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Concrete sewage structures are difficult to maintain since they are constructed under the ground and their surfaces inside are exposed to various deteriorations such as acid and sulfate ingress. In this study, their repair costs were eval‑ uated both deterministically and probabilistically considering the extended service life through repairing of conven‑ tional repair mortar and a newly developed bacteria repair material. Unlike the conventional deterministic method, the probabilistic manner evaluates repair cost continuously, taking into account variations in the initial service life and extended service life through repair. For the work, variations in the sulfate ion diffusion coefficient and protection parameters (cover depth and repair layer thickness) were obtained experimentally. Based on the target service life (60 years), the repair cost increased to 123% as the maintenance‑free period (MFP) decreased by half, and decreased to 77% as the MFP increased to 1.5 times. As the extended service life through repair decreased by half, the repair cost increased to 180% due to the increasing repair frequency. When the repair‑ extended service life increased to 1.5 times, the repair cost decreased to 73%. Considering exterior sulfate concentrations (120 and 200 ppm) and entire sewage pipelines (3268 m), the bacteria repair material showed the lowest repair cost (1376 K$ and 1498 K$ with the deterministic and probabilistic method, respectively) since the repair‑service life increased from 10.4 to 25.3 years and the number of repairs decreased from 9 to 4 due to the low diffusion coefficient of the bacteria repair material. Keywords: MFP (maintenance‑free period), bacteria repair material, service life, repair cost, maintenance 1 Introduction Anaerobic bacteria that live in the sludge sediment RC (reinforced concrete) sewage structures are repre- inside sewage pipelines decompose and consume depos- sentative national SOC (social overhead capital) struc- ited organic matter as nutrients during their growth. In tures and serve as key life-line systems. They are difficult the process, they generate a large amount of hydrogen 2− to maintain since mostly buried in the ground, and their sulfide gas (H S) by reducing sulfate ions (S O ) (De 2 4 frequent repairing incurs significant social and economic belie et al., 2004; Monteny et al., 2000). As the strong costs. For such structures that are difficult to maintain acid H S gas reduces pH of the concrete surface, the and degraded continuously, it is very important to deter- population of sulfur-oxidizing bacteria (e.g., io Th bacillus mine the target service life and evaluate the related repair thiooxidans and Acidithiobacillus thiooxidans) in neu- costs (Fenner, 2000; Parande et al., 2006). tral environments increases, this allows sulfur-oxidizing bacteria, which generate sulfuric acid (H SO ) and pol- 2 4 ythionic acid during their metabolic process for further decreasing pH of the concrete surface. In addition, the *Correspondence: jjuni98@hannam.ac.kr Department of Civil and Environmental Engineering, Hannam University, factors such as the presence of sulfate ions and sulfu- Deajeon, Korea ric acid deteriorate the internal pore structure through Full list of author information is available at the end of the article chemical reactions with cement hydrates in the sewage Journal information: ISSN 1976‑0485 / eISSN 2234‑1315 © The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/. Yoon et al. Int J Concr Struct Mater (2022) 16:22 Page 2 of 12 concrete surface (Grengg et al., 2018; Islander et al., 1991; constructing databases for the maintenance and quanti- Joseph et al., 2012). These reactions decrease concrete fication of probabilistic patterns for the unit repair stage density and aggressively affect physical properties such as by analyzing variations in the service life of each compo- pore structure, permeability, and strength. nent, the models cannot provide the actual repair cost Because sulfuric acid generally deteriorates the con- considering the intended service life and repair-extended crete surface, the deterioration can be monitored through service life (Lee & Ahn, 2018; Park et al., 2018). surface observation, however the continuous inspection The service life of the target structure varies depending and maintenance of sewage pipelines are difficult due to on the quality, constructability, and exposure environ- the generation of toxic hydrogen sulfide gas, presence of ment. The probabilistic method for repair cost consid - effluents, and insufficient oxygen, which can lead to casu - ers variations in the service life which are derived from alties (Oh et al., 2006). the actual deterioration model and extended service International Design Codes and Specifications on durabil - life through repair. Several researches in this area have ity design consider carbonation, chloride attack, freezing and extended to repair cost evaluation for each deteriora- thawing, sulfate attack, and the alkali-aggregate reaction as tion, sensitivity analysis on service life and repair cost, major deterioration factors. However, no clear quantitative and various probability-of-service-life function (PSLF) design formula for service life for sulfate attack is available. modeling. In particular, some studies attempted the This is because the penetration of the deteriorating agents probabilistic method for evaluating the total repair cost and concrete cracking due to the expansion of hydrates of the entire structure during service life as well as the inside occur simultaneously. Currently several techniques repair cost of each process for public housing (Jung et al., such as the deterioration depth evaluation method (Atkinson 2018; Kwon, 2017a, 2017b; Yang et al., 2020b; Yoon et al., & Hearne, 1989; Lee et al., 2013), sulfate diffusion method 2021a). In the case that LCC is evaluated through the which considers multiple layers (Yang et al., 2020a), and probabilistic methods, it is possible to manage the actual strength reduction evaluation which considers accelerated repair cost that may occur in the various situations, since testing and strength degradation (Qin et al., 2020; Zhang the repair cost is evaluated over time with a continuous et al., 2018) are mainly used for service life evaluation under curve, unlike the stepwise repair cost of the deterministic sulfate attack. method (Lee et al., 2020). Repair cost estimation usually adopts a deterministic In this study, the total repair cost during service life was life-cycle cost (LCC) method considering the stepwise evaluated for sewage pipelines that have been exposed to (step function) repair cost during the period extended sulfate ingress, considering newly developed repair mate- with repair to the end of intended service life. Recently, rial with bacteria (Rhodobacter capsulatus) and effects probabilistic repair cost evaluation method has been of design parameters. The sulfate diffusion coefficient proposed, where the model probabilistically consid- and the coefficient of variation (COV) of the cover depth ers the connection strength between the repair cost and were derived from the test and measurements, and vari- each analysis parameter, however, the deterioration pro- ations in service life were evaluated using Monte Carlo cess is not physically modeled. Neural networks (NNs) simulation (MCS). The total repair cost was analyzed are employed in several cost estimation models, but using the probabilistic and deterministic methods con- the changes in the service life of structures due to dete- sidering changes in the maintenance-free period (MFP) rioration which governs the service life are not consid- and the extended service life through the developed bac- ered. The connectivity among influencing parameters is terial and conventional repair techniques. The differences regarded as probabilistic variations (Mulubrhan et al., between the repair costs from the proposed techniques 2014; Nasir et al., 2015; Rahman & Vanier, 2004; Salem were analyzed, and the effects of design parameters on et al., 2003). In addition to NNs, genetic algorithm (GA), service life and repair cost are also discussed. and fuzzy logic system (FL) have been used for LCC (Ammar et al., 2013; Firouzi & Rahai, 2012; Sun & Car- 2 Background Theory of Probabilistic Repair Cost michael, 2018). Several studies have proposed adaptive Calculation and the Exposure Conditions network-based fuzzy inference system (ANFIS), which 2.1 Deterioration of Sewage Pipelines Under Sulfate combined the advantages of NNS and FL systems to pro- Attack cess imprecise, uncertainty, and vague data, evaluated the RC sewer systems in anaerobic-sulfate environments maintenance cost of various structures (Flintsch & Chen, deteriorate with the growth of sulfate-reducing bacteria 2004). and the subsequent generation of hydrogen sulfide gas Some studies have investigated the repair cost for (Parker, 1945), as explained in Fig. 1. Anaerobic sulfate- each process for public housing by analyzing its proba- reducing bacteria that live in the sediments, introduced bilistic patterns. Although these studies are effective for into sewer pipes, generate a large amount of hydrogen Y oon et al. Int J Concr Struct Mater (2022) 16:22 Page 3 of 12 Fig. 1 Deterioration of sewage concrete by sulfate attack. 2− sulfide (H S) gas by reducing sulfate (SO ) when causes cracking due to the lack of dimensional stability 2 4 decomposing and consuming organic sediments (De (Aviam et al., 2004). belie et al., 2004). Meanwhile the bacteria oxidize organic 2− SO + ATP → adenosylphospate - sulfate matter using the oxygen bonded with sulfur instead 4 2− of molecular oxygen for protein synthesis and energy (APS) → SO (+AMP) 2− acquisition, as shown in Eq. (1). Thiosulfate (S O ) 2 3 2− 2− 2− 2− S O → S O +S O 3 2 2 6 3 3 and tetrathionate (S O ) are generated together with 4 6 (1) H S, all of which decrease pH of the concrete structure, thereby inducing the reproduction of sulfur-oxidizing Ca(OH) + H SO → CaSO · 2H O 2 4 4 2 (2) bacteria, which exhibit optimal growth efficiency in neu - tral and acidic environments. The polythionic acid (a CaO · SiO · 2H O + H SO → CaSO + Si(OH ) + H O 2 2 2 4 4 4 2 sulfur-based chemical) formed during their growth fur- (3) ther decreases pH as well. Sulfur-oxidizing bacteria form 3CaO · Al O +3(CaSO · 2H O) + 26H O 2 3 4 2 2 sulfuric acid by using thiosulfate and elemental sulfur (S) (4) → 3CaO · Al O · 3CaSO · 32H O 2 3 4 2 as intermediates in the reduction of the energy acquisi- tion reaction for their growth. The generated sulfuric acid deteriorates the concrete structure through chemi- cal reactions with the cement hydrates on the concrete 2.2 Background of Service Life and Repair Cost Evaluation pipeline surfaces that are in contact with microorgan- Method isms. Once an environment dominated by sulfuric acid 2.2.1 D eterministic and Probabilistic Service Life Evaluation has been created, the sulfuric acid reacts with cement Several studies on service life prediction under sulfate hydrates and generates gypsum dihydrate (C aSO ·2H O) 4 2 ingress have been performed and some models have and anhydrous gypsum (CaSO ), as shown in Eqs. (2 and handled complicated chemical reactions of sulfate ion 3) (Monteny et al., 2000). Gypsum dihydrate, being water with calcium hydroxide and calcium silicates, which soluble, is easily dissolved from the cement matrix, cre- generated gypsum and ettringite, however cracking and ating coarse pores in the structure and accelerating the simultaneous intrusion of sulfate ion are still difficult performance degradation of concrete. In addition, anhy- for actual durability design in engineering level. As pre- drous gypsum expands through forming ettringite (3CaO viously mentioned, several service life evaluation meth- ·Al O ·3CaSO ·32H O) through reaction with aluminate 2 3 4 2 ods in engineering level adopt simplified patterns such (C A, 3CaO·Al O ) in cement as listed in Eq. (4), which 3 2 3 Yoon et al. Int J Concr Struct Mater (2022) 16:22 Page 4 of 12 as multi-layer diffusion in the surface layer (Yang et al., is the probability distribution for cover depth, and p is 2020a), the linear deterioration depth with diffusion the target durability probability (maximum allowable and cement compositions (Atkinson & Hearne, 1989), probability during intended service life). In Eq. (6), the and relative strength reduction rate (Zhang et al., 2018). external sulfate ion concentration ( c ), diffusion coeffi - Among the models, the second is predominantly used cient ( c ), roughness coefficient ( α ), and cover depth ( c ) 0 d since it can handle chemical component in cement which are random variables. reacts with sulfate ion, diffusion characteristics in mate - rial, exposure concentration of sulfates, and roughness of surface. This model considers the deterioration depth 2.2.2 D eterministic and Probabilistic Repair Cost Evaluation as a linear function of exposure period by assuming the This section outlines the probabilistic repair cost evalu - penetration of sulfate ions into concrete through diffu - ation based on previous studies. For probabilistic repair sion, reactions between sulfate and aluminum hydrates, cost evaluation, variations in the extended service life and volumetric expansion confined to the surface. Equa - through repairing and initial service life (MFP: main- tion (5) shows the deterioration rate by sulfate (Atkinson tenance-free period) are the primary factors. When the & Hearne, 1989; Lee et al., 2013): period during which the first deterioration depth reaches the cover depth is assumed to be T (the first service life), E · B · c · C · D 0 E i the number of repairs becomes zero for the period, which R = , (5) α · γ (1 − ν) f requires no repair. In this case, the initial condition can be given by Eq. (7) (Total Information Service Corpora- where E is the elastic modulus of concrete (MPa), B is tion, 2010; Yang et al., 2020b): the linear deformation coefficient by 1 mol of sulfate ions −6 3 T ≥ T , reacting in a unit volume (1.8 × 10 m /mol), c is the 1 (7) 0 end concentration of sulfate ions (mol/m ), D is the sulfate where T is the initial service life, and T is the final tar - 2 1 end ion diffusion coefficient (m /s), α is the roughness coef- get service life of the structure to be used. ficient, γ is the concrete fracture energy (= 10 J/m ), ν is If the average value of the first repair timing is set to T , the Poisson’s ratio of concrete, and C is the sulfate ion the safety index ( β ) and the probability that no repair is concentration reacting with ettringite (mol/m ). required ( P ) can be expressed through Eq. (8) and Eq. (9) In the method, the service life of structure is determined (Jung et al., 2018; Kwon, 2017b; Yoon et al., 2021b): when the increasing deterioration depth with exposure period exceed to the design cover depth. Material reduc- T − T end 1 β = , (8) tion factors and environmental factors are considered for marginal durability safety in the design process. Unlike deterministic durability design, in the proba- ∞ 2 1 β bilistic service life evaluation, the probability of exceed- P = √ exp( − )dβ, (9) ing the critical condition during the target service life is 2π defined and service life is evaluated based on the critical where σ is the standard deviation of T at the time of the 1 1 probability. For chloride attacks and carbonation, service first repair event. life limit conditions and target durability failure prob- In the theory, the condition for the number of repairs abilities are defined (EN 1991, 2000; Stewart & Mullard, to be N is that T is smaller than the target service life 2007), however, for sulfate attack, no clear target failure (T ), and the sum of T and T ( N-th repair tim- end N+1 N probability has been proposed. Assuming that the limit ing) is larger than T . In the condition, the safety index end condition is the time for the deterioration depth by sul- can be given by Eq. (10), and the probability ( P ) that N+1 fate penetration to reach the cover depth, the govern- the sum of T and T is larger than T is as shown in N N+1 N ing equation can be written as Eq. (6) for probabilistic Eq. (11): method: T − T + T N N+1 E · B · c (μ, σ) · C · D (μ, σ) end 0 E i β = , p (t)> C (μ, σ) > p , N f d d (10) α(μ, σ) · γ (1 − ν) 2 2 σ + σ N N+1 (6) where p (t) is the durability failure probability for the deterioration depth, which increases with time, C (μ, σ) d Y oon et al. Int J Concr Struct Mater (2022) 16:22 Page 5 of 12 β ∞ N+1 to pollution sources (public house and facilities) was P = 1 − f (β)dβ = f (β)dβ N+1 200 ppm section and that more than 1.0 km away from −∞ β N+1 pollution sources was 120 ppm. The average sulfate con - ∞ 2 1 β centration in sewage pipelines is reported to be approxi- = √ exp − dβ, 2π β mately 120 ppm (Yoon & Yang, 2020), but it varies with N+1 (11) flood and rainfalls. The total lengths of the exposure envi - where σ is the standard deviation of T . The failure N N ronments for the 120 and 200 ppm sections were found probability when the number of repairs is N (P ) can be to be 1.425 km and 1.843 km, respectively. The cover generalized as shown in Eq. (12). In addition, if the repair depth of sewage concrete structure is usually designed as cost for the unit member ( i ) is constant at C , the total 30 mm, and the thicknesses of the bacteria repair mate- repair cost can be shown as Eq. (13). rial and conventional protective mortar are 5 and 10 mm, Details of the equations and conceptual diagrams can respectively. Table 1 summarizes design parameters for be found in previous studies (Jung et al., 2018; Kwon, the service life evaluation, where several results were 2017b; Yang et al., 2020a; Yoon et al., 2021c). obtained from the previous study (Yang et al., 2021; Yoon et al., 2021a). N−1 P = 1 − P × P , N N (12) k=1 C = (k × C × P ), T i (13) k=1 where C is the total repair cost which considers the unit repair costs (C ). Fig . 2 illustrates the schematic diagram of the probabilistic method and comparison with deter- ministic method for repair cost evaluation. 3 Evaluation of Environmental Conditions and Service Life of Target Structure 3.1 D istribution and Service Life of Target Sewage Pipelines The distribution of sewage pipelines in the target area is shown in Fig. 3. For evaluation of service life, exterior sulfate concentration was assumed that the section close Fig. 3 Sewage pipelines in district A. Fig. 2 Conceptual comparison of deterministic and probabilistic repair cost evaluation methods. Yoon et al. Int J Concr Struct Mater (2022) 16:22 Page 6 of 12 Table 1 Design parameters for sewage concrete, conventional COV should be given. Variations in the service life were repair, and bacteria repair materials. analyzed using the measured cover depth and sulfate ion diffusion coefficient (Yoon et al., 2021b). Assuming nor - Variable Sewage concrete Conventional Bacteria repair mortar repair mal distribution, random variables were generated con- material sidering the average and COV of each design factor, and the service life was derived at each step using Eq. (5), then c (ppm) 120/200 120/200 120/200 2 −12 −12 –12 the average and COV of the evaluated service life were D (m /s) 2.12 × 10 2.09 × 10 0.17 × 10 obtained. Regarding concrete, conventional repair mor- E (MPa) 25700 21500 21500 tar, and bacteria repair material, the random variables ν 0.17 0.27 0.27 of them were obtained by 10 time-measurement during α 1.5 1.5 1.5 construction. Fig. 4(a) shows the test on the sulfate ion γ 10 10 10 diffusion coefficient, and Fig. 4(b) shows the measure- Binder weight (kg/ 400 300 300 ment of the cover depth, and these values were observed m ) to follow a normal distribution. The probabilistic varia - C 207 196 462 tions (average and COV) of the derived design factors are Cover depth (mm) 30 10 5 shown in Table 2. Each service life was evaluated using the information of Table 1 and Eq. (5). The average and COV of the service 4 Probabilistic Repair Cost Evaluation Considering life obtained from 1000 times random simulations were Exposure Environment derived through the process in Fig. 5 and the results are In order to evaluate the repair cost in probabilistic man- summarized in Table 3 with the conventional unit cost ner, the average and COV of the MFP as well as the ser- of each repair technique (Dongyang Economic Research vice life extended through each repair material and its Institute, 2021). (a) Sulfate ion diffusion test (b) Cover depth measurement Fig. 4 Evaluation of random variable of diffusion coefficient and cover depth. Table 2 Random variable derivation of diffusion coefficient and cover depth. Variable Sewage concrete Conventional repair mortar Bacteria repair material Cover depth/repair thickness (mm) 30.300 10.260 5.120 COV 0.121 0.132 0.108 −12 2 Diffusion coefficient (× 10 m /s) 2.120 2.090 0.170 COV 0.135 0.192 0.121 Y oon et al. Int J Concr Struct Mater (2022) 16:22 Page 7 of 12 Fig. 5 Flowchart for derivation of service life and COV. Table 3 Initial and extended service life and their COV with different repair technique. N = 1000 Concrete Normal repair Bio-slime – 294.4 $/m 197.8 $/m Service life Average COV Average COV Average COV 200 ppm 21.33 0.19 6.24 0.27 15.65 0.25 120 ppm 35.71 0.18 10.36 0.25 25.30 0.17 Table 4 Simulation of repair cost (control case). MFP and COV Changing MFP Changing extended service life with Changing COV of extended service life repair 21.3/0.19 0.5, 1.0, 1.5 times with constant COV (0.19) 0.5, 1.0, 1.5 times with constant COV (0.25) 0.125, 1.0, 2.0 times with constant extended service life (15.7 years) 15.6/0.25 Yoon et al. Int J Concr Struct Mater (2022) 16:22 Page 8 of 12 5 Probabilistic Repair Cost Calculation decreased (Jung et al., 2018; Yang et al., 2020b). After and the Factors Influencing Cost 60 years, the repair cost was evaluated to be $724.40 5.1 Simula tion on Repair Cost Due to Variations in Design for 0.5 × MFP, $590.50 for 1.0 × MFP, and $453.30 for Parameters 1.5 × MFP, respectively. The extended service life with In the section, the influence of the average and standard repair also significantly affects the total repair cost. deviation of the design factors in RC sewage concrete When the extended service life through repair increased was analyzed on the total repair cost. With respect to by a factor of 1.5 times to 23.5 years, the repair cost the simulation conditions, the changes in the repair decreased to $428.40. However, when it was shortened to cost were analyzed while the average and COV varied 7.8 years (a half of 15.7 years), the repair cost significantly in the 200 ppm exterior condition. The effect of chang - increased to $1060.70. The COV of extended service ing MFP, the service life with repair, and variations in life depends on quality of repairing and it shows inter- repair materials was analyzed on repair cost. The analy - esting results. When the COV of the extended service sis conditions for the repair cost simulation are listed in life decreased from the given condition (0.25) to 0.063 Table 4. and 0.5, the repair costs after 60 years was $590.60 and Under the given condition, MFP was derived as $582.50, respectively, which showed insignificant effect 21.3 years. The changes in the repair cost were analyzed on repair cost, however the shape of a step function is for 0.5 × MFP and 1.5 × MFP. In this case, the service clearly shown with decreasing COV since the tendency life extension with repair (15.6 years) and COV (0.25) becomes more identical to that of the deterministic were fixed. As in the previous studies, when MFP was method as COV goes to zero (Jung et al., 2018; Kwon, extended in the early construction stage, the frequency 2017b; Yang et al., 2020a). The repair cost with changing of repairs and the related maintenance cost significantly MFP, the extended service life, and affected by COV in Deter. (Bacteria repair material: control case) Deter. (Bacteria repiar: control case) Prob. (Bacteria repair material: 21.3 years) 700 Prob. (Bacteria repair material: 15.6 years) Prob. (Bacteria repair material: 10.6 years) 1000 Prob. (Bacteria repair material: 23.5 years) 600 Prob. (Bacteria repair material: 31.9 years) Prob. (Bacteria repair material: 7.8 years) Intended serviec life (years) Intended serviec life (years) (b) Variationin repair cost with varying extended (a) Variationin repair cost with varying MFP service life with repair (average) Deter. (Bacteria repiar: control case) MFP Prob. (Bacteria repair material: COV 0.25) Extended service life 1.8 Prob. (Bacteria repair material: COV 0.063) Deter. Prob. (Bacteria repair material: COV 0.50) COV 1.6 1.4 1.2 200 1 100 0.8 0.6 0102030405060 0.40.6 0.81 1.21.4 1.6 Changing ratio to control case Intended serviec life (years) (d) Variation in repair ratio with varying MFP, extended (c) Variationin repair cost with varying extended service life with repair (COV) service life,and its COV after 60 years Fig. 6 Repair cost analysis considering changing MFP, extended service life, and COV. 2 2 Repair cost ($/m ) Repair cost ($/m ) Repair cost ($/m ) Ratio of repair cost Y oon et al. Int J Concr Struct Mater (2022) 16:22 Page 9 of 12 the extended service life are shown in Fig. 6(a–c), respec- showed a continuous line due to the COV of service life tively. Fig. 6(d) shows the ratio of the repair cost com- (Jung et al., 2018; Kwon, 2017b). When the exposure pared with the given condition. environment was 120 ppm, the repair cost was evalu- In Fig. 6d, when MFP and extended service life ated to be $883.20/m for the deterministic method and increased to 1.5 times, the repair cost decreased to 77% $818.30/m for the probabilistic method, respectively. and 73%, respectively, however when they decreased to The external sulfate concentration increased from 120 0.5 times, the repair cost increased to 123% and 180%, to 200 ppm, the number of repairs increased from three respectively, which means that it is preferentially required to seven, and the repair cost showed $2060.80/m for the to secure the extended service life with repair and MFP deterministic method and $1931.50/m for the probabilis- for the limited target service life. tic method. Fig. 7b shows the results of evaluating the repair cost 5.2 E valuation of Total Repair Cost Considering Sewer for the bacteria repair material derived in this study. In Networks the case of 120 ppm, the number of repairs was one, 5.2.1 Evaluation of Repair Cost with the Unit Length and the repair cost was $197.8/m for the deterministic of the Target Structure method and $287.93/m for the probabilistic method. In The target service life was determined as 60 years and the harsh condition (200 ppm), the number of repairs the repair cost per unit length with the exposure envi- increased to three, and the repair cost was $593.40 for the ronment was analyzed, as shown in Fig. 7(a) for conven- deterministic method and $590.00 for the probabilistic tional repair technique. As done in previous studies, the method. The probabilistic method can reduce the repair stepwise repair cost was modeled in the deterministic cost, but more importantly, it can consider the service method, but the repair cost with probabilistic method life which varies through the repair material, and reason- ably reduces the repair cost compared to the determin- istic method when the target service life is changed. For example, in the case of a bacteria repair material with a concentration of 120 ppm, the service life has a cycle of 25.3 years for service life for the deterministic method. For the probabilistic method, it is evaluated as a con- tinuous function so that the probabilistic method is eco- nomical for 12.2 years after the initial service life (MFP: 35.7 years). 5.2.2 E valuation of Total Repair Cost in Target Sewage Network As described in Sect. 3.1, the length of sewage pipelines (a) Variation in repair cost with increasing service was found to be 1425 m for the 120 ppm section and life forconventional repair mortar 1843 m for the 200 ppm. With the probabilistic method, the total repair cost could be easily calculated through simple sum of each repair cost with pipe length since the repair cost had a continuous repair cost function. How- ever, for the deterministic method, the repair cost due to the extended service life irregularly varied depending on the repair event and environment. Therefore, the total repair cost was calculated based on the calculation pro- cedure in Fig. 8 and the total repair cost results are plot- ted in Fig. 9. As shown in Fig. 9, the repair cost increases alongside the increase in service life, and the stepwise repair cost shows complicated rise depending on the two exposure environments. In the previous study (Jung et al., 2018), (b) Variation in repaircostwith increasing service the repair cost analysis was performed for chloride life forbacteriarepairmaterial ingress of RC structures by probabilistic method. In the Fig. 7 Variation in repair cost with increasing service life for normal work, the probability distributions of design parameters and bacteria repair materials. such as diffusion coefficient, surface chloride content, Yoon et al. Int J Concr Struct Mater (2022) 16:22 Page 10 of 12 Fig. 8 Flowchart for repair event‑based total repair cost with deterministic method. Table 5 Total repair cost to intended service life. Conventional repair mortar (K $) Bacteria repair material (K $) Deterministic Probabilistic Deterministic Probabilistic method method method method 5057.00 4725.80 1376.00 1498.60 6000 120 100.0 93.5 5000 100 4000 80 Fig. 9 Variation of total repair cost with varying exposure conditions 3000 60 and repair method (deterministic and probabilistic method). 2000 40 29.6 27.2 1000 20 and cover depth were assumed with one repair event. In 0 0 this study, a sulfate-resistant repair mortar was devel- Conventinal Conventinal Bacteria repair Bacteria repair repair mortar- repair mortar- material- material- oped, and the probability distributions the analysis Deterministic Probabilistic Deterministic Probabilist variables were evaluated and defined through lab tests Case and field survey. In addition, this study has proposed a Fig. 10 Total repair cost and its ratios to normal repair cost. method for estimating the total repair cost of the sewage system with different exposure conditions and service life. material was used, the repair cost decreased to 1376 K$ When the target service life of 60 years arrived, the total for the deterministic method and 1498 K$ for the proba- repair cost was evaluated to be 5057 K$ for the determin- bilistic method, respectively. The significant difference istic method and 4725 K$ for the probabilistic method in from the repair method was caused by the difference in the the conventional repair method. When the bacteria repair number of repairs. The number of repairs was nine for the Total repair cost to 60 years (K$) Ratio of repair cost Y oon et al. Int J Concr Struct Mater (2022) 16:22 Page 11 of 12 conventional repair material but only four for the bacte- sulfate ion) with a length of 1425 m and the harsh ria coating. This is because the application of the bacteria region (200 ppm of sulfate ion) with 1843 m, the coating significantly extended the service life through the repair cost for each region and the repair cost for the low diffusivity of sulfate ions. entire networks were evaluated considering the tar- Table 5 lists the repair cost results for each method when get service life (60 years). Within the target service the target service life of 60 years was reached and the cost- life, the total repair cost was evaluated to be 5057 K$ effectiveness is shown in Fig. 10. When the bacteria repair (deterministic method) and 4725 K$ (probabilistic material was used, the repair cost decreased to 27%–31% method) for the conventional repair method. How- of that of the conventional repair material. ever, when the bacteria coating repair material was The newly developed show significantly reduced repair utilized, it was greatly reduced to 72.8% and 68.3%, cost, however, it has still limitations. The number of sam - respectively, indicating that it is a highly economical ples for probability distribution characteristics is very lim- repair method. Through changing repair material, the ited and the maintenance of quality and performance is repair frequency was reduced from nine to four since not the same as the lab-scaled experiments considering the use of the bacteria repair material significantly the mass production and construction process (Yang et al., extended the service life through the low diffusivity 2021; Yoon et al., 2021c). In addition, the repair cost from of sulfate ions. probabilistic method may lead to unrealistic and uneco- nomical results if COVs of MFP and extended service life Acknowledgements from repair are too big, so that reasonable PSLF (probabil- This research was supported by a grant (21SCIP‑ C158976‑02) received from ity-of-service-life function) and COV are required. the Construction Technology Research Program funded by Ministry of Land, Infrastructure and Transport of the Korean government and by the National Research Foundation of Korea (NRF: No.NRF‑2020R1A2C2009462). 6 Conclusions Authors’ contributions In this study, the repair cost for RC sewage pipelines HSY conducted the experiments and collected the data; SJK processed the exposed to sulfate ingress was evaluated using determin- data, proposed the analytical method, conducted the modeling, and drafted this manuscript; YSY conducted review and investigated previous studies; istic and probabilistic methods. From the measurement KHY checked the proposed method and writing and supervised the entire of diffusion coefficient and coating thickness, random research. All the authors read and approved the final manuscript. variables for design parameters were obtained and they Author’s information were utilized for total repair cost evaluation. The follow - H.S. Yoon is a research professor at Department of Architectural Engineer‑ ing conclusions are drawn: ing, Kyonggi University, Suwon 16227, Korea. S.J. Kwon is a professor at Department of Civil and Environmental Engineering, Hannam University, Daejeon 34430, Korea. Y.S. Yoon is a post‑ doctoral researcher at Department 1. The probabilistic variations (average and COV) of the of Civil and Environmental Engineering, Hannam University, Daejeon 34430, bacteria repair material, conventional repair mortar, Korea. K.H. Yang is a professor at Department of Architectural Engineer‑ cover depth, and diffusion coefficient were evaluated ing, Kyonggi University, Suwon 16227, Korea. through actual measurement and the sulfate ion dif- Funding fusion test. The exposure environment was classified Funding was received from the Ministry of Land, Infrastructure, and Transport into two cases (120 and 200 ppm), and the service life of the Korean government (21SCIP‑ C158976‑02) and National Research Foun‑ dation of Korea (NRF) (No. NRF‑2020R1A2C2009462). and its COV were evaluated considering three vari- ations of design parameters (concrete, conventional Availability of data and materials repair mortar, and bacteria repair material). Based on The experimental data used to support the observations of this study are included in the article. COV of extended service life, the probabilistic repair cost was evaluated. Declarations 2. In the given condition of target service life of 60 years, the maintenance-free period (MFP) and the Competing interests extended service life with repair were evaluated to be The authors declare that they have no competing interests. important factors since MFP and the extended ser- Author details vice life with repair increased to 1.5 times, the repair Department of Architectural Engineering, Kyonggi University, Suwon, Korea. cost decreased to 77% and 73%, respectively. Department of Civil and Environmental Engineering, Hannam University, Deajeon, Korea. 3. Unlike the deterministic method, the probabilistic repair cost evaluation method can handle service Received: 18 October 2021 Accepted: 9 February 2022 life variations and is implemented as a continu- ous cost line. It can reduce the repair cost in a rea- sonable manner by altering the target service life of the structure. For the normal region (120 ppm of Yoon et al. 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International Journal of Concrete Structures and Materials – Springer Journals
Published: Dec 1, 2022
Keywords: MFP (maintenance-free period); bacteria repair material; service life; repair cost; maintenance
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