ISSN 2534-9228 (2020) VUZF review, 5(1) Development of methodology of alternative rationale for financial ensuring of bridges building Igor Britchenko 1; Maksym Bezpartochnyi 2; Yaroslava Levchenko 3 Received: March 3, 2020 | Revised: March 28, 2020 | Accepted: March 31, 2020 JEL Classification: D61, E22, H54, R42, R53 Abstract The purpose of the article is to develop a methodology for alternative substantiation of financial support for bridge construction. To achieve the purpose, the following general scientific and special methods and techniques of research were used: "golden ratio" rule; systematization and generalization; generalization of the results of the analysis and the logical generation of conclusions. Initially, the article analyzed the state of bridge structures in Europe and Ukraine. Based on the analysis, a disappointing situation has been identified, namely that a significant ratio of bridges number require major overhaul or are in critical condition. During the research, the following tasks were solved, namely: physical wear of the bridge as a failure was considered; the feasibility of investing in reconstruction or new bridge construction was determined. For the purpose of rational use of financial resources, which are limited in the age of economic challenges, and on the basis of the rule of "golden proportion", the maximum percentage of investment in reconstruction is determined. If the limit is exceeded, it is decided to build a new bridge. This result allows making an economically sound decision and evaluating the effectiveness of the invested resources. It is proved that if the wear index of the overhaul bridge construction is higher than the wear rate of the new bridge construction by λ2 / λ1, and the amount of funds for overhaul reaches 70% of the funds needed to build a new one, it is better to build a new bridge. Keywords: financial support for bridge construction, physical wear, failure, economically sound decision, effectiveness of the invested resources. Introduction Transport and its infrastructure are an important factor determining the development and security of each country. Its stable, uninterrupted and efficient functioning is the key to successful interaction of all sectors of the economy, improving the welfare of the population, as well as ensuring the defense capability of the state and its interests (Yavuz, Attanayake, Aktan, 2017). As part of the European integration, an effective platform for cooperation at the regional level within the framework of the Eastern Partnership Transport Panel has been formed, the 1 State Higher Vocational School Memorial of Prof. Stanislaw Tarnowski in Tarnobrzeg, Poland, Faculty of Technical and Economic Sciences, Doctor of Economics, Professor, e-mail: ibritchenko@gmail.com, ORCiD: 0000-0002-9196-8740 2 National Aerospace University named after N. Zhukovsky "Kharkiv Aviation Institute", Ukraine, Faculty of Soft Engineering and Business, Doctor of Economics, Professor, e-mail: confer.piel@gmail.com, ORCiD: 0000-0003-3765-7594 3 Kharkiv National Automobile and Highway University, Faculty of management and business, Ukraine, e-mail: slavalevcenko1984@gmail.com, ORCiD: 0000-0002-4979-1101 main purpose of which is to help improve transport links between the EU and its closest neighbors (Ministry, 2019). Transport networks and services ensure a key role in improving the quality of citizens' life of the country and in increasing the opportunities for industrial development. Therefore, transport is one of the key areas of cooperation between the EU and Ukraine, and in accordance with Article 368 of the Association Agreement between Ukraine and the EU, the main purpose of such cooperation is to facilitate the restructuring and updating of the transport sector of Ukraine and the gradual 43 ISSN 2534-9228 (2020) VUZF review, 5(1) harmonization of existing standards and policies with those in the EU (European integration, 2019). Inspections of bridges in Italy witnessed disappointing conclusions: 300 bridges in the country are in disrepair and may collapse at any time. And not far from the Sicilian town of Agrigento, traffic on the bridge has already been blocked. The reason for this is structural damage to the supports. Most of the bridges and roads in Italy were built in the 50-60s of the last century and are in poor condition. The shelf life of the concrete from which they are made, depending on the grades, is the same 50-60 years (Ministry, 2019). In France, roads are in "critical condition" too: about 50% of the road surface is in need of repair, every tenth bridge is in poor condition. A recent government check showed that one third of the bridges need urgent repairs, and 841 of them are at risk of collapse. In her report, the Minister of Transport of France, Elizabeth Bourne, said that one third of the 12 thousand French bridges need cosmetic repairs in order to exclude structural changes. In 7% of cases, the damage is quite serious. They can lead to collapse. It is necessary to close these bridges for heavy vehicles, and maybe for all cars (Bridges, 2020). In Germany, a similar study last year was carried out by the Federal Research Institute of Roads. The result is also alarming: the state of 12.4% of German bridges inspires serious concern, only 12.5% of German bridges are in absolutely good condition, that is, every eighth one. Many bridges were built in the 60-70s of the last century and are not designed for the so intensive traffic of our days. By the way, thanks to the renovation program adopted after the reunification of the two Germanys, the condition of the bridges in the east of the country is better than in the west, where heavy vehicles are already prohibited on a number of bridges, including the Leverkusen bridge across the Rhine north of Cologne (Bridges, 2020; Agócs, Vanko, 2016). In the Netherlands, federal bridges are doing relatively well, but the bridges operated by cities and provinces are alarming: only in the province of North Holland are 14 bridges in disrepair (Ministry, 2019). The Bulgarian government in 2018 announced plans to repair more than 200 bridges, most of which were built 35-40 years ago. Bulgaria is considered the poorest country in the European Union, so the modernization of transport infrastructure will take place at the expense of EU funds (Levchenko, 2020). According data of the association "Bridges of Ukraine" 80% of structures are in need of repair (Bodnar, Panibratets, Zavgorodnii, Chursin, 2016). Table 1. – Ranking of road bridges by age Bridge age Total, % 1-20 21-40 41-60 61-80 80 and more % 3,39 21,24 52,97 12,07 10,33 100 Number of bridges 549 3438 8574 1954 1672 16187 Source: formed by the authors on the basis of data (Bodnar, Panibratets, Zavgorodnii, Chursin, 2016) According to the observation (Koshchenko, 2017), the average service life of Ukraine's bridges is 47-50 years, which is almost two times lower than the regulated one. However, at present, the transport industry is only meeting the current needs of both population and economy in quantitative terms (Levchenko, 2019). And the most common reason for this is the lack of funds (Bezpartochnyi, Britchenko, Jarosz, 2018). Sometimes the need to be guided by the saying: "We are not rich enough to pay twice" (Smyrnov, Borysenko, Trunova, Levchenko, Marchenko, 2020). Therefore, the purpose of this study is to develop a methodology of alternative rationale for financial ensuring of bridges building. To achieve this purpose, the following tasks were set: 44 ISSN 2534-9228 (2020) VUZF review, 5(1) To prove that physical wear of the bridge is a failure; To determine the feasibility of investing in reconstruction or new bridge construction. Bridges, traditionally, are the most expensive infrastructure projects. They are built slowly and require billions UAH. Neither the central nor the local authorities are in a hurry to invest in projects that will last for years (A bridge to concession, 2019). Therefore, in the first place, the most emergency overpasses are being repaired. Today, logistics, the number of cars, freight transport, passengers transport has grown so much that without bridges the economy of entire regions suffocates (Yavuz, Attanayake, Aktan, 2017; Faoziyah, 2016). Here the question arises as follows: When, and is it worth it at all, to spend money on the reconstruction of the bridge? Maybe is need to build a new one? The authors of this study offer the following answer to this question. Material and methods To achieve the purpose, the following general scientific and special methods and techniques of research were used: «golden ratio» rule; systematization and generalization; generalization of the results of the analysis and the logical generation of conclusions. Numerous studies have established that harmonization processes proceed according to the rule of the "golden ratio". The structure of many well-known self-organizing structures is subject to this rule. In such systems, the ratio of the whole and its parts is in accordance with the rule of the "golden ratio". The number 1,618 is called the "golden ratio", and the division of the segment in the indicated ratio is called the "golden ratio". Denote: Vp – bridge reconstruction costs; Vн – new bridge construction costs. Then we have income Vн – Vp. According to the "golden ratio" rule, we get: 382,0 618,0 618,0 =− = == − pн нp н p p pн VV VV V V V VV . In our case (70% for reconstruction), we get: 3,07,01 =−=− pн VV . 0,382 > 0,3. The percentage of income under the "golden ratio" rule is greater than the percentage of income with 70% of reconstruction costs. It can be concluded that if the funds for the reconstruction of the bridge are large from 61.8% of the cost of building a new bridge, the reconstruction is economically disadvantageous. Further calculations also confirm these considerations. To do this, we will conduct additional research. Failure – one of the main terms of the theory of reliability, means a violation of the health of the object, in which the system or its element ceases to fulfill its functions in whole or in part, otherwise a malfunction of the device, system, part. Consider the physical deterioration of the bridge structure as a failure. The proportion of physical wear of the bridge structure is determined by the formula: U(t) = eλ(t−T) − 1, (1) Where: U (t) – physical wear rate at the time t; λ – indicator of the wear rate of the structure (located in the tables in accordance with the material of which the bridge is made); t – current time from the start of operation in years; T – initial period of operation, at which wear does not occur yet. The wear index of the design of the new bridge λ1 will be equal to 0.009. Taking into account the fact that old elements remain during the reconstruction of the bridge, we will 45 ISSN 2534-9228 (2020) VUZF review, 5(1) take the wear indicator of the bridge after reconstruction λ2 higher and equal to 0.012. If the wear rate of the structure is 0.7, then the structure is subject to demolition, or is it still reconstruction? In our case, we will not take into account bridges of historical value. Calculations of the share of wear are presented in table 2. Table 2. – Calculation of the share of wear Of the year New bridge Overhaul λ1 = 0,009 λ2=0,012 20 9,42% 27,12% 25 14,45% 34,99% 30 19,72% 43,33% 35 25,23% 52,20% 40 31,00% 61,61% 45 37,03% 71,60% 50 43,33% 55 49,93% 60 56,83% 65 64,05% 70 71,60% Source: calculated by the authors For the adopted parameters, the new bridge will serve approximately 70 years, and the bridge after overhaul – 45 years. In time, we have a gain of 70 45 = 25 years. The efficiency of the service life is 25/70 = 0.3571 or 35.71%. The effectiveness of the invested funds (building a new bridge – Q UAH., reconstruction of the bridge – 0.7 * Q UAH.) is (1-0.7)/1 = 0.3 or 30%. The conclusion can be drawn as follows: with this ratio of funds needed for the construction or reconstruction of the bridge, the decision made in favor of the construction of the new bridge will be more effective. Results and discussion Let's will carry out the calculation for other indicators and the generalization results will be presented in table 3. In the authors` opinions of this work, it all depends on the assessment of the physical condition of the bridge. If its condition does not require volumetric reconstruction, then the following indicators can be selected and calculated (then, accordingly, the gap between the wear indicators is small). This is evidenced in table 4. According to the interest received, we have the volume of funds for reconstruction (Graph 1). So, let λ1 is the wear rate of the new bridge structure, and let λ2 is the wear rate of the bridge structure after reconstruction. Considering that after reconstruction of the bridge old elements remain, the rate of wear of the wear rate of the bridge should be higher. We accept that += 12  . 46 ISSN 2534-9228 (2020) VUZF review, 5(1) Table 3. – Calculation of effectiveness (E) for other indicators Of the year λ1 λ2 Of the year λ1 λ2 Of the year λ1 λ2 0,008 0,01 0,008 0,011 0,009 0,011 20 0,0833 0,2214 20 0,0833 0,2461 20 0,0942 0,2461 22 0,1008 0,2461 22 0,1008 0,2738 22 0,1140 0,2738 24 0,1185 0,2712 24 0,1185 0,3021 24 0,1343 0,3021 26 0,1366 0,2969 26 0,1366 0,3311 26 0,1549 0,3311 28 0,1549 0,3231 28 0,1549 0,3607 28 0,1759 0,3607 30 0,1735 0,3499 30 0,1735 0,3910 30 0,1972 0,3910 32 0,1924 0,3771 32 0,1924 0,4219 32 0,2190 0,4219 34 0,2117 0,4049 34 0,2117 0,4535 34 0,2411 0,4535 36 0,2312 0,4333 36 0,2312 0,4859 36 0,2636 0,4859 38 0,2511 0,4623 38 0,2511 0,5189 38 0,2866 0,5189 40 0,2712 0,4918 40 0,2712 0,5527 40 0,3100 0,5527 42 0,2918 0,5220 42 0,2918 0,5872 42 0,3338 0,5872 44 0,3126 0,5527 44 0,3126 0,6226 44 0,3580 0,6226 46 0,3338 0,5841 46 0,3338 0,6586 46 0,3826 0,6586 48 0,3553 0,6161 48 0,3553 0,6955 48 0,4078 0,6955 50 0,3771 0,6487 50 0,3662 0,7143 49 0,4205 52 0,3993 0,6820 52 0,3882 51 0,4463 54 0,4219 0,7160 54 0,4106 53 0,4726 56 0,4448 56 0,4333 55 0,4993 58 0,4681 58 0,4564 57 0,5265 60 0,4918 60 0,4799 59 0,5543 62 0,5159 62 0,5038 61 0,5825 64 0,5403 64 0,5281 63 0,6112 66 0,5652 66 0,5527 65 0,6405 68 0,5904 68 0,5778 67 0,6703 70 0,6161 70 0,6032 69 0,7006 72 0,6421 72 0,6291 74 0,6686 74 0,6553 76 0,6955 76 0,6820 77 0,7092 77 0,7092 E = (77-54)/77 = 29,87% E = (77-49)/77 = 36,36% E = (69-48)/69 = 30,43% Source: calculated by the authors Table 4. –Calculation of the effectiveness of the options Option 1 Option 2 Option 3 Option 4 λ1 0,008 0,009 0,009 0,008 λ2 0,009 0,1 0,095 0,0085 Et 23,38% 23,19% 17,39% 18,18% Source: calculated by the authors 47 ISSN 2534-9228 (2020) VUZF review, 5(1) Graph 1. – Boundary amounts of funds for reconstruction Source: formed by the authors based on own calculations Then the difference between the share of physical wear of the bridge structure after reconstruction and the new one will be: UР(t) − UН(t) = e (λ1+Δ)(t−T) − 1 − eλ1(t−T) + +1 = e(λ1+Δ)(t−T) − eλ1(t−T) =, t − T = k = e(λ1+Δ)k − eλ1k = eλ1k(eΔk − 1) We compose the following proportion: UН(t) − 1 UР(t) − UH(t) − х From the proportion we have: х = UР(t) − UH(t) UН(t) = eλ1k(eΔk − 1) eλ1k = = eΔk − 1 eΔk − 1 = 0,3 eΔk = 1,3 ln(eΔk) = ln(1,3) Δ ⋅ k = 0,2624 Δ = 0,2624 k Table 5. – Summary table Bridge constructions Tkp-T λ1 λ2 λ2 / λ1 Wooden bridge 42 0,015 0,024 1,6 Reinforced concrete and stone bridge 70 0,0125 0,02214 1,58 Metal bridge 85 0,009 0,0135 1,5 If the wear indicator of the overhaul bridge construction is higher than the wear indicator of the new bridge construction by λ2 / λ1, and the amount of funds for overhaul reaches 70% of the funds needed to build a new one, it is better to build a new bridge. 10% 12% 14% 16% 18% 20% 22% 24% 26% 28% 30% 32% 34% 36% 38% 0,008-0,0085 0,008-0,009 0,008-0,01 0,008-0,011 0,009-0,095 0,009-0,01 0,009-0,011 48 ISSN 2534-9228 (2020) VUZF review, 5(1) Conclusions Representation of the physical wear of the bridge as a failure made it possible to determine the proportion of the physical wear of the bridge structure. 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