接上文：
4. The maintenance reliability threshold determination during bridge early operation stage
4.1 Example analysis
Take the data collected from the sensor named 2-3MID-2 embedded in the mid-span section base plate between 2# and 3# pier of the bridge for example, process the data according to the method suggested in Section 3.3, convert the data into stress data, and then do statistical analysis of the stress data and deal with the statistical data by Gauss distribution fitting, which can be seen in Fig. 5.
Fig. 5 Stress distribution statistics and Gaussian distribution fitting
Through the above statistics analysis of the converted data, the mean and standard deviation of the measured load effects probability distribution can be obtained for each time section, of which the standard deviation is shown in Table 3:
Table 3 The standard deviation of the measured load effects probability distribution in each time section
As can been seen in Fig. 6, the load distribution function fs(s) is gradually close to the tensile strength distribution function fRt(s) . Therefore, this paper only calculates βt. Based on the method suggested in Section 2, we can get the point time-dependent reliability around the embedded position in the bottom plate in the mid-span cross-section, which is illustrated in Fig. 6. Fig. 6 shows that the reliability βt reduced significantly when the bridge was in service about a year’s time. Fortunately, it remains stable a year later. The reason may be that the early concrete shrinkage and creep, prestress loss and other factors are not calculated precise enough.
Fig. 6 The reliability change over time which is calculated by
4.2 Brief introduction of “Three Sigma” principle
Since the last twentieth century, the human productivity continuously develops, and the product and quality are continuously improved. In twenty-first century, the quality becomes the theme of the new century. There is firstly “Three Sigma” principle in quality management in the past, and now “Six Sigma principle” is suggested. At present, the procedure guarantee capability and management level of the majority enterprises (Including construction enterprises) in the world is in the range about “Three Sigma” to “Four Sigma”.
“Three Sigma” principle itself is generated from normal distribution of the statistics. The normal distribution is determined by two important parameters: the mean and standard deviation. In total quality management, there is:
The above formula shows that the probability of the quality characteristic values falling without the confidence interval (μ-3σ ，μ+3σ ) is only 0.27%.
Bridge construction project is inherently a planned or under construction building products, and obsess the same quality connotation with other products, namely a set of natural characteristics to meet the need, which includes: safety, adaptability, reliability, economy and environmental suitability etc, of which the main influence factors are: the human factors, technical factors, management factors, environmental factors and social factors etc. Therefore, the idea of total quality management can also be applied on the bridge from design, construction, operation, to maintenance.
4.3 The calculation of maintenance reliability threshold for the bridge early operation stage
Generally, the modern large-span continuous rigid frame bridge construction is under monitoring, and so the failure probability or reliability index of the components or the cross-section can be obtained by the above method. Frangopol (1999) put forward 5 kinds of bridge reliability status, and assume that the bridge life can be seen as a reliable state process from the intact (β≥9.0) to the unacceptable (β<4.6). However, Frangopol just suggested the maintenance reliability threshold 4.6 of the steel-concrete composite bridge according to theory and experiences. As for this problem, combined with the monitored data, this paper puts forward a method to determine the maintenance reliability threshold of the prestressed concrete bridge during early operation stage.
As can been seen in Fig. 5, the stress state of the mid-span base plate is gradually changed from compression to tension, and then the pressure safety reserve become small. Seen from Fig. 5 (d) – (g), there is compressive stress between 2 ~ 3MPa of the unfavorable load state which is unfavorable on the bridge, which means that the pressure safety reserves is too low and is inconsistent to the general engineering experience request that the pressure safety reserve is at least 2 ~ 3MPa under the most unfavorable load conditions.
According to the above description in Section 4.2, at present, the procedure guarantee ability and management level of most enterprises in the world are about in the range from “Three Sigma” to “ Four Sigma”. Therefore, this paper adopts “Three Sigma” standard management level to determine the maintenance reliability threshold of the bridge. According to the request that the pressure safety reserve is at least 2~3 MPa under the most unfavorable load condition, this paper takes the value 2 MPa. Then, the bridge maintenance reliability threshold is calculated as follows:
Firstly, according to “Three Sigma” standard and the minimum 2 MPa pressure safety reserve requirement, this article defines a critical load effects distribution function for calculating the maintenance reliability threshold, and the calculation diagram is shown in Fig. 7, in which we only consider the probability of the abnormal load effects fall in the right confidence interval [ -2MPa，+∞ ], and the reason is: taking into account the compressive properties of the concrete, the probability of the abnormal load effects which does not comply with the design requirements falling in the left confidence interval [-∞，μ-3σ ] is too small and can be basically neglected. Among them, the critical load distribution function standard deviation σth is obtained by the monitored data, and this paper takes the mean σth=1.388 from Table 3 in Section 4.1. So, based on Fig. 7, we can get the critical load effects distribution function mean which is μth=-5.86MPa.
Fig. 7 Diagram of the determination of the critical load effect distribution function
Secondly, based on the mean μth and standard deviation σth of the above determined critical load effects distribution function, use the mean and the standard deviation of the tensile strength shown in Table 1, combined with Eq. (2), we have calculated and find the corresponding critical reliability value βtth=6.13 , and this value is taken as the maintenance reliability threshold of the bridge.
Actually, the maintenance reliability threshold is calculated by the concrete early tensile strength parameters when the bridge is in early operation. Therefore, the maintenance reliability threshold suggested in this paper is mainly aimed at the regulation of the early appeared unfavorable internal force state because of the early concrete shrinkage and creep, prestress loss etc.
However, the critical reliability value βtth=6.13 should be revised, of which the main reason is that the traffic loads of each bridge is different and so leads to Eqs. (5), (6) and (7) not precise enough.
5. Conclusions
As for the difficulties of the bridge maintenance strategy, based on the monitoring data collected from The SHMS of a prestressed concrete continuous rigid frame bridge, this paper put forward a kind of this type bridge point time-varying reliability and early operation maintenance reliability threshold calculation methodology, and the main conclusions are as follows:
● The monitoring data shows that the load effects of concrete bridges basically obey Gauss distribution, and so we can use Eq. (2) for reliability calculation.
● Based on “Three Sigma” management principle and the strain monitoring data, the critical load effects distribution function of this kind bridge is suggested in this manuscript.
● By the basis reliability theory and the above determined critical load effects distribution function, the early operation maintenance reliability threshold 6.13 of the prestressed concrete continuous rigid frame bridge with C50 strength grade concrete is recommended. Of course, the suggested reliability threshold should be revised by actual traffic loads statistics.
● The next stage research should focus on the bridge maintenance reliability threshold study after the bridge is in long-time operation, which is in order to develop maintenance strategy of replace, repair, and reinforcement of the bridge components due to the bridge material strength degradation.
The method suggested in this paper can provide a reference for bridge engineers doing rational bridge maintenance in operation.
Acknowledgements
During the research, Dr sun provide help for the article. So, the first author is very grateful for this.
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