Atmospheric corrosion can seriously affect the performance of steel structures over long periods of time; thus, it is essential to evaluate the rate of corrosion and subsequent modification of dynamic properties of a structure over different time periods. Standards and codes represent the general guidelines and suggest general protection techniques to prevent structures from corrosion damage.
Structural steel tends to corrode naturally due to exposure to moisture and oxygen and the annual cost due to corrosion of steel structures, especially at coastal sites, can be tremendous. According to the last report of National Association of Corrosion Engineers (NACE), the global cost of corrosion was estimated about USD 2.5 trillion annually, which is 3.4% of the global gross domestic product (GPD) 
. However, structural systems can be protected against corrosion and exhibit adequate lifetimes by employing appropriate maintenance techniques and rational design.
The effect of corrosion is defined by the average depth loss; D, relative to the initial thickness and mass loss ratio as follows:
where m and m0 are the mass of corroded and uncorroded components in the same order and t0 is the thickness of the undamaged element. Corrosion mass loss can reduce the overall structural performance by changing the inherent structural characteristics of the system.
Recently, a study 
was conducted regarding the dynamic characteristics of two code-consistent steel truss structures with respect to corrosion propagation in marine environment. The results showed that the frequency was reduced for all modes of vibration and structures, considering maximum corrosion depth, D, equal to 1.4 mm. It is worth noticing that the first transversal mode of a truss roof was reduced by 17% which corresponded to the maximum D
and 20 years of exposure.
Material mechanical properties are modified after severe corrosion attacks. Recently, some researchers focused on the efficacy of the corrosion loss on the physical properties and seismic performance of corroded components through tensile strength testing 
. The value of material properties (yield and ultimate strength, module of elasticity and elongation) were declined with the growth of corrosion damage level. Additionally, 
showed that a structure can experience a decrease in the amount of energy dissipation and an increase in the maximum story drift ratio when the mass loss increases.
There are a number of corrosion wastage models for steel structures which relate the effective environmental factors to the exposure over time 
. Most of these models were calibrated in marine environments that have the highest rate of damage, and are impractical in other corrosive environments with different environmental conditions (different rates of sulfur, chloride ion or relative humidity). Indeed, there is scarce literature regarding the assessment of corrosion effects in urban and especially in industrial zones with medium rates of pollutants, whereas the European codes 
provide general recommendations, mostly related to appropriate surface protection techniques and materials to prevent corrosion occurrence, but there are no guidelines on the evaluation of thickness loss with time.
The objective of the present study is to provide a comprehensive review of available corrosion models of steel structures in the literature and study their effectiveness in structural performance in different atmospheric environmental conditions in long-term of exposure, focusing on low to high (C2 to C4) corrosivity classes. These levels can be expressed by the presence of corrosive factors in air from rural atmosphere (low rate of pollutant) to industrial atmosphere (high rate of pollutant, see Table 1).
Different corrosivity categories based on ISO9223 
||Typical Outdoor Atmospheric Environments
||Dry or cold zone with very low pollution and TOW *
e.g., deserts, Antarctic zone
||Temperate zone with low pollution (SO2 (μg/m3) < 5), e.g., rural areas.
|Dry and cold zone with short TOW, e.g., deserts and subarctic areas
||Temperate zone with medium pollution
(5 < SO2 (μg/m3) < 30) and low chloride effect, e.g., urban areas and coastal areas with low concentration of chloride ions
Subtropical and tropical zones with low pollution
||Temperate zone with high pollution (30 < SO2 (μg/m3) < 90) or considerable effect of chlorides, e.g., polluted urban areas, industrial areas, coastal areas without spray of salt water or, de-icing salts influences
Subtropical and tropical zone with medium pollution
||Temperate zones with high pollution levels (90 < SO2 (μg/m3) < 250); high chloride deposition rates, e.g., industrial areas, coastal and sea zones and sheltered positions on coastline.
||Subtropical and tropical zone with significant TOW, atmospheric environment with very high level of SO2 deposits (SO2 (μg/m3) > 250) including accompanying and production factors with profound effect of chloride concentration, e.g., extreme industrial areas, coastal areas and contact with salt spray
2. Corrosion of Metals
Metals are rarely in their elemental forms and they are combined with oxygen and other abundant chemicals to form thermodynamically stable ores. These tend to be oxides and mineral ores; hence, they are found in this form and must be purified in energy intensive processes (Figure 1
). Corrosion is defined chemically as a spontaneous chemical or electrochemical reaction between a material (generally metal or alloy) and a corrosive environment that leads to destruction of material 
Figure 1. Refining corrosion cycle of steel components.
The chemical reactivity of a metal often involves the transfer of its electrons to environmental electron scavengers and an electrochemical process that tends to see the electrons move in order to complete an electrical circuit, which can occur when certain electrolyte solutions come in contact with the metals, either from moisture, soils or gasses. The difference of potential between two areas of the metal, named cathodic (reduction of hydrogen or oxygen ions) and anodic (oxidation or dissolution of the metal), can produce an electric current which can result in thickness loss on the entire surface or locally 
Corrosion can be classified using different approaches. The most conventional classification divides the corrosion types according to their appearance which some of them can be identified visually and others are not visible (Figure 2
). The most common types of corrosion attacks on steel components can be expressed as follows 
Uniform corrosion: generating a uniform layer of rust (formation of oxide) over the surface of the metal exposed to atmosphere. In principle, uniform corrosion can reduce the rate of corrosion by limiting the contact surface between metal and the atmosphere. This is the most common type of corrosion in steel bridges.
Galvanic corrosion: When two metals with different corrosive potential are placed together with the presence of a corrosive environment (electrolyte), the current flow and hence corrosion damage occur.
Pitting Corrosion: One of the most common forms of corrosion with local attack which sometimes taking the form of deep holes (pits) into steel surface. This kind of corrosion in the presence of imperfection in steel components or dirt on its surface can engender cracks into the metal surface.
Crevice Corrosion: This type of localized corrosion occurs by the differences between ion concentration in dissimilar environments (different ion concentration) inside and outside of the small crevice.
Erosion Corrosion: When flowing of fluid with the relatively high velocity attacks over the surface of the metal, it can remove the coating film and accelerate the corrosion process.
Stress Corrosion: In the presence of corrosive environment and applied tensile stress, brittle cracking occurs into the metal.
Fatigue Corrosion: Repeated applied load with the corrosive environment causes stress concentration which leads to cracks into the metal.
Fitting Corrosion: When two surfaces are in close contact in the presence of load provoke the abrasion of the surfaces by oxide.
Intergranular Corrosion: The corrosion attack between steel grain boundaries which affect the mechanical properties of the material.
Figure 2. Prevalent forms of corrosion in steel structures: (a) uniform; (b) pitting; (c) crevice; (d) galvanic; (e) fatigue; (f) stress; (g) erosion; (h) intergranular; and (i) fitting corrosion.
This research focuses on the outdoor atmospheric corrosion as the most common form of corrosion in steel structures.
There are several factors that affect the rate and progress of corrosion including environmental effects such as temperature, moisture, atmospheric pollutants (sulfur and chloride), type of material (different grade of steel), protection techniques and presence of crevice, stress or pollutants. The presence of these detrimental factors initiate corrosion and thus, decrease the capacity and make tremendous economic losses 
. In the following section, a brief overview of the available models in the literature are discussed.
3. Corrosion Modeling
The existing numerical models are divided into two groups, namely heuristic and deterministic. Deterministic approaches are multi-scale models that account for the fundamentals of corrosion mechanisms to simulate the corrosion rate. Simulating the kinetics of a corroding system and/or metal-electrolyte interface to describe the corrosion rate can improve the robustness of the model. However, the model can become complex when several parameters are considered, referring to the interaction with gaseous and liquid environment, anodic and cathodic reaction of zinc and iron as well as diffusion of oxygen in immersed conditions 
. On the other hand, the heuristic models that the present study focuses on are described from the regression of measured data, e.g., weight loss measurements or corrosion rate as a function of varied environmental parameters, e.g., temperature, relativity humidity, time of wetness as well as chloride deposition and time. Thus, they are simple in calibration, though they cannot be applicable to environmental conditions other than the one that the model was calibrated for. In general, it is possible to divide this approach into first and second level. The first-level studies the model from the initial chemical compound which initializes damage. The second-level, which the present study focuses on, interests engineers and is obtained from the observation and statistical analysis of experimental data with respect to the time of exposure.
The power function models (heuristic) were calibrated in different environmental conditions. The problem of these models pertained to the deficiency of a sufficient number of environmental factors in the calculation of the corrosion loss. To calculate the corrosion depth (in μm or g/m2
) for the long-term, the time-dependent model that relates the corrosion loss at the first-year of exposure (A
) with time according to the statistical analysis of the experimental data was obtained as follows 
where A is the first-year corrosion rate, B is the coefficient which shows the long-term exposure effect considering the effect of protective products and environmental factors and t is time of exposure in years. From the mathematical point of view, if B > 1, it is clear that the corrosion process is accelerated. Alternatively, in the case of B < 1, the deceleration of process governs the corrosion loss and if B = 1, the corrosion rate is constant. Generally, when the coating layer is damaged, the corrosion process starts. This process ends when the rust layer covers all the steel surface.
As mentioned by Benarie and Lipfert 
, the B
coefficient shows the chemical activity and performance of the product layer on the metal’s surface, which is influenced by the environmental factors and pollutants. Based on the collected data in this paper, the estimation of A
(first-year corrosion rate) for steel was identified with concentration of sulfur ions (SO2
), and the calculation of the B
coefficient was found based on the average rain pH. Few years later, Feliu et al. 
proposed a similar power model (Equation (1)) accounting for the A value as the relation between different pollutants and metrological parameters in the form of binary interactions. Moreover, the value of B for different environmental conditions was discussed. Furthermore, Ma et al. 
coefficients by accomplishing several experiments on mild carbon steel with different distances from the sea in a tropical marine environment over 3 years. They showed that due to the presence of chloride ions (Cl−
) adjacent to the sea water (marine environment), the transition point (where the corrosion rate changes with respect to time) moved forward compared to the industrial atmosphere.
International Standard ISO 9224 in 1992 
, provides a bi-linear model which states that the corrosion loss is in accordance with two separated linear parts (see Equation (3)). This general model divides the corrosion process into the initial average corrosion rate (rav
) and subsequent years based on the average steady corrosion rate (rlin
) up to the 10th year. It is assumed that the corrosion rate will be diminished after 10 years due to the creation of rust layers. These average corrosion losses are revised in the latest reports of ISO in 2012 
where t is time of exposure during the structure lifetime.
A similar power-linear function method is studied in 2016 which appropriate for up to 50 years old structures and the results are valid just for C1 to C3 corrosivity classes 
. They concluded that after six years exposure of the structure in corrosive environment, the corrosion rate remained constant with respect to time (steady-state phase; rlin
, in Equation (3)).
Additionally, a new power-linear model was described by 
. In this case, the corrosion rate becomes linear after 20 years of exposure (Equation (4)) and it is given by:
where rcor is the corrosion rate in the first year of exposure in grams per square meter per year (g/(m2·yr)) or micrometer per year (μm/year) consistent with ISO9223 . Adjustment work reported by Albrecht and Hall Jr in 2003  where the steady-state point was modified to subsequent years after the first year of exposure (instead of year 10 in Equation (3)). A nonlinear time-dependent model was recommended by Soares and Garbatov  in 1999, was separated into three main parts (Figure 3). At the first stage (OA) there is no corrosion due to the presence of protection layer. The second part (AB) is the initiation of corrosion because of damage to coating layer. The slope of the plot (corrosion rate) decreases until the corroded layer appears on the entire element surface (zero corrosion rate at C). This model can be utilized in different environmental conditions (Equation (5)) and it holds that:
where τc is coating life, d∞ is the long-term thickness of the corroded component and τt is transition time which is calculated as d∞/tg∝.
Corrosion degradation model by Soares et al. 
Indeed, corrosion initiates after damaging the protection layer (coating) and continues until the connection between metal surface and atmosphere stops, and the corrosion rate becomes zero. This model is calibrated with the data on member of bulk carrier in marine environment 
A model was represented in 2003 by 
, considering the interaction between corrosion protection system and environment as pitting corrosion, before the coating layer was completely damaged. In other words, after the coating layer loses its effectiveness, the general corrosion starts, and the corrosion rate decreases due to development of corrosion products on the metal surface. A few years later a new model considering the interaction between environmental variables (TOW, sulfur oxide, chloride and annual temperature) was proposed which represented in the form of dose-function model as follows 
where TOW is annual time of wetness (h/year), T is air temperature (C) and A, B, D, E, F, G, H, J and T0 are coefficients proposed in the paper.
In Figure 4
, the comparisons among selected models in atmospheric environment are displayed from low to high class of corrosivity using MATLAB programming software 
Figure 4. Comparison between different corrosion models: (a) C2; (b) C3; (c) C4 corrosivity level.
The corrosion loss before the 10th year are relatively close in all approaches, except in Klinesmith et al. model 
. Results show that Klinesmith et al. 
model overestimated the corrosion loss in long exposure of time, and accordingly, this model is not appropriate for estimating the corrosion loss in long-term. It should be noticed that the ISO9224 (1992) model 
is similar to Albrecht and Hall Jr method 
with different transition point.