A Method for Controlling Seismic Damage of RC Bridge Piers Subjected to Strong Aftershocks

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1 A Method for Controlling Seismic Damage of RC Bridge Piers Subjected to Strong Aftershocks Yonggang Shen 1, Chengquan Wang 1, Xu Xie 1, Yan Wang 2* 1 College of Civil Engineering and Architecture, Zhejiang Universit Hangzhou, Zhejiang , China 2 School of Civil Engineering and Architecture, Zhejiang SCI-TECH Universit Hangzhou, Zhejiang , China Abstract The influence of aftershocks on reinforced concrete bridge piers was analzed with the seismic damage index, and the results confirmed the necessit of considering the effect of aftershocks on bridge seismic design. To mitigate the accumulated seismic damage of bridge piers, partial longitudinal reinforced steel bars were substituted with high-strength finishing rolling rebars with the same sectional area in the plastic hinge region of bridge piers. Because of the characteristic, i.e. the same elastic modulus as steel bars but bigger strength, post-ielding stiffness and restore stiffness after damage of piers are enhanced without changing the sectional ield strength, thus its structural resistance to aftershocks can be improved. The result shows that substituting partial reinforced steel bars with finishing rolling rebars can effectivel reduce the seismic accumulated damage during aftershocks. Kewords - aftershocks; finishing rolling rebar; seismic; damage index; bridge concrete pier I. INTRODUCTION The seismic performance of bridge structure subjected to earthquake will degrade when it goes through the process of mainshock and aftershock. There is a great probabilit of occurrence for the strong aftershock after strong mainshock. Man structures collapse under the action of strong aftershock although the have avoided serious damage in mainshock [1-2]. Therefore, the current seismic design should not onl consider the mainshock effect, but the influence of strong aftershock on structure damage should not be ignored. Man scholars have focused on aftershock damage for a long time. Zhai [3] investigated the strength reduction factor of single degree of freedom sstem with constant ductilit performance subjected to the mainshockaftershock sequence-tpe ground motions. The results indicated that the strong aftershock ground motion has more obvious influences on strength reduction factor in short period region than on those in long period region; Murata [4] investigated the aftershock earthquake destructive evaluation method b taking the wooden structure as the object; Adeel [5] compared the performance between steel and SMA-FRP reinforced frames subjected to sequential ground motions. He found that increased demands from the effects of aftershocks caused accumulation of residual drifts in steel reinforced frames which is mitigated in SMA-FRP reinforced frame through re-centering capabilit; Kimura [6] tested the one single degree of freedom pier structure and studied the effects of cumulative damage and seismic performance including the foreshock, mainshock and aftershock b using the seismic damage index, but the foreshock and aftershock waves in the calculation were simulated under the same spectrum characteristics and main vibration, without considering the actual seismic records. In this paper, the aftershock earthquake wave records of the same observation point as the mainshock were taken as input waves. The structural damage characteristics of the concrete bridge piers under the aftershock were analzed. The cumulative effect of aftershock on bridge pier damage was explored. Furthermore, this paper discussed the structural seismic damage control method with allocating a certain amount of finishing rolling rebar in the potential plastic zone. On the premise of no changing the plastic region, the substituted finishing rolling rebars can provide bridge piers with secondar structural stiffness after reinforced steel bars ielded. So the damaged piers can be controlled no collapse in the strong aftershocks. II. SEISMIC DAMAGE INDEX OF THE BRIDGE PIERS A large number of experiments show that the seismic damage of concrete structure not onl effected b the maximum instantaneous seismic response, but also b the cumulative plastic deformation under cclic loading. Seismic damage index of concrete pier structure is generall evaluated b three parameters, i.e. the ratio of the maximum seismic displacement of the structure u M and the monotonic ultimate displacement u u, the relative energ absorption of plastic deformation under cclic loading, and the residual deformation. The first parameter reflects the instantaneous maximum plastic seismic response of structure, the second parameter reflects the cumulative plastic deformation, and the third parameter shows repairing performance of the structure subjected to the earthquake. The Park-Ang model [7, 8] is the best known and most widel used damage index, which consists of a simple linear combination of normalized deformation and energ absorption: DOI /IJSSST.a.16.4B ISSN: x online, print

2 u E D u F u M n (1) u Where u M is the maximum displacement reached in the loading, u u is the monotonic ultimate displacement, u is the monotonic ield displacement, F is the ield force, E n is the absorbed hsteretic energ, and β is an energ parameter, the value of which is determined b the low ccle fatigue tests, and is related to the structure of the cross section shape. For the reinforced concrete structure the value is roughl 0.15 [9]. III. EFFECT OF AFTERSHOCKS ON THE SEISMIC DAMAGE OF THE BRIDGE PIER A. The Calculation Model In this paper, a reinforced concrete single column pier was modeled b fiber finite element method. The structure seismic response under mainshock and aftershock ground motions was calculated with nonlinear time-histor analsis. The pier is 20 m high and rectangular hollow section, with outline dimension 6 m (along the direction of the bridge) 7 m (transverse direction) and wall thickness 1 m. The reinforced steel bars are verticall arranged with spacing 15 cm in all sides of the wall. The thickness of reinforced protective laer is 30 mm. The vertical force acted b dead load on the top of the pier is kn [10]. The bottom of the pile cap is restricted b springs with specific stiffness. The bridge pier is simulated with three-dimensional nonlinear fiber beam column element in order to consider the influence of plastic development on seismic response. The whole model is divided into the core concrete fiber element, the protective laer of concrete fiber element and the steel fiber element, which are shown in Figure 1. For the core concrete, the lateral restraint effect should be considered, so the Sakai - Kawashima model shown in Figure 2(b) is used as the material hsteretic curve. In this model, the allowable strength is 0.8 times of its peak stress. The steel skeleton curve is the bilinear model shown in Figure 2(c). Where σ 1 ε 1 is the ield strain and the ield strength of steel bar, respectivel; ε cu is the ultimate tensile strain. The modified Menegotto-Pinto model considering Bauschinger effect is used to represent the steel hsteretic performance [11]. The ield stress and Young s modulus of reinforced steel bar is 345MPa and MPa, respectivel. Stress(Mpa) εce εcu εcc σbt (a) cover concrete σcu σcc Strain(μ) (b) cored concrete σ1 Stress(Mpa) -ε1 ε1 Strain(μ) Figure 1 The fiber elements in FEM model of concrete bridge pier The nonlinear material models are emploed to calculate the seismic response of fiber elements. Taking no account of the lateral restraint effect for protective laer concrete, the material hsteresis curve is shown in Figure 2(a). Where, σ bt, σ cc, σ cu is the tensile strength, peak stress and ultimate strength of concrete, respectivel; ε cc is the strain corresponding to the peak stress value; ε cu is the ultimate compressive strain; ε ce is the allowable compressive strain. Figure 2 -σ1 (c) reinforced steel bar The non-linear constitutive model of concrete and reinforced steel bar The bridge pier is modeled as an elastic-plastic beam with three crucial stages of concrete cracking, reinforced DOI /IJSSST.a.16.4B ISSN: x online, print

3 steel bar ielding and concrete crush under seismic loading. The nonlinear effect is alwas expressed b the relationship between curvature and bending moment of structure. In this paper, the modified Takeda model [12] in Figure 5 is adopted to simulate the elastic-plastic process b three lines and three corresponding control points of concrete cracking (Ø c, M c ), steel ielding (Ø 0, M 0 ) and ultimate deformation (Ø u, M u ) of structure. K 1, K 2 and K3 are structure stiffness before concrete cracking, steel ielding and structure failure. So the degradation rigidit K d of structure under earthquake can be expressed as: max K d K 0 (2) 0 Where, K 0 is the unloading stiffness when the curvature does not exceed the second break point, γ is degradation index of stiffness, which generall is -0.4 for the reinforced concrete structure, Ø max is the maximum curvature values of structure seismic response. M (a) Riuetan Pool records of Chi Chi earthquake in Taiwan, 1999 min M 0 K 2 M c K 1 K 0 c 0 K 3 K d max (b) Urakawa records of Tokachi-oki earthquake in Japan, 2003 Figure 4 The mainshock and aftershock of seismic waves Figure 3 The modified Takeda model for restoring force curve of elastoplastic element in concrete pie B. Seismic Wave Records The mainshock and aftershock earthquake waves from the same observation point were emploed as the input conditions to model the actual seismic loading. Two groups of strong earthquake records with different periodic characteristics were selected to consider the influence of earthquake with different tpes. The first group of seismic waves from Riuetan Pool records of the 1999 Chi-Chi earthquake in Taiwan, waveforms shown in Figure 4 (a), had a mainshock magnitude M7.3 and an aftershock magnitude M6.7. The characteristics of Riuetan Pool records indicate that the mainshock effect was ver large, while the aftershock effect was relativel small. So the structure was severel damaged in the mainshock. The second group of seismic waves was recorded in September 2003 from the Urakawa observation point of Tokachi-oki earthquake in Japan. The waveforms of Urakawa records were shown in Figure 4(b) with the magnitude of the mainshock M8.0 and the magnitude of aftershock M7.1. Compared with the first group of seismic waves, the mainshock intensit of Urakawa records was smaller. C. Energ Dissipation of Bridge Piers Under Strong Mainshock and Aftershock The mainshock-damaged pier was modeled to analze the seismic resistance of aftershock with Newmark β method and elastoplastic calculation. The damping ratio of concrete pier is 0.02, and β is 0.25, the interval of integration time is s. The hsteretic curves of energ dissipation on the bottom of piers under mainshock and aftershock were showed in figure 5. It can be seen from the figure that the energ dissipation in the mainshock of Riuetan Pool earthquake was significantl greater than that of Urakawa. There was about 92 percent of energ dissipated in mainshock of Riutan Pool seismic, while onl 45 percent of energ dissipation occured in mainshock of Urakawa earthquake. The main reason was that the intensit of the mainshock of Riuetan Pool earthquake was greater than that of Urakawa. The pier rigidit degraded seriousl in the mainshock of Riuetan Pool earthquake, there was little abilit to resist aftershock. For Urakawa earthquake, there was 55 percent of energ dissipation in Urakawa aftershock, which indicated the aftershock occup a crucial proportion in seismic damage of Urakawa earthquake. DOI /IJSSST.a.16.4B ISSN: x online, print

4 IV. CONTROL METHOD FOR REDUCING SEISMIC DAMAGE OF THE REINFORCED CONCRETE PIER En/MN m Figure 5 The hsteretic curves of energ dissipation on the bottom of piers under mainshock and aftershock Figure 6 shows a comparison of the energ dissipation results of two aftershocks. The figure shows that the piers had different degrees of damage in mainshock under the action of the two kinds of seismic waves, at the same time their energ dissipation results were also different, such as the energ dissipation of Riuetan Pool earthquake was 2.9MN m and the energ dissipation of Urakawa earthquake was 4.9MN m, this result agrees with the Figure 5. However, when the pier was directl affected b two kinds of aftershock seismic waves, the pier in the Urakawa earthquake with larger intensit didn t absorb more energ, instead, the energ dissipation of the pier in the Riuetan Pool earthquake which intensit was smaller was up to 5.1MN m. It can be concluded that the correlation between the structural energ dissipation in the aftershock and the mainshock seismic response is not obvious. It can t be simpl inferred b seismic intensit but should be determined b the calculation. A. Steel Configuration and the Change of the Secondar Stiffness According to the above results, the influence of the aftershock on the seismic performance of bridge structure mainl reflected in the cumulative absorption of seismic energ. In this paper, the partl configuration of the finishing rolling rebar method was used to improve the capacit of the structure to resist damage from strong aftershocks. In this paper, some finishing rolling rebars were configured in the potential plastic hinge to improve the pier secondar stiffness (Figure.7), that is, in the 6 m long region above the top of the pier foundation (the equivalent height of section) the longitudinal reinforced steel rebar was theoreticall replaced b the finishing rolling rebars and were anchored into the foundation, which can change the sectional bending deformation characteristic after entering the plastic range with the stress-strain relationship of the precision twisted steel. The double linear stress-strain curve is used to model the material propert of finishing rolling rebar, and the ield stress is 930 MPa, the elastic modulus were MPa. Figure 6 The hsteretic curves of energ dissipation on the bottom of piers under aftershock The above results show that combined effect of the mainshock and aftershocks on bridge seismic response is ver complex, the effect of aftershocks on the seismic damage index mainl reflects in the cumulative absorption energ. When the earthquake resistance design considers the aftershock effect, the cumulative damage degree of earthquake is also increased for the increase of seismic time and hsteresis loops of bridge pier. Figure 7 The finishing rolling rebar configuration in the potential plastic hinge The allocation rate of the finishing rolling rebar was set as 0%~15% of the total area of reinforcement to keep the total area of reinforcement(the sum of steel area and the finishing rolling rebar area) unchanged. Fig.8 shows the section moment -curvature curve of the pier bottom section, as shown in the figure, which indicates the mechanical properties of structure (the cracking strength, the ield strength of cross section) were not affected b the finishing rolling rebar configuration before the ordinar steel ielded. Under the earthquake loads, the assumed position of the pier DOI /IJSSST.a.16.4B ISSN: x online, print

5 cross section can ield at first, and the secondar stiffness (the stiffness after the ordinar longitudinal steel ield) was improved compared with that of the ordinar reinforced concrete piers, the improving secondar stiffness was related to the cross-sectional area of the finishing rolling rebar, which is similar to the linear relationship (Figure.9). When the finishing rolling rebars were configured in the pier, due to the sectional neutral axis at the limit state was relativel close to the sectional centroid axis, the ultimate curvature had a certain degree of decline compared with the ordinar reinforced concrete pier, which affected the ductilit of the structure. ductilit of the bridge pier, allocating too man finishing rolling rebars will affect the structural seismic energ absorption and decline the structural ultimate flexural capacit. B. The Effect of the Finishing Rolling Rebar on the Earthquake Damage of Bridge pier In order to verif abilit of the above design method to control the structural seismic damage, the elastic-plastic seismic response calculation of the bridge pier was analzed and discussed. Figure 10 illustrates the pier bottom section moment-curvature curve with the Riuetan Pool waves as input, it can be seen that after allocating the finishing rolling rebars the response of the pier plastic curvature decreased and there is a significant improvement of the structural stiffness. Figure 8 The relationship between flexural moment and curvature of pier top K3 / GN m 2 Figure 9 The impact of the finishing rolling rebar to the sectional secondar stiffness The elastic modulus of the finishing rolling rebar is similar to the ordinar rebar, but the strength of the finishing rolling rebar is 4 times of the ordinar rebar, therefore, the configuration of the finishing rolling rebar in bridge pier has the following characters: (1) In normal service or medium minor earthquakes, the pier has the same resistance with the reinforced concrete pier, that is, the configuration of the finishing rolling rebar can have the abilit to resist the medium and small earthquakes. (2) Don't change the initial ield strength of the cross section and control the potential damage section position in the structural seismic design better. (3) When the ordinar rebars ielded in rare earthquake, the finishing rolling rebar didn t ield, which can provide higher secondar stiffness than the ordinar reinforced concrete structure and is conducive to resist the strong aftershock and meet the requirements of emergenc use. (4) The configuration of the finishing rolling rebar improves the structural secondar stiffness but reduces the Figure 10 The bottom section moment-curvature curve of the pier with the finishing rolling rebars Table 4 lists the results of structural damage index and structural stiffness with different finishing rolling rebar configuration rates. In the table, the relative stiffness k is the ratio secant stiffness relative to the maximum displacement and the ield stiffness. From the table results, it can be seen that with the increasing of the finishing rolling rebars, ultimate displacement of structure decreases, which results in the damage index increase. But the accumulated energ of the structure significantl reduced, the plastic strain is obviousl controlled, and the damage degree of the structure decreases. In particular, due to the configuration of the finishing rolling rebars, the bridge pier stiffness after the earthquake has increased significantl, which ensure the working performance of bridge pier under strong earthquake. Earthquake wave TABLE 4 THE IMPACT OF FINE ROLLING REBAR ON PIER DAMAGE INDEX The proportion of fine rolling rebar u u M u u u 0.15 de Fu D k DOI /IJSSST.a.16.4B ISSN: x online, print

6 Riuetan Pool Urakawa 0% % % % % % % % V. CONCLUSION In this paper, the effect of aftershocks on structural seismic damage index was analzed b the elastic-plastic earthquake response calculations. The design method of allocating the finishing rolling rebar in bridge pier to control the seismic damage was put forward. Through the analsis of the seismic response parameters under different conditions, the following conclusions were obtained: (1) The impact of the aftershock on the cumulative seismic damage led b the plastic deformation can t be ignored, which occupies a relativel large proportion in the overall damage index. (2) The configuration of the finishing rolling rebars can improve the structural secondar stiffness but excessive numbers of finishing rolling rebars will reduce the ductilit of the bridge pier. (3) The damage index of the bridge pier with the finishing rolling rebars is smaller than that of the ordinar reinforced concrete pier, and the bridge pier with the finishing rolling rebars has a greater structural stiffness after damaged, which can meet the service requirement of the pier after the earthquake. ACKNOWLEDGEMENT Supporting project: Natural Science Foundation of Zhejiang Province (LY16E080006) REFERENCES [1] Page R. Aftershocks and microaftershocks of the great Alaska earthquake of 1964, Bull Seism Soc AmPr, vol. 5, no. 8, pp , [2] Lv Xiaojian, Gao Mengtan, Gao Zhanwu and Mi Suting, Comparison of the spatial distribution of ground motion between shocks and strong aftershocks. ACTA SEISMOLOGICA SINICA. vol. 29, no. 3, , [3] Zhai Changhai, Wen WeiPing, Li Shuang, Xie Lili, The ductilitbased strength reduction factor for the mainshock-aftershock sequence-tpe ground motions. Bull Earthquake engineering. vol. 1, no. 3, pp , [4] Murata A. et al., Prediction of damage to structures through fatigue response spectra considering number of earthquake response ccles, Proceedings of the 13th world conference on earthquake engineering, vol. 33, no.648, pp , [5] Adeel Zafar, Bassem Andrawes, Seismic behavior of SMA-FRP reinforced concrete frames under sequential seismic hazard. Engineering Structures, vol. 9, no. 8, pp , [6] Kimura Y, Kawano K, Nakamura Y, Effects on accumulated damages for seismic performance evaluation, Journal of structures engineering, JSCE, vol. 53A, no. 8, pp , [7] Young-Ji Park and Alfredo H.-S.Ang. Mechanistic seismic damage model for reinforced concrete. Journal of structural engineering, ASCE, vol. 111, no. 4, pp , [8] Young-Ji Park and Alfredo H.-S.Ang,Yi Kwen Wen, Seismic damage analsis of reinforced concrete buildings. Journal of structural engineering, ASCE, vol.111, no. 4, pp , [9] Fajfar P., Equivalent ductilit factors, taking into account low-ccle fatigue, Earthquake engineering and structural dnamic, vol. 21, no. 10, pp , [10] XIE Xu, Bu Zhan-u. Elementar stud on usefulness of carbon fiber for controlling bridge pier seismic damage. Journal of Zhejiang Universit (Engineering Science). vol.39, No.10, pp , [11] Sakai J, Kawashima K. Modification of the Giuffre, Menegotto and Pinto model for unloading and reloading paths with small strain variations. DOTOKU GAKKAI, [12] Takeda, T., Sozen, M. A., Nielsen, N. N. Reinforced concrete response to simulated earthquakes, Journal of the Structural Division. Proceeding of the American Societ of Civil Engineers. pp. 2257, DOI /IJSSST.a.16.4B ISSN: x online, print