Fragility Analysis of Prestressed Containment under Thermal-Compressive Coupling Condition
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摘要: 本文对预应力安全壳结构进行了建模，利用有限元分析软件ABAQUS模拟热-压耦合试验，利用拉丁超立方抽样法得到的安全壳随机样本进行计算，得到两条安全壳易损性曲线，分析安全壳整体功能性失效、结构性失效对应的易损性。计算结果表明，安全壳的下限和上限内压承载力分别是0.9666 MPa和1.0352 MPa。钢衬里功能性失效准则下，HRB400钢筋弹性模量对安全壳的内压承载力影响最大；钢衬里最大拉应变集中分布在设备闸门洞口附近。预应力筋结构性失效准则下，HRB500钢筋弹性模量对安全壳的内压承载力影响最大；预应力筋最大拉应变的分布没有明显的规律。Abstract: In this paper, a prestressed containment structure is modeled, the finite element analysis software ABAQUS is used to simulate the thermal-compressive coupling test, and random samples of the containment obtained by using the Latin hypercube sampling method are calculated to obtain 2 containment susceptibility curves for analyzing the susceptibility corresponding to the overall functional failure and structural failure of the containment. The calculation results show that the lower and upper limits of the inner pressure bearing capacity of the containment are 0.9666 MPa and 1.0352 MPa, respectively. Under the steel lining functional failure criterion, the elastic modulus of HRB400 reinforcement has the greatest influence on the inner pressure bearing capacity of the containment; the maximum tensile strain of the steel lining is concentrated near the equipment gate opening. Under the structural failure criterion of prestressed tendons, the elastic modulus of HRB500 steel bars has the greatest influence on the internal pressure bearing capacity of the containment; the distribution of the maximum tensile strain of prestressed tendons has no obvious pattern.
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图 4 沿筒壁厚度方向节点温度
Figure 4. Nodal Temperature along the Cylinder Wall Thickness Direction
图 7 混凝土开裂时安全壳结构变形图
Figure 7. Deformation Diagram of Containment Structure during Concrete Cracking
图 8 不同失效准则对应的安全壳结构变形图
Figure 8. Deformation Diagram of Containment Structure under Different Failure Criteria
图 9 热-压耦合作用下安全壳内压承载力分布
Figure 9. Distribution of Pressure Bearing Capacity in Containment under Thermal-compressive Coupling Condition
图 10 安全壳在热-压耦合作用下的易损性曲线
Figure 10. Fragility Curve of Containment under Thermal-compressive coupling Condition
图 11 部分钢衬里在达到功能性失效应变阈值时的应变图
Figure 11. Strain Diagrams of Some Steel Liner at the Time of Functional Failure
图 12 部分预应力筋在达到结构性失效应变阈值时的应变图
Figure 12. Strain Diagrams of Partially Prestressed Tendons at the Time of Functional Failure
表 1 随机变量概率统计特性
Table 1. Probabilistic and Statistical Properties of Random Variables
随机变量 分布类型 均值/MPa 变异系数 混凝土抗压强度 对数正态 46 0.10 预应力筋弹性模量 正态 200000 0.03 预应力筋抗拉强度 对数正态 1860 0.07 HRB400钢筋弹性模量 正态 200000 0.03 RB400钢筋抗拉强度 对数正态 435 0.07 HRB500钢筋弹性模量 正态 200000 0.03 HRB500钢筋抗拉强度 对数正态 540 0.07 钢衬里弹性模量 正态 200000 0.03 钢衬里屈服强度 对数正态 320 0.07 
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表 2 荷载施加步骤
Table 2. Load Application Procedure
步骤 内压/MPa 壳内温度/℃ 1（施加重力荷载） 0 0 2（进行预应力张拉） 0 0 3 0.10 40 4 0.30 56.7 5 0.45 90 6 0.45 140 7 0.52 145 8 0.60 145 9 每个荷载步增加0.1 MPa。内压达到1.3 MPa前温度维持在145℃，在1.3 MPa后温度维持在160℃ … 直到破坏
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表 3 热传导模型材料参数
Table 3. Material Parameters of Heat Transfer Model
材料 线膨胀
系数/℃−1比热容
/[J ·(kg·℃)−1]热传导系数
/ [W·(m·℃)−1]热对流系数
/ [W·(m2·K)−1]混凝土 1.0×10−5 960 1.355 16 钢衬里 1.2×10−5 470 45 8
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表 4 热传导分析模型单元类型
Table 4. Types of Units in Heat Transfer Analysis Model
单元编号 单元类型 模拟部分 单元数量/个 结点数量/个 DC3D8 热传导单元 混凝土 1898430 2176198 DS4R 热传导单元 钢衬里 21307 共84460 DS3 热传导单元 钢衬里 1264
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表 5 安全壳易损性曲线参数
Table 5. Containment Fragility Curve Parameters
失效准则 pm/MPa β 钢衬里功能性失效准则 1.0005 0.0208 预应力筋结构性失效准则 1.4099 0.0663
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表 6 安全壳不同失效准则对应5%、95%分位内压承载力
Table 6. Different Failure Criteria of Containment Corresponding to 5% and 95% Internal Pressure Bearing Capacity
失效准则 5%分位内压
承载力/MPa95%分位内压
承载力/MPa钢衬里功能性失效准则 0.9666 1.0352 预应力筋结构性失效准则 1.3035 1.5215
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表 7 两种失效准则随机变量的归一化敏感度指数
Table 7. Normalized Sensitivity Index of Random Variables under Two Failure Criteria
随机变量 归一化敏感度指数 钢衬里功能性
失效准则预应力筋结构性
失效准则混凝土抗压强度 −0.00464 0.01396 预应力筋弹性模量 −0.30079 −0.03254 预应力筋抗拉强度 −0.06129 0.08001 HRB400钢筋弹性模量 −0.33510 0.48352 HRB400钢筋抗拉强度 0.08307 −0.10999 HRB500钢筋弹性模量 −0.05173 0.73778 HRB500钢筋抗拉强度 −0.01596 −0.26238 钢衬里弹性模量 0.15805 0.08134 钢衬里屈服强度 0.01535 −0.05939
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