The paper describes the proposed model for predicting the temperature dependence of the corrosion rate of steel in contact with concrete. The predicted values of the corrosion current density depending on the monthly temperature change are described. The main relations of the new mathematical model are formulated, taking into account a set of extended criteria for analyzing the influence of temperature changes on corrosion processes. For this case, changes in the value of the corrosion current density over the years are presented. In this way, the most optimal criteria and the procedure for developing these criteria using information technologies for assessing the resource of nano-concrete with reinforcement have been considered.
relation steel, metal of pipeline, strength criterion, surface defect, crack, mathematical model, corrosion rate, effect of temperature, corrosion current, nano-concrete, interface, reinforcement, Kaeshe type
Reinforcements for concrete constructions of the sewage network are made of steel. The efficiency of the system of transportation, cleaning and disposal of dirty sewage depends on the thermal regimes of sewer pipes, which creates conditions of potential environmental risk and emergency danger for the local population.
During the construction of networks, underground reinforced concrete pipes with a diameter of 1200 mm are used, which are made of high-strength concrete [1].
Corrosion processes take place on the interface between reinforcement and concrete in underground sewer pipes, which are facilitated by soil moisture. The result of corrosion is the formation of microcracks and cracks. The growth of the cracks eventually ends with the corrosive destruction of concrete.
In this context, it is expedient to analyze the dynamics of corrosion processes and develop recommendations regarding the forecast regarding the influence of thermal regimes on the conditions of destruction of concrete elements of structures. Forecasting of thermal regimes should be performed,
2022 Copyright for this paper by its authors. since changes in the effect of humidity on the metal of the pipe fittings during periodic (climatic) changes in the ambient temperature (winter ... summer) stimulate corrosion processes.
Solving the tasks of ensuring technical and environmental safety for sewerage network facilities is an actual direction of research, since the existing sewerage system of large cities of Ukraine is "worn out" by 70%, and in most small cities with a population of up to 30–50 thousand people, it is completely absent , or is not used [1]. The relevance is connected with the prospect of controlling corrosion processes on the interphase surface of the metal of the armature, taking into account the relevant effects of temperature and humidity on these processes. In this context, it is worth diagnosing the modes of influence of changes in temperature and humidity and developing measures aimed at assessing the resource of sewer pipes in operating conditions.
Temperature effects on the metal surface in aggressive environments have been analyzed in many scientific works, in particular in [2, 3]. In scientific articles [4, 5], elements of modeling thermal effects in underground structures that are in contact with the soil electrolyte are proposed.
Important in this context is the study of corrosion formations in surface and interfacial metal defects such as pores and cracks [5, 6]. The change in metal temperature and the effect on corrosion processes in underground elements of structures can be manifested seasonally [6, 7]. Such changes are accompanied by the influence of heat on the migration processes of moisture in concrete.
It is also known that oxygen diffusion through the soil layer around the perimeter of the pipe will be variable under the influence of temperature [7]. It also affects the rate of corrosion formations. In the complex, consideration of the following effects such as seasonal influence on concrete of variable temperature, oxygen diffusion in soil and concrete, as well as the rate of corrosion formations at the interface between steel reinforcement and concrete are not considered in scientific publications. Moisture and oxygen pass through the concrete and reach the surface of the metal. There, corrosion products are formed on the interfacial surface. Corrosion products initiate the formation of corrosion defects. And corrosion defects, i.e. cracks, lead to corrosion destruction of concrete.
Corrosion of reinforcement causes horizontal cracks that violate the integrity of the protective layer of concrete [8]. Randomly located cracks arise from concrete shrinkage [8]. Exfoliation of the surface layer of concrete occurs due to the effects of an aggressive environment, alternating freezing and thawing, moistening and drying [8].
The description of this type of triple effect is an important scientific problem. The study of these effects will allow to model the corrosion (anode) current and predict the development of cracks, as well as to estimate the resource of underground reinforced concrete structures.
The methods [9, 10] describe the prediction of currents and voltages in the defect on the interphase surface between concrete and steel reinforcement taking into account artificial neural networks (ANNs) [11, 12]. These data are useful for modeling the same processes and for other similar materials. However, studies were conducted for gas and oil pipelines. Criteria and parameters are considered in works [13–19]. The topics of corrosion detection and resource assessment are investment-attractive projects [20, 21]. Because repair or replacement requires large capital investments.
The purpose of the study is to model the anodic current in a crack-like defect on the interphase surface of the reinforcement and to study its influence on the corrosion destruction of nano-concrete taking into account temperature changes, the influence of mechanical loads, humidity and diffusing oxygen.
Achieving the formulated goal involves the performance of such tasks: • prepare information on corrosion currents for thermal regimes in surface defects at the interface with reinforcement. • to form criterion relations of a new mathematical model for analyzing the influence of temperature changes on corrosion processes and conditions of concrete destruction. • to form criterion relations and optimization procedure of a new mathematical model for analyzing the influence of mechanical loads and thermal conditions on corrosion processes and the conditions of the destruction of nano-concrete in the nanoconcrete- reinforcement system.
According to methods [9, 10], taking into account artificial neural networks (ANNs) [11, 12], it is proposed to forecast currents and voltages in the defect on the interface between concrete and steel reinforcement. Experimental data for this type of assessment were obtained as a result of diagnosing a section of an underground metal structure with
NCCM (non-contact current meter) and PPM (polarization potential meter) devices [10–13]. It is also proposed to use the method of predicting the metal resource of an underground structure with a surface crack-like defect, taking into account the hydrogen index of the soil electrolyte at the interface with the metal [3, 10–13].
From Figure 1, there is presented the reinforcement covered with corrosion and the destruction that
occurs when corrosion spreads into the concrete. In the first stage, small cracks begin to appear from
the metal, then the cracks widen and chipped parts are formed. Such cracking leads to the destruction
of the structure itself in the future.
interface [15].
generalized equation of the Kaeshe type [6, 16]:
,
(
– crack opening; is the angle at the crack tip; χ is the electrical conductivity of the electrolyte; ΔΨak – is the ohmic change of potential between the anode and cathode parts (anode - top, cathode crack sides); h+c+r – total depth of defect (pores and cracks); WPL is the energy of plastic deformation per unit of surface.
The results of experimental studies (Fig. 2) can be used to estimate the concentration of hydrogen in the pores at the concrete- reinforcement interface [15]. , 1 = 1 ,
The first two formulas are written for plane strain; E, – Young's modulus and Poisson's ratio, respectively; – critical stress (in particular, corresponding to the limit of strength в), Pa; WPL – surface energy of plastic deformation of nanoconcrete, J/m2; K1C – fracture toughness of nanoconcrete material, Pa/m1/2; LT – defect length (pores), m; WPL = J/2; J – the Rice integral for nanoconcrete.
Limit value δ1=δ1С is included in the criterion of strength (critical crack opening), which determines the ultimate equilibrium state of an elastoplastic body (pipe) at the moment when the crack reaches the opening δ1С, to which a certain value corresponds K1C and surface energy of plastic deformation WPL concrete [16, 17]: 1( ∙ ) = 1 , 1 = 2 ∙
Since в > Tunder the condition of the given operating internal pressure p, the crack will propagate
until the Irwin condition is fulfilled K1=K1C (destruction criterion) (
Between the concrete (nanoconcrete) and the metal of the reinforcement, it should be sufficient adhesion. The interphase layer between metal and nanoconcrete is characterized by 4 main energy parameters: the energy of adhesive bonds ad and its change ad; change in interfacial tension m; change of interfacial energy m; change in adhesion performance Aad [18].
There are formulated restrictions on the listed parameters, which are similar to those in the article [18]:
≤ ∗, ≤ ∗, ≤ ∗, ≤ ∗, ≤ ∗. (
Ratios (
Term of trouble-free operation of a reinforced concrete sewer pipe TS (i.e. resource) can be estimated = (ℎ ℎ − ℎ )⁄ = 1 + 2, using a similar formula [17]: (the initial value that is set). where h=hC – geometric size of the corrosion pore; TS1 – the term of preliminary operation of the pipe
Quality criteria for the nanoconcrete-steel reinforcement system. Similarly to the article [18], the
multiplicative qualitative quality criterion for reinforced concrete of a sewer pipe is given in the form:
business system [19];
[20] ;
concrete pipe).
(
Here it can be also considered alternative utility functions, such as Chebyshev scalarization, Derringer Suich or Harrington Desirability functions. They have strong conceptual advantages.
There is also introduced a quality criterion Z2 in the additive form similarly to [18] and the combined
criterion ZK taking into account a number of parameters k j [18]:
2 = 1 10 + 2 11 + 3 12 + 4 13 + 5 14 + 6 15 + 7 16 + 8 17 + 9 18,
(
= 10 1 + 11 2, where aj (j=1, 2, …, 11) – weighting factors, which are determined by the expert method.
Parameters k j characterize:
k10 – methods of providing intermediate and periodic reviews;
k11 – change management techniques and clearly defined impulses for re-evaluation;
k12 – methods of ordering roles and responsibilities;
k13 – methods of using a deep learning neural network;
=1
1 =
∏ , = 1 ∙ 2 ∙ 3 ∙ 4 ∙ 5 ∙ 6 ∙ 7 ∙ 8 ∙ 9 →
,
k14 – methods of forming relations with personnel and involving them in order to improve the
k15 – methods of strengthening concrete using the addition of nanoparticles;
k16 – methods of improving the compressive strength of nanoconcrete material;
k17 – methods of the influence of innovations on the improvement of the structure of nanoconcrete
k18 – methods of estimating the period of trouble-free operation TS (resource) structure (reinforced
In the first approximation, there is choosen:
1 = 2 = ⋯ = 9 = 1⁄9 ; 10 = 11 = 0,5.
(
Coefficient k13 takes into account the procedure of using a deep learning neural network. It corresponds to a probabilistic generative model in which functions from several layers of hidden nodes are embedded [18]. A neural network is used to process the results of the examination of sections of a reinforced concrete pipe. With the help of a neural network, a model is developed that provides a forecast of the depth and length of a corrosion defect, which can be used to calculate the conditions for the increase in the size of a corrosion pore (crack).
Ratios (
To optimize the compressive strength of nano-concrete and the adhesion between nano-concrete and reinforcement, there is used, similarly to the paper [19], the quality functional taking into account the inverse relationship: where ̅ – vector of given influences (yj(t) – components of the vector, j = 1,2,…,n); t – time; ̅– control vector; ̅– vector of uncertain disturbances; [t0, tk] – time interval in which the process is considered (formation of optimal values of model parameters and energy characteristics of interphase layers between concrete and reinforcement, k=1,2,…,m); m – the total number of information and parameters related to the technology of manufacturing sewage pipes; ( ̅, ̅, ̅) – a function that displays a quality indicator; FB(Xi) – a function that characterizes feedback (Feedback) between parameters Рі and input data taking into account risks and expert opinions. Here the symbol opt corresponds to the optimality condition of the functional (9).
due to the change of state. the metal surface in defects. considered. Constant humidity and temperature changes lead to the occurrence of corrosion processes, which causes the destruction of the structure over time. The number and size of defects may increase under the influence of these external factors. Particular attention should be paid to places near stations or pipelines that are in a hot state.
Since Ukraine is in a temperate climate, there is an average temperature change of 269 K in the winter period, and 294 K in the summer period. These temperature changes cause defects to increase With the help of NCCM and PPM devices [8, 22, 23], it is possible to measure anodic currents on The results of measuring corrosion currents in works [14, 16] and average monthly air temperatures in Ukraine from publicly available sources were used to model such a corrosion process. of the anode current at 1 and 3 years of operation.
Ia (1 year), А/м2 Ia (3 year), А/м2 268.65 269.85 274.25 281.75 287.85 291.35 292.85 292.25 287.65 281.65 276.15 271.75
May
December months for the values collected after one and three years.
Figure 4 shows the difference between the anode current values, which are described in Table 1. The figure shows the change in temperature according to the average temperature by month.
The biggest difference is observed in the summer months of the year and reaches 18.6 K, and the average difference is 18 K.
It can be simulated the situation of changes in anode current over time from 1 year to 9 years. Temperatures are higher, such as 331 K – 333 K can be observed near such oil pumping stations.
The values of the anode current change within 1.5 A/m2 when the temperature changes by 20 K [14, 16].
With a fixed step for each temperature, it is possible to estimate the change in the anode current density. Therefore, at a temperature of 293 K, the fixed step of changing the value can be considered 18.6, 313 K – 20.1, and 333 K – 21.6. Figure 5 shows in a bar chart what a linear simulation of such a process might look like.
In the same way, it is possible to perform simulations at other temperatures and time periods. However, the strength of the construction will decrease with the time of operation when the anode current increases, which affects the rate of corrosion propagation and destruction of the structures as a whole.
The modeling of such processes depends on the climate and average monthly temperatures in a certain part of the world. The ambient temperature may differ from place to place, so for more specific calculations, it is worth taking into account the climatic features of the region.
Seasonal temperatures fluctuate within 5 degrees from one month to another. Sewage networks are constantly in a wet state, because they are in the ground. The water that falls puts a different load on the system depending on the month. Moreover, there are months in which there is a greater amount of rain, such as spring-autumn. These factors, together with others, influence the rate of corrosion propagation. From the results obtained in the paper, it can be concluded that the anodic current in such defects decreases at a lower temperature and, on the contrary, increases at an increase in temperature.
Over the years of operation and under the influence of mechanical loads and external factors, corrosion begins to spread, which affects the destruction of concrete at the interface with reinforcement. It is worth paying attention that the strength of concrete is affected by the components, the best ways to strengthen nanoconcrete are nanoparticles of SiO2 [24] or CuO [25, 26]. Thus, it will affect the duration of operation and delay the destruction.
In addition, from the obtained results, the ratio of the value of the anode current from January to July is approximately equal to 0.92 and between each month is approximately equal to 0.98.
In the work, the mathematical model takes into account Keshe-type relations for the anodic current density, a new comprehensive strength criterion for concrete, and a quality criterion, taking into account the inverse relationship between the material parameters and the corresponding initial values.
Based on the temperature values and the corresponding values of the anode current, it is possible to
estimate the resource of a certain material. For this, it is worth considering the criteria in the ratios for
the new mathematical model (
Modeling of such processes can be improved for interrelated parameters using the approach of neural networks [10, 11] taking into account the specified criterion ratios. Thus, a new mathematical model can be formed.
Temperature changes can also be monitored with the help of thermal imaging optics using computer vision to identify the most vulnerable places in the studied area. In this case, it is best to study the internal sections of the sewage system, because detection requires a photo or video stream [27]. However, such defects often appear later on the inner surface. However, this type of defect detection can be applied to a small area [25].
Thus, modern information technologies, taking into account investment projects [28, 29], methodology of constructing a production function using quality criteria (e.g. classic production function of Cobb-Douglas) [30, 31], and monitoring material degradation processes [32], can obtain optimal criteria, which are important to consider for concrete failure analysis.
1. The anodic current density is evaluated for thermal regimes in surface defects at the interface between nanoconcrete and reinforcement. It is found that in the temperature range T = 313...333 K, the change in the anodic current density in the corrosion pore at the interface between nanoconcrete and reinforcement takes a value of approximately 3%, but this is enough to transform the pore into a corrosion crack.
2. Criterion ratios of a new mathematical model for analyzing the influence of seasonal temperature changes on corrosion processes and conditions of concrete destruction are formed. Modeling is performed on the basis of average monthly temperatures for the anode current.
3. The main relations and peculiarities of the functioning of the new mathematical model (
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