ABSTRACT
Structural reliability and life-time assessment is the key step when designing the structure or deciding about its maintenance and rehabilitation. When performing either reliability assessment or advanced engineering design, it is essential to take uncertainties into account using a probabilistic analysis. Hand in hand with the development of computer technology and advanced software tools, a utilization of probabilistic methods in combination with nonlinear analysis and global safety levels assessed according to appropriate Standards is offered as an alternative to conventional procedures. An application of these methods ensures that the safety and reliability of the structure reach the target level. The fully probabilistic solution also leads to more realistic estimation of the load-bearing capacity. Consequently, using probabilistic methods can also provide significant cost savings to bridge owners (Enevoldsen 2011).
While forward reliability methods have been applied widely and successfully in reliability engineering in various fields, inverse reliability approaches have not received the same degree of both attention and application, although they are particularly useful due to their important role in engineering design.
To determine design parameters (material properties, geometry, etc.) related to particular limit states a “trial and error” procedure by repeating forward reliability analyses can be used but insufficiency is obvious. In the paper a soft-computing based small-sample inverse reliability method is employed to find selected design parameters of a single-span post-tensioned composite bridge to ensure its reliability and load-bearing capacity. The proposed inverse analysis is based on the coupling of a small-sample stochastic simulation of Monte Carlo type and an artificial neural network (ANN), Lehký & Novák (2012). Since finding an analytical solution of such inverse problem is not possible an ANN based surrogate model is utilized instead. Once the ANN has been trained, it represents an approximation consequently utilized in the following way: To provide the best possible set of design parameters corresponding to prescribed reliability. Resulting values of design parameters and corresponding reliability indices.
Design parameter
value
β 1
β 2
β 1,target
β 2,target
mean (ft ) [MPa]
2.92
0.03
1.35
0
1.3
mean (P 1) [MPa]
14.60
The analyzed bridge has been made of precast post-tensioned concrete girders, each composed of six segments that are connected by the transverse joints. According to diagnostic survey the bridge exhibits a spatial variability of deterioration which brings uncertainty into actual values of concrete strength in transverse joints and of actual loss of pre-stressing. Because of their significant effect on the bridge load-bearing capacity and reliability, both were considered as uncertain design parameters with the aim to find their critical values corresponding to desired reliability level and load-bearing capacity. Target reliability indices were considered as β 1 = 0 for SLSD, and β 2 = 1.3 for SLSC, respectively. According to diagnostic survey and needs of bridge administrator desired load-bearing capacity related to normal loading class was considered as 25 t.
Results of inverse reliability analysis confirmed that bridge load-bearing capacity Vn = 25 t related to normal loading class is a realistic demand for required safety level.
