Predicting the residual life of concrete structures in biocorrosion from the position of the theory of mass transfer

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Introduction For a long time, they considered that concrete and reinforced concrete structures have an unlimited life, because concrete only gains strength over time [1; 2]. However, during operation, building structures are influenced by various aggressive environments, which eventually result in their destruction. Thus, corrosive destruction of building materials, including biodegradation, is most often found in of food, chemical and other industries' buildings. Figure 1 shows photographic materials from the inspection of corrosively damaged structures of an industrial building. Currently, there are no guidelines in the building regulations for the design and calculation of structures taking into account corrosive damage. Predicting the life of concrete and reinforced concrete structures, assessing the residual life of their operation is an urgent task, which solution is possible by applying the theory of mass transfer. The works of V.P. Selyaev [3; 4], V.T. Erofeev [5; 6], V.I. Rimshin [7], B.V. Gusev [8; 9], N.K. Rosenthal [10] and other scientists are devoted to the development of methods for calculating structures exposed to corrosive destruction, modeling of biocorrosive damage. The most common structural damages during operation in aggressive environments are described in the N.K. Rosenthal's works [10]. The article describes in more detail the process of corrosive destruction of concrete during biofouling. 144.jpg 149.jpg Figure 1. Corrosion damage to the coating of an industrial building in Moscow Nowadays, it has been established that biocorrosive destruction of concrete and reinforced concrete structures in its pure form is rare, most often it develops in aggregate with other types of corrosion [11-13]. Additional impact of the bioaggressive environment results in an even greater increase in the material porosity, intensification of diffusion processes in the body of concrete and, as a consequence, stimulation of corrosion destruction in general. Building structures operated in an aquatic environment or an environment of high humidity are particularly often subjected to biocorrosive destruction. When examining operated concrete and reinforced concrete structures, it is usual to determine their residual life. By mathematical modeling of the corrosion destruction of concrete, taking into account the biofactor, it is possible to establish the essence of the exchange processes occurring between cement stone and biota, predict this exchange and formulate ways to prevent such corrosion damage, thereby saving an impressive amount of money. Methods The development of a mathematical description of the biocorrosive destruction of concrete was carried out from the standpoint of the theory of mass transfer. The “concrete - biofilm - liquid” system, which is typical for the case of biofouling of a concrete structure exposed to an aquatic environment during operation, was considered. This system consisted of two unlimited plates in contact with each other. Each of the plates was characterized by the size and properties of the simulated object. The task was to determine the concentration change of the transferred component (Ca(OH)2) over time by the thickness of the concrete structure. A mass transfer model in an unlimited two-layer plate was compiled in the form of a system of partial differential equations of the parabolic type with boundary conditions of the second kind at the boundary of concrete with liquid and of the fourth kind at the boundary between concrete and biofilm [14]. The boundary condition of the second kind characterizes the absence of a flow of matter. The boundary condition of the fourth kind is characteristic for the case of equality of concentrations of the transferred component (Ca(OH)2) and mass flows at the phase boundary. In order to solve the boundary value problem for differential equations, the Laplace integral transformation method was used [15]. Discussion and results As a result of mathematical modeling, a system of equations (1)-(8) was compiled. (1) (2) (3) (4) (5) (6) (7) (8) where C1(x, τ) - a concentration of the transferred component in the body of concrete, kg of CaO/kg of concrete; C2(x, τ) - a concentration of the transferred component in the biofilm, kg of CaO/kg of biomass; k1,2 - mass conductivity ratios, m2/s; δ1 - a concrete structure thickness, m; δ2 - a biofilm thickness, m; C1,0 - an initial concentration of the transferred component, kg of CaO/kg of concrete; C2,0 - a initial concentration of the transferred component, kg of CaO/kg of biomass; ρcon, ρbiom - concrete and biomass densities, kg/m3; qn(τ) - a density of the mass flow leaving the biofilm into the liquid flow, m is a Henry's equilibrium constant, kg of biofilm/kg of concrete. The previously published works of the authors [13; 16] describe in detail the process of solving this system of differential equations. By replacing the functions of real variables with their images, that are connected via the Laplace operator, a complex system of differential equations has been reduced to the simplest algebraic operations. The solution of the system in general has taken the form: (9) (10) (11) (12) (13) where Z1(x̅, Fom) - a dimensionless concentration of the transferred component over the thickness of the concrete structure; Z2(x̅, Fom) - a dimensionless concentration of the transferred component over the thickness of the biofilm; x̅ = x/δ1 - a dimensionless coordinate; Kk = k2 / k1, Kδ = δ2 / δ1, N - a ratio that considers the characteristics of the phases; Fom = (k1τ) / - the Fourier criterion; μm - the roots of the characteristic equation; - the Kirpichev mass-exchange criterion. During the vital activity of microorganisms, the biofilm density changes over time as a result of the growth, reproduction and death of biota [17; 18]. This fact was considered in the mathematical model by introducing the ratio . The correctness of the proposed mathematical model was verified by conducting numerical experiments, those results illustrate the influence of similarity criteria (Fourier, Kirpichev) on the dynamics of concrete biodegradation process (Figures 2 and 3). The calculated data obtained had a high similarity with the experimental data received by the authors in earlier studies [15; 19]. Large gradients of the concentrations of the transferred component as a result of changes in the values of the Kirpichev mass-exchange criterion are observed in Figure 2. Figure 3 shows the curves of changes in dimensionless concentrations of the transferred component at different values of the Fourier mass transfer criterion. Figure 2. Profiles of dimensionless concentrations of the transferred component over the thickness of concrete and biofilm at Kk = 1, Kδ = 0.1, N = 1; Fom = 1 with different values : 1 = -0.5; 2 = -1; 3 = -1.5; 4 = -2; 5 = -2.5; 6 = -3 Figure 3. Profiles of dimensionless concentrations of the transferred component over the thickness of concrete and biofilm at Kk = 1, Kδ = 0.1, N = 1, = 0.5 with different values Fom: 1 = 0.5; 2 = 1; 3 = 1.5; 4 = 2; 5 = 2.5; 6 = 3 Conclusion The obtained solutions (9)-(13) provide for determining the concentration values of the transferred component over the thickness of both the concrete structure and in the biofilm itself, at any time. At the same time, the obtained relationships make it possible to predict the numerical value of the transferred component over the thickness of the concrete structure according to the available experimental data. The generality of the mathematical model allows us to extend it to predict the durability of various types of concrete. Based on this, it becomes possible to determine the residual life of building structures during operation in aggressive environments.

About the authors

Sergey V. Fedosov

Moscow State University of Civil Engineering (National Research University)

Email: mr.fedosow.2011@yandex.ru
ORCID iD: 0000-0001-6117-7529

Academician of the RAACS, Doctor of Technical Sciences, Professor, Professor of the Department of Technology and Organization of Construction Production

26 Yaroslavskoye Shosse, Moscow, 129337, Russian Federation

Svetlana A. Loginova

Yaroslavl State Technical University

Author for correspondence.
Email: sl79066171227@yandex.ru
ORCID iD: 0000-0001-6025-8968

Candidate of Technical Sciences, Associate Professor of the Department of Building Structures

88 Moskovskii Prospekt, Yaroslav, 150023, Russian Federation

Anna A. Shalygina

Yaroslavl State Technical University

Email: miss-anna.shalygina@yandex.ru
ORCID iD: 0000-0002-8263-4546

student

88 Moskovskii Prospekt, Yaroslav, 150023, Russian Federation

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