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Life cost of a pavement is the total cost incurred during the life period. It consists of the initial capital outlay and a recurrent upkeep cost.

The model is based on certain assumptions and concentrates on main cost items only, as follows.

 

Both the capital and upkeep costs are evaluated as unit costs per 1 square meter of the designed pavement (COST/m2). The figures thus obtained should be used for engineering comparisons, rather than detailed financial analysis. The capital outlay is derived from the unit cost of concrete (COST/m3), unit cost of steel (COST/t), unit cost of subbase (COST/m3), unit cost of subgrade (COST/m2), and unit cost of fibres (COST/kg) . When appropriate, different unit costs are used for different types of pavement.

 

The unit cost of concrete is applied to the volume of concrete, which depends on its thickness.

 

The unit cost of steel is applied to the mass of steel used, which depends on the diameter, length and spacing of steel used either as dowels, or as continuous reinforcement.

 

The unit cost of subbase is applied to the volume of subbase, which depends on its thickness.

 

The unit cost of subgrade is applied to the area of the layers below the subbase.

 

The unit cost of fibres is applied to the mass of fibres, in kg, used in one square-meter of concrete slab.

 

The program calculates the simplified capital cost, in COST/m2, from these values. Typical 2006 values of the capital unit costs are shown in the table below.

 

 

Note: The lower unit costs of continuously reinforced concrete (CR) and the ultra-thin reinforced concrete (UT) are due to the absence of transverse joints. The high cost of the ultra-thin continuously reinforced concrete (UT) is due to the high-strength concrete being used. The cost of the subgrade also includes costs of the layers between the subbase and the subgrade.

 

The cost of upkeep is incurred at certain time intervals. The upkeep is assumed to be a major maintenance action during which damage to pavement is thoroughly repaired. The pavement is thus fully rehabilitated and made serviceable for another period of time.

 

The first rehabilitation action is assumed to take place after t1 years, when a certain percentage of the concrete pavement area will be shattered (meaning broken slabs, or punch-outs in case of continuously reinforced concrete). After t1 years a certain percentage of the surface will be pumping. In case of plain and dowel concrete there will be faulting. The program evaluates the extent of these afflictions, depending on the pavement type selected, and the design parameters given as input. The extent of each type of affliction is expressed as percentage.

 

It is assumed that, when the shattered concrete is rehabilitated, other maintenance actions - those attending pumping, faulting, cracking and other defects - are performed as well. The cost of this combined remedial action consists of two components - the cost of structural repair (attending to broken slabs, shattered concrete, potholes, grinding down faulting) and the cost of surface repair (sealing cracks, re-sealing of joints, filling of pop-outs and other minor work done on the pavement surface). The unit costs of these two components are input constants. Typical 2006 values of the upkeep unit costs are shown in the table below.

 

 

It is assumed that the surface repairs are done when need may arise. To meet the associated financial requirements annual contributions are made to a surface-repair fund. The annual contribution multiplied by the number of years to the next rehabilitation action is then added to the cost of structural repairs to obtain the total rehabilitation cost.

 

The program thus calculates the cost of the first rehabilitation action from the unit cost of structural repair, the percentage of shattered concrete surface, and the unit cost of surface repair. The result is expressed in R/m2 of pavement surface. Since this cost is incurred in the future, the present worth of the figure is taken into consideration. The program uses a fixed discount rate of 4 % p.a. and evaluates the present worth from the magnitude of the structural repair cost when it occurs and the annual payment series funding the cost of surface repair.

 

The rehabilitation action is performed because certain amount of pavement damage has occurred during the period t1. If such an amount of damage occurs again, the pavement will again have to be rehabilitated. It is assumed that the nature of a rehabilitation action, as well as its cost, are always the same. As a consequence, the subsequent rehabilitation actions will occur in periods different from t1, depending on the magnitude of heavy-vehicle traffic in the initial year (ADTT0), and the traffic growth. Except for the relatively small total of annual contributions to the surface-repair fund, which depends on the length of the rehabilitation period, the rehabilitation cost is constant. However, its present worth is not - it depends on the discount rate and the time when the action takes place.

 

The present worth of pavement upkeep is the sum of all discounted rehabilitation costs undertaken during the life period of the pavement.

 

The life cost of pavement is the total of the capital cost and the present worth of the upkeep, expressed in R per one square meter of pavement surface.

 

After a successful run, a typical rehabilitation schedule is displayed in a table on the Facts Page. The table has five columns as follows:

 

Rnd      round of rehabilitation action; 1st, 2nd, 3rd, 4th, etc.

Step      period of time, in years, after which the particular rehabilitation action will be needed      

Year      the year, after the beginning, in which the action will be needed

pwr       present worth, in R/m2, of the particular rehabilitation action      

PWR     present worth, in R/m2, of all rehabilitation actions performed so far

 

It is assumed that, should the effect of the last rehabilitation outlast the life period, the extent of the last action will be limited to cover only the interval from this action to the end of life period. The cost of this limited rehabilitation action is calculated on a pro-rata basis for the shortened period. In this case, the pwr and PWR figures pertain to this shortened period only, and the Step and Year of a would-be-next rehabilitation are shown in brackets.

 

Consider a simple example to demonstrate the above statement: The life period is 40 years. A rehabilitation cost whose present worth pwr is R20/m2 is required in year 34. The next rehabilitation would be needed in year 42.

 

Since the effect of a full rehabilitation performed in year 34 would outlast the end of the life period, only a limited rehabilitation will be done in that year. The present worth of that action is calculated on a pro-rata basis: R20/m2 x (40 - 34) / (42 - 34) = 20 x 6 / 8 = R 15/m2. The last rehabilitation thus contributes R15/m2 rather than R20/m2 to the present worth PWR of the upkeep during the life period of 40 years.

 

The costs mentioned above do not include road user's costs, such as the extra vehicle-operating cost, the cost of time when being delayed during road works (due to slow and extra travel on detours, stopping for one-way traffic control, etc.), and the general cost of inconvenience. Should these costs be an issue you could use the following simplification to include them in the calculation.

 

Assume that a temporary surface is provided by the contractor to accommodate traffic during the road works. Say that the cost of this temporary facility is comparable with some percentage of the cost of subgrade, e.g. 60 % of the R65/m2 - about R40/m2. Increase the cost of subgrade accordingly, to R65/m2 + R40/m2 = R105/m2 , and use this inflated figure to represent both the cost of subgrade and the road user's costs.

 

If no temporary surface is provided by the contractor during the road works then simply assume that the equivalent cost incurred by the afflicted users still amounts roughly to the R105/m2 estimated above, and use this figure anyway.

 

Although the above method may be regarded as somewhat rough and not entirely accurate, at least it makes a step in the right direction.