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APPENDIX A
Details of Metal Loss Models
This appendix describes the history and pertinent details of Darbin/Romanoff Model
metal loss models that have been proposed for estimating sac-
rificial steel requirements for MSE reinforcements. Most state Romanoff (1957) describes 47 years of data collected by
highway agencies use some form of the AASHTO specifica- the U.S. National Bureau of Standards (NBS) from extensive
monitoring of metal samples buried in situ. In general, the
tions for the design of MSE walls. Therefore, the AASHTO
corrosion rate was observed to be greatest during the first few
metal loss model is used in this study to compute nominal
years of burial, subsequently decaying to a steady but signifi-
sacrificial steel requirements that serve as a basis for calibra-
cantly lower rate. Romanoff suggested the following expo-
tion of resistance factors for LRFD. This appendix will describe
nential equation to predict the amount of general corrosion
earlier metal loss models and corresponding data sources
at some time (t) after burial:
leading to the development and adoption of the AASHTO
model. These models include the Darbin/Romanoff Models
x = Kt n (A-1)
and the Stuttgart Model.
Galvanized steel reinforcements are most often employed
In Equation (A-1) x is the loss of thickness in the material at
for the construction of MSE walls, particularly with respect to
time, t, and K and n are parameters that are soil and site depend-
transportation-related projects. However, the behavior of ent. In Equation (A-1) lower case "x" describes metal loss that
plain steel is also of interest, as this is compared or related to may include zinc and steel for galvanized elements. Capital "X"
the loss of steel after the zinc is depleted from the surface. Fur- is used for other metal loss equations in this appendix to denote
thermore, the AASHTO metal loss model only considers the loss of steel subsequent to depletion of zinc.
use of galvanized reinforcements, and other models need to Comprehensive as it was, less than 10% of those data from
be identified to consider the behavior of plain steel (i.e., not the NBS study came from free-draining granular soils such as
galvanized). those used in MSE walls, and even less of these data came from
Metal loss models used to estimate sacrificial steel require- galvanized steels. Darbin et al. (1988) addressed this shortcom-
ments for MSE are empirical, and therefore it is important ing during a 20-year study not only to evaluate the corrosion
to describe the data sources considered in their develop- of metallic earth reinforcements in typical MSE wall backfill,
ment. Although fill characteristics are important consider- but also to identify the soil parameters that determine the
ations, these models do not explicitly relate fill characteristics kinetics of the corrosion process. Using the form of Equation
in terms of their electrochemical properties to corrosion (A-1), Darbin et al. (1988) proposed that metal loss of galva-
rates. In general, the models consider the effects of time on nized steel could be described with a constant exponent "n"
corrosion rates and apply to particular ranges of fill char- equal to 0.65, and coefficient "K" depending on soil aggressive-
acteristics. Care must be exercised when using these mod- ness (K = 25 m/year for soils with resistivity 1,000 -cm
els to be sure that fill materials have electrochemical and K = 20 m/year for soils with 3,000 -cm).
properties within the range for which the models are Maximum corrosion rates and loss of reinforcement ten-
intended. Metal loss models that may be applied to fill sile strength from corrosion may be estimated by multiplying
materials, that do not necessarily meet AASHTO require- the general corrosion rate obtained from Equation (A-1) by
ments, are also identified. a factor of 2 (Elias, 1990). This factor is applied to the metal

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loss of base steel subsequent to depletion of zinc from the sur- zinc consumption is greatest during the first 2 to 4 years, fol-
face. Thus, a factor of 2 is applied to the Darbin Model to con- lowed by a significantly reduced rate. Therefore, the reduced
sider strength loss as follows: rate considers passivation of zinc that occurs in backfill soils
typical of MSE wall construction. Steel consumption is con-
for galvanized elements: sidered to begin after the zinc layer is consumed, but at a rate
observed from samples of plain steel appropriate to the age of
1.54
z m 0.65 the reinforcements (i.e., rate of corrosion for steel that has
if t f > i then X ( m ) = 50 × t f ( yr )
25 yr been in service for more than 2 years). This model was the
basis for the sacrificial steel requirements for galvanized rein-
- 2 × z i ( m ) (A-2) forcements recommended by Task Force 27 (1990); AASHTO
1.54 (2002a) later adopted a different, more conservative, piece-
z
if t f i then X ( m ) = 0 wise linear model as described later in this appendix.
25
Metal loss models are proposed considering galvanized or
In Equation (A-2), X is loss of steel (base metal) in units of plain steel reinforcements and fill materials with low and high
m, and tf is service life in years. Loss of base steel occurs sub- salt contents. Low salt contents are described as materials
sequent to depletion of the zinc coating, and zi is the initial with 4.5 1,000 -cm, chloride content less than
zinc thickness. Equation (A-2) is applicable to the range of fill 50 ppm, and sulfate content less than 200 ppm. For this con-
conditions representative of MSE wall construction that dition, the Stuttgart model is as follows:
exhibit min greater than 1,000 -cm.
Elias (1990) proposed the following model for plain steel for galvanized elements:
reinforcements which also has the same form as the original
equation proposed by Romanoff [Eq. (A-1)]: m ( zi - 12m )
X ( m ) = 9 × t f - 2 yr - yr (A-4)
yr m
m 0.8 2
X ( m ) = 80 × tf (A-3) yr
yr
for plain steel elements:
Data reviewed for Equation (A-3) are based on the NBS data
set for plain steel and include a wide range of fill conditions, m m
X ( m ) = 45 × 2 yr + ( t f - 2 yr ) × 9 (A-5)
many not meeting the stringent electrochemical requirements yr yr
for MSE fills. However, given the scatter inherent to measure-
ments of fill properties and corrosion rates for plain steel, For fill materials that are saturated with chloride or sul-
Equation (A-3) is used as a conservative estimate of metal loss fate concentrations greater than the threshold values, the
in fills that meet MSE fill requirements, but not by a wide mar- Stuttgart model is as follows:
gin. Equation (A-3) also includes a factor of 2 to consider the
maximum metal loss. for galvanized elements:
Although corrosion rates for both galvanized steel and car-
bon steel clearly vary exponentially with respect to time, sim-
m ( zi - 51m )
ple models involving linear extrapolation have been proposed X ( m ) = 12 × t f - 3 yr - yr (A-6)
and are considered valid (Elias, 1990) over the limited time yr m
2
frame from which metal loss measurements of earth re- yr
inforcements were available (<20 years). Given this limited
time frame, most observations of metal loss for galvanized for plain steel:
reinforcements are observations of the loss of the zinc coating,
m m
not the carbon steel (i.e., steel was not exposed during the X ( m ) = 80 × 2 yr + ( t f - 2 yr ) × 12 (A-7)
monitoring period). The following models, including the yr yr
Stuttgart, Caltrans, and AASHTO models, are linearized forms
of the Romanoff/Darbin equation.
AASHTO Model
Stuttgart Model According to AASHTO, MSE fill must comply with the fol-
lowing electrochemical criteria:
Rehm (1980) proposed an alternative piecewise linear
model for describing metal loss. The longevity of the zinc coat- · pH = 5 to 10
ing is considered using a bilinear model such that the rate of · Resistivity 3,000 -cm,

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Table A-1. Summary of data sources for metal loss models for MSE reinforcements.
MODEL DATA SOURCE MAXIMUM
Stuttgart NBS NO
Darbin Controlled conditions - YES
electrochemical test specimens &
samples buried in soil box
AASHTO Stuttgart & Darbin YES
· Chlorides 100 ppm, that could be related to metal loss, and corresponding corro-
· Sulfates 200 ppm, and sion rates averaged over longer time intervals.
· Organic content 1%. Thus,theAASHTOmodelconsiders a variety of data sources,
each with its own set of strengths and limitations. However,
The fill requirements are intended to control corrosion results from these different data sources compare reasonably
potential with fills that are between noncorrosive and "mildly" well. The outstanding limitations of each data source involve
corrosive. The AASHTO metal loss model defines the follow- a lack of data to document the corrosion/metal loss of the base
ing rates at which first zinc, then steel, will be lost from the steel subsequent to depletion of zinc from the surface. Thus,
MSE reinforcement section: similar to the Stuttgart model, the AASHTO model considers
steel consumption to begin after the zinc layer is consumed,
· Loss of zinc (first 2 years): 15 m/yr; but at a rate observed from samples of plain steel appropriate
· Loss of zinc (to depletion): 4 m/yr; and to the age of the reinforcements.
· Loss of steel (after zinc depletion): 12 m/yr. Figure A-1 illustrates the comparison between the Stuttgart
and AASHTO models. The corrosion rates for the zinc coating
Using the AASHTO Model the steel loss per side (X) in during the first 2 years of service and for steel subsequent to
m/yr for a given service life, tf, and initial thickness of zinc depletion of zinc roughly correspond to the Stuttgart model
coating, zi, is computed as that applies to higher salt contents (e.g., chlorides in excess of
50 ppm). However, the corrosion rate for zinc after 2 years in
m ( zi - 30m ) service of 4 m/year is twice the value of 2 m/year from the
X ( m ) = 12 × t f - 2 yr - yr (A-8) Stuttgart Model. The rationale for the use of the higher corro-
yr m
4 sion rate may be understood by examining the comparison
yr
with the Darbin model as depicted in Table A-2.
Both the Darbin/Romanoff and the Stuttgart Models con-
tribute to the basis of the AASHTO Model. Table A-1 identi- STUTTGART
fies sources of data associated with each. These data sources
ZINC
include the NBS studies from metal samples that were buried
within a wide range of fill conditions at sites located through- CR = 17 m/yr for t < 3
out the United States; and from carefully controlled labora-
CR = 2 m/yr for t > 3
tory tests conducted in France, specifically with regards to AASHTO
MSE reinforcements. Laboratory studies included electro-
chemical test cells and burial boxes. The electrochemical test CR = 15 m/yr for t < 2
cells were assembled using relatively small (compared to bur-
CR = 4 m/yr for 2 < t < 16 ? Factor of 2 ??
ial boxes) plastic tubes containing specimens of reinforce-
ment surrounded by soil. Electrodes were sealed into the ends CR = 12 m/yr for t >16 PLAIN STEEL
of the tubes, serving as reference and counter electrodes, to
CR = 80 m/yr for t < 2
facilitate measurements of corrosion rates at frequent inter-
with zi = 86 m
vals. Compared to the electrochemical test cells, burial boxes CR = 12 m/yr for t > 2
incorporated representative specimens of MSE reinforce-
ments and conditions that more closely resemble field instal- Figure A-1. Comparison of AASHTO and Stuttgart
lations. The burial boxes employed weight loss measurements Models.

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Table A-2. Comparison of AASHTO and Darbin models.
Darbin Model X (m) = 50t0.65 - 2 (zi) (Includes Factor of 2)
AASHTO Model X (m) = (t-C) x 12 (m/yr) (C= 16 years with zi = 86 m)
Computed Metal Loss X (m)
t (yrs) DARBIN AASHTO
50 464 408
64 574 576
75 655 708
100 825 1,008
Table A-2 indicates that metal losses computed with the specifications used by Caltrans (2009) do not allow use of
AASHTO model compare reasonably well with the Darbin reinforced fill with minimum resistivity less than 2000 -cm.
model. The differences depend on time (service life), and The steel loss, X, for design life, tf, is described by the Caltrans
the two models render nearly the same metal loss when t = interim model as:
64 years. Apparently, using a higher corrosion rate for zinc
m
of 4 m/year renders metal loss consistent with the Darbin X ( m ) = ( t f - C ( yrs )) × K (A-9)
model, which directly considers applying a factor of 2 yr
to consider maximum metal loss. Note that although the
AASHTO specifications require fill with > 3,000 -cm, the where C is the time for zinc depletion (years) assuming an ini-
basis of the models (both Stuttgart and Darbin) are referred tial zinc thickness of 86 m and K (m/yr) is the corrosion
to fill with > 1,000 -cm. Thus, the AASHTO model and rate of the base steel. Table A-3 provides values for C and K
corresponding specifications for fill are conservative. as functions of fill conditions.
Current specifications used by Caltrans (2009) do not
allow use of reinforced fill with minimum resistivity less than
Caltrans-Interim Design Guide
2,000 -cm. Specifically, the current Caltrans specification
Based on the results from limited field studies, Caltrans allows for backfill with a resistivity greater than 2,000 -cm, a
(Jackura et al., 1987) has proposed design guidance for a wider pH between 5.5 and 10, and maximum chloride and sulfate
range of reinforced fill conditions than those considered by concentrations of 250 ppm and 500 ppm, respectively. Califor-
AASHTO. Higher rates of metal loss are specified for comput- nia considers these conditions by using a higher rate of metal
ing sacrificial steel requirements when reinforced fills that are loss in determining sacrificial steel and reducing the design life
more aggressive relative to corrosion are considered during of the MSE wall to 50 years. Caltrans assumes that the zinc
design. These metal loss rates are based on limited data col- coating provides 10 years of service life for the specified mini-
lected from MSE wall sites in California (Jackura et al., 1987), mum coating thickness of 2 oz/ft2 (86 m per side). This is less
and use data available from the earlier NBS studies. Interim than the 16 years of zinc life inherent to the AASHTO metal
design guidance considered fill properties that include mini- loss model. A corrosion rate of 1.10 mils/yr (28 m/yr) is con-
mum resistivity more than 1,000 -cm. However, current sidered to affect the base steel after the zinc has been consumed
Table A-3. Summary of parameters for Caltrans-Interim
guidelines (Jackura et al., 1987).
K C
Fill Type
(m/yr) (years)
Neutral & Alkaline 28 10
Acidic 33 10
Corrosive 71 6
Select Granular 13 30
Notes: Neutral and alkaline: minimum resistivity > 1,000 -cm and pH > 7.
Acidic: minimum resistivity > 1,000 -cm and pH < 7.
Corrosive: minimum resistivity < 1,000 -cm.
Select granular soils are clean, free draining gravels with less than 5% fines and
minimum resistivity > 1,000 -cm.

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and used to compute the sacrificial steel requirements. These fines and with plasticity index (PI) <6. Caltrans reduces the
corrosion rates account for the potential for localized corro- steel corrosion rate to 13 m/yr for backfill meeting addi-
sion and pitting; that is, a factor of 2 relating the loss of tensile tional requirements for select granular fill. For select granu-
strength to idealized uniform corrosion rates is included. lar fill, lower resistivity and higher salt concentrations are
Caltrans specifications provide incentives to use select allowed, but the allowable fines content is less compared to
granular fill, which is a better quality fill with less than 5% current AASHTO requirements.