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The New ous possible strategies for maintenance and repair affect the York City Department of Transportation is in charge of cost and performance of the system over some period of some bridges with spans having a deck area time? Their average age in values of uncertain and intangible factors?
And, above all, was 75 years. A quantitative model is needed to form the basis for a The average bridge condition over the last 10 years has formal optimization of the allocation of budget resources remained near the rating of 4. Bridge maintenance level assessment state of bridge management equilibrium was described and actual federally mandated inspections. The scales employed analyzed by Yanev a. The New York State Depart- costs, bridge managers must seek more effective funding ment of Transportation condition reports for bridges and allocation.
In Yanev b , the average annual rate, r, their components are available from onward and use of bridge deterioration is shown to be the dominant factor a numerical rating from 1 to 7 as previously stated State of determining the average bridge condition rating R. This rate New York, Cost-effective optimization must, therefore, consider permit evaluation of the direct link with deterioration rate, all these factors as well as replacement costs.
That can best nor will it support a probabilistic treatment in the model. Therefore, the approach here will be empirical and deter- In a stable bridge condition environment, it seems rea- ministic, although the potential remains to introduce prob- sonable that deterioration rates are directly related to bridge abilities into the model at a later stage.
Each span of rate of bridge deterioration r and, consequently, raise a bridge is discretized into as many as 60 components the overall bridge condition rating R of a large group to be inspected and rated.
Thirteen of those components of bridges, such as those in New York City. The present have been selected by New York State Table 1 to estab- model, developed as part of a project at Columbia Univer- lish the bridge rating.
The minimum rating from 1 to 7 sity for updating the New York City Bridge Main- assigned during inspection to one of these 13 components tenance Manual, aims to formulate the required relation- over all spans of a bridge is the value of the compo- ships in the manner outlined in Yanev and Testa nent rating, Ri , for the bridge. The rating of each one and to give a rapid spreadsheet solution to evaluate alter- of these 13 components contributes to the overall bridge natives.
Some sample results are presented for New York rating, R, through a weight wi that indicates the relative City bridges. Therefore, the weighting York City, if any, was minimal. This conjecture, however, is refuted capital funding.
Any change in the values of these weights can indicate possible bilinear deterioration histories, a constant easily be introduced in the present model. The values in The average condition ratings for bridges of all ages can Table 1 are estimated for each component. It is precisely be computed for any or all of the available 19 years on because of the suspected low reliability of such an assump- record for New York City bridges and the value of 4.
How rates of deterioration vary with maintenance can under which a bridge can safely operate. Although bridges be estimated in at least two extreme cases. Examples of with such ratings have not collapsed, they are load-posted cases approaching the condition in which all maintenance and receive emergency repairs. In Table 1, critical compo- is excluded have been presented in Yanev b , where nents are listed as failing at a rating Ric of 2 and all others all available condition rating records for a given component at a rating of 1.
Bridge maintenance level assessment frequencies under no funding constraints and the costs for detailing of the structure, etc. These include not only individual com- and on the discrete values that may apply. This nance management. Other levels of repair also occur, such as partial one, that indicate the effect of each of the 15 maintenance rehabilitation, which addresses only selected components activities i on the deterioration rate of each of the 13 com- at a cost of about one-third that of full rehabilitation and is ponents j.
These values are digested from the input of completed in 1 year. In addition, one should consider total experienced bridge engineers in charge of maintenance and bridge replacement at a cost that is problematic to estimate inspection in New York City.
Dual values of Iij are listed but could exceed four times the cost of rehabilitation. The or without open gratings. All of these values can be selected means of evaluating their effect at any assumed level should by the operator. In the model, these component repairs be built into the model. Costs incurred by the vehicle oper- are grouped at 5 year intervals, critical components being ators due to time lost and by the jurisdiction due to lost repaired at the 5 year mark preceding the time at which business should be, and are, listed separately.
The expected life, L, will not be a The overall bridge condition rating R and deterioration rate linear function of M. Data on the expected life spans for compo- mining annualized cost is simply a matter of adding those nents in Table 1 indicate the most rapid deterioration rate costs that are already expressed per annum to other total rio no maintenance and slowest rate ri1 full maintenance present day values after dividing by the expected life.
This if one assumes that the deterioration occurs uniformly in approach applies as long as the budget for all bridge activi- time. Such would be the life- tenance, and having an estimate of the importance of each time costs of component repairs and eventual major rehabil- maintenance task on each component Iij , one may deter- itation as well as total user costs modeled here as follows.
Because the deterioration rate is repair events during the lifetime, and the other with the dis- likely to increase monotonically with decreasing level of ruptions that result from operating a bridge while it has a maintenance, a linear rule may be assumed for the present low rating.
For the former, there is a certain discrete cost work. It may be expected This rate of deterioration together with a repair protocol that such costs will increase as deterioration progresses will determine the life of a bridge that can be associated and, therefore, a three tiered schedule is applied for each with the maintenance schedule prescribed by the values Mi.
Using the values given in the preceding tables, purposes. In addition, the bridge rating history over ment. This becomes all the more important when many its expected life is shown in Figure 2 for the cases of of those parameters have uncertain values.
From the parameters from New York City bridge experience, while results, one can see that the annualized cost decreases, other parameters, such as the user costs, are chosen simply albeit not smoothly, with increasing levels of maintenance, as illustrations.
Therefore, these results should be viewed and that as expected, the bridge life decreases and the cost as just that, illustrations, and not as values to be used in increases when repairs are omitted. A further observation actual application. Annualized cost.
In fact, the user costs is well suited. Lifetime bridge rating history. In other words, limited mainte- mended maintenance frequencies. The reduced budgets are nance budget resources should generally be allocated so as apportioned by cutting maintenance tasks selectively rather to maximize the overall maintenance level M, which takes than cutting uniformly all of the tasks. Intu- fraction as the budget expressed as a percentage of the bud- itively, this is what experienced bridge managers would do get for full recommended maintenance; only when all task without the aid of a quantitative model such as this.
It is frequencies are reduced uniformly will M and the budgeted also seen here, however, that there are differences in annu- percentage be the same. This model can help to select the optimal allocation. Indeed, one might consider considerably for the same budget but different allocations.
Moreover, it gate options systematically and eventually to apply statisti- does not adequately consider the uncertain, but very real, cal assessments and mathematical optimization techniques. By the tasks and components described in this model. Indeed, breaking down the subjective elements into smaller compo- these are subject to revision even in application to New nents, the subjectivity may become less dominant and can York bridges as better information becomes available.
It is eventually be minimized further with statistical analyses. In exploring reduced levels of ing degrees of neglect. To date, reality, the model for deterioration rate applies to new nationally recommended bridge life cycle cost analysis has bridges. Data for bridges with an uneven past history would fallen short of enthusiastic implementation, in part because be needed to determine how the rates are affected once a of this. Making the relationship explicit in this model is given maintenance and repair protocol are applied.
Other maintenance tasks an optimal allocation of budget resources. Optimization algorithms based on the model are cost greatly exceeds other costs, might be treated as a cap- being developed.
April Unless such a Inspection Manual. Bridge maintenance level assessment Yanev, B. April 26—28, Related Papers. Bridge management system with integrated life cycle cost optimization. By Hatem ElBehairy. By George Kwok.
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