Time-dependent reliability analysis of deteriorating reinforced concrete bridges considering nonstationary processes
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摘要: 采用Gamma随机过程描述车辆荷载频率函数，提出了基于荷载频率增大的钢筋混凝土桥梁时变可靠度分析方法。考虑历史荷载信息对桥梁时变抗力的验证作用，改进了抗力变异系数为时间变量的桥梁时变可靠度计算公式。采用上述方法，对某装配式预应力混凝土桥进行时变可靠度分析，结果表明，车辆荷载频率增量关联与否不影响结构时变可靠度的变化；结构在20至40 a的时变失效概率介于验证荷载为31.6%至36.4%初始抗力的失效概率之间，证明改进的公式具有更高的精度。当荷载频率λ小于10 a−1，考察范围不超过35 a，若历史荷载强度不高于初始抗力的29.1%，可以采用基于荷载频率函数λ(t)的可靠度计算方法；若一年两遇的车载强度超过结构初始抗力的36.4%，且年均增长率γ超过150%时，在海洋环境建造的钢筋混凝土梁桥在20 a内的失效概率较高，需引起注意，在设计和施工时增强钢筋的耐锈蚀性。Abstract: Traffic volume and vehicle loads are increasing with time during the bridge service life. Time-dependent reliability theory considers the time-varying effects of loads and resistance, which has been commonly adopted in recent engineering reliability research. The degradation of bridge resistance and increase of vehicle load and frequency varies with time, as described by a nonstationary stochastic model. The gamma stochastic process is adopted to describe the frequency function of vehicle load occurrence to promote the application of nonstationary processes in reliability studies, and time-dependent reliability analyzing approach is proposed for reinforced concrete bridges based on increasing load frequency. The time-dependent reliability equation is modified to account for the verifying effect of historical load information on time-varying resistance by including the coefficient of variation of bridge resistance as a time-associated variable. The above two methods are then used to perform a time-dependent reliability analysis on a prefabricated prestressed concrete bridge. The results show that the structural time-dependent reliability immunes the correlativity of frequency increment of vehicle loads; the time-dependent failure probabilities within 20 to 40 years range from those obtained by proof load tests with load intensities between 31.6% and 36.4% of the initial resistance, indicating higher precision of the modified equation. When the load frequency λ is less than ten times a year, the inspecting time interval is within 35 years, and the historical load intensity is less than 29.1% of the initial resistance, the approach based on load frequency function λ(t) is available. When the load frequency exceeds 36.4% of the bridge’s initial resistance, and the annual growth rate of frequency (γ) exceeds 150%. The RC bridge structure constructed in the marine environment has a higher failure probability within 20 years; thus, extra attention must be paid as corrosion resistance of reinforcements should be enhanced during its design and construction.
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图 3 不同尺度参数的
$ \tilde \lambda {(t)_{\text{I}}} $ Figure 3. Fig. 3
$ \tilde \lambda {(t)_{\text{I}}} $ with different scale parameters
图 4 不同尺度参数的
$ \tilde \lambda {(t)_{\text{D}}} $ Figure 4. Fig. 4
$ \tilde \lambda {(t)_{\text{D}}} $ with different scale parameters
图 5 抗力衰减与倒推初始抗力过程示意图
Figure 5. Resistance degradation and process of initial resistance retrospection
图 7 基于验证荷载实验的结构时变可靠度
Figure 7. Structural time-dependent reliability based on proof load testing
图 8 频率增大的多强度历史荷载对R20的验证结果及时变失效概率.(a)
$ \mu \left( {{R_{20}}} \right) $ ；(b)$ {P_{\text{f}}}\left( {20} \right) $ Figure 8. Verification of R20 by multi-intensity historical loads with increasing frequencies and time-dependent failure probability: (a)
$ \mu \left( {{R_{20}}} \right) $ ; (b)$ {P_{\text{f}}}\left( {20} \right) $ 
图 11 λ(t)为二次函数时公式(7)与MCS的时变失效概率对比
Figure 11. Comparison of time-dependent failure probabilities between Eq. (7) and MCS when λ(t) is quadratic
表 1 多强度历史荷载对R20的验证结果及时变失效概率
Table 1. Verification of R20 by multi-intensity historical loads and time-dependent failure probability
Historical load/
(kN·m)μ(R20)/
(kN·m)σ(R20)/
(kN·m)CoV. Pf(20) 0 16892 2533.8 0.15 0 5500 16892.7 2532.0 0.1499 0.00028 5750 16895.1 2532.5 0.1499 0.00053 6000 16895.9 2529.2 0.1497 0.00096 6250 16899 2525.6 0.1495 0.0017 6500 16903 2522.5 0.1492 0.0028 6750 16912.2 2518.2 0.1489 0.0045 7000 16918.9 2509.7 0.1483 0.0071 7250 16933.8 2502.0 0.1478 0.0107 7500 16951.5 2490.6 0.1469 0.0157 7750 16974.4 2477.3 0.1459 0.0224 8000 17005 2461.7 0.1448 0.0313 
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表 2 MCS和式(7)的Pf(20)结果比较
Table 2. Comparison of Pf(20) between MCS and Eq. (7)
Historical
load/(kN·m)$ {P_{\text{f}}}\left( {20} \right) $
by MCS$ {P_{\text{f}}}\left( {20} \right) $
by Eq.(7)5500 0.00043 0.00047 6000 0.0015 0.0017 6500 0.0042 0.0047 7000 0.0105 0.0116 7500 0.0229 0.0252 8000 0.0450 0.0490
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