CC BY
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BUILDING STRUCTURES,
BUILDINGS AND CONSTRUCTIONS
UDC 691.175
Rostov State University of Civil Engineering D. Sc. in Engineering, Prof. of Dept. of Automobile Roads
L. R. Mailyan
Russia, Rostov-on-Don, tel.: (863)263-11-43; e-mail: vestnik_vgasu@mail.ru
Voronezh State University of Architecture and Civil Engineering Ph. D. in Engineering, Senior lecturer of Dept. of Organization of Construction,
Examination and Property Management
S. I. Ushakov
Russia, Voronezh, tel.: (473)274-84-53; e-mail: istroy@inbox.ru
L. R. Mailyan, S. I. Ushakov
COMPREHENSIVE SAFETY ASSESSMENT OF COMPRESSION ELEMENTS OF STRUCTURES FROM EPOXY POLYMER CONCRETE
Problem statement. The aim of the paper is to describe the results of comprehensive nondestructive safety assessment of compression elements of structures from epoxy polymer concrete under monotonous loading.
Results and conclusions. A mathematical model is constructed on the basis of the theory of fuzzy sets to assess the state of structures from epoxy polymer concrete operating under load. Three safety levels of polymer concrete structures operating under load are recognized using microcrack formation criterion. The proposed criterion is useful for practical implementation due to the special feature of operation of polymer concrete structures in chemically hostile environments.
Keywords: epoxy polymer concrete, ultrasound, acoustic emission, deformations, modeling, safety assessment. Introduction
One of the most important and pressing issues to be addressed in the current research is safety assessment of bearing polymer concrete structures used in chemically hostile and corrosive
environments [1, 3, 4]. According to [2], safety is such a state of a complex system (a building structure) when an impact of external (chemically hostile environments) and internal (stresses) factors does not cause a system to deteriorate (i. e. a reduction in durability) or be no longer suitable for service and development (i. e. overloading).
In view of polymer concrete structures being operating mainly in chemically hostile or corrosive environments as well as damage likely to be caused should these structures fall down, the challenges posed by establishing levels and criteria to be used in their safety assessment remain to be tackled.
A failure of ferroconcrete structures impacted by corrosion active environments is often due to reinforcement corrosion that is induced, as pointed out above, by an excessive microcrack formation in a protective concrete layer. Therefore, the criteria for safety assessment of these structures should be based not only on the characteristics of polymer concrete strength but also on particular ways in which micro cracks occur and evolve in the structure of a protective concrete layer. The authors of the paper made a study into the processes of compressive microcrack formation in epoxy polymer concrete using three methods (ultrasonic testing, deformation, acoustic emission monitoring) different in their physical nature. Based on the results obtained in the course of the study, a mathematical model was proposed for safety level assessment of structures made of epoxy polymer concrete operating under load. A complex criterion for safety assessment was set forth.
The paper looks at the basic stages of modeling, assumption and acceptance incorporated into the model as well as the outcome of its experimental application.
1. Safety levels of load-operating structures and basic stages of modeling
According to the character of negative effects that may be caused by various stresses, the entire loading process of a structure can be basically broken down into three safety levels (Fig. 1):
1. AS (Admissible Stress) — admissible (safe) stress level;
2. RS (Restricted Stress) — restricted stress level (the level that is unlikely to result in impending failure of a structure but does compromise its chemical resistance and therefore its performance and durability);
3. CS (Critical Stress) — critical (beyond project) stress level — a high chance of a structure falling down.
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0
Relative stress level g/R
Fig. 1. A membership function of a relative stress level in the stages AS, RS and CS
Since we are dealing with safety level assessment of stress in structures operating under load, the input parameters would be a set of assessments obtained by means of non-destructive testing methods: A is a velocity of acoustic emission signals passage related to a unit volume of material, U is a relative velocity of longitudinal ultrasonic pulses and D is a density defect of concrete that is established according to deformation measurements. The input parameters (complex assessments) of the model are values that describe changes occurring in the structure of polymer concrete operating under load. Based on the laboratory tests performed on specimen of epoxy polymer concrete, we can assume the possibility of identifying each of the input parameters (A, U, D) as three safety levels (A1, A2, A3, U1, U2, U3 and D1, D2, D3).
In order to design a mathematical model that allows a safety level assessment (AS, RS, CS) of compressed elements of structures made of epoxy polymer using the above complex assessments of the state of concrete (A(i), U(i), D(i)), Mamdani’s fuzzy inference method was utilized. A more detailed study of Mamdani’s algorithm is a major concern of the theory of fuzzy sets.
The output parameters of the model are complex a complex assessment H = [0-1], i. e. a response function of the model and a discrete value S = {“AS”, “RS”, “CS”} like a linguistic variable necessary for H to be identified as a certain safety level. In the theory of fuzzy sets there can be a gradual understanding of the membership of elements in a set. A degree of its membership is described by a membership function. The membership functions of stress levels in this or that safety level (AS, RS, CS) are presented in Fig. 1, the membership functions for each of the input parameters of the model are presented in Fig. 2—4.
The corresponding safety levels of acoustic emission activity can be characterized as follows: (Fig. 2): A1 is a low acoustic emission activity, stress generated by this kind of activity can be considered safe; ^2 is an activity that indicates a drop in corrosion resistance owing to a sig-
nificant amount of microcracks occurring in its structure; ^3 is acoustic emission activity typical of an impact of beyond-project loads, risks of a structure falling down.
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Velocity of acoustic emission V, 1/sec Fig. 2. Membership function of change in acoustic emission activity in safety levels
Safety levels of a relative velocity of ultrasound passage is described as follows (Fig. 3): U1 — significant or no change in a velocity of ultrasound passage, polymer concrete is in the process of compaction or slight decompaction is observed; U2 is significant decompaction of concrete resulting from a number of microcracks occurring that cause a drop in corrosion resistance; U3 is decompaction typical of beyond project load impacts. According to changes in a defect of concrete density, safety levels are described as follows (Fig. 4): D1 — deformations comply with Hooke’s linear law, i. e. the total elastic performance dominates the behavior of a material; D2 — stress are over the level R that corresponds to the onset of intensive
cracking [1], that results in a drop of corrosion resistance of a structure; D3 — deformations typical of beyond-project load impacts, risks of a structure falling down.
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A relative velocity of passage of an ultrasound pulse Ui / U Fig. 3. Membership functions of change in a relative velocity of passage of an ultrasound in safety levels
In order to produce membership functions presented in Fig. 1—4, a series of related experiments was carried out that provided essential theoretical and statistical data (acoustic emission indicators, ultrasonic indicators, data on changes in volume deformations).
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Difference of actual and theoretical volume deformations Ad* 10 Fig. 4. Membership functions of a defect of density in safety levels
2. Outcome of application of the model in epoxy polymer concrete testing
The analysis of sets were performed using Mamdani’s fuzzy logic algorithm, which is one of the basic algorithms to obtain logic inferences in the theory of fuzzy sets, with MatLab Fuzzy Logic toolbox. The dependence of a response function of the model H on a relative stress level obtained as a result of testing of fifteen specimen is shown in Fig. 5. The response function indicates a numerical value of the parameter H, which is returned by the model depending on a combination of initial data input.
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Relative stress level o/R
Fig. 5. Response of a three-parameter model during testing of epoxy polymer concrete
Both boundaries o/R1 and o/R2 are distinct in the resulting graph. The corresponding values of H are Hi(0,62) = 0,173 and H2(0,95) = 0,842. The values Hi and H2 are criteria for the assessment of a stress deformed state of epoxy polymer concrete in compression. The depen-
dence of the characteristic H on a relative stress level o/R unlike the direct measurement results does not need smoothing, since there is almost no scatter in the index in relation to a moving average.
In Graph 3 three stages AS, RS and CS are clearly seen to have clear boundaries. These make an indirect characteristic more handy for the assessment of a structure’s state under load than a proper analysis of the direct measurement results. Furthermore, an indirect characteristic H is calculated based on a complex analysis of the results obtained using three measurement methods simultaneously, which makes this index more reliable for practical applications.
Conclusions
A mathematical model was designed that enables a complex assessment of safety levels of structures made of epoxy polymer concrete. Three safety levels of polymer concrete structures under load were identified using a microcracking criterion. The strengths of the suggested assessment criterion H are its reliability underpinned by a simultaneous use of three independent methods of non-destructive testing, handy analysis of the outcomes as there are no significant fluctuations in the parameter H, as well as its multiple use due to the criterion H being related not only to a material’s strength characteristics but also to decompaction characteristics and microcraking intensity. Taking into account how polymer concrete structures mainly operate in chemically hostile environments, the criterion suggested can be considered viable for practical applications.
References
1. O. Ya. Berg, Physical Foundations of Concrete and Ferroconcrete Strength Theory (Moscow, 1961) [in Russian].
2. V. M. Zaplatinsky, “Terminology of Science of Safety”, in Zbornikprispevkov z med-zinarodnej vedeckej konferencie “Bezhecnostna veda a bezpecnostne vzdelanie ” (Lip-tovsky Mikulas: AOS v Liptovskom Mikulasi, 2006) (CD-ROM).
3. P. G. Cheremskoy, V. V. Slezov, V. I. Betekhtin, Pores in a Solid Body (Moscow, 1990) [in Russian].
4. I. S. Surovtsev, Yu. B., Potapov, Yu. M., Borisov, “Ferroconcrete flexural structure reinforcement with the use of polymer composition materials”, Scientific Herald of Voronezh State University of Architecture and Civil Engineering. Construction and Architecture, 2008, N 1, pp. 12—21.
