Basic Rules of Cost Calculation

There are several basic rules for calculating the economic costs of any engineer- ing project, as well as for applying those rules to select the type of protection and method of repair for a structure. The most popular methods of economic analysis tools are the present value, future value, and interest rate of return. Here, the method of calculating the present value is described briefly as it is the easiest way to select the appropriate method of economic repair and an appropriate system to protect the structure from the effects of corrosion.

9.2.1 Present Value Method

The cost of protecting reinforced concrete from corrosion consists of the prelimi- nary costs of the method of protection and the money paid with the beginning of construction. On the other hand, the cost of maintenance and repair will be over the lifetime of the structure. In many cases, the cumulative cost of maintenance and repair is higher than initial costs. In many projects, cost calculation is often based on the initial costs only, but the result is that the total cost is very high compared to the structure’s cost estimate, which is only the initial cost.

A method of present value is used to calculate the present value of future repair, including the cost of equivalent current value with the assumption that the repair will take place after a number of years, n:

Present value = repair cost (1 + m)–n _(9.1)

where m is the discount rate, which is the interest rate before inflation. For example, assuming that the interest rate is 10% and the inflation rate is 6%, the discount rate

m is equal to 4%, or 0.04.

The entire structural cost consists of the initial cost, which is called capital cost (CAPEX), and the sum of the present values of future costs due to maintenance, which is called operating cost (OPEX). When the rate of inflation increases, the cost of future repair will not be affected. But when it decreases, the present value of future repair will increase. In this chapter, we will assume an inflation rate of about 4% that depends on a country’s general economy. Every country has its own published inflation rate.

9.2.2 rePair tiMe

The time required to repair the structure as a result of steel corrosion is the time at which corrosion begins in the steel reinforcement bars and the time needed to spall the concrete cover with signs of concrete deterioration. This essentially requires work with repair. Tutti (1982) gave a simple explanation of a process of corrosion with time; the steps were for all types of corrosion and there was no difference if

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corrosion happened as result of chloride attack or carbonation propagation. However, the invasion of chlorides, as well as the carbonation of concrete, takes a long time to break the passive protection layer on the steel bars and start corrosion.

After that, from the beginning of corrosion to a significant deterioration in the concrete, when repair will be necessary, will take more time. Raupach (1996) pointed out that in the case of concrete bridges, degradation occurs in about 2–5 years. Therefore, the time for repair is the total time required for the protection of depassivation in addition to 3 years.

The steps of corrosion’s effect on a concrete structure are illustrated in figure 9.1. Note that after construction it will take time until chloride concentration or car- bonation accumulates on a structure’s surface and then spreads into the concrete, as shown in the figure. The next step is the propagation of chlorides or carbonation until the steel bars are reached. The third step is the start of corrosion on the steel bar, which at this time will have an impact on the concrete strength by reducing steel diameter and cracks occurring on the concrete surface. The last step is an increase in crack width until spalling of the concrete cover.

From the preceding analysis, we find that the time required for repair depends on the time needed to increase the percentage of chloride concentration to the limit that will initiate the corrosion, in addition to the rate of corrosion, which will happen after that. The previous chapter discussed several methods for protecting the struc- ture from corrosion. These different methods delay the start of corrosion for a longer period of time as they reduce the rate of the chloride or carbonation propagation in concrete. They will reduce the rate of corrosion after that as well. Note that the pre- ceding analysis relies on the noninterference of the hair cracks on the concrete in the rates of spread of chlorides or carbonation within the concrete. It is assumed that the design was based on the absence of an increase in the cracks more than that permis- sible in codes (as in chapter 5), as well as that the concrete was produced based on a quality control procedure according to code; thus, the presence of cracks is assumed to be within allowable limits.

The time required to start the structural repair depends on the nature of the sur- rounding weather and environmental factors that affect the beginning, as well as the rate, of corrosion. This time is determined by knowing the rate of corrosion and the required time to spall the concrete cover. The deterioration of concrete increases the

C on cr et e D et er io ra tion St ar t Chloride or St ar t _Start Crac ks Sp al lin g C on cr et e

probability of a structure’s collapse with time; some studies have identified the prob- ability of failure, which should not be beyond the structural reliability classified in various specifications.

A study on residential buildings by El-Reedy and Ahmed (1998) focused on how to determine the appropriate time to perform repair due to corrosion on the concrete columns. It considered environmental conditions around the structures: They were affected by humidity and temperature, which have a large impact on the increasing rates of corrosion. A corrosion rate of 0.064 mm/year reflects dry air, while a rate of 0.114 mm/year is based on a very high moisture rate. This study took into account the increasing resistance of the concrete over time, as well as the method of determi- nation in the case of higher steel or low steel columns, with different times required for the repair process.

9.2.3 CaPaCity lossin reinforCed ConCrete seCtions

According to the fundamentals of design of any reinforced concrete member, the member’s capacity depends on the cross-sectional dimensions (concrete and steel area) and material strength (concrete strength and steel yield strength). In the case of uniform corrosion, as shown in figure 9.2, the total longitudinal reinforcement area can be expressed as a function of time, t, as follows:

As t n D ( ) / ... = π 2 _{4 .. ..} / ... for t T n D C t T fo i r i ≤ −

( )

D = the diameter of the bar

n = number of bars

Ti = time of corrosion initiation

Cr = rate of corrosion

This equation takes into account the uniform corrosion propagation process from all sides.

The curves in figures 9.3 and 9.4 show that, over time, the collapse of a structure is more likely with the increase in the rate of corrosion. The El-Reedy and Ahmed

Steel Bars without Corrosion Uniform Corrosion on the Steel Bars

D

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study revealed that concentrically loaded reinforced concrete columns will be due for maintenance about 4 or 5 years from the initial time of corrosion with lowest steel ratio and higher corrosion rate. In cases of higher steel ratios and lower cor- rosion rates, this period may increase to about 15–20 years. Moreover, this study expects columns with eccentricity to increase the moment on the column, so the design should increase the percentage of steel. In such a case, it is expected that the deterioration of a structure and movement toward criticality will be after a couple of years in the case of lowest reinforcing steel ratio and very high corrosion rate. On the other hand, in the case of higher reinforcing steel ratio and lower corrosion rate, the maintenance will be due after about 6 years.

0 0 10 20 30 40 50 1 2 3 4 5 Time, Years Re lia bi lit y In de x Cr = 0.064 mm/year Cr = 0.089 mm/year Cr = 0.114 mm/year

fIgure 9.3 Effects of corrosion rate on the reliability index at reinforcement ratio equal

to 1%. 0 1 2 3 4 5 6 0 10 20 30 40 50 Time, Years Reliability Inde x Cr = 0.064 mm/year Cr = 0.089 mm/year Cr = 0.114 mm/year

fIgure 9.4 Effects of corrosion rate on the reliability index at reinforcement ratio equal

As we expected, the time required for repair is linked closely to the nature of a structure and the method of design, as well as to the importance of the building. For example, important vital structures, such as those in which nuclear activities take place, need protective measures with a time much different from that of other struc- tures such as residential buildings.

We will apply the method of calculating costs through an example of protecting the reinforced concrete foundation in a petrochemical processing plant near the Red Sea. We will consider the same protection methods as those in Bentur, Diamond, and Berke (1997), who explained an economic study of a bridge surface for corrosion; because it always used salt to melt ice, the probability of chloride attack was very high. It is worth mentioning that the cost of repair and protection methods in the example is roughly based on the cost in Egypt. When applied in different countries, it will vary, but the price is stated just to perform cost comparison between the dif- ferent ways of protection.