混凝土坝水库水动力相互作用计算模型研究
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摘要
大坝-库水动力相互作用是混凝土坝在强震作用下的动力响应重要影响因素之一,合理地确定坝面在地震作用下的动水压力及其对坝体地震响应的影响是大坝安全评估的重要基础。然而大坝体积巨大,且坝面动水压力受到库水可压缩性、库底淤沙的吸收作用、地基柔性、河谷形状等多种因素的影响,因此现场测试还难以准确获得坝面动水压力的分布和大小。在理论分析和数值分析方面,Westergaard首先(1933)对刚性坝面动水压力进行了开创性研究,之后许多学者采用解析法、有限元和边界元等数值方法进行了大量、深入的研究。但计算模型的精度及效率仍未能满足工程应用的需要。因此,研究新型高效、高精度的数值方法将对坝面动水压力的研究具有重要的科学研究价值和工程意义。本文基于比例边界有限元方法(SBFEM),针对坝体上游水库为半无限棱柱形、坝前库区形状不规则的情况,提出了坝面动水压力的计算模型和辐射边界条件,并完善了大坝-地基-库水系统动力响应的有限元和SBFEM耦合计算模型。主要内容如下：
(1)在SBFEM的基础上,建立了坝体上游水库为半无限棱柱水域情况的坝面动水压力计算模型。利用加权余量、Hamilton变分原理两种方法,考虑了库水可压缩性、库底吸收条件,提出了坝面动水压力的SBFEM计算模型。该模型只需离散坝面,且解自动满足水库上游无穷远处的辐射边界条件。利用二维重力坝与三维拱坝的多个数值算例,对坝面几何形状变化,坝体特性,地震动激励对坝面动水压力大小和分布的影响进行了详细研究,并与边界元、有限元、解析法对比,验证了本文方法的准确性和高效性。
(2)针对复杂形状的库区,基于SBFEM,是出了一种新的能够满足无穷远辐射条件,并且可以考虑库水可压缩性、库底吸收条件。该方法仅对近场有限库区边界进行离散,从而可以大大降低求解的规模,提高计算效率。数值算例表明,本文方法可适用于坝前水域形状复杂条件下坝面动水压力的计算,而且所提出的无反射边界条件具有较高的精度和较为广泛的适应性。
(3)将求解坝面动水压力和无限地基的SBFEM计算模型与坝体结构的有限元模型相结合,完善了大坝-库水-地基系统的耦合计算模型。SBFEM在处理无限域问题时具有很大的优势,通过与有限元方法相结合,可以充分发挥两种方法的优点,同时由于本文提出的动水压力模型更为精确,从而提高了耦合计算模型的整体计算精度。利用耦合模型,针对坝-库水-地基系统,重点分析了坝-库水动力相互作用对坝体动力响应的影响,计算模型及分析结果将对高坝建设和抗震安全评价具有重要的参考价值。
Dam-reservoir dynamic interaction is one of the most important influence factors of the dynamic response of concrete dams subjected to the strong earthquakes. Reasonable determination of the hydrodynamic pressures on the dams and its effects on the dam body during earthquakes are the basis of the safety evaluation of the dams. However, the volume of the dam is huge and the water compressibility, the absorption of the reservoir sediments, the flexibility of the foundation, the geometry of the reservoir all affect the hydrodynamic pressures. Therefore, the field test method can not be obtained the accurate value and the distribution of the hydrodynamic pressures. In terms of numerical and theory analysis, Westergaard gave the pioneer work on hydrodynamic pressures acting on rigid dam. After, many researches have extensively studied earthquake analysis of dam-reservoir system using various methods including analytical method, finite element method, and boundary method and so on. But the accurate and the efficiency of the computation model can not satisfy the demand of the engineering application and science research. So it is necessary to study a high efficient and precision numerical method for computing the hydrodynamic pressures. Based on Scaled Boundary Finite Element Method (SBFEM), this dissertation presents a computation model of dam reservoir hydrodynamic interaction and a novel radiation boundary condition for dam-reservoir systems, and also improves the coupled finite element and scaled boundary finite element approach for the earthquake response analysis of arch dam reservoir foundation systems. The major content of this dissertation is organized as follows:
(1) Based on SBFEM, it presents the computation model for hydrodynamic pressures acting on the dam when the reservoir extended to infinity with uniform cross-section. It can be derived the governing equations of hydrodynamic pressure in the frequency domain by weight residual method or Hamilton variable principle. The water compressibility and absorption of reservoir sediments can be conveniently taken into consideration. Only the dam-reservoir interface needs to be discretized to model the fluid domain, the solution is automatic satisfy with the radiation condition at the infinity, and the hydrodynamic pressure in the stream direction is solved analytically. Several numerical examples including a gravity dam with an inclined upstream face and an arch dam with a reservoir of arbitrary cross-section are provided to demonstrate the computational efficiency and accuracy of the proposed model.
(2) Based on SBFEM, it provides a new boundary condition of the stress on the truncation boundary suited for the complex shape of the reservoir-dam systems. The proposed approach can conveniently consider the water compressibility, the absorption of the reservoir boundary and the shape of the reservoir. Only the boundary of the dam-reservoir systems in the near field needs to be discretized. The numerical examples explain the proposed approach is not only satisfied the radiation condition boundary, but also for reducing computational efforts.
(3) Coupling the SBFEM model for computing the hydrodynamic pressures on dam and the unbounded foundation with the FEM model for dam body, it improves the computation model of the dam-reservoir-foundation systems. SBFEM is good at solving the unbounded domain problems, and it can be seamlessly coupled with FEM, therefore, they can give full play to dam-reservoir-foundation problem. Besides, the computation model of hydrodynamic pressures based on SBFEM is much more accurate, and it can improve the precision of the coupled model. This paper presents the influence of dam-reservoir hydrodynamic interaction to the response of the dam, the computation model and the results can be of significant reference value for the high dam construction and the seismic safety evaluation.
(1)在SBFEM的基础上,建立了坝体上游水库为半无限棱柱水域情况的坝面动水压力计算模型。利用加权余量、Hamilton变分原理两种方法,考虑了库水可压缩性、库底吸收条件,提出了坝面动水压力的SBFEM计算模型。该模型只需离散坝面,且解自动满足水库上游无穷远处的辐射边界条件。利用二维重力坝与三维拱坝的多个数值算例,对坝面几何形状变化,坝体特性,地震动激励对坝面动水压力大小和分布的影响进行了详细研究,并与边界元、有限元、解析法对比,验证了本文方法的准确性和高效性。
(2)针对复杂形状的库区,基于SBFEM,是出了一种新的能够满足无穷远辐射条件,并且可以考虑库水可压缩性、库底吸收条件。该方法仅对近场有限库区边界进行离散,从而可以大大降低求解的规模,提高计算效率。数值算例表明,本文方法可适用于坝前水域形状复杂条件下坝面动水压力的计算,而且所提出的无反射边界条件具有较高的精度和较为广泛的适应性。
(3)将求解坝面动水压力和无限地基的SBFEM计算模型与坝体结构的有限元模型相结合,完善了大坝-库水-地基系统的耦合计算模型。SBFEM在处理无限域问题时具有很大的优势,通过与有限元方法相结合,可以充分发挥两种方法的优点,同时由于本文提出的动水压力模型更为精确,从而提高了耦合计算模型的整体计算精度。利用耦合模型,针对坝-库水-地基系统,重点分析了坝-库水动力相互作用对坝体动力响应的影响,计算模型及分析结果将对高坝建设和抗震安全评价具有重要的参考价值。
Dam-reservoir dynamic interaction is one of the most important influence factors of the dynamic response of concrete dams subjected to the strong earthquakes. Reasonable determination of the hydrodynamic pressures on the dams and its effects on the dam body during earthquakes are the basis of the safety evaluation of the dams. However, the volume of the dam is huge and the water compressibility, the absorption of the reservoir sediments, the flexibility of the foundation, the geometry of the reservoir all affect the hydrodynamic pressures. Therefore, the field test method can not be obtained the accurate value and the distribution of the hydrodynamic pressures. In terms of numerical and theory analysis, Westergaard gave the pioneer work on hydrodynamic pressures acting on rigid dam. After, many researches have extensively studied earthquake analysis of dam-reservoir system using various methods including analytical method, finite element method, and boundary method and so on. But the accurate and the efficiency of the computation model can not satisfy the demand of the engineering application and science research. So it is necessary to study a high efficient and precision numerical method for computing the hydrodynamic pressures. Based on Scaled Boundary Finite Element Method (SBFEM), this dissertation presents a computation model of dam reservoir hydrodynamic interaction and a novel radiation boundary condition for dam-reservoir systems, and also improves the coupled finite element and scaled boundary finite element approach for the earthquake response analysis of arch dam reservoir foundation systems. The major content of this dissertation is organized as follows:
(1) Based on SBFEM, it presents the computation model for hydrodynamic pressures acting on the dam when the reservoir extended to infinity with uniform cross-section. It can be derived the governing equations of hydrodynamic pressure in the frequency domain by weight residual method or Hamilton variable principle. The water compressibility and absorption of reservoir sediments can be conveniently taken into consideration. Only the dam-reservoir interface needs to be discretized to model the fluid domain, the solution is automatic satisfy with the radiation condition at the infinity, and the hydrodynamic pressure in the stream direction is solved analytically. Several numerical examples including a gravity dam with an inclined upstream face and an arch dam with a reservoir of arbitrary cross-section are provided to demonstrate the computational efficiency and accuracy of the proposed model.
(2) Based on SBFEM, it provides a new boundary condition of the stress on the truncation boundary suited for the complex shape of the reservoir-dam systems. The proposed approach can conveniently consider the water compressibility, the absorption of the reservoir boundary and the shape of the reservoir. Only the boundary of the dam-reservoir systems in the near field needs to be discretized. The numerical examples explain the proposed approach is not only satisfied the radiation condition boundary, but also for reducing computational efforts.
(3) Coupling the SBFEM model for computing the hydrodynamic pressures on dam and the unbounded foundation with the FEM model for dam body, it improves the computation model of the dam-reservoir-foundation systems. SBFEM is good at solving the unbounded domain problems, and it can be seamlessly coupled with FEM, therefore, they can give full play to dam-reservoir-foundation problem. Besides, the computation model of hydrodynamic pressures based on SBFEM is much more accurate, and it can improve the precision of the coupled model. This paper presents the influence of dam-reservoir hydrodynamic interaction to the response of the dam, the computation model and the results can be of significant reference value for the high dam construction and the seismic safety evaluation.
引文
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