroughly investigated by carrying out several finite element analyses using the Seismo-Structure software [¹¹]. First, the numerical model was validated against series of selected test data [¹²–¹⁵]. In the second step, the damage index was assessed and compared to the observed damage.

Experimental analysis

Fifteen RC columns subjected to cyclic loadings tested by the authors and other researchers are selected in this study. The specimens were divided into two categories. The first category contains columns tested under different axial load intensity and the second category includes columns showing different transverse reinforcement ratios. The selected columns for this database were of various configurations, namely cantilevers or double-ended columns as illustrated in Fig. 1. For cantilever specimens the forces and deflections were used as reported by the original researchers. However, for double ended specimens, the original lateral forces were divided by two and the deflections were kept the same because the elements were fixed at both ends. Material properties, as well as geometric characteristics are shown in Tables 1–2.

Experimental results

To investigate the effect of the axial load ratio and the transverse reinforcement ratio on the cyclic behavior of the selected RC columns, the lateral load capacity and the total dissipated energy during the loading test were evaluated. Variation of the equivalent viscous damping factor (H_eq) was also computed using the first cycle loops to each of the imposed drift angle [¹⁶]. The equivalent viscous damping, H_eq, was computed using the following expression:

(1)H_{\mathrm{e}\mathrm{q}}=\frac{\mathrm{1}}{\mathrm{4}\mathrm{\pi }}{\displaystyle \frac{\mathrm{\Delta }W}{W_{\mathrm{e}}}},

where DW is the area enclosed by one cycle of hysteresis loop and W_e is the equivalent potential energy.

Effect of axial load ratio

Based on the analyzed test results, shown in Figs. 2–5, of the 11 specimens under different axial load intensity, the following observations can be drawn:

• The yield drift ratio was almost constant for different axial load ratio;

• The post-elastic range decreased significantly with increasing axial load ratio;

• The lateral load capacity of the columns increased with increasing axial load ratio.

For specimens under a unidirectional loading, and beyond a certain limit, increasing the axial load intensity caused a rapid decrease of the dissipated energy by the columns. These observations are also valid for specimens under a bidirectional loading, as shown by the results of specimens 14 and 15 [¹⁷,¹⁸].

Increasing the axial load ratio causes a decrease in ductility levels as clearly shown in Fig. 4. This indicates that, columns with high axial load ratio will not show enough ductility during a seismic loading and hence, may experience important damage that can be beyond repair after a seismic event.

Observed damage

The following remarks emerged from the observed damage of specimens:

• The spalled concrete zone increases significantly with increasing the scale of columns (large scale). It can be clearly seen that for small scale column, damage is concentrated at the lower part;

• Buckling of the longitudinal rebar is more important with the large scale columns for the same displacement.

It can be concluded that scale effect has also a significant influence on the seismic performance of a column, especially on the damage pattern.

Effect of the transverse reinforcement ratio

The following remarks emerged while analyzing the experimental results of the six specimens with different shear reinforcement ratios, as shown in Figs. 6–9:

• The post-elastic range increases significantly with increasing the amount of the transverse reinforcement (r_t);

• For the analyzed specimens, the amount of transverse reinforcement has no significant effect on the lateral load capacity of the columns and on the yield drift ratio, d_y;

• The capacity of energy dissipation of the columns increases with increasing the amount of transverse reinforcement.

Increasing the transversal reinforcement ratio caused an increase in ductility levels as shown in Fig. 7 for the specimens having a volumetric transversal reinforcement ratio varying between 0.32% and 2%.

As illustrated in Figs. 8–9, the ductility enhancement due to the increase of the transverse reinforcement leads to an increase of the dissipated energy as well as the equivalent viscous damping.

Observed damage

The following remarks emerged from the observed damage of specimens:

For all specimens, concrete cover spalled first followed by buckling of longitudinal corner reinforcement. As test progressed, concrete at the corners started crushing and gradually load carrying capacity was reduced as damage penetrated toward the column core. Strain of the external hoop started to reduce while an increase in strain of the internal hoop took place. This means that concrete at the peripheral of the core was severally damaged, hence effective concrete area reduced considerably.

Concluding observations

The axial load ratio and transverse reinforcement ratio have significant effects on the ultimate ductility of columns. The latter increases with the amount of transverse reinforcement and decreases when increasing the values of the axial load ratio.

Numerical analysis

To estimate quantitatively the effects of axial load ratio and transverse reinforcement ratio, several finite element models were elaborated using the Seismo-Structure software.

Seismo-Structure is a finite element package capable of predicting the large displacement behavior of space frames under static or dynamic loading, taking into account both geometric and material nonlinearities. Here after, the theoretical background, modeling and the adopted material models used in our study are briefly described.

Geometric nonlinearity

Large displacements/rotations and large independent deformations relative to the frame element’s chord (also known as P-Delta effects) are taken into account in our model through the employment of a total co-rotational formulation [¹⁹]. The implemented total co-rotational formulation is based on an exact description of the kinematic transformations associated with large displacements and three-dimensional rotations of the member. This leads to the correct definition of the element’s independent deformations and forces, as well as to the natural definition of the effects of geometrical nonlinearities on the stiffness matrix. The implementation of this formulation considers, without losing its generality, small deformations relative to the element’s chord, not with standing the presence of large nodal displacements and rotations. In the local chord system of the beam-column element, six basic displacement degrees-of-freedom and corresponding element internal forces are defined, as shown in Fig. 10.

Material inelasticity

Distributed inelasticity elements are becoming widely employed in earthquake engineering applications, either for research or professional engineering purposes. While their advantages in relation to the simpler lumped-plasticity models, together with a concise description of their historical evolution and discussion of existing limitations [²⁰,²¹], here it is simply noted that distributed inelasticity elements do not require (not necessarily straightforward) calibration of empirical response parameters against the response of an actual or ideal frame element under idealized loading conditions, as is instead needed for concentrated-plasticity phenomenological models. In Seismo-Structure, the so-called fiber approach is used to represent the cross-section behavior, where each fiber is associated with a uniaxial stress-strain relationship; the sectional stress-strain state of elements is then obtained through the integration of the nonlinear uniaxial stress-strain response of the individual fibers in which the section has been subdivided. The discretisation of a typical reinforced concrete cross-section is shown, as an example, in Fig. 11.

Such models feature additional assets, which can be summarized as: no requirement of a prior moment-curvature analysis of members; no need to introduce any element hysteretic response (as it is implicitly defined by the material constitutive models); direct modeling of axial load-bending moment interaction (both on strength and stiffness); straightforward representation of biaxial loading, and interaction between flexural strength in orthogonal directions. However, the bond effect concrete-steel was not taken into account in this analysis and was considered as a “perfect bond”.

Distributed inelasticity frame elements can be implemented with two different finite elements (FE) formulations: the classical displacement-based (DB) ones [²²,²³], and the more recent force-based (FB) formulations [²⁴,²⁵]. In a DB approach the displacement field is imposed, while in a FB element equilibrium is strictly satisfied and no restraints are placed to the development of inelastic deformations throughout the member [²⁶,²⁷]. Both aforementioned DB and FB element formulations are implemented, with the latter being typically recommended, since, as mentioned above, it does not in general call for element discretisation, thus leading to considerably smaller models, with respect to when DB elements are used, and thus much faster analyses, notwithstanding the heavier element equilibrium calculations. An exception to this non-discretisation rule arises when localization issues are expected, in which case special cautions/measures are needed [²⁸]. In addition, the use of a single element per structural element gives users the possibility of readily employing element chord-rotations output for seismic code verifications (e.g., Eurocode 8, FEMA-356, ATC-40, etc.). Instead, when the structural member has had to be discretised in two or more frame elements (necessarily the case for DB elements), then users need to post-process nodal displacements/rotation in order to estimate the member’s chord-rotations [²⁹].

Material models

Menegotto-Pinto steel model

This is a uniaxial steel model initially programmed by Yassin based on a simple, yet efficient, stress-strain relationship proposed by Menegotto and Pinto [³⁰,³¹], coupled with the isotropic hardening rules [³²]. The current implementation follows that carried out by Monti et al. [³³]. An additional memory rule proposed by Fragiadakis and Papadrakakis is also introduced, for higher numerical stability/accuracy under transient seismic loading [²¹]. Its employment should be confined to the modeling of reinforced concrete structures, particularly those subjected to complex loading histories, where significant load reversals might occur. As discussed by Prota et al., with the correct calibration, this model, initially developed with ribbed reinforcement bars in mind, can also be employed for the modeling of smooth rebars, often found in existing structures [³⁴].

Mander et al. nonlinear concrete model

This is a uniaxial nonlinear constant confinement model, initially programmed by Madas, that follows the constitutive relationship proposed by Mander and the cyclic rules proposed by Martinez-Rueda and Elnashai [³⁵–³⁷]. The confinement effects provided by the lateral transverse reinforcement are incorporated through the rules proposed by Mander, whereby constant confining pressure is assumed throughout the entire stress-strain range.

Comparison between numerical and experimental results

A numerical model was developed based on the adopted hypotheses and the material models described above to simulate the seismic performance of the reinforced concrete columns described in section 2. Hereafter, the experimental results are compared to the numerical ones in terms of load-displacement envelope curves, energy dissipation capacity and equivalent viscous damping. These comparisons are shown through Figs. 12–17.

Effect of the variation of axial load ratio

Table 3 shows a comparison between the experimental and the analytical results in terms of the lateral load capacity, the dissipated energy, and equivalent viscous damping. The experimental and the analytical results are in good agreement as can be seen through the ratio (Num/Exp) given in Table 3. The average values of the ratios (Num/Exp) of specimen 3, for instance, are equal to 0.94, 0.96, and 0.90 for the lateral load capacity, the dissipated energy, and equivalent viscous damping, respectively.

Effect of the variation of volumetric transverse reinforcement ratio

Both the numerical and experimental results, together with their ratios are given in Table 4, while the corresponding curves are shown in Figs. 15–17. The average values of the (Num/Exp) ratios for the lateral load capacity, the dissipated energy and the equivalent viscous damping are within the range of 0.82–1.03 for all the specimens. A good agreement is obtained between the numerical and experimental results with a trend of an experimental excess margin particularly for the equivalent viscous damping.

Local damage index

Structural damage prediction under cyclic loading has been extensively studied and various models have been inventoried [³⁸]. In this section, the damage index formulation of Park and Ang is introduced. This is a local damage index for the design of reinforced concrete structures, ranging from 0 (undamaged structures) to 1 (failure). It includes both the maximum displacement ductility and cumulative dissipated energy [³⁹]. The local damage index, D, is given by the following equation:

(2)D={\displaystyle \frac{x_{\mathrm{m}}}{x_{\mathrm{u}}}}+{\displaystyle \frac{\beta }{F_{\mathrm{y}}{x}_{\mathrm{u}}}}{\displaystyle \int \mathrm{d}E},

where x_m is the maximum deformation under cyclic loading; x_u is the ultimate deformation under monotonic loading; F_y represents the yield strength; dE is the incremental dissipated hysteretic energy; and b is a dimensionless parameter.

Table 5 summarizes the relationships between the degree of damage, the physical appearance and the damage index value of Park and Ang. In the present case, the monotonic load-displacement relationship and the maximum deformation, x_u, were assessed for each column. The b values calculated using Eq. (3), shows a negative correlation with the transverse reinforcement percentage (r_t), a positive correlation with the longitudinal reinforcement percentage (r_l), a weak correlation with both the shear span ratio (l/d) and the level of axial load (N/f_cA_c). No correlation was found between the calculated b values and the compressive strength of concrete f_c.

(3)\beta ={\mathrm{0.66}}^{{\rho }_{\mathrm{t}}}\left[-\mathrm{0.28}+\mathrm{0.19}{\rho }_{\mathrm{l}}+\mathrm{0.06}{\displaystyle \frac{l}{d}}+\mathrm{0.47}{\displaystyle \frac{N}{f_{\mathrm{c}}{A}_{\mathrm{c}}}}\right].

The observed damages during the tests (crushing of concrete and buckling of rebars) are given at the corresponding displacement. The computed damage matched well the observed damage during the test for all specimens as illustrated in Table 6. It can be observed that, for specimens that suffered some buckling of the longitudinal reinforcement, the computed damage index gave a numerical value greater than 0.8. Effects of axial load intensity and transversal reinforcement ratio on the damage progress were clearly observed as it will be discussed in the following section.

Effect of the transverse reinforcement ratio

Figure 18 shows a comparison of the damage index progress between specimens having different transverse reinforcement ratios, whereas, the other parameters were kept identical.

It is clearly noticed that for a given drift, specimen with a larger amount of transverse reinforcement presented less damage and sustained more deformation. As an example, at a drift of 3% specimen 2 with r_t = 0.8% showed a damage index greater than 0.8, however, specimen 1 with r_t = 1.2% showed a damage index of 0.6.

Effect of axial load intensity

Effect of the axial load on the damage progress in shown in Fig. 19. It illustrates an increase of the damage slope curves with respect to the axial load intensity for all specimens. It can also be noticed that, specimens with a moderate axial load (N/f_cA_c less than 0.21) sustained nearly the same maximum drift like the case of specimens 9, 10, and 11. However, for large axial loads (N/f_cA_c greater than 0.4) the maximum drift is significantly reduced. This can be clearly seen in Fig. 19 while comparing specimen 3 and 7 and also specimens 6 and 8.

Conclusions

Some of the main results drawn from tests and numerical simulations of 15 reinforced concrete columns with different axial load intensities and transverse reinforcement ratios were presented and discussed in this paper. The purpose of this research is to investigate the seismic behavior of RC columns by analyzing the effect of some crucial parameters on the overall performance of RC columns. Numerical models for the tested specimens were developed and analyzed using Seismo-Structure software. The analytical results show reasonable agreement with the experimental ones. The analysis did not only predict accurately the stiffness, load, and deformation at the peak level, but also captured the post-peak softening as well. It was shown that both factors, axial load intensity and transverse reinforcement ratios, have an important influence on strength, maximum sustained displacements as well as on the energy dissipation capacity of the column. Damage was assessed for the specimens using Park and Ang damage index and the model performs well in predicting the observed damage. The authors intend to extend their research were to study the effect of other parameters in the future such as concrete compressive strength and yielding strength of the transverse and the longitudinal reinforcement.

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