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LCC is the sum of all the recurring and non-recurring costs over a specified period of a structure. LCC for a roadway section includes initial construction costs and varying maintenance costs over the specific period. Not all maintenance activities on roadway surfaces take place each year. In fact, frequency of maintenance activities differs for each roadway surface based on roadway conditions and traffic volumes. A major maintenance activity such as regravelling may take place only once every 6–7 years depending on the traffic load, but basic maintenance activities that occur on gravel roads, such as blading and resurfacing/reshaping, take place more frequently.

Blading removes minor surface defects and corrects the crown to proper slope. Blading is utilized more frequently than many other activities, occurring at least twice each year for low traffic conditions to approximately 6–8 times per year for heavy traffic conditions as a result of increased disturbance to the gravel surface. Resurfacing/reshaping, typically carried out once every year, recovers gravel material from the ditch or the shoulder in order to improve drainage and defects throughout the cross section of the road. Spot gravelling, typically also conducted once a year

depending on the needs of the surface, corrects isolated defects on roadway surface areas that are less than 1000 square meters.

Maintenance activities on paved roads include periodic overlays of asphalt, crack sealing, and surface treatments such as chip seal, patching, stripping, and marking. However, not all activities occur during each year. In fact, one particular maintenance practice may affect the need for another maintenance practice. For example, use of chip seal may extend the life of the pavement and increase the intervals between overlay treatments. Crack sealing and patching typically occur once each year or once every two years. Chip sealing is done every 3–4 years, and overlay is usually applied every 20 years.

In this study, the frequency of maintenance activities was obtained through literature review and detailed Kansas county data. Maintenance costs for each activity differ, however, varying by state and even within counties of one state. Because maintenance practices and maintenance frequencies differ for gravel roads and paved roads, it cannot be compared based on per year cost of maintenance for each roadway type. However, the cost of maintenance for a period of approximately 20 years could be determined (which is considered as a life cycle) and then compared to the maintenance cost of each roadway surface type in order to make a decision about a better alternative.

The equation to calculate total LCC is rather simple if inflation is not taken into consideration (i.e., consistent maintenance cost for all years of period of analysis). However, when considering inflation for the maintenance cost, the equation to calculate the LCC becomes complex. Because costs accrue over several years, the LCC must be calculated to the present value of the dollar by evaluating the present worth value. The present worth evaluation combines all investments and costs and all annual expenses into a single present worth sum that represents the

analysis period. When comparing alternatives, the one with the lowest present worth is considered to be the most economical option. For this analysis, a default value of 4% interest rate was used, which is generally compatible with government bonds and other government financing plans. The study in South Dakota used an interest rate value of 3.5% (Zimmerman and Wolters, 2004).

However, any other interest value can be used as well.

Equation 4.1 was used to calculate the LCC while accounting for inflation. This equation is formulated to be used for any roadway surface type (gravel or paved) for any number of maintenance activities over the roadway surface with varied maintenance cost per mile and varied maintenance frequency for each activity. This equation provides flexibility to calculate the LCC for any road for any local scenario.

LCC_total= ∑ C_j

a

j=1

×∑(1 + r)^{fj × i}

k

i=1

(4.1)

where,

LCCtotal = life cycle cost for a roadway surface during the analysis period of N years N = analysis period (years)

a = total number of maintenance activities on the roadway surface j = each maintenance activity (j = 1, 2, 3,….., a)

k = |N/fj| = number of times each activity j occurs during LCC analysis period of N years

i = count for each activity j (i = 1, 2, 3,….., k) Cj = maintenance cost per mile of activity j ($/mile) fj = frequency of maintenance of activity j (years) r = rate of inflation (in decimals [e.g., 4% = 0.04])

Note: The mod (| |) sign for |N/fj| the number of times a certain activity will occur during a life cycle. For

When inflation rate is not considered, maintenance costs per mile for each activity remain the same throughout all the years of the analysis period. Therefore, r = 0 and Equation 4.1 becomes:

LCC_total= ∑ C_j appropriate discount rate. Discount rate is the interest used to determine the present value of future cash value. Equation 4.3 can be used to calculate the present worth value of the LCC of a roadway surface type with inflation.

LCCPW = present worth value of LCC for maintaining a roadway surface during the analysis period of N years

Special Case:

When the rate of inflation and discount rate are equal (i.e., r = d), Equation 4.3 becomes

LCC_PW = ∑ C_j

Therefore, the present worth value of the total LCC is equal to the total LCC with no inflation (r

= 0). In that case, Equation 4.2 and Equation 4.4 become identical.

All previously formulated equations considered only maintenance cost. However, when conversion of a roadway surface occurs, the initial construction cost, also referred to as the conversion cost, should be added to the equations. Therefore, Equations 4.1 to 4.4 become

LCC_total = IC_c+∑ C_j

ICc = initial construction cost or conversion cost