AlllDQ T1S1E4

publications'

NBSIR 81-2390

NAT'L INST. OF STAND & TECH R.I.C,

AlllDS flfl7Efl7

Analysis and Modeling of

Corrosion of Steel in Prestressed

Concrete

[•

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

I National Engineering Laboratory

i Center for Building Technology

I Materials Division

I Washington, DC 20234

November 1981

Prepared for Treaty of Friendship and Cooperation

between Spain and the United States

of America

NBSIR 81-2390

t f • ANALYSIS AND MODELING OF

CORROSION OF STEEL IN PRESTRESSED

CONCRETE

MATIODAL UVIBR*'-' 5 »TA>IDA«t>8

tlo-t a : - 6

ClCf

m,

Spencer T. Wu

James R. Clifton

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Materials Division

Washington, DC 20234

November 1 981

Prepared for Treaty of Friendship and Cooperation

between Spain and the United States

of America

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Analysis and Modeling of Corrosion of Steel in Prestressed Concrete

by

Spencer T. Wu

and

James R. Clifton

Structures and Materials Division

Center for Building Technology

National Bureau of Standards

Washington, DC 20234

ABSTRACT

Development of conceptual and mathematical models describing the corrosion of

steel in prestressed concrete is outlined. The application of the principles

of stress corrosion and general corrosion to understanding the mechanisms

involved in corrosion of steel in prestressed concrete is discussed. The

first step in estimating the failure time of a prestressed concrete structural

system because of corrosion of the reinforcing steel is to estimate corrosion

rates under various realistic conditions. A simplified approach based on mathematical modeling of concrete properties for estimating corrosion rates is

proposed.

Before the proposed mathematical model can be applied to practical problems

information is needed on the specific mechanisms of corrosion cell processes of

steel in prestressed concrete. In addition, well designed corrosion tests need

to be performed in which the important factors affecting the corrosion rates

are considered.

Key words: concrete; corrosion; general corrosion; mathematical modeling;

prestressed concrete; prestressing steel; stress corrosion.

lii
TABLE OF CONTENTS

Page

ABSTRACT iii

1. Introduction 1

1.1 Problem Identification 1 1.2 Purpose of the Investigation 1 1.3 Scope of the Report 1

2. Stress Corrosion Cracking 3

2.1 Laboratory Corrosion Tests for Prestressing Steel 3

2.2 Field Test Experiences 6

2.3 Needed Information 6

3. Corrosion Processes 8

3.1 Electrochemical Reactions 8

3.2 Diffusion Processes 9

3.3 Factors Governing the Corrosion Rates 9

3.3.1 Fundamental Concepts 9

3.3.2 Effect of Chemical Variables 10

4. Quantitative Analysis of Corrosion Rates 13

4.1 Formulation Based on General Corrosion Theory 13

4.2 A Simplified Approach for Predicting Corrosion Rates ... 14

4.3 Design Considerations 15

5. Summary and Needed Research 16

6. Acknowledgements 17

7. References 18

Iv
1 . INTRODUCTION

Corrosion is the deterioration of a metal- or its- properties by chemical or electrochemical reactions with its environment. Development of a physical model

describing the corrosion of steel in prestressed concrete (PC) is extremely

difficult because the local environmental parameters are complex, and the mechanisms of the corrosion processes are not adequately understood, especially

microcell processes. In this report, the basic knowledge of corrosion of prestressing steel in concrete is reviewed, the development of a mathematical model

for the corrosion processes is described, and research needs are identified.

The following is a description of the problem, the specific purpose, and the

scope of our investigation.

1.1

PROBLEM IDENTIFICATION

The concrete of PC systems generally is of a better quality than that in

reinforced concrete: the concrete of PC is designed to be less permeable and

to have a higher reserve of alkalinity than normal concrete. Further, fewer

macro-cracks should develop in PC because of the imposed tensile forces. Thus,

the steel in prestressed concrete is generally less susceptible to general

corrosion than steel reinforcing bars embedded in concrete. In addition to

general corrosion, the present investigation addresses the associated problems

of to stress corrosion cracking (SCC) and hydrogen embrittlement (HE) processes

as well as corrosion rates. Certain engineering features such as the utilization of metal ducts in the construction of post-tensioned beams can influence

the corrosion process, but the methodology to consider such effects is straightforward if the corrosion mechanism is known. Therefore it is not addressed in

this report.

1 .2 PURPOSE OF THE INVESTIGATION

The purpose of the investigation is to Identify the significant factors and

processes responsible for the corrosion of steel in prestressed concrete and

then develop a model that can be used for describing the processes and for

evaluating the effects of important factors. The first step in developing the

model is to examine the basic mechanisms of the corrosion phenomena. SCC and

HE processes have both been considered to be responsible for the degradation of

high tensile strength steel. Therefore, both SCC and HE processes as well as the general theory of corrosion become important considerations in the study.

1.3 SCOPE OF THE REPORT

The processes by which steel in PC corrodes are described in section 2, and

experimental data from the field and laboratory tests are discussed. In addition, a standard stress corrosion test proposed by RILEM-FIP-CEB group is

mentioned. In section 3, the generally accepted theory and mechanisms of

corrosion of steel in concrete are discussed. Polarization processes and the

criteria that may govern the initiation of the corrosion process are also

discussed. Quantitative analysis for steel corrosion in concrete is given in

section 4. The existing theory for a computation model is briefly described

and a simplified approach for evaluating the corrosion rates is proposed.

1
Design concerns for structural performance are also mentioned. Then in section

4, specific research needs are outlined.

2
2. STRESS CORROSION CRACKING

For the present purposes, we consider SCC as a generic term to describe the

various forms of environmentally Induced fraction of engineering alloys. In

steels, it is accepted that HE is responsible for the failures of high strength

(quenched and tempered) alloys. The mechanism of HE is itself uncertain, but

is thought to involve the reduction in cohensive strength of the iron. The

low strength (ferricic) alloys are considered to fall by anodic dissolution,

specifically by the film-rupture model [2]

.

The prestressing steels are generally pearlltlc and fall somewhat between the above extremes, so that either

mechanism of the environmentally-induced failure may occur (depending upon the

specific environment and microstructure). Experimental studies and failure

analyses are the major means for determining which process occurs. The tests

from laboratory and field are presented separately in the following. A general

discussion is given afterwards.

2.1 LABORATORY CORROSION TESTS FOR PRESTRESSING STEEL

In the United States, published data on the corrosion testing of prestressing

steel is limited. A brief summary of the available information is given in

table 1. Test media, test parameters, and important results are outlined in

the table. The development of research in the United States on corrosion of

steel in PC is traced in the reports. In the early research, tests were developed for identifying the important metallurgical and environmental

factors. Only in tests recently .developed were the effects of the individual

factors measured. For example, the main purpose of the test conducted at the

Oak Ridge National Laboratory in 1975 [7] was to consider the effects of test

media and stresses (see table 2). Later, another series of tests were conducted at the Oak Ridge Laboratory [8] in which the effectiveness of coatings

were studied, and detailed information on failure modes were obtained. The

test results were mostly as expected, e.g. , the time to failure increases as the stress level decreases. However, the quantitative data presented in the

report is valuable for developing a general theory of the corrosion of steel

in prestressed concrete.

Treadaway [9] reported the results of a series of tests in which the variables

selected were water to cement ratio, cement type, and the amount of added calcium chloride. Various types of corrosion were observed. These were surface

corrosion, general corrosion, and pitting. However, the data for the breaking

loads from the strength test were highly variable in terms of the exposure

period. It has been known that reproducibility is one of the major difficulties in corrosion testing of prestressing steel.

A RILEM-FIP-CEB working group recently summarized all the studies carried out

between 1970-1978 and presented a report [10] at the 7th FIP Congress. Ammonium thiocyanate was recommended as the standard test medium for prestressing

steel. The recommendation was based on a series of tests for stress corrosion

by utilizing various test media including boiling nitrates solutions, hydrogen

sulfide solutions, and water. As was pointed out in the FIP report, tests with

ammonium thiocyanate were found to be the most reproducible.

3
<ion Sciidies of Prestressing Steel

Other Authors Experimental Significant

(year of Test Specimen Conditions Data & publication) & Media & Variables Results

Monroe & Verbeck [4] a. Prestressing steel wires 0 Applied stress was o Corrosion of prestressing

(1960) were exposed to solutions 1 .0 gPa. steel was found to be an

of calcium chloride, erratic process. Quanti- calcium hydroxide. 0 Most beams were in moist tative evaluation was sodium chloride, sodium storage for about six difficult

hydroxide

months

b. Prestressing steel wires 0 For beams, test variables o Tensile strength reduc- were in mortar or con- were cement type, tempera- tion of prestressing

crete beams containing ture, amount of calcium wire due to corrosion

between 0 to 4 percent chloride, and presence varied from 0 to 32 of calcium chloride of voids. percent

by weight.

0 Corrosion of prestressing

steel occurred whether

the wire was hard drawn

or stress relieved.

Godfrey [5] Pretensioned concrete beams o Wire strands were 9.7 o Oil tempered wires failed

(1961) with calcium chloride con- mm in diameter. through stress corrosion.

tents from 0 to 2 percent,

by weight0 Applied stress was 11.8 0 Hard-drawn stress relieved

gPa. wires failed through

pitting or general

0 Beams were placed in an corrosion. industrial atmosphere

for three years.

Moore, Klodt & a. Prestressing steel wires o Applied stresses varied o Stress cracking of the Hensen [6] were exposed to solu- from 1.0 gPa to 1.6 gPa. prestressing steel did

(1970) tions of calcium hydrox- not occur in chloride

ide, sodium chloride, sodium hydroxide, and hydrogen sulfide.

0 Wire strands were 9.7 mm

in diameter.

ion environment.

0 Cracking of prestressing

steel occurred after

short exposure times in distilled water into which hydrogen sulfide was bubbled. When calcium hydroxide was also added,

the cracking was accelerated

b. Pretensioned concrete

beams with sodium chloride contents of 3.5 percent, by weight.

o Same applied stresses

and wire strands as above

o Concrete cover over

the prestressing

strands varied from

13 to 51 mm.

o No direct correlation was found between applied load

and the amount of corrosion.

o Serious corrosion was observed even when the crack width in the surface

of the concrete was only

.10 mm. Pitting of the steel occurred

GRIESS [7] a. Prestressing steel wires o AISI 1080 steel wires were 0 Time to break was recorded

(1978) were exposed to solutions tested at constant strain

of ammonium nitrite. rates

o pH values were measured potassium chloride, hydrogen sulfide, sodium 0 Strain rate was usually

(see table 2).

sulfide, and hydrochloric

acid (more detailed

4.17 X 10.7“7s-I.

information given in table 2).

0 Temperature was varied.

b. Wires exposed to solutions o Corrosion rates were o Corrosion rates varied from

of sodium chloride. measured at 1000 and 5.1 to 23.1 u®/yt. sodium sulfate, as well

as pure water.

2000 hours.

o Hydrogen contents of tested wires were measured in

some cases.

Naus [8] Prestressing steel wires o Both stressed and o Useful data such as the (1979) exposed to solution of hydrogen sulfide, sodium unstressed tendons tested. failure loads, failure

times, and reduction in chloride, and ammonium 0 Some tendons were coated cross-section areas of nitrate

with organic coatings or Portland cement grout. failed tendons were

reported.

Survey of U.S. Literature

4
Table 2. Results Obtained from Constant-Strain Rate Tests with AISI 1080 Steel Wires [7]^

Time to

Test

Test

Medium

Temperature

(°C)

pH

Start/Finish

Break

(hr)

Load

(kg) Cracks

1 Air 21 0.2 3990 No

2 Air 21 55.5 4280 No

3 0.2 M NH4 NO3 21 5. 0/7.0 57.5 4100 No

4 0.2 M NH4 NO3 21 5. 3/7.0 66 .6 4010 No

5 0.2 M NH4 NO3 38 5. 3/7.

47.0 3980 No

6 0.2 M NH4 NO3 52 5. 3/7.

49.5 3970 Yes

7 0.2 M NH4 NO3 66 5. 0/7.

50.5 3970 Yes

8 0.2 M NH4 NO3 66 5. 0/7.0 5.2 3950 Yes

9 0.01 M KCl + CaO 21 11.9/11.5 55.3 3990 No

10 0.01 M KCl 66 5. 3/6.

60.8 3970 No

11 0.03 M KCl 21 5. 5/6.

58.1 4010 No

12 0.03 M KCl + HCl 21 3. 0/3.1 60.8 4010 No

13 0.1 M NaHS 03 21 4. 5/6.

44.0 3920 Yes

14 0.1 M II2 S + HCl 21 3. 0/3.0 6.6 1530 Yes

15 0.1 M H2

S 21 ~4 4.7 1130 Yes

16 0.001 M Na2

S 21 11 . 1 / 11.2 57.8 3920 No

17 0.001 M Na2

S + HCl 21 7. 4/7.

53.8 3990 No

18 0.001 M Na2 S + HCl 21 4. 3/6.0 19.3 3600 Yes

19 0.003 M Na2 S + HCl 21 4. 3/7.0 17.0 3490 Yes

20 0.003 M Na2 S + HCl ' 21 6.3/ 52.0 4010 No

21 0.003 M Na2

S + HCl 21 4.3/ 54.8 4010 No

22 Deionized H2 O 21 7 57.5 3980 No

23 Deionized H2 O + CO2 21 4. 0/4.0 55.8 4010 No

24 H2 O + CO2 +750 ppm H3ASO3 21 5. 1/5.1 57.6 3980 No

25b Zn plate, H

2 O 21 5. 8 / 6 .

60 .4030 No

26^ Zn plate, 0.2 M Na2

S 04 21 6 . 7/6.0 54.9 4030 No

CM u Corroded in H

2 O, three days 21 5. 9/6.

50.9 4010 No

a The

test

strain rate was 4.17 x 10“^/s,

8 where it was 4.17 x 10~^/s.

except in test No. 1 where it was 1.08 X 10~^/s; and in

^ Specimen except center 12.5 mm was zinc-plated before test.

^ Specimen was place in 8 mm glass tubing and surrounded by tap water for three days before

straining

5
2.2 FIELD TEST EXPERIENCES

The performance of prestressing steel in concrete under natural environments

may be different from that predicted by simulated laboratory tests. For this

reason, two types of structural systems subjected to special environments are selected for consideration which are oceanic structures and prestressed

concrete pressure vessels systems.

The U.S. Army Engineer Waterways Experiment Station conducted a series of tests on pretensioned beams as well as post-tensioned beams. The tests gave several

important findings even though there was no quantitative measurements of corrosion rates. Only the results for the post-tensioned beams [11] are discussed

here. It is felt that the conditions related to the post-tensioned beams may

be more unpredictable from the analytic viewpoint. The test beams were placed

at half tide elevation at Treat Island, Maine, and subjected to twice daily tidal

inundations plus freezing in air and thawing in sea water for 12-13 years. The

major results of interest were: (a) each strand of each beam was corroded to some degree; (b) the corrosion was not confined to the ends, nor concentrated

at certain spots but was spread over the entire length; (c) no quantitative

measurement was given, but it was stated in the report that the corrosion on

the strands was usually less than .127 mm for the strand with diameter of 4.88

mm; (d) one set of strands was protected with paper conduit and filled with

grease (this set of strands suffered the worst corrosion during the test); and

(e) analysis showed that the chloride content within the beams was less than

0.02 percent by weight of the grout. The pH values of the grout were in the

vicinity of 12.5.

Little information is available concerning the corrosion of steel in an operating prestressed concrete pressure vessel. One power station in the

United Kingdom suffered pitting corrosion, which was reported in detail [12].

The conclusion from the laboratory tests indicated that the corrosion was due

to the combined action of contaminating salts from the sea and the moisture from

the air. However, the effect of temperature on corrosion rates also should be

considered

.

2.3 NEEDED INFORMATION

While reviewed test results give useful information, several questions are posed

that require further investigation. Two of the most important ones which need

to be considered are:

1. Why does steel corrode when the prestressing strands are protected by the

metal ducts?

2. How to establish a resistance index for the prestressing steel? For

example, a NH4 CNS solution has been selected by FIP as the medium in a proposed standard test for establishing a resistance index. However, it

has not been demonstrated that this test simulates the corrosive conditions encountered in the field.

6
s

There are no simple answers for either of these questions. For the first, an Indepth Investigation should be made on the test conditions as well as the

failure processes. It Is possible that another corrosion mechanism along with

the accepted corrosion phenomenon may exist. For the second question the solution could be more complex. Fracture processes of specimens tested In different media can differ, e.g., stresses steel specimens corroded In H2S have been

found to be highly cracked, but were not as highly cracked by the NH4CNS test.

The approach of measuring the tensile strength In the air (Kjq) and In the specific environments (Kj3(;jc) is reasonable for the evaluation of the failure load

for a system. Creation of a set of curves for various environments could

be the first step in developing a resistance Index for specific environments.

7
3. CORROSION PROCESSES

Corrosion of steel in concrete can be separated into two major mechanistic

processes, diffusion and electrochemical reactions. The generally accepted

theory of corrosion will be briefly described in terms of these mechanisms.

Factors such as polarization that govern the corrosion rates are addressed

separately. It should be pointed out that the present theory has largely

evolved based on the phenomena observed. A more complete theory has not been

formulated because of the complex nature of the problem.

3.1 ELECTROCHEMICAL REACTIONS

The localized reactions at or near the surface have been proposed to be:

^ Oo + HoO + 2e" ->-2 (OH)" (cathode) (1)

2

^ z

Fe -> Fe"*^ + 2e~ (Anodic) (2)

Fe^"*" + 20H" -> Fe (0H)2 (3)

With further oxidation at the anode, Fe(0H)3 or Fe 304 may be obtained.

Fe2+ Fe3+ + e” (4)

oxidation

There would be other reactions involved in the corrosion of steel in concrete,

e.g., from the cloride ions, the role of chloride ion may preserve the charge

neutrality and promote pitting. It can also contribute to the breakdown of the

protection oxide layers, and in retarding the reformation of these films. A

recent study by the Federal Highway Administration [13], however, indicated

that high rates of corrosion of steel could occur in oxygen depleted limewater

solutions. The corrosion products in the tests were yellowish-green or greenblue in color. These products were found at anodic sites and were believed to

be ferrous chloride and hydrated ferrous chloride. Therefore, a new hypothesis

was proposed for the reactions near anodic sites based on the equations:

Fe + 2 Cl“ ^ [Fe2+ + 2C1“] + 2e“ (5)

followed by

[Fe"^ + 2 Cl“] + 2 H

2 O Fe(0H)2 + 2H'*’ + 2Cl" (6)

In contrast, recent tests conducted in NBS indicated that the chloride affected

the initiation of the corrosion process as described in the previous paragraph

[14].

8
3.2 DIFFUSION PROCESSES

Based on thermodynamic principles, diffusion is caused by a difference in chemical

potential. However, Flck's laws are usually used to express mathematically the

kinetics of the diffusion behavior of materials. For the problem under consideration, the components which need to be considered are: chloride ions, ferrous

(and/or ferric) ions, oxygen, and water. Each of these species should diffuse in

accordance with Fick’s laws. Certain modifications may need to be introduced

based on perturbing effects. Electric fields, for instance, may influence the

state of the ionic flow. The conditions near electrodes are extremely complex.

Various theories have been developed for the diffusive layers, e.g., quantum

theory was proposed to explain the bonding orbitals of diffused layers [15]. However, a rigid theory has not been established sufficiently well to explain the

entire phenomenon. Current theory has been developed largely based on classical

microscopic electrostatics and involved continuum concepts. Application of cor- relation functions to express the diffusion layers in the concentration solutions

is an example of this type of treatment. A similar approach will be described in

section 4 in the development of a computational model for evaluating corrosion

rates

3.3 FACTORS GOVERNING THE CORROSION RATES

3.3.1 Fundamental Concepts

When steel is immersed in an aqueous medium, it will devleop an electrode

potential at its surface. This potential plays an important role in determining

the rate of electrochemical reactions at the surface, e.g., the corrosion reaction, eq.(2). Under certain conditions, the corrosion rate of iron, expressed

as a current density, i^, is given by the Tafel equation.

where 3 and n are constants for a given metal and environment, both being

dependent on temperature and iQ is the exchange current. The over voltage, q, is defined as the difference between the electrode potential of the steel and

the reversible potential for reaction (2). This term maybe expressed by Nerst

equation

E = potential difference between electrodes,

Eq = standard electrode potential

R = gas constant, 8.31 J/°K

T = absolute temperature in °K

F = Faraday (96,500 Coulombs)

n = ionic valence of the species

^oxid»®red ~ activities of the metal in the oxidized and reduced states

q = 3 log iir, (7)

^oxid

( 8 )

where

9
In some instances, the rate of an electrochemical reaction is determined by the

transport of species to or from the surface. Such behavior is termed concentration polarization.

Concentration polarization increases as the diffusion rates of the ions decrease.

Considering the corrosion of steel in concrete and the quasi-static conditions

in concrete, concentration polarization probably has a significantly greater

effect on the corrosion rate than IR drop and activation polarization combined.

The effect of concentration polarization can be expressed as;

A4>c= In

^ nF

(9)

where

AcfiQ = potential difference between the electrodes due to concentration

polarization

i^ = limiting diffusion current (constant)

i = current

The electrical potential state of a corroded metal generally follows the path

shown in figure 1. The state could be active, passive or transpassive. Local

environments near the electrodes usually have the largest Local influence on

the corrosion state.

Steel in concrete is protected from corrosion by a surface film of Fe203 . The

passivating effect of this film has been discussed in many reports, e.g.,

refs. 16-17. It takes time for aggressive ions such as Cl“ to depasivate the

film. The overall steps involved in the depassivation are as follows: a)

transport of aggressive ions from bulk solution to the concrete-steel interface,

b) adsorption of chloride ions on the suface of the steel, followed by c)

chemical reactions causing depassivation. Details of these steps depend

strongly on the local conditions and the measures used for protecting the

reinforcing bars [e.g., ref. 18].

3.3.2 Effect of Chemical Variables

For many years, pH values and electric potentials (E) were taken to be the major

parameters controlling the corrosion susceptibility of steel in concrete. The

corrosive behavior of prestressing steels as a function of E and pH is indicated

in figure 2. It was recently realized that other factors, such as the presence

of chloride ion, may significantly affect the corrosion rates [1]. Bazant [20]

has used an expression for pH values near the surface of steel bars in concrete

in terms of the chloride concentration based on Gjorv's data [21]. Escalante,

et al. [14] recently investigated the relationships and constructed Interaction

surfaces between O

2

, Cl~, and pH, that indicated which one of these variables

controlled the initiation of corrosion under various conditions. The boundaries

for corrosive and passive states have been determined for pH values between 10.5

and 12.5. The research is still being pursued and findings will be useful in

developing a computational physical model for describing the corrosion process.

10
^— Transpassive

C

Passive

Active

CURRENT

Figure 1

Polarization curve for iron [19].
FIELD I - Field of corrosion in the electrochemical sense of the term,

' Field of possibility of change through general dissolution.

FIELD II - Field of passivation (covering) by Fe20a

,

- Field of possibility of change by local dissolution (pitting).

FIELD III - Field of immunity in the electrochemical sense of the term,

- Field of possibility of change through hydrogen embrittlement.

FIELD IV - Field of formation of Fe 3 04 .

- Field of the possibility of change by stress corrosion cracking.

Figure 2. Possible alternative corrosion processes in prestressing steels

under mechanical stress, as a function of the various fields

of the Pourbaix diagram [10].

12
4. QUANTITATIVE ANALYSIS OF CORROSION RATES

In this section, a mathematical model based on general corrosion theory is

briefly described. A simplified approach is proposed for evaluating the

corrosion rates. Design considerations for prestressed concrete are also

discussed

4.1 FORMULATION BASED ON GENERAL CORROSION THEORY

The description given here is largely based on Bazant's work [18]. In an electric field, Ohm's laws and the conservative laws for electric charges

are the fundmental laws to be considered. These laws are assumed to be

valid in the electrochemical process, i.e..

Xi = V(}) (10)

Vi = o (11)

where

X = resistivity of the substance

i = current density

(j) = electric potentials

Fick's laws with some modification are used for describing the diffusion

process. They are:

Jj = Cj V Uj + A jj (12a)

- VJj- J, V Uj + M .= o

j = 1, N

(12b)

where

J

CuAJ

t Jw

ra Sub . j

N

mass flux

diffusivlty constant

concentration

an expression for modifying the Fick's laws, e.g., charged ions in

the electric field.

time

water mass flux

sink or source terms

quantities of substance j

total number of substances under consideration

The important substances to be considered are oxygen, chlorides, ferrous (and

or ferric) ions and water. For each substance, the form of the Fick's law

may be slightly different, e.g., the 3rd term in equation (12b) vanishes for some cases. The rate law for the chemical reactions needs to be Included

with the expression:

13
mj = Kii-UiU (13)

where

Kir = a constant which is a function of activation energy.

The mass sink or source terms can be evaluated based on equation (13).

Equations (10) to (13) forms a set of equations that govern the field processes.

When the specific boundary and initial conditions are specified, the problem

is completely formulated. More complete details may be found in Bazant's

paper [20] . An important term is that representing the differential potential

between the electrodes. This term can be expressed in the following form:

where the superscripts c represents the condition at cathode and A represents

the condition at anode. A<()q, is a potential term that covers the effects

discussed in section 3.3.1.

If N is to be taken to be 4, there are a total of 13 equations including

equation (13). It is not a simple effort to solve such a large set of equations. Even if a solution is obtained, the results may not reflect the actual

corrosion behavior because of difficulties in selecting realistic values for

the coefficients. Therefore, a simplified approach for evaluating the corrosion rates is being pursued and is described in the following section.

4.2 AN SIMPLIFIED APPROACH FOR PREDICTING THE CORROSION RATES

In this section, a simplified scheme is proposed for evaluating the corrosion

rates. Several material functions are introduced which need to be determined.

Only conditions that are considered to be Important are covered. The proposed

scheme is based on the assumption that equations (1) through (4) describe the

entire corrosion process.

The diffusion equations, equations (12a) and (12b), for oxygen diffusing in

concrete still need to be considered. The sink or source terms may be neglected. The chloride concentration near the electrode must be evaluated if the

ions are diffusing to the steel surface, e.g., pretensioned beam without conduit. At the electrodes, the proposed equations are:

A(j) = A(})q + n^ log - n^ log (14)

dU

o Cq — + Cl (A()), Uq) + C2(U(,]^) (15)

dt

dUf

dt

(16)

14
Where Uq, Uf , and Ud represent the concentrations of oxygen, ferrous and

ferric ions, and chloride ions, respectively in the diffusive layers. The

values of the superscript b depend on the concentrations of oxygen and ferrous

and ferric ions at the boundaries of ionic and hydrous layers surrounding the

prestressing steel. Cq and Cf are the equivalent dif fusivities of oxygen, and

ferrous and ferric ions at corrosive site on prestressing steel. The parameters

ai and S2 define the thickness of effective ionic and hydrous layers around

corrosive sites. The variables C]^ , C2, C3 , and C4 are functions to be

determined.

It is anticipated that the functions C3 and C3,will fepresent physical

parameters. They should include the effects due to the adsorption of oxygen and

other implicit reactions at corrosion sites. C2 is dependent on depassivation

processes due to chloride ions. C4 has a function similar to C2, except it is

used to consider the effect of chloride ions as given in equations (5) and (6).

All of these functions will be determined analytically based on experimental

data.

Equations (14) to (16) are the basic equations to be solved. The boundary and

initial conditions should be based on the real physical conditions such as the

geometry of the ducts in the post-tensioned beams or the surface condition of

the beams without a metal conduit.

4.3 DESIGN CONSIDERATIONS

Severe steel corrosion will undoubtedly affect the performance of the PC systems.

Other than the reduction in sectional area, the major direct effect will probably

be the reduction of the strength due to the fracture of the steel. Using

as an indication of the effects of corrosion is a reasonable approach, (as noted

in section 2.3), but the interpretation of the magnitudes of KjgQQ from various

test environments under consideration could be difficult. There may be some secondary effects such as the reduction of the ductility of the prestressing

steel or an increase in the prestressing loss.

The effect of the geometric shape of the steel cracking on Kj(;; is another

problem which needs to be solved. The determination of Kjq as a function of the

original cracking shape has been investigated for prestressing steel [21].

Further work in this area is needed to demonstrate the validity of this approach.

15
5. SUMMARY AND NEEDED RESEARCH

The application of the principles of stress corrosion and general corrosion to

the steel in prestressing concrete has been discussed. The first step in estimating the failure time of a structural system because of corrosion of the steel

is to estimate corrosion rates assuming general corrosion.

A simplified approach based on mathematical modeling concepts, is proposed for

fulfilling such a goal. Further research must be performed before the model can

be numerically applied to practical problems and further developed to include

see and HE processes. The following is an outline of the needed research.

1. A more complete identification of the specific mechanisms of general

corrosion cell, See and HE processes of steel in concrete.

2. Perform corrosion tests in which the Important factors affecting the

corrosion rates are taken into consideration.

3. Determine the functions in equations (15) and (16) using the data

obtained in research need no. 2.

4. Validate the proposed model by comparing predicted corrosion rates with

experimental data.

The subject items listed above should be performed sequentially, except 1 and 2 may be performed simultaneously.
6 . ACKNOWLEDGEMENTS

The valuable information contributed by Mr. Edward Escalante, and Dr. Neville

Pugh, National Bureau of Standards, and Mr. Kenneth Clear, Federal Highway

Administration, are greatly appreciated by the authors. The authors are particularly grateful to Dr. Pugh for his detailed review and many constructive

suggestions in the preparation of this report. The sponsorship of this

research by the U.S. Department of State is gratefully acknowledged.

17
7. REFERENCES

1. Uhlig, H. H., "Corosion and Corrosion Control," 2nd edition, John Wiley

& Sons, Inc., 1971.

2. Pugh, E. N., "A Post Conference Evaluation of Our Understanding of The

Failure Mechanisms", Stress Corrosion Cracking and Hydrogen Embrittlement of Iron Base Alloys, NACE Conference held in France, NACE Publication, 1977.

3. Hertzberg, R. W., "Deformation and Fracture Mechanics of Engineering

Materials," John Wiley & Sons, Inc., 1976.

4. Monfore, G. E. and Verbeck, G. J., "Corrosion of Prestressed Wire in

Concrete," Research Department Bulletin 120, Portland Cement Association,

December 1960.

5. Godfrey, H. G., "Corrosion Tests on Prestressed Concrete Wire,"

Corrosion 17, 1961.

6. Moore, D. G., Klodf, D. T., and Hensen, R. J., "Protection of Steel in

Prestressed Concrete Bridges," National Cooperative Highway Research

Program Report 90, Highway Reserch Board, 1970.

7. Griess, J. C., "Corrosion of Steel Tendons in Concrete Presure Vessels - Review of Recent Literature and Experimental Investigations," Oak Ridge

National Laboratory, ORNL-NUREG-37 , June 1978.

8. Naus, D. J., "An Evaluation of the Effectiveness of Selected Corrosion

Inhibitors for the Protection of Prestressing Steels in PCPVs," Oak

Ridge National Laboratory, ORNL/TM 6479, March 1979.

9. Treadaway, K. W. J., "Corrosion of Prestressed Wire in Concrete," Br.

Corros. J., vol. 6, March 1971.

10. FIP, "Stress Corrosion Cracking Resistance Test for Prestressing Tendons,

Report on Prestressing Steel, September 1980.

11. O'Neil, E. F., "Durability and Behavior of Prestressed Concrete Beams,"

Technical Report No. 6-570, U.S. Army Engineer Waterways Experiment

Station, February 1977.

12. Fontain, M. J. et al., "Corrosion Protection of Prestressing Randoms,"

Paper 149/75, Experience in the Design, Construction, and Operation of

Prestressed Concrete Pressure Vessels and Containments for Nuclear

Reactors, University of York, England, September 8-12, 1975.

13. Clear, K. C., "Annual Progress Report for the Project, Cost Effective

Rigid Concrete Construction and Rehabilitation in Advanced Environments,"

Federal Highway Administration, September 1980.

18
lA. Escalante, E., Ito, S., and Cohen, M., "Measuring the Rate of Corrosion

of Reinforcing Steel in Concrete," National Bureau of Standards, NBSIR

80-2012, March 1980.

15. Bockris, J. O’M. and Khan, S. U. M., Quantum Electrochemistry, Plenum

Press, 1979.

16. Foley, C. L., Kruger, J., and Bechteddt, E. J., "Electron Diffraction

on Active, Passive, and Transpassive Oxide Films Formed on Iron," JECS114, 1967, pp. 994-1001.

17. Bloom, M. C. an Goldenburg, L., ’'F2 O3 and the Passing of Iron," Corro.

Sci. J., 1965, pp. 623-630.

18. Clifton, J. R., Beeghly, H. F., and Mathey, R. J., "Nonmetallic Coatings

for Concrete Reinforcing Bars," National Bureau of Standards, BSS 65,

August 1975.

19. Pourbaix, M., "Lectures on Electrochemical Corrosion," Plenum Press,

1973.

20. Bazant, Z. P., "Phsical Model for Steel Corrosion in Concrete Sea

Structures — Theory," Journal of Structural Div., ASCE, vol. 105, No.

ST6 , Proc. Paper 14656, June 1979, pp. 1137-1153.

21. Gjorv, 0. E. and Vennesland, 0., "Effect of Sea Salts on the Alkalinity

of Concrete," report, Department of Civil Engineering, Technical University, Trondheim, Norway, 1975.

22. Galligo, J. M. and Climent, J., "Factors Affecting the Corrosion of

Steel in Prestressed Concrete," Central Construction Materials Testing

Laboratory, Spain, 1980.

19
NB$«114A (REV. 2«8C) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 81-2390

2. Performing Organ. Report No, 3. Publication Date 11/10/81

4. TITLE AND SUBTITLE

Analysis and Modeling of Corrosion of Steel in Prestressed Concrete

5. AUTHOR(S)

Spencer T. Wu and James R. Clifton

S. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9.

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Department of State

10.

SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

il. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bl iography or literature survey, mention it here) Development of conceptual and mathematical models describing the corrosion of steel in

prestressed concrete is outlined. The application of the principles of stress

I corrosion and general corrosion to understanding the mechanisms involved in corrosion

j of steel in prestressed concrete is discussed. The first step in estimating the

failure time of a prestressed concrete structural system because of corrosion of the

reinforced steel is to estimate corrosion rates under various but realistic conditions.

A simplified approach based on mathematical modeling of concretes properties for

estimating corrosion rates is proposed.

Before the proposed mathematical model can be applied to practical problems information

is needed on the specific mechanisms of corrosion cell processes of steel in prestresse(^

concrete. In addition, well designed corrosion tests need to be performed in which all

the Important factors affecting the corrosion rates are considered.

12. KEY WORDS fS/x to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) concrete; corrosion; general corrosion; mathematical modeling; prestressed concrete;

prestressing steel; stress corrosion.

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