The science of pipe corrosion: A review of the literature on the corrosion of ferrous metals in soils

Corrosion Science 56 (2012) 5–16

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Review

The science of pipe corrosion: A review of the literature on the corrosion of ferrous metals in soils I.S. Cole ⇑, D. Marney CSIRO Materials Science and Engineering, Private Bag 33, Clayton South, Victoria 3169, Australia

a r t i c l e

i n f o

Article history: Received 18 September 2011 Accepted 3 December 2011 Available online 11 December 2011 Keywords: Corrosion Soils Moisture content Resistivity Oxygen A. Iron

a b s t r a c t The paper reviews the literature that may assist in forming a multiscale model of corrosion in soils. This model should take into account macro-environmental processes (rainfall, etc.), soils processes (water movement, oxygen transport, etc.), processes within the oxides, and the electrochemical activity occurring at the metal surface. The literature reviewed includes traditional corrosion research such as surveys and historical analysis of buried pipelines, scientific exposures of buried metal, results from buried sensors, and laboratory studies aimed to duplicate soil exposures. Also included are wider studies on water and solute movement in soils, and oxygen transport through soils. Crown Copyright Ó 2011 Published by Elsevier Ltd. All rights reserved.

1. Introduction The corrosion of ferrous metals in soils is a major problem for owners and managers of water, sewerage and oil and gas distribution systems. For example, Kirmeyer et al. [1] reported that water utilities in the United States of America (USA), replace 0.6% of their water mains each year, with the major cause of replacement being the condition of aging pipes. Kirmeyer et al. also noted that in 1992, 48% of water pipes were spun cast iron (and 19% ductile iron), and that these were considered the most susceptible to corrosion. The most recent statistics for Australia, suggest that there is around 260,000 km of pipelines used by water utilities, and around 80% of these are buried – of this >70% are of some form of ferrous metal, with the most critical transmission mains generally constructed of ferrous metal; i.e. around 150,000 km for a population of around 22 million [2]. The most common corrosion failure mechanism for buried ferrous pipes is localized corrosion leading to leaking [1,2]. The study of the corrosion of buried pipes has a long and substantial history. However, while much detailed information has been collected this has not lead to the development of a comprehensive understanding or model of corrosion in soils. Corrosion in soils is a multiscale process: at its core is the electrochemical process at the metal surface, which is highly influenced by film/droplet formation on the metal, the geometry and liquid phase chemistry of such films, as well as the development of oxide layers on the metal surface. The ⇑ Corresponding author. E-mail address: [email protected] (I.S. Cole).

metal/moisture environment is in turn controlled by the local micro-environment and in particular the dynamics of moisture, oxygen and other species migration through the soil to the metal surface. Lastly, the macro-environment (in terms of rain and temperature) will influence the soil conditions. This review aims to support the development of a multiscale model of the corrosion of ferrous metals in soils. Given that critical failures are due to pitting the models would focus on localized rather than general corrosion. Such a model would need to encompass: (1) Electrochemical activity occurring on the soil facing surfaces of buried ferrous structures such as pipes and tanks. (2) The processes on the metal pipe surface, such as oxide build up, that affect electrochemical activity and promote localized corrosion. (3) The impact of local macro-environmental parameters such as temperature, humidity, soil salinity/pH/porosity, cation exchange capability, upon surface processes. These environmental parameters are controlled by soil-to-metal, soil-toliquid and soil-to-air interactions. (4) The influence of general external environmental factors such as rainfall, diurnal or seasonal variations in temperature on the local and surface interface between the metal and the soil. This review addresses the corrosion of steel and cast iron pipes, however, the emphasis is on research that can provide information relative to the four levels of a multiscale model as defined above

0010-938X/$ - see front matter Crown Copyright Ó 2011 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.corsci.2011.12.001

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rather than materials development or particular instances of degradation. The relevant past research can be divided into the following sections: (1) Surveys of the condition of buried structures [3–9], historical analyses [10–14], and risk or systems analyses [15,16]. (2) Scientific exposures of buried metals [17–19]. (3) Sensor-based studies or monitoring of buried structures [20–25]. (4) Laboratory and in particular electrochemical simulations of exposure conditions that influence corrosion [17,18,25–34], including studies of soil characteristics and interaction with the metal surface [17,32,35]. (5) Models of electrochemical processes in soil [14,16,34, 36–46]. (6) Other types of corrosion-based research [47,48], including geographic information systems [49] and archaeological exposures [50]. The paper is written in the context of water utility (and other pipeline) organisations [45] wishing to base strategic, maintenance and replacement decisions on the remaining service life of individual pipe segments, rather than simply current condition measures, such as water main failure per kilometre per year. A number of authors have developed methodologies to predict remaining service life and these rely on parameters associated with the inherent strength of the pipe material, factors influencing the strength in combination with the design loads and pressures of the pipe, and include: (1) Prediction of corrosion pit growth. (2) Effects of pits on residual tensile strength of pipes. (3) Determination of other factors affecting tensile strength (thermal effects). (4) Load determination (earth, traffic and frost effects). (5) Failure criteria for pipes. (6) Calculation of remaining life (considering factor of safety). It is not the aim of this review to consider the full methodology for remaining service life prediction, rather it will focus on models of corrosion and pit growth. The review does not look at microbialinduced corrosion (MIC) as, although this is an important factor, it deserves a separate full review of its own. However, many of the factors covered in this review, such as the movement of water or oxygen through soils, will also affect MIC. Other researchers have developed multiscale models (MSM) of corrosion for different systems; these include the holistic model developed by Cole et al. [51] for the atmospheric corrosion of zinc, and the GILDES model developed by Graedel et al. [52] for the atmospheric corrosion of a range of metals. Such models can provide a framework for a MSM of soil corrosion, however the components of such a MSM of soil corrosion will be significantly difference to the atmospheric models as for soil corrosion all the factors outlined above will need to be incorporated.

2. Surveys of the condition of buried structures, historical analyses, and risk or system analyses The basic theory of the electrochemistry of the pitting corrosion of ferrous metals in soils was outlined in 1932 by Denison and Darniele [12] and expanded on in 1969 by Rossum [14]. As with all corrosion, initially anodic and cathodic areas are established, with the position of the anodic area being determined by microstructural or local effects. Such local effects may arise from, for example, a crack in the iron oxide layer. In this instance, an anode

will be established at the base of the crack, while a cathode will be established on the surface some distance from the pit. Subsequently there will be anions movement (OH, Cl), from the cathode to the anode accompanied by cation movement from the anode to the cathode. However, a film or ‘‘tubercle’’ will develop over the pit, which will initially be a thin layer of ferrous hydroxide [Fe(OH)2]. As this layer expands, its top surface will be converted to ferric hydroxide [Fe(OH)3], and later an intermediate layer of magnetite (Fe3O4) will form. The formation of this pit cap will restrict the migration of anions and cations, leading to the accumulation of ferrous ions close to the anode and hydroxide ions close to the cap. The early work of Denison and Darniele [12] involved exposures with 2 weeks duration and focused on early stages of corrosion and did not address long term effects. Rossum extended the analysis of these early stages of pitting corrosion postulating that there will be oxygen depletion at the cathode and this, together with the aforementioned ion accumulation, will drop the electrode potential. In addition, Rossum argued that the formation of ferric oxide at the top of the cap will lower the solution concentration. Early work by Romanoff [11] considered corrosion in soils from the basics of corrosion theory in an analogous manner to that proposed by Denison and Darniele [12]. Romanoff highlighted the factors that may affect underground corrosion, such as aeration, electrolyte type and concentration, and electrical factors. He defined aeration factors as those that affect the transport of oxygen and moisture to the metal surface, and highlighted moisture content, factors affecting the pore space of soils, such as particle size and distribution, and soil shrinkage effects. For electrolyte factors, Romanoff highlighted pH, concentration of soluble salts and the occurrence of chemical reactions between the corrosion products and the electrolyte. He indicated that soil resistivity was a useful measure of the concentration of dissolved salts, and that it appeared to correlate with corrosion in that body of soil. For electrical factors, he concentrated on those that determine the size and number of anodic areas on metal surfaces, and focused this analysis on microstructural effects, differential oxidation or intermetallic effects. In a more recent review, Fitzgerald [10] highlighted very similar parameters including resistivity, level of dissolved salts, moisture content, pH, presence of bacteria and oxygen concentration. Many authors have surveyed the conditions of buried pipes and structures, and related these conditions to soil characteristics. Much of this work is historic and has been well documented by Romanoff [11]. For example, Logan and Koenig [6] examined the condition of a 16-year-old asphalt-covered buried steel pipe in south-east Texas, USA, and correlated the maximum pit depth with a variety of soil measures. They found that the strongest correlation was with the Denison test cell [12], and a weak correlation with soil resistivity. The Denison cell can be regarded more accurately as an accelerated test procedure, rather than a soil property. In the Denison cell, a soil sample is placed between a cathode and an anode, with the anode and cathode being positioned so that the cathode has greater access to air setting up a differential aeration scenario. The current flowing between the electrodes is then monitored for periods of 2–26 weeks. Other researchers including Weidner and Davis [7] and Ewing [3] have also observed a weak correlation between steel corrosion and soil resistivity. More recently, Doyle et al. [4] surveyed the measured maximum pit depths and soil parameters across cast iron water mains in Toronto, Canada. Doyle used the ANSI/AWWA (1999) C105/A21.5-99 standard [77] to classify soils. This standard considers, resistivity, pH, redox potential and sulfide content. Only soil resistivity showed a significant correlation with pit depth, and this was a relatively weak with a correlation coefficient, R2 of 0.32. A multivariate model that included pH resulted in a marginal improvement of the correlations coefficient to 0.41. Soil corrosivity scoring systems, such as that of the American Water Works Association (ANSI/AWWA C105/

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A21.5-99), were found to be ineffective in differentiating between corrosive and non-corrosive environments. Kajiyama and Koyama [5] investigated the environmental factors that promoted the corrosion of ductile cast iron pipes after 17 years in sandy marine sediments that contained sulfate-reducing bacteria (SRB), which in turn generated ferrous sulfide. The strongest correlations were between water content and ferrous sulfide levels. Katano et al. [8] considered pit depth profiles with 9000 observations of 127 pipes aged from 0.4 to 11 years, which were extracted from three different areas in Japan. The maximum pit depth distribution appeared to be lognormal correlated with soil type, sulfate and chloride levels. These researchers suggested that the correlation with sulfate level may associated with microbiological activity. Thus, although much work has been undertaken to develop correlations between soil parameters and corrosion rate, such correlations have been generally weak. Nicholas and Ferguson [9] argue that such parametric studies were not effective because although the models provided information about the influence of the soil chemistry parameters they only articulated the soil tendency to be corrosive or not and did not accurately define the corrosion rate that would be experienced by ferrous materials buried in these soils. The lack of strong correlations indicates that there are significant additional factors controlling variations in soil corrosion, and that a single- or multi-parametric approach may not readily and/or fully encompass all interactions between the possible factors that drive soil corrosion.

3. Scientific exposures of buried metals Generally, two types of direct soil exposures have been undertaken: relatively short-term indoor exposures, and longer term outdoor exposures. According to Murray and Moran [18], although valuable, many of these studies [11,53,54] failed to monitor or control soil moisture content. Murray and Moran conducted both indoor and outdoor soil exposures, monitoring soil moisture content using in situ electrochemical impedance spectroscopy (EIS) measurements. In this work, bare line pipe steel (X65), polyethylene-coated steel and polyethylene-coated samples with defects, were exposed in both clay and sandy soils. Interestingly, for both the bare steel and the polyethylene-coated steel with defects, the authors found that: (a) the corrosion current density depended primarily on soil moisture content in both environments, and (b) the current density for the two soils at the same moisture content was equivalent. In the field exposures, the EIS technique was able to clearly delineate the effects of rain on soil moisture content, and thus on current density. In a series of laboratory tests, Gupta and Gupta [17] studied steel samples exposed in soils taken from three locations in India: Jabalpur, Teijpur and Bareilly. The respective soil types of the three sites were sandy, sandy loam and loamy soils and there were significant variations in bicarbonate content between the soils (Bareilly showing the highest and Teijpur the lowest). Each test was at single moisture content, over duration of 6 months and corrosion was determined by mass loss. Gupta and Gupta found that there was a close correlation between mass loss and moisture content, with mass loss increasing up to an intermediate moisture content, before decreasing with any further increases in moisture content. This critical point appeared to occur at around 65% water holding capacity (water holding capacity is the ratio of moisture content to saturated moisture content). However, the maximum corrosion rate did vary between soil types, being lowest in the Teijpur and highest in the Jabalpur soil. Interestingly, the inverse was true for the minimum soil resistivity, being highest for Tejpur and lowest for Jabalpur, thus the lowest corrosion was recorded in the soil with the highest resistivity. The current density values observed by Murray and Moran [18] and Gupta and Gupta [17] were equivalent at the same moisture

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content. However, there was at least one significant difference between the two studies. While Gupta and Gupta found that current density decreased at the highest moisture contents, Murray and Moran did not, perhaps because they used lower moisture than Gupta and Gupta. Interestingly, unlike Gupta and Gupta, Murray and Moran did not find a dependence on soil resistivity independent of moisture content. In both the works of Murray and Moran [18] and Gupta and Gupta [17] no distinction is made between general and local corrosion as the measurement techniques look at total current density or mass loss over the whole specimen. In contrast Norin and Vinka [19] studied the corrosion of buried steel samples, differentiating uniform and local corrosion, along with the effects of the type of backfill material. Generally, after a trench is dug and a pipe is laid, the trench will be backfilled with available soil. Frequently, this backfill material will contain transported soil and building waste in a heterogeneous mixture with the original soil. Norin and Vinka buried steel and zinc panels at depths of 0.5, 1.1 and 1.5 m within backfill material made up of original ‘‘till-type’’ soil, wood fragments, metal pieces, bricks, seashell debris and other organic matter. Mass loss and two sensor technologies [linear polarization resistance (LPR) and electric resistance (ER)] was used to determine uniform corrosion, while deepest observed pit were used to determine localized corrosion. A major finding of study was that localized corrosion of all samples buried in the backfill material was extremely high compared to those buried in the ‘‘natural’’ soils. An additional significant conclusion was that while uniform corrosion was positively correlated with water content and negatively correlated with soil resistivity, these correlations were reversed for local corrosion. The high alkalinity and high carbonate contents of the soils appeared to promote protective corrosion products such as calcite and siderite which act to reduce the corrosion rate. In general, the LPR and ER measurements did not correlate well with the measured uniform corrosion rates, although they did show trends consistent with high rainfall promoting further corrosion. In fact for the LPR sensors, only at a depth of 1.5 m was the steel mass loss estimated by the LPR comparable with steel mass loss measured by buried coupons, at the shallower depth the LPR results were less than 1/5 of the coupon data. In contrast the steel mass loss estimated from ER measurements (only taken at 0.5 and 1.5 m) was 2–3 times higher than measured by the buried coupons. Norin and Vinka argued that the difference in local and general corrosion may be that local corrosion is stimulated by the greater oxygen supply and higher ion content of soil solutions that occurs at lower moisture contents. These authors did not observe a peak in the variation of uniform corrosion rate with moisture as observed by Gupta and Gupta. Thus, while all workers observed a correlation between water content and the uniform corrosion of buried samples, a consistent correlation between soil resistivity and uniform corrosion, independent of moisture content, has not been established. This finding is in line with prior observations in field surveys that only weak correlations were established between soil resistivity and corrosion. The reverse correlation between moisture content and localized correlation observed by Norin and Vinka [19] would be potentially very significant in those cases where the development of protective oxides restricts general corrosion.

4. Sensor-based studies or monitoring of buried structures Numerous papers have reported on sensor-based detection of corrosion in soils (including wire bean electrodes, linear polarization, EIS and electrochemical noise), however, it is not the intention here to review the methodologies used, but rather to

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highlight the results that throw light on corrosion mechanisms occurring in soils. Moore and Hallmark [32] studied the relationship between the corrosion of buried steel wire probes and soil conditions across 15 sites in Texas, USA. The probes were buried at depths of 0.5 and 1.5 m, and the effective loss in cross-sectional area of the wires was determined by the summing the current flow. A large range of soil parameters were monitored, including minimum resistivity, concentration of soluble salts, electrical conductivity of extracted saturated soil paste, soil type and moisture content. Loss in cross sectional area had the strongest correlations with soluble salts and electrical conductivity. Moore and Hallmark also found that the USA Soil Conservation Service’s corrosivity rating system tended to overestimate the corrosivity of many soils, and subsequently proposed modifications to that classification system. To examine the variations in anodic and cathodic activity in various soils, Aung and Tan [20] developed a (multi) wire beam electrode (WBE), consisting of 100 identical mild steel electrodes, bundled together but insulated from each other by an epoxy layer. In this way, each wire acts as a mini-electrode while the bundle’s surface forms the corrosion substrate. This technique allows the determination and visualization of anodes and cathodes on the corroding substrate. Interestingly, Aung and Tan found that a large number of anodes and cathodes were established and persisted throughout a test in damp soil, while after about 50 h exposure to sodium chloride-containing sand, anodic activity became concentrated and increased dramatically at only a few sites (closing down in others). Huang et al. [21] carried out laboratory studies of the corrosion of an X70 steel in alkaline–saline soils of high porosity and very low moisture content from Kuerle in China using electrochemical noise (EN) measurements supported by direct observations of the exposed steel. Both the EN study and direct observations indicated a three-stage process occurred, consisting of an unstable germination or initiation stage, a quick development stage, and a stable development stage characterised by the build-up of corrosion product ‘‘piles’’. Castaneda et al. [22] combined EIS measurements of steel pipelines with reliability analysis, which indicated a very high dependence of corrosion rate on soil resistivity. Scully and Bundy [24] pioneered the use of both linear polarization and EIS to detect soil corrosion, and found that electrochemical measures supported the inverse dependence of soil corrosion on soil resistivity, and a decrease in corrosion rate with time of exposure. Sancy et al. [25] carried out EIS analyses in both water and water-saturated sand, using samples cut from a cast iron pipe used in a water distribution network. The authors found that while both the inner and outer surfaces of the pipe sample were covered with corrosion products, the internal surfaces showed markedly lower corrosion rates than external surfaces, and significantly different forms in the impedance data, suggesting that the role of soil in determining the corrosion rate is significant. Sancy et al. interpreted the EIS of the inner surfaces as indicating that the cast iron electrode behaved as a semi-infinite conducting porous electrode, but one in which the development of a carbonate layer on the pore edges restricted the cathodic reaction to the bottom of the pores. In contrast, the EIS of the outer surfaces indicated that they behaved as a planar electrode with a non-conducting porous layer. For the outer surface, the cathodic reaction is thought to be mass-transfer limited and predominantly controlled by diffusion through the non-conducting porous layer. The work of Sancy et al. indicated that the exact nature of oxide development can have a significant effect on the corrosion processes, and further that the carbonate/ bicarbonate level can have a significant effect on oxide development. Sancy et al. also found that the corrosion rate of the pipe outer surface in water was an order of magnitude greater than that in

sand. They argued that while the corrosion rate is diffusion limited in both cases, when the specimen is immersed in water oxygen only has to diffuse through the porous layer, however when the specimen is immersed in sand, it needs to diffuse through both the sand and the porous oxide layers. These electrochemical studies make a strong contribution to the understanding of the development of corrosion with time (an understanding not possible from field exposures where corrosion is only monitored or measured at the end of tests). The diverse methods (EIS, EN, WBE) all show transitions with time, with the rate of the transition depending on the environmental conditions. A common trend is the build-up of a porous oxide layer and a decrease in electrochemical current with time, along with an equivalent increase in charge resistance, particularly as measured by EIS. One of the limiting factors controlling corrosion appears to be the diffusion of oxygen through the porous layer, and the soil separating the metal surface from the air. However as demonstrated by Aung and Tang [20], the resultant decrease in overall corrosion can lead to localization of anodic activity and an increase in local current. Thus, this last understanding from the work of Aung and Tan supports the observations by Norin and Vinka [19] that factors controlling local and general corrosion may be different. The electrochemical studies also highlighted the contribution of environmental parameters in promoting corrosion, in particular pore water acidity, especially when derived from acid rain.

5. Laboratory and in particular electrochemical simulations of exposure conditions A number of researchers have carried out electrochemical studies using soils that simulated real service conditions [29–31,33]. In addition, there are a number papers in the literature on the performance of metals in solutions designed to simulate the types of physico-chemical conditions those that occur in soils [24,26–29]. Wu et al. [26] performed weight loss and electrochemical tests on steel samples in solutions designed to simulate soil conditions. The solutions contained NaCl, CaCl2, Na2SO4, MgSO4, NaHCO3 and KNO3, and they were adjusted to pH 3–7 using sulphuric acid, however the authors did not provide a rigorous explanation of why a particular solution composition was chosen. The results indicated that both mass loss and electrochemical parameters which included the corrosion current and potential (Icorr and Ecorr), were strongly dependent on pH, with the greatest mass loss and Icorr occurring at pH 3. Wu et al. [27] also investigated the effect of acid rain on the corrosion of steel in acid soils, by using a laboratory rain simulator and soil samples derived from the field. The authors found that the extent of corrosion was highly dependent on the pH of acid rain, and that the soil itself was further acidified with the application of acid rain. Liu et al. [28] carried out electrochemical tests to study the effect of electrolyte composition. The electrolyte was based on 0.01 M NaCl, but also included 0.01 M of CaCl2, MgCl2, KCl, Na2SO4, NaHCO3 or NaNO3. Potentiodynamic tests indicated that the aggressiveness of the additional cations followed the order K+ > Mg+ > Ca2+, while that of the anions followed the order SO42 > HCO3 > NO3. It is worth noting that the different effects of these additions was significant but not dramatic, causing a modest increase in the corrosion current around the free corrosion potential. Both Wu et al. [26,27] and Liu et al. [28] adopted a threeelement equivalent circuit (with some modification in the case of Wu et al. [26]) consisting the resistance of the corrosive electrolyte (Rs) in series with the charge transfer resistance (Rt),which itself was in parallel with the constant phase element (Q). Wu et al. argued that both soil and acid rain pH decreased Rt. Liu et al. indicated that while the presence of K+ decreased Rt, Ca2+ and Mg2+

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increased it. All anions decreased the charge transfer resistance, while all ions decreased the solution resistance. Benmoussa et al. [29] used electrochemical tests to study the factors affecting the aggressivity to a line pipe steel of a solution designed to simulate a basic soil (containing KCl, NaHCO3, CaCl2 and MgSO4) from Algeria. In agreement with Wu et al. [26,27] Benmoussa et al. found that the aggressivity of the solution increased with acidity and temperature. Additionally, they found that charge transfer resistance increased with time, which they associated with the development of a protective film. Belmorke et al. [30] had previously found that when an X60 steel was exposed to a soil-simulating solution, a corrosive layer developed that caused both an initial decrease in the charge transfer resistance and a continuous increase in the double-layer capacitance (Q in the threeelement circuit). In tests on painted steel, the authors found that the pore resistance of the paint film initially decreased, while its capacitance initially increased as the electrolyte penetrated the coating. In a series of laboratory tests using a wide range of soils, Kasahara et al. [31] observed a relatively high correlation between polarization resistance and mass loss. Nie et al. [33] used LPR and EIS to examine carbon steel immersed in an alkaline test soil. Nie et al. analysis of the low frequency impendence in their EIS studies indicated a diffusion control mechanisms from which they postulated that the mass transfer of dissolved oxygen played an essential role in the kinetics of the corrosion process, and that the entire corrosion process was limited by a combination of activation and diffusion control. A protective iron oxide formed on the metal surface at ambient temperatures but not at elevated temperatures of ca. 50 °C. Ferreira et al. [35] compared various corrosion measures obtained from the field and from tests in conditions designed to simulate soil pore chemistry. They found that the resistivity in the field did not match that in the laboratory, and that the electrochemical parameters derived from soil solution tests did not match field corrosivity tests. This emphasises the ongoing difficulty in trying to find suitable means of accelerating corrosion in the laboratory environment. Thus, tests on solutions aim to simulate soil conditions do highlight some interesting effects of the chemistry of the solution, notably the effect of pH, solution conductivity and the beneficial effect of oxide development. However uncertainty remains on the relevance of soil solution tests to actual performance in soils. This uncertainty may arise from the many additional factors that affect corrosion in soils (oxygen diffusion, etc.) and indicates that soil solution chemistry is only one of many factors controlling soil corrosion.

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Rossum [14] derived an early model of soil corrosion from electrochemical principles of pit growth in steel. He considered the different scenarios that arise depending on the aeration level of the soil, so that: 6.1. For well-aerated soils Precipitation of a calcium carbonate layer may occur at the cathode, thus acting as a barrier and limiting corrosion, leading to the following approximation for pit depth (P):

P ¼ ð6KÞ1=6 t 1=6

ð1Þ

where K is a constant, and t is time. 6.2. For soils with fair aeration Rossum suggested that a precipitate (as previously suggested by Romanoff [9]) will form over the pit, limiting diffusion into the pit and thus also the anodic current, leading to the following approximation for pit depth:

P ¼ K 1=3 io t1=3

ð2Þ

where io is the initial current per pit. 6.3. For poorly aerated soils Rossum argued that corrosion product formation will not impair either cathodic or anodic reaction, and that the pit area only will determine the corrosion current, with pit depth given by:

P ¼ Kt 1=2

ð3Þ

6.4. For very poorly aerated soils Rossum argued that the ferrous ions produced by the anodic reaction control the resistivity of the solution in or adjacent to the corroding pit, leading to the following approximation for pit depth:

P ¼ Kt 2=3

ð4Þ

Thus, according to Rossum, in all scenarios pit depth can be given by:

P ¼ Kt n

ð5Þ

where n depends on the state of aeration. Rossum further discussed the role of cell potential (E), pH and resistivity (q) in controlling pit growth, and argued that:

6. Models of electrochemical and soil processes

P ¼ K n En qn t n

Models of the electrochemical and soil processes controlling corrosion can be divided into a number of categories:

Further, he argued that pH is the predominant variable in determining E, and that:

(1) Stochastic or empirically derived models from field exposures [37,46]. (2) Parameter-based (including stochastic) models of soil corrosion [14,16,36,39,40]. (3) Data-driven estimates [45]. (4) Partially multiscale models or components of a possible multiscale model [41–44]. Corrosion models and corrosion rate estimate models may be stand-alone, or they may be embedded in methodologies to estimate remaining service life. In general, embedded models tend to be simpler than stand-alone ones, and they often follow the original formulation of Rossum [14].

E ¼ Kð10  pHÞ

ð6Þ

ð7Þ

So that Eq. (6) becomes:

Pc ¼ K n Z n

ð8Þ

where

Z ¼ ½ð10  pHÞt=qsoil 

ð9Þ

and pc is the corrosion pit dimension, qsoil is the soil resistivity, n is a soil aeration constant (the value of n ranges from 0.17 for soils of good aeration to 0.67 for soils of very poor aeration), a, b, c and Kn are constants, and t is time in years. As mentioned previously, many authors have developed life prediction methods based on the work of Rossum [14]. For

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example, in a methodology to estimate residual life, Rajani and Maker [45] indicated that pit depth may be estimated either by a oneoff measurement followed by growth rate calculations derived using Rossum’s Eqs. (8) and (9) above, or by multiple inspections. Other workers such as Doleac et al. [55] have used Rossum’s equations as the pit model to estimate remaining life. Velazquez et al. [34] have developed a statistical model from an analysis of data on (257 discrete samples) coated steel pipe (cathodically protected) that had been buried for 17 years. The pipes were buried in clay, sandy clay loam, clay loam, silty clay loam, silty clay and silt loam although there was only a statistically significant number of data for the first 3 soil types. The data collected included maximum pit depth, exposure time, coating type, pipe to soil potential, soil properties including redox potential, pH, resistivity, water content, bulk density, chloride, bicarbonate and sufate content. They based their analysis on a modified form of Rossum’s Eq. (6):

P ¼ Kðt  t o Þn

ð10Þ

where to is the pit initiation time. K and n were derived from regression analysis of a range of soil and pipe parameters. The authors found that K primarily depended on soil pH, redox potential, resistivity and dissolved ion concentration, while n primarily depended on pipe coating, pipe-to-soil potential, soil bulk density and water content. With requard to soil type the value of K were found to be 0.178, 0.163 and 0.144 for clay, clay loam and sandy clay loam, respectively while the value of n was found to be 0.829, 0.793 and 0.734 for the same soil types. The pipe to soil potential in this study was on the average close to the optinium level for cathodic protection and thus the relevance of the data to pipes without cathodic protection is unclear. Velazquez et al. [34] also found that the corrosiveness of soils followed the order clay > clay loam > sandy clay loam. Caleyo et al. [39] extended the probability-based model of Velazquez et al. by applying a Monte Carlo simulation of environmental conditions. They observed a steady decrease in crack growth rate (which is modelled by n < 1), and showed that after extended periods the pit distribution data fitted a Frechet distribution, thus highlighting how estimated pit distributions may change with time. In addition, Caleyo et al. [40] adopted a Markov chain methodology to predict pit development, in which the transition probability between pit ‘‘states’’ as a function of environmental factors is derived from the original model of pit growth rate developed by Velazquez et al. [34]. The simulated pit depth distribution is then fitted to a generalized extreme value distribution. What is notable about the simulation is that it predicts a significant broadening of the pit size distributions with time, particularly for more aggressive soils. Thus, with time, the maximum in the pit size distribution becomes significantly larger than the mean of the pit size. Ahammed and Melchers [56] developed a probabilistic model for estimating the failure of steel pipes, based on a power function for corrosion (similar to Eq. (8)):

D ¼ kt

n

ð11Þ

where D is the loss of wall thickness at time t, and k and n are regression parameters derived from experimental measurements. This same power law formulation is used quite frequently in decision support systems for rehabilitation and maintenance, such as the UtilNets program developed by the European Union [57]. Kleiner and Rajani [58] recently reviewed the large body of work on statistical models used to estimate the structural deterioration of water mains. These approaches do not incorporate any explicit exploration of corrosion or pitting, rather it is embedded in the probability treatment of pipe leaks.

Although the work of Rossum [12] was based on geometric and proportionality arguments rather than on a rigorous assessment of electrochemical or chemical processes, it has been instrumental in guiding the development of reliability models over the last 30 years. However, it is uncertain whether more rigorous analyses of pit growth kinetics and their relationship to factors affecting anodic and cathodic processes (including oxide formation) would yield the same relationships. Some researchers have developed different parametric propagation laws, and these have been well summarized by Rajani [16]. For example, Alamilla et al. [36] proposed a model for steel corrosion in soils that was formulated in terms of pit propagation, so that pit depth is given by:

P ¼ mP t þ ðmo  mp Þ=qo ½1  expðqo tÞ

ð12Þ

where mo and mP are the initial and long-term pitting rates, respectively, and qo is a constant. Alamilla et al. then considered that mP alone should be considered dependent on environmental factors, and introduced various electrochemical and chemical arguments to support this contention. These environmental factors were pH, resistivity, redox potential and pipe–soil potential (incorporating cathodic potential). However, rather than build a physical model, the authors proposed a statistical model in which mP are considered to depend independently on the above variables. The dependence on these environmental variables was formulated in terms of extreme probability distribution functions (Gumbel) using three separate datasets (Mexican database on gas transmission pipelines [36], National Bureau of Standards (NBS) database [13], New York database on gas pipelines [59]). The variability in pit growth associated with variations in environmental factors was different for the three datasets. For example, the analysis of the Mexican database highlighted the strong synergy of acid pH and soil humidity on crack depth, the NBS database analysis highlighted that oxidizing soils (via redox potential) should lower pit depths compared to equivalent soils with a lower redox potential, while the New York database showed a strong dependence on soil resistivity. The derived models exhibited close correlations with experimental results. Mughabghab and Sullivan [46] have developed a model for buried carbon steel containers based on previous NBS data (and so looked at only soil resistivity and pH). Their formulation for pit growth is based on Rossum’s Eq. (6), but is derived separately for soils of different aeration. While the authors found that the maximum pit growth parameter K for each class of soil depended on pH alone, these dependences varied between acidic (Ka) and alkaline soils (Kb). For example, for poorly aerated acidic soils they found that:

K a ¼ 5:74ð9:87  pHÞ

ð13Þ

While for alkaline soils:

K b ¼ 5:05ð2  pH  10:26Þ

ð14Þ

While Mughabghab and Sullivan argued that pit growth in acidic soils was under ohmic control, and pit growth in alkaline soils was under diffusion control due to the presence of corrosion products, their conclusion is not supported by rigorous modelling or analysis. They also statistically analysed the variation in the value of n, and found that it increased as aeration decreased, and that a linear relationship between n and the moisture and clay content of soils could be derived. The authors found that the pitting rates were ‘‘essentially identical’’ for carbon steel, wrought iron and open-hearth steels. Bushman and Mehalick [76] suggested that soil characteristics including moisture, resistivity, permeability, chloride, sulphide, sulphate and oxygen content, presence of corrosion activating bacteria, acidity and hardness of soil moisture when combined in a

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multiple regression model of the form showed below as a reasonable predictor corrosion rate, and hence the time to corrosion failure.

11

sues have been extensively researched by soil scientists and hydrologists. 7.1. Moisture content and water flow in soils

Y ¼ B0 þ B1 X 1 þ B2 X 2 þ . . . Bk X k þ e

ð15Þ

where Y is the dependant variable such as mean time to corrosion failure, Xk is each independent variable noted previously which impacts the failure, Bk is the constant or y intercept, and e is the random error possessing a normal probability distribution and having a mean equal to zero with a constant variance. All the work so far in this section is based on simple parametric laws for the temporal development of damage. More recently, a few researchers have begun to explore the metal/soil/external environment system in more detail. For example, Jiang et al. [41] have highlighted the role of the gas/liquid/solid boundary – the three-phase boundary (TPB) – on corrosion in soils. Their model assumes that soil particles are pressed against the metal surface and thus moisture on the surface will be dispersed into droplets between the soil grains (see Fig. 1). The model assumes that the electrochemical process is under cathodic control and that, in turn, oxygen diffusion through the droplet controls the rate of the cathodic process. The model calculates the possible geometry of the droplets on the metal surface as a function of moisture content, and then introduces a number of semi-empirical relationships for the cathodic-limiting current density as a function of drop thickness. The calculated corrosion densities as a function of moisture content were found to show good agreement with experimental results. In a related experimental study, Jiang et al. [41] carried out steady-state polarization and electrochemical impedance tests to determine the effect of the length of the TPB on the cathodic current. Their experimental method consisted of simply immersing a square steel electrode at different orientations and depths to produce different TPBs. They found that both the cathodic-limiting current density and the corrosion current density increased with TPB length. The work of Jiang et al. [41,42] is a very useful starting point to building a multiscale model, but at present it does not consider the factors that control soil conditions, the rate of movement of species through soil, or external conditions. However, the soil literature does provide information and models in these areas.

7. Relevant soil science and hydrology literature In order to understand and predict the corrosion of pipes in soils, it is necessary to ascertain the conditions in the soil, in particular the moisture content, the oxygen concentration reaching the buried pipe, and the flux of any other corrosive salts. These is-

Fig. 1. Schematic of three-phase boundaries that arise at the soil/pipe interface (from Jiang et al. [40]).

As the literature on water content and flow in soils is extensive, and a wide range of models having been developed [60], this paper will outline approaches of interest to a multiscale model of corrosion in soils and not attempt to review the field. Water content in soils is closely related to: (1) Water flow patterns. (2) Ground topography, soil profiles and position of the watertable. (3) Soil type and water saturation limits. Traditional models [61] of water movement in soils have treated the soil as a continuum using Darcy’s law [59]:

m ¼ K gradðhÞ

ð16Þ

where m is Darcy’s velocity vector, k is relative hydraulic water conductivity, and h is the hydraulic head. This leads to an expression for soil water diffusivity [D(h)], so that:

DðhÞ ¼ KðhÞdh=dh

ð17Þ

where h is the soil water content. Thus, given a knowledge of the soil water retention curve dh/dh, the moisture content could be calculated. In the 1980s and 1990s, however, it was recognized that flow through soils can be regulated by macropores [62], and a range of new models were developed [63]. Typical of such models is the MACRO model of Jarvis [64], in which flow is treated in two domains: the matrix, and the macropores. The traditional approach is used in the matrix, while hydraulic conductivity is assumed to follow a simple power law function in the macropores. Typically, the saturated hydraulic conductivity will be 5–20 higher in the pores than in the matrix [62]. The variation in moisture content in the near-surface due to surface rain, as predicted by such models, is most extreme in the first meter of soil and thus is likely to affect buried pipes [65]. Continuum models based on Darcy’s law can be applied to various landforms [60], and so can predict moisture content both in the vicinity of water sources such as rivers and dams, and due to various soil profiles. It is self-evident, but nevertheless worth remembering, in corrosion studies that such terrain and soil features will have a dominant effect on soil moisture. The relative position of the watertable will also have a profound effect on the moisture content of the soils adjacent to buried pipes. By definition, soil water content is at saturation at the watertable, at near-saturation close to the watertable, and it will then generally decrease towards the surface (although near-surface moisture contents will varying according to recent climatic events). The watertable can vary significantly in one region, depending on terrain and soil type and depth. For example, in the metropolitan area of Melbourne in Victoria, Australia, the watertable varies from less than 5 m in sandy coastal soils to greater than 20 m at higher elevations. Given that pipes tend to be buried at depths of 600–900 mm in Australia (deeper in colder climates), this implies that the relatively shallow watertable depth in coastal regions of Melbourne could affect moisture levels in soils adjacent to buried pipes. Lastly, the moisture content of the soil will be profoundly affected by soil type, with analysis by Neale et al. [66] indicating that the saturation water content may vary from as low as 0.5% for sand to as high as 217% for bentonite clay (see Fig. 2). Thus, even close to the watertable, the moisture contents in sand will be low.

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Fig. 2. Field capacity of soils as a function of sand content.

7.2. Oxygen diffusion and concentration in soils Many researchers have looked at gas transport in unsaturated soils, however the significant aspects of this issue will be illustrated by reference only to the works of Chesnaux [43] and Neale et al. [66]. Chesnaux [43] adopted groundwater seepage and transport models to look at gas flux through soils. Chesnaux’s model assumed that transport was a Fickian process, with the diffusion constant modified to include the different diffusion rates of a gas in air and water in soil, the porosity of the soil, and how the gas was partitioned portioned between the air and the water phase. It is also necessary to consider how oxygen could also be consumed by the soil. Chesnaux also applied the model to look at oxygen diffusion through soil, assuming a vadose zone of 5 m from the topsoil to the watertable, a sand soil (porosity 39%) of differing reactivity (Kr), and a temperature of 10 °C. The simulated oxygen concentrations are reproduced in Fig. 3, in which it is apparent that the oxygen concentration was highly dependent on soil reactivity (Kr = 0 implies an inert soil and Kr = 105 s1 implies a very reactive soil), and that it dropped dramatically close to the watertable. In fact, there was a capillary fringe close to the watertable (about 0.5 m in this case) where the soil moisture approached 100%, with this high water content effectively stopping oxygen diffusion. Neale et al. [66] carried out a series of laboratory trials to look at oxygen diffusion through a variety of soils. For the trials, soils were packed in columns (20.3 cm long) at controlled moisture contents, and two prime values were subsequently determined. These were the oxygen consumption rate Rsoil (in mg/cm3 s), which is analogous to Chesnaux’s Kr, and the re-aeration flux JO2 (in mg/m2 day). While Rsoil depended on moisture content, it ranged from effectively zero for sand (all moisture contents), to around 4  108 for dry loamy sands, to 1  106 for moist silty clays. Interestingly, only two values were recorded for JO2: around 11000–12000 or around 1000–2000. The major effect on re-aeration was moisture content, with values falling when the water content was higher than 75%. The results obtained by Chesnaux [43] and Neale et al. [66] are not directly comparable due to the different soil column depths used in each case. In particular, the greater dependence of oxygen concentration on soil reactivity in Chesnaux’s simulation reflects the longer pathway through the 5 m of soil. Nevertheless, both studies have highlighted the effects on soil oxygen of soil reactivity, moisture content, and the relative position of the point of interest to the watertable. The studies have also highlighted that as the saturation water content of soils varies dramatically, so will the absorption of oxygen in the soils. 7.3. Solute movement in soils The transport of solutes through soils could strongly influence both the conductivity of soil water, and the presence of aggressive species at the pipe/soil interface, and thus is of clear interest in

Fig. 3. Simulated oxygen concentration in the vadose zone (at 10 °C) depending on the soil reactivity Kr, and the effective constant of reaction (T1) (from Chesnaux [41]).

understanding soil corrosion. Fortunately, significant studies of solute transport have been undertaken by soil scientists, particularly those interested in soil contamination [63,67–70]. Three types of models are commonly used: continuum, bi- or multiphase, and network approaches [70]. The continuum approach assumes that soil is a porous medium with continuous properties, and that solute transport can be modelled by convective dispersive flow [67]. Bi- or multiphase models assume that there are structural pores or defects in soil where flow occurs at a dramatically different rate to the rest of the soil. One variation assumes that flow occurs through isolated stream tubes without lateral mixing, and can be modelled by a Convective Lognormal Transfer function (CLT). The Mobile–Immobile Model (MIM), like the CLT model, assumes that there are soil region where flow is possible, but other regions where the soil micropore network is poorly connected and flow is immobile. Solute is transported by convection–dispersion in the water-mobile regions, and by diffusion in the water-immobile regions and between the regions. Network approaches are a recent development that build discrete fracture models, with exchange occurring between the matrix and fractured networks by advection–diffusion processes. In continuum models, water and solute transport may be driven by pressure head differences, while bi- or multiphase models assume that water transport occurs through convective film flow in the mobile regions, without exchange with the immobile regions. In both case, the dispersion coefficient of the solute will increase with the effective pore water velocity [67]. It has been shown that bi- or multiphase models can quite accurately predict solute concentrations in soil. Interestingly, Villholth and Jensen [62] found that the maximum chloride concentrations were at an intermediate depth between the surface and the watertable. In fact, the maximum penetration of tracer chloride ions varied from 0.6 m to 0.1 m on two different plots, which the authors associated with different macropore structures, the plot with the greater chloride penetration having more vertically connected macropores. In tests on a real soil block but using artificial rainfall, Williams et al. [71] showed that solute movement into soil was highly non-uniform, with strongly preferred pathways developing, particularly when rainfall was above 2 mm h1. The study of solute movement in soils is a dynamic and expanding field, and a full analysis of the diverse approaches to it is outside the scope of this review. However, what is relevant is that a range of solute transport models do exist, and that these models have been developed to look specifically at non-equilibrium solute transport driven by stream tubes or pore networks. Thus, in devel-

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oping models of pipe corrosion, it should not be assumed that solute transport, and thus solute concentration, is uniform. Rather, the possibility of non-uniform solute distribution should be considered, particularly for soils such as clays where transport through the matrix will be limited, but is likely through shrinkage cracks in the soil structure. Further, solute transport will predominantly occur when rain or other factors that cause changes in the water gradient at structural pores, promote convective film flow in the same pore structure, and thus solute transport will be intermittent. 7.4. Summary of effects of soil moisture and solute concentrations From this brief overview of the literature on moisture, oxygen and solute transportation in soils, three major points are relevant to the corrosion of buried pipes: (1) The moisture content at the point where a pipe is buried will be highly affected by terrain effects, the depth of the watertable and climatic parameters. (2) The saturation moisture content in soils varies dramatically and, as a consequence, so will the rate of oxygen diffusion (being highest at low moisture contents). (3) Both moisture and solute transport in soils may be quite heterogeneous, being promoted by preferential paths. 8. Discussion The corrosion literature – covering field surveys, the examination of buried samples and electrochemical tests – indicates two major points: (1) While the rate of pitting of ferrous metals is of prime interest many research has used measurement techniques that total mass loss or current flow and thus cannot define pit growth rates. This unfortunately reduces the utility of these studies. Nevertheless total corrosion rates appear to depend on electrical resistance and moisture content, although tests undertaken at constant moisture content have not revealed a separate dependence on electrical resistance. (2) In some cases, the build up of oxides may decrease the corrosion rate, apparently by increasing pathways for oxygen diffusion and limiting cathodic reaction. In addition, corrosion rate does appear to be influenced by environmental factors, in particular acid rain. In general, models of soil corrosion have not developed substantially since the work of Rossum [14], who highlighted that pit growth rates will vary depending on the extent of aeration. Much of the subsequent work has involved modifying Rossum’s parametric formulation, or a related formulation, by fitting a probability or reliability formulation to the pit growth functions. An exception is the work of Jiang et al. [41,42], who highlighted the role of threephase boundaries (soil/liquid/gas) on the corrosion of buried pipes. The soil literature, particularly that related to water, oxygen and solute movement, can significantly enhance our understanding of soil corrosion. Specific applications include: (1) Observed variations of corrosion rate with soil moisture and soil resistivity. The corrosion literature is somewhat ambiguous on whether correlations exist between corrosion rate and soil resistivity, independent of variations in soil moisture. The weight of evidence indicates that much of the variation in corrosion rate is likely associated with soil moisture, but where two soils have a very similar moisture content, then variations in soil resistivity can increase the corrosivity variation between the soils. This is supported by the observation that

13

anion concentration (which would be measured in soil resistivity) can lead to variations in soil corrosivity. What the soil literature highlights dramatically (Fig. 2) is that the field capacity (and also transport properties) of soils varies dramatically, and thus it is highly unlikely that different soil types would be at the same moisture content. (2) A comparison between the work of Gupta and Gupta [17] (on the relationship between moisture content and corrosion rate) and soil oxygen transport studies, as exemplified by Neale et al. [66] illustrates the interaction of moisture content and oxygen transport in controlling soil corrosion. Gupta and Gupta found that corrosion rate reached a maximum at around 65% of a soil’s water-holding capacity, before decreasing with increasing moisture content, which they associated with decreasing oxygen diffusion. Indeed, Neale et al. demonstrated that oxygen movement in a soil will decrease significant as the moisture content of the soil approaches saturation, but only in those soils with high saturation moisture contents. (3) A number of corrosion studies have looked at the effect of rain on subsurface corrosion [24,26,27]. Notably, Wu et al. [26,27] performed laboratory studies of the effect of acid rain on soils, and EIS sampling with buried probes that detected peaks in corrosion with surface rain. The models of water penetration and solute penetration into soils developed by Wu et al. could be used to enrich the study of soil corrosion, in particular, how water penetration is related to both soil structure and macropore formation. 9. Construction of a multiscale model of soil corrosion To accurately model corrosion in soils, it is necessary to understand the electrochemical processes that occur at metal surfaces, particularly the development of anodic and cathodic sites and the rate of reactions at these sites, how the development of an oxide layer may impact on this electrochemical activity (particularly its role in controlling oxygen diffusion to the cathodic regions), what form pore moisture/steel and pore moisture/air/soil interfaces take, and how this influences both the diffusion of species through the moisture layer to the metal surface, and the position of anodes/cathodes on the surface. Moving to higher scales, it is critical to understand how soil transport properties and chemical interactions in the soil control the moisture, oxygen and solute concentrations at the steel interface, and how these are then controlled by the macro-environment. The macro-environment may include terrain factors, the position of the watertable, and climatic factors, notably rainfall and temperature. Thus, a multiscale model of the corrosion of ferrous metals in soils (shown schematically in Fig. 4), would need to encompass five levels: (a) Anodic/cathodic activity. (b) Oxide effects. (c) Pore water/pipe interface (a triple phase boundary (soil/ water/metal) develops at this interface. (d) Soil dynamics. (e) Macro-environment. 9.1. Anodic/cathodic activity In principle, the basic factors controlling anodic and cathodic processes, their positions and rates, should be the same in soil corrosion as in other environments where ferrous metals are subject to corrosion (although of course the boundary conditions affecting these processes may be quite different). The work by Stratmann and Muller [72] has highlighted the factors controlling major

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cathodic reactions (oxide reduction, and the role that the oxide scale has in facilitating this reaction), while the review of Stratmann [73] has highlighted the interaction between anodic and cathodic sites, and their relationships to oxide formation and moisture droplet shape. 9.2. Oxide effects The impact of a corrosion products on corrosion rate in an iron system is complex and depends on the nature of the oxide. A detailed study of the interaction of moisture films with the oxides (and the reactions within oxides) that develop on ferrous metals in soils has not been undertaken. However the work of Straman and Muller [72] on the reactions’ within oxides that develop under cyclic moisture films provides guidance to the factors that are likely to be of importance to corrosion in soils. As outlined by Stratmann and Muller [72], oxides on iron tend to be thick and porous, and they may have a number of effects. For example, they may act as a diffusion barrier, particularly to oxygen, however they may also act as a site for oxygen reduction, while Fe3+ ions in the oxide layer may be reduced to Fe2+ Oxygen reduction is favoured on FeOOH, and thus the rate of oxygen reduction can be dramatically increased as the diffusion barrier is substantially lowered if oxygen reduction takes place within the scale. However the corrosion products formed in atmospheric corrosion (as studied by Stratman and Muller) may not be the same as formed in soil corrosion. Indeed Pons et al. [78] detected substantial magnetite in iron exposed for long periods in soils. Further Saheb [79] also found substantial magnetite in ferrous archeological artifacts corroded in anoxic soils. Indeed there study indicated that conductive phases such as magnetite can provide a conductive path to the metal surface which permits the spatial separation of the anodic and cathodic reactions. In contrast the extent of magnetite formation in atmospheric corrosion is not yet clear. These brief discussion indicates that the different iron corrosion products can influence the conductivity of the oxide layer and the ability of the oxide layer to support the cathodic reaction and highlights the need for accurate definition of the composition of oxide layers of ferrous metals exposed to steels. The replacement of iron oxides with iron carbonates, which a number of researchers have associated with a decrease in the corrosion rate [5,7,30], may then be attributed not only to the barrier properties of the iron carbonates themselves, but also to the elimination of the oxides’ role in promoting oxygen reduction.

9.3. Pore water/pipe interface As indicated by Jiang et al. [42], a particular geometry will develop at the pipe/soil interface (see Fig. 1). This geometry is not dissimilar to that which develops in atmospheric corrosion, and it has been historically modelled by Evans [74] and recently revisited by Cole et al. [75] According to the Evans model, oxygen reduction is favoured at a droplet edge, as oxygen can readily diffuse to the metal surface, leading to passivation in this zone and anodic activity occurs at the centre of the drop. The later work of Cole et al. highlighted that this diffusional control only occurs for medium sized drops, and that with fine drops the diffusional barrier through the liquid is not sufficient to promote preferred cathodic sites. According to the model of Jiang et al., the pore size and the drop size should be aligned, and thus different soils would have different size droplets, which may or may not be influenced by the Evans mechanism.

9.4. Soil dynamics The soil dynamics will control the moisture content that develops with depth, and the diffusion of oxygen and solute to the pipe/ soil interface. This module can be constructed from existing soil and contamination research highlighted in this review. It will be important to consider non-equilibrium behaviour, such as that generated by macropores, as these may have a significant influence on moisture and solute contents at the interface. It may be appropriate to divide the pipe/soil interface into two separate regimes: one where the pipe intersects a macropore and one where the pipe intersects the soil matrix. The soil dynamics module must inform the pore water/interface module of the moisture content, oxygen diffusion rate, and solute level and diffusion rate at the soil/pipe interface, and the variations in these parameters.

9.5. Macro-environment The macro-environment module will need to define the hydraulic, soil and climatic environments, i.e. the terrain factors and watertable variations, and how they impinge on water movement and soil moisture, variations in soil profiles, critical soil parameters such as soil chemistry, porosity, structure and field capacity, and climatic factors such as rainfall and temperature. The macro-environment module must to inform the soil dynamics module of the parameters that have a strong effect on soil moisture, oxygen diffusion and solute diffusion. It is evident that the macro-environment module has the potential to be quite complex, however two approaches can reduce this complexity: considering only those factors of first-order importance to moisture, oxygen and solute concentrations in soil, and applying the model to particular scenarios to develop a strong understanding of the factors influencing these key parameters.

10. Conclusions A number of conclusion can be drawn after reviewing both the corrosion in soils and the general soils literature:

Fig. 4. Proposed multiscale model for soil corrosion.

(1) Researchers in the literature postulate that soil corrosion may be related to a number of factors including soil resistivity, level of dissolved salts, moisture content, pH, oxygen concentration and the presence of bacteria (although we have not considered this area in this review). However the only factor that is consistently found to control corrosion of ferrous metals in soil moisture content.

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(2) In general researchers have investigated general corrosion (particularly via mass loss) however some workers have investigated localized corrosion such as pitting and have found that the dependence of local corrosion on climatic and soil parameters may be quite different from general corrosion with local corrosion favoured at low moisture contents. (3) Electrochemical studies has shown that corrosion rates may decrease significantly with time which has been associated with the development of oxide layers that limit oxygen diffusion to the metal surface. (4) While of models have been developed to predict remaining life of ferrous pipelines these are in the main based on modification of Rossum’s [14] empirical equations relating pit growth and time and do not attempt to model soil corrosion processes. An exception is the work of Jiang et al. [41], which introduces the role of the three phase boundary (gas/liquid and solid) at the pipeline surface. (5) A framework for developing a multiscale model (MSM) of soil corrosion is outlined. Such a model would need to incorporate models of water and solute transport and well as oxygen diffusion, but as these models are well developed in soil science, the MSM could make use of these established models.

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