**2. Literature Review**

There is a wide range of corrosion problems in the industry, resulting from the different combinations of materials, environments, and service conditions [22]. Therefore, the concern about corrosion is not new. The science of atmospheric corrosion started with Faraday in the nineteenth century [23]. Another important contribution was made by Vernon who began systematic experiments in atmospheric corrosion in the 1920s [24]. In 1986, Benarie and Lipfert published their work on atmospheric corrosion [25], relating this phenomenon to the concentration of certain pollutants and pH of the rain. Subsequently, Feliu et al. developed regression equations for mild steel, zinc, copper, and aluminium [26].

There are several kinetic corrosion models that attempt to predict atmospheric corrosion over time: the general linear model [27], the power function models [28], and the power-linear models [29]. However, the corrosion process is influenced by multiple environmental factors [30]. Therefore, these corrosion kinetic models are valid at specific locations. When the environmental condition changes, the model may no longer be applicable [31]. It would be interesting to classify the aggressiveness of different atmospheres, which would allow preventive measures to be taken. Therefore, it is important to introduce the interaction parameters between environmental factors and corrosion rates for their efficient prediction.

In accordance with this approach, the ISOCORRAG program was launched in 1986 [32]. The ISO 156 technical committee developed this project with the intention of obtaining sufficient information to standardise atmospheric corrosion on metals and alloys. Four

international standards were created as a result of this project: ISO 9223 [21], ISO 9224 [33], ISO 9225 [20], and ISO 9226 [34]. Since then, these standards have served as practical guidelines and aids for the design of both structures and their corrosion protection. In September 1987, the Executive Body for the Convention on Long-Range Transboundary Air Pollution (CLRTAP) decided to launch an International Cooperation Program with the United Nations European Economic Commission (ICP/UNECE) [35] whose objective was to carry out a quantitative assessment of the effect of pollutants on atmospheric corrosion [6]. In addition, a third cooperative program was launched, named MICAT [36] (Ibero-American Atmospheric Corrosivity Map). Its objective was to understand the mechanisms that take place when this phenomenon occurs, to generate, with the data obtained, mathematical models to calculate corrosion as a function of climate condition or pollutant levels [13]. The three projects evaluated corrosion by measuring mass loss and were based on what was indicated in the standard for measuring SO2 or Cl− levels and other pollutant concentrations.

In 1992, the ASTM (American Society for Testing and Materials) published a study discussing an alternative method for measuring corrosion penetration, with models that are tighter and more rational than the traditional potential model [37]. In 2003, several workers compiled atmospheric exposure data from many research reports and journal articles [38]. R.E. Melchers, an engineer at Newcastle University, focused on studying the corrosion of metals in marine atmospheres in his studies in 2008 [39] and 2013 [40]. Later, Morcillo et al. [27] made a comprehensive compilation in the scientific literature on weathering steel atmospheric corrosion [6]. In addition, they developed Damage Functions to know the damage that a metallic structure can suffer depending on weathering conditions. In the subsequent years, there have been local experimental studies to characterise this phenomenon, such as those in Greece [41] and the Czech Republic [42].

The dose–response function is the most widely used. It directly correlates the influencing environmental factors with the corrosion parameters [43]. The basic form of this function follows the simple linear [36,44] or logarithmic–linear relationships [45]. However, many researchers also started to depart from judging the effect of each environmental factor separately and established a new multi-factor combination model [46,47]. A response surface model (RSM) takes into account the interactive effect and the non-linearity of the atmospheric corrosion process and allows a better approximation compared to conventional dose–response function models [48]. The models offer a closer approximation of corrosion rate by introducing different input variables. Temperature, humidity, sulphur dioxide concentration, and chloride concentration are typically used.

In conclusion, there are different options to predict corrosion rates of metals based on experimental input data. However, for the cases when pollutants' concentration is unknown, the options are limited. Time and cost constraints make the development of these measurements difficult as they would be unrepresentative when only completed at a specific point in time. As the environmental conditions continuously change, it is necessary to know their distribution over larger distances and longer periods of time. All corrosion related research carried out so far showed that there are certain factors that clearly influence the corrosion process. Regarding atmospheric corrosion, the factors include temperature, relative humidity, precipitation level, and pollutant concentrations (SOx, Cl−, etc.) [49,50]. A combination of parameters, such as Time of Wetness (TOW), is also used. TOW represents the fraction of time when relative humidity exceeds 80% and ambient temperature is above 0 ◦C (h/year) [51].

Climate has a significant influence on corrosion since some of the factors mentioned above depend on the climatic zone. A Köppen–Geiger classification [52] is the most popular technique for climate characterisation. According to this method, six precipitation levels can be distinguished [52]: desert (0), steppe (1), totally humid (2), summer dry (3), winter dry (4), and monsoon (5). Temperature and relative humidity are easily analysable climatic variables, and their values are generally accessible. There are also additional factors besides climate, mainly derived from human activities, whose importance is also significant. It is evident that the most populated and most-developed areas with accumulations of vehicles and high industrial activity have greater corrosive potential. It is also known that materials situated in areas closer to the sea tend to have a worse corrosion performance. Therefore, it is necessary to include these additional factors as well as they are critical for the successful operation of the model.

#### **3. Materials and Methods**

#### *3.1. Data*

This work seeks a more practical approach to characterise the environment. After a complete analysis of the data from existing experimental studies, it has been concluded that ISOCORRAG program data [32] should be used as it also analysed the corrosion in helical samples. Corrosion rates on helical samples have higher average corrosion rate values and do not limit corrosion loss to a single direction. This approach is useful in our case, as it more closely relates to galvanised structures used in civil engineering. Besides, it includes enough helical specimens distributed globally to represent a wide variety of cases. The project was carried out at more than 50 different locations in Asia, Europe, and America (Figure 1). During the ISOCORRAG program, the exposed specimens were used to determine the first-year corrosion rate. Nevertheless, some of the specimens were also used to study long term corrosion exposure. Grouped in different sets, triplicate samples were exposed every 6 months, and left for up to 1 year. The monitoring process lasted from 1986 to mid-1989.

**Figure 1.** ISOCORRAG program sample's location.

ISO 9223 and ISO 9224 standards are highlighted for this project. First, ISO 9223:2012 [20] divides the corrosivity of atmospheres into 6 categories. Each of these categories corresponds to a different corrosion level. For zinc, data are shown in Table 1.

**Table 1.** Corrosion rates of zinc for first-year exposure for different corrosivity categories according to ISO 9223:2012.


Second, ISO 9224:2012 proposes a relationship for long-term corrosion exposures. This relationship is based on the power function according to the following equation:

$$D = \mathbf{r}\_{\text{corr}} \ t^b \tag{1}$$

In Equation (1), rcorr is the first-year corrosion rate, *t* is the number of years to be analysed, and *b* is the environment and metal-specific time exponent.

### 3.1.1. Variables

Willing to characterise any location worldwide, its atmospheric corrosivity and climate need to be considered. For this work, three specific types of atmospheric environments have been introduced as binary synthetic variables, trying to represent the behaviour of sulphates-related pollution and chlorides deposition:


Regarding the climate characterisation, temperature, relative humidity, TOW, and Köppen–Geiger level of precipitation were the main characteristics, unified in a simple, accessible, and complete way. Therefore, a total of seven numeric predictor variables were set for the model: mean annual temperature, mean annual relative humidity, TOW, precipitation, industrial, marine, and urban. The variable to be predicted was the zinc corrosion loss during first-year exposure, directly taken from experimental studies, and its atmospheric corrosivity category, based on the standard. Each sample was characterised, following the rules mentioned above, as explained in Figure 2.

**Figure 2.** Flow chart for database creation and future locations characterisation.

A summary of variables is shown in Table 2. The mean annual temperature is represented as T\_annual and mean annual relative humidity as RH\_annual in the table.


**Table 2.** Information on new continuous and discrete variables added.

3.1.2. Data Analysis

Data quality and representativeness are crucial for modelling; otherwise, the results obtained would be inconsistent. Frequency distributions of the 4 discrete variables are shown in Figure 3. All possible combinations between different environment types (Rural/Urban, Industrial, Marine) have been observed. In addition, colours show the number of samples in each of the 5 possible precipitation levels. All precipitation levels were represented; however, there some combinations were represented more often than others (urban, industrial, and marine zone).

Regarding continuous variables, Figure 4 shows the geographical distribution of temperature and mean annual relative humidity in each location, according to the numerical values obtained. The data are obtained from web services that use weather stations spread all over the world. Worldwide distribution of cases has been achieved.

**Figure 4.** Analysis of continuous variables at each location. (**a**) Distribution of mean annual relative humidity. (**b**) Distribution of mean annual temperature.
