=Paper=
{{Paper
|id=Vol-3312/paper10
|storemode=property
|title=Simulation of Corrosion Fracture of Nano-Concrete at the Interface with Reinforcement Taking into Account Temperature Change
|pdfUrl=https://ceur-ws.org/Vol-3312/paper10.pdf
|volume=Vol-3312
|authors=Roman Dzhala,Volodymyr Yuzevych,Roman Mysiuk,Vasyl Brych,Ruslan Skrynkovskyy,Vitalii Lozovan,Yuriy Tyrkalo
|dblpUrl=https://dblp.org/rec/conf/momlet/DzhalaYMBSLT22
}}
==Simulation of Corrosion Fracture of Nano-Concrete at the Interface with Reinforcement Taking into Account Temperature Change==
https://ceur-ws.org/Vol-3312/paper10.pdf
Simulation of Corrosion Fracture of Nano-Concrete at the
Interface with Reinforcement Taking into Account Temperature
Change
Roman Dzhala1, Volodymyr Yuzevych1, Roman Mysiuk2, Vasyl Brych3,
Ruslan Skrynkovskyy4, Vitalii Lozovan1 and Yuriy Tyrkalo5
1
Karpenko Physico-Mechanical Institute of NAS of Ukraine, 5 Naukova Str., Lviv, 79060, Ukraine
2
Ivan Franko National University of Lviv, 1 University Str., Lviv, 79000, Ukraine
3
West Ukrainian National University, 1 Lvivska Str., Ternopil, 46009, Ukraine
4
Lviv University of Business and Law, 99 Kulparkіvska Str., Lviv, 79021, Ukraine
5
Lviv Polytechnic National University, 12 Bandery Str., Lviv, 79013, Ukraine
Abstract
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.
Keywords 1
steel, metal of pipeline, strength criterion, surface defect, crack, mathematical model, corrosion
rate, effect of temperature, corrosion current, nano-concrete, interface, reinforcement, Kaeshe type
relation
1. Introduction
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,
MoMLeT+DS 2022: 4th International Workshop on Modern Machine Learning Technologies and Data Science, November, 25-26, 2022,
Leiden-Lviv, The Netherlands-Ukraine
EMAIL: dzhala1@ipm.lviv.ua (R. Dzhala); yuzevych@ukr.net (V. Yuzevych); mysyukr@ukr.net (R. Mysiuk); v.brych@wunu.edu.ua
(V. Brych); uan_lviv@ukr.net (R. Skrynkovskyy); vitalulozovan@gmail.com (V. Lozovan); yuriy.tyrkalo1@lpnu.ua (Yu. Tyrkalo)
ORCID: 0000-0002-0197-0389 (R. Dzhala); 0000-0001-5244-1850 (V. Yuzevych); 0000-0002-7843-7646 (R. Mysiuk); 0000-0002-4277-
5213 (V. Brych); 0000-0002-2180-8055 (R. Skrynkovskyy); 0000-0002-7405-7849 (V. Lozovan); 0000-0003-2535-4238 (Yu. Tyrkalo)
©️ 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
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.
2. Related works
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.
3. Proposed methodology/model/technique
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.
Figure 1: Example of influence reinforcement concrete after corrosion
Concrete is a porous material, as well as reinforced concrete. Reinforced concrete sewer pipes are
underground and in contact with the soil. The soil is characterized by a certain moisture content at
different times of the year. Moisture, together with oxygen, penetrates through porous concrete and
condenses at the concrete-reinforcement interface [14]. The rate of moisture passage through concrete
to reinforcement can be described by diffusion equations (for example, as in [14]).
Corrosion products of steel and hydrogen accumulate in the pores at the concrete- reinforcement
interface [15].
To estimate the electric current density in the pore, which turns into a crack, there is used a
generalized equation of the Kaeshe type [6, 16]:
𝐷𝐸 𝛼 ∙ 𝜒 ∙ ∆𝛹𝑎𝑘 (1)
𝐼𝑎 = 𝐼0 ∙ (exp ( )) ∙ (1 + 𝛽𝑊 ∙ 𝑊𝑃𝐿 ); 𝐼0 = ,
𝑎 ℎ + 𝑐 + 𝑟𝑐
𝛿 ∙ ln ( )
𝛿
where a is the Tafel parameter of the anode metal dissolution process; DE = E0 – Ea;
I0, E0 – corrosion current density and corrosion potential of metal;
Ia, Ea – is the anode current density and the anode potential for metal.
– 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].
Figure 2: Dependence of the residual rate of corrosion and the volume of released hydrogen on the
degree of excess of the cathodic protection current over the limiting oxygen current
Figure 2 shows the residual corrosion rate density Ia* mm/year a long the Y axis on the left, and the
volume of released hydrogen VH mL/cm2 on the right Y axis.
As criteria for the destruction of concrete (in particular, nano-concrete), there is taken into account
the Griffiths–Irwin–Orovan criterion and the Irwin condition for KIN K1 [16, 17]:
(2)
2𝐸 ∙ 𝑊𝑃𝐿 2𝐸 ∙ 𝑊𝑃𝐿
𝜎∗ = √ , 𝐾1𝐶 = √ , 𝐾1 = 𝐾1𝐶 ,
𝜋 ∙ 𝐿 𝑇 (1 − 𝜈 2 ) 1 − 𝜈2
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]:
𝑊𝑃𝐿 (3)
𝛿1 (𝐿 𝑇 ∙ 𝜎𝑇 ) = 𝛿1𝐶 , 𝛿1 = 2 ∙ .
𝜎𝑇
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) (2).
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]:
𝛥𝜎𝑚 ≤ 𝛥𝜎𝑚∗ , 𝛥𝛾𝑚 ≤ 𝛥𝛾𝑚∗ , 𝛥𝐴𝑎𝑑 ≤ 𝛥𝐴𝑎𝑑∗ , 𝛥𝛾𝑣𝑎𝑑 ≤ 𝛥𝛾𝑎𝑑∗ , 𝛥𝑊𝑃𝐿 ≤ 𝛥𝑊𝑃𝐿∗ . (4)
where m , m , Aad , ad , WPL – empirical constants. Restrictions on the energy parameter
WPL written similarly to the previous 4 parameters.
Ratios (2)–(4) constitute a complex criterion of strength for nanoconcrete, which is in contact with
the corrosion pore formed at the interface between the metal of the reinforcement and concrete. The
parameters of expressions (2)–(4) are determined on the basis of the experiment, and the parameters
of the ratio (1) will be determined on the basis of the computational experiment.
Term of trouble-free operation of a reinforced concrete sewer pipe TS (i.e. resource) can be estimated
using a similar formula [17]:
𝑇𝑆 = (ℎ𝑐ℎ − ℎ𝐶 )⁄𝑉𝐶 = 𝑇𝑆1 + 𝑇𝑆2 , (5)
where h=hC – geometric size of the corrosion pore; TS1 – the term of preliminary operation of the pipe
(the initial value that is set).
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:
𝑚
(6)
𝑍1 = ∏ 𝑘𝑖 , = 𝑘1 ∙ 𝑘2 ∙ 𝑘3 ∙ 𝑘4 ∙ 𝑘5 ∙ 𝑘6 ∙ 𝑘7 ∙ 𝑘8 ∙ 𝑘9 → 𝑚𝑎𝑥,
𝑖=1
where ki – parameters (i=1, 2, ..., 9) that characterize the technological process improvement plan, in
particular: k1 – management and control of data related to the monitoring of the "metal-concrete"
system; k2 – susceptibility and risk techniques; k3 – methods of estimating parameters of the state of
interphase layers taking into account (1)–(5); k4 – methods of assessing the condition of surface defects
(pores, cracks) taking into account strength criteria, (2)–(5); k5 – methods of evaluating the results of
the evaluation of corrosion currents (1); k7 – risk assessment techniques; k8 – methods of responding to
emergency situations; k9 – performance management techniques (key performance indicators).
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]:
𝑍2 = 𝑎1 𝑘10 + 𝑎2 𝑘11 + 𝑎3 𝑘12 + 𝑎4 𝑘13 + 𝑎5 𝑘14 + 𝑎6 𝑘15 + 𝑎7 𝑘16 + 𝑎8 𝑘17 + 𝑎9 𝑘18 , (7)
𝑍𝐾 = 𝑎10 𝑍1 + 𝑎11 𝑍2 ,
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;
k14 – methods of forming relations with personnel and involving them in order to improve the
business system [19];
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
[20] ;
k18 – methods of estimating the period of trouble-free operation TS (resource) structure (reinforced
concrete pipe).
In the first approximation, there is choosen:
𝑎1 = 𝑎2 = ⋯ = 𝑎9 = 1⁄9 ; 𝑎10 = 𝑎11 = 0,5. (8)
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 (1)-(8) form the basis of a new mathematical model, the results of which help to predict the
strength of reinforced concrete with nanoparticles from the point of view of the probability of failure
and evaluation of nanoconcrete shrinkage and resource.
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:
𝑡𝑘 (9)
𝐽(𝑃𝑘 (𝑋𝑖 ), 𝐹𝐵(𝑋𝑖 ) = ∫ 𝑓(𝑦,
̅ 𝑢̅, 𝑠̅)𝑑𝑡 => 𝑜𝑝𝑡,
𝑡0
where 𝑦̅ – vector of given influences (yj(t) – components of the vector, j = 1,2,…,n); t – time; 𝑢̅–
control vector; 𝑠̅– 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; 𝑓(𝑦̅, 𝑢, ̅ 𝑠̅) – a
function that displays a quality indicator; FB(Xi) – a function that characterizes feedback (Feed-
back) 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).
4. Results
An example of modeling the anodic current in defects on the metal surface in sewage networks is
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
due to the change of state.
With the help of NCCM and PPM devices [8, 22, 23], it is possible to measure anodic currents on
the metal surface in defects.
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.
Table 1 presents the values of the average air temperature for each month and the interpolated values
of the anode current at 1 and 3 years of operation.
Table 1
The result of calculating the anode current density indicators according to the average temperature
in Ukraine every month.
Average temperature, K Month Anode current density Anode current density
Ia (1 year), А/м2 Ia (3 year), А/м2
268.65 January 51.34607509 34.29184
269.85 February 51.57542662 34.44502
274.25 March 52.41638225 35.00666
281.75 April 53.84982935 35.96399
287.85 May 55.01569966 36.74263
291.35 June 55.68464164 37.18939
292.85 July 55.97133106 37.38085
292.25 August 55.85665529 37.30427
287.65 September 54.9774744 36.7171
281.65 October 53.83071672 35.95123
276.15 November 52.77952218 35.24918
271.75 December 51.93856655 34.68754
The highest value is observed in July and the lowest in January, due to the highest and lowest
temperatures of the year, respectively. The value of the anode current decreases by almost half in 2
years of unchanged operating conditions.
The results were visualized using Table 1. Fig. 3 shows the change in the anode current during the
months for the values collected after one and three years.
Figure 3: Changes in indicators of anode current density according to the average temperature in
Ukraine every month
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.
Figure 4: Difference between anode current densities for 3 year and 1 year
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.
Figure 5: Estimation of change in indicators of anode current density every two years based on the
fixed calculated steps 293K – 18.6 A/m2, 313 K – 20.1 A/m2, and 333 K – 21.6 A/m2
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.
5. Discussion
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 (1)–(9).
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.
6. Conclusion
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 (1)–(9) for
analyzing the influence of temperature changes on corrosion processes, which lead to the formation of
corrosion pores at the interface between concrete and steel reinforcement, are formulated. In particular,
the basis of the new model is the Keshe-type ratio for the anodic current density, a new comprehensive
strength criterion for concrete, as well as an optimization approach for calculating interconnected
parameters using neural networks and a quality criterion and taking into account the inverse relationship
between the material parameters and corresponding initial values.
7. References
[1] Reinforced concrete elements for sewage networks. Available at:
http://zbpk.pp.ua/index.php?route=information/news&news_id=3. Date accessed: 08 nov. 2022
(in Ukrainian)
[2] P. R. Roberge, Handbook of Corrosion Engineering. Second Edition (McGraw-Hill Education,
2012).
[3] L. Yuzevych et al., “Improving the diagnostics of underground pipelines at oilandgas enterprises
based on determining hydrogen exponent (PH) of the soil media applying neural networks,”
Eastern-European Journal of Enterprise Technologies, vol. 4, no. 5 (100), pp. 56–64, Jul. 2019,
doi: 10.15587/1729-4061.2019.174488
[4] D. Fürtbauer, and C. Cheng, “Investigation of Pipeline Heat Loss to Ground Influenced by
Adjacent Pipelines,” 14th Pipeline Technology Conference, 18-21 March 2019, Estrel Congress
Center, Berlin, Germany. URL:
https://www.researchgate.net/publication/332396916_Investigation_of_Pipeline_Heat_Loss_to_
Ground_Influenced_by_Adjacent_Pipelines. Date accessed: 08 nov. 2022
[5] M. Čarnogurská, M. Příhoda, R. Dobáková, and T. Brestovič, “Model of heat losses from
underground heat distribution system,” AIP Conference Proceedings, 2017, doi:
10.1063/1.5004337
[6] H. Kaeshe, Die Korrosion der Metalle. Physikalisch–Chemische Prinzipien und Aktuelle Probleme
(Berlin–Heidenberg–New York: Springer-Verlag: 1979).
[7] N. A. Garris, and G. A. Askarov, “Activation of corrosion processes on big-diameter gas mains
under impulse temperature changes,” Electronic Scientific Journal Oil and Gas Business, vol. 2, p.
17, 2009.
[8] E. M. Babych, V. V. Karavan, and V. Ye. Babych, Diagnostics, certification and restoration of
buildings and engineering structures: Textbook. Rivne: Volyn amulets, 2018. 176 p. (in Ukrainian)
[9] V. Yuzevych, R. Skrynkovskyy, and B. Koman, “Intelligent Analysis of Data Systems for Defects
in Underground Gas Pipeline,” 2018 IEEE Second International Conference on Data Stream
Mining & Processing (DSMP), Aug. 2018, doi: 10.1109/dsmp.2018.8478560
[10] L. Yuzevych et al., “Improvement of the toolset for diagnosing underground pipelines of oil and
gas enterprises considering changes in internal working pressure,” Eastern-European Journal of
Enterprise Technologies, vol. 6, no. 5 (102), pp. 23–29, Nov. 2019, doi: 10.15587/1729-
4061.2019.184247
[11] V. Lozovan, R. Skrynkovskyy, V. Yuzevych, M. Yasinskyi, and G. Pawlowski, “Forming the
toolset for development of a system to control quality of operation of underground pipelines by oil
and gas enterprises with the use of neural networks,” Eastern-European Journal of Enterprise
Technologies, vol. 2, no. 5 (98), pp. 41–48, Apr. 2019, doi: 10.15587/1729-4061.2019.161484
[12] L. Yuzevych, R. Skrynkovskyy, and B. Koman, “Development of information support of quality
management of underground pipelines,” EUREKA: Physics and Engineering, vol. 4, pp. 49–60,
Jul. 2017, doi: 10.21303/2461-4262.2017.00392
[13] B. Koman, O. A. Balitskii, and V. Yuzevych, “The Nature of Intrinsic Stresses in Thin Copper
Condensates Deposited on Solid State Substrates,” Journal of Nano Research, vol. 54, pp. 66–74,
Aug. 2018, doi: 10.4028/www.scientific.net/jnanor.54.66
[14] V. I. Khizhnyakov, A. V. Negodin, and V. S. Kalinichenko, “Pipeline cathode protection analysis
for identification of corrosion and stress-corrosion formation,” Journal of Construction and
Architecture, vol. 20., no. 5., pp. 128-139, 2018
[15] V. M. Yuzevych, and P. M. Soprunyuk Diagnostics of materials and environments. Energy
characteristics of surface layers. Lviv: FMI named after H. V. Karpenko, NAS of Ukraine,
“SPOLOM”. 2005. 292 p.
[16] V. M. Yuzevych, R. M. Dzhala, and B. P. Koman, “Analysis of Metal Corrosion under Conditions
of Mechanical Impacts and Aggressive Environments,” Metallofiz. Noveishie Tekhnol., vol. 39,
no. 12, pp. 1655–1667, Mar. 2018, doi: 10.15407/mfint.39.12.1655
[17] V. М. Yuzevych, and V. P. Lozovan, “Influence of Mechanical Stresses on the Propagation of
Corrosion Cracks in Pipeline Walls,” Materials Science, vol. 57, no. 4, pp. 539–548, Jan. 2022,
doi: 10.1007/s11003-022-00576-z
[18] V. Yuzevych, N. Pavlenchyk, O. Zaiats, N. Heorhiadi, and V. Lakiza, “Qualimetric Analysis of
Pipelines with Corrosion Surfaces in the Monitoring System of Oil and Gas Enterprises,”
International Journal of Recent Technology and Engineering (IJRTE), vol. 9, no. 1, pp. 1145–
1150, May 2020, doi: 10.35940/ijrte.a1341.059120
[19] V. Yuzevych, O. Klyuvak, and R. Skrynkovskyy, “Diagnostics of the system of interaction
between the government and business in terms of public e-procurement,” Economic Annals-ХХI,
vol. 160, no. 7–8, pp. 39–44, Oct. 2016, doi: 10.21003/ea.v160-08
[20] N. Popova, A. Kataiev, A. Nevertii, O. Kryvoruchko, and R. Skrynkovskyi, “Marketing Aspects
of Innovative Development of Business Organizations in the Sphere of Production, Trade,
Transport, and Logistics in VUCA Conditions,” Studies of Applied Economics, vol. 38, no. 4, Feb.
2021, doi: 10.25115/eea.v38i4.3962
[21] N. Popova, A. Kataiev, R. Skrynkovskyy, and A. Nevertii, “Development of trust marketing in the
digital society,” Economic Annals-ХХI, vol. 176, no. 3–4, pp. 13–25, Aug. 2019, doi:
10.21003/ea.v176-02
[22] Technical diagnostics of materials and structures: Reference manual in 8 volumes. Editor-in-Chief
Z.T. Nazarchuk. Vol.4: Electrophysical methods for nondestructive testing in structural elements.
Editor R.M. Dzhala. Lviv: Prostir-M, 2018. 356 p. (In Ukrainian)
[23] R. М. Dzhala, B. Ya. Verbenets’, М. І. Mel’nyk, А. B. Mytsyk, R. S. Savula, and О. М.
Semenyuk, “New Methods for the Corrosion Monitoring of Underground Pipelines According to
the Measurements of Currents and Potentials,” Materials Science, vol. 52, no. 5, pp. 732–741, Mar.
2017, doi: 10.1007/s11003-017-0016-8
[24] C. Zhuang and Y. Chen, “The effect of nano-SiO2 on concrete properties: a review,”
Nanotechnology Reviews, vol. 8, no. 1, pp. 562–572, Dec. 2019, doi: 10.1515/ntrev-2019-0050
[25] X. Wang, “Effects of nanoparticles on the properties of cement-based materials”, doi:
10.31274/etd-180810-5865.
[26] A. Nazari, M. H. Rafieipour, and S. Riahi, “The effects of CuO nanoparticles on properties of self
compacting concrete with GGBFS as binder,” Materials Research, vol. 14, no. 3, pp. 307–316,
Aug. 2011, doi: 10.1590/s1516-14392011005000061
[27] M. Al-Faris, J. Chiverton, D. Ndzi, and A. I. Ahmed, “A Review on Computer Vision-Based
Methods for Human Action Recognition,” Journal of Imaging, vol. 6, no. 6, p. 46, Jun. 2020, doi:
10.3390/jimaging6060046
[28] R. M. Skrynkovskyi, “Methodical approaches to economic estimation of investment attractiveness
of machine-building enterprises for portfolio investors,” Actual Problems of Economics, vol.
118(4), pp. 177–186, 2011.
[29] R. Skrynkovskyi, “Investment attractiveness evaluation technique for machine-building
enterprises,” Actual Problems of Economics, no. 7(85), pp. 228–240, 2008.
[30] R. M. Skrynkovskyy, V. M. Yuzevych, A. V. Kataev, G. Pawlowski, and T. B. Protsiuk, “Analysis
of the Methodology of Constructing a Production Function Using Quality Criteria,” Journal of
Engineering Sciences, vol. 6, no. 1, pp. b1–b5, 2019, doi: 10.21272/jes.2019.6(1).b1
[31] V. Lozovan, R. Dzhala, R. Skrynkovskyy, and V. Yuzevych, “Detection of specific features in the
functioning of a system for the anti-corrosion protection of underground pipelines at oil and gas
enterprises using neural networks,” Eastern-European Journal of Enterprise Technologies, vol. 1,
no. 5 (97), pp. 20–27, Jan. 2019, doi: 10.15587/1729-4061.2019.154999
[32] R. Mysiuk, V. Yuzevych, B. Koman, and M. Yasinskyi, “High Availability System for Monitoring
Material Degradation Processes at the Concrete-polymer Interface,” 2022 12th International
Conference on Advanced Computer Information Technologies (ACIT), Sep. 2022, doi:
10.1109/acit54803.2022.9913086