A Comparative Study of Fragility Model for RC Girder Bridges and Buildings

Field surveys and data on the earthquake reveal that RC (reinforced concrete) bridges and buildings have been widely found in engineering structures, with abundant samples at disposal. By taking actual seismically damaged samples in the Wenchuan Earthquake happened in 2008 as examples, the paper established probability models for fragility matrix within Intensity VH-X/XI for the said two engineering structures based on EMS-98, MSK-81 and CSIS-08, and analyzed the comparative models for failure ratio and exceedance probability curves defined by these three scales. The paper, according to these analytical findings, proposed relevant measures and methods for improving the earthquake resistance of RC bridges.


Introduction
The Wenchuan Earthquake happened at Wenchuan county in 2008 blew a heavy blow to massive bridges and tunnels and posed a great threat to human lives and properties.In particular, bridges, partially or wholly collapsed, resulted in great causalities.As lifeline engineering, bridges, once savaged, would prevent people from emergency rescue.Post-earthquake surveys and media reports show that mainshocks and aftershocks cause different damage to bridges in different areas, while bridges that fall or have excessive displacement would hit their structures hard.As a result, it's important to investigate and analyze the actual seismic damage to bridges and delve deeper into their seismic fragility to build more earthquake-resistant bridges with desirable structural stability when great shocks occur.These features further serve the purpose of protecting human lives and properties.Information on empirical fragility and seismic damage to bridges in the Wenchuan Earthquake suggests that bridges surveyed are diverse in type, but 80% are reinforced concrete bridges and masonry arch bridges.This proportion indicates that these two bridges are prevalent, with abundant information on seismic damage [1][2][3][4][5].

Typical non-linear model for bridges
To better analyze the fragility of bridges in the earthquake-stricken areas, a large amount of program editing and comparative analysis were performed through numerical analysis and functional analysis before their fragility was evaluated with typical intensity scales.The discrete points of these samples were so unevenly distributed that most functional models hardly approached the sample point.Therefore, the models established in the survey could not meet expectations in degree of fitting (regression precision), variance, convergence, robustness and regularity.After the program of 50 functional models at least was compared, models for polynomial fitting, Gaussian fitting, exponential fitting, Fourier regression and spline interpolation approximation and Power Model performed better in approaching the sample point of seismic damage to bridges.The array of models was iterated and interpolated within 95% confidence interval, the R 2 and modified R 2 were both above 0.99, and the established matrix was favourable diagonal.Among Equations 1-4, Sd stands for the sample size or fragility parameters of seismic damage to bridge, Rd for the grade of seismic damage (as the fragility model for the surveyed areas that was numbered between integer one and five, and these integers corresponded to the five seismic damage grades), n0, n1, n2, n3 and n4 for polynomial regression parameters, c1, c2, d1, d2, m1 and m2 for Gaussian regression parameters, a1, a2, b1 and b2 for exponential regression parameters, and f, g1, g2, g3, g4, p1 and p2 for Fourier regression parameters [6][7][8][9][10][11].

Typical exceedance probability model for bridges
Bridge fragility mainly pertains to the conditional probability of bridges hitting or exceeding a certain limit of earthquakes at different magnitudes and can describe the probability distribution of bridges within various limits against seismic loads.The distribution is represented by matrix models for fragility curve or probability.Logarithmic and probability demand distribution functions are widely applied to the fragility analysis of bridges by deploying standard cumulative distribution function and taking peak ground acceleration (PGA), spectral acceleration and spectral displacement as ground motion demand parameters.Meanwhile, these parameters were analyzed for their relationship with the probability model for the performance of bridges.Nevertheless, most studies adopt ground motion as demand parameters to measure the fragility of bridges, and few analysis deals with fragility through intensity grades defined by different intensity scales.The paper, drawn on non-linear and probability models, proposed a cumulative distribution function model for exceedance probabilities based on intensity grades, as Equation 8shows.

Comparative analysis of fragility model for RC girder bridges and buildings
Bridges and buildings both are engineering structures made from reinforced concrete (RC).The survey implies that these two structures present some similar features in fragility at different intensities, while different structural forms and service purposes lead to differences.The paper established a matrix model for the fragility of RC bridges and buildings in areas whose intensities measured VII-X/I and the whole earthquake-stricken areas for comparative analysis by employing intensity scales EMS-98, MSK-81 and CSIS-08 and norms on the seismic damage grades of lifeline engineering, as shown in

Conclusions
The paper evaluated and analyzed the fragility of seismically damaged samples collected from the bridges and buildings in the Wenchuan Earthquake based on intensities scales EMS-98, MSK-81 and CSIS-08.As such, RC bridges were found more fragile when the intensity measures VII than RC buildings, most damage to RC bridges were caused by shocks graded DS2, indicating that buildings were more earthquake-resistant in low-intensity areas.In the areas whose intensity measured VIII, seismic damage to RC bridges were noticeably better than those to buildings.This is the same case for low, intermediate and high-intensity fragility.The features and distribution of bridges should be properly considered to improve the earthquake resistance of RC buildings within Intensity VIII.Based on the analysis of models for the comparative matrix and curves of fragility, bridges performed significantly better than buildings in response to the earthquake within Intensity IX.The failure ratio accounted for a greater proportion at Grade DS4 and Grade DS5 for buildings, the break ratio of bridges concentrated at Grade DS2 and Grade DS3, and bridges performed better in fragility than buildings at Grade DS1.From the perspective of all intensity scales, damage to bridges within Intensity X and Intensity XI were mainly found at Grades DS3 and Grade DS4, and most structural damage were detected at Grade DS5.The comparative analysis indicated that damage to bridges were obviously better than buildings in high-intensity areas.

Suggestions
The actual seismically damaged bridges and the fragility of buildings are evaluated through EMS-98, MSK-81 and CSIS-08, and the fragile models for bridges and buildings are compared in the paper.The findings suggest that the damage to bridges and buildings are measured Grade DS2 and DS1 respectively in low-intensity areas.In response, bridges should be improved to resist the light damage caused by an earthquake within the intensity.
In intermediate or high-intensity areas, bridges are more earthquake-resistant than buildings and less likely to collapse in meizoseismal areas, while buildings would partially or wholly collapse in meizoseismal areas.The greater resistance can be attributed to their simple strutbeams and proper structure and stress design that provide bridges with room for deformation and energy-dissipating capacity.
Based on these analysis, further studies should be conducted to better understand the earthquakeresistance performance of bridges in high-intensity areas and rationally introduce their advantages to the design and construction of buildings, so that they can perform as well as bridges in earthquake resistance in high-intensity or meizoseismal areas.

Table 1 .
Vulnerability matrix probability model of RC girder bridge and buildings investigation sample in VII degree region (EMS-98)

Table 2 .
Vulnerability matrix probability model of RC girder bridge and buildings investigation sample in VIII degree region (EMS-98)

Table 3 .
Vulnerability matrix probability model of RC girder bridge and buildings investigation sample in IX degree region (EMS-98)

Table 4 .
Vulnerability matrix probability model of RC girder bridge and buildings investigation sample in X/XI degree region (EMS-98)

Table 5 .
Vulnerability matrix probability model of RC girder bridge and buildings investigation sample in VII degree region (MSK-81)

Table 6 .
Vulnerability matrix probability model of RC girder bridge and buildings investigation sample in VIII region (MSK-81)

Table 7 .
Vulnerability matrix probability model of RC girder bridge and buildings investigation sample in IX degree region (MSK-81)

Table 8 .
Vulnerability matrix probability model of RC girder bridge and buildings investigation sample in X/XI degree region (MSK-81)

Table 9 .
Vulnerability matrix probability model of RC girder bridge and buildings investigation sample in VII degree region (CSIS-08)

Table 10 .
Vulnerability matrix probability model of RC in VIII degree region girder bridge and buildings investigation sample (CSIS-08)

Table 11 .
Vulnerability matrix probability model of RC girder bridge and buildings investigation sample in IX degree region (CSIS-08)

Table 12 .
Vulnerability matrix probability model of RC girder bridge and buildings investigation sample in X/XI degree region (CSIS-08)

Table 13 .
Vulnerability matrix probability model of RC girder bridge and buildings investigation sample in overall region