Bridge Safety Assessment
A bridge is safe when the load is less than the bridge resistance. More precisely, a bridge is safe when the probability is very small that the bending moment or shear force due to load is less than the corresponding resistance. The RDS staff have extensive experience in quantifying this probability, with a particular strength in Reliability Theory.
The Eurocode specifies that the general requirements of the code do not need to be specified provided the overall requirement for the safety level is satisfied. Safety is defined in terms of the reliability factor, β.
Prof O’Connor has used Reliability Theory to justify the retention of many road and railway bridges Internationally that would othersise have to be replaced or repaired.
Bridge Traffic Loading
As safety depends on applied load as well as resistance, a probabilistic assessment of traffic load is an important element in bridge safety assessment – most bridges are never subject to the full code design loading. Assessment of traffic load usually involves an analysis of vehicle weight data (see Weigh-in-Motion [3.3]).
New bridges are designed for a notional load model. However the actual vehicles crossing a bridge are generally much lighter so bridges are often safer than the code-loading model would suggest. Permit vehicles need to be separated from standard non-permit vehicles. Permit vehicles are better controlled so lower factors of safety can be justified. RDS can identify the vehicles likely to have a permit from the axle configuration which is available in Weigh-in-Motion data.
For short-span bridges [provide hyperlink to 220.127.116.11], safety is governed by extreme examples of individual heavy vehicles.
For long-span bridges [provide hyperlink to 18.104.22.168], safety is governed by extreme combinations of moderately heavy vehicles, i.e., by traffic congestion events.
Short-Span Bridge Traffic Loading
The weights and dimensions of permit vehicles are specified by the permit issuing authority and may not be factored when assessing a bridge. Non-permit vehicles are much more challenging and require a statistical analysis for accurate evaluation. For short-span bridges, the critical non-permit loading event generally involves very few vehicles. It may consist of just one or two vehicles, either meeting or overtaking one another on the bridge. The governing case depends on the transverse stiffness of the bridge (which determines the extent to which load is shared between the girders).
In short-span bridges, the critical case is for free-flowing traffic where bridge dynamics [provide hyperlink to 3.2.4] applies. The characteristic maximum vehicle weight can be found for a specified return period from a statistical analysis of vehicle weights. However, it is more common to use an influence line to calculate the load effects (bending moments or shear forces) due to each passing vehicle and hence to find the characteristic maximum load effect. A commonly assumed return period for bridge assessment is 75 years. A database of Weigh-in-Motion (WIM) data can be used to identify vehicles at the site and calculate the corresponding load effects on the bridge. This can be done directly using the WIM data but there is rarely enough data and a modelling process known as Monte Carlo simulation is usually required.
Long-Span Bridge Traffic Loading
For longer spans, congested traffic conditions govern where many vehicles are closely spaced on the bridge and no significant dynamics applies. Most Weigh-in-Motion [provide hyperlink to 3.3] (WIM) technologies only operate in free flowing traffic conditions so information on both weights and inter-vehicle gaps are not available for congested conditions. A conservative solution is to ‘collapse’ the free-flowing WIM data by reducing inter-vehicle (back-axle to front-axle of following vehicle) gaps to a minimum. For example, in the derivation of the Eurocode, a minimum axle-to-axle gap of 5m was assumed.
In such calculations, cars make a big difference. To be accurate, cars should be present in these loading events as they create significant lightly-loaded gaps between trucks. However, it is also important to account for the possibility of occasional convoying, i.e., the occurrence of long lines of truck-only vehicles for some reason. Such an event could happen, for example, during a truckers’ protest or due to a truck-specific toll booth nearby.
Load Monitoring on Forth Road Bridge, Scotland, just prior to its closure to general traffic
Bridge Health Monitoring
When there are safety concerns with bridges, they can be kept in service by installing a monitoring system to keep track of accelerations, rotations, strains, etc. – indicators of its condition. Structural Health Monitoring is challenging as not all sensors will respond to particular types of damage. RDS staff have worked extensively in bridge health monitoring and can design a monitoring installation to suit a particular issue of concern.
Oranmore Railway bridge in Ireland and site-measured mode shape envelopes, before and after its rehabilitation.
Bridge Dynamics and Vehicle/Bridge Dynamic Interaction
Some bridges have particular problems with dynamics, in which case particular investigations may be necessary. For others, the Eurocode allowance for vehicle/bridge dynamic interaction tends to be conservative and evaluating it more accurately can sometimes be a way of demonstrating that the bridge is safe due to that conservatism.
RDS staff have access to a range of dynamic bridge and vehicle models and the skills to do probabilistic studies in order to incorporate dynamic issues into a study of bridge safety. They also have experience of direct measurement of dynamic amplification factors (see figure) which overcomes many of the shortcomings of numerical models.