Innovative Hysteresis Model and Parameter Identification Method for Reinforced Concrete Rectangular Hollow Piers
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摘要: 为了准确模拟RC (reinforced concrete)矩形空心桥墩的刚度退化特性,为桥梁震后可恢复性能研究提供理论基础,进行了不同设计参数的14个RC矩形空心墩模型拟静力试验. 通过引入峰值位移影响系数体现刚度退化与峰值位移的关联,建立修正的Bouc-Wen-Baber-Noori (BWBN)滞回模型;基于粒子群-引力搜索混合智能优化算法(combination of particle swarm optimization and gravitational search algorithm,PSOGSA)识别实测滞回曲线对应的滞回参数,并建立桥墩设计参数与滞回参数间的对应关系,进而总结滞回参数的经验预测方法. 研究结果表明:修正的BWBN滞回模型曲线与实测滞回曲线吻合程度高,相关性系数在0.98以上,且新型滞回模型能准确地反映出桥墩侧向刚度随墩顶位移退化的特性;PSOGSA算法能精确地识别实测滞回曲线的模型参数;采用经验预测方法得到的模型曲线与实测滞回曲线的相关性系数为0.83,该方法适用于缺乏实测滞回曲线的桥墩.Abstract: In order to precisely simulate the stiffness degradation of RC (reinforced concrete) rectangular hollow piers and provide the theoretical base for the research on post-earthquake resilient bridges, 14 RC rectangular hollow pier specimens with different design parameters were tested under semi-static loading. A modified Bouc-Wen-Baber-Noori (BWBN) hysteresis model was built, in which a peak-displacement coefficient was introduced to reflect the correlation between stiffness degradation and peak displacement. The hysteresis model parameters of each measured hysteresis curve were identified by combination of particle swarm optimization and gravitational search algorithm (PSOGSA). The relationship between the design parameters of hollow piers and hysteresis model parameters were regressed, and an empirical prediction method was summarized. The results show that the modified BWBN hysteresis curve is well matched with the measured hysteresis curve and the correlation coefficients are all above 0.98. The new hysteresis model can reflect how the lateral stiffness of piers degrades with peak displacement. PSOGSA is able to identify the hysteresis model parameters of the measured hysteresis curve precisely. The correlation coefficients between the measured hysteresis curve and modelling curve generated by empirical prediction method is 0.83. The method is applicable to the cases of bridge piers without the measured hysteresis curves.
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表 1 各试件的滞回参数识别结果
Table 1. Identified hysteresis model parameters
试件编号 ω0 α β γ n δη / × 10−5 δν r ζs p q ψ δψ / × 10−4 λ D-1 1.17 0.07 0.75 −0.06 1.15 1.04 0.08 0.06 0.63 0.46 0.05 0.57 1.58 1.73 D-2 1.03 0.02 0.95 −0.35 0.84 10.80 0.07 0.03 0.72 0.20 0.05 0.58 1.61 2.57 D-3 1.48 0.02 1.36 −0.50 0.94 1.00 0.11 0.11 0.69 0.91 0.05 0.33 1.54 4.68 E-1 1.21 0.06 1.34 −0.26 1.74 1.00 0.11 0.05 0.61 0.71 0.09 0.37 1.54 3.91 E-2 1.34 0.04 0.80 0.01 0.91 1.00 0.05 0.08 0.66 0.63 0.08 0.56 1.56 1.99 F-1 1.48 0.04 1.13 −0.50 1.22 5.51 0.07 0.09 0.64 0.50 0.18 0.40 1.51 4.60 F-2 1.48 0.04 1.21 −0.49 1.73 1.00 0.09 0.10 0.59 0.75 0.14 0.31 1.57 2.80 G-1 1.21 0.02 0.71 −0.40 0.88 1.00 0.08 0.17 0.63 0.59 0.07 0.54 1.50 3.39 G-2 1.13 0.04 0.54 0.12 1.25 21.30 0.09 0.06 0.64 0.50 0.17 0.44 1.23 1.61 G-3 1.37 0.03 1.26 −0.46 1.14 1.09 0.11 0.12 0.66 1.02 0.28 0.35 1.48 3.80 H-1 1.15 0.02 0.59 −0.28 1.50 1.00 0.30 0.15 0.60 0.64 0.18 0.27 1.78 3.64 H-2 1.19 0.02 0.70 −0.34 0.89 24.70 0.15 0.20 0.58 0.62 0.06 0.53 1.48 4.37 I-1 1.25 0.03 0.90 −0.50 0.93 4.92 0.06 0.15 0.61 0.41 0.06 0.62 1.74 2.76 I-2 1.17 0.04 0.85 −0.16 1.24 1.00 0.09 0.06 0.69 0.47 0.05 0.51 1.42 1.83 M-A 1.16 0.05 1.38 −0.34 1.47 4.75 0.12 0.05 0.72 1.03 0.17 0.41 1.15 2.70 M-C 1.07 0.02 0.70 −0.17 2.12 10.90 0.12 0.12 0.67 0.56 0.05 0.70 1.97 1.59 表 2 相关性系数与误差函数值
Table 2. Correlation coefficient and error function value
试件编号 ρ E 试件编号 ρ E 试件编号 ρ E D-1 0.989 0.000 7 F-1 0.990 0.000 9 H-1 0.990 0.000 7 D-2 0.991 0.001 1 F-2 0.991 0.000 7 H-2 0.992 0.000 7 D-3 0.992 0.000 9 G-1 0.986 0.001 0 I-1 0.992 0.000 8 E-1 0.994 0.000 8 G-2 0.992 0.000 8 I-2 0.994 0.000 7 E-2 0.992 0.001 0 G-3 0.992 0.001 0 M-A 0.986 0.003 6 M-C 0.987 0.002 9 表 3 桥墩设计参数与滞回参数对应关系的经验系数值
Table 3. Empirical coefficient of relationship between design parameters and hysteresis model parameters
滞回参数 x1 x2 x3 x4 x5 x6 x7 x8 ω0 −0.248 −0.268 0.101 −0.678 −0.102 −0.093 −0.058 1.103 α −0.993 −2.600 −0.172 −5.049 0.372 0.298 0.122 −2.473 β −0.524 −5.445 0.169 −3.676 0.000 0.150 0.116 −0.051 γ −0.310 −16.783 0.261 −2.943 −1.211 0.202 −0.265 5.768 n −0.436 −5.623 0.003 1.451 0.412 0.424 0.090 −0.397 δη 0.428 −0.878 −0.993 0.788 −0.969 −0.883 −0.213 −0.893 δν 0.194 19.570 0.086 −1.908 0.212 1.000 0.838 −16.067 r 1.151 0.725 −0.035 5.272 −0.519 −0.266 −0.304 −0.305 ζs −0.043 1.485 0.018 −0.443 0.071 −0.016 0.071 −1.447 p −0.022 −4.656 0.220 −3.524 0.187 0.068 0.217 −2.569 q 0.618 5.006 0.316 −7.662 −0.093 0.475 0.624 −10.946 ψ 0.245 −19.424 −0.114 4.005 −0.307 −0.340 −0.607 9.579 λ −0.226 −3.248 0.150 −2.645 −0.423 0.160 −0.031 2.237 表 4 拟静力试验的设计参数
Table 4. Design parameters of semi-static specimen
参数 b1/mm b2/mm d//mm h/mm n0 值 360 360 100 1 600 0.1 参数 ρ0/% ρv/% fy/MPa fc/MPa 值 1.4 0.72 335 38.7 表 5 经验预测滞回参数
Table 5. Identified hysteresis model parameters ofsemi-static specimen
参数 ω0 α β γ n δη 值 1.25 0.03 0.55 −0.11 0.56 1.18 × 10−4 参数 δν r ζs p q ψ λ 值 0.14 0.12 0.71 0.34 0.07 0.2 2.15 -
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