Author：Li Yinghua
Abstract
when to do bridge maintenance and which individual component of the bridges needing maintenance is a world problem at present, and the health monitoring system is considered to a very helpful tool for solving this problem. As the continuous monitoring over a long-term period can increase the reliability of the assessment, so, a large number of strain data acquired from the structural health monitoring system (SHMS) installed on a long-span prestressed concrete continuous rigid frame bridge is adopted in this paper. Firstly, a calculation method of point time-dependent reliability is proposed based on the basic reliability theory, and introduced how to calculate reliability of the bridge by using the stress data transformed from the strain data. Secondly, combined with “Three Sigma” principle and the basic pressure safety reserve requirement, the critical load effects distribution function of the bridge is defined, and then the maintenance reliability threshold for controlling the unfavorable load state which appears in the early operation stage of this type bridge is suggested. Finally, the advantages and drawbacks of the methodology suggested in this article are discussed. To sum up, the method can help bridge engineers do effective maintenance of the bridges.
Keywords
structural health monitoring; point time-varying reliability; the critical load effects distribution function; maintenance reliability threshold; continuous rigid frame bridge; “Three Sigma” principle
1. Introduction
In the world, people have recognized the importance of the SHMS for monitoring large-span bridges during in construction and service. At present, the health monitoring system becomes an indispensable part of long-span bridges, of which the role is to supply safety evaluation of bridge construction and operation (Muria et al. 1991, Cheung and Tadros 1997, Curran and Tilly 1999, NIuadi 2002, Cheung and Naumoski 2002, Mufti 2002, Wong 2004, Chan et al. 2006, Simon 2011, Li et al. 2014). Due to many influence factors of the data collected from the SHMS, such as: environmental factors, large size of the data itself, instability of material properties and the structure shape, load and resistance changing with time during the bridge operation etc., therefore, it makes to evaluate the bridge safety and help do effective maintenance in bridge operation by the data collected from the SHMS very difficult.
At present, many international experts and scholars have done effective work in the area of using the information from SHMS for rational maintenance planning of deteriorating structures. Thoft-Christensen (1995) proposed to apply reliability theory in bridge management systems. The international workshop (Frangopol et al. 1996a, 1998b) on structural reliability in bridge engineering has demonstrated the advantages of using reliability based methods in the key field of civil infrastructure systems. Frangopol (1999) developed the basis for cost-effective bridge management incorporating lifetime reliability and life-cycle cost. Frangopol and Das (1999) and Thoft-Christensen (1999) defined the bridge reliability states and proposed a reliability-based approach to bridge maintenance, and suggested the maintenance reliability threshold of the steel- concrete composite bridge to take the value 4.6 based on theory and experience. Dan M. Frangopol (2001) systematically concluded the birth and growth of bridge management systems, and suggested that the limitations of current bridge management systems could be overcome by using the reliability-based approach. Dan M. Frangopol et al (2001) suggested that the limitations of bridge management systems can be overcome by reliability-based method. K.J.M. et al (2005) suggested an idea of calculating the bridge reliability by using the basis reliability theory and the stress monitored data. F. Akgul and D. M. Frangopol (2005) explored the general methods for the analysis of the bridge performance in the life cycle and applied their research achievements in more than a dozen concrete bridges located in American Crow Leader states. M. G. Stewart and J. A. Mullard (2007) proposed a space and time related reliability analysis method to predict the probability of crack and damage degree under environmental erosion in concrete bridges. Mustafa Gul and F. Necati Catbas (2009) investigated the statistical pattern recognition for SHMS by using time series modeling of theory and experimental verifications. Sunyong Kim and Dan M. Frangopol (2010) provided an approach for cost-effective monitoring planning of a structure system based on a time-dependent normalized reliability importance factor (NRIF) of structural components. André D. Orcesia and Dan M. Frangopol (2011) researched the optimal maintenance strategies based on monitoring information and shown the benefits of SHMS. Helder Sousaa et al (2013) did long-term prediction of prestressed concrete bridges based on monitoring data, and discussed the differences between the measurements and the results obtained with the numerical model, namely the trends due to shrinkage and creep and the variations due to the temperature. Liu Yuefei et al (2014) adopted the Bayesian dynamic models (BDMs) to predict the structural load effects based on the monitored data (everyday monitored extreme stresses) and predicted the structural reliability indexes with First Order Second Moment method (FOSM).
To sum up, there is little monitoring data of SHMS for the assessment of bridge safety at the time, and the bridge maintenance strategy by the use of SHMS during operation is mainly based on expert experience and theoretical analysis at present. Therefore, in this paper, combined with large amount of strain monitoring data of a bridge SHMS and “Three Sigma” principle, a new methodology of calculating reliability and determining maintenance reliability threshold for the concrete continuous rigid frame bridge in early operation stage is presented. This method is useful for bridge engineers to do bridge maintenance.
2. The main idea of reliability calculation based on strain monitoring data
2.1 Calculation method
According to the method adopted by J. M. Ko et al. (2005), the failure probability Pf (or safety index β) of the structural components can be evaluated by means of considering both the member resistance R and the load effects S as random variables and can be written as:
In the formula: fR(r) and fs(s) are the probability density functions of R and S .
If fR(r) and fs(s) both obey normal distribution respectively, the calculation formula of the reliability index can be written as:
In the formula: Φ-1 is the inverse function of the standard normal distribution; μR and μs are the mean of the resistance and load effects respectively; σR and σs are the standard deviation of the resistance and load effects respectively.
2.2 The probability density function of the structure resistance
For concrete bridges, the concrete strength probability distribution function is taken as the probability density function of the resistance R , which generally obeys Gauss distribution and can be obtained by in situ material tests. As the tensile and compressive properties of concrete are different, two equations are adopted to represent the compressive and tensile strength distribution function:
In the formula: fRc(r)and fRt(r) are the Gauss distribution function of the compressive and tensile strength of concrete respectively; μc is the mean of the compressive strength of concrete; σ2c is the variance of the compressive strength of concrete; μt is the mean of the tensile strength of concrete; σ2t is the variance of the tensile strength of concrete. The mean compressive strength μc of concrete material is got by in situ test in this article. As for the variance σ2c , according to the highway reinforced concrete and prestressed concrete design specification JTG D62-2004 (2004), the variation coefficient can take δf=0.11 , and then the variance σ2c of the compression strength of concrete used in the bridge can be got. In this paper, the compressive strength mean and standard deviation of the concrete used in the bridge for a case study (seen in section 3) can be acquired, seen in Table 1.
According to the specification (2004), there is a relationship between the mean axial tensile strength of the concrete used in the bridge member and the mean standard cube compressive strength:
On the above, it has been written that the mean compressive strength can be obtained by in situ test. Therefore, the concrete member axial tensile strength μft can be got by the above formula (4). Also, according to the variation coefficient δf suggested in the specification (2004), which can take the value 0.11, then, the variance σ2t of the axial tensile strength of the concrete can be acquired. Therefore, the tensile strength mean and standard deviation of the concrete used in the bridge can be got, seen in Table 1.
Table 1 The mean and standard deviation of the concrete compressive and tensile strength
In fact, due to the durability and fatigue and other factors, concrete strength changes over time. D. T. Niu et al (1995) statistically analyzed the test results of long-term exposure concrete and in-service structures, and the results showed that concrete strength still subjected to normal distribution, but its mean and standard deviation changed, and the time-varying model of concrete cube compressive strength under the general atmospheric environment were given by
In the formula: μfcu0 and σfcu0 are the mean and standard deviation of cube compressive strength of concrete (28 days curing) respectively; μfcu(t) and σfcu(t) are the mean and standard deviation functions of the compressive strength of concrete cubes respectively after t years service.
因字数限制，未完待续。。。
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