采用钢管加强的桥墩在横向力作用下的有限元分析

FINITE ELEMENT ANALYSIS OF STEEL TUBE STRENGTHENED DAMAGED BRIDGE PIERS UNDER LATERAL LOADS

Xueqiong Li, Jun Deng

School of Civil and Transportation Engineering, Guangdong University of Technology, Guangzhou 510006, P.R.China

Abstract: The seismic loads can induce large moments and lateral forces to the columns of bridges. The lateral cyclic earthquake force will degrade the concrete and the reinforcing steel bar instantaneously, and the reinforced concrete columns will fail prematurely. The bridge pier damaged during earthquakes need be repaired to meet the design standards. The shear forces in the original columns are resisted mainly by the lateral reinforcement. As an alternative, steel tube jacketed the damaged columns has been used to retrofit the bridge columns. In this paper, finite-element (FE) method was used to set up a model to calculate the hysteretic behaviour of steel tube strengthened damaged reinforced concrete beams under lateral loads. Convergence analysis also used to improve the result. The general purpose software package ANSYS was used. A nonlinear 3-D FE Model was established. Comparing the FE results of damaged columns and retrofitted damaged columns indicates that: (1) Steel tube jacketing is very efficient to increase the strength and ductility of the damaged columns; (2) The retrofitted columns meet the requirements of the design standards and can be reused safely.

Keywords: Bridge pier, seismic load, hysteretic behavior, steel tube

1 INTRODUCTION

In recent years, bridge piers all over the world result in different damage after a majority of the devastating earthquake (Li et al., 2008; Brown and Saiidi, 2011). Apart from the victims and the direct economic costs associated with the replacement of these damaged bridge piers, the disruption of crucial roads over a large time period created tremendous difficulties in the logistics of getting assistance to the impacted areas, therefore aggravating the initial consequences of the earthquakes (Han et al., 2009). If damaged bridge piers could be repaired and rehabilitated rapidly, it would be both more economical than demolishing and reconstructing the bridges, and also extremely important for rescue efforts after an earthquake.

Significant research has been devoted to hysteretic behavior of reinforced columns and numerous models were proposed. Sun et al. had simulated hysteretic behavior of the piers using ANSYS finite element analysis software, and got the hysteresis curve which was more consistent with the experiment (Sun et al., 2007). Relatively little research, however, has focused on the finite element analysis of steel tube jacketed the damaged columns.

This paper studies on the hysteretic behavior of concrete column and steel tube jacketed damaged concrete comlumn using ANSYS, and analyses the difference between the hysteretic bebaviors of them.

2 FE MODES

The bridge pier had a circular section of a diameter of 260mm and a clear height of 2000mm, the bottom was the pedestal of pier. The concrete of specimen used C30 fine aggregate concrete,and the actual cubic compressive strength of concrete was 44MPa. The specimens contained nine longitudinal bars of 12 mm in diameter with a measured yielding strength of 400 MPa. In addition, 6mm diameter bars with measured yielding strength of 273 MPa were used for spiral bars spaced at 40. The tube jacketed the damaged column had outside diameter of 300mm, wall thickness of 1.7mm and clear height of 2000mm. There was fine aggregate concrete between the steel tube and damaged column. The details of the specimens

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are shown in Figure 1.

Concrete is modeled with 8-noded Solid65 elements and the steel tendons are modeled with one-dimensional elements Link8, the steel tube is modeled with shell181 elements, the backing plate is applied for loading which effectively avoid the stress concentration of the loading

node.

Figure 1. The Details of bridge piers

Concrete is modeled with multilinear isotropic hardening (MISO), the compressive stress-strain curve bases on Concrete Structure design code which is defined the constitutive relationship of concrete under uniaxial compression (Si et al. 2007). In order to guarantee the convergence of calculation, this paper did not consider the descent segment of compressive stress-strain curve of confined concrete, as shown in Figure 2. Improved William-Warnke five parameter failure surfaces is the failure surface of SOLID65 element. The cracking of the concrete is used the Rankine maximum tensile stress criterion. concrete cracks instantaneously when reaching the maximum tensile stress, then the tensile stress will relax; the shear transferring coefficient of concrete βt take 0.5, βc take 0.95 after cracking.

The steel material of the bar is simulated using 2-line multilinear kinematic hardening (BKIN) model, as shown in Figures 3,4.

The steel tube is simulated using 2-line multilinear kinematic hardening (BKIN) model shown in Figure 5.

The column was modeled with the separating type finite elemnent. Concrete,steel bars and tube were joined with common nodes (Chang Sy et al. 2004). The finite element did not consider concrete protective cover of 15mm, due to simplify calculation. The model contained nine longitudinal bars which evenly distributed around the cross-section along the pier. To

consider the convenience of the finite element modeling, rectangular pedestal in the experiments wound simplify a truncated cone with a peripheral constraint completely, at the same, it had a equal height with the experimental cone. Concrete columns and steel were modeled together and element birth and death method was applied to steel tube after the loading

process.

Figure 2.

The Stress-strain relationship of concrete

Figure 3. The Stress-strain relationship of reinforce bar of grade Ⅱ

Figure 4. The Stress-strain relationship of reinforce bar of grade Ⅰ

Figure 5. The Stress-strain relationship of

steel tube

3 LOADING PROGRAM

Loading scheme based on force - displacement compound. The specimen had an axial load of 0.2 Agfc, where Ag is the gross cross-sectional area of the pier and fc is the concrete compressive strength.control, translated into surface loads for 2.83N/mm2 and remain unchanged in the calculation (Su et al.,2007). The element birth and death method was applied to kill tube element before loading. The lateral displacement was applied to the pier specimen at a distance of 0.1m at the top of the column. Each amplitude loaded two weeks, and continued to four times yield displacement. The steel tube element wound be activated at the end of the calculation. The pier was imposed renewedly with the lateral displacement untill six times the yield displacement.

In this paper, the Newton - Raphson nonlinear solver option was applied. In order to accelerate the calculation convergence, the concrete crushing option should be closed (and even if the uniaxial compressive strength UnCompSt = -1); The load of each load step was gradually applied through a series of load substep, and adjusted to load substeps repeatly of the trial calculation. 50 times was incremented iterationg times of each load supstep. The convergence criterion based on force while convergence accuracy was relaxed to 5%, opened the AUTOTS options, all calculations are carried out untill can not converge.

4 RESULTS AND DISCUSSIONS

At the end of the calculation, ANSYS was entered the post-process of time-history, defined the top displacement and reaction of load node, and then presented the corresponding data (Sun ZG et al., 2011; Ozbakkaloglu T et al.,2006; Cheng CT et al., 2003). The hysteresis curve and skeleton curve are plotted by other drawing tools.The hysteresis curve and skeleton curve is

shown in Figures 6,7.

Figure 6. Hysteretic curves of pier medels compare with the experimental results

In the article, the simulated results were compared with the experiment’s. Figures 6,7 exhibited the hysteresis curves and sketelon curves were similar for experimental results. However, when the bridge pier suffered severe damage, the test results behaved that slight spalling of the concrete cover were observed within the plastic hinge region of the specimens and bucking of longitudinal bars, decreasing of the lateral capacity while cycle time increasing. Thus, the finite element analysis had no descent segment of hysteretic curves and sketelon curves, it was related to the finite element model can not simulate concrete core crushing and longitudinal bar buckling. In order to guarantee the calculation convergence,concrete crushing option should be closed in the simulate pier.Meanwhile, the longitudinal bars were modeled with LINK8 element that is a uniaxial tension-compression

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element with three degrees of freedom, so it can not simulate the buckling of the longitudinal bars. However, the shape of the hysteresis curves tested and calculated are more full, approximate spindle-shaped, indicating that the plastic deformation capacity of the pier, good seismic behavior and energy dissipation

capacity.

Figure 7. Sketelon curves of pier medels compare with the experimental results

In this study, the repaired pier was imposed lateral displacement of 13mm, then kept compression strength of the top of column (Cao

et al., 2011; Cheng et al., 2005).

In general, the retrofitted specimens

performed well under the simulated lateral displacement. The repaired specimens showed a significant improvement in the hysteresis loops and exhibited larger lateral strength and ultimate displacement when compared to the original specimens. Figure 8 indicated that the repair technique has influenced the rate of stiffness degradation. The stiffness of the repaired specimens reached or exceeded that of the original specimens as the lateral displacement increased. This may be because the steel tube delayed the development of damage in the repaired piers. The Load-displacement curves

without considerding element birth and death mothod compared with experimental results are shown in Figure 9. It was indicated that the simulated results were similar for the

experimental’s.

Figure 8. Load-displacement curve of pier medel comparative analysis before and after

repaired

Figure 9. Load-displacement curve without considering element birth and death mothod compare with experimental result

5 CONCLUSIONS In this study, a finite element analysis to evaluate the strengthening effectiveness of the steel tube jacketed technique for earthquake-damaged bridge piers was conducted. A nonlinear 3-D FE model was established to severe damage under constant axial load and reversed cyclic displacement. The damaged piers were repaired using steel tube and tested to failure. The seismic performance of the repaired specimens was evaluated and compared to the original specimens. The hysteretic curves and skeleton curves were evaluated and compared

(1) Steel tube jacketing is very efficient to increase the strength and ductility of the damaged columns.

(2)The hysteretic bahavior of the simulated specimens before retrofitted are similar to the experimental results and show a significant improvement.

(3) The repaired piers meet the requirements of the design standards and can be reused safely.

ACKNOWLEDGEMENTS

This work is supported by the National Natural Science Foundation of China through grant 50808085 and Fok Ying Tong Education Foundation through grant 131073.

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