应力相关阻尼模型及其在梁式桥动力分析中的应用
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摘要
阻尼对桥梁结构的动力响应有着重要的影响。众多研究表明在桥梁振动过程中,阻尼是一个变化的参数,然而现有的很多模型不能体现阻尼的变化。阻尼参数的不确定性严重制约着桥梁动力响应的求解精度。
本文在开展混凝土材料阻尼试验的基础上,提出了混凝土材料阻尼的识别方法和计算公式,并利用试验结果对Kelvin模型在混凝土材料耗能计算中的应用进行了修正。此外,本文收集了大量的实测桥梁阻尼比数据并分析了其分布规律,利用提出的应力相关阻尼模型进行了桥梁的车桥耦合振动和地震响应计算。本文的主要研究内容如下：
1.针对混凝土材料阻尼的应力相关性能,开展了轴向滞回试验,利用试验结果,区分了混凝土的塑性耗能和阻尼耗能,同时考虑振动应力幅值、振动频率和应力水平对混凝土阻尼耗能的影响。试验结果表明：混凝土材料的阻尼耗能随着振动的应力幅值增大而增大,二者的关系可以用幂函数或指数函数表示。混凝土材料的阻尼耗能对加载频率和应力水平敏感性较差。
2.针对四种常见的粘弹性模型,推导了周期性荷载作用下耗散能量和模型参数的关系式。利用材料阻尼试验的结果,提出了Kelvin模型中混凝土的粘滞系数的表达式,并进行了试验验证。计算结果表明：混凝土的粘滞系数不是定值,它随着应力幅值的增大而增大,提出的频率不相关粘滞系数,能够很好的模拟混凝土阻尼耗能的频率不敏感性,通过与其他试验结果的对比分析,验证了所推导粘滞系数表达式的有效性。
3.收集了114座桥梁的动力测试数据和4座桥梁的动力监测数据,测试了两座桥梁在环境激励和车辆激励下阻尼比数值,并对影响因素进行了分析。数据分析表明：不同桥型的阻尼比差距较大,相同桥型的阻尼比分布较为离散。随着桥梁的运营,阻尼比趋向于稳定值,维修和加固对桥梁阻尼比的影响不明显。车辆激励下测试的阻尼比要明显大于环境激励下测试的阻尼比。结合收集的阻尼比数据给出了不同桥型阻尼比的建议取值。
4.编制了车桥耦合振动响应计算程序,提出了桥梁结构应力相关阻尼的计算方法,求解了桥梁在车桥耦合振动下的动力响应,并同实测结果进行了对比。结果表明：应力相关阻尼理论能够体现桥梁振动过程中的阻尼变化,更加符合实际情况。与常阻尼比5%和Rayleigh阻尼相比,利用应力相关阻尼计算的车桥耦合振动响应更加接近于实测结果。
5.提出了区分钢筋混凝土柱在拟静力试验中的塑性耗能和阻尼耗能的方法,并通过试验验证了区分方法的有效性。考虑应力相关阻尼理论计算了钢筋混凝土柱拟动力试验动力响应,并与实测结果进行了对比分析。结果表明：考虑应力相关阻尼理论计算的结果要比常阻尼比(5%)下计算的结果更接近于实测结果,尤其是在小震和中震的情况。以一座连续刚构桥为背景,利用反应谱方法对桥梁的应力相关阻尼比进行了计算。计算结果表明：应力相关阻尼比随着地震烈度的增加而增大。
Damping has great influence on dynamic response of bridge. Numerous studies indicate that damping value is a variable during vibration process of bridge; however, most existing damping models cannot reflect this variation. The uncertainty of damping parameter severely restricts the solving accuracy of dynamic response.
On the basis of material damping experiment of concrete, a damping identification method and relevant calculation formula are proposed in this paper. Based on experimental data, the Kelvin model is proposed and employed for the energy dissipation calculation of concrete.In addition, full-scale data on the damping ratios of highway bridges in China have been collected and analyzed, a calculation method of stress-related damping is proposed for the bridges. The dynamic responses of vehicle-bridge and earthquake are calculated. Main researching works of this dissertation are as follows:
(1) A uniaxial hysteretic experiment including the influence of dynamic stress amplitude, frequency and stress level is conducted to study the stress-related damping characteristic of concrete. By use of the experimental results, the plastic energy dissipation and damping energy dissipation are separated, showing that the damping energy dissipation of concrete increases with the increase of stress amplitude, and the relationship can be represented by a power function. Moreover, the damping energy dissipation of concrete is not sensitive to loading frequency and stress level.
(2) The relationship between dynamic energy dissipation and model parameters are derived for four common viscoelastic models. A formula for calculating viscosity coefficient of Kelvin model is proposed and validated by experimental results. The calculating results show that the viscosity coefficient of concrete increases with increase of stress amplitude. The proposed viscosity coefficient being independent of frequency can well simulate the frequency insensitivity of the damping energy dissipation of concrete. Finally, the validity of the formula is verified by the comparison with others test results.
(3) Full-scale data on the natural frequencies and the damping ratios of114highway bridges in China, and the dynamic characteristics monitoring data of four bridges under ambient excitation, have been collected and analyzed. The data indicate that the damping ratios of different bridge types have large difference, and for the same bridge type, the damping ratios are scattered. With the increase in service ages, the damping ratios of the bridges decrease and tend toward stable after certain years; maintenance and reinforcement do not considerably affect the damping ratios. The test results of damping ratios under vehicle excitation are much larger than that of ambient excitation. The proposed damping ratios of different bridge types are given on the basis of damping ratio data.
(4) A calculation method of stress-related damping is proposed for bridges, and a vehicle-bridge coupled programming is developed to calculate the dynamic response. A helpful conclusion is obtained by comparing the test results; it shows that the stress-related damping is capable of presenting the variation of damping during the vibration process of bridge, and fitting the reality better. In comparison with the traditional constant damping ratio (5%) and Rayleigh damping, the stress-related damping is also much closer to the measured data.
(5) A calculate method is proposed for reinforcement concrete column to separate the plastic energy dissipation and the damping energy dissipation in quasi-static test. Correctness and validation of the method is testified by the comparison of measured data and the calculation result. Using stress-related damping theory, the dynamic response of reinforcement concrete column is calculated and compared with the quasi-static test result. Comparing with measured test, the result calculated by the stress-related damping is more accurate than that by constant damping ratio (5%), especially in small-moderate earthquake. Taking continuous rigid frame bridge as an instance, the stress-related damping ratio of a bridge is calculated by the method of response spectrum. The calculating results show that the damping ratio increases with the increase of earthquake intensity.
本文在开展混凝土材料阻尼试验的基础上,提出了混凝土材料阻尼的识别方法和计算公式,并利用试验结果对Kelvin模型在混凝土材料耗能计算中的应用进行了修正。此外,本文收集了大量的实测桥梁阻尼比数据并分析了其分布规律,利用提出的应力相关阻尼模型进行了桥梁的车桥耦合振动和地震响应计算。本文的主要研究内容如下：
1.针对混凝土材料阻尼的应力相关性能,开展了轴向滞回试验,利用试验结果,区分了混凝土的塑性耗能和阻尼耗能,同时考虑振动应力幅值、振动频率和应力水平对混凝土阻尼耗能的影响。试验结果表明：混凝土材料的阻尼耗能随着振动的应力幅值增大而增大,二者的关系可以用幂函数或指数函数表示。混凝土材料的阻尼耗能对加载频率和应力水平敏感性较差。
2.针对四种常见的粘弹性模型,推导了周期性荷载作用下耗散能量和模型参数的关系式。利用材料阻尼试验的结果,提出了Kelvin模型中混凝土的粘滞系数的表达式,并进行了试验验证。计算结果表明：混凝土的粘滞系数不是定值,它随着应力幅值的增大而增大,提出的频率不相关粘滞系数,能够很好的模拟混凝土阻尼耗能的频率不敏感性,通过与其他试验结果的对比分析,验证了所推导粘滞系数表达式的有效性。
3.收集了114座桥梁的动力测试数据和4座桥梁的动力监测数据,测试了两座桥梁在环境激励和车辆激励下阻尼比数值,并对影响因素进行了分析。数据分析表明：不同桥型的阻尼比差距较大,相同桥型的阻尼比分布较为离散。随着桥梁的运营,阻尼比趋向于稳定值,维修和加固对桥梁阻尼比的影响不明显。车辆激励下测试的阻尼比要明显大于环境激励下测试的阻尼比。结合收集的阻尼比数据给出了不同桥型阻尼比的建议取值。
4.编制了车桥耦合振动响应计算程序,提出了桥梁结构应力相关阻尼的计算方法,求解了桥梁在车桥耦合振动下的动力响应,并同实测结果进行了对比。结果表明：应力相关阻尼理论能够体现桥梁振动过程中的阻尼变化,更加符合实际情况。与常阻尼比5%和Rayleigh阻尼相比,利用应力相关阻尼计算的车桥耦合振动响应更加接近于实测结果。
5.提出了区分钢筋混凝土柱在拟静力试验中的塑性耗能和阻尼耗能的方法,并通过试验验证了区分方法的有效性。考虑应力相关阻尼理论计算了钢筋混凝土柱拟动力试验动力响应,并与实测结果进行了对比分析。结果表明：考虑应力相关阻尼理论计算的结果要比常阻尼比(5%)下计算的结果更接近于实测结果,尤其是在小震和中震的情况。以一座连续刚构桥为背景,利用反应谱方法对桥梁的应力相关阻尼比进行了计算。计算结果表明：应力相关阻尼比随着地震烈度的增加而增大。
Damping has great influence on dynamic response of bridge. Numerous studies indicate that damping value is a variable during vibration process of bridge; however, most existing damping models cannot reflect this variation. The uncertainty of damping parameter severely restricts the solving accuracy of dynamic response.
On the basis of material damping experiment of concrete, a damping identification method and relevant calculation formula are proposed in this paper. Based on experimental data, the Kelvin model is proposed and employed for the energy dissipation calculation of concrete.In addition, full-scale data on the damping ratios of highway bridges in China have been collected and analyzed, a calculation method of stress-related damping is proposed for the bridges. The dynamic responses of vehicle-bridge and earthquake are calculated. Main researching works of this dissertation are as follows:
(1) A uniaxial hysteretic experiment including the influence of dynamic stress amplitude, frequency and stress level is conducted to study the stress-related damping characteristic of concrete. By use of the experimental results, the plastic energy dissipation and damping energy dissipation are separated, showing that the damping energy dissipation of concrete increases with the increase of stress amplitude, and the relationship can be represented by a power function. Moreover, the damping energy dissipation of concrete is not sensitive to loading frequency and stress level.
(2) The relationship between dynamic energy dissipation and model parameters are derived for four common viscoelastic models. A formula for calculating viscosity coefficient of Kelvin model is proposed and validated by experimental results. The calculating results show that the viscosity coefficient of concrete increases with increase of stress amplitude. The proposed viscosity coefficient being independent of frequency can well simulate the frequency insensitivity of the damping energy dissipation of concrete. Finally, the validity of the formula is verified by the comparison with others test results.
(3) Full-scale data on the natural frequencies and the damping ratios of114highway bridges in China, and the dynamic characteristics monitoring data of four bridges under ambient excitation, have been collected and analyzed. The data indicate that the damping ratios of different bridge types have large difference, and for the same bridge type, the damping ratios are scattered. With the increase in service ages, the damping ratios of the bridges decrease and tend toward stable after certain years; maintenance and reinforcement do not considerably affect the damping ratios. The test results of damping ratios under vehicle excitation are much larger than that of ambient excitation. The proposed damping ratios of different bridge types are given on the basis of damping ratio data.
(4) A calculation method of stress-related damping is proposed for bridges, and a vehicle-bridge coupled programming is developed to calculate the dynamic response. A helpful conclusion is obtained by comparing the test results; it shows that the stress-related damping is capable of presenting the variation of damping during the vibration process of bridge, and fitting the reality better. In comparison with the traditional constant damping ratio (5%) and Rayleigh damping, the stress-related damping is also much closer to the measured data.
(5) A calculate method is proposed for reinforcement concrete column to separate the plastic energy dissipation and the damping energy dissipation in quasi-static test. Correctness and validation of the method is testified by the comparison of measured data and the calculation result. Using stress-related damping theory, the dynamic response of reinforcement concrete column is calculated and compared with the quasi-static test result. Comparing with measured test, the result calculated by the stress-related damping is more accurate than that by constant damping ratio (5%), especially in small-moderate earthquake. Taking continuous rigid frame bridge as an instance, the stress-related damping ratio of a bridge is calculated by the method of response spectrum. The calculating results show that the damping ratio increases with the increase of earthquake intensity.
引文
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