- Open Access
Experimental and Numerical Researches on the Seismic Behavior of Tubular Reinforced Concrete Columns of Air-Cooling Structures
- Ning-jun Du^{1},
- Guo-liang Bai^{1},
- Ya-zhou Xu^{1}Email author and
- Chao-gang Qin^{1}
https://doi.org/10.1007/s40069-017-0207-6
© The Author(s) 2017
- Received: 20 February 2016
- Accepted: 16 June 2017
- Published: 13 September 2017
Abstract
Tubular reinforced concrete columns of air-cooling condenser structures, which undertake the most weight of air cooling equipment, are the major components to resist lateral forces under earthquake. Once collapsed, huge casualties and economic loss would be caused. Thus, four 1/8 scaled specimens were fabricated and tested through the pseudo-static testing method. Failure modes and crack patterns of the specimens under cyclic loading were observed. Then, finite element models of tubular reinforced concrete columns were established using OpenSees and were verified with the experimental results. Finally, the influence of axial compression ratio and longitudinal reinforcement on energy dissipation capacity and stiffness degradation were studied based on the validated finite element modes. It is confirmed that tubular reinforced concrete columns of air-cooling condenser structure exhibit a moderate ability of energy dissipation, and the nonlinear finite element model could reasonably simulate its seismic behavior. Furthermore, axial compression ratio and longitudinal reinforcement are main factors which affect the seismic behavior of the tubular reinforced concrete columns. The experimental results and simulation method provide an available way to design this kind of large tubular reinforced concrete columns with thin-wall.
Keywords
- tubular reinforced concrete column
- seismic performance
- pseudo-static test
- OpenSees
1 Introduction
Compared with the traditional natural draft cooling process,the direct air-cooling technique can achieve water conservation nearly 70–80%. So, it has priority to be used in thermal power plants, especially those built in regions which are short for water and rich for coal, e.g., North China areas (Xu et al. 2015; Li et al. 2008). With the improvement of energy saving and environment protection requirements, construction and operation of large capacity air-cooling units in thermal power plants are imperative to balance the increasing electricity consumption and water resource shortage.
Generally, the air-cooling structure in a large thermal power plant mainly consists of tubular reinforced concrete columns,spatial steel truss platform and A-shaped steel truss. Tubular reinforced concrete columns have the characteristics of thin-wall and great sizes, typically which are about 4 m in diameter, 0.3–0.5 m in thickness and 40 m in height. Spatial steel truss platform is 4–8 m high. Above the spatial steel truss platform, there is 10–15 m high A-shaped steel truss on which most equipment are installed. An air-cooling structure supports millions of tons of weight of the upper equipment. Once the columns collapsed under earthquake, huge casualties and economic loss would be caused.
For common reinforced concrete members, lots of experimental investigations have been conducted (Nilson and Arthur 1968; Bathe and Ramaswamg 1979; Priestly and Benzoni 1996; Priestly et al. 1996; Lehman et al. 1995; Phan et al. 2007; Hindi 2005; Hindi et al. 2005; Wang et al. 2014; Afefy and El-Tony 2016; Jiong 2004; Li and Ren 2009; Elmorsi et al. 1998; Esmaeily and Shirmohammadi 2014; Shao et al. 2005; Zendaoui et al. 2016; Ren et al. 2010). Previous studies of reinforced concrete members have demonstrated that slender ratio, material property, axial compression ratio, reinforcement ratio, detailing art and stirrups played significant roles in the seismic behavior, especially the hysteretic performance of reinforced concrete members. While, the seismic performance, especially hysteretic performance of tubular reinforced concrete columns with thin-wall and great sizes used in air-cooling condenser structure has not yet been clarified so far.
Additionally, with the fast development of computer technology, numerical simulation methods play a more and more important role in the nonlinear analysis of structures. Popular finite element codes such as Abaqus, Ansys, OpenSees have been developed to simulate the structural responses of reinforced concrete members. For circular columns, Masukawa et al. (1999) investigated failure modes of hollow bridge piers using three-dimensional nonlinear finite element method. Shirmohammadi and Esmaeily (2015) proposed an analytical algorithm and confirmed its accuracy, and it was also used to perform a parametric study considering the effects of axial load variation and lateral force/displacement paths on the flexural strength and energy dissipation capacity of reinforced concrete columns. Kim et al. (2012) proposed a framework for assessment of the seismic performance of hollow reinforced concrete and prestressed concrete bridge columns.
The primary objective of this study is to investigate the seismic response and failure modes of tubular reinforced concrete columns by pseudo-static testing, and develop a simple, yet reasonably accurate finite element model to predict the nonlinear cyclic response of this kind of columns. Accuracy of the FEM model was validated against experimental results. Furthermore, based on the validated analytical model, a parametric study was finally carried out to clarify the effect of axial compression ratio and longitudinal reinforcement on the ultimate strength, ductility and energy dissipation capacity.
2 Experimental Program
2.1 Details of Specimens
2.1.1 Determination of the Axial Compression Ratio
Axial compression ratio of full-scale tubular reinforced concrete columns under different combined load cases.
Combined load cases | Maximum value | Minimum value | ||
---|---|---|---|---|
Axial force/kN | Axial compression ratio | Axial force/kN | Axial compression ratio | |
1.35DL + 1.5LL | 24244.08 | 0.20 | 16045.09 | 0.12 |
1.35DL + 1.5 W(+X) | 22306.86 | 0.17 | 13237.49 | 0.10 |
1.35DL + 1.5 W(+Y) | 20561.50 | 0.16 | 13638.27 | 0.10 |
1.35DL + 1.35LL + 1.35S + 1.35 W(+X) | 22760.59 | 0.17 | 15767.53 | 0.12 |
1.35DL + 1.35LL + 1.35S + 1.35 W(+Y) | 24396.77 | 0.20 | 15981.41 | 0.12 |
1.2DL + 0.55LL + 0.7S + 1.0EQ(+X) | 19825.45 | 0.15 | 13119.34 | 0.10 |
1.2DL + 0.55LL + 0.7S + 1.0EQ(+Y) | 19819.36 | 0.15 | 13155.10 | 0.10 |
1.0DL + 1.0LL + 1.0S + 1.0 W(+X) | 16859.70 | 0.13 | 11679.65 | 0.09 |
1.0DL + 1.0LL + 1.0S + 1.0 W(+Y) | 18071.68 | 0.14 | 11838.08 | 0.09 |
In Table 1, DL is dead load, LL is live load, S is snow load, W is wind load and EQ is earthquake action. X and Y are the directions of the earthquake. According to the Table 1, 0.09, 0.15, 0.20 was taken for the test.
2.1.2 Determination of Specimen Section
The cross section of the prototype column is 4000 × 400 mm while the cross section of the scaled column is 500 × 50 mm according to the 1/8 scaled ratio. In order to investigate whether the change of wall thickness will influence the seismic performance of columns, the cross sections of 500 × 70 mm and 500 × 100 mm were designed. 15, 16, 22, 20 longitudinal steel bars with the diameter of 10 mm were used in the Tube1–Tube4, respectively. The circular stirrup was 8 mm in diameter and arranged with the spacing of 200 mm except for the top and bottom 500 mm of the columns, in which the spacing is 100 mm. Experimental yielding strength values of steel reinforcement and circular stirrup were 461.7 and 315.8 MPa.
2.1.3 Determination of the Axial Force
Details of specimens.
Specimen | Diameter (mm) | Thickness (mm) | Axial Force (kN) | Axial compression ratio | \( f_{\text{c}}^{\text{s}} \) (MPa) | f _{cuk} (MPa) | f _{ck} (MPa) | Reinforcement(mm^{2}) |
---|---|---|---|---|---|---|---|---|
Tube1 | 500 | 50 | 180 | 0.09 | 28.88 | 38.1 | 25.5 | 1178 (15C10) |
Tube2 | 500 | 100 | 360 | 0.09 | 31.92 | 42.0 | 28.1 | 1257 (16C10) |
Tube3 | 500 | 50 | 434 | 0.20 | 27.36 | 36.0 | 24.1 | 1728 (22C10) |
Tube4 | 500 | 70 | 422 | 0.15 | 34.96 | 46.4 | 31.0 | 1571 (20C10) |
2.2 Test Setup and Instrumentation Layout
2.3 Loading System
During the testing process, the vertical axial force was firstly applied on the top of the specimens with specified values and kept constant. The cyclic lateral displacement was then exerted to simulate seismic action through displacement control method. The specific loading system is as follows:
2.3.1 Axial Compression Load
- (1)
A 3-mm initial cyclic lateral displacement was exerted through the MTS actuator at first. Then, the value of the target displacement increased with increment of 1 mm each cyclic until visible cracks were observed on the specimens during the loading system.
- (2)
The displacement increment value and the cycle number then increased to 2 mm and 2 times during the loading process until the specimen yielded. The yield point of the specimen was determined according to the load–displacement curve.1000kN, ± 250 mm.
- (3)
The target displacement and the cycle number were next adjusted according to the yield displacement. The displacement increment was multiples of the yield displacement. When the bearing capacity of a specimen dropped to 85% of its ultimate load, the loading process was terminated.
Loading system of Tube 1.
Vertical axial force 180 kN | ||||
---|---|---|---|---|
Target displacement (mm) | Displacement increment (mm) | Cycle number | Loading rate (mm/s) | |
1 | 3 | 1 | 1 | 0.2 |
2 | 7 | 2 | 2 | 0.5 |
3 | 13 | 3 | 2 | 0.5 |
4 | 22 | 3 | 3 | 0.5 |
5 | 37 | 3 | 3 | 1.0 |
6 | 79 | 6 | 3 | 1.0 |
Loading system of Tube 2.
Vertical axial force 360 kN | ||||
---|---|---|---|---|
Target displacement (mm) | Displacement increment (mm) | Cycle number | Loading rate (mm/s) | |
1 | 3 | 1 | 1 | 0.2 |
2 | 9 | 1 | 2 | 0.4 |
3 | 15 | 3 | 3 | 0.5 |
4 | 39 | 6 | 3 | 0.5 |
5 | 63 | 6 | 3 | 0.8 |
6 | 69 | 9 | 3 | 1.0 |
Loading system of Tube 3.
Vertical axial force 434 kN | ||||
---|---|---|---|---|
Target displacement (mm) | Displacement increment (mm) | Cycle number | Loading rate (mm/s) | |
1 | 3 | 1 | 1 | 0.2 |
2 | 10 | 3 | 2 | 0.5 |
3 | 34 | 6 | 3 | 1.0 |
Loading system of Tube 4.
Vertical axial force 420 kN | ||||
---|---|---|---|---|
Target displacement (mm) | Displacement increment (mm) | Cycle number | Loading rate (mm/s) | |
1 | 3 | 1 | 1 | 0.2 |
2 | 12 | 3 | 2 | 0.5 |
3 | 30 | 6 | 3 | 1.0 |
4 | 48 | 9 | 3 | 1.0 |
5 | 75 | 12 | 3 | 1.0 |
3 Experimental Results And Specimen Behavior
3.1 Failure Mode
As shown in Fig. 4, it was observed that the scope of cracks appearance can reach 3/4 of the column height. The crack distribution of the tubular columns demonstrates that in comparison to the conventional circular columns there is need for more zones with dense stirrups to improve the ductility of the columns.
3.2 Lateral Load versus Displacement Relationship
Characteristic points of the skeleton curves.
Specimen | Crack point | Yielding point | Ultimate point | Ductility coefficient | |||
---|---|---|---|---|---|---|---|
Displacement (mm) | Load (kN) | Displacement (mm) | Load (kN) | Displacement (mm) | Load (kN) | ||
Tube1 | 4.0 | 17.0 | 23.3 | 44.2 | 115.0 | 59.1 | 4.94 |
Tube2 | 6.0 | 33.6 | 16.0 | 51.0 | 114.0 | 67.4 | 7.13 |
Tube3 | 8.0 | 31.8 | 27.5 | 62.5 | 64.0 | 79.8 | 2.33 |
Tube4 | 10.0 | 38.4 | 22.8 | 56.2 | 99.0 | 74.4 | 4.34 |
3.3 Calculation of Normal Section Strength
Comparison of the ultimate bending moment through the method in the code and test result.
Specimen | Tube 1 | Tube 2 | Tube 3 | Tube 4 |
---|---|---|---|---|
Calculation method (kN m) | 141 | 170 | 212 | 206 |
Test result (kN m) | 181.4 | 206.9 | 245.0 | 228.4 |
D-value (%) | 22 | 17.5 | 13.5 | 9.8 |
The comparison in Table 8 shows that it is conservative to calculate the normal section bearing capacity through the method proposed by the Code for design of concrete structures of China.
4 Numerical Simulation
OpenSees is an object-oriented framework for building models of structural and geotechnical systems to perform nonlinear analysis. OpenSees supports a wide range of simulation applications in earthquake engineering and its good nonlinear numerical simulation precision has been widely confirmed.
4.1 Finite Element Model
4.2 Constitutive Laws of Steel and Concrete
As well-known, it is crucial to select a reasonable concrete and steel material models in the nonlinear finite element simulation. Three concrete stress–strain material models are available in the OpenSees code, i.e., Concrete0 l, Concrete02 and Concrete03. Concrete02, a linear tension softening material model in which the compression skeleton curve is specified by the Kent-Park stress–strain relationship (Kent and Park 1971), was used to construct a uniaxial concrete material with a linear tension softening branch.
Since the restraint effect of stirrups on concrete was so small that it could be ignored and concrete was treated as an unconfined material according to the researches of Mander et al. (1998) and Scott et al. (1982).
R _{0} is the parameter which determines the transition from elastic to plastic braches and the recommended values are 10–20 according to the OpenSees user’s manual and examples primer (Mazzoni and McKennna 2003; Mazzoni et al. 2003). a _{1} is the isotropic hardening parameter which is related to the increase of compression yield envelope after a plastic strain of a _{2}*f _{y}/E _{0}. a _{2} and a _{4} are the isotropic hardening parameters. a _{3} is the isotropic hardening parameter which is related to the increase of tension yield envelope after a plastic strain of a _{4}*f _{y}/E _{0}. In order to determine these parameters in the absence of detailed testing results of the materials, it is necessary to identify the values of the parameters in a reasonable range during the simulation process, so that the simulation results are in good accordance with the experimental results of the columns. Then, the verified FEM models can be employed to study the influence of the axial force, and so on.
For finite element simulations, the axial force was firstly applied and the displacement on the top node was then exerted to simulate lateral loading. Finally, Newton algorithm and norm displacement increment method were adopted to find numerical solutions.
4.3 Model Validation
However, the predicted hysteretic curves by OpenSees are much more plump and the pinching effect is not obvious as the experimental one. Adopting plane section assumption and no consideration in bond-slip between concrete and steel should be the main reason. In fact, due to the uncertainty of the experiment and deficiency of numerical models, it is often difficult to accurately simulate the declining branches and pinching effect of experimental results.
5 Parametric Studies
As well-known, ductility and energy dissipation capacity are mainly influenced by parameters such as ratio of axial compression and longitudinal reinforcement. Owing to the limited number of specimens, numerical simulation was then performed to investigate the influence of parameters based on the validated finite element models.
5.1 Influence of Axial Compression Ratio
5.1.1 Hysteretic Loops and Skeleton Curves
It is obvious that with the increase of axial pressure ratio, the corresponding maximum load also increases. However, as the axial compression ratio is exceedingly large, the ultimate load increases slowly.
It also can be found that the smaller axial compression ratio is, the less the skeleton curve declines. Therefore, taking the importance of tubular reinforced concrete columns into account, it is indispensable to restrict the maximum value of the axial compression ratio to ensure the seismic performance.
5.1.2 Energy Dissipation Capacity
E and h _{e} with different axial compression ratio for Tube2.
Axial compression ratio | Yielding stage | Limit stage | ||||||
---|---|---|---|---|---|---|---|---|
S _{(ABC + CDA)} (kN mm) | S _{(OBE + ODF)} (kN mm) | E | h _{ e } | S _{(ABC + CDA)} (kN mm) | S _{(OBE + ODF)} (kN mm) | E | h _{ e } | |
n = 0.14 | 198.3115 | 715.3398 | 0.2772 | 0.0441 | 1517.5058 | 2506.6128 | 0.6054 | 0.0964 |
n = 0.20 | 170.1344 | 648.1608 | 0.2625 | 0.0418 | 1446.9708 | 2442.3400 | 0.5925 | 0.0943 |
n = 0.25 | 181.8989 | 847.2856 | 0.2147 | 0.0342 | 1486.9411 | 2975.6870 | 0.4997 | 0.0795 |
n = 0.30 | 189.2101 | 898.9050 | 0.2105 | 0.0335 | 1682.7438 | 3382.3282 | 0.4975 | 0.0792 |
n = 0.35 | 211.7772 | 1040.3058 | 0.2036 | 0.0324 | 1784.3739 | 3604.5775 | 0.4950 | 0.0788 |
n = 0.40 | 215.8960 | 1086.6254 | 0.1987 | 0.0316 | 844.4114 | 2628.8536 | 0.3212 | 0.0511 |
From Table 9, it is easy to find that the equivalent viscous damping coefficient h _{e} and energy dissipation coefficient E in the limit stage are bigger than the yielding stage. As expected, with the increase of axial compression ratio, the equivalent viscous damping coefficient h _{e}, energy dissipation coefficient E and energy dissipation capacity of the columns decreases gradually. This is mainly because that as a large eccentric compression member, the height of compression zone for tubular reinforced columns is relatively small which is in favor of energy dissipation capacity and ductility. If the axial compression ratio increases, the height of relative compression zone will increase as well which would weaken the ductility and energy dissipation performance of the columns. When the axial compression ratio is too large, the tubular reinforced columns would become members with large compression zones, which deteriorates the energy dissipation capacity and ductility.
5.1.3 Stiffness
One can find that values of the secant stiffness for the tubes with higher axial compression ratio are larger than the others. With the development of plastic deformation, the tendency of stiffness degradation gradually becomes moderate. Figure 17 also shows that the tubes with different axial compression ratio share the same pattern of stiffness degradation.
5.2 Influence of Longitudinal Reinforcement
On the basis of Tube 2 and Tube 4, finite element models with different longitudinal reinforcement were established to study its influence on the bearing capacity, energy dissipation capacity and stiffness degradation. The longitudinal reinforcement ratios of these 4 models are 1.00, 1.25, 1.56, 1.87, respectively. The loading procedure is the same as mentioned above.
5.2.1 Hysteretic Loops and Skeleton Curves
5.2.2 Energy Dissipation Capacity
E and h _{e} with different longitudinal reinforcement ratios for Tube2.
Longitudinal reinforcement ratio (%) | Yielding stage | Limit stage | ||||||
---|---|---|---|---|---|---|---|---|
S _{(ABC + CDA)} (kN mm) | S _{(OBE + ODF)} (kN mm) | E | h _{ e } | S _{(ABC + CDA)} (kN mm) | S _{(OBE + ODF)} (kN mm) | E | h _{ e } | |
ρ = 1.00 | 181.8989 | 847.2856 | 0.2147 | 0.0342 | 1486.9411 | 2975.6128 | 0.4997 | 0.0795 |
ρ = 1.25 | 274.8453 | 1158.6722 | 0.2372 | 0.0378 | 2603.9790 | 4096.8782 | 0.6356 | 0.1012 |
ρ = 1.56 | 414.7068 | 1661.2259 | 0.2496 | 0.0397 | 4747.6610 | 5823.3371 | 0.8153 | 0.1298 |
ρ = 1.87 | 538.7275 | 2151.6598 | 0.2504 | 0.0398 | 7278.6079 | 7564.3521 | 0.9622 | 0.1531 |
Studies of energy dissipation coefficient E and equivalent viscous damping coefficient h _{ e } suggest that E and h _{ e } in yielding stage and limit stage become larger with the increase of longitudinal reinforcement ratio. This demonstrates again that longitudinal reinforcement ratio is in favor of improving energy dissipation capacity of the tubular columns.
5.2.3 Stiffness
6 Conclusions
In this study, a pseudo-static test and experimental results for four 1/8 scaled tubular reinforced concrete columns of air-cooling condenser structures are reported. Seismic behaviors, hysteretic properties and failure modes were evaluated based on experimental results. Then, finite element models using OpenSees were established to simulate their hysteretic loops. The constitutive laws in OpenSees, Steel02 and Concrete02, were chosen to model the behaviors of steel and concrete subjected cyclic loading. At last, numerical specimens were established to investigate the influence of axial compression ratio and longitudinal reinforcement ratio on bearing capacity of the columns.
- (1)
Tubular reinforced concrete columns of air-cooling condenser structures exhibit a moderate ability of energy dissipation.
- (2)
The predicted results obtained by the OpenSees finite element can reasonably capture the main features of the tubular reinforced concrete columns. Nevertheless, it is hard to accurately simulate the severe damage stage of the experimental results. Further researches are still needed to improve the accuracy and convergence for numerical simulations.
- (3)
With the increase of axial pressure ratio, the corresponding maximum load also increases. But after the axial compression ratio reaches a certain value, the skeleton curves drop much more steeply and exhibits poor ductility. Besides, longitudinal reinforcement is indeed in favor of improving the seismic performance of the reinforced concrete tubular columns.
- (4)
It is conservative to calculate the normal section bearing capacity through the method proposed by the Code for design of Concrete Structures of China. Besides, the crack distribution of the tubular columns demonstrates that in comparison to the conventional circular columns there is need for more zones with dense stirrups to improve the ductility of the columns.
Declarations
Acknowledgements
The support of the Natural Science Foundation of China (Grant No. 51478381,51578444) and Ministry of Education Plan for Yangtze River Scholar and Innovation Team Development (No. IRT13089) is acknowledged.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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