Framework for a National Database System for Maintenance Actions on Highway Bridges (2010)

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73 Basic Computation The NBMD system in its NBMD viewer application com- putes costs of maintenance actions that improve conditions of bridge elements. These costs can be related to costs of Pontis actions. The NBMD implementation is valid for any condi- tion reporting system that yields element quantities in condi- tion states. The unit costs of actions that improve bridge elements are Allocated costs and improved quantities of elements are determined by analysis of NBMD production data and asso- ciated NBMD element-level inspection data. The process has three steps: 1. Identify a maintenance event and collect element-level condition data. 2. Identify elements that are the appropriate bridge compo- nent and that show improvement to conditions after the maintenance event. 3. Allocate maintenance costs to elements. Maintenance Events and Element Condition Data For each maintenance event, element-level inspections before and after the event are identified in an NBMD Inspection_ Cross_Reference_Table. Inspection IDs are obtained from the cross reference table and element quantities are collected into arrays. These are the element quantities for the single bridge (or culvert) in the maintenance event. Changes to element quanti- ties, Δqi, are computed for each condition state. Unit Allocated prove Costelement Costelement = Im dQuantityelement ( )Eq. 1 where Δqi Change in element quantity in condition state i qi,post Element quantity in condition state i after the main- tenance event qi,prior Element quantity in condition state i prior to the maintenance event Values Δqi are computed for every element of the bridge. Maintenance events that improve element conditions produce positive changes to element quantities in better condition states and negative changes to quantities in poorer condition states. Improvements will be observed for some but usually not all elements of the bridge. The total quantity (inventory) of each element is computed too, since maintenance events may alter element quantities or introduce new elements to bridges. Identifying Elements Elements are included in a cost computation if element com- ponent agrees with the component of maintenance actions and if elements show improvement. Element Component and Maintenance Component All bridge elements and some maintenance actions are asso- ciated with specific components of bridges. Elements are kept in the cost computation if their component matches the action component. Some components, such as Substructure, can admit several elements at the same bridge. One component, Bridge, admits all elements. Δq q qi i post i prior= −, , ( )Eq. 2 C H A P T E R 5 Element-Level Costs of Maintenance Actions

Element Improvement The quantity of element that is improved is computed as the sum of gains in element quantities in better condition states. The improved quantity is computed as Equation 3 computes improvement quantity as the sum of non-negative quantity changes in better condition states. The sum terminates before the first negative quantity changes. The transition in conditions is obtained as well. The best con- dition state with a negative quantity change is the prior condi- tion for the element, the worst condition state with a positive quantity change is the post condition of the element. An example for operation of Equation 3 is provided. Con- sider that a reinforced concrete abutment that has minor dete- rioration for 20% of its width and defects for 40% of its width. The condition report for this element is shown in Table 61. A repair action is performed on the worst defects at the abutment. The result is that sections that had been in condi- tion state 3 are improved to condition state 1. The condition report, after repair, is shown in Table 62. Differences in element quantities are computed using Equation 2. Results are shown in Table 63. Operation of Equation 3 yields an element improvement quantity equal to 40% of the element quantity. The summa- tion includes condition states 1 and 2, but not state 3 since its change is a loss (removal, actually) of element quantity due to the effects of repair action. Elements that show positive values of improved quantity are kept in the cost computation. Elements that do not show improvement are eliminated. Cost Allocation After obtaining the short list of elements that are the right bridge component and that show improvement, the Improved q qQuantityelement i i j i= ≥ = ∑Δ Δ 1 0while ( )Eq. 3 total cost of the maintenance event is allocated equally to all elements. Where ElementCount is the number of elements in the short list Now the unit costs for actions and elements are computed using Equation 1. Element_Unit_Cost_Table Element unit costs are reported in a table that is generated by the NBMD viewer application. The element unit cost table is a derived table. Its entries are collected or computed from other NBMD tables. Data fields in the unit costs table are listed in Chapter 2. The element unit cost table contains a record for each ele- ment in each maintenance event. Records list maintenance events, components and operations for maintenance actions, inspections before and after maintenance, element identifica- tions and units, allocated costs, inventory changes, improved quantities, and unit costs. List of Element Unit Costs Element-level costs are computed from data collected from the California DOT, Michigan DOT, Oregon DOT, and Ten- nessee DOT. Data from the Pennsylvania DOT do not have sufficient number of element-level inspections to evaluate improvement quantities for elements. The complete list of element-level unit costs of actions is presented in Appendix C. The list presents median unit costs by DOT in the order of element numbers. For each element, a matrix of costs is pre- sented that indicates the condition state before maintenance, the condition state after maintenance, the unit cost, and the maintenance operation. Comparison Element-level maintenance costs are compared for bare concrete deck in Figure 41. The operations include Main- Allocated Event Element Costelement TotalCost C = ount ( )Eq. 4 74 Condition State 1 2 3 4 Reinforced Concrete Abutment 40% 20% 40% 0% Condition State 1 2 3 4 Reinforced Concrete Abutment 80% 20% 0% 0% 1 2 3 4 Reinforced Concrete Abutment +40% 0% -40% 0% Δq Table 63. Condition differences for reinforced concrete abutment. Table 61. Condition report for reinforced concrete abutment. Table 62. Condition report for reinforced concrete abutment, after repair.

tenance (unspecified action), Coating, and Repair. All costs are per square meter of deck. Costs are similar for California, Oregon and Tennessee, but differ strongly for Michigan. Michigan costs are taken from maintenance contract data. Costs from the other three DOTs are crew costs. Estimates of Pontis costs for deck repairs are collected from Delaware and Louisiana and shown in Figure 42. Cost estimates from Delaware and Louisiana were collected in the 2009 domestic scan on bridge management decision- making (NCHRP Project 20-68A, Scan 07-05). The com- puted costs for California, Oregon, and Tennessee are in the same range of values as the estimated costs for Delaware and Louisiana. Other comparisons may be made among DOTs for unit costs for maintenance of similar bridge elements. Some gen- eral trends are apparent. Costs for replacement are often higher than costs of repairs. Costs for repairs increase for ele- ments in poorer condition states. However, unit costs vary considerably among DOTs and among condition states. 75 California 12 Concrete Deck - Bare / square meter Condition After 1 2 3 Condition Before 1 2 $ 0.30 Maint $ 106 Coat $ 1.70 Repair 3 $ 1.20 Repair 4 $ 0.82 Repair 5 Michigan 12 Concrete Deck- Black Bars /square meter Condition After 1 2 3 Condition Before 1 2 $ 11.41 Coat $ 12.81 Repair 3 $ 8.51 Coat $ 19.15 Repair $ 6.94 Repair 4 $ 18.85 Repair $ 52.15 Repair 5 $ 67.08 Repair Oregon 12 Concrete Deck - Bare / square meter Condition After 1 2 3 Condition Before 1 2 $ 0.07 Maint 3 $ 0.14 Repair 4 $ 0.02 Maint 5 Tennessee 12 Concrete Deck - Bare / square meter Condition After 1 2 3 Condition Before 1 2 3 $ 0.32 Repair 4 5 Figure 41. Element-level costs for concrete deck. Condition State % of Deck Delaware Cost / square meter Louisiana Cost / square meter 2 1 $ 2.01 $ 0.90 3 6 $12.08 $ 5.40 4 17 $ 34.23 $ 15.31 5 25 $ 50.34 - Figure 42. Estimated costs of Pontis actions.