Compensation Factors for Bridges Built With a Reinforced Concrete Strength Below Its Nominal Value and Located on Seismic Hazard Zones

David De-León-Escobedo

doi:10.3389/fbuil.2018.00076

Abstract

Sometimes, in the absence of a strict supervision, bridges are built with a reinforced concrete strength below its nominal value. If the difference is not so high to consider the bridge demolition, a question arises about how much the compensation should be. In this paper, a rational basis to orient negotiations, taken as the ratio between expected life-cycle costs for the actual and nominal concrete strengths is proposed and illustrated for a bridge in Mexico City. The calculation of the expected life-cycle cost includes the bridge annual failure probability under the dead, live and seismic loads and the costs of failure consequences. Uncertainty is considered only on the seismic load. The bridge annual failure probability is calculated by FORM approximation and by considering scenario ground accelerations and the seismic hazard curve for the bridge site. With the total probability theorem, the overall bridge annual failure probability is approximated and the expected life-cycle costs are calculated. The process is repeated for several values of reinforced concrete strength and the compensation factors are calculated and plotted for several costs of consequences. In order to explore several cases, two reinforced concrete strength, two pier heights: 4 and 8m, three sites in Mexico with different seismicity and three levels of failure consequences, are considered. In these examples, the dominant failure mode is the pier axial load-bending moment interaction as a result of the acting loads combination. As expected, the factors increase for a larger difference of concrete strengths, for the higher piers, for a stronger seismicity and for larger costs of failure consequences. The factors were calculated for a nominal concrete strength of 200 Kg/cm2, and variations of 180 and 160 Kg/cm2, and for a nominal strength of 420 Kg/cm2, and variations of 400 and 380 Kg/cm2.

Highlights

Reinforced concrete bridges are critical components for the transportation network all around the world
Where Ci is the bridge initial cost and E(DC) the present value of the expected cost of damage for a year, which is composed by the present value factor PVF, the annual failure probability and the cost of the failure consequences
As the pier height increases, the compensation factor increases because a certain deficit on concrete strength produces larger deficits on the resisting moments and, larger failure probabilities and larger expected losses

Summary

Introduction

Reinforced concrete bridges are critical components for the transportation network all around the world. In places where the supervision tasks are not strict, bridges are built with reinforced concrete provided with a strength lower than the specified value. If the difference is considered to be too high, demolition and reconstruction are mandatory actions. If that difference allows for the consideration of reinforcements/repairs a question arises about how much. Several reliability-based approaches have been presented to calculate compensation factors (Rosenblueth et al, 1974). In this treatment the earthquake occurrence was represented by a Poisson process and the cost of failure consequences were not included explicitly

Methods

Discussion

Conclusion