Research on the remaining life assessment method of corrosive steel pipe structures in substations based on thickness measurement and testing

2.1. Preparation of specimens

In this study, eight circular hollow columns were selected, including one intact specimen and seven specimens exhibiting varying degrees of corrosion. These columns were extracted from the Zhenyang substation. This structure had been subjected to atmospheric corrosion for 30 years, as illustrated in Fig. 1. The substation columns were fabricated from Q235 mild steel, a material commonly used in construction, with its chemical composition detailed in Table 1. The steel tube columns studied in this paper, which had undergone 30 years of corrosion, were all in normal service at a substation. The corrosion these columns experienced was primarily uniform atmospheric corrosion. Although some localized corrosion was also present, it was generally concentrated at the ends of the components. During sampling and test preparation, these end sections were typically cut off and removed. Each specimen had a nominal length of 410 mm, an external diameter of 100 mm, and a designed thickness of 3 mm; however, the measured thickness varied depending on the extent of corrosion.

Fig. 1Zhenyang 220kV substation’s corroded steel columns

Over the decades, environmental factors contributed to the progressive corrosion of the steel pipes. The corrosion primarily affected the external surfaces of the pipes, while the internal surfaces remained largely intact. The outer surface of the steel pipes exhibited uniform corrosion, leading to the formation of a reddish-brown rust layer. This layer, a direct consequence of industrial weathering, is indicative of prolonged exposure to aggressive environmental conditions typical of industrial regions.

2.2. Environmental conditions of the substation

The substation is situated in Yancheng, Jiangsu province, China, an area that has experienced substantial environmental and climatic changes over the past 30 years, driven by rapid industrialization, urbanization, and changing climate patterns. The substation is likely to experience specific challenges due to these environmental factors, particularly concerning corrosion. The city has faced challenges with air pollution, including particulate matter (PM2.5 and PM10), nitrogen dioxide (NO₂), sulfur dioxide (SO₂), and ozone (O₃). Studies have shown that pollutant levels generally peak during winter months; the environmental characteristics of Yancheng are given in Table 2. Air pollution, primarily from industrial emissions and vehicle exhaust, combined with the city’s climatic conditions, leads to occasional severe acid rain.

2.3. Corrosion rate

The rust layer on the corroded specimens was dark brownish-yellow, with the outer layer being loose and easily peeled off. The zinc anti-corrosive paint on the intact specimens and the rust from the corroded specimens were removed following international standards, using a solution composed of 50 mL of hydrochloric acid (HCl), 3.5 g of hexamethylenetetramine, and distilled water at room temperature. After cleaning, the specimens were dried before measuring the thickness loss with a standard ultrasonic thickness gauge.

This study used a new Single-Point Differential Measurement (SPDM) method to measure the average corrosion depth of corroded specimens. The average corrosion depth is calculated by directly comparing the initial thickness with the corroded thickness at the key points and averaging the results. Compared with traditional thickness measurement methods, the core idea of the SPDM is to perform a differential operation between two measurements of the same point under different times or conditions, or between a single measurement and a fixed reference value. This approach effectively eliminates systematic errors and environmental interference (such as temperature drift and zero-point offset), thereby accurately extracting changes or absolute values of the target physical quantity. It achieves a good balance between usability and accuracy, making it well-suited for rapid and reliable assessment. The average corrosion depth for each specimen was determined from ten-point measurements taken across the corroded surface area. Each specimen’s average corrosion depth (Dc) is calculated as follows:

For each point, the local corrosion depth is determined by subtracting the post-exposure thickness from the initial thickness: $∆T_i=T_{0i}-T_{1i}$, where $i$ represents each measurement point. The SPDM technique provides a simple yet effective way to measure the average corrosion depth of a specimen. By focusing on a few strategically chosen points and using straight forward thickness measurements, this method offers a balance between ease of use and accuracy, making it an excellent choice for quick assessments or situations where simplicity is key.

2.4. Tensile specimens

For tensile experiments, a total of 16 specimens were prepared from the corroded steel columns, the rust was cleared by a physical method. Tensile specimens, including fourteen corroded and two uncorroded, were cut into standard samples for tensile testing following GB/T228.1-2021. The corroded tensile specimens were directly extracted from the corroded column sections of the field-retrieved columns, thus their material degradation reflects authentic service conditions. The dimensions of the conventional tensile coupon, 210 mm long, 20 mm wide, and thickness varied as per corrosion depth, made of Q235 steel shown in Fig. 2. The unidirectional tensile test of the steel specimens was conducted using a 100 kN capacity electronic universal testing machine (CMT5105).

The engineering stress is calculated using the minimum cross-sectional area, which was measured at the fracture location after testing using a digital Vernier calliper, and the corresponding minimum cross-sectional area was established. A gauge line was drawn 25 mm from the centre point on both sides of the front and back sides of the specimen, and its purpose was to obtain the elongation after the break of the specimen by measuring the distance of the gauge section again after the tensile test.

Fig. 2Tensile experiment specimens and testing setup

A full-scale extensometer with an adjustable gauge length was employed to collect strain within the given range of the gauge length of 50 mm. Using the strain rate control test method, the tensile test is carried out according to GB/T 228. In this test, the loading rate of the steel before yield is 1mm/min, and the loading rate after yield is 5 mm/min. The engineering stress-strain values are directly obtained from experiments and then converted to true stress-strain by using:

where ${\sigma }_{eng}$ and ${\epsilon }_{eng}$is the engineering stress and strain and ${\sigma }_{true}$ and ${\epsilon }_{true}$ is the true stress and strain, respectively. Their assessment is essential for a more thorough evaluation of material behaviour. Table 3 lists the calculations of the experimental results, where ${\sigma }_u$ is ultimate strength, ${\sigma }_y$ is yield strength, $E$ is Modulus of elasticity, ${\epsilon }_u$is ultimate strain, ${\epsilon }_y$is yield strain and ${\epsilon }_f$is fracture strain.

2.5. Axial loading setup

The axial loading test was conducted using a 200-ton electro-hydraulic servo-pressure testing machine in the structural laboratory of Southeast University. Fig. 3 illustrates the dynamic acquisition instrument used, with strain data being collected simultaneously throughout the loading process. The strain acquisition was performed using the strain tester TST3826-2, as depicted in Fig. 3. Given the symmetrical cross-section of the round steel pipe, the strain gauges were arranged based on the principle of uniform symmetry. Specifically, the strain gauges were positioned in the upper, middle, and lower sections of the specimen, with the upper and lower sections centred 2 cm from each end. To monitor the structural behaviour and detect failure modes, the specimens were equipped with eight linear variable differential transducers (LVDTs). Two LVDTs were oriented orthogonally to measure both longitudinal and transverse strains, while four additional LVDTs were used to gauge axial compressive deformations. This setup ensured comprehensive monitoring of the specimen’s responses under axial loading.

The restraint configuration of the testing machine features a hinged connection at the lower end of the loading device, with the vertical loading end fixed at the upper end. The entire loading process was conducted using a hierarchical loading system. The experimental loading mode employed force-controlled loading with an initial loading rate of 1 kN/s. During this phase, the load-displacement curve was closely monitored. As the curve approached the end of the linear elastic region and neared the elastic limit, the loading rate was reduced to 0.5 kN/s to allow for more precise control. Loading continued until the specimen exhibited plastic deformation and eventual failure, with strain data being collected throughout the process. The field setup for loading is depicted in Fig. 3. As shown in the figure, the lower end is connected to the loading plate, which in turn is attached to a movable cart. The cart was designed to facilitate specimen installation and alignment. During the experiment, however, the cart remained stationary, allowing the lower end of the column to be reasonably regarded as fixed.

Fig. 3Experimental setup for axial loading test

The steel columns were taken with different corrosion rates, and the localized corrosion ratio ${CR}_L$calculated as:

where $t_c$ is the corrosion-damaged column thickness, as measured by an ultrasonic thickness gauge, and $t$ is the designed thickness of the column. The load-carrying capacities of the experimental and simulated corroded columns were $P_{Exp}$ and $P_{FEM}$, respectively.

The deterioration ratio ${\beta }_{Exp}$ of the ultimate strength of the tested specimens is calculated as:

where $P$ and $P_c$ are the ultimate load capacity of the intact and corroded columns, respectively. For the strain and stress data as well as the related plots, please refer to Section 4.1 of this paper.

4.1. Stress-strain curves

The stress-strain curves of the specimens with varying degrees of corrosion are shown in Fig. 5. As the corrosion rate increases, significant changes are observed in the stress-strain behaviour. As detailed in Table 3, the ultimate tensile strength, yield strength, and elastic modulus of the steel specimens decrease notably with increasing corrosion, primarily due to the thickness loss caused by corrosion. Furthermore, the elongation at break decreases sharply as the corrosion rate rises, with the values falling below the specification requirements. The strengthening phase of the stress-strain curve becomes markedly shorter in corroded specimens compared to non-corroded ones, indicating a reduced capacity for plastic deformation. Both ultimate strain and yield strain decrease significantly as a result of corrosion. For instance, the TC-7 specimen exhibited a 15.08 % reduction in ultimate strength and a 10.45 % reduction in yield strength compared to the intact specimen. Additionally, the ultimate strain and fracture strain decreased by 30.24 % and 36.21 %, respectively.

This degradation in mechanical properties is attributed to the combined effects of reduced thickness and stress concentrations induced by corrosion-related defects. These defects include uneven thickness reduction, enlarged rust pits, and surface roughness, which exacerbate the material's vulnerability to failure. As a result, the stress-strain curves of corroded specimens display shorter strengthening phases and more pronounced brittle fracture characteristics, leading to an earlier onset of plastic damage and reduced overall ductility.

Fig. 5Engineering stress-strain curves of tensile specimens

4.2. Load-displacement curves

Experiments were conducted on corroded steel columns to evaluate their performance under axial compression. The results revealed that, during the initial loading phase, the load-displacement curves of the specimens exhibited a predominantly linear behaviour, with minimal surface deformation. However, as the load increased, the columns transitioned into plastic deformation, leading to significant distortions at both ends. Upon reaching the ultimate load, buckling was consistently observed at the ends of all specimens. The axial load-displacement curves, presented in Fig. 6, clearly demonstrate the influence of corrosion on the deformation behaviour under axial loading. Corrosion not only reduced the ultimate load capacity but also led to shallower slopes in the initial stages of deformation, indicating a decrease in rigidity and structural integrity. The presence of corrosion accelerated the onset of plastic deformation and reduced the columns load-bearing capacity. While the load-deformation curves for specimens with similar corrosion levels exhibited consistent slopes, variations in ultimate load capacity were evident due to differences in localized corrosion patterns.

Corrosion significantly compromised the structural integrity of the circular hollow columns, leading to increased axial deformation under compression. As the degree of corrosion intensified, the resulting strain increased, further diminishing the material’s stiffness and ultimate load capacity. The maximum load-bearing capacity of each specimen was quantified, and the rate of degradation due to corrosion was systematically calculated, highlighting the detrimental impact of corrosion on the structural performance of steel columns.

4.3. Effect of $\mathit{D}$/$\mathit{t}$ ratio caused by corrosion

The reduction in thickness due to corrosion increases the $D/t$ ratio, thereby accelerating the decline in compressive strength. The experimental results demonstrated a significant decrease in compressive strength with an increasing diameter-to-thickness ($D/t$) ratio, a critical parameter affecting the load-bearing capacity of corroded steel columns. Corrosion intensifies these effects by further compromising the structural integrity of the steel columns. As the $D/t$ ratio increased, the restraint effect weakened, leading to a deterioration in material properties and a subsequent reduction in ultimate compressive strength. Specifically, specimens with lower $D/t$ ratios exhibited outward deformation upon failure, with no noticeable local buckling. In contrast, specimens with higher $D/t$ ratios showed pronounced local buckling near the points of maximum load, reflecting a more brittle failure mode.

This is evident in the CX-4 specimen, given in Table 4, which had the highest $D/t$ ratio of 36.36 and the lowest ultimate strength of 327.99 kN, representing a 29.99 % reduction compared to less corroded specimens. The stress-strain curves for these specimens, as depicted in the results, illustrate a steep decline in load-bearing capacity as corrosion progresses, with the curves becoming shorter and steeper as the material’s ductility and strength diminish. The presence of corrosion not only reduces the ultimate strength but also increases the susceptibility to local buckling and other failure mechanisms, particularly in specimens with higher $D/t$ ratios.

4.4. Ultimate strength reduction

Fig. 6 presents the results of this study, showing a clear reduction in key mechanical parameters, yield strength, ultimate strength, elongation, elastic modulus, and ultimate strain of Q235 steel as the corrosion rate increases. This decline is consistent with findings from previous literature, which attribute the deterioration primarily to a stress concentration around corrosion pits. The stress concentration exacerbates the local deformation, leading to a reduction in the overall mechanical performance of the steel.

The malleability of Q235 steel, which is crucial for its structural applications, is particularly compromised by these stress concentration effects. The relationship between the mechanical properties of Q235 steel and the corrosion rate is depicted in Fig. 7. This figure illustrates a linear decrease in the yield strength, ultimate strength, elongation, elastic modulus, and ultimate strain of corroded Q235 steel, underscoring the detrimental impact of corrosion on structural stability. As corrosion progresses, the ability of the steel to withstand loads diminishes, leading to a higher likelihood of failure under stress, especially in structural applications where these mechanical properties are critical.

Fig. 6Axial load vs vertical displacement curves of corroded circular steel column specimens

a) CX-0

b) CX-1

c) CX-2

d) CX-3

e) CX-4

f) CX-5

g) CX-6

h) CX-7

The results clearly demonstrate that as the corrosion rate increases, key mechanical properties including yield strength, ultimate strength, elongation, elastic modulus, and fracture strain exhibit a marked decline. This degradation is primarily attributed to stress concentration around corrosion pits, which exacerbates the reduction in ductility and overall structural performance of the steel. The yield strength, ultimate strength, elongation, elastic modulus, and fracture strain of corroded Q235 steel decrease linearly with increasing corrosion rates, indicating a systematic and predictable deterioration in mechanical properties. Corrosion-induced defects, such as pitting and surface roughness, intensify the stress concentration effects, further weakening the material's capacity to withstand applied loads.

The study also compares the load-vertical displacement curves obtained from finite element analysis (FEA) with those from experimental tests. The comparison reveals that the FEA results closely match the experimental data in both trend and shape, particularly in the initial stiffness of the curves for short columns. For uniformly corroded components, as the corrosion rate increases, the initial stiffness of the load-vertical displacement curve decreases, reflecting the diminished structural integrity. The average corrosion rate and the coefficient of variation of pitting depth emerge as critical factors influencing the load-bearing capacity of uniformly corroded components, underscoring the significant impact of corrosion on the mechanical properties and ultimate strength of steel columns.

Fig. 7Degradation ratio corrosion rate

a) Ultimate strength ratio

b) Yield strength ratio

c) Ultimate strain ratio

d) Modulus of elasticity ratio

A significant reduction in column thickness due to corrosion was the primary cause of failure in all test specimens. Corrosion not only reduced the cross-sectional area but also altered the failure modes of the columns. The weakening effect of corrosion on the column ends led to local bulging deformation at the edges during testing. At maximum stress, the specimens exhibited noticeable bending, with their axes forming a half-sinusoidal shape. As the applied force progressively decreased, the deflection of the specimens increased correspondingly. The experimental results indicate that the overall discrepancy between the test data and the finite element simulation results was maintained within 5 % for most of the specimens, demonstrating the reliability of the simulation model. These findings underscore the critical impact of corrosion on structural stability and highlight the importance of accounting for corrosion-induced degradation in both experimental and numerical analyses. Fig. 8 illustrates a clear linear relationship between the degradation rate of bearing capacity and the weight loss rate of round steel under conditions of uniform corrosion.

Fig. 8Bearing capacity degradation ratio with localized corrosion ratio

5.1. Corrosion-mechanical interaction model

The Corrosion-Mechanical Interaction Model is an advanced approach for predicting the remaining life of steel structures by integrating the effects of corrosion on the material’s mechanical properties. This model accounts for how corrosion degrades critical mechanical properties such as yield strength, tensile strength, and toughness over time, reducing the structure’s ultimate load-carrying capacity. By understanding this interaction, the remaining life of corroded steel structures can be calculated more accurately. The primary goal of the Corrosion-Mechanical Interaction Model is to predict the degradation of a steel structure’s load-bearing capacity over time due to corrosion. This model considers the material properties degrade as corrosion progresses and how this degradation affects the structure’s ability to withstand applied loads.

Unlike other models that only consider cross-sectional area loss, our approach accounts for the deterioration of the steel’s inherent strength. The coefficient α is not a theoretical constant but an empirical parameter calibrated from experimental data. It quantifies the rate at which the yield strength decays per unit of corrosion rate over time.

The corrosion rates of the steel tube columns examined in this study exhibited notable variations. Some columns corroded more rapidly, while others degraded at a slower pace. These differences are likely attributed to their distinct locations and varying service environments. Observations indicate that corrosion occurred predominantly in a uniform manner, with localized non-uniform corrosion appearing only at a limited number of positions. The material degradation function models how the mechanical properties of steel deteriorate over time due to corrosion. The function is expressed as:

where $M_{\left(t\right)}$ is yield strength at time $t$, $M_0$ is yield strength of intact specimen, CR is corrosion rate (mm/year) and $\alpha$ is material degradation coefficient, which is derived from empirical data or experimental results. The function $e^{-\alpha \times CR \times t}$ represents an exponential decay of the mechanical property over time, indicating that as corrosion progresses with a higher CR, the mechanical properties degrade more rapidly. The model explicitly incorporates time ($t$), allowing for the prediction of mechanical property degradation at any point during the structure’s service life. The value of $\alpha$ is crucial and determined from experimental data specific to the type of steel and environmental conditions. The degradation of mechanical properties affects the ultimate load capacity of the steel structure over time. This is modelled as:

where $F_{\left(t\right)}$ is ultimate load capacity at time $t$, $F_0$ is initial ultimate load capacity before corrosion and is calculated as, $F_0=F_{y}A$, $F_y$ is yield strength, $A$ is cross-section area.

5.2. Remaining life calculation

The remaining life of the steel structure is estimated by determining when the ultimate load capacity $F_{\left(t\right)}$ falls below a critical threshold $F_{critical}$. This threshold represents the minimum load capacity required for safe operation. The remaining life $t_{remaining}$ is calculated using the equation:

The remaining life of the substation structure is calculated based on the mechanical properties of specimens that are obtained from tensile experiments. These mechanical properties have been mentioned in (Table 3). Based on experimental data and the corrosion rate of carbon steel Q235, the Corrosion degradation factor $\alpha$ is taken as 0.05 per year, which is a critical parameter in the Corrosion-Mechanical Interaction Model, representing the rate at which corrosion impacts the mechanical properties of steel over time. The remaining service life of the substation steel columns, determined using the yield strength of the TC-0 specimen, is estimated to be 33 years. To further validate this model, the remaining life was also calculated based on the yield strength of the TC-7 specimen, resulting in an estimate of 30 years. The accuracy of the proposed model exceeds 95 %. As TC-7 is the most severely corroded specimen and TC-0 represents the new (uncorroded) condition, the remaining service life in this study is derived based on the complete life cycle from the pristine state (TC-0) to the loss of load-bearing capacity. According to this formulation, the more severe the corrosion, the shorter the remaining life and the greater the associated estimation error. Consequently, TC-7 exhibits the largest error. This model provides a detailed and accurate prediction of the remaining life by considering both the corrosion rate and the degradation of mechanical properties. It can be applied to various types of steel structures and adjusted for different mechanical properties and environmental conditions.

Eq. (8) is fundamental in modelling the time-dependent degradation of materials under corrosive environments, and it is verified by the plotted curves for different values of $\alpha$ on the graph. A higher $\alpha$ results in a steeper decline in yield strength, meaning the material will lose its mechanical properties more quickly under the same corrosive conditions. Conversely, a lower $\alpha$ slows down the degradation process, preserving the material’s strength for a longer period. The proposed model offers a more focused and scientifically substantiated approach to understanding and predicting the life expectancy of steel structures under corrosive influences. This model’s strength lies in its ability to integrate real-world corrosion rates with the resultant mechanical degradation, providing a crucial tool for engineers and maintenance planners to manage the lifecycle of critical infrastructure.

To quantitatively validate the proposed model, its predictions were compared against a conventional method that estimates remaining life based solely on cross-sectional area loss. This area-loss method assumes that load capacity degrades linearly with thickness reduction. The model by Adasooriya and Siriwardane [1] is a notable example for fatigue life assessment of corroded bridges. While our focus is on axial capacity, a parallel can be drawn: their model incorporates a corrosion fatigue strength reduction factor based on pit depth, whereas our model uses the empirically-derived coefficient $\alpha$ to account for the broader material degradation. For the TC-7 specimen (highest corrosion), the conventional area-loss method predicts a load capacity reduction of 12.1 % (equal to the thickness loss). However, our experiments measured an actual ultimate strength reduction of 15.08 %. Our proposed model, using the $\alpha$ coefficient, accurately captured this higher level of degradation (as shown in the accurate life prediction based on TC-7 data). The conventional method, by ignoring the reduction in material strength, would overestimate the remaining load capacity by approximately 3 %. In terms of remaining life, this translates to an overestimation of several years, which could have critical implications for structural safety. This comparison underscores the conservatism and improved accuracy of the proposed Corrosion-Mechanical Interaction Model, as it captures degradation mechanisms that pure geometric models miss.