Comparison of microcrack formation boundaries determined by complex of physical methods with long-term strength of expanded clay concrete under different types of stress state

. This work aims to experimentally study the strength and strain of expanded clay concrete during short-term and long-term compression and tension under various loading modes. A technique for testing expanded clay concrete under short-term and long-term compression and tension, including the boundaries of microcrack formation by a complex of physical methods (tensometric, ultrasonic pulsed, and acoustic emission), is given. The results of tests of expanded clay concrete under short-term and long-term monotonic loading under compression and tension and low-cycle loading under compression, as well as the boundaries of microcrack formation by a complex of physical methods, are obtained. The boundaries of microcrack formation are compared with the long-term strength of expanded clay concrete under various types of stressed states. Strain diagrams of expanded clay concrete under axial compression and tension, and "ultrasound transmission speed - stress level" and "number of acoustic pulses - stress level" diagrams are also obtained. Empirical formulas are proposed for determining the boundaries of microcracking in expanded clay concrete and the relationship between the level of long-term strength and the time of staying specimens under load in compression and tension. The results allow the formulation of several proposals and clarifications for normative documents to calculate and design lightweight concrete elements and structures.


Introduction
The widespread use of local artificial porous aggregates instead of natural heavy aggregates in seismic regions of the Republic of Uzbekistan with a dry, hot climate is a governing condition for increasing the efficiency of capital investments in the construction of transport and other important structures.A distinctive feature of expanded clay, which in terms of producing lightweight concrete from porous aggregates, ranks first in comparison with other porous aggregates, is its relatively high strength at a relatively lower bulk density.Expanded clay concrete in bridge building instead of traditional concrete can significantly reduce the weight of structures, material consumption, transport and installation costs, and labor costs while maintaining the necessary strength, reliability, and durability of structures.It can improve performance, reduce loads on foundations, reduce the cost of bridge construction and, at the same time, speed up their construction [1 -7].
Theories of strength and fracture under compression and tension are of great importance for predicting the physical and mechanical characteristics of concrete, in particular, the concepts of the boundaries of microcracking (ܴ and ܴ ௩ ) [3, 8 -15] and long-term strength (R bl and R btl ) [2,3,16,17].With these theories, it is possible to assess the kinetics of the process of microcracking in concrete and the safety margins of structures.The boundaries of microcracking and long-term compressive and tensile strength should be considered important characteristics of concrete to ensure reliable operation of the structure.The values of the boundaries of microcrack formation are quite important for describing the features of concrete behavior since they allow concluding the stage of the stress-strain state (SSS) [9].
An analysis of the results of studies on the boundaries of microcrack formation shows that these characteristics are ambiguously related to the compressive strength R b and can vary significantly depending on the proportion of expanded clay concrete mix, the type and consumption of coarse aggregate, and other factors [3,[8][9][10][11][12][13][14].
Particular attention is paid to the upper limit of microcrack formation since reaching this boundary indicates the transition to the third stage of the SSS, i.e., this indicates that microcracks merge into macrocracks and divide the concrete structure into blocks.The blocks under load are displaced relative to each other, which causes the concrete matrix destruction [9][10][11][12].If the load level is close to the upper limit of microcracking but does not exceed it, plastic strains under static loading stabilize over time (even under cyclic changes of loading [18,19]).At present, the derivation of new formulas (more universal ones) applicable to concretes of different types and classes is relevant.
The opinions of researchers in determining the relative limit of long-term strength differ, as evidenced by the data given in [2,3,15,16].
In recent years, several formulas have been proposed that allow a more differentiated approach to assessing the relative limit of the long-term strength of concrete.Therefore, for heavy concretes of ordinary classes, used earlier, good results are given by the following formula [16] ܴ /ܴ = 0.92 − 0.4 lg(‫ݐ‬ − ߬ ଵ ) where ߬ ଵ is the age of concrete at the time of loading.
For heavy concrete of class B30 and higher at an old age, the following dependence can be used: If the concrete of the same classes is loaded at middle age, when the hardening processes continue to influence parameter R, then the long-term strength can be determined by the following formula Since the parameters depend mainly on the class of concrete, its age at the time of loading, the gain in strength, and the conditions of moisture exchange with the surrounding medium, it can be assumed that the ultimate strength depends mainly on the same factors.
However, several issues related to the study of lightweight concrete elements and structures, including their operation under various stress states and loading modes, have not yet been studied or are insufficiently studied.The proposed article presents the main results of these studies, which allow us to formulate several proposals and specifications for regulatory documents on the calculation and design of lightweight concrete elements and structures.

Methods
The composition and main characteristics of concrete are given in Tables 1 and 2. Expanded clay gravel of two fractions, 5-10 and 10-20 mm in a ratio of 40:60, was taken as a coarse aggregate produced in the Tashkent cement plant.As Portland cement, the cement of the Navoi cement plant was used, and the sand of the Tashkent quarry was used as quartz sand.

Monotonic loading under compression and tension.
Loading of specimens (prisms) of 70x70x280 mm and 150x150x600 mm dimensions and cylinders of 70 mm in diameter and 235 mm in height, made of expanded clay concrete under short-term compression and tension, was performed according to the standard procedure on testing machines UMM-20 and P-250 with a maximum capacity of 200 and 2500 kN, respectively.Specimen loading was conducted in steps of no more than 0.1 of the expected breaking load with staying on the steps until the increase in short-term creep deformations ceased.The duration of staying on the steps under stepwise compression loading of specimens did not exceed 5 min.
Low-cycle loading under compression.Some specimens were tested under cyclic loading.Each step contained 1 cycle of loading and destruction.The duration of load staying at the upper and lower stress levels of a given step was determined by reaching such a shape of the deformation diagram when, within the measurement accuracy, the hysteresis loop ceased to increase.This loading pattern was realized up to a stress level not exceeding the upper limit of microcrack formation [20,21].
During short-term tests, longitudinal and transverse strains were measured with wiring strain paper gauges of the CNIISK experimental mechanical plant with their bases of 20 and 50 mm.
To obtain information about the integral value of strains, longitudinal and transverse strains were measured in several sections along the length of the specimen, covering a certain volume of material [5].The adopted pattern of strain gauge gluing is shown in Figures. 1 a, b, c.The dimensions of the tested prisms and the base of strain gauges determined the use of each pattern.Strain gauges were glued according to the standard method -three months before the start of the test.The scheme of prisms and cylinders installation in a testing machine is shown in Figure 2.

The procedure for testing expanded clay concrete during long-term testing; measuring instruments
Long-term loading of specimens to a given level of stresses under compression and tension was conducted in spring and lever installations with a maximum force of 210 kN and 30 kN, respectively.
One or two specimens were placed in the installation.The first scheme was used under high loading levels (Figure 3, a), and the second was used under low loading levels (Figure 3, b).
Metal plates 20 mm thick were laid between them when installing two prisms, and when installing two cylinders, a Hooke hinge was laid (Figure 3, c).The value of the load was set according to the range of springs, pre-calibrated on the press, on which the short-term loading was performed.
Under tensile tests, the cylinders were placed in the installation using collets and Hooke's hinges, and under compression tests, the prisms were installed with metal base plates 30 cm thick with ball joints glued to the ends.The range of springs during calibration was measured with PAO-6 deflection meters with a division value of 0.01 mm, installed on two opposite sides (generatrices) of springs.
To eliminate the error related to non-additivity of shrinkage and creep, the specimens before loading were waterproofed from the sides with a layer of paraffin 2-3 mm thick and two layers of polyethylene film with seams glued by insulating tape.

Monotonic compression and tension loading.
The strength and strain characteristics of expanded clay concrete under compression and tension are summarized in Tables 3 and 4. The data obtained (Table 3) on the increase in time of cubic R and prism R b strength of expanded clay concrete confirmed that the measures we took to protect specimens from drying out during storage were sufficient, and they provided a normal hardening condition for 800 days, which is very important when comparing the results of short-term and longterm tests.
The increase in the elasticity modulus of expanded clay concrete under compression over time by the end of the experiment (W 1 = 800 days) was 30-50% higher than at the age of W 1 =28 days (Tables 2 and 3).The increase in the tensile modulus was less significant.So, by W 1 = 530 days, it increased only by 5% compared to W 1 = 220 days, while under compression over this time interval, the value of E b increased by 15%.
For expanded clay concrete, the values of R b /R exceed the ones specified in the existing standards for traditional concrete.Other researchers noted the increased prismatic strength of expanded clay concrete as well [1][2][3][4][5][9][10][11][12][13].They explained that porous aggregates have a more developed surface and better adhesion with the cement-sand component than dense aggregates.This largely restrains the transverse deformations of the prisms.However, with an increase in age, there was a noticeable decrease in the prism strength coefficient of expanded clay concrete (Table 3), and at the age of 800 days, R b /R was 88% of R b /R at 28 days of age (Table 2).
According to our experimental data, the coefficient of variation for the strength and strain properties of expanded clay concrete under compression and tension was 1-6% and 3-14%, respectively.
High values of the coefficients of variation under tension obtained in the experiments are due to two factors associated with the different nature of concrete destruction under compression and tension, respectively, and with different relative accuracy of measurements.Under axial tension, the destruction of the sample passes along one section due to a local defect in the macrostructure.As experiments have shown [5], there is practically no redistribution of stresses and strains between sections in concrete, and a weak section determines the strength of the entire sample.
Under compression, the effect of strain and stress localization is less pronounced due to their partial distribution over the entire volume of the specimen.The relative accuracy of measurements under compression and tension is because the values of stress and strain measured during tensile testing are an order of magnitude less than under compression, while the resolution of force gauges and especially strain gauges is the same.This factor is especially pronounced when measuring tensile strains since their measurement accuracy, which does not exceed 1(10-5, is commensurate with the measured strains, especially at low loading levels. The ratio of compressive and tensile strengths.The results of determining the axial tensile strength R bt were compared with the results obtained for the cubic strength R and prism strength R b (Tables 1-3).
In our experiments, the R bt /R ratio was 0.05...0.06, and R bt /R b was 0.06...0.07.The high ratio of R bt /R for expanded clay concrete in our experiments is explained by the test procedure, where practical axial tension was ensured under the testing of cylinders.In addition, tensile tests of cylinders show better results than prisms due to the smaller effect of friction in the corners of the specimen.The ratio of R bt /R for expanded clay concrete can be approximately taken equal to 0.05.
Low-cycle compressive loading.The test results under low-cycle compressive loading are summarized in Table 5.A comparison of the data obtained with the data given in Tables 2 and 3 showed that low-cycle loading under compression did not affect the strength of expanded clay concrete and mixes (the difference between the values of R b did not exceed 6%).The results indicate the best resistance of expanded clay concrete under low-cycle compressive loading and the expediency of their use in transport engineering, where the structure is subject to multiple low-cycle loads.The values of Poisson's ratio Q e practically did not change and did not differ from those obtained under monotonic loading.The elasticity modulus E b of expanded clay concrete decreased by the last cycle by approximately 4%.

Determination of the boundaries of micro-crack formation in expanded clay concrete by a complex of physical methods
Tensometric method.Determination of o crc R and Q crc R by tensometric methods based on the analysis of experimental "K-H" diagrams was performed according to the method described in [15] by measuring longitudinal and transverse strains under loading.
Figures 4 and 5 show averaged diagrams of expanded clay concrete deformation obtained when testing specimens under compression and tension.Visually, general patterns of the deformation diagrams under axial compression and tension are similar.However, in the case of compression, the nonlinearity of the diagrams manifested itself earlier, and the degree of its curvature was greater than in the case of tension.A characteristic feature of all strain diagrams was an almost linear dependence between stresses and strains over a large part of the stress range.Inelastic strains were noted only at loading levels greater than 0.70.Based on the measurement results, the average values of the longitudinal H х and transverse H у strains of the specimen were calculated, and, on their basis, volumetric strain H v , its increment 'H v , and the differential coefficient of transverse strain were determined at each stage loading.The graphs of changes in these characteristics (Figure 4) were plotted depending on the relative level of loading.Five prisms were tested for expanded clay concrete.The values of mechanical characteristics (prism strength, modulus of elasticity, Poisson's ratio) were determined as an average of data for five specimens.

Fig. 4. Strain of expanded clay concrete under axial compression (prism dimensions 70x70x280 mm)
A comparison of the strains determined by individual strain gauges on the specimen showed that the spread of their values was relatively small and changed little as the load increased.The coefficient of variation of readings from longitudinal strain gauges glued on different faces of the prism did not exceed 10%.This scatter was mainly because the actual axis of load application did not coincide with the physical axis of the specimen.In comparing the readings from strain gauges located in different sections along the height on the same face, their coefficient of variation did not exceed 5%.Considering these results, the strains were determined as the arithmetic average values according to the readings of all strain gauges.
A comparison of the values of transverse strains, determined by individual strain gauges on the specimen, showed that they were characterized not only by a higher spread (the coefficient of variation of their values was up to 40%) but by a sharp difference in the readings of individual strain gauges at individual points on the surface of the specimen (in the zone of potential destructions) almost from the beginning of loading.From experimental diagrams, strain values at 0.95 of breaking load were determined since data on the compressibility and extensibility of concrete are used to solve several issues in the design and evaluation of research results.For expanded clay concrete and heavy concrete, compressibility depends on several factors, of which the most important are the strength of concrete, the material of the aggregate, and the stress level of concrete [2,6,17].

Fig. 5. Strain of expanded clay concrete under axial tension
Ultrasonic pulse method.The average diagrams of the change in the velocity of transmission of the generated ultrasonic pulses through the specimen are shown in Figures 6 and 7, and the results of determining ܴ are given in Table 6.Here, as well as in the case of the tensometric measurement method, the values of ܴ , determined from different scanning traces, can from each other by 20%.

Acoustic emission method.
The experiments show (Figure 8) that the acoustic pulses accompanying the destruction of concrete structures are recorded almost from the moment of application of the compressive load and have several intensity peaks during the loading process.A point on the "K -N" diagram before the beginning of the first peak of the intensity of the growth of impulses N is taken as the lower boundary of microcracks, and a point before the last peak is taken as the upper boundary of microcracks.The first peak corresponds to the microcrack development scheme proposed in [3,15], to the formation of a system of microcracks originating from the initial cracks on the grains of the coarse aggregate.The next possible peaks should correspond to the formation of local systems of intergrown microcracks, and the subsequent peak should correspond to the formation of main macrocracks of destruction.The values of ܴ , obtained by the acoustic emission method (Table 6) are in good agreement with the values of ܴ Q , obtained by the tensometric method in the fracture zone (the discrepancy is no more than 8%).
To determine the boundaries of microcrack formation in high-strength expanded clay concrete of a dense structure according to formulas (4 and 5), the values of numerical coefficients are determined by the least squares method based on the experimental data obtained by the authors The average values of ܴ and ܴ ௩ obtained by the authors in the experiment for expanded clay concrete were compared with the values calculated using empirical formulas (proposed by Semenyuk S.D., Moskalkova Yu.G. (4, 5) [9,24] and the authors of (7, 8)) (Table 7).The data given in Table 4 clearly demonstrate the adequacy of the application of the empirical formulas proposed by the authors in (7,8) to determine the relative values of the boundaries of microcracking in high-strength expanded clay concrete of a dense structure.

Long-term strength of expanded clay concrete
On the graphs of Figure 6, the values of the level of long-term strength in semilogarithmic coordinates are plotted depending on the staying time of the specimens under load (t-W 1 ).At the same time, curves corresponding to dependence (3) were plotted.Figure 3 shows that for expanded clay concrete, there is a good agreement between the experimental data and the approximating dependence.The deviations of the experimental values of the level of Analysis of the comparison results shows that for expanded clay concrete, the best comparison of the values of the limit of long-term strength R bl and the upper limit of microcracking ܴ Q under compression [22] gives the value of ܴ Q The acoustic emission method and the tensometric method in the fracture zone under cyclic loading are determined.From this, it follows that to determine the long-term strength based on the results of short-term tests, it is recommended to test specimens with both monotonically increasing and cyclic loads with the unloading at each stage, measuring strains on loading and unloading in several sections (more than three) along the height of the specimen in the zone of a homogeneous stressed state.As the limit of the long-term strength of expanded clay concrete, we take the stress corresponding to the extremum on the diagram of the inelastic component of volumetric strain, determined from the measurement data of strains in the destruction zone as the difference between the total diagram ߝ Q according to the results of monotonic loading and the elastic component ߝ Q according to the results of cyclic loading.Or else, it is recommended to determine the value of ܴ Q by the method of acoustic emission under monotonic loading.
A comparison of the values of the long-term strength and the upper limit of microcracking under axial tension (Table 8) shows that for expanded clay concrete, the values of ܴ Q and R btl correspond to each other (the discrepancy is no more than 13%).

Conclusions
1.It was determined that the ratio of R bt /R was 0.05...0.06, and R bt /R b -0.06...0.07, and the values of the initial Poisson's ratio of expanded clay concrete under compression and tension correspond to the values regulated by building standards in SNiP.
2. The results obtained indicate the best resistance of expanded clay concrete under lowcycle compression loading and the expediency of their use in the structures of transport facilities, where the structures are subject to multiple low-cycle loads.
3. It was determined that the values of ܴ Q , calculated by different methods are in good agreement with each other, which cannot be said about R . The values of ܴ Q , obtained by the acoustic emission method are in good agreement with the values of ܴ Q , obtained by the tensometric method in the fracture zone (the discrepancy is no more than 8%).
4. The statement confirmed that for expanded clay concrete, the values of relative levels of crack formation R /R ୠ and R Q /R ୠ are higher than traditional heavy concrete of the same strength.
5. An empirical formula appropriate for practical application was obtained for determining the boundaries of microcrack formation and describing the pattern of change in the long-term strength of expanded clay concrete under axial compression and tension; this formula allows (at the stage of projecting) considering the long-term strength for any time interval.
6.It was determined that for expanded clay concrete, the best comparison of the values of the long-term strength R bl and the upper limit of microcrack formation ܴ Q under compression gives the value of ܴ Q , determined by the acoustic emission method and the tensometric method in the fracture zone under cyclic loading.

Fig. 1 .Fig. 2 .
Fig. 1.Scheme of ultrasonic and tensometric measurementsUnder compression tests, the specimens were centered along the physical axis by trial loading of no more than 0.20R b (Figure2, a).Under tensile testing, the load on the specimen was transferred through Hooke's hinges using collet grippers, ensuring uniform strain distribution along the specimen's length and reliable transfer of axial tensile force to the specimen.(Figure2, b).

Fig. 8 .
Fig. 8. Diagram "number of acoustic pulses vs. stress level in expanded clay concrete specimens"

Table 1 .
Composition of expanded clay concrete (EC)

Table 2 .
Characteristics of expanded clay concrete

Table 3 .
Results of short-term axial compression testsNote: Results for expanded clay concrete at the age of 220 and 530 days were obtained for specimens 70x70x280 mm, at the age of 800 days -for specimens 150x150x600 mm.

Table 4 .
Results of short-term axial tensile tests b , at the age of 220 and 530 days, respectively, GPa; 23.3 and 23.5 Poisson's ratio, Q e, at the age of 220 and 530 days, respectively 0.20 and 0.20 Tensile strength at 0.95R bt H x(V=0.95Rb) 10 -5 , at the age of 220 and 530 days, respectively 10 and 10

Table 5 .
Test results under low-cycle compressive loading

Table 7 .
Calculation results of relative values of microcrack boundaries