大型钢制储液罐在地震激励下的强度与稳定性研究
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摘要
大型钢制储液罐是我国国家战略石油储备的核心设施,而我国有多达9个石油储备基地的抗震设防烈度达到或超过7度,储液罐的抗震安全性正成为我国国家能源供给与经济安全的保障。在1964年的Alaska地震以后,储液罐的抗震设计开始以反应谱理论为基础,并以许用压应力为基准进行稳定验算,但储液罐的震害事故仍时有发生。储液罐的设计地震力由设防地震下的弹性地震力采用折减系数确定,各国设计规范对该系数的取值存在一定争议,而储液罐设计规范现所采用的静力稳定校核方式,也不足以全面反映地震动的不确定性与复杂频谱特性。上述问题至今仍未得到很好解决,因此,确定合理的地震力折减系数以及探索高效的动力稳定性分析手段,具有重要理论意义与工程实用价值。
本文将分别提出动力推覆方法、Floquet乘子法、Lyapunov指数法三类分析方法,就钢制储液罐的地震力折减系数、动力不稳定域以及动力失稳概率进行深入研究：
考虑多维地震影响并采用Rayleigh阻尼假定,从“位移-压力”格式的流固耦合方程出发,推导出压力凝聚模型的动力平衡方程,并就流固耦合系统模态特性在压力凝聚前后的一致性进行了证明。以Clough模型罐为例,分别从模态特性与时程分析结果验证了压力凝聚模型的有效性。分析了10万方浮顶储液罐与5万方拱顶储液罐的主模态特性,重点考察了抗风圈、拱顶网壳等附属件的影响。
考虑重力影响并合并同频模态,由压力凝聚模型导出性能曲线的投影方程,通过控制谐波参数,实现流固耦合系统的单向动力推覆。以10万方浮顶储液罐为例,通过对比广义本构模型与流固耦合模型的时程分析结果,验证了动力推覆方法的有效性。基于动力推覆分析归纳了11种浮顶储液罐的幂次失效模型,以此构建等向强化的单自由度恢复力模型,选择40条最不利地震波,在特定延性下迭代求解储液罐的地震力折减系数,就规范GB50341、SH/T3026中地震力折减系数取值的合理性进行了讨论。
从“位移-压力”格式的流固耦合方程出发,以周期变化的几何刚度矩阵考虑壳体应力变化,基于压力凝聚模型,建立储液罐在简谐地面加速度下的周期系数扰动方程,通过计算Floquet乘子,递归搜寻动力不稳定域边界。以Chiba模型罐为例,基于模型试验结果与B-R准则法分析结果共同验证了Floquet乘子法的有效性。选择三类典型大型钢制储液罐作为分析对象,系统研究了静液压、储液密度、储液深度、抗风圈、网壳连接模式、隔震参数等因素对钢制储液罐动力不稳定域的影响。
从“位移-压力”格式的流固耦合方程出发,以时变几何刚度矩阵考虑壳体应力变化,基于压力凝聚模型,建立储液罐在地震激励下的等效动力扰动方程,通过实时调整扰动向量模长步进求解动态Lyapunov指数,据此确定储液罐的临界地震动峰值加速度以及动力失稳概率。以10万方浮顶储液罐为例,在简谐激励与地震激励下进行动力稳定性分析,分别采用Floquet乘子法与B-R准则法验证了Lyapunov指数法的有效性。参考储液罐的震害报告,建立多维地震动数据库,选择10万方与5万方钢制储液罐作为分析对象,重点研究了地震动多维特性、附属件设置、储液深度等因素对钢制储液罐动力失稳概率的影响。
Large steel liquid storage tanks are the core facilities of our National Strategic Petroleum Reserve, and China has as many as nine oil reserve bases whose seismic fortification intensity meets or exceeds7degree, thus the seismic safety of liquid storage tanks is becoming the guarantee of our national energy supply and economic safety. After the1964Alaskan earthquake, the seismic design of liquid storage tanks has began to be implemented based on the theory of response spectrum, and the allowable compressive stress is applied on checking calculation of stability. However, the liquid storage tank accidents caused by the earthquake still occur frequently. The design seismic force of liquid storage tank is determined by the elastic seismic force multiplied by the reduction factor under moderate earthquake, and there is some controversy on the value of above reduction factor between design specifications of different countries. Meanwhile, the static stability checking method currently adopted by the design specifications for liquid storage tanks is not sufficient to fully reflect the uncertainty and the complex spectral characteristics of ground motion. The above-mentioned issues have not been successfully solved, and so it is of great theoretical significance and practical engineering value to determine an appropriate seismic force reduction factor and to explore an efficient method of dynamic stability analysis.
This dissertation will respectively propose three types of analysis method including the dynamic pushover method, the Floquet multiplier method and the Lyapunov exponent method, and deep research on the seismic force reduction factor, the dynamic instability region and the dynamic instability probability of steel liquid storage tanks is then conducted:
Taking account of the impact of multidimensional earthquake and adopting Rayleigh damping assumption, the dynamic equilibrium equations of pressure condensation model were derived from fluid-solid coupling equations with "displacement-pressure" form, and then the consistency of modal characteristics of fluid-solid coupled system before and after pressure condensation was proved. With the example of Clough model tank, the validity of the pressure condensation model was separately verified in terms of modal characteristics and time history analysis results. The fundamental modal characteristics of100,000m3floating roof storage tank and50,000m3dome roof storage tank were analyzed, with emphasis on the investigation of the influences of subsidiary components such as wind girder and lattice dome shell.
Taking account of the impact of gravity and merging the vibration modes with the same frequency, the projection equation for capacity curve was derived based on pressure condensation model, and unidirectional dynamic pushover of fluid-solid coupled system was realized by controlling the harmonic parameters. Taking the100,000m3floating roof storage tank for example, the validity of the dynamic pushover method was then verified by comparing the time history results between the generalized constitutive model and fluid-solid coupled model. The power failure model of11types of floating roof storage tanks was summed up based on the dynamic pushover analysis, based on which a restoring force model with single degree of freedom and isotropic hardening was established, and then40severest ground motions were selected, and under which the seismic force reduction factors were then iteratively solved under specific ductility values, by comparing with which the reasonableness of the value of the seismic force reduction factor in GB50341and SH/T3026was discussed.
Starting from fluid-solid coupling equations with "displacement-pressure" form, the perturbation equations with periodic coefficients of liquid storage tanks under harmonic ground acceleration were established based on pressure condensation model, in which the shell stress change was considered with period-varying geometric stiffening matrix, and the dynamic instability boundaries were then iteratively obtained by the calculation of Floquet multipliers. Taking Chiba model tank for example, the validity of the Floquet multiplier method was separately verified by the model test results and analysis results of B-R criterion method. Taking3typical large steel liquid storage tanks as analysis objects, the influences of hydrostatic pressure, liquid density, liquid depth, wind girder, lattice shell connection type, isolation parameter on the dynamic instability regions of steel liquid storage tanks were systemically studied.
Starting from fluid-solid coupling equations with "displacement-pressure" form, the equivalent dynamic perturbation equations of liquid storage tanks under earthquake excitation were established based on pressure condensation model, in which the shell stress change was considered with time-varying geometric stiffening matrix, and the dynamic Lyapunov exponents were then calculated with time-stepping techniques by adjusting perturbation vector length in real-time, based on which the critical peak ground accelerations and the dynamic instability probabilities of liquid storage tanks were determined. Taking the100,000m3floating roof storage tank for example, the dynamic stability analysis under harmonic excitations and earthquake excitations were executed, by which the validity of the Lyapunov exponents method was separately verified based on the Floquet multiplier method and the B-R criterion method. According to the earthquake damage reports of liquid storage tanks, a multidimensional ground motion database was established, and taking the two steel liquid storage tanks with the volume of100,000m3and50,000m3as analysis objects, the influences of multidimensional characteristic of earthquake, installation pattern of subsidiary components, liquid depth on the dynamic instability probabilities of steel liquid storage tanks were primarily studied.
本文将分别提出动力推覆方法、Floquet乘子法、Lyapunov指数法三类分析方法,就钢制储液罐的地震力折减系数、动力不稳定域以及动力失稳概率进行深入研究：
考虑多维地震影响并采用Rayleigh阻尼假定,从“位移-压力”格式的流固耦合方程出发,推导出压力凝聚模型的动力平衡方程,并就流固耦合系统模态特性在压力凝聚前后的一致性进行了证明。以Clough模型罐为例,分别从模态特性与时程分析结果验证了压力凝聚模型的有效性。分析了10万方浮顶储液罐与5万方拱顶储液罐的主模态特性,重点考察了抗风圈、拱顶网壳等附属件的影响。
考虑重力影响并合并同频模态,由压力凝聚模型导出性能曲线的投影方程,通过控制谐波参数,实现流固耦合系统的单向动力推覆。以10万方浮顶储液罐为例,通过对比广义本构模型与流固耦合模型的时程分析结果,验证了动力推覆方法的有效性。基于动力推覆分析归纳了11种浮顶储液罐的幂次失效模型,以此构建等向强化的单自由度恢复力模型,选择40条最不利地震波,在特定延性下迭代求解储液罐的地震力折减系数,就规范GB50341、SH/T3026中地震力折减系数取值的合理性进行了讨论。
从“位移-压力”格式的流固耦合方程出发,以周期变化的几何刚度矩阵考虑壳体应力变化,基于压力凝聚模型,建立储液罐在简谐地面加速度下的周期系数扰动方程,通过计算Floquet乘子,递归搜寻动力不稳定域边界。以Chiba模型罐为例,基于模型试验结果与B-R准则法分析结果共同验证了Floquet乘子法的有效性。选择三类典型大型钢制储液罐作为分析对象,系统研究了静液压、储液密度、储液深度、抗风圈、网壳连接模式、隔震参数等因素对钢制储液罐动力不稳定域的影响。
从“位移-压力”格式的流固耦合方程出发,以时变几何刚度矩阵考虑壳体应力变化,基于压力凝聚模型,建立储液罐在地震激励下的等效动力扰动方程,通过实时调整扰动向量模长步进求解动态Lyapunov指数,据此确定储液罐的临界地震动峰值加速度以及动力失稳概率。以10万方浮顶储液罐为例,在简谐激励与地震激励下进行动力稳定性分析,分别采用Floquet乘子法与B-R准则法验证了Lyapunov指数法的有效性。参考储液罐的震害报告,建立多维地震动数据库,选择10万方与5万方钢制储液罐作为分析对象,重点研究了地震动多维特性、附属件设置、储液深度等因素对钢制储液罐动力失稳概率的影响。
Large steel liquid storage tanks are the core facilities of our National Strategic Petroleum Reserve, and China has as many as nine oil reserve bases whose seismic fortification intensity meets or exceeds7degree, thus the seismic safety of liquid storage tanks is becoming the guarantee of our national energy supply and economic safety. After the1964Alaskan earthquake, the seismic design of liquid storage tanks has began to be implemented based on the theory of response spectrum, and the allowable compressive stress is applied on checking calculation of stability. However, the liquid storage tank accidents caused by the earthquake still occur frequently. The design seismic force of liquid storage tank is determined by the elastic seismic force multiplied by the reduction factor under moderate earthquake, and there is some controversy on the value of above reduction factor between design specifications of different countries. Meanwhile, the static stability checking method currently adopted by the design specifications for liquid storage tanks is not sufficient to fully reflect the uncertainty and the complex spectral characteristics of ground motion. The above-mentioned issues have not been successfully solved, and so it is of great theoretical significance and practical engineering value to determine an appropriate seismic force reduction factor and to explore an efficient method of dynamic stability analysis.
This dissertation will respectively propose three types of analysis method including the dynamic pushover method, the Floquet multiplier method and the Lyapunov exponent method, and deep research on the seismic force reduction factor, the dynamic instability region and the dynamic instability probability of steel liquid storage tanks is then conducted:
Taking account of the impact of multidimensional earthquake and adopting Rayleigh damping assumption, the dynamic equilibrium equations of pressure condensation model were derived from fluid-solid coupling equations with "displacement-pressure" form, and then the consistency of modal characteristics of fluid-solid coupled system before and after pressure condensation was proved. With the example of Clough model tank, the validity of the pressure condensation model was separately verified in terms of modal characteristics and time history analysis results. The fundamental modal characteristics of100,000m3floating roof storage tank and50,000m3dome roof storage tank were analyzed, with emphasis on the investigation of the influences of subsidiary components such as wind girder and lattice dome shell.
Taking account of the impact of gravity and merging the vibration modes with the same frequency, the projection equation for capacity curve was derived based on pressure condensation model, and unidirectional dynamic pushover of fluid-solid coupled system was realized by controlling the harmonic parameters. Taking the100,000m3floating roof storage tank for example, the validity of the dynamic pushover method was then verified by comparing the time history results between the generalized constitutive model and fluid-solid coupled model. The power failure model of11types of floating roof storage tanks was summed up based on the dynamic pushover analysis, based on which a restoring force model with single degree of freedom and isotropic hardening was established, and then40severest ground motions were selected, and under which the seismic force reduction factors were then iteratively solved under specific ductility values, by comparing with which the reasonableness of the value of the seismic force reduction factor in GB50341and SH/T3026was discussed.
Starting from fluid-solid coupling equations with "displacement-pressure" form, the perturbation equations with periodic coefficients of liquid storage tanks under harmonic ground acceleration were established based on pressure condensation model, in which the shell stress change was considered with period-varying geometric stiffening matrix, and the dynamic instability boundaries were then iteratively obtained by the calculation of Floquet multipliers. Taking Chiba model tank for example, the validity of the Floquet multiplier method was separately verified by the model test results and analysis results of B-R criterion method. Taking3typical large steel liquid storage tanks as analysis objects, the influences of hydrostatic pressure, liquid density, liquid depth, wind girder, lattice shell connection type, isolation parameter on the dynamic instability regions of steel liquid storage tanks were systemically studied.
Starting from fluid-solid coupling equations with "displacement-pressure" form, the equivalent dynamic perturbation equations of liquid storage tanks under earthquake excitation were established based on pressure condensation model, in which the shell stress change was considered with time-varying geometric stiffening matrix, and the dynamic Lyapunov exponents were then calculated with time-stepping techniques by adjusting perturbation vector length in real-time, based on which the critical peak ground accelerations and the dynamic instability probabilities of liquid storage tanks were determined. Taking the100,000m3floating roof storage tank for example, the dynamic stability analysis under harmonic excitations and earthquake excitations were executed, by which the validity of the Lyapunov exponents method was separately verified based on the Floquet multiplier method and the B-R criterion method. According to the earthquake damage reports of liquid storage tanks, a multidimensional ground motion database was established, and taking the two steel liquid storage tanks with the volume of100,000m3and50,000m3as analysis objects, the influences of multidimensional characteristic of earthquake, installation pattern of subsidiary components, liquid depth on the dynamic instability probabilities of steel liquid storage tanks were primarily studied.
引文
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