DEVELOPMENT OF INFORMATION SUPPORT OF QUALITY MANAGEMENT OF UNDERGROUND PIPELINES

Recommendations are worked out in relation to the evaluation of longevity and quality of underground metallic pipelines in the conditions of corrosion fatigue. The features of early exposure of crisis (before accident) situations are set. A complex qualimetric criterion is offered for determination of level of quality of pipeline by the account of his technological specific. The elements of investment project and methodology of estimation of resource are worked out and also influences of factors of different nature on risks and possibility of accident of gas pipelines. The model of corrosion fatigue of metal is based on strength criterion of fracture mechanics according to which there is an act of destruction in an arbitrary elemental volume of a material if the total irreversibly scattered energy of plastic deformation for all load cycles will reach a critical value equal to the energy of destruction. In order to control the corrosion process taking the polarization potential into account, a criterion relation is used to determine the rate of residual corrosion of a metal in the defect of the insulation coating, in particular, at the top of the crack, which is an anode region. The adhesive strength criteria of biocorrosive aggressive soil, mechanical criteria for the stress intensity factor, the criterion of corrosion resistance defect, criterion correlation for estimating the speed of residual corrosion in defect of insulation coating with imposed diagnostic weight characteristics and diagnostic value of tests, that complement, clarify and improve the corrosion monitoring system of pipelines, helpful for controlling and optimizing of the corrosion process, and Development of recommendations for anti-corrosion protection of metal are used in areas with non-stationary plastic deformation.

In the case of a decrease in strength characteristics of the metal below the requirements of NDs, but maintaining satisfactory characteristics of ductility and toughness, continued operation with design parameters is allowed with satisfactory results of the verification test for strength from internal pressure (safety margin relative to the actual yield strength of at least 1.5) and compliance with requirements of NDs [1]. It should be noted that existing normative documents are based on methods for assessing the maximum permissible strength characteristics of a metal, not including a sufficient amount of data to diagnose changes in the operation process.
Criteria characterizing the technical condition and residual life of the pipeline are the following parameters: pressure, temperature, working medium, mechanical load, vibration loads, fatigue strength, wear during operation [5].
When compiling the lists of pipeline systems, the defining characteristic is the functional affiliation of the pipeline [5]. For this, the pipelines are systematized and the criteria for their strength and reliability are established, taking into account the belonging of the software to a certain type [5]. An example can be trunk gas pipelines and oil pipelines, underground steel pipelines of cold and hot water supply system, etc.
Let's confine ourselves to the consideration of underground gas pipelines located in the soil electrolyte under conditions of low cycle fatigue. For MUPs, high-frequency fatigue is not observed [6]. To improve the NDs [1−3], it is advisable to build a complex mathematical model that will combine the physicochemical model of fatigue-corrosion processes of the type [7], the method of damage accumulation [8] and elements of the risk theory [9].
To estimate the rate of growth of the fatigue crack in the metal at the mean rectilinear section of the kinetic curve, let's use the Paris equation [10]: where 2a = L T -crack length, N -the number of load cycles, K -stress intensity factor (SIF) (used in linear fracture mechanics to describe stress fields near the crack tip), DK -SIF range, C t and n -the so-called Paris constants, DK th -fatigue threshold, K IC -fracture toughness of the material. The relation (1) is improved [11,12]: where F -the symbol of the functional dependence, C i -the constants characterizing the materialenvironment system, P j (s) -the parameters characterizing the stress-strain state of the material and are functions of the external forces applied to the body, A n (t) -the parameters that determine physicochemical processes occurring between the deformed metal and the corrosive medium in time t, B m (S) -parameters characterizing the state of the surfaces of the material S, which are formed upon destruction.
The rate of growth of the corrosion crack is characterized by three main parameters K max , pH tC , E tC and the corresponding equation takes the form [12,13]: where K max -the maximum SIF value in the cycle for normal breakaway cracks, pH tC -the hydrogen index of the medium, E tC -the electrode potential of the metal.
Let's generalize the Paris equations for determining the crack propagation velocity V a , taking into account the information of [10][11][12]14]: where Da -the fracture quantum, Ds -stress range, n, C a -the constants characterizing the "material (steel) -medium" system.

Mechanical Engineering
The durability (resource) of a structural element with a crack, that is, the period N P is calculated by a formula similar to [11,14]: where ai -the initial size of the macrocrack in the material, ac -the critical size of the fatigue macrocrack, N P* -the number of load cycles of the base sample, and k N -the relative number of load cycles. The parameter ai=d * , where d * is the size of the pre-destruction zone [13,14]. pH tC , E tC parameters can be used for local anodic dissolution (LAD) and hydrogen cracking (HC) mechanism [12].
The method of quantitative estimation of LAD and the mechanism of HC is based on the assumption [12,13]: The expression in the first approximation, based on the Faraday law, can be obtained as follows [12,15]: where b A -the coefficient characterizing the "material (steel)-medium" system under investigation and depends on the density and atomic mass of the metal, the charge of cations that penetrate into solutions, the Faraday constant, the conductivity of electrolytes, the shape of the crack and the stress-strain state in the vicinity of the crack, DE A -takes into account the synergetic effects (influence of voltage, hydrogen electrolytes present) on LAD, b H -the coefficient characterizing the "material (steel) -medium" system and depends on the exposure time of the medium, the quantities of hydrogen and the fullness of the crack, the diffusion rate, the critical concentration of hydrogen in the stress section with the maximum tension, the stress-strain state in the vicinity of the crack, and other parameters that can' yet be determined accurately, DE H -takes into account synergistic effects (stress effect, processes LAD, etc.) and provides these changes in hydrogen depolarization in the fracture as a result of corrosion fatigue. The energy criterion for fracture mechanics is also based on the energy criterion of fracture mechanics, according to which an act of destruction occurs in an arbitrary elementary volume of material if the total irreversibly dispersed energy of plastic deformation W of all load cycles reaches a critical value W Z equal to the material destruction energy [16,17]: where W Z -the material destruction energy for a single static load, a -the Morrow coefficient [16], W 0 =g T0´D a, W 0 and g T0 -the energy and specific dissipation energy of plastic deformations under the previous load, respectively, s 0f » (s T + s B )/2, s T , s -the yield strength and strength of the material, respectively, d fC -critical crack opening, g T = s 0f´d -specific fracture energy needed to form a unit of crack length.
For the component W S related to the averaged stresses W 0 = g T0´D a, W 0 and the cyclic strain energy WC, the following expressions are given [17,18]:

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where d max -the maximum crack opening, d fmax (s t )=(1-R)´d max (s t )/2 -the opening of the sides of the additional cut (0£s t £l pf ), which is implied with the opening under static load, l pf -length of the plastic zone, R=P min /P max -load cycle asymmetry coefficient, P min , P max -minimum and maximum loads in the sample with a crack. The values of W, W Z (8) are determined through the parameters of the stress-strained state (SSS) in the zone of the fracture advance as the area of the corresponding sections under the model tension diagram for the reinforcement material, approximated by the power law for the voltage s [16,18]: where z -coefficient of strain hardening of the material, s T , z, m -experimentally established constants for this material. The critical expansion of the crack tip, taking into account the strengthening z, is calculated by the formula [19]: where n -Poisson ratio, E -Young's modulus.
The critical opening δ fС of the crack tip enters into the CCO criterion of strength (critical crack opening), which determines the ultimate equilibrium state of an elastic body with a crack at the time of reaching the opening crack δ fС [20]: With crack opening δ fС in a simplified version connected SIF K and overpotential h of metal dissolution reaction on the basis of the known relationships [20,21]: where Z si -the formal charge of the solvated (hydrated) ions, F=96500 Kl/mol -the Faraday constant, δ=2r -the width of the front of the impending microcrack, m, M is the molecular weight of the metal, Kg/mol (M=0,0558 kg/mol -for steel), K 1SCC -the threshold value of the SIF, that is, the minimum value of the corresponding to the beginning of the crack propagation under the influence of the mechanical load and the corrosive medium, WPL -the surface energy of plastic deformation, h -electrochemical overpotential (B), that is, the deviation of the electrode potential from its equilibrium (with respect to the electrode composition of the solution) thermodynamic value when the electrode under the current is polarized. It should be noted that the second relation (12) for K 1SCC follows from the CCO of the strength criterion (critical crack opening) (11).
The WPL parameter is included in the known formula (strength criterion) of Griffiths-Irvine-Orowan [20,22]: where the first formula is written for plane deformation, the second for a plane stress state, s * -the critical stress, WPL = J/2, J -the Rice's integral [23].
In the ratio (15), it is necessary to set a 1 =226, a 2 =6,98, then the dimension of K will be given in MPA MPa m ⋅ , and WPL will be obtained in (MJ 2 )/m 2 .
To determine the density of the anode current I A at the crack tip, taking into account the energy characteristics of the surface WPL layer, let's use the generalized Kaeshe-type relationship [15,21]: where a -the angle at the crack tip, c -the electroconductivity of the electrolyte, Dy ak -the ohmic change in the electric potential between the anodic and cathodic parts, h, c -the depth of the cavity and the crack, respectively, r -the radius of the projection curvature of the juvenile surface. The relation (16) is written for the crack tip, which is the anode, β W , S, WPL0 are experimentally deter-  --D = D -D = r D D z , D f -the integral volume damageability of the material and its critical value, W a -the specific energy value W s at the end of the first stage of the process of fatigue damage accumulation at low cycle fatigue (LCF), W fp -the local value of the specific fatigue damage accumulation energy corresponding to the creation of the macroscopic crack for LCF, r ij , e ij -the components of the residual microstress tensors and the deviator of elastic deformations, respectively, s ii , s -the principal components and the first invariant of the macroscopic stress tensor, a s , r s , k s -parameters (physical characteristics) of the material (determined experimentally).
The law of damage can be summarized as follows (including the period of energy accumulation) [ where e=e kk /3 -the first invariant of the strain tensor, (20) introduces 2 damage parameters: the impact force Z S and the damage index l. As a criterion for completing the stage of development of scattered microdamages and creating a microcrack, the criterion for achieving a critical value D f (19) can be adopted.
Relation (1)-(20) is useful for describing the LCF of the material both in zones with developed non-stationary plastic deformations and in elastic zones of the material (metal) under cyclic loading.
Let's add the system (1)- (20) with information on the parameters characterizing a particular underground pipeline under operating conditions. For this, it is necessary to take into account the influence on the reliability Y N of MUP of the internal working pressure p S , the stresses s y from the temperature differences DT, the unevenness of laying the pipeline in the trench, in particular [29]: where, r K -the pipe curvature in the pipeline section, H -the design change in the pipeline location mark, DН -the depth error of the pipeline laying (depth), L x -the pipeline length with the same curvature r K , Y N -the reliability function of the pipeline section (mathematical expectation of the safety reserve ), Y S -standard (normative) value of the reserve strength, b Y -safety characteristic. For a pipe weakened on the outer surface by a cavern-like defect of depth h with a crack at the tip of depth c, we can write the ratio for the stress concentration coefficient K t and the internal critical pressure p=p S , similar to those presented in [ r ; dc b= -D -diameter of the pipe, d -the thickness of the pipe wall, the critical pressure p S corresponds to the condition for reaching the limiting (plastic) state at the crack peak, according to the Huber-Mises-Hencky yield criterion [30].

Mechanical Engineering
This is a solution of scientific and applied problems of improving regulatory documents for operational safety and lifetime of the terminal of reactor nuclear power plants by developing a scientific and reasonable mathematical model and diagnostic algorithm [31]. Based on the research, normative acts were developed to assess the technical condition of the pipeline metal and to determine its resources for reassignment of operation and safe operation during the project period [31].
Three UPs modes are considered: NO -normal operation, VNO -violation of normal operating conditions, HT -hydraulic tests. Then the accumulated fatigue damage of equipment and pipelines from operating cycles of loading is determined by the coefficient a ex [31]: To check the corrosion process taking into account the polarization potential (PP) U P , a criterial relationship is used to determine the rate of residual corrosion of the metal in the defect of the insulation coating, in particular at the crack tip, which is the anode region [32]: where c E -the average corrosion potential, I AY -the density of the corrosion (anode) current (metal corrosion rate) at cp EE = , b at -Tafel slope of the anodic polarization curve. To control the corrosion process in the type of stress concentrator, let's use the results of experimental studies [11] for steel 20 and the relation (24).
Let's consider the situation when the relative tensile stress s/s T varies from 0 to 1 [11]. At the same time c E =-0.092 V, while the corrosion current for steel 20 in a 3 % solution of NaCl increases linearly from 0.1 A/m 2 to 0.4 A/m 2 . Taking these experimental data into account, let's generalize (24) and, as a result, obtain: where b S -a dimensionless empirical parameter for steel 20 in a 3 % solution of NaCl.
The polarization potential (PP) U P is considered the main criterion for corrosion protection of metal structures in an electrically conductive medium [32,33]. It is empirically established and confirmed by many studies that the protective PP for steel underground pipelines should be in the range from -0.85 to -1.15 V relative to the mid-sulfate reference electrode (RE) [33].
In real conditions, the relationship between the constant and alternating current components i A flowing between the metal and the medium can significantly differ through different characteristics of rectifiers and reactances. These shortcomings of known methods were eliminated using the proposed method for determining the PP with the ohmic component removed from the measurements of constant and variable electric voltages [33]. To get rid of the ohmic component from the measurement of the potential difference U MG , the value of the alternating voltage was set in accordance with the constant using the harmonic coefficient determined from the measurements of the constant U GG and the variable voltage V GG at the same resistance between the reference electrode (RE) and the auxiliary electrode (AE). PP is determined by the formula [33]: where U MG -the potential difference between the pipeline metal and the electrode installed on the soil surface, k G =V GG /U GG -the measured harmonic coefficient.

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The destruction of the pipe is possible when the defect depth h+c reaches the critical size h cr , and the crack length L T will exceed the critical value L cr . To estimate h cr , let's use the relation [1,34]: where, K K -the coefficient of crack sensitivity, c cr -the critical value of the crack depth, K S -the coefficient that takes into account the change in pipe thickness in the defective section of the pipeline, K С the crack resistance parameter, which is determined experimentally by known mechanical testing methods. To determine K K , laboratory mechanical tests are also carried out, in which the ratio of the strength limits of the defective and solid samples is taken into account [34]. It should be noted that the first formula (27) for h cr is empirical.
The term of accident-free operation of the T S facility (MUP) can be estimated from the formula [34]: ( )

SA cr max
T, h h /I =- (28) where h max -the geometric size of the defect of the maximum permissible depth, the dimension of the anode current I A -1 mm/year. Just as in [35] let's use the product k P =k 1 ×k 2 ×k 3 , k 1 -the coefficient of commercial gain, k, k 2 -the coefficient of MUP competitiveness, k 3 -MUP reliability factor (k 3 =Y N ). Taking into account these indices (k P =k 1 ×k 2 ×k 3 ), just as in [35] the qualitative criterion (quality criterion) of the generalized MUP level takes the multiplicative form: where a j (j=1, 2, …, 8) -the weight coefficients.
Taking into account the information in [36][37][38][39][40], let's formulate the basic quantitative criteria for assessing the reliability of the investment project (improving the technology of corrosion protection of metal PTs) as in [39,40], taking into account: DROI -the discounted rate of return on investment in the project, DPP -the payback period of the project, taking into account the discounting, the sensitivity of the project SR -safety margin of the project by its key parameters:

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where DCF INV -the discounted cash flow from investment activity, NPV -the net present value of the project, PI -the project profitability index, T P -the performance indicator horizon, N DROI , N DPP -the reliability indicators of the project according to the DROI and DPP criteria. The overall index of reliability of investment project N Z , taking into account the risk, is determined in the same way as in [36,38] by the criterion: where SR -integral evaluation of project sensitivity using the key parameters of (1)- (28) and the risk R.
In areas with unsteady plastic deformation is expedient to use the criteria for adhesive strength biocorrosive aggressiveness of soil, mechanical criterion for the stress intensity factor (accounts for overstress of corrosion process), the criterion of defect corrosion resistance, criterion correlation to estimate the residual metal corrosion rate in the defect of the insulating coating together with introduced diagnostic weight characteristics and diagnostic value surveys that complement refines and improves the system of corrosion pipeline monitoring and can be used to control and optimize the corrosion process, and the development of corrosion protection guidelines [39,40]. Optimization of the conditions for the protection of structural elements of oil and gas industry, that are described and regulated by the state standard [2], can be conducted with their help. The joint use of relations (1)-(32) and criteria for corrosion monitoring of pipelines [39] allows to study, in detail, from the standpoint of corrosion fatigue, electrochemistry, physics of surface processes, fracture mechanics and risk theory, the mechanisms of propagation of corrosion fatigue cracks in underground metal pipelines located in aggressive environments, in particular, in sea water and soil electrolyte.
Taking into account information on the uncertainties of the density of the corrosion current I A (16), additional information about I A (25) and a number of parameters of the type p S , c cr , h cr are decreased the uncertaintydT S in the ratios (1)-(27) from 37 % (33) to 9 %.
Based on the obtained results, it is possible to improve the normative and technical documents [1,2] for metal pipelines in conditions of low-cycle corrosion fatigue.

Conclusions
1. A new complex mathematical model is proposed for estimating the resource and improving the quality of corrosion protection of metallic underground pipelines from the standpoint of corrosion fatigue, electrochemistry, surface physics, fracture mechanics and risk theory. The simulation takes into account the accumulation of damage in metals and allows to study the mechanisms of the propagation of corrosion fatigue cracks in underground metal pipelines located in corrosive environments, in particular, in sea water and soil electrolyte. These relationships are the basis for developing techniques for improving regulatory and technical documents for metal pipelines, which are in conditions of low-cycle corrosion fatigue.
2. The joint use of the criteria of corrosion fatigue and criteria for corrosion monitoring of pipelines proposed in this paper [39] will allow to study in detail the mechanisms of propagation of corrosion fatigue cracks in underground metal pipelines in the area of corrosion fatigue, electrochemistry, surface physics, fracture mechanics and risk theory in aggressive environments.
3. The presented research results make it possible to predict the change in the corrosion state of the pipeline metal with time and to calculate the service life of local sections and the entire pipeline as a whole.

4.
A mathematical model has been developed and the research results can be used by the organizations of Ukrtransgaz (structural subdivisions with the right of branches whose production facilities Mechanical Engineering are located in all regions of Ukraine) [41] to solve problems related to the improvement of regulatory documentation for the protection of steel pipelines against corrosion and their technical diagnosis.