RELIABILITY ANALYSIS FOR FLEXURAL CAPACITY OF PRESTRESSED CONCRETE GIRDERS WITH BONDED CFRP REINFORCEMENTS
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摘要:
为提出基于可靠度分析的有粘结预应力CFRP筋混凝土梁抗弯承载能力极限状态设计方法，该文建立了包含32座预应力CFRP筋混凝土梁桥的设计空间。该空间涵盖了常见的高跨比范围和两种弯曲破坏模式(受拉破坏和受压破坏)。基于已有文献中115根梁的试验结果，确定了预应力CFRP筋混凝土梁抗弯承载力计算模型的统计参数。在此基础上，采用验算点法开展了预应力CFRP筋混凝土梁可靠度分析，校准了预应力CFRP筋材料分项系数γf，并通过Monte Carlo模拟验证了验算点法计算结果的准确性。结果表明：对于受拉破坏控制的梁，当γf从1.2提高到1.3，可靠指标β约增加0.5；对于受压破坏控制的梁，γf对可靠指标β几乎没有影响。为满足行业标准JTG 2120−2020规定的脆性破坏目标可靠指标，建议预应力CFRP筋材料分项系数取1.3。对预应力CFRP筋混凝土梁弯曲破坏模式进行概率分析，确定了受拉破坏和受压破坏皆可能发生的过渡区范围(0.7ρb<ρ≤1.5ρb，其中ρb为平衡配筋率)，并建议1.5ρb为确保发生受压破坏的最小配筋率。
Abstract:To achieve a reliability-based design provisions for the flexural strength of the concrete bridge girders prestressed with bonded carbon fiber-reinforced polymer (CFRP) reinforcements, this paper first establishes a design space of 32 benchmark bridges. This space covers a range of common height-to-span ratios and two types of flexural failure modes (tensile failure and compressive failure). Subsequently, statistical parameters for the flexural strength model are estimated based on an extensive experimental database of 115 beams from the existing literature. On this basis, the checking point method is applied to conduct a reliability analysis and calibrate the partial material factors associated with prestressed CFRP γf. The accuracy of the results obtained from the checking point method is verified by the Monte Carlo simulation. The results show that increasing the value of γf from 1.2 to 1.3 leads to an approximate 0.5 increase in the reliability index β for tension-controlled girders. However, for the compression-controlled girders, the variation in γf has an insignificant effect on their reliability indexes. To meet a uniform target reliability level for brittle failure, as specified in JTG 2120−2020, a prestressed CFRP partial material factor of 1.3 is recommended. Finally, a probabilistic analysis of flexural failure modes of CFRP prestressed concrete beams is conducted to determine the transition region where tension failure and compression failure are possible (0.7ρb<ρ≤1.5ρb, where ρb is the balanced failure mode). As a result, a minimum flexural reinforcement ratio of 1.5ρb is proposed to ensure a compression failure mode.
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图 1 20 m跨径梁横截面图和T梁截面尺寸图 /mm
Figure 1. 20 m-span bridge section and T-shaped girder section
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图 2 抗弯承载力试验值与计算值对比
Figure 2. Comparison of predicted flexural capacities with experimental results
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图 4 失效概率与模拟次数关系
Figure 4. Relationship between failure probability and number of trials
表 1 设计空间
Table 1 Design space
梁编号 截面高度/m 跨径/m 破坏模式 MD/(MD+ML) Mud/(kN·m) B1.1-13-T 1.10 13 受拉破坏 0.30 2048 Z1.1-13-T 1.10 13 受拉破坏 0.35 1817 B1.1-27-C 1.10 27 受压破坏 0.46 6011 Z1.1-27-C 1.10 27 受压破坏 0.51 5444 B1.3-16-T 1.30 16 受拉破坏 0.35 2815 Z1.3-16-T 1.30 16 受拉破坏 0.40 2525 B1.3-31-C 1.30 31 受压破坏 0.48 7600 Z1.3-31-C 1.30 31 受压破坏 0.54 6935 B1.5-20-T 1.50 20 受拉破坏 0.42 4168 Z1.5-20-T 1.50 20 受拉破坏 0.47 3737 B1.5-36-C 1.50 36 受压破坏 0.53 10452 Z1.5-36-C 1.50 36 受压破坏 0.59 9537 B1.75-25-T 1.75 25 受拉破坏 0.48 5951 Z1.75-25-T 1.75 25 受拉破坏 0.53 5504 B1.75-40-C 1.75 40 受压破坏 0.56 12725 Z1.75-40-C 1.75 40 受压破坏 0.62 11874 B2.0-30-T 2.00 30 受拉破坏 0.52 8223 Z2.0-30-T 2.00 30 受拉破坏 0.58 7690 B2.0-43-C 2.00 43 受压破坏 0.58 14899 Z2.0-43-C 2.00 43 受压破坏 0.64 14006 B2.25-35-T 2.25 35 受拉破坏 0.56 10917 Z2.25-35-T 2.25 35 受拉破坏 0.61 10300 B2.25-47-C 2.25 47 受压破坏 0.61 17921 Z2.25-47-C 2.25 47 受压破坏 0.66 16963 B2.5-40-T 2.50 40 受拉破坏 0.59 14052 Z2.5-40-T 2.50 40 受拉破坏 0.64 13386 B2.5-49-C 2.50 49 受压破坏 0.63 20559 Z2.5-49-C 2.50 49 受压破坏 0.67 19616 B2.5-48-T 2.50 48 受拉破坏 0.63 19056 Z2.5-48-T 2.50 48 受拉破坏 0.67 18497 B2.5-50-C 2.50 50 受压破坏 0.63 20793 Z2.5-50-C 2.50 50 受压破坏 0.68 20182 注：B表示为边梁，Z表示为中梁；第一个数字代表截面高度，第二个数字代表桥梁跨径；最后一个字母代表破坏模式(T：受拉破坏；C：受压破坏)； MD、ML分别为永久作用、可变作用(汽车和人群)产生的弯矩标准值；Mud为弯矩设计值。 
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表 2 随机变量的统计信息
Table 2 Statistics of random variables
影响因素 参数 偏差系数
λX变异系数
δX分布类型 参考文献 作用模型 构件自重 1.021 0.046 正态分布 文献[24] 沥青桥面铺装自重 0.989 0.111 正态分布 文献[24] 汽车冲击系数 1.200 0.050 正态分布 文献[24] 汽车荷载 0.800 0.086 极值I型 文献[24] 人群荷载 0.579 0.391 极值I型 文献[24] 材料性能 混凝土抗压强度 1.221 0.110 正态分布 文献[25] 混凝土极限压应变 1.000 0.150 对数正态 文献[26] CFRP筋抗拉强度 1.090 0.050 Weibull分布 文献[27] CFRP筋弹性模量 1.000 0.040 正态分布 文献[19] CFRP筋预应力损失 1.000 0.300 正态分布 文献[28] 几何尺寸 梁截面有效高度 1.012 0.023 正态分布 文献[24] 梁宽、翼缘宽 1.001 0.008 正态分布 文献[24] 梁翼、腹板厚 1.032 0.102 正态分布 文献[24] CFRP筋截面面积 1.000 0.030 正态分布 文献[29]
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表 3 计算模型不确定系数的统计参数
Table 3 Statistical parameters of model uncertainty
破坏模式 偏差系数λP 变异系数δP 分布类型 受拉破坏 1.038 0.079 Weibull分布 受压破坏 1.030 0.096 正态分布
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表 4 校准的预应力CFRP筋材料分项系数
Table 4 Calibrated prestressed CFRP material partial factor
编号 验算点法
校准γfMonte Carlo
校准γf编号 验算点法
校准γfMonte Carlo
校准γfB1.1-13-T 1.04 1.06 Z1.1-13-T 1.03 1.04 B1.3-16-T 1.12 1.13 Z1.3-16-T 1.11 1.12 B1.5-20-T 1.10 1.11 Z1.5-20-T 1.15 1.15 B1.75-25-T 1.15 1.16 Z1.75-25-T 1.21 1.22 B2.0-30-T 1.17 1.18 Z2.0-30-T 1.22 1.22 B2.25-35-T 1.19 1.20 Z2.25-35-T 1.23 1.23 B2.5-40-T 1.22 1.22 Z2.5-40-T 1.25 1.26 B2.5-48-T 1.27 1.28 Z2.5-48-T 1.28 1.29 建议γf 1.30 建议γf 1.30
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