SIMULATION METHOD OF LOW CYCLE RECIPROCATING LOADING OF PIER COLUMN CONSIDERING BOND-SLIP EFFECT
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摘要: 针对桥梁墩柱和承台内的粘结滑移现象，基于fib混凝土规范(fib Model Code)推荐的混凝土粘结滑移模型，推导了纵筋滑移量的计算公式，并通过对墩柱塑性区域受拉纵筋的应力-应变本构进行修正，以引入墩柱塑性区域和承台内的纵筋滑移量，作为一种等效方法，以考虑粘结滑移对墩柱地震响应的影响，并用试验结果验证了该方法的合理性。此外，还对所提等效方法和零长度截面单元法的计算结果进行了对比。结果表明：未考虑粘结滑移会高估墩柱的侧向刚度、累计滞回耗能和残余位移，且无法客观反映滑移导致的墩柱强度退化问题；零长度截面单元法和所提等效方法均能考虑强度退化问题，但前者对粘结滑移的模拟效果受纵筋直径影响显著，后者则能合理捕捉滑移影响下的墩柱往复加载过程。Abstract: Based on the stress-slip model of concrete proposed by fib Model Code, the slip of rebar was derived and formulated to consider the bond-slip phenomenon occurring both in the column and in the footing. Furthermore, the stress-strain constitutive model of the tensile rebars located within the plastic zone of the column was modified to incorporate the rebar slips in the column and in the footing. In this way, the effect of bond-slip on the seismic responses of the column can be equivalently considered. The feasibility of this method was verified by experimental results. Besides, the comparison was made of the results between the proposed method and the Zero-Length Section Element (ZLSE) method. It can be concluded that the lateral stiffness, the cumulative hysteretic energy, and the residual displacement are all overestimated without considering the bond-slip phenomenon. Apart from that, the strength degradation of the column is unable to reflect objectively. Both the ZLSE method and the proposed equivalent method have the capability to resolve the issue of strength degradation. However, the former method yields the numerical results prominently susceptible to the rebar diameter, while the latter one can efficaciously capture the reciprocating loading process of the column affected by the bond-slip phenomenon.
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图 1 锚固段纵筋应变、滑移、粘结应力分布示意图
Figure 1. Distribution diagrams of bar strain, slip and bond stress along the anchorage
图 3 原式与近似式的拟合程度
Figure 3. The fitting degree between the original and the approximate curves
图 4 等效钢筋本构参数计算流程图
Figure 4. The flowchart of parameter computations for the equivalent constitutive law of rebar
图 5 墩柱截面构造及纤维划分 /mm
Figure 5. Cross-sectional configuration and fiber discretization of the columns
图 9 有限元模拟所得墩柱侧向力-位移滞回曲线与试验曲线的对比
Figure 9. Comparison of the lateral force-drift hysteretic curves of the columns obtained from the finite element models and the tests
图 10 墩柱累计耗能的模拟值与试验值对比
Figure 10. Comparison of the cumulative energies of the columns obtained from the finite element models and the tests
图 11 墩柱规则化残余位移的模拟值与试验值对比
Figure 11. Comparison of the regularized residual drifts of the columns obtained from the finite element models and the tests
表 1 等效钢筋本构的关键参数计算
Table 1. Key parameters of the equivalent constitutive law of rebar
试件名称 纵筋应力状态 关键参数计算过程 /mm 墩柱
L407屈服 Lei=16.5d=262.4, s0=0.119, εse=0.00117, La=127.5, Lb=130.8, se=0.204, sy=0.441, Lp=153, $ E_{ \rm{s} }' = 0.{\text{286} }{E_{ \rm{s} } } $, $ \varepsilon _{\rm{sy}}' $=0.00807; 断裂 Lej=29.5d=469, s0=0.0605, εse=0.00097, La=90.6, Lb=152.9, se=0.121, sy=0.372, su=12.027,$ {b'} $=0.0038, $ \varepsilon _{ { \rm{su} } }' $=0.227. 墩柱
TP5屈服 Lei=20d=400, s0=0.106, εse=0.00122, La=202.5, Lb=190, se=0.225, sy=0.603, Lp=138, $ E_{\rm {s} }' = 0.{\text{219} }{E_{\rm {s} } } $, $ \varepsilon _{ {\rm {sy} } }' $=0.0117; 断裂 Lej=32d=640, s0=0.066, εse=0.00125, La=172, Lb=185, se=0.197, sy=0.549, su=14.731, $ {b'} $=0.0026, $ \varepsilon _{ { \rm{su} } }' $=0.323 
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表 2 受压钢筋本构屈曲后参数计算
Table 2. Post-buckling parameters of the compressive constitutive law of rebar
试件名称 纵筋屈曲长度Leff/d 无量纲参数λ 中间点应变ε*/εsy 墩柱L407 8.0 17.2 15.5 墩柱TP5 5.5 12.4 26.4
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表 3 墩柱累计滞回耗能的模拟值与试验值对比
Table 3. Comparison of the cumulative hysteretic energies of the columns obtained from the finite element models and the tests
试件
名称漂移
比/(%)试验结果 未考虑
滑移效应零长度
截面单元等效钢筋
本构法累计
耗能/
(kN·m)累计
耗能/
(kN·m)相对
误差/
(%)累计
耗能/
(kN·m)相对
误差/
(%)累计
耗能/
(kN·m)相对
误差/
(%)墩柱L407 1.1 2.16 2.41 11.3 1.52 −29.8 1.86 −13.8 1.6 5.63 6.45 14.4 4.96 −12.0 5.35 −5.0 2.1 8.68 10.67 22.9 8.96 3.2 8.06 −7.2 3.1 16.89 19.92 17.9 18.04 6.8 16.50 −2.3 5.2 34.69 40.70 17.3 37.25 7.4 34.72 0.1 墩柱TP5 1.7 13.76 16.08 16.8 12.48 −9.3 12.46 −9.5 3.0 20.77 35.05 68.7 30.21 45.4 23.98 15.4 4.6 40.73 56.98 39.9 52.50 28.9 45.73 12.3
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表 4 墩柱残余位移的模拟值与试验值对比
Table 4. Comparison of the residual displacements of the columns obtained from the finite element models and the tests
试件名称 漂移比/(%) 墩柱残余位移/mm 试验结果 未考虑滑移效应 零长度截面单元 等效钢筋本构法 正向
加载反向
加载正向
加载相对
误差/(%)反向
加载相对
误差/(%)正向
加载相对
误差/(%)反向
加载相对
误差/(%)正向
加载相对
误差/(%)反向
加载相对
误差/(%)墩柱L407 1.1 3.1 −3.3 4.2 35.5 −5.5 65.3 3.0 −4.5 −2.9 −13.3 3.1 −0.4 −3.0 −11.2 1.6 9.5 −11.6 13.8 45.1 −13.8 18.9 10.7 12.9 −10.9 −6.1 9.1 −4.1 −10.8 −6.8 2.1 16.5 −20.0 23.8 44.6 −23.7 18.6 19.9 21.1 −19.9 −0.1 17.2 4.6 −18.3 −8.3 3.1 33.7 −38.5 45.2 34.0 −44.8 16.5 39.8 18.0 −39.3 2.0 37.1 10.0 −37.2 −3.4 5.2 73.7 −81.6 91.9 24.8 −91.7 12.3 87.2 18.4 −86.2 5.6 80.5 9.2 −80.8 −1.0 墩柱TP5 1.7 15.9 −3.4 18.0 13.2 −4.8 42.1 12.6 −20.5 −2.0 −40.6 13.4 −15.6 −2.4 −27.3 3.0 26.0 −22.4 35.1 35.1 −36.4 62.7 29.9 15.1 −31.2 39.3 27.4 5.4 −28.2 26.0 4.6 46.4 −44.8 58.0 25.1 −60.1 34.2 52.8 13.8 −55.2 23.4 47.3 2.0 −48.8 9.1
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