Keywords: damage, simulation, assessment, reinforced concrete, road bridge.

Damage of structures is an everyday experience in civil engineering. A wide variety of mechanical, physical, chemical and biological material damage processes consequently weakens structural resistance, limits serviceability and lifetime. In that context, computer simulation of structural damage, prediction of structural degradation and lifetime as well as health monitoring during service life is an important part of computational structures technology.

The simulation of damage processes in structures requires complex multidisciplinary approaches combining numerical methods of continuum, damage, fracture as well as structural mechanics [1,2]. Besides, real load carrying structures contain diverse sources of uncertainty causing a significant scatter of their mechanical properties, strength, stiffness and durability. A reasonable assessment of structural lifetime requires, on the one hand, a deep insight into the physics of the degradation processes, and on the other hand, non-deterministic approaches to account for uncertainty [3].

After an overview of damage-relevant computational problems, the present work proposes a rational approach to simulation and assessment of structural damage and lifetime, which is then applied to a road bridge at Hünxe in the Ruhr-Area of Germany. This arch bridge has been built in 1951 as reinforced, pre-stressed, concrete structure. Since 1989, it was continuously observed due to increasing deflections, concrete cracks and corrosion of the pre-stressing tendons.

For damage simulations, the structure is discretized by multi-layered continuum-based shell elements suitable for geometrically and physically nonlinear finite element (FE) analyses. The time-independent material response of concrete is simulated within the elasto-plastic continuum damage theory, the concept of smeared cracks and fracture energy [4]. The pre-stressing tendons and steel reinforcement bars, which experience dominantly tensile stresses, are modelled by dimensionless steel layers with a uniaxial elasto-plastic material behaviour including damage. Three relevant long-term damage mechanisms, namely fatigue and corrosion of steel, as well as bond damage are taken into account by means of empirical models.

The degradation of structural performance is simulated by lifetime-dependent nonlinear quasi-static FE governing equations. Each simulation starts at time T=0 (virgin state) with a selected load combination and proceeds over lifetime step-by-step, until one of the selected numerical criteria for structural failure is reached.

In order to account for possible uncertainties three groups, design, material and damage parameters, are considered as random values. Basic material properties and damage parameters are simulated as random fields by use of the orthogonal transformation of the covariance matrix and latin hypercube sampling (LHS). The LHS provides a reasonable compromise between efficiency and accuracy for nonlinear stochastic simulations.

The obtained computational results regarding damage state of the bridge after 54 years of service life are currently being compared with the actual state observed shortly before demolition in 2005. The structural and material state of the bridge has been monitored by our colleagues from the Special Research Center 398. Vibration tests under impulse excitation delivered information concerning the global structural stiffness, whereas core samples from different structural elements provided important data on aging material properties.

1

W.B. Krätzig, Y.S. Petryna, "Assessment of structural damage and failure", Archive of Applied Mechanics, 71, 1-15, 2001. doi:10.1007/s004190000120

2

W.B. Krätzig, Y.S. Petryna, "Structural damage and life-time estimates by nonlinear FE simulation", Engineering Structures, 27(12), 1726-1740, 2005. doi:10.1016/j.engstruct.2005.04.015

3

Y.S. Petryna, W. B. Krätzig, "Computational framework for long-term reliability of RC structures", Computer Methods in Applied Mechanics and Engineering, 194 (12-16), 1619-1639, 2005. doi:10.1016/j.cma.2004.09.002

4

W.B. Krätzig, R. Pölling, "An elasto-plastic-damage model for reinforced concrete with minimum number of material parameters", Computers and Structures, 82, 1201-1215, 2004. doi:10.1016/j.compstruc.2004.03.002

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