Influence of Damage Level on Dynamic Characteristics of Reinforced Concrete Structures when Assessing their Seismic Resistance

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1. Introduction During operation, buildings and structures sustain damage, the origin of which can be divided into two main categories: man-made (explosions, fires, removal of structural elements, accidents) and natural. In the modern world, reinforced concrete buildings and structures account for 70-80% of the total volume of construction. Due to the influence of aggressive media, as well as man-induced factors, the process of corrosion of load-bearing reinforced concrete elements can start, which in turn leads to a decrease in the rigidity and load-bearing capacity of the building. Special attention should be paid to the assessment of the technical condition of existing buildings located in seismic regions of the Russian Federation. Considering the reduction of stiffness parameters of buildings due to existing damage, integral dynamic characteristics are noticeably reduced. Assuming unchanged mass characteristics of the object, the eigenfrequencies of vibration become lower, which in turn affects such parameters as the period and shape of free vibrations, which characterize the degree of dynamic impact on the object and the change in shape at various points under study [1-5]. The main regulatory document in the field of monitoring and technical inspection of buildings and structures is GOST 31937-2011[2] interstate standard. This document regulates the definition of dynamic parameters of buildings and structures, which characterize the dynamic properties that are exposed under dynamic loads. The definition of dynamic properties includes frequencies, periods, decrements (X, Y, Z axes) of vibrations, transfer functions of the structure (as well as its individual parts and elements) [6]. Measurement of dynamic parameters should be performed after the construction of the facility, as well as 2 years after. If the measurement results of the dynamic characteristics do not differ by more than 10% from the previous inspection, the subsequent measurement must be repeated after 2 years. If the deviation of 10% from the original parameters is exceeded, a full mandatory unscheduled inspection should be carried out. In addition, these dynamic parameters can be used for the following tasks: ➢ refinement (validation) of the numerical model; ➢ evaluation of the actual seismic resistance; ➢ implementation of seismic strengthening measures; ➢ determination of the damage degree; ➢ localization of damage locations. The main measurement rules and instrumental methods for determining eigenfrequencies, periods and logarithmic decrements of vibrations are established by GOST R 54859-2011[3] national standard of the Russian Federation. The main purpose of the study is to investigate the influence of the level of corrosion damage of reinforced concrete structures on the change of their dynamic characteristics. Based on the obtained and analyzed data on the influence of corrosion on the dynamics of reinforced concrete structures located in earthquake-prone regions, it is possible to predict their earthquake resistance. 2. Methods In [7], seismic resistance of a cast-in-situ reinforced concrete building was evaluated based on experimental data from the Polytechnic University in Hong Kong. The tower-type building was subjected to structural damage. At each stage, the fundamental vibration frequency was measured at each damage level, and the results are summarized in Table 1. The building was modeled in Abaqus CAE, and according to the calculation results, the building collapse occurs at the degree of reduction of natural vibration frequency ≥ 15%. The calculation results confirm the results of the field experiment. In [8], short-term monitoring of 6 multistory buildings of different years of construction (from 1973 to 2014), with different number of storeys and sections was performed. Monitoring was conducted between July and October 2017. Based on the test results, the author concludes that the method of dynamic monitoring can be applied to assess building damage as an integral method with mandatory additional technical inspection. Table 1 Results of the experiment in paper Degree of damage Value of fundamental vibration frequency, Hz Decrease in frequency of natural vibration, % No damage 4.61 0 Light 4.55 1.3 Moderate 4.32 6.3 Serious (severe) 3.70 19.7 Catastrophic (before complete destruction) 2.58 44.0 S o u r c e : Chauskin A.Yu. [7] In [9], an experimental evaluation of an 11-storey frame building of the KUB-2.5 series was performed to analyze the level of seismic resistance of residential buildings. The research results are based on the parametric analysis of forced vibrations (microseismic vibrations), which allowed to estimate the change in the integral stiffness of load-bearing structures due to damage accumulation. The initial dynamic characteristics were determined, which will allow further monitoring of the technical condition of the building. The author of [10] states that the advantage of the dynamic control method is its “integrality”, which reflects the deformation of bond of reinforcement with concrete in reinforced concrete structures, and allows to evaluate strength, stiffness and crack resistance. The author investigated a reinforced concrete beam with a length of 6 meters and a cross section of 40×70 cm. The beam had a 15×15×3 cm defect located at a distance of 3 meters from one of the supports. The modeling was performed in ANSYS PC (Figure 1). The experiment showed that with the increase of the defect size there is a decrease in the eigenfrequencies of vibration. The best result about the location of the defect was shown by the method of changing the shape of vibrations, the basis of which is the modal convergence criterion (MAC): n * 2 j=1 (x) j (x) j MAC x( ) = n 2 n *2 , (1) j=1 (x) j j=1 (x) j where x is the distance to the measurement point, n is the number of vibration measurement points, φ and φ* are the values of vibration shape displacements without and with damage. The error of the method amounted to 2.33%, which is a positive result. a b Figure 1. Defect detection by modal convergence method: a - FE model of beam with defect (first and second eigenfrequencies); b - location of the defect along the length of the beam S o u r c e : Kadomtsev M.I. et al. [10] The modal convergence criterion (MAC) varies from 0 (no correlation between modes of vibration) to 1 (100% matching). Paper [11] considers the problem of predicting the consequences of earthquakes, man-made accidents, natural factors, and other impacts on the load-bearing structures of operating buildings. It is recommended to use eigenfrequencies, decrements, and periods of vibration as the main parameters for verification of the analysis model. To predict the seismic resistance of buildings with damage, it is necessary to create a model with the closest possible values of dynamic characteristics. As an example, the author considers a large-panel building located in St. Petersburg. Based on the results of the survey, the frequencies of natural vibrations were determined, and the model was created in ANSYS. The results are summarized in Table 2. Table 2 Results of the calculation in paper Shape of vibration according to the model Vibration frequency recorded during testing, Hz Frequency of vibration according to the model adjusted by dynamic characteristics, Hz Mismatch of vibration frequency in relation to the design frequency, % 1 1.25 1.291 3.1 2 1.92 1.944 1.2 3 1.94 2.045 5.1 4 5.96 5.604 5.9 5 6.98 6.832 2.1 6 7.812 7.456 4.5 S o u r c e : Savin S.N., Smirnova E.E. [11] Based on the obtained data, calculations were performed considering the damage to buildings from the unevenness of building settlement with subsequent partial failure. The author concluded that this method could solve various problems, both in evaluating the technical condition of the building, and for forecasting the residual life of damaged objects. To evaluate the reduction of dynamic characteristics of corrosion-damaged structures, an experiment is conducted on reinforced concrete columns with dimensions of 100×100×700 mm [12-17]. Damage to reinforcement is achieved by electrocorrosion of specimens in salt solution. The undamaged specimen is fixed by the widening in the base to the floor. At a distance of 150 mm from the free edge of the column, a displacement sensor parallel to the impact is installed, and a force sensor is fixed to the end of the column above the displacement sensor (Figure 2). The test methodology and processing of the results are as follows: 1. The force sensor is struck with a hammer to excite forced vibrations in the column. 2. Recording equipment reads the impact force and records at a frequency of 1000 Hz. 3. Based on the test results, the time graph of the vibration amplitude is plotted and the first eigenfrequency of vibration, vibration period, logarithmic decrement of vibration and damping coefficient are analytically determined (Figure 3). The first eigenfrequency for the intact sample was 37.037 Hz, and the vibration period was 0.027 s. To estimate the damping of the system, we introduce the logarithmic decrement of vibration - δ. The rate of damping is defined as the natural logarithm of the ratio of peak vibration amplitudes spaced by one period: yi T (2) δ =ln α .= yi+1 Also, in dynamic analysis, important characteristics are the coefficient of energy absorption ψ characterizing the cyclicity of deformation process, which in the form of the ratio to the number 2π gives inelastic deformation coefficient γ. The inelastic drag coefficient (equation (3)) and energy absorption coefficient (equation (4)) were determined based on the experiments performed [18-25]. ЕЙСМОСТОЙКОСТЬ СООРУЖЕНИЙ ψ γ = = , (3) 2π π t T dy y ψ =-2 t+ y00 = 2ln yi+i1 2π.= (4) a b Figure 2. Specimen testing: a - reinforcement model; b - testing of samples S o u r c e : made by A.G. Tamrazyan, M.V. Kudryavtsev Figure 3. “Amplitude, mm vs time, s” graph S o u r c e : made by A.G. Tamrazyan, M.V. Kudryavtsev 3. Results and Discussion Equations (2)-(4) were used to calculate the main dynamic characteristics obtained experimentally on reinforced concrete column specimens undamaged by corrosion. The results of calculations are presented in Table 3. Table 3 Results of the authors’ calculations № Sample ID Impact along the axis Vibration period Vibration frequency Logarithmic decrement of vibration Circular frequency Inelastic drag coefficient Energy absorption coefficient T ν δ ω γ ψ 1. 1с-1 Х 0.027 37.04 0.263 232.6 0.0837 0.525 Y 0.031 32.26 0.173 202.6 0.0552 0.347 2. 1с-2 Х 0.027 37.04 0.369 232.6 0.1175 0.738 Y 0.026 38.46 0.133 241.5 0.0423 0.266 3. 1с-3 Х 0.024 41.67 0.230 261.7 0.0734 0.461 Y 0.028 35.71 0.236 224.3 0.0750 0.471 4. 1с-4 Х 0.026 38.46 0.246 241.5 0.0784 0.492 Y 0.026 38.46 0.808 241.5 0.2572 1.615 5. 1с-5 Х 0.031 32.26 0.468 202.6 0.1491 0.937 Y 0.029 34.48 0.911 216.6 0.2903 1.823 6. 1с-6 Х 0.026 38.46 0.156 241.5 0.0496 0.311 Y 0.027 37.04 0.308 232.6 0.0982 0.617 7. 1с-7 Х 0.028 35.71 0.400 224.3 0.1274 0.800 Y 0.027 37.04 0.355 232.6 0.1130 0.710 8. 2с-1 Х 0.028 35.71 0.169 224.3 0.0537 0.338 Y 0.035 28.57 0.122 179.4 0.0389 0.244 9. 2с-2 Х 0.031 32.26 0.330 202.6 0.1052 0.661 Y 0.03 33.33 0.423 209.3 0.1348 0.846 10. 2с-3 Х 0.026 38.46 0.289 241.5 0.0921 0.579 Y 0.027 37.04 0.271 232.6 0.0865 0.543 11. 2с-4 Х 0.026 38.46 0.644 241.5 0.2049 1.287 Y 0.029 34.48 0.402 216.6 0.1282 0.805 12. 2с-5 Х 0.026 38.46 0.344 241.5 0.1095 0.687 Y 0.029 34.48 0.201 216.6 0.0639 0.401 13. 2с-6 Х 0.03 33.33 0.144 209.3 0.0459 0.288 Y 0.03 33.33 0.264 209.3 0.0840 0.527 14. 2с-7 Х 0.026 38.46 0.223 241.5 0.0710 0.446 Y 0.029 34.48 0.216 216.6 0.0687 0.432 Mean value: 35.89 0.325 225.4 0.1035 0.650 S o u r c e : made by A.G. Tamrazyan, M.V. Kudryavtsev Since the experimental study with artificial corrosion of reinforced concrete takes a long time, the test results with a comparison of the obtained results will be presented in the upcoming articles. ЕЙСМОСТОЙКОСТЬ СООРУЖЕНИЙ Structural Mechanics of Engineering Constructions and Buildings 4. Conclusion 1. Based on the scientific studies using methods of mathematical analysis, computer modeling and in-situ tests, conclusions were made about the significant effect of reducing the frequency of natural vibrations on the degree of damage to the building under dynamic action such as seismic loading. This effect arises due to the accumulation of damages of different nature in the nodes of structures and elements of buildings, making them less rigid and more compliant, which affects the overall degradation of the rigidity of the structure. 2. The method of dynamic assessment of the technical condition of buildings and structures is popular among surveyors, but there are difficulties in comparing measured values with the original indicators, because the latter, in turn, have not been measured. This problem can be solved by designing a high quality model in a CAE software. Also, to estimate the residual life of buildings and to assess the seismic resistance of buildings, the results of measurements can be introduced into the calculation to refine the FEM model considering the technical condition of the building. 3. Conducting the experiment will allow to expand the field of assessment of the technical condition of buildings considering the corrosion damage of load-bearing structures, which will increase the accuracy of solving the problems of earthquake resistance.

About the authors

Ashot G. Tamrazyan

Moscow State University of Civil Engineering (National Research University)

Author for correspondence.
Email: tamrazian@mail.ru
ORCID iD: 0000-0003-0569-4788
SPIN-code: 2636-2447

Doctor of Technical Sciences, Professor, Head of the Department of Reinforced Concrete and Masonry Structures

Moscow, Russia

Maksim V. Kudryavtsev

Moscow State University of Civil Engineering (National Research University)

Email: KudryavtsevMV@mgsu.ru
ORCID iD: 0000-0002-2585-5684
SPIN-code: 2543-0639

Postgraduate student, Department of Reinforced Concrete and Masonry Structures

Moscow, Russia

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