Shear-critical reinforced concrete columns under various loading rates

Abstract

This paper presents an experimental study of shear-governed reinforced concrete columns subjected to different loading rates. Four typical short columns were tested cyclically with loading rate of 0.05, 1, 3, and 5 Hz, simulating seismic load. Test result indicated that the loading rate does not affect the column behavior when the rate is up to 5 Hz. Furthermore, Carbon Nano-Fiber Aggregates (CNFAs) were utilized as internal sensors to detect the damage in the column. The test result shows that the CNFAs work well sensing the structural behavior. The CNFA output was further quantitatively correlated to the structural damage level. Finally, a finite element analytical model was constructed to describe the behavior of short columns with shear failure. The analytical model successfully modeled the cyclic loading test results.

Graphical abstract

Keywords

reinforced concrete columns / shear failure / loading rate / Carbon Nano-Fiber Aggregates (CNFAs) / finite element analysis / OpenSees

1 Introduction

The shear failure mode has always been the most undesired failure mechanism in reinforced concrete (RC) structural elements due to its brittle behavior, especially under seismic loads. However, most of the RC structures designed prior to 1970s code were vulnerable to shear failure as the code had not introduced ductile design and the strength hierarchy. Therefore, many researchers have studied the shear mechanism in the past few decades to understand its behavior [1−6]. The studies resulted in several robust theories with corresponding analytical models to describe the shear behavior [7−13].

The effect of loading rate on typical construction materials is well understood. Based on uniaxial tests performed on concrete and steel, it is widely known that higher loading rates result in higher material strength. Research works in literature have also observed that higher loading rates may shift the failure mode of a structure from a preferred gradual and ductile manner to a less desirable sudden and brittle mode [14−17]. Such phenomenon in RC structures is deemed dangerous under a seismic activity. However, full-scale testing on RC structures has not been adequately conducted due to the incapability of testing equipment to perform high rate loading tests. With the new MTS actuator at Tongji University, which is capable of simulating seismic loading rate effects, a unique experimental test on full-scale structural elements was conducted to study the behavior of shear-critical RC structures subjected to different loading rates.

Much attention in the past few years has been given to develop a robust and reliable structural health monitoring technology, which would be useful in determining real-time damage levels to structures after a catastrophe such as an earthquake. Most of such structural health monitoring sensors developed in the past lack durability and reliability. In this work, a new type of sensor, Carbon Nano-Fiber Aggregates (CNFAs) developed at the University of Houston [18−20], which are capable of performing self-sensing, were implemented on the test specimens to monitor the localized damage on the structure. The CNFAs are believed to be durable, robust and reliable in determining the damage level when placed in critically locations in a structure. Introduced in Howser [20], the CNFAs utilize a four-probe method (see Fig. 1) to measure change in the electrical resistance of a carbon nano-fibrous cement mortar matrix under a stress regime. In this method, electric current is supplied through the outer probes (1 and 4) and the voltage drop can be measured across the inner probes (2 and 3), as shown in Fig. 1.

The electrical resistance on the CNFA is then calculated using Ohm’s law, represented in Eq. (1). The Electrical Resistance Variation (ERV) can be calculated based on Eq. (2).

(1)V=RI,

(2)ERV={\displaystyle \frac{R_i-R_{\mathrm{0}}}{R_{\mathrm{0}}}},

where, V is the voltage (V), R is the electrical resistance (Ω), I is the electric current (A), R_i is the resistance at step i (Ω) and R₀ is the original resistance (Ω). In the past research, the ERV was proven to correlate well in term of the phase angle with the displacement history as well as load history [19,20]. In this study, the previous findings were extended to correlate the electrical resistance variation in the CNFAs directly with the damage state of the structural member.

2 Research significance

This research provides three valuable key points in understanding shear critical RC structure. First, it provides insight on the loading rate effect on shear critical RC columns. Moreover, it serves as a reference or guide in development and application of the CNFAs as internal sensor for structure health monitoring. Furthermore, an accurate finite element model was developed to predict the shear behavior of short RC columns.

3 Experimental program

3.1 Column specimens

Four identical RC columns were constructed and tested to failure in this study. The typical column cross-section and the plan view are presented in Fig. 2. The cross-section of the column was 450 mm square with 1300 mm effective length. The columns were reinforced with 14-25 mm diam. longitudinal rebar, providing a longitudinal reinforcement ratio of 3.4% by volume of concrete. The column also contained 8mm diam. stirrups with a spacing of 200 mm. This resulted in a transverse reinforcement ratio of 0.195% by volume of concrete. The columns were designed to fail in shear (i.e., shear critical) and hence were provided with larger amounts of longitudinal steel. The European standard rebars were used on the columns with the nominal properties shown in Table 1. The tests were conducted without any axial load applied on the columns.

Standard compression tests on concrete cube samples showed that the average concrete strength at the testing day was 28 MPa while the tensile tests on rebar samples indicated that the average yielding strength of rebar were 354.5 MPa and 333.7 MPa for bar #25 and bar #8, respectively.

3.2 Installation of CNFAs

After the rebar cages were built and the footing poured, the columns were instrumented with internal sensors. Twelve CNFAs and twelve strain gauges were attached on each column at critical locations. The alignment and the location of the sensors can be found in Fig. 2.

Figure 3 shows one of the installed CNFAs before the concrete was poured. The CNFAs were fixed to the rebar using plastic zip ties. The rebar adjacent to the CNFA were painted with epoxy so that the electrical properties of the rebar would not affect the electrical properties of the CNFAs.

To measure the electrical resistance, the outer wires of the CNFA were connected in series with a 10 kΩ resistor and a 10 V DC power supply, as shown in Fig. 4. The voltage drop across the inner wires of the CNFA and the resistor was measured using a Data Acquisition System (DAS).

3.3 Test setup

The testing was carried out at Tongji University’s Structures Laboratory. Each column’s footing was attached to the strong floor using four long bolts to represent fixed condition (Fig. 5). The actuator was connected to a reaction wall and provided lateral force on the RC column via four rods connected integrally at top of the RC column specimen (Figs. 2 and 5). Four Linear Variable Displacement Transducers (LVDTs) were attached to the column. One LVDT was installed on the top of column and connected to a reference frame to measure the horizontal displacement at column top (i.e., drift) throughout the test, two LVDTs were attached vertically on the column footing to measure rotation on the footing and one LVDT was attached horizontally on the foundation to measure horizontal displacement on the footing. The full setup of the column test is shown in Fig. 5.

3.4 Loading protocol

This study employed a cyclic loading protocol to test the columns to simulate an earthquake. Horizontal Displacement control loading protocol was utilized for the test with the actuator displacement target shown in Table 2. Three cycles of loading were applied for each target displacement. All four columns were subjected to the same cyclic loading protocol, however, with different loading rate. Loading rate of 0.05, 1.0, 3, and 5 Hz were applied to column 1, 2, 3, and 4, respectively.

4 Experimental results and discussion

4.1 Global force displacement result

Figure 6 shows the global Force - Horizontal Displacement behavior of all RC column specimens. It can be seen that all the RC column specimens had almost same shear strengths, maximum lateral displacements and stiffness. It is clear that all of the columns exhibited a very brittle behavior with excessive pinching, typical of a cyclic-shear failure. The column strength decreased significantly after reaching the ultimate point indicating lower residual strengths and post-peak ductility. All of the columns also showed sudden drop in strength and stiffness on the pull-side at approximately -10 mm displacement. This may have been caused by the first push cycle which would have resulted in the onset of first tensile cracking of concrete on the pull-side. This sudden reduction in stiffness was found to be correlated with the buckling of the longitudinal rebar.

Figure 7 shows the damage pattern of the RC columns at the end of the tests. The failure photos clearly indicate a combined failure mode i.e., flexural concrete crushing (indicated by large longitudinal concrete spalling at the extreme fiber, resulting in loss of confinement of main rebars and subsequent buckling under excessive compressive stresses) and shear. It is noteworthy that the concrete spalling and consequent failure of all the RC column specimens occurred on the pull-side, corresponding to the initial reduction in column stiffness and strength on this side, depicted in Fig. 6.

Figure 8 shows the global Force-Horizontal Displacement envelope curve of all the RC columns plotted together. All of the columns displayed almost identical ultimate force and stiffness pattern. There were also no clear and distinct indications of any particular effects of the varied loading rate on the shear behavior of tested RC column specimens. Therefore, it can be concluded that when the loading rate is small, approximately up to 5 Hz, the effect of loading rate is not significant.

4.2 Results of structural health monitoring with CNFA

The horizontal force, horizontal displacement, and measured ERV using the CNFAs were compared for the 12 - CNFAs placed in a group of threes’ on each of the four rows, as depicted in Fig. 2. Figure 9 provides the comparison plot sample of CNFA 7, 8, 9 (Fig. 2) from RC Column-3. Qualitatively, the CNFAs work reasonably well sensing the column behavior. The ERV measured by CNFAs increased as the force or stress increased, remained stable as the force/stresses remained stable and decreased as the force/stresses decreased. This is the best response one can expect from a reliable sensor. CNFAs have also proved well in catching the sudden changes in force and stiffness of the structure with corresponding changes in the measured ERV, almost without any time-lag. The phase angle of ERV match very well with the phase angle of force and displacement measurements.

Although, the ERV-vs-time pattern matched the force and displacement-vs-time pattern, the reference lines were not at a stationary point. The reference line could shift with no clear direction. However, it was observed that there was a clear tendency that the amplitude of the ERV kept increasing from the initial time until 590 sec. It is remarkable that this time i.e. 590 sec corresponded exactly to the ultimate point of Column-3 during the test, which means that the CNFAs could sense the structures behavior until it reaches failure in real-time without any time or signal lag. This is indeed a robust characteristic of the CNFA sensor.

Results similar to the ones depicted in Fig. 9 were also observed for the rest of the CNFAs used in this study, thus proving the ability of CNFAs to perform reliably and accurately as sensors. As the measured ERV amplitude increased with corresponding increase in the displacements for all CNFAs, therefore change in ERV i.e., ΔERV was calculated, using Eq (3), for each displacement to compare the responses of various CNFAs.

(3)\mathrm{\Delta }ERV=ER{V}_{\max }-ER{V}_{\min },

where, ERV_max and ERV_min were the maximum and minimum ERV amplitude for certain displacement, respectively. The plots of all of the ΔERV versus displacement are shown in Fig. 10. The plots were limited up to 13 mm displacement since most of the plots showed reduction of the ΔERV value thereafter. In this study, the reduction of ΔERV value was considered as the physical failure of CNFAs, hence not considered in the analysis or discussion. Sudden increase of ΔERV value beyond 1 was also considered as physical failure of CNFAs and not considered in the analysis or discussion.

It is noteworthy that many CNFAs show relatively less increase in ΔERV values than the others. This really shows the sensitivity of CNFAs to location i.e. critical and non-critical in the structure. The ΔERV values for the same displacements were averaged and plotted as mean value (solid line) in Fig. 10. Interestingly, the mean value line shows an increasing trend in ΔERV corresponding to the displacement. All of the mean ΔERV lines of each columns were compared in Fig. 11. It is very clear that there is no correlation between the ΔERV to the loading rate.

Damage levels, designated as onset of first cracking and complete failure, was linked to the measured ΔERV values by the CNFAs. In Column-1, the first visible crack was observed when the displacement reaches 5 mm. Based on the mean ΔERV value of Column-1, the cracking displacement is corresponding to ΔERV value of 0.06. Similarly, the cracking displacement for Column-2, 3, and 4 was observed at displacement 6.5 mm, 3 mm, and 2.5 mm which is corresponding to ΔERV value of 0.064, 0.14, and 0.065, respectively. The ΔERV values at cracking for all columns were very close to each other except for Column-3.

Due to the variation of mean ΔERV value of each column, the lower bound, upper bound and global mean of ΔERV were introduced (red lines in Fig. 11). The global mean ΔERV is considered sufficient to represent the variation in ΔERV value. A polynomial trend line (solid black line in Fig. 11) was proposed to represent the global mean ΔERV. The proposed line was terminated at displacement 11.5 mm since the global mean of ΔERV showed reduction in value.

Based on the proposed ΔERV line, the onset of cracking representing the initiation of first visible crack in concrete, which was observed at a displacement of about 4 mm for most of the RC columns, correlated with a mean ΔERV value of 0.08, indicative of onset or initiation of structural damage in structure. This may be defined as the minima of damage level or first damage level. The ultimate failure point of all tested RC column specimens was approximately at 11.5 mm displacement, which correlated with mean ΔERV of 0.2. This may be defined as the maxima of damage level or terminal damage level. More research work is required to establish meaningful and useful damage levels based on the mean ΔERV values as measured by the CNFAs.

5 Finite element analysis

An analytical model was developed in finite element software - OpenSees [21] to simulate the experimental result of this study. Each column was modeled using the finite element mesh illustrated in Fig. 12. In the tested shear-critical RC columns, although the primary force acting was shear dominant, development of some amount of bending induced stresses at the extreme fibers of column cross-section was unavoidable. Therefore, in the model, Fiber Beam-Column elements were introduced to simulate bending behavior at the extreme fibers of column cross-section (Fig. 12). The column web, which resists shear stresses, alone was modeled using Quadrilateral RCPlaneStress elements. The width of quadrilateral element that resists the shear stresses was assumed to be 50% of the gross cross-section dimension as shown in Fig. 12. Both the fiber beam-column elements and the quadrilateral element were tied together so as to work together to resist the lateral load in unison considering strain-compatibility and force-equilibrium across the elements.

The Kent and Park [22] constitutive model, represented by the “Concrete01” uniaxial material model in OpenSees, was used to model the unconfined and confined concrete stress-strain relationship in fiber element. The steel-fiber was modeled using a bilinear constitutive model with hardening ratio of 0.5%. The bilinear steel model was represented by “Hysteretic” uniaxial material model in OpenSees. The “ConcreteZ01” and “SteelZ01” material models, which were developed at the University of Houston (UH) to simulate shear in concrete panels, were utilized as the smeared constitutive model for the Quadrilateral RCPlaneStress element.

The results of the finite element OpenSees analysis for Column-3, typically representative of all the columns, is shown in Fig. 13. The comparison of the analytical and measured results, which corresponds very well with each other (Fig. 13) prove that the proposed finite element analytical model predicts the test result accurately. The initial stiffness in the elastic region as well as the ultimate forces fit very well with the test results. The analytical model successfully captured the severe “pinching” effect as observed in the tested RC columns (Figs. 6 and 13). Strength degradation beyond the ultimate point was also modeled well. However, the buckling behavior, which was observed in all of the tested specimens, was not incorporated in the analytical model. Therefore, the analysis results could not predict the sudden drop of force due to buckling.

Table 3 provides the comparison of the analytical and experimental test results, in terms of the ultimate force, of the RC columns tested in this work. In general, all the predicted and experimental values match quite well. The largest error was for RC Column- 2 of 18%, while the average standard deviation was about 5.5%, which is well within the acceptable limits of structural engineering.

6 Concluding remarks

The shear behavior of reinforced concrete column with respect to the loading rate was studied experimentally. It was found that with loading rate up to 5 Hz, the shear behavior was not significantly influenced by loading rate. The CNFAs were proven to work well detecting the damage of the reinforced concrete column. The current study showed that the ΔERV of 0.08 corresponded to onset of first cracking of concrete (i.e. a minima of damage level) and ΔERV of 0.2 indicated substantial failure (i.e. maxima of damage level or terminal damage level) of RC column. Further tests would be required to verify and establish appropriate correlation between the damage level and ΔERV measured by the CNFAs. Comparison of the analytical model with the test data indicated that the analytical model could adequately capture the global cyclic force-displacement behavior.

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