Modelling of corrosion protection for reinforced concrete structures with surface coatings/Gelzbetoniniu konstrukciju su pavirsinemis dangomis korozines apsaugos modeliavimas.
Kamaitis, Zenonas
1. Introduction
Deterioration of reinforced concrete structures exposed in man-made
or atmospheric aggressive conditions is a common problem in many
countries of the world. Frequently, due to corrosion, the resistance of
structures decreases much earlier than their expected service life and
the need to carry out repairs of degraded structures is increasing
exponentially.
The durability of reinforced concrete structures depends both on
the resistance of the concrete against physical or chemical attack and
on its ability to protect steel bars against corrosion. Many fundamental
works have been published on this subject. Several studies have been
conducted on modelling the corrosion processes and assessing the effect
of corrosion on the performance of concrete structures. The synthesis of
investigations on concrete and reinforcement degradation and general
guidelines for probabilistic durability design, for instance, is
presented in Dura Crete Project (Dura Crete 1998), a consortium of 12
European Union member states. Most available studies have been focused
on the corrosion of reinforcement caused by concrete carbonation and
chloride attack. The publications on corrosion of reinforced concrete
structures are very extensive and will not be discussed here.
Concrete is not chemically resistant and impermeable to gases and
fluids. In a number of situations, concrete and embedded steel needs
some additional protection against chemical attack which can only be
afforded by a barrier resistant to the action of the chemical agents
encountered. Several methods have been elaborated for anti-corrosion
works such as corrosion-inhibiting admixtures, non-reactive reinforcing
bars (stainless steel, nonmetallic or epoxy-coated reinforcement),
cathodic protection, re-alkalisation, desalination, various protective
coatings.
Impermeable barriers, which prevent contact with the external
attack, are among anti-corrosion protection methods currently being
adopted to reduce the risk of reinforcement corrosion or to protect a
whole concrete structure. Methods for improving the performance of
reinforced concrete structures by surface treatment or coatings have
been investigated for many years (e.g., Almusallam et al. 2002, 2003;
Chung 2004; Delicchi et al. 2004; [TEXT NOT REPRODUCIBLE IN ASCII] 1992;
Kamaitis 2007a, b; McCarty et al. 2004; Medeiros, Helene 2008; Raupach,
Wolff 2005; Remmele 2003; Rodrigues et al. 2000; Schiessl 1994;
Seneviratne et al. 2000; Vipulanandan, Liu 2005) and many standards are
published (ASTM, ACI, JIS, JASS, etc.) (Mays 1999). Generally, Standards
and Recommendations specify materials and methods of application and are
no more than general guides for choosing the coating for a particular
application. Much of the work mentioned above has been carried out on
the mechanical properties and durability of polymer-based materials,
surface preparation for coatings, coating adhesion to concrete, concrete
crack-bridging ability, permeability, and different coating systems
evaluation in laboratory or "in situ" conditions. The results
of research show that surface treatments delay and retard the rate of
deterioration and permeability to aggressive substances and can increase
the service life of structures when repair is required.
Time-dependent modelling of corrosion in reinforced concrete
structures are based mainly on two phases--initiation phase and
propagation phase with few sub phases. The latter include formation of
cracks and spalling of concrete cover as well as loss of steel
cross-section and/or bond between reinforcement and concrete. Over a
long period, this may result in structural failure. In case of a coated
structure, three levels of protection can be considered: protection
barrier, concrete cover and reinforcement itself. Note, that epoxy
coatings sometimes are used for protecting steel reinforcement. Fibre
reinforced polymer bars provide another option for corrosion protection
at the level of reinforcement.
However, there are only limited attempts to provide satisfactory
analytical methods to assess the durability of protective measures, as a
whole. In general, only the recommendations for selecting protective
coatings for exposure environments are presented. The current state of
research in resistance deterioration of protected structures remains
unsatisfactory and further research on the prediction of service life of
reinforced concrete structures with the various protective measures is
needed.
In this paper, a concept is introduced and used for considering
multi-level anticorrosion protection durability for evaluation and
service life prediction of reinforced concrete structures. The approach
takes into account the performance of protective surface barrier,
concrete cover and steel reinforcement as a whole that can be denoted as
corrosion protection system (CPS). Lifetime functions of each component
in the system can be used to predict the service lifetime of CPS. The
effect of recoating and repair of CPS components on extending the
service life of a whole protective system in aggressive environments is
also considered.
2. Limit state definition of reinforced concrete structures with
protective surface barriers
Design and verification of durability of new or existing reinforced
concrete structures are not simple. Corrosion is a stochastic process.
Durability of structures is influenced by:
* introduction of new conceptions, materials and construction
techniques, requiring repeated trials and errors as well as the tendency
to provide the structures at the lowest possible cost;
* very wide variation of exposure conditions during service life,
which depend on the situation of a structure and location of an
individual member within a structure;
* significant number and rates of deterioration mechanisms and
interactions, which result from combinations of the environment,
quality, size and configuration of a structure;
* manifestation of the durability problems after a long time when
the degradation of the existing structures is well advanced; very often
the causes of degradation are obscure, and the construction records or
condition survey data are missing;
* different levels of maintenance, that is directly related to the
condition state of the structures;
* gross errors during design, execution or operation.
[FIGURE 1 OMITTED]
Fig. 1 illustrates the life-cycle performance of a typical
reinforced concrete component. Once designed and constructed structures
undergo gradual degradation in resistance and serviceability. In
general, the performance of components decreases with time due to
mechanical, physical or chemical process. By using protective barriers,
it is possible to reduce the rate of degradation and to extend the
service life of structures exposed to aggressive environments. The
degree to which CPS will provide the durability of a structure in a
given environment is a function of the type of protective barrier, the
quality and the depth of concrete cover, and the degree to which the
degradation of steel reinforcement is acceptable. Unacceptable level of
reinforcement degradation is governed by material (or diameter) and bond
between reinforcement and concrete losses.
Generally, according to Codes and Recommendations corrosion of
reinforcement is not tolerated. However, the structures with corroding
steel are often observed in practice (e.g., Kamaitis 2002). Some typical
examples are shown in Fig. 2.
The necessity of protective barrier on a new or existing structure
can be based, for example, on the ratio t/[t.sub.d], where t and
[t.sub.d] are expected (or observed) and required (or designed) service
time of the structure, respectively. If t/[t.sub.d] [greater than or
equal to] 1, it is evident, no special protection measures are needed.
If t/[t.sub.d] = 0,8--1, it is believed, the level of performance can be
achieved only by modification of concrete cover and/or structural
detailing. If t/[t.sub.d] < 0,8, special protective barriers either
to the concrete surface or to the reinforcement to meet the durability
requirements should be provided.
[FIGURE 2 OMITTED]
The limit states of deteriorating structures are based on the
effect of actions, S(t), compared to materials or structural
time-variant resistance, R(t). The verification can be performed in
resistance or lifetime format:
g(t) = R(t)--S(t) = [R.sub.0][[phi].sub.R](t)[[theta].sub.R] -
S(t)[[theta].sub.S] > 0, (1)
g(t) = t[[theta].sub.t] - [t.sub.d] > 0, for all 0 < t [less
than or equal to] [t.sub.d], (2)
where g(t) is the margin of safety with g(t) > 0 denoting safe
and g(t) [less than or equal to] 0 denoting failure; [R.sub.0] is
component capacity in the undegraded (original) state;
[[phi].sub.R](t)--degradation function; [[theta].sub.i],--uncertainty of
the calculation models and errors in data observation and recording;
t--the time of assessment; [t.sub.d]--the design or target service life.
Reliability of deteriorating structures without and with protective
barriers is defined, respectively, as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (3)
P{t [greater than or equal to] [t.sub.2]) = P{[g.sub.2](t) > 0}
= P[[R.sub.0][[phi].sub.R2](t) > S(t)[[theta].sub.S]} [greater than
or equal to] [P.sub.t arg], for all 0 < t [less than or equal to]
[t.sub.d2], (4)
where [P.sub.targ] is acceptable level of structural reliability.
The time-dependent monotone decreasing degradation function
[[phi].sub.R](t) can be expressed in different forms (linear, parabolic,
square root, etc.) with the following boundary conditions:
at t = [t.sub.0], [[phi].sub.R1]([t.sub.0]) =
[[phi].sub.R2]([t.sub.0]) = 1,0;
at t = [t.sub.d], [[phi].sub.R1]([t.sub.d1]) =
[[phi].sub.R2]([t.sub.d2]) = [[phi].sub.min];
at [t.sub.d] > t > [t.sub.0], [[phi].sub.R2](t) >
[[phi].sub.R1]([t.sub.d]),
where [[phi].sub.min] is min acceptable deterioration function.
The greater [[phi].sub.R2](t) is, the more reliable structure with
prolonged service life can be obtained.
The effectiveness of protective barrier on the durability of
reinforced concrete structures can be expressed, for instance, by
rapport [[mu].sub.t2]/[[mu].sub.t1] > 1 or [t.sub.2]/[t.sub.1] >
1. The problem is to be able to assess the degradation level and service
life [t.sub.1] and [t.sub.2] for given situations.
Anticorrosion protective measures are costly. Costs of protection
may be a significant part of the overall lifecycle costs of a concrete
structure. Therefore, the benefits to be gained from special protection
should be balanced between required level of reliability and cost. The
design of optimum protection system can be based on wellknown
optimization problem:
[C.sub.tot] [right arrow] min
subject to P{t [greater than or equal to] [t.sub.d]} [greater than
or equal to] [P.sub.t arg],
where [C.sub.tot] is total direct and indirect costs including
inspections, repair and expected losses due to failure of the structure.
The objective of the optimization process is also to evaluate the
different protection scenarios. Many studies have been done to determine
optimal maintenance strategies for deteriorating structures. They are
reported in numerous publications and are beyond the scope of this
paper.
This section illustrates the importance of protective barriers for
the extension of service life on RC structures exposed to aggressive
environments. It is evident that detailed and realistic investigations
in this subject are needed. On the other hand, accurate predictive
analysis associated with corrosion protection measures for the
development of design procedures is of particular interest.
3. CPS model and assumptions
Fig. 3 represents the service life model of CPS exposed to
aggressive agents. It is obvious that the required protection ability of
CPS for reinforced concrete is governed by the resistance of all
component materials to the agents involved and penetration/diffusion
properties of protective barrier and concrete cover. Protective barriers
as well as concrete cover and steel in aggressive environments have
limited service lives.
The service life of CPS can be divided into 3 stages: service life
of protective barrier ([t.sub.b]), concrete cover ([t.sub.c]), and the
last phase during which an unacceptable loss of reinforcement section
has occurred ([t.sub.s]). Protective barrier is the most important and
extremely loaded component of a protective system. After failure of such
a barrier the lifetime of CPS is governed by degradation of concrete or
penetration of aggressive substrates through the concrete cover and then
by the rate of steel bars corrosion. The corrosion of reinforcement
relates closely to the deterioration and safety of the structure.
[FIGURE 3 OMITTED]
The basic assumptions made to model the durability of CPS are:
a--degradation function of CPS is independent of the load history;
only deterioration due to an external aggressive attack is considered;
b--the system consists of three non-identical components, i.e.
protective barrier, concrete cover and reinforcement; all components are
activated continuously upon failure of an operative component;
c--shape and rate of the degradation functions for protective
barrier, concrete cover, and reinforcement are specific and must be
known;
d--all components of system are repairable; the repaired components
are restored to an as-good-as-new condition (to initial performance
level), each time repair is applied;
e--failure of CPS is the result of failure of all components making
up the CPS.
Based on these assumptions, a model representing service life of
CPS was chosen and is shown in Fig. 3. This model presents the
protection ability as a function of time. The CPS is composed of three
components, each having different performance curves with several
alternative rehabilitation strategies. In general case, we assume that
reinforcement is also repairable.
4. Service life formulation of CPS
The service life of CPS can be expressed by Eq. (Fig. 3):
[T.sub.CPS] = ([t.sub.bm] + [t.sub.cm])[v.sub.t] + [t.sub.sm], (5)
where [t.sub.bm] is service time of protective barrier as a
function of type and thickness of cover; [t.sub.cm]--time for concrete
deterioration as a function of concrete cover quality and thickness;
[t.sub.sm]--time for reinforcing bars to cause acceptable corrosion
level as a function of environment conditions, type of structure and
reinforcement. It is obvious that [t.sub.bm], [t.sub.cm], and [t.sub.sm]
can be different lengths of time.
[FIGURE 4 OMITTED]
Quality and thickness of a protective barrier and concrete cover
are known to vary spatially over the structure's surface. In
practice, the deterioration process also is not uniform and at any time
different parts of protection system will be in different states. It is
unlikely that deterioration of these components will take place in the
same critical sections. Hence, the corrosion resistance of the system
composed of protection barrier and concrete cover is not equal to the
sum of corrosion resistance of individual components (Fig. 4). Then, a
chance that the critical sections in the protective barrier and concrete
cover match-up is small and can be evaluated by the parameter
[v.sub.t] = actual value/predicted value = [t.sub.bc]/[t.sub.bc.d]
[greater than or equal to] 1,0, (6)
where [t.sub.bc] and [t.sub.bc.d] (= [t.sub.bm] + [t.sub.cm]) are
actual and predicted (design) service time of protective barrier +
concrete cover, respectively.
Note also that [t.sub.bc.d] is defined by standard testing
procedures and naturally reflects some conservatism.
Components of protection system allow controlling the corrosion
rates of structures by periodic recoating or repairing the components
over the lifetime of a structure. Taking into consideration the number
of recoatings, [n.sub.b], repairs of concrete cover, [n.sub.c], and that
of reinforcement, [n.sub.s], during the required service time of
structure, [t.sub.d], the main design time of protective system can be
found as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (7)
The limit state of CPS or its components is defined as
g(t) = [R.sub.CPS](t)[[theta].sub.R] - [S.sub.cor]
(t)[[theta].sub.S] > 0 (8)
or in life-time format
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (9)
The variables [S.sub.cor](t) and [R.sub.CRS](t) entering the Eqs
(8) and (9) can be of any quantities and expressed in any units. In the
design or verification of durability of CPS or its components,
[S.sub.cor](t) can be penetration depth [x(t)] or concentration of
aggressive agents on the depth x ([c.sub.x]), extent of barrier cracking
or delaminating, concrete cover cracking/spalling or reinforcement
corrosion intensity. [R.sub.CRS](t) is the resistance of a system to
corrosive actions or limiting performance criteria which can be
interpreted as the actual depth of protective barrier ([d.sub.b]) or
concrete cover ([d.sub.c]), critical concentration of aggressive agents
on concrete or reinforcement surface ([c.sub.cr]), admissible level of
barrier delaminating or concrete cracking/spalling, loss of rebar
diameter.
It is evident that aggressive environmental service actions as well
as physical and geometrical parameters of CPS components are random
variables. Hence, to preserve serviceability and safety of protection a
reliability analysis is indispensable.
In the probability based approach the distribution of [T.sub.CPS]
according to Eqs (5) and (7) can be found, if the distributions of the
random variables [t.sub.bi], [t.sub.ci] and [t.sub.si] are known.
Statistical parameters should be obtained from laboratory or field
experimental data.
In general, the probability distributions of the degradation of
building materials and components are close to the normal or lognormal
distribution. For instance, if the probability distribution of the time
to first failure of CPS components is normal, the normal should be and
time to failure distribution of CPS. The service time of CPS and its
components in Eqs (5), (6), (7) and (9) are presented in terms of their
mean values. Then, the time to the first failure of component j is
defined as
[t.sub.j] = (1 - [[beta].sub.tj][V.sub.tj])[t.sub.jm], (10)
where [beta]. and V. is safety index and coefficient of variation
of respectively.
The reliability index of component j is defined as
P{[t.sub.j] [greater than or equal to] [t.sub.dj]} =
P{[R.sub.j](t)[[theta].sub.Rj] > [S.sub.cor.j](t)[[theta].sub.Sj]} =
[PHI]([[beta].sub.tj]) [greater than or equal to] [P.sub.t arg.j]. (11)
For the given acceptable probability [P.sub.targ.j], the time to
the first failure [t.sub.j] of component j can be determined.
That the protection system will work for the prescribed period of
time, [t.sub.d], the following expression should be verified
P{[T.sub.[CPS] [greater than or equal to] [t.sub.d]} =
P{[[summation]t.sub.j] [greater than or equal to] [t.sub.d]} =
[PHI]([[BETA].sub.T]) [greater than or equal to] [P.sub.targ], (12)
where [P.sub.targ] is a target reliability indice, which is based
on the failure consequences of protection system.
According to Eq (6), the parameter [v.sub.t] can be determined:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (13)
5. Life cycles of CPS components
It is obvious that the shape and rate of degradation functions in
Eqs (8) and (9) are specific for protective barrier, concrete cover and
reinforcement bars are strongly influenced by nature and quality of
structure components as well as exposure conditions, which define the
degree of protection required.
Table 1 gives a summary of the effects of some destructive agents
on reinforced concrete components and polymer coatings. This information
is based on literature sources as well as the author's experience
and is only general information to be used as the basis for beginning an
investigation. It is obvious that the number of physical and chemical
destructive agents which can attack structure components is large and is
not the only factor which determines the rate of attack, but also
embodies the chemical nature and concentration of the substances,
temperature, pressure, as well as their cyclic changes.
It is necessary to note that well-designed concrete structures,
made with good quality concrete are relatively impervious to most
waters, soils, and atmospheres. Good quality concrete can be made
resistant by a proper proportioning, compacting, curing, and use of
different admixtures to yield adequate strength and low permeability.
Although permeability to liquids and gases may vary considerably among
different concretes, even the best concretes have always some degree of
permeability. Penetration of gases and fluids into the concrete is
frequently accompanied by chemical reactions mainly with cement or by
physical actions due to formation of oxides, salts or ice, causing
expansion and disintegration of the concrete.
Steel corrosion in reinforced concrete leads to concrete cover
cracking/spalling, to a reduction in bond strength and a reduction in
bar cross-sections. In practice these degradations are randomly
distributed in terms of location and intensity.
Protective barriers such as polymer coatings are also not
absolutely resistant to the action of all agents encountered and, in
general, also have limited service lives. Various thermoplastic and
particularly thermosetting polymers (e.g., epoxies, polyesters,
urethanes) are proposed to use as protective coatings. Disintegration of
coatings named in the table is specified as degradation by swelling,
dissolution, scission or weathering involving also the diffusion
phenomena. However, resistance to attack is, in general, much better for
polymers than for cement concrete or steel.
Given the complexity of the deterioration of CPS components, we
will consider that the rate of corrosion of protective barrier, concrete
cover and steel reinforcement may be expressed, for instance, as
corrosion rate, X, that is, the reduction of the mechanical strength due
to physical/chemical degradation or permeability/diffusion due to the
transfer of destructive agents, even without compositional changes,
which can be viewed as a degradation of mechanical properties and
cross-section (thickness) losses per unit of time. Corrosion rate is a
function of many variables and usually should be determined by
mathematical models of the physical transport processes and of empirical
data.
The survivor function in Eq. (5) or (7) of polymer protective
barrier in aggressive chemical solutions, for instance, can be expressed
by an exponential distribution (Kamaitis 2007b):
[x.sub.b](t) = [d.sub.b] [1 - a exp(-[[lambda].sub.b]t)] for
[t.sub.b] > t > 0, (14)
where[x.sub.b](t) is attack-penetration depth; [d.sub.b]- coating
thickness at t = 0; [[lambda].sub.b]--the rate of coating degradation.
In a probability-based approach and normal distribution of
variables, the survivor function of protective coating can be expressed
as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (15)
where [d.sub.bm], [x.sub.bm], [[theta].sub.dm]. and
[[theta].sub.xm] are the mean values and [sigma](*) is standard
deviation of *; [P.sub.targ.b] is barrier target reliability.
Design and detailing of concrete cover and reinforcement in the
presence of concrete deterioration due to sulphate attack, freeze-thaw
cycling, and reactive aggregate reactions as well as reinforcement
corrosion caused by concrete carbonation and chloride penetration have
been treated by a number of authors and reported in numerous
publications. Recently, degradation models for the application of
de-icing salts, atmospheric C[O.sub.2] or marine exposure have been put
forward which include two or three stages of initiation, crack formation
and propagation to a defined limit state. In general, the last two
components --concrete cover and reinforcement can be designed separately
according to numerous recommendations (e.g. Dura Crete 1998). For
instance, for atmospheric or chloride induced corrosion (bridges,
parking garages) the increase of carbonation or chloride penetration
depth, [x.sub.c](t), with time leading to depassivation of reinforcement
can be predicted using simplified equation:
[x.sub.c] (t) = [[lambda].sub.c][t.sup.n] for t > [t.sub.b] (16)
or
[t.sub.c] = [nth root of [d.sub.c]/[[lambda].sub.c]], (17)
where [[lambda].sub.c] is a constant; [d.sub.c]--thickness of
concrete cover; n--exponent of time.
Similar approach can be used for modelling concrete degradation in
liquid aggressive solutions.
Once the passivity of reinforcement has destroyed, some lap of time
is needed to cause the concrete cover cracking or spalling. This time
can exceed the value of 6 years (Bentz 2003) or can be taken, for
example, as [10T.sub.cr1] (Val, Stewart 2003), where [T.sub.cr1] is the
time to first concrete cracking. At this stage, the loss of bar diameter
generally is very low (e.g. Andrade et al. 1993; Allam et al 1994;
Maruyama 1999; Almusallam 2001) and it is very unlikely the corrosion
will considerably affect the strength of a structure.
When the concrete cover has cracked or spalled, the intensive
corrosion of exposed reinforcement is initiated. As a corrosion of steel
bars proceeds, the rust layer increases in thickness leading to loss of
cross-sectional area and relating closely to the deterioration of a
structure (e.g. Jokubaitis 2007). This non-linear phase is controlled by
diffusion of oxygen or aggressive substrates through the rust layer.
This process can be modelled in a simplified form as
[x.sub.s](t) = [[alpha][lambda].sub.s][t.sup.n.sub.s], for t >
[t.sub.b] + [t.sub.c] (18)
or
[t.sub.s] = [nth root of [d.sub.s.adm]/[[alpha][lambda].sub.s],
(19)
where [x.sub.s] (t) is the depth of steel corrosion;
[d.sub.s.adm]--maximum admissible depth of corrosion which depends on
the type of structure and that of reinforcement; [[lambda].sub.s] the
rate of uniform steel corrosion; [alpha]--a coefficient depending on the
type of attack: for uniform corrosion [alpha] = 2, in the case of
pitting [alpha] = 4-8. The values of both parameters [[lambda].sub.s]
and n are influenced by environment and type of reinforcement.
It should be pointed out that it is difficult to decide an
acceptable limit for steel reinforcement corrosion. As it was mentioned
above, according to Codes and Recommendations, corrosion of
reinforcement is not tolerated. Admissible depth of corrosion frequently
is expressed as limiting value of reinforcement diameter or area. The
cross-sectional area reduction by 25-30% of reinforcement bars seems to
be the failure criterion of corrosion-affected reinforced concrete
structures (e.g. Amey et al. 1998; Gonzales et al. 1996; Val, Stewart
2003). In epoxy coated reinforcement the deterioration of epoxy coating
can be accepted as a limit state. The admissible depth of reinforcement
corrosion is always the matter of discussion.
Similar to protective barrier [see Eq (15)] the probabilistic
analysis for concrete cover and reinforcement degradation also can be
carried out. It is obvious that suitable examinations are necessary for
each deterioration factor to fix the mean values and their dispersions.
Optimal life cycle performance of CPS can be achieved in many ways.
Different barrier materials, concrete compositions and reinforcement
corrosion criteria as well as repair scenarios including initial and
maintenance costs, can be considered to obtain desirable protection
abilities for particular applications. This will be not discussed herein
due to the limited space of paper.
As far as we know, it is very few investigations, which combine the
consequences of protected structure corrosion with SLS or ULS, although
a number of studies has been conducted on durability of protective
coatings, as it is mentioned above. A classification of structures
according to the type of deterioration and consequences of failure
should be considered. In a high aggressive environment for important
structures, including prestressed concrete structures for which
corrosion of steel reinforcement is not allowed, for SLS the
delaminating of coating, depassivation of steel in concrete or the
concrete cover cracking/spalling can be accepted as the end of service
life. A possible approach to modelling the durability of ancillary
components is to take into account visible degradation of reinforcement
based on safety or appearance requirements of a member. For ULS loss in
reinforcement cross-section or bond strength is generally accepted
(Coronelli 2002).
6. Illustrative example
To illustrate the application of CPS probabilistic analysis a
semi-realistic reinforced concrete storage rectangular tank for
industrial inorganic acid water is considered.
Given: sulphuric acid concentration of [c.sub.0] = 49 mg per litre
and pH ~3. Concrete B35, cement content C = 400 kg/[m.sup.3]; W/C =
0,42; [k.sub.CaO] [approximately equal to] 620 gr; D = 5,76 x
[10.sup.-2] [cm.sup.2]/h. Other data on statistical parameters are given
in Table 2.
The target level of reliability of CPS components is taken as
[P.sub.targ] = 0,9 ([BETA] = 1,28). Due to short service time of steel
reinforcement in acid environment, the initiation of reinforcement
corrosion is accepted as SLS. Therefore, the third term in Eq (5) or (7)
disappears. For simplicity we assume that [v.sub.t] = 1,0. The design
service time of reinforced concrete storage structure [t.sub.d] = 30
years.
1. Concrete cover degradation depth
It is assumed that deterioration will lead to a uniform reduction
in the thickness of cover. Substituting in Eq (15) the relevant values
for concrete cover ([d.sub.bm] = [d.sub.cm]; [x.sub.bm](t) =
[x.sub.cm](t)), the following equation is obtained P{[t.sub.c]} =
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Solving this expression, we can find the unknown mean value of
deterioration depth [x.sub.cm](t) = 15,15 mm.
2. Service life of concrete cover
Degradation of concrete cover can be expressed using Eq (16), where
n = 2 and
[[lambda].sub.c] = [square root of [2Dc.sub.0]/[CK.sub.CaO]] =
[square root of 2 x 0,00576 x 0,049/400 x 0,62] = 0,0048cm/[h.sup.1/2].
Substitution of previously obtained value of [x.sub.cm](t) and
computed value of [[lambda].sub.c]c into Eq (16) gives the mean time
[t.sub.cm] = 11,4 years. Then
[t.sub.c] = [t.sub.cm] (1 - [[beta].sub.t][V.sub.t]) = 11,4(1 -1,28
x 0,3) [congruent to] 7 years < [t.sub.d].
The structure needs additional protection coating against acid
attack.
3. Design ofprotection coating
It is suggested to use a three-layer coat based on IKA resin. The
mean thickness of coating is 1,0 mm, [V.sub.d] = 0,12. The reliability
of coating can be verified using a similar procedure as for concrete
cover. P{[t.sub.b]} =
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
from which the mean deterioration depth of coating [x.sub.bm](t)
[congruent to] 0,61 mm.
Eq (14) gives deterioration depth of coating in acid water, where a
= 1 + [[lambda].sub.b]t. Then deterioration mean depth is
0,61 = 1,0[1--(1 + 0,131 x t) exp(-0,131 x t)],
from which the mean service time of coating [t.sub.bm]
= 15,7 years.
The service time of coating is expressed as [t.sub.b] = [t.sub.bm]
- [[beta].sub.t][V.sub.t]([t.sub.bm] - [t.sub.cm]) = 15,7 -1,28 x
0,3(15,7 - 11,4) [congruent to] 14 years.
When [t.sub.b] + [t.sub.c] = 14 + 7 = 21 < [t.sub.d], the
recoating at the age of 14 years should be done. Assuming that the
recoating time is negligible, further coating deterioration and failure
at 28 years is expected.
4. Service life of CPS
Mean service life of CPS is calculated as
[T.sub.CPS] = 2 x [t.sub.bm] + [t.sub.cm] = 2 [lambda] 15,7 + 11,4
= 42,8 years, and reliability of protection system is
[P.sub.CPS] {[T.sub.CPS] [greater than or equal to] [t.sub.d]} = (2
x 14 + 7) = 35 > [t.sub.d] = 30 years.
7. Conclusions
Based on this study, the following conclusions can be drawn:
1. Deterioration of reinforced concrete structures exposed in
man-made or atmospheric aggressive conditions is a common problem in
many countries of the world. Frequently, due to corrosion, the
resistance of structures decreases much earlier than their expected
service life. One of the ways to protect reinforced concrete structures
from corrosion is to use protective coatings. In current practice, the
use of coatings is based on the standard recommendations in the proper
choice of the correct type of the coating material for the particular
application. A simplified and unified design procedures based on the
mechanism of degradation for the full range of reinforced concrete
structures exposed in various aggressive conditions is a more rational
way. Design of durability of concrete structures with protective
coatings needs to be established.
2. A model of deterioration and service life prediction of
corrosion protection multi-level system, which is represented by
protective surface barrier, concrete cover, and steel reinforcement
itself, of reinforced concrete structures was developed [Eqs (6), (7),
(8) and (9), Fig. 3]. The model relates the entire service life of
corrosion protection system to the rate of degradation of its
components. Reliability based assessment of protection system taking
into account its components degradation is indispensable [Eqs (10),
(11), (12), (13)]. Variables in the model are uncertain and must be
described using probability distributions.
3. The model developed may be applied to a variety of new or
existing structures in order to predict the time to first
repair/rehabilitation of reinforced concrete structures and to develop
reliability-based corrosion protection systems. Although the practical
use of this model requires further study. Degradation models and their
characteristics, including failure rates, [[lambda].sub.i], must be
identified for a particular structures (transportation structures,
marine structures, chemical storage tanks, pipes, sewers, and other
facilities) and exposure conditions. It is believed, when these studies
are conducted the variables to be investigated will be consistent with
the proposed concept of multi-layer protection system and will provide
more realistic service-life predictions and adequate basis for
anticorrosion protection design. Since protection measures are costly
decisions, final protection system should be taken into analysis and
economic considerations.
DOI: 10.3846/1392-3730.2008.14.23
Received 7 Jan 2008; accepted 8 Oct 2008
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[TEXT NOT REPRODUCIBLE IN ASCII.] [Kamaitis, Z. Repair and
strengthening of structures and buildings by synthetic resins]. [TEXT
NOT REPRODUCIBLE IN ASCII.] 280 c.
Zenonas Kamaitis
Dept of Bridges and Special Structures, Vilnius Gediminas Technical
University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania, e-mail:
zenonas.kamaitis@ts.vgtu.lt
Zenonas KAMAITIS. Dr Habil, Prof Emeritus at the Dept of Bridges
and Special Structures, Vilnius Gediminas Technical University (VGTU),
Lithuania. Member of IABSE since 1999. Author and co-author of more than
160 publications, including 6 books. Research interests: special
structures and bridges, structural analysis, materials, durability,
monitoring, and refurbishment.
Table 1. Physical and chemical effect on corrosion protection
components by various agents
Polymer Cement Steel in
Effect coatings concrete concrete
Acids DS DR IC
Alkalis DS NH NH
Salt solutions NH NH IC
De-icing salts NH scaling IC
Water DS NH C
Sea water DS D C
Fats, oils, wastes DS DS C
Gases (C[O.sub.2], Cl, DS moist
S[O.sub.2], diesel) DS concrete C
Freezing and
thawing NH D NH
NH = not harmful; D = disintegrates; DS = disintegrates slowly;
DR = disintegrates rapidly; C = corrosion; IC = intensive
corrosion.
Table 2. Statistical parameters of random variables
Parameter * Mean COV
Concrete cover, [d.sub.c] mm 22,2 0,15 determined
Polymer coating, [d.sub.b] mm 1 ,0 0,12 determined
Rate of degradation,
[[lambda].sub.c]
cm/[h.sup.1/2] 0,0048 0 computed
[[lambda].sub.b] 1/year 0,131 0 determined
Time to failure 0,3 assumed
Model errors, [[theta].sub.d] 1,0 0,1 assumed
[[theta].sub.x] 1,0 0,15 assumed
* all parameters are assumed as normal distributed.
