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Literature review indicates that most studies on pavement management have been on reconstruction and rehabilitation, but not on maintenance; this includes routine, corrective and preventive maintenance. This study developed linear regression models to estimate the total maintenance cost and component costs for labor, materials, equipment, and stockpile. The data used in the model development were extracted from the pavement and maintenance management systems of the Nevada Department of Transportation (NDOT). The life cycle maintenance strategies adopted by NDOT for five maintenance prioritization categories were used as the basis for developing the regression models of this study. These regression models are specified for each stage of life-cycle maintenance strategies. The models indicate that age, traffic flow, elevation, type of maintenance, maintenance schedule, life cycle stage, and the districts where maintenances are performed all are important factors that influence the magnitude of the costs. Because these models have embedded the road conditions into the life-cycle stage and type of maintenance performed, they can be easily integrated into existing pavement management systems for implementation.

Over the past decade or so, the population in Nevada has increased dramatically, especially within and near the urban areas. This increase has resulted in the need to expand Nevada’s transportation system, particularly roadways. This expansion includes the construction of some new roadways; however, the greatest need involves improving nearly all existing major roadways. These improvements typically include additional lanes, turning lanes, sound walls, shoulder widening, upgrading older cross-section standards, adding guardrail, and more landscaping. New and improved existing roadways have to be maintained, which adds to the demand for maintenance manpower, equipment, and materials.

Estimating the demand on the maintenance resources is needed when the maintenance districts of the Nevada Department of Transportation (NDOT) submit their maintenance requests to headquarters. In turn, headquarters integrates the submissions and sends a request to state legislators for approval. Currently, NDOT’s Maintenance Division is responsible for the following maintenance activities:

1) Flexible Pavement,

2) Rigid Pavement,

3) Miscellaneous Concrete,

4) Roadside Infrastructure,

5) Roadside Cleanup,

6) Roadside Facilities,

7) Roadside Appurtenances,

8) Traffic Services,

9) Snow and Ice Control,

10) Bridge, and

11) Stockpile Production.

Ideally, the funding decision depends on the additional number of positions needed and the funding increase for equipment and materials for all these maintenance activities over the life cycle of the highway system expansion. That decision could fully or partially meet the estimated demand for maintenance resources over the life cycles.

The objective of this research is to develop maintenance cost estimation models. These models estimate the total expected short-term and long-term maintenance burden required for NDOT. Short-term and long-term maintenance schedules for NDOT are shown in

In this study, linear regression models were developed for each individual stage of the life cycles in all these categories. These models estimated not only the annual maintenance costs, but also estimated the component costs for manpower, materials, equipment, and stockpile. With this objective in mind, this study included a literature review on estimating maintenance cost. Data also were collected on maintenance cost and road characteristics. These data were used to develop linear regression models.

This paper consists of seven sections. The first section provides an introduction on

the background and objective of the study. In the second section, a literature review is presented. The third section proposes a methodology on developing linear regression models. Section 4 describes the data collection process. In Section 5, the development of linear regression models for estimating annual maintenance costs is presented; this is followed by the last section, which summarizes the model development and identifies needs for future study.

According to [

1) The pavement management system (PMS) direct approach,

2) The simple roughness approach,

3) The econometric approach,

4) The cost allocation approach, and

5) The perpetual overlay indirect approach.

Among these five approaches, the most relevant ones to this study are the PMS approach and the econometric approach. A PMS usually consists of a database that records the history of MR&R work on a roadway system and a pavement performance model that can estimate the roadway surface condition, given the MR&R history and future maintenance policies and traffic usage of that roadway segment. Optimal procedures usually are applied to search for the optimal MR&R schedule. As a product of the optimal procedure, maintenance costs can also be derived.

The econometric approach classified in [

In the 1990s, NDOT studied on various methods to estimate maintenance costs [

1) Correlating annual maintenance costs to the present serviceability index (PSI) level,

2) Correlating annual maintenance costs to the probability of their occurrence,

3) Establishing an overall annual maintenance cost for each treatment, and

4) Establishing a fixed-period, cumulative, annual maintenance cost for each treatment.

The first technique correlates annual maintenance costs to pavement performance, represented as the PSI level. This technique was proposed based on the understanding that the costs of maintenance vary with the nature of maintenance activities that are triggered by the pavement conditions. Recognizing the fact that there is a time element involved in pavement performance―for example, not every maintenance activity occur every year―the maintenance costs fluctuate significantly between years. Therefore, the second method correlates the annual maintenance costs to the probability of the occurrence of maintenance activities. The third technique calculates the annual maintenance costs by considering the life of pavement after a certain treatment. The annual maintenance costs are the average of the total maintenance costs over the year before next maintenance treatment. By the fourth technique, the annual maintenance costs consider the time since the last pavement treatment.

In NDOT’s study ( [

In this study, regression models were developed for different maintenance costs, maintenance prioritization categories for various highway routes, and different life-cycle stages. The maintenance costs were broken down into manpower, materials, equipment, and stockpile costs.

In NDOT, the highway routes are classified into five maintenance prioritization categories, each with different maintenance strategies over their life cycles (see

There is no clear maintenance treatment pattern that has been adopted for Category 5. In this study, three life cycle stages are proposed for Category 5 routes: Beginning Stage (1^{st} Stage), Middle Stage (2^{nd} Stage), and Last Stage (3^{rd} Stage), where the middle stage can be employed repeatedly.

Linear regression models were developed for each life cycle stage of these five different maintenance prioritization categories. The models can be written as:

The dependent variables Y_{i} are the maintenance costs for total maintenance cost and for man power, materials, equipment, and stockpile, separately. The X_{i} indicates the independent variables, which include age after the start of a life cycle stage, the pavement surface type, total traffic volume, truck flow volume, urban/rural area, and the elevation of a road segment.

The goal of data collection was to extract maintenance cost data, road section characteristics, and traffic flow data. The first step was to develop an inventory of roads maintained by NDOT that could be used as a population for sampling. In the second step, time-space diagrams were developed for the selected roads, in which the history of maintenance activities on each selected road could be presented. The third step utilized the time-space diagrams to identify the road sections that showed uniform maintenance treatments. The fourth step involved extracting maintenance cost data for selected road sections. In the last step, data on road characteristics were collected for the identified road sections.

NDOT uses a pavement management system database that contains a data item for each maintenance prioritization category. This data item is used to extract the road inventory data for every road of each county in Nevada. Note that one road could be divided into multiple sections, each with a different maintenance prioritization. Maintenance time-space diagrams present the maintenance tasks historically performed on a road. As shown in

The mile-by-mile traffic flow data available in the PMS database varies over a given road section. Thus, averaging has to be performed for the mile-by-mile traffic flow data. When the length of road section is great, the mile-by-mile midpoint elevations on the road section may vary; in that case, the average of these mile-by-mile midpoint evaluation data needs to be derived. Usually, however, road characteristics data for the most recent years have the complete mile-by-mile midpoint elevation data. Other road characteristics data―such as number of lane, type of road surface, and urban/rural―do not vary over the length of a road section; therefore, they can be collected by various methods. Maintenance cost data were extracted from the NDOT MMS database. To facilitate the data extraction, a Microsoft spreadsheet program was developed.

Linear regression models were developed for total maintenance cost and the component costs for labor, equipment, materials, and stockpiles. The results of these models are listed in

When the total maintenance cost was analyzed, it was shown that the maintenance cost in the year when a reconstruction happened was significantly less than previous years. This observation can be validated from the model for labor costs, which implies that those maintenance activities involving expensive equipment and materials were not performed in a year during which major construction was scheduled.

Category 1 | Category 2 | ||||||
---|---|---|---|---|---|---|---|

Total Cost | Total Cost | ||||||

Dependent Variable: | lntot | Dependent Variable: | lntot | ||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic |

one | 8.20468 | 0.54838 | 14.96167 | one | 5.46705 | 0.44544 | 12.27327 |

age | 6.28091e−002 | 1.25052e−002 | 5.02264 | lyear | −0.53229 | 0.21494 | −2.47648 |

lyear | −0.34813 | 0.20126 | −1.72979 | elev | 4.81895e−004 | 9.19892e−005 | 5.23861 |

ac | 0.95257 | 0.21990 | 4.33179 | aadt | 3.76878e−005 | 1.08794e−005 | 3.46415 |

elev | −9.52315e−004 | 1.69739e−004 | −5.61045 | ||||

aadt | 2.81009e−005 | 3.89760e−006 | 7.20981 | ||||

Number of Observations | 201 | Number of Observations | 93 | ||||

Corrected R-squared | 0.46536 | Corrected R-squared | 0.23575 | ||||

Mean of Dependent Variable | 7.88086 | Mean of Dependent Variable | 7.76939 | ||||

Labor Cost | Labor Cost | ||||||

Dependent Variable: | lnlabor | Dependent Variable: | lnlabor | ||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic |

one | 7.65243 | 0.51194 | 14.94798 | one | 4.96110 | 0.38960 | 12.73369 |

age | 5.84997e−002 | 1.16742e−002 | 5.01104 | elev | 3.95786e−004 | 8.00296e−005 | 4.94550 |

lyear | −0.33534 | 0.18788 | −1.78483 | urban | −0.32518 | 0.13213 | −2.46100 |

ac | 0.91071 | 0.20529 | 4.43621 | aadt | 4.40071e−005 | 9.81890e−006 | 4.48188 |

elev | −9.38479e−004 | 1.58459e−004 | −5.92252 | ||||

aadt | 2.58324e−005 | 3.63858e−006 | 7.09957 | ||||

Number of Observations | 201 | Number of Observations | 93 | ||||

Corrected R-squared | 0.46627 | Corrected R-squared | 0.25454 | ||||

Mean of Dependent Variable | 7.23326 | Mean of Dependent Variable | 6.93872 | ||||

Category 1 | Category 2 | ||||||

Materials Cost | Materials Cost | ||||||

Dependent Variable: | lnma | Dependent Variable: | lnma | ||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic |

one | 5.87373 | 0.75837 | 7.74515 | one | 2.52197 | 0.74212 | 3.39834 |

age | 7.38305e−002 | 1.68890e−002 | 4.37151 | lyear | −1.31390 | 0.35809 | −3.66918 |

ac | 1.02915 | 0.30212 | 3.40644 | elev | 8.60610e−004 | 1.53256e−004 | 5.61550 |
---|---|---|---|---|---|---|---|

elev | −8.36852e−004 | 2.36656e−004 | −3.53615 | aadt | 4.80663e−005 | 1.81253e−005 | 2.65190 |

aadt | 3.46083e−005 | 5.37191e−006 | 6.44246 | ||||

Number of Observations | 200 | Number of Observations | 93 | ||||

Corrected R-squared | 0.37965 | Corrected R-squared | 0.28931 | ||||

Mean of Dependent Variable | 6.20744 | Mean of Dependent Variable | 6.36397 | ||||

Equipment Cost | Equipment Cost | ||||||

Dependent Variable: | lneq | Dependent Variable: | lneq | ||||

Indept Variable | Estimated Coefficient | Standard Error | t-Statistic | Indept Variable | Estimated Coefficient | Standard Error | t-Statistic |

one | 7.03420 | 0.59595 | 11.80334 | one | 4.25812 | 0.47823 | 8.90389 |

age | 6.51333e−002 | 1.33239e−002 | 4.88845 | lyear | −0.86702 | 0.23076 | −3.75726 |

ac | 0.92762 | 0.23842 | 3.89062 | elev | 4.30691e−004 | 9.87603e−005 | 4.36097 |

elev | −1.07228e−003 | 1.84905e−004 | −5.79908 | aadt | 3.55617e−005 | 1.16802e−005 | 3.04463 |

aadt | 2.61492e−005 | 4.23932e−006 | 6.16825 | ||||

Number of Observations | 201 | Number of Observations | 93 | ||||

Corrected R-squared | 0.43240 | Corrected R-squared | 0.22537 | ||||

Mean of Dependent Variable | 6.41503 | Mean of Dependent Variable | 6.29168 |

shows that the total cost each year did not change with time. It presents significant less cost than the previous year, when the road was under reconstruction. This observation is similar to that for the roads in Category 1. It implies that some maintenance work may not need to be performed when a road is scheduled for reconstruction. The coefficient for “elevation” is positive, which indicates that the roads at high elevation tend to cost more for maintenance, probably due to work in extreme weather conditions, such as snow, for which additional work (snow removal) has to be done.

The samples collected for Category 2 were from areas across the state, unlike the case for Category 1, in which samples were taken from Clark County only. The coefficient for traffic “AADT” is positive, which is consistent with the expectation that more traffic accelerates the deterioration of roads, and thus produces more conditions for maintenance. Similar patterns regarding the impact of influencing factors on total maintenance cost also can be found in the models for the component maintenance costs, except for stockpile cost.

Three sets of linear regression models were developed, one set for each life cycle stage, as shown in

The results in

The coefficient for elevation is positive, which makes sense because roads at higher elevations may have more chance of extreme weather as well as other road features that require maintenance (e.g., a guard rail). These observations also can be found in other maintenance cost components, including labor cost, equipment cost, and materials cost.

The results for the life-cycle stage Flush Seal indicates that only the variable representing the maintenance work when Chip Seal is performed is significant. This observation is consistent with practice, delaying maintenance work to be done when such a major preventive maintenance as Chip Seal is performed. This result also can be found in other maintenance cost components.

Based on the results for these three life cycle stages, it can be seen that the maintenance costs in the years when construction, flush seal, and chip are performed significantly vary from those of other years. They cost more or less than the regular year, depending upon the nature of the maintenance work. Elevation is an important influencing factor to the maintenance costs. Traffic is another factor that plays a significant role. Age, however, does not show a significant impact on the maintenance cost.

For Category 4, four linear regression models were developed, one for each life-cycle stage as shown in

The results on estimating total maintenance cost for the first life-cycle stage indicates that the coefficient for the “maintenance activities performed in the last year” is positive, which implies that more expenditure was incurred in the last year for flush seal, because a major preventive maintenance was preformed. Another significant variable is

Reconstruction | Total Cost | Labor Cost | ||||||
---|---|---|---|---|---|---|---|---|

Dependent Variable: | lntot | Dependent Variable: | lnlabor | |||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | |

one | 5.22175 | 0.60923 | 8.57101 | one | 6.22976 | 9.86522e−002 | 63.14873 | |

lyear | 0.76511 | 0.24410 | 3.13439 | |||||

elev | 2.61157e−004 | 1.27936e−004 | 2.04131 | |||||

Number of Observations | 88 | Number of Observations | 198 | |||||

Corrected R-squared | 0.12134 | Corrected R-squared | 0.00000e+000 | |||||

Durbin-Watson Statistic | 0.85384 | |||||||

Mean of Dependent Variable | 6.62413 | Mean of Dependent Variable | 6.22976 | |||||

Flush Seal | Total Cost | Labor Cost | ||||||

Dependent Variable: | lntot | Dependent Variable: | lnlabor | |||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | |

one | 7.23358 | 8.94882e−002 | 80.83270 | one | 6.36667 | 7.74854e−002 | 82.16616 | |

lyear | 1.35252 | 0.17832 | 7.58490 | lyear | 0.97188 | 0.15440 | 6.29458 | |

Number of Observations | 135 | Number of Observations | 135 | |||||

Corrected R-squared | 0.29670 | Corrected R-squared | 0.22374 | |||||

Mean of Dependent Variable | 7.57421 | Mean of Dependent Variable | 6.61145 | |||||

Chip Seal | Total Cost | Labor Cost | ||||||

Dependent Variable: | lntot | Dependent Variable: | lnlabor | |||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | |

one | 5.95503 | 0.46492 | 12.80873 | one | 5.37183 | 0.44704 | 12.01641 | |

lyear | 0.52712 | −0.18476 | −2.85306 | lyear | −0.48416 | 0.17765 | −2.72532 | |

elev | 2.29486e−004 | 8.29841e−005 | 2.76542 | elev | 1.51135e−004 | 7.97929e−005 | 1.89409 | |

aadt | 5.97617e−004 | 1.41487e−004 | 4.22384 | aadt | 6.34517e−004 | 1.36046e−004 | 4.66399 | |

Number of Observations | 87 | Number of Observations | 87 | |||||

Corrected R-squared | 0.19072 | Corrected R-squared | 0.21000 | |||||

Mean of Dependent Variable | 7.40151 | Mean of Dependent Variable | 6.47436 |

Reconstruction | Material Cost | Equipment Cost | ||||||
---|---|---|---|---|---|---|---|---|

Dependent Variable: | lnma | Dependent Variable: | lneq | |||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | |

one | 2.76351 | 0.80326 | 3.44035 | one | 3.23098 | 0.68499 | 4.71685 | |

lyear | 1.36009 | 0.32184 | 4.22592 | elev | 3.99350e−004 | 1.44481e−004 | 2.76404 | |

elev | 4.61092e−004 | 1.68682e−004 | 2.73351 | |||||

Number of Observations | 88 | Number of Observations | 88 | |||||

Corrected R-squared | 0.21176 | Corrected R-squared | 7.09088e−002 | |||||

Mean of Dependent Variable | 5.24172 | Mean of Dependent Variable | 5.09624 | |||||

Flush Seal | Material Cost | Equipment Cost | ||||||

Dependent Variable: | lnma | Dependent Variable: | lneq | |||||

Indept Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | |

one | 5.46978 | 0.17230 | 31.74660 | one | 6.13286 | 0.19015 | 32.25351 | |

lyear | 1.81760 | 0.34332 | 5.29418 | age | −0.13997 | 7.10209e−002 | −1.97088 | |

lyear | 1.07427 | 0.23502 | 4.57098 | |||||

Number of Observations | 135 | Number of Observations | 135 | |||||

Corrected R-squared | 0.16785 | Corrected R-squared | 0.12471 | |||||

Mean of Dependent Variable | 5.92755 | Mean of Dependent Variable | 6.02601 | |||||

Chip Seal | Material Cost | Equipment Cost | ||||||

Dependent Variable: | lnma | Dependent Variable: | lneq | |||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | |

one | 4.13053 | 0.70597 | 5.85082 | one | 4.00296 | 0.52272 | 7.65788 | |

age | 0.11679 | 6.19514e−002 | 1.88524 | lyear | −0.63538 | 0.20773 | −3.05871 | |

lyear | −0.87590 | 0.27677 | −3.16474 | elev | 3.50827e−004 | 9.33017e−005 | 3.76014 | |

elev | 2.70935e−004 | 1.18212e−004 | 2.29195 | aadt | 5.96674e−004 | 1.59078e−004 | 3.75083 | |

aadt | 6.77556e−004 | 1.99749e−004 | 3.39203 | |||||

Number of Observations | 87 | Number of Observations | 87 | |||||

Corrected R-squared | 0.15002 | Corrected R-squared | 0.20177 | |||||

Mean of Dependent Variable | 6.11288 | Mean of Dependent Variable | 6.01471 |

Reconstruction | Flush Seal | ||||||
---|---|---|---|---|---|---|---|

Total Cost | Total Cost | ||||||

Dependent Variable: | lntot | Dependent Variable: | lntot | ||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic |

one | 6.84434 | 0.13647 | 50.15368 | one | 5.19255 | 0.79175 | 6.55835 |

lyear | 0.79590 | 0.16331 | 4.87348 | age | −0.20196 | 6.26297e−002 | −3.22469 |

aadt | 6.28703e−004 | 2.73911e−004 | 2.29528 | lyear | 2.09167 | 0.20415 | 10.24556 |

dist1 | 0.37462 | 0.21830 | 1.71610 | ||||

dist2 | 0.84941 | 0.19924 | 4.26331 | ||||

elev | 3.97635e−004 | 1.30377e−004 | 3.04989 | ||||

aadt | 5.71083e−004 | 3.41515e−004 | 1.67221 | ||||

truck | 6.07142e−003 | −3.59775e−003 | −1.68756 | ||||

Number of Observations | 97 | Number of Observations | 78 | ||||

Corrected R-squared | 0.24126 | Corrected R-squared | 0.67316 | ||||

Mean of Dependent Variable | 7.29449 | Mean of Dependent Variable | 7.68789 | ||||

Labor Cost | Labor Cost | ||||||

Dependent Variable: | lnlabor | Dependent Variable: | lnlabor | ||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic |

one | 5.13562 | 0.33914 | 15.14314 | one | 2.38281 | 0.54250 | 4.39225 |

lyear | 0.60321 | 0.16132 | 3.73924 | lyear | 1.25990 | 0.16808 | 7.49565 |

elev | 1.84367e−004 | 6.63267e−005 | 2.77967 | dist2 | 1.07410 | 0.16622 | 6.46196 |

aadt | 5.36600e−004 | 2.70457e−004 | 1.98405 | elev | 6.78541e−004 | 9.43481e−005 | 7.19188 |

Number of Observations | 97 | Number of Observations | 78 | ||||

Corrected R-squared | 0.21081 | Corrected R-squared | 0.59666 | ||||

Mean of Dependent Variable | 6.37113 | Mean of Dependent Variable | 6.72726 | ||||

Reconstruction | Flush Seal | ||||||

Material Cost | Material Cost | ||||||

Dependent Variable: | lnma | Dependent Variable: | lnma | ||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic |

one | 5.59434 | 0.14065 | 39.77414 | one | 6.16959 | 0.28903 | 21.34551 |

lyear | 1.20364 | 0.15429 | 7.80099 | age | −0.29715 | 0.10351 | −2.87087 |

dist1 | −0.49562 | 0.16484 | −3.00669 | lyear | 3.07651 | 0.34700 | 8.86597 |

aadt | 7.02351e−004 | 2.64015e−004 | 2.66027 | dist2 | 0.60091 | 0.25766 | 2.33222 |

Number of Observations | 96 | Number of Observations | 78 | ||||

Corrected R-squared | 0.47495 | Corrected R-squared | 0.51891 | ||||

Mean of Dependent Variable | 6.07392 | Mean of Dependent Variable | 6.34646 |

Equipment | Equipment | ||||||
---|---|---|---|---|---|---|---|

Dependent Variable: | lneq | Dependent Variable: | lneq | ||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic |

one | 5.76825 | 0.10346 | 55.75149 | one | 2.14434 | 0.76851 | 2.79024 |

lyear | 0.51890 | 0.21725 | 2.38850 | age | −0.25160 | 7.70902e−002 | −3.26374 |

lyear | 1.53446 | 0.25827 | 5.94137 | ||||

dist1 | 0.70683 | 0.28343 | 2.49387 | ||||

dist2 | 1.20197 | 0.22563 | 5.32727 | ||||

elev | 6.91082e−004 | 1.40269e−004 | 4.92683 | ||||

Number of Observations | 97 | Number of Observations | 78 | ||||

Corrected R-squared | 4.67198e−002 | Corrected R-squared | 0.52516 | ||||

Mean of Dependent Variable | 5.88594 | Mean of Dependent Variable | 6.15327 | ||||

Chip Seal-1 | Chip Seal-2 | ||||||

Total Cost | Total Cost | ||||||

Dependent Variable: | lntot | Dependent Variable: | lntot | ||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic |

one | 6.91182 | 0.11215 | 61.63111 | one | 6.16464 | 0.61684 | 9.99388 |

lyear | 1.81242 | 0.19820 | 9.14448 | age | 7.30700e−002 | 4.75945e−002 | 1.53526 |

dist1 | 0.31118 | 0.15951 | 1.95086 | lyear | −0.51297 | 0.21971 | −2.33473 |

dist1 | −0.35433 | 0.19684 | −1.80010 | ||||

elev | 1.73129e−004 | 7.67915e−005 | 2.25453 | ||||

aadt | 1.51324e−003 | 7.35471e−004 | 2.05750 | ||||

truck | −1.29371e−002 | 6.05241e−003 | −2.13752 | ||||

Number of Observations | 110 | Number of Observations | 89 | ||||

Corrected R-squared | 0.44573 | Corrected R-squared | 0.24460 | ||||

Mean of Dependent Variable | 7.41292 | Mean of Dependent Variable | 7.01842 | ||||

Labor Cost | Labor Cost | ||||||

Dependent Variable: | lnlabor | Dependent Variable: | lnlabor | ||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic |

one | 5.64555 | 0.21227 | 26.59612 | one | 4.05502 | 0.47710 | 8.49922 |

lyear | 1.29042 | 0.17225 | 7.49169 | age | 0.12064 | 4.42940e−002 | 2.72354 |

dist1 | 0.74466 | 0.23196 | 3.21034 | lyear | −0.65300 | 0.20709 | −3.15322 |

dist2 | 0.63657 | 0.23240 | 2.73915 | elev | 2.91755e−004 | 6.84721e−005 | 4.26093 |

aadt | 1.77472e−003 | 6.58573e−004 | 2.69479 | ||||

Number of Observations | 110 | Number of Observations | 89 | ||||

Corrected R-squared | 0.36502 | Corrected R-squared | 0.24512 | ||||

Mean of Dependent Variable | 6.51891 | Mean of Dependent Variable | 6.24271 |

Chip Seal-1 | Chip Seal-2 | ||||||
---|---|---|---|---|---|---|---|

Material Cost | Material Cost | ||||||

Dependent Variable: | lnma | Dependent Variable: | lnma | ||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic |

one | 5.47692 | 0.13377 | 40.94294 | one | 5.70053 | 0.15453 | 36.88976 |

lyear | 2.49629 | 0.29912 | 8.34551 | dist1 | −0.79064 | 0.23831 | −3.31764 |

Number of Observations | 110 | Number of Observations | 88 | ||||

Corrected R-squared | 0.38643 | Corrected R-squared | 0.10315 | ||||

Mean of Dependent Variable | 5.97618 | Mean of Dependent Variable | 5.36810 | ||||

Equipment | Equipment | ||||||

Dependent Variable: | lneq | Dependent Variable: | lneq | ||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic |

one | 5.48704 | 0.13220 | 41.50479 | one | 3.50169 | 0.57218 | 6.11988 |

lyear | 1.33063 | 0.23364 | 5.69523 | age | 0.13717 | 5.31210e−002 | 2.58223 |

dist1 | 0.32468 | 0.18803 | 1.72669 | lyear | −0.76871 | 0.24836 | −3.09514 |

elev | 3.18557e−004 | 8.21175e−005 | 3.87929 | ||||

aadt | 1.34731e−003 | 7.89815e−004 | 1.70586 | ||||

Number of Observations | 110 | Number of Observations | 89 | ||||

Corrected R-squared | 0.24098 | Corrected R-squared | 0.21175 | ||||

Mean of Dependent Variable | 5.89780 | Mean of Dependent Variable | 5.71003 |

traffic flow, which is consistent with expectation. These findings also can be found in the models for the four cost components: labor, equipment, materials, and stockpile.

For the second life-cycle stage starting after flush seal is performed, relatively more variables are identified as significant to the maintenance cost. It can be seen that the variable representing the last year is significant, which is reasonable. Traffic flow is also significant. Age is significant, but with a negative coefficient. If the life-cycle span is short and many maintenance activities are frequently reserved for the last year, it is possible that the maintenance cost appears to decline with year; this has been confirmed by respondents from some state DOT’s Maintenance Divisions as part of the survey conducted in this study.

Where maintenance was performed is important. The results indicate that the maintenance―highly likely, chip seal―in Districts 1 and 2 in NDOT were more expensive than those in District 3 in NDOT; maintenance done in District 2 was more expensive than in District 1. Probably this is due to the fact that maintenance in District 2 was more complicated, involving more sophisticated technologies than in other districts. Another significant variable is elevation, the higher a road is located, the more expensive it is to maintain it; this is consistent with our expectations. These findings also can be found from the results for the four maintenance cost components.

The results for the third stage―starting from after a chip seal and ending at another chip seal―indicate that there are fewer significant variables. Whether or not a chip seal was performed in a year is important. The coefficient for the variable “last year”, which is the year with a chip seal was performed, is positive. This is reasonable. In this life- cycle stage, District 1 showed the most costly maintenance. This observation may be relevant regarding what type of equipment is used for the second chip seal in various districts; this is because the results for the four cost components indicate that the material costs between Districts 1 and 2 are the same, statistically.

The results for the last life cycle stage are very different from those for the first three segments. Age is significant. The total maintenance cost increased each year, which is understandable. The coefficient for the maintenance cost incurred in the last year is negative, which implies that the “last year” maintenance less expensive because other maintenance tasks were saved to be done during the reconstruction in this year. Among the three districts, District 1 has the least cost. This observation is relevant to maintenance practice, probably regarding the type of materials used in different districts. This result also can be found from the data for the four cost components. Traffic flow AADT is significant, which is consistent with expectations

There is no clear definition in NDOT on the life cycle for routes in maintenance prioritization Category 5. For simplicity, this study proposes three stages for the life cycle of a Category 5 route. The first stage starts after the completion of reconstruction, such as “2'' PBS with OG”, and ends at a flush seal or a chip seal. The second stage starts after a flush seal or a chip seal and ends at the completion of another flush seal or chip seal. The third stage starts after a flush or a chip seal, and ends at a construction. The second stage could be repeated many times; this is different from the life-cycle stages for Category 4, in which the middle stages are each performed one time only.

The results for the first life-cycle stage in

The results for the second life-cycle stage indicate that the last year maintenance and elevation of roads significantly influences maintenance costs. The impact of aging cannot be found in the result, probably due to the fact that the samples are a combination of life cycle stages that started or ended with flush seals or chip seals; these could be

1^{st} Life Cycle Stage | Total Cost | Labor Cost | ||||||
---|---|---|---|---|---|---|---|---|

Dependent Variable: | lntot | Dependent Variable: | lnlabor | |||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | |

one | 4.73205 | 0.47258 | 10.01314 | one | 4.32551 | 0.42914 | 10.07945 | |

age | 0.12385 | 4.50500e−002 | 2.74927 | lyear | 0.78063 | 0.15558 | 5.01760 | |

lyear | 0.87737 | 0.17353 | 05.05593 | elev | 3.48566e−004 | 8.71128e−005 | 4.00132 | |

elev | 3.91701e−004 | 9.00566e−005 | 4.34950 | |||||

Number of Observations | 159 | Number of Observations | 159 | |||||

Corrected R-squared | 0.30239 | Corrected R-squared | 0.20756 | |||||

Mean of Dependent Variable | 7.21153 | Mean of Dependent Variable | 6.21859 | |||||

2^{nd} Life Cycle Stage | Total Cost | Labor Cost | ||||||

Dependent Variable: | lntot | Dependent Variable: | lnlabor | |||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | |

one | 5.57972 | 0.24429 | 22.84037 | one | 4.64925 | 0.20747 | 22.40961 | |

lyear | 1.35616 | 0.10931 | 12.40674 | lyear | 0.91641 | 9.28310e−002 | 9.87185 | |

elev | 2.27820e−004 | 4.75289e−005 | 4.79329 | elev | 2.46666e−004 | 4.03643e−005 | 6.11100 | |

aadt | 3.03482e−003 | 7.75647e−004 | 3.91263 | aadt | 2.35182e−003 | 6.58724e−004 | 3.57026 | |

Number of Observations | 448 | Number of Observations | 448 | |||||

Corrected R-squared | 0.31453 | Corrected R-squared | 0.26197 | |||||

Mean of Dependent Variable | 7.38172 | Mean of Dependent Variable | 6.35050 | |||||

3^{rd} Life Cycle Stage | Total Cost | Labor Cost | ||||||

Dependent Variable: | lntot | Dependent Variable: | lnlabor | |||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | |

one | 7.31532 | 0.25695 | 28.47024 | one | 6.31538 | 0.25468 | 24.79744 | |

age | 0.11737 | 8.69821e−002 | 1.34939 | age | 0.19669 | 7.89160e−002 | 2.49238 | |

lyear | 0.59437 | 0.32084 | 1.85257 | |||||

Number of Observations | 94 | Number of Observations | 94 | |||||

Corrected R-squared | 6.75674e−002 | Corrected R-squared | 5.30684e−002 | |||||

Mean of Dependent Variable | 7.79547 | Mean of Dependent Variable | 6.86568 |

1^{st} Life Cycle Stage | Material Cost | Equipment Cost | ||||||
---|---|---|---|---|---|---|---|---|

Dependent Variable: | lnma | Dependent Variable: | lneq | |||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | |

one | 1.77701 | 0.86607 | 2.05181 | one | 2.45308 | 0.50058 | 4.90043 | |

age | 0.25317 | 8.25596e−002 | 3.06651 | lyear | 0.88297 | 0.18148 | 4.86544 | |

lyear | 1.22293 | 0.31802 | 3.84543 | elev | 6.22756e−004 | 1.01615e−004 | 6.12858 | |

elev | 5.75305e−004 | 1.65039e−004 | 3.48586 | |||||

Number of Observations | 159 | Number of Observations | 159 | |||||

Corrected R-squared | 0.23406 | Corrected R-squared | 0.28343 | |||||

Mean of Dependent Variable | 5.60475 | Mean of Dependent Variable | 5.70657 | |||||

2^{nd} Life Cycle Stage | Material Cost | Equipment Cost | ||||||

Dependent Variable: | lnma | Dependent Variable: | lneq | |||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | |

one | 4.52583 | 0.18490 | 24.47656 | one | 4.29400 | 0.29732 | 14.44254 | |

lyear | 2.38705 | 0.18875 | 12.64682 | age | 0.10612 | 3.07889e−002 | −−3.44663 | |

aadt | 5.12930e−003 | 1.33309e−003 | 3.84767 | lyear | 1.04501 | 0.13215 | 7.90795 | |

elev | 2.52489e−004 | 5.38903e−005 | 4.68523 | |||||

aadt | 2.04244e−003 | 8.90404e−004 | 2.29384 | |||||

Number of Observations | 446 | Number of Observations | 448 | |||||

Corrected R-squared | 0.28976 | Corrected R-squared | 0.18172 | |||||

Mean of Dependent Variable | 5.74258 | Mean of Dependent Variable | 5.70223 | |||||

3^{rd} Life Cycle Stage | Material Cost | Equipment Cost | ||||||

Dependent Variable: | lnma | Dependent Variable: | lneq | |||||

Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | Indep Variable | Estimated Coefficient | Standard Error | t-Statistic | |

one | 6.20010 | 0.14017 | 44.23313 | one | 6.31784 | 0.16710 | 37.80960 | |

lyear | 0.63605 | 0.27740 | 2.29287 | lyear | 0.78032 | 0.33069 | 2.35967 | |

Number of Observations | 94 | Number of Observations | 94 | |||||

Corrected R-squared | 4.37733e−002 | Corrected R-squared | 4.68188e−002 | |||||

Mean of Dependent Variable | 6.36249 | Mean of Dependent Variable | 6.51707 |

performed at different stages of road deterioration conditions. Traffic flow shows a positive impact. The results for the last life-cycle stage show that age and the last year maintenance (reconstruction) are significant factors. It is understandable that more maintenance is needed as roads age.

In the last year, when reconstructions were performed, some costs of these reconstructions were counted as maintenance equal to those for flush seals or chip seals. Thus, the last year maintenance becomes outstandingly expensive.

The annual maintenance cost profiles for these five categories of roads are presented in

For a road section in Category 4, the profile of the annual maintenance cost is calculated using the values of the coefficients in

It is clear that the annual maintenance costs for Categories 1 and 2 are higher than that for the other three categories. Major preventive or reconstruction activities significantly influence the maintenance cost, and have to be considered when calculating the annual maintenance costs.

In this study, linear regression models were developed to estimate annual maintenance costs for highway maintenance. Consistent with the maintenance road classification adopted by NDOT, five prioritization categories of roads were considered for model development. Categories 1 and 2 each included only one life-cycle stage, spanning eight and ten years, respectively. Categories 3 and 4 include three and four life-cycle stages, respectively; each stage is associated with certain maintenance activities and has three to four years duration. At NDOT, there was no specific definition on the life cycle for Category 5; therefore, three stages were defined in this study. For each stage of the life cycles in these five categories of roads, linear regression models were developed. In addition to total maintenance cost, this study also developed linear regression models for four maintenance cost components: labor, equipment, materials, and stockpile.

Important influencing factors on annual maintenance costs were considered in this study: age of road, the type of maintenance activities in the last year of maintenance life cycle, elevation, district, and traffic. The results indicate that road age is a significant factor for some life cycle stages and some maintenance cost components. During the time period of a life-cycle stage, the annual maintenance cost may be kept the same. The maintenance activities in NDOT may have been scheduled by considering whether they are close to the time when a preventive maintenance or reconstruction is to be performed.

As reflected in the maintenance cost profile, the annual maintenance cost may decline with time and then jump up to a high level, indicating costs for prevention maintenance or construction activities. Flush seal and chip seal are two preventive maintenances performed by NDOT work forces. The costs incurred in these preventive maintenance activities are significantly higher than other routine and corrective maintenance. Thus, they were singled out in the cost estimation of this study by using indicator variables. Roadways with high elevation tend to be constructed with special safety features, such as guard rails, which would produce high maintenance costs. This perception was validated from the results of the models. Traffic flow deteriorates roads and generates the need for maintenance. Its impact on maintenance cost is also reflected in the model estimation results. Different districts may adopt different maintenance practices in terms of the materials and equipment used in their districts; this was observed from the models developed in this study.

It can be seen that the developed models uniquely integrate the life-cycle concept of pavement by developing different models for different stages in the life cycles. These life-cycle stages also represent the conditions of a road section. The practice of maintenance activities adopted in NDOT was fully considered in developing these models. The variables used in the models can be easily made available, and can provide the basis for the models to be incorporated into NDOT’s pavement management and maintenance management systems for estimating future maintenance costs. NDOT could use these models to estimate the maintenance costs in order to submit cost requirements to the State of Nevada’s legislation.

Sampling is a major issue for developing the regression models for some categories of road like Categories 1 and 2. With samples covering more areas in Nevada, useful variables such as district can be used, by which more accurate estimation of annual maintenance cost can be produced. The definition of life cycle influences the availability of sufficient samples. For example, the life cycle for Category 1 starts after a certain construction and ends at the same type of construction. This life cycle may be hard to find in the database. Certain approximation was used in this study to extract the samples for Category 1. This sampling may need to be revisited when the model is adopted by NDOT.

The first author would like to thank Mr. Kent E. Mayer of the Nevada Department of Transportation who provided assistance in collecting the maintenance data.

Teng, H.L., Hagood, M., Yatheepan, Y.V., Fu, Y.Y. and Li, H.Q. (2016) The Development of Regression Models to Estimate Routine Maintenance Costs for State Highway Infrastructure. Journal of Transportation Technologies, 6, 339-359. http://dx.doi.org/10.4236/jtts.2016.65030