Effect of Different Prestressed Conditions on Seismic Response of Nuclear Containment Structure under Ultimate Safety Ground Motion
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摘要: 为了研究极限安全地震作用下混凝土预应力对核安全壳结构地震反应的影响，本文设定仅考虑预应力的瞬时损失、考虑预应力的长期损失和孔道灌浆后预应力均布等3种预应力工况和无预应力工况，并建立核安全壳结构精细有限元模型，进行核安全壳结构地震反应的非线性时程分析。计算结果显示，极限安全地震作用下无预应力工况下安全壳结构在抗震薄弱位置产生大量贯穿截面厚度的裂缝，基本上进入了功能失效状态；而3种有预应力工况下安全壳结构整体处于弹性状态，但是在安全壳主要开洞区域产生了开裂，并且在预应力均布工况下核安全壳在筒身底部产生了一定数量的受拉裂缝。研究表明采用预应力混凝土结构能显著提高核安全壳结构的抗震能力，但设计中需要关注孔道灌浆后可能产生的预应力均布对核安全壳结构抗震安全性能的不利影响。研究结果可为核安全壳结构设计合理利用预应力混凝土的抗震优势提供指导。Abstract: In order to study the influence of prestressed conditions of concrete structure on the seismic response of the nuclear containment structure under ultimate safety ground motion, in this paper, only three prestressed conditions, which are instantaneous prestress loss, long-term prestress loss and uniform distribution of prestress after duct grouting, and the no prestressed condition are considered, and then the nonlinear time history analysis of the seismic response of the nuclear containment structure is conducted by establishing their refined finite element models. The simulation results show that for the no prestressed condition, the containment structure has a large number of cracks running through the thickness of the section in the weak seismic position under ultimate safety ground motion, and the structure basically enters the state of functional failure; while the whole containment structure is in an elastic state under the three prestressed conditions. However, cracks occur in the main opening areas of the containment, and a certain number of tension cracks are generated at the bottom of the containment body under the condition of uniform prestress distribution. The research shows that the prestressed concrete structure can significantly improve the seismic capacity of the nuclear containment structure, but it should be paid attention to the adverse impact of the uniform prestress distribution that may occur after the duct grouting on the seismic safety performance of the nuclear containment structure in design. The research results can provide guidance for the rational use of the seismic advantages of prestressed concrete in the design of nuclear containment structure.
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图 4 预应力筋有限元模型
H—筒身环向预应力筋；V—倒U型预应力筋；D—穹顶环向预应力筋
Figure 4. Finite Element Model of Prestressed Tendons
图 7 普通钢筋本构曲线
$ {f}_{\mathrm{y},\mathrm{r}} $—钢筋屈服强度标准值；$ {f}_{\mathrm{s}\mathrm{t},\mathrm{r}} $—钢筋极限强度标准值；$ {{ \varepsilon }}_{\text{y}} $—钢筋的屈服应变；$ {{ \varepsilon }}_{\text{u}} $—钢筋极限拉应变
Figure 7. Constitutive Curve of Ordinary Reinforcement
图 9 3种预应力工况下环向预应力筋预应力分布
Figure 9. Prestress Distribution of Hoop Tendons under Three Prestressed Conditions
图 10 3种预应力工况下倒U型预应力筋预应力分布
Figure 10. Prestress Distribution of Inverted U-shaped Tendons under Three Prestressed Conditions
图 14 混凝土受拉损伤（工况三）
安全壳底部有部分区域的损伤云图不易看清，由红色虚线框标出，以便受到关注
Figure 14. Concrete Tensile Damage（Prestressed Condition Ⅲ）
图 17 工况三下A1、B1和C1位置主拉应变时程
Figure 17. Time History of Principal Tensile Strain at A1, B1 and C1 Positions under Prestressed Condition Ⅲ
表 1 安全壳混凝土CDP参数
Table 1. Parameters of CDP of Containment Concrete
膨胀角 偏心率 fb0/fc0 k 粘性系数 30° 0.1 1.16 0.667 0.001 fb0—混凝土双轴极限抗压强度；fc0—混凝土单轴极限抗压强度；k—拉伸子午面上与压缩子午面上的第二应力不变量之比[6] 
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表 2 安全壳混凝土损伤参数取值
Table 2. Damage Parameters of Containment Concrete
非弹性应变 受压损伤因子 开裂应变 受拉损伤因子 0 0 0 0 0.0006988 0.2071 0.0003270 0.9470 0.003020 0.6877 0.01100 0.9988 0.005741 0.8985
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表 3 3种预应力工况所考虑的预应力损失
Table 3. Prestress Loss Considered for the Three Prestressed Conditions
工况编号 考虑的预应力损失 备注 工况一 $ {\sigma }_{\mathrm{l}1}\mathrm{、}{\sigma }_{\mathrm{l}2}{\mathrm{、}\sigma }_{\mathrm{l}3} $ 仅考虑瞬时损失 工况二 $ {\sigma }_{\mathrm{l}1}\mathrm{、}{\sigma }_{\mathrm{l}2}\mathrm{、}{\sigma }_{\mathrm{l}3}\mathrm{、}{\sigma }_{\mathrm{l}4}\mathrm{、}{\sigma }_{\mathrm{l}5} $ 考虑瞬时损失和长期损失 工况三 $ {\sigma }_{\mathrm{l}1}\mathrm{、}{\sigma }_{\mathrm{l}2}\mathrm{、}{\sigma }_{\mathrm{l}3} $ 由工况一按预应力筋伸长量相等原则取平均
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表 4 安全壳结构前20阶模态特征
Table 4. Characteristics of the First 20 Order Modals of Containment
模态
阶数自振频
率/Hz振型特征 模态
阶数自振频
率//Hz振型特征 1 4.086 梁式一阶振型 11 10.593 局部振动 2 4.117 梁式一阶振型 12 11.404 局部振动 3 5.694 局部振动 13 11.679 局部振动 4 5.733 局部振动 14 11.693 局部振动 5 6.541 局部振动 15 11.772 局部振动 6 6.582 局部振动 16 11.966 梁式二阶振型 7 7.216 局部振动 17 12.094 梁式二阶振型 8 7.331 局部振动 18 12.215 Z向一阶振型 9 8.661 绕Z轴扭转 19 13.553 局部振动 10 10.436 局部振动 20 13.680 局部振动
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表 5 代表性位置主拉应变峰值
Table 5. Peak Value of Principal Tensile Strain at Representative Position
预应力工况 主拉应变峰值/10−4 A1 A2 A3 A4 A5 B1 B2 B3 B4 B5 C1 C2 C3 C4 D1 D2 D3 D4 工况一 1.00 0.51 0.29 0.34 0.54 0.90 0.41 0.23 0.35 0.56 0.82 0.42 0.35 0.54 1.12 1.46 2.27 1.86 工况二 1.01 0.49 0.29 0.32 0.49 0.94 0.39 0.23 0.34 0.49 0.79 0.42 0.33 0.48 0.84 1.10 1.65 1.40 工况三 1.43 0.44 0.29 0.36 0.52 1.16 0.38 0.24 0.35 0.53 1.57 0.68 0.43 0.55 1.27 1.57 2.39 1.97 位置编号中数字表示在径向上由外至内的单元次序，例如：A1表示位置A最外层单元
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