Linear Programming Approach for Upgrading Bridge Infrastructure Networks
Authors: Muhunthan Bala 
Published: October 2011

<p>Bridges are important links in the road network. Over the years, bridges have been designed to various standards as they were built in different periods. As funds availability is tightened, road authorities around the world are facing challenges related to the implementation of optimal bridge management programs based on lifecycle cost, remaining life and bridge capacity considerations.</p>
<p>The road network in any country originated with roads connecting the capital city with regional centres. Next, the rural towns were connected with villages and regional centres. The road network grew as the population grew and settled in various parts of the country. In the past bridges were considered to be permanent ever since they were built and minimum maintenance was carried out. Now there is more awareness of the need for bridge maintenance and rehabilitation. Road authorities realise the need to allocate sufficient funds for this purpose.</p>
<p>Bridges are relatively more expensive to construct than road pavement, and are therefore designed for a longer service life. Failure of a bridge has more severe consequences than a road failure – none more spectacularly illustrated than by the loss of three spans of the Tasman Bridge in Hobart because of ship collision in 1975 (Bureau of Transport Communications Economics (BTCE), 1997).</p>
<p>As the road network grew over the years, different bridge design standards were used at different times of the development of the road network. Therefore the current road network in Australia consists of bridges of different standards, i.e. bridges with different load capacities and geometric configurations. Bridge Infrastructure Network is a collection of bridges in a region connected by a network of roads. These roads are identified by route numbers, and the load-carrying capacities of these routes are controlled by the individual structural capacities of the bridges.</p>
<p>The range of age and strength in Australia‟s bridge infrastructure network reflects the longer service life and the increase in mass and number of heavy vehicles. For example, bridges presently in service on national highways were designed and constructed more than 50 years ago for loads half the size of those applied by contemporary heavy vehicles (BTCE, 1997). It is the strength of these older bridges reaching the maximum use of their capacities, owing to increased mass of newly introduced heavy vehicles that limits the potential productivity enhancements associated with these increases.</p>
<p>Vehicle technology has also developed over the years. So has the demand for transportation of goods by road. Settlement of population also has been widely spread across the country. Therefore the road network has to be upgraded to meet current and future demands. This has not been the case in the past owing to lack of resources (Bureau of Transport Economics, 1984). Bridges were built when they were due for replacement or when a new route was added to the existing network.</p>
<p>If a new operational load or a new legal load is to be introduced, or if the bridges in the network are to be upgraded to a most recent load standard using available funds, a clear strategy is not available for implementation. The aim is to propose a strategy to achieve a level of preparedness by the road authorities to upgrade the bridges of the network in a systematic and affordable manner.</p>
<p>It is a common practice in the construction industry to develop design standards to accommodate future requirements. The design standards are regularly revised or completely replaced by new ones owing to research and development into new materials and technology. The situation is the same with bridges; bridges have been designed in the past to various different design standards as they became effective and these design standards were revised as the transport industry demand grew. It has not been possible to upgrade all of the bridges to the newly introduced design standard owing to obvious economic reasons.</p>
<p>There is considerable pressure from the transport industry to make the road authorities allow heavier loads on the roads. The heavy vehicle technology has developed to a level where large and long heavy vehicles can manoeuvre without any difficulties. But many of the existing bridge structures do not have adequate load capacity to carry these loads.</p>
<p>The paper contributes to the challenge of sustainable infrastructure by reducing the cost of transport by making efficient use of existing bridge infrastructure especially the structural capacity of existing bridges fulfilling the present societal needs while reducing impacts on future generations.</p>
<p>The paper explores the different design standards that have been used to design bridges in Australia, and the different operational loads that are currently in use on Australian roads. The service levels that can be applied to sub-networks in terms of operational loads are determined and a methodology developed using a hypothetical network to identify bridges that require upgrading in a sub-network. Appropriate decision-making tools in route upgrading are identified and their application demonstrated with particular emphasis on the use of Linear Programming.</p>
<p>A spreadsheet was in MS-Excel activating Solver using a method called “Simplex” method on a hypothetical route. The model demonstrates a relationship between the traffic volume and the cost of upgrading. Here the cost of upgrading, Annual Average Daily Traffic, desired maximum traffic volume and the load capacity in terms of a service level are input. Solver distributes the traffic volume according to the set load capacity on all three routes on the hypothetical network and the transport cost per unit is calculated and a sensitivity analysis is performed.</p>