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 Federal Highway Administration > Publications > Research Publications > Infrastructures > Structures > 09044 > Integrity of Infrastructure Materials and Structures

Publication Number: FHWA-HRT-09-044
Date: October 2009

## APPENDIX

### CALCULATIONS

In this appendix, calculations that were used to convert laboratory measurements to units in text, tables, and graphs are provided as examples.

### Example 1. Convert Weight/Area (Corrosion in g/inches2) to mils (or mm) Corrosion Penetration

Data for specimen W48: test condition was 30 cycles, 2 soaks, 0.5 percent NaCl, and pH 8.

Typical Data Weight
(Initial)
Weight
(Final)
Area
(L by Wx2)
Corrosion
( wt/inches2 )
Coupon W48 124.90766 g 119.02947 g 34.16 inches2 0.1721 g/inches2

1 inch = 25.4 mm
1 oz = 28.35 g

Convert to centimeters:

Convert weight per surface area to penetration (divide by density):

Also:

Convert to mils (1 inch = 1,000 mils):

These are the penetration rates in mm, m, cm, or mils for corrosion occurring on one surface. In the case of corrosion occurring on both sides, the overall thickness loss would be doubled.

### Example 2. Conversion of ZRA Current to Coulombs

Where:

I = Current.
t = Time.
A = Amperes.
s = Seconds.
C = Coulombs.

• ZRA data logger recorded averaged current (i) each hour.

• The eight-bit analog-to-digital converter stored the sum of six readings in hexadecimal format, that is, the summed eight-bit readings (0 to 255 hex) were summed to give a value between zero and 05 FA (hex) and stored.

• Stored data were downloaded from the logger to the computer. Scaling was 255 (hex) = 100 µ A (full-scale).

• Microsoft Excel® macro converted hexadecimal to decimal, divided by 6, and scaled by 100/255.

• The result was µ A average current reading per hour.

• The Microsoft Excel® macro also summed the hourly average current readings (in microamperes) and multiplied them by 3,600 s to yield microcoulombs (i × t = C).

Example: For constant, half-scale readings (50 µA) for 15 days converted to coulombs:

Note that the data logger recorded a value equal to an average current value each hour. In this example, 0.18 C was measured each hour. Summing (integrating) these hourly values for 15 days yielded 64.8 C.

### Example 3. Conversion of Sensor Output (µA) to Corrosion Rate (mpy or mmpy)

Where:

m = Mass (g).
I = Current (A).
t = Time (s).
a = Atomic weight; (g).
n = Number of equivalents, eq, (number of electrons exchanged, for Fe = Fe2+ + 2e- ).
F = Faraday's constant, 96,500 C per equivalent.

For 1 µ A output per year (recall that C=A × s):

For 1 µ A output in an area of 1 cm2 and given an iron density of 7.87 g/cm3:

Equation 17 demonstrates the conversion of constant or average current density to mils per year or mm per year. The data logger provided the average of six current measurements at 10-minute intervals each hour. These hourly averages are summed and presented in table 15.

### Example 4. Comparison of Mass Loss and Sensor Results in Terms of Penetration

Sensor anode area is the two-dimensional ring between the inner washer, r1 , and the outer coated perimeter, r2:

To calculate the mass loss from the downloaded converted sensor output (microamperes), substitute C = A × s, (i.e., replace It in equation 15 with the coulomb value). For example, use the first value (7,261 µ A) in table 15 that is an hourly value requiring conversion to seconds (1 h = 3,600 s) as follows:

The calculated mass loss per unit area of the sensor anode is converted to penetration using the density of iron as follows:

For the cable sensor, no direct comparison with weight loss was possible with the available data. An estimate of corrosion rate (penetration) was made based on sensor area and current output.

Area calculation where:

 Anode wire diameter = 0.08 cm. Active length = 2.5 cm. Anode area is π dl = 3.14 × 0.08 cm × 2.5 cm = 0.63 cm2.

Sensor output:

From equation 17, 1 µ A/cm2 = 0.46 mpy. For a 0.63-cm2 sensor giving a current reading of 1 µ A, the current density is (1 µ A / 0.63 cm2) = 1.6 µA / cm2, and a sensor reading of 1 µA corresponds to 0.74 mpy as follows:

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