Why Finite Element Analysis for Assessment of historic bridges and structures?

With the aging infrastructure of developed countries and the rapidly growing infrastructure of developing nations, the maintenance, reuse, and sustainability of existing infrastructure have become of paramount importance for the economies of these countries. 

For example, several railway bridges in the UK were constructed in the early 20th century or late 19th century. These bridges were designed for lighter loads and less impact. However, with the requirement of the rail network of the UK, these bridges are loaded heavily and undergo severe dynamic stress changes due to high-speed traffic. Some of the bridges have relinquished their so-called design life. Others are severely corroded or spread with defects. 

An argument can be put forward to demolish and replace these bridges with smart, efficient and economic infrastructure. However, demolition can be a more costly affair considering the temporary closure of rail traffic and road closures to demolish the bridge and incurring a loss tuning to a few million pounds. Furthermore, some bridges are historic in nature and drive major tourism in the cities that they inhabit. There is also a question of sustainability. Bridge construction involves a significant impact on the environment in terms of its carbon footprint. Reuse of old bridges can reduce the burden to the environment. 

So what do we do to encounter this problem? The answer lies in assessing the old structures. Now assessment comes with its own limitations. Traditional structural engineering standards use limit state design tools or allowable stress methods with tweaks to check the structural capacities of old structures. Howsoever realistic their assumptions are, a majority of the structures still fail to pass the check, which poses a serious question " How on earth does a century-old bridge still carry the trains at such speeds if it has failed on paper using a code based check?" The answer was always there in front of us. Only we engineers looked at it from a traditional code-based perspective. What if we could go beyond the simple static checks? What if finite element analyses could be used to accurately represent the full capacity of the bridge bringing nonlinearity into the picture. Modern codes in the UK like the Network Rail Standards have implemented provisions for a higher detail of analyses called the Level 2 Assessments which go beyond the traditional simple static checks. Finite Element Analysis is the crux of these detail assessments

Finite element analysis allows structural engineers to carry assessments of the existing structure in a more realistic way taking advantage of geometric and material nonlinearities in a structure. The finite element approach involves the following.

1. Going beyond the usual line beam idealisation of a structure and implementing a full 3-dimensional shell or volume element based modelling in sophisticated numerical analysis software. This lets us accommodate the realistic geometry i.e. defects involving loss of sections to various plates in a built-up girder bridge.
2. Using geometric nonlinearities into the analyses i.e. large displacement or P-delta effects of the geometry influencing the stiffness of the structure. So the increasing deformations in the structure improve the flexibility of the structure and the load carrying capacity. However, this is limited by the buckling of the structure under large deformations.
3. Using material nonlinearities i.e. using plastic material models like Von-Mises for metallic structure yielding in order to allow the structure to strain further than the yield point and make use of the hardening effects of steel till the point of ultimate rupture. Taking the structure to its plastic limits instead of just limiting the capacity to an elastic check.
4. Using construction stage analysis to correctly simulate the accumulation of stresses over the years due to any widening, strengthening or repair works in the past.
5. Using Contact nonlinearities to simulate actual lift-off at supports for simply supported girders. The traditional approach of pinning an end of a beam leads to high concentration of stresses. Using correct boundary conditions i.e. incorporating contact properties such as sliding, or friction contact allows engineers to extract realistic stresses and derive greater capacities out of the old structure.

With the help of finite element analysis, bridges can be assessed economically and we can extract larger capacities out of the existing structure. This means that we need not demolish or replace the bridge. Perhaps a local strengthening of the structure or a speed restriction or a weight limit on a highway bridge will suffice. Not surprisingly, a century-old bridge with a lot of corroded areas can still be functionally okay.

Although Finite Element Analysis is a saviour for crippling infrastructure, it should be used judiciously. Appropriate software tools and proficient human analytical skills are a must before venturing into any kind of assessment using FEA. Nevertheless, a detailed finite element analysis is always dependent on very accurate site inspection, good quality archive drawings and very often required engineering judgement or interpretation of finite element results. This article has taken the UK rail sector as an example. However, this culture of using detailed finite element assessment must be brought to all economies of the world and there should be a robust asset management system incorporated in all the growing economies to monitor old infrastructure.