In this study, the effect of adding nano-silica (NS) particles on the properties of concrete containing coal fly ash were explored, including the mechanical properties, impact resistance, chloride penetration resistance, and freezing–thawing resistance. The NS particles were added into the concrete at 1%, 2%, 3%, 4%, and 5% of the binder weight. The behavior under an impact load was measured using a drop weight impact method, and the number of blows and impact energy difference was used to assess the impact resistance of the specimens. The durability of the concrete includes its chloride penetration and freezing–thawing resistance; these were calculated based on the chloride diffusion coefficient and relative dynamic elastic modulus (RDEM) of the samples after the freezing–thawing cycles, respectively. The experimental results showed that the addition of NS can considerably improve the mechanical properties of concrete, along with its freezing–thawing resistance and chloride penetration resistance. When NS particles were added at different replacement levels, the compressive, flexural, and splitting tensile strengths of the specimens were increased by 15.5%, 27.3%, and 19%, respectively, as compared with a control concrete. The addition of NS enhanced the impact resistance of the concrete, although the brittleness characteristics of the concrete did not change. When the content of the NS particles was 2%, the number of first crack impacts reached a maximum of 37, 23.3% higher compared with the control concrete. Simultaneously, the chloride penetration resistance and freezing–thawing resistance of the samples increased dramatically. The optimal level of cement replacement by NS in concrete for achieving the best impact resistance and durability was 2–3 wt%. It was found that when the percentage of the NS in the cement paste was excessively high, the improvement from adding NS to the properties of the concrete were reduced, and could even lead to negative impacts on the impact resistance and durability of the concrete. However effects ,11,12,13 effects ,15,16.Compared with other nanoparticles, NS particles have a higher activity and a particularly large specific surface area; therefore, NS can exhibit a higher level of pozzolanic activity in concrete. In addition, NS can provide nucleation sites for calcium silicate hydrate (C–S–H), and act as a catalyst for pozzolanic reactions to promote the dissolution of tricalcium silicate and the formation of C–S–H ,18. TherReducing carbon emissions and promoting carbon neutrality are the main measures taken by authorities around the world to respond to environmental changes . Cement A growing number of concrete structures are of the types frequently affected by impact loads under service conditions. For example, airport runways are subject to impacts from aircraft landing, and offshore structures are subject to the impacts of waves. Therefore, under these impact loads, the structural safety of traditional Portland cement concrete with brittle fracture characteristics poses a significant challenge. Researchers have conducted numerous studies on enhancing the impact resistance of ordinary concrete. For example, Siddique et al. evaluated a concrete that replaced 40% natural sand with fine ceramic aggregate. They observed that the impact energy absorbed by the specimens increased from 0.94 J with plain concrete to 0.99 J . Li et a2O3 and NS, and that the performance of a concrete containing nano-Al2O3 was better than that of a concrete containing the same dose of NS [It is well known that durability is a critical factor in evaluating the lifespan of concrete. Resistance to chloride permeability and freezing–thawing are two vital elements of this durability. In an environment with a high concentration of chloride ions, for instance, coastal areas and cold areas where deicing salt is used, chloride ions can access the concrete through diffusion, adsorption, and capillarization, causing damage to the internal reinforcement and corrosion of the concrete . Freezinse of NS . They alse of NS . Gonzalese of NS .Although there have been a large number of studies on the impact resistance of ordinary concrete, and the mechanical properties and durability of concretes containing NS, results correlated with the impacts of NS particles on the impact resistance and durability of coal fly ash concretes are relatively rare. Therefore, in this study, the effects of different NS dosages on the impact resistance, chloride penetration resistance, and freezing–thawing resistance of concretes containing coal fly ash were studied using a drop-weight impact test, single-sided freezing–thawing test, and rapid chloride migration (RCM) test, respectively; then, the optimal NS content was determined.In this study, P·I 42.5 Portland cement produced by Shandong Luneng Cement Co., Ltd.  and first-grade coal fly ash from Datang Luoyang Thermal Power Plant  that met Chinese standards were used ,52. The A laser diffraction-type particle size analyzer  was used to measure particle size distribution (PSD), the PSD of coal fly ash and cement is shown in 3) constant for all of the mixtures, six different mix proportions were prepared, including a control group and five groups containing different NS dosage mixtures. Among them, NS was used to replace cement in proportions of 1%, 2%, 3%, 4%, and 5%, respectively. The concrete mix proportions are presented in The experiment in this study was based on the concrete mix design specification JGJ 55-2011 , and the2 nanoparticles and fabricate homogenous and uniform concrete mixtures, the following procedures were employed. The uniform dispersion of the NS is the key to ensuring the quality of a concrete, and is also the basis for achieving excellent characteristics in a specimen . To achiThe NS and superplasticizer are added into water and agitated evenly for 90 s.The coarse and fine aggregates were added into the wetted concrete mixer and mixed for 90 s.The cement and coal fly ash were added into the mixer, and the ingredients were mixed for 90 s.Mixing water (containing NS and superplasticizer) was added into the mixer and mixed for 90 s.The remaining water or the entire quantity of water (in the control mixtures) was added into the mixer and mixed for approximately 90 s.3. The specimens were demolded after being placed horizontally at room temperature for 24 h, and were then placed in water at room temperature and removed for testing after 28 days of curing.Immediately after mixing, the fresh mixture was cast into an oiled cube mold with a size of 150 × 150 × 150 mm3 were used in the compressive and splitting tensile strength tests. Specimens with sizes of 100 × 100 × 400 mm3 and a flexure testing machine with a maximum range of 1000 kN (meeting the performance test requirements) were used in the flexure strength test. The three tests  were all in accordance with JTG E30-2005 . Cube sp3. The impact energy range of the falling weight was 50–2000 J. An impact process was defined as a cycle after each cycle was completed, and the surface of the specimen was carefully observed. When the first crack appeared in the specimen, the number of impacts at this time was denoted as “N1” for the initial cracks in the concrete specimen. The next impact cycle was continued until the width of a crack on the surface of the specimen expanded to 1 mm, when the test was terminated. At this time, the number of impacts was denoted as “N2.” The impact test results are shown in The impact tests were performed on a drop hammer test machine, with specimen sizes of 150 × 150 × 150 mm−12 m2/s; The rapid chloride migration (RCM) method proposed by Tang and Nilsson  was usedTo accurately simulate an environment in which concrete undergoes salt freezing in the atmosphere, a single-sided freezing–thawing test method closer to the actual freezing–thawing damage environment of concrete was adopted in this study, as shown in Compared with the control concrete, the mechanical properties of the coal fly ash concretes mixed with NS were significantly improved. To make the results more illustrative, the effects of different NS contents on the 28-day compressive and flexural strength of the specimens and contents of NS are shown in 2+ in the calcium hydroxide (Ca(OH)2) crystals and forms a C–S–H gel [The pozzolanic reaction and nano-filling effect are the two main reasons for the enhanced strength of the concrete . In part–S–H gel . Moreove–S–H gel . Simulta–S–H gel .The influences of the NS content on the number of blows at the first crack and at the failure of the concrete are shown in The effect of the NS content on the impact energy of the concrete is shown in 2 crystals arranged in the ITZ between the cement paste and aggregate to form a C–S–H gel [Owing to its high pozzolanic activity, NS can react rapidly with the Ca(OH)–S–H gel . Further–S–H gel . Moreove–S–H gel . The inc–S–H gel . The genThe chloride penetration resistance of concrete is mostly dependent on the pore sizes of the concrete. Metha et al. stated that pores in concrete with pore sizes larger than 100 nm will significantly reduce the mechanical properties and permeability resistance of the concrete . NS is aThe effects of different amounts of NS on the RDEM of the concrete after 0, 4, 16, and 28 freezing–thawing cycles are shown in 2 react to form compound salts. This destroys the state of the C–S–H gel, promotes the scaling of the concrete surface, and destroys the freezing–thawing resistance of the concrete [The internal cause of the damage to concrete caused by freezing–thawing cycles is mainly determined by the porosity and pore distribution of the concrete , and theconcrete .2 formed by the calcium silicate hydration to form a more orderly C–S–H gel [2 for reaction. As a result, the porosity of the concrete increases, and the freezing–thawing resistance of the concrete decreases.In the early stages, i.e., after experiencing only a few freezing–thawing cycles, the interiors of the concrete specimens had not yet undergone freezing–thawing cracking, and the expansion of the micro-cracks was small. In addition, the generation of frozen water in the early stages would squeeze the concrete, increasing the density and improving the RDEM of the concrete. The experimental data in this study also show that the RDEM of concrete was above 90% after four freeze-thaw cycles. As the number of freeze–thaw cycles increased, the pressure of the water inside the pores owing to icing and expansion would damage the microstructure inside the concrete ,73, and –S–H gel , making (1)2 at the ITZ to produce more C-S-H gel and the densification of the microstructure. However, the optimum amount for each mechanical property was different; the splitting tensile strength reached a maximum when the NS replacement level was 2%, and when the NS replacement level was 3%, the compressive and flexural strengths reached their maximums.Coal fly ash concrete containing NS significantly improved the mechanical properties of concrete specimens relative to a control concrete (without NS), which was due to the reaction of NS particles with Ca(OH)(2)Adding NS particles can dramatically improve the impact resistance at the first cracking of the concrete; however, the speed from initial cracking to failure was faster, and the brittleness of the concrete did not change. After being impacted, the concrete specimens containing NS were divided into two halves along the impact direction, and the concrete specimens still exhibited brittle failures, as in ordinary concrete.(3)Compared with the control concrete, the low dosage of NS can greatly ameliorate the chloride penetration resistance and freezing–thawing resistance of the concrete. At the 2% replacement level, a uniform dispersion of NS particles was easily achieved. The improvement of the pore structures in the concrete and filling effect of the NS were responsible for the reduction in the chloride diffusion coefficient, and ameliorated the freezing–thawing resistance of the concrete.In this study, the influences of NS particles on the mechanical properties, impact resistance, and durability resistance of coal fly ash concretes were analyzed and discussed, based on the experimental results obtained through mechanical properties tests, impact resistance tests, resistance to chloride penetration tests, and freezing-thawing cycle resistance tests. The following conclusions were drawn:


The article presents the results of original and relevant tests from the point of view of using self-compacting concrete admixtures, especially their compatibility with the cement and mutual compatibility in the case of using several admixtures in one mixture. The research contributes to the recognition of the effect of an unintentionally air-entraining superplasticiser (SP), anti-foam (AFA), viscosity-modifying (VMA) and air-entraining (AEA) admixtures on the internal frost resistance and compressive strength of self-compacting concrete. Positive and undesirable effects of the combined use of several admixtures in this area have not been the subject of extensive analyses and publications so far. Superplasticiser, which unintentionally introduced a large amount of air to the concrete mixture, had a negative effect on the strength of the concrete and a positive effect on frost resistance. The addition of AFA to such concrete did not change the strength but worsened the values of the parameters estimating frost resistance. The AEA admixture resulted in a decrease in the strength of concrete but contributed to a change in the tendency to weaken the frost resistance observed in non-air-entrained concrete. The article also deals with the problem of compliance of the frost resistance criteria estimated upon various measures. It may be disturbing that finding frost resistance based on one criterion does not always mean frost resistance on another criterion. The discrepancies can be significant and misleading. Frost-resistant concrete, including self-compacting concrete (SCC), should have an appropriate porosity structure. Intentional aeration is achieved by the use of air-entraining admixtures. Air-entraining agents have a foaming effect and, most of all, they stabilise the introduced air, providing the appropriate structure (distribution and size) to the air microbubbles. The bubbles act as stress-compensating chambers. Water freezing in the capillaries can press into the empty bubbles, which prevents the concrete structure from bursting. The microbubbles interrupt the continuity of the capillaries in the concrete, which prevents capillary and osmotic transport of water. As a result, the mechanisms mentioned above make the concrete resistant to the damaging effects of frost. Unfortunately, other admixtures besides air entrainment, the necessity to obtain the proper consistency of SCC concrete or anti-segregation such as viscosity-modifying admixtures (VMA) ,2, are nA side effect of using some superplasticisers may be the introduction of a significant amount of air into the concrete mix. Industrially produced superplasticisers of this type often contain a significant amount of unreacted macromonomer about 10%). Therefore, a substantial foam generation mechanism is common. Excessive air entrainment is mainly caused by the reduction in the surface tension of the liquid phase in the cement paste. Standard requirements ,9 for ch%. TherefA self-compacting concrete mix should have good flowability and, at the same time, a viscosity that will resist aggregate segregation during and after the mix is placed. It is possible to use an additive in the form of a modifier regulating the internal consistency of the concrete mix, commonly known as viscosity-modifying admixture (VMA), which increases the viscosity of the cement paste without the need to reduce the water content or increase the content of the dust fraction ,16. VMA 3 of the mixture. In addition, VMA admixtures do not indifferently affect the strength of concrete, which is also related to its frost resistance.The test results  confirmeThe effect of the VMA addition on the compressive strength of concrete is described in . In concIn other tests , slightlAn anti-foam agent (AFA) can be used to reduce excessive air content in self-compacting concrete. AFA causes destabilisation, breaks the surface of air bubbles into the foam and causes coalescence. AFA influences the structure and distribution of pores in the concrete ,22. HoweThe experimental studies presented in this article aimed to determine the effect of the application of chemical admixtures with different effects in self-compacting concrete and their mutual interaction. The research concerned two types of superplasticisers (SP), including one that caused an unintentional air-entrainment of the concrete mix, anti-foaming (AFA), air-entraining (AEA) and viscosity-modifying (VMA) admixtures. The analysed properties of concrete were internal frost resistance and compressive strength. The information in  on the fMoreover, a question was asked whether the influence of additional admixtures on the porosity characteristics of concrete would be consistent with the results of its frost resistance, determined by the destructive and non-destructive method? For this purpose, the porosity characteristics of self-compacting non-air-entrained and air-entrained concrete, modified with additional AFA and VMA admixtures, were determined and then compared with the frost resistance of concrete estimated by the methods mentioned above. Finally, it was checked whether the non-destructive method allows for quantitative estimation of the frost resistance of self-compacting concrete modified with several simultaneously used admixtures.Seven types of self-compacting concrete were tested. Their basic composition is summarised in Ed, can be estimated. The dynamic modulus of elasticity is a mechanical feature of concrete that is very sensitive to changes caused by the formation of macro- and microcracks [Ed is expressed byt is the propagation time of the ultrasonic wave over a length of l, ρ is the density of the medium, while vA is a factor depending on the Poisson’s ratio.Several different measures and criteria are used to assess the internal frost resistance of concrete. Ultrasonic non-destructive methods are very popular. Based on the measurement of the parameters of the ultrasonic pulse induced on the surface of the specimen at one point and received at another, the dynamic modulus of elasticity of concrete rocracks . In frosrocracks . The valEd.UPTT). The second method is based on the measurement of fundamental resonant frequency (Ed.FF) of concrete specimens vibrating using a modal hammer and recorded by an accelerometer. Ed.FF tests can be performed according to the ASTM C 215 [Ed.FF, along with the number of freezing and thawing cycles of concrete, can be used directly to assess frost resistance, which was performed in the studies described, for example, in [The values of the dynamic modulus of elasticity can be determined in two ways. The first one is related to measuring the ultrasonic pulse transit time between the point at which the ultrasonic wave was induced and received , the value of the relative dynamic modulus of elasticity calculated based on the change of the transition time of the ultrasonic pulse RDMFF, is determined. The values of the relative dynamic modulus of elasticity, RDMUPTT, are used to estimate concrete frost resistance in the CEN/TR 15177 [RDMFF is used to determine frost resistance following CEN/TR 15177 [If the measured parameter is the fundamental resonant frequency, the relative dynamic modulus of elasticity, TR 15177  standardTR 15177 ,36. RDMFTR 15177 , ASTM C TR 15177  standardTR 15177 ,36,38,39DFT [Among other parameters used to assess the frost resistance of concrete based on ultrasonic tests, one can also mention the so-called level of damage, DFT ,41, and DFT . More adDFT ,43,44.fF calculated as a percentage from the formulafF1 is the mean compressive strength of reference specimens, not frozen, and saturated with water, while fF2 is the mean compressive strength of specimens, after the last thawing, saturated with water.In the research described in this article, two more methods of frost resistance assessment were used, which are included in the Polish annexe to the EN 206 standard . The firmF, which is calculated as a percentage from the equationmF1 is the mean mass of the specimen before their first freezing, in a state of water saturation, while mF2 is the mean mass of the specimen after the freezing and thawing cycles, saturated with water.The second method is the mean weight loss after the test ΔThe measures of concrete frost resistance must be associated with the appropriate criteria, i.e., limit values, after exceeding which it is assumed that the tested concrete is not frost-resistant.RDMUPTT (3) or RDMFF is used as a measure of frost resistance, according to the criteria contained in the RILEM TC-176 [When the relative dynamic modulus of elasticity M TC-176 , it is afF > 20% (4). If the mean weight loss of the concrete specimens, ΔmF (5), in the form of damaged corners and edges, aggregate spalling, etc., exceeds 5%, the concrete is considered not to meet the frost resistance criterion.According to the Polish national annexe to EN 206 , it is aN, with the value of the ratio of ultimate compressive stress to uniaxial strength, σ3/f, and the ratio of lateral stress restraining deformations of concrete to uniaxial strength, σ2/f, was proposed. In the study [There are also original criteria combining different properties of concrete. For example, in the article , a critehe study , the froN. Cubic specimens  were not subject to frost resistance tests. They were used for compressive strength evaluation after 28 and 128 days of curing in the state of saturation with water. The remaining cubic specimens  were used to determine the compressive strength of concrete after 300 freezing and thawing cycles.The tests were carried out on cuboidal specimens of hardened concrete with a length of 400 mm and a 100 × 100 mm cross-section and cubic specimens with a side length of 150 mm. Specimens of the first type  were subjected to frost resistance tests and were used to measure the velocity of the ultrasonic pulse before freezing and after a designated number of freezing and thawing cycles, Ultrasonic wave transition time was measured in the tests conducted by the so-called direct transmission method. A 54 kHz pulse was generated and received using flat ultrasonic transducers applied to specimens on the opposite, frontal, and parallel surface sizes 100 × 100 mm. The ultrasonic transducers were coupled acoustically to the concrete surface using technical vaseline. The tests were carried out using a Proceq Pundit Lab + device with a resolution of the ultrasonic wave transition time of 0.1 μs until the lowest value of the pulse transit time was obtained, which indicated that the thickness of the coupling agent layer was reduced to the minimum.All concrete specimens were demoulded after three days of curing at 20 °C. After removing moulds, cubic specimens not submitted to frost resistance tests were stored until testing in the water at 20 °C. After 28 and 128 days of curing, such specimens were removed from the water, wiped and compressed in a testing machine.L, specific pore surface α, total air content A, the content of air voids with a diameter smaller than 300 μm A300.The pore distribution in hardened concrete after 28 days of curing was determined using the method specified in EN 480-11 [The freezing and thawing procedure of the specimens, and the method of their preparation and testing, were following the requirements of the Polish standard PN-B-06265 , which iVmv for individual concrete types obtained after serial numbers of freezing and thawing cycles. Trends in velocity changes as the number of cycles increases were approximated by linear regression. Severe frost damage to the S2 concrete structure prevented ultrasonic testing after 350 freezing and thawing cycles. All recorded ultrasonic wave velocities obtained in the tested concretes ranged from 4689 to 5242 m/s, with a coefficient of variation for individual concrete types (in a group of three specimens) not exceeding 4.54%. However, a coefficient of variation greater than 1.50% was obtained only for S2 and S2.V concretes.V0.mv after 28 days of curing of 5153 m/s was obtained for non-air-entrained concrete S2 and S2.V. The lowest initial velocities in the range 4875 to 4967 m/s were recorded for concretes S1, S1.F and S1.F.V. For S2.A and S2.A.V concrete, initial velocities V0.mv of 4983 and 4967, respectively, were obtained.The highest initial mean ultrasonic velocity RDMUPTT for all tested concretes depending on a number of freezing and thawing cycles N. Calculated based on the change in ultrasonic wave propagation time, the RDMUPTT values ranged from 83.6 to 112.0%. The coefficient of variation νRDM determined for three specimens of each concrete after N cycles did not exceed 7.92%, with values higher than 4.0% obtained only for S2 and S2.V concrete. The mean values of the relative dynamic modulus of elasticity were higher than 100% except, again, specimens of S2 and S2.V and S1.F concrete until the number of N cycles reached 100.N on the velocity Vmv and the RDMUPTT.mv modulus was obtained for concretes containing VMA admixture. This is evidenced by the lowest values of the coefficient of determination R2.The graphs shown in mrel determined after N = 300 freezing and thawing cycles. The highest values were obtained for concrete S1.F and S1.F.V. In no case, the relative weight loss exceeded 1.0%. For other concrete types, it can be considered that no weight loss occurred or was negligible.fc.mv.28d, and 128 days, fc.mv.128d, on specimens not subjected to frost resistance tests are summarised. The strength of reference cubic specimens frozen and thawed over 300 cycles, fc.mv.300FT, in the same manner and under the same conditions as the cuboid specimens used to tests the ultrasonic pulse transition time, is also given. The highest strength after 28 and 128 days of curing was demonstrated by S2 and S2.V concrete types, in which air was not introduced into the concrete mix . The opposite situation occurred in the case of specimens subjected to freezing and thawing. These concrete types had the lowest compressive strength after 300 cycles of frost resistance testing.The mean compressive strengths of concrete determined on cubic specimens with a side length equal to 150 mm are shown in The tests have shown that the use of concrete admixtures  with theV0.mv and compressive strength fc.mv.28d with an increase in the air content Ac. Error bars represent a typical range of variation (mX ± sX).The relationship between the initial compressive strength of concrete, the velocity of the ultrasonic wave and the air content in the concrete mix is shown in fc.abs.d, and the relative, Δfc.rel.d, mean compressive strength of concrete that was not subjected to freezing and thawing between 28 and 128 days of curing. This table also includes the absolute, Δfc.abs.300FT, and the relative, Δfc.rel.300FT, decreases in the mean compressive strength of reference specimens after 300 freezing and thawing cycles concerning the strength of non-frozen concrete after 128 days of curing.fc.rel.d. Increases in mean compressive strength were obtained in the range from 3.2 to 17.4 N/mm2 and relatively from 4.4 to 31.1%. The smallest increase in relative and absolute strength occurred in non-air-entrained concrete S2.V with viscosity-modifying admixture. The most significant growth in mean strength was obtained in the case of intentionally air-entrained concrete S2.A. In three types of concrete, S1, S1.F and S2.A, slight mean strength gains were obtained. For the following two concrete types, S1.F.V and S2.A.V, minor decreases were observed. The changes in the mean strength of S1.F.V and S2.A.V concrete did not exceed 2.4 N/mm2 and 3.3% and can be considered insignificant. The mean compressive strength of non-air-entrained S2 and S2.V concretes after 300 freezing and thawing cycles drastically decreased. The reductions in mean compressive strength for these concretes were 43.2 N/mm2 (49.3%) and 24.9 N/mm2 (32.6%), respectively.Usually, the higher the ultrasonic wave velocity, the larger the compressive strength of the concrete ,51,52. Ifc.abs.28d-300FT, and the mean changes in ultrasonic wave velocity, ΔVabs.28d-300FT, obtained after 28 days of curing of specimens not subjected to freezing and specimens after 300 cycles of frost resistance testing. fc.rel.28d-300FT, and the differences in the relative dynamic modulus of elasticity, ΔRDM28d-300FT, of concrete of the same age not subjected to freezing  and after 300 cycles of freezing and thawing. The graphs  and regression lines shifted to these curves (thick red and blue lines). Confidence interval curves were determined to assume a continuous Student’s t-test probability distribution with n − 2 degrees of freedom and a 0.90 confidence factor. Therefore, the regression lines shifted to the confidence interval represents the relationship Δf − ΔV and Δf − ΔRDM with a 90% probability of occurrence.e graphs  contain The use of the SP1 superplasticiser based on polycarboxylates had the side effect of introducing a large amount of air into the mix  and FiguThe only additive used in the S2 mixture was the SP2 superplasticiser, which did not cause the undesirable effect of significant air entrainment. The measured air content in this mixture and hardened concrete was about 2%.RDMUPPT, concrete S2 could be considered frost-resistant:-RDMUPPT after 300 cycles of freezing and thawing was 92.9% —Value of -No loss in mass of the specimens was found;According to two criteria for the assessment of frost resistance, i.e., the loss of mass of the specimens and the change in the relative dynamic modulus of elasticity 2)—Using the criterion of the change in compressive strength after 300 cycles, concrete S2 cannot be considered frost-resistant. The decrease in strength was as high as 49.3% —-RDMUPPT values were > 100% regardless of the number of freeze and thaw cycles—-No weight loss of the specimens occurred.2, respectively)—2 (17.4%). The highest achieved ultrasonic pulse velocity—5153 m/s  and 18.2 N/mm2 (21%), respectively—Lower mean compressive strength was determined after 28 and 128 days of curing, by 13.0 N/mm-There was a lower strength gain between days 28 and 128—-There was a decrease in the initial velocity of the ultrasonic pulse by 5.1%—In the case of the unintentionally air-entrained concrete S1, in relation to concrete S2, the following conclusions can be drawn:t-Test determined whether two samples are likely to have come from the same two underlying populations that have the same mean. In the case of concretes S1 and S2, the statistical test results showed that the compressive strength after 28 and 128 days of curing and the strength and RDMUPTT after 300 cycles of frost resistance test come from populations with different mean values. This proves that the influence of SP1 and SP2 superplasticizers on the parameters mentioned above is significant.A statistical test was used to conclude the influence of individual admixtures. Calculations associated with a Student’s The concrete mix S1.F uses a superplasticiser SP1 that introduces a significant amount of air into the mix, and the anti-foam admixture AFA, whose task was to reduce air content. In this study, concerning concrete without AFA, the air content decreased by over 5%  in the mAll three criteria for the assessment of frost resistance indicate that concrete S1.F was frost-resistant, because-There was no decrease in strength (a slight increase was obtained)—-RDMUPPT values were > 100% when the number of cycles exceeded 150 cycles—-The weight loss of the specimens was less than 1%.-An increase in strength after the frost resistance test was smaller—-RDMUPPT values were about 5% lower—-Specimen weight loss increased from zero to less than 1%.The reduction in the amount of air in the concrete resulted in the following, compared to S1 concrete without AFA:The use of AFA in concrete S1.F caused, compared to concrete S1, insignificant change to the 28- and 128-day compressive strength. Thus, the differences in the increase in strength between 28 and 128 days were also insignificant—The statistical test showed that the mean strengths after 28 and 128 days of curing and after 300 freeze–thaw cycles correspond to the population with the same mean values. This means that the influence of the AFA admixture added to S1 concrete is not significant from the point of view of the analyzed strength parameters.Few studies have been published on the effect of AFA admixture on the internal frost resistance and strength of concrete. In studies , an incrIn the concrete mix S1.F.V, apart from the superplasticiser SP1 and AFA admixture, an admixture modifying the viscosity was introduced. SP1 and VMA additives can contribute to the high amount of air in the mixture. The results of testing the amount of air in the S1.F and S1.F.V mix see  showed t-There was a slight decrease in the strength by about 3%—-RDMUPPT oscillated at about 103%—-Weight loss slightly exceeded 0.5%.Based on the criteria used in the tests, the frost resistance of concrete S1.F.V was confirmed: -There were slight drops in strength, instead of equally slight increases;-RDMUPPT values were higher—The use of the VMA additive resulted in the fact that concerning concrete S1.F without this additive:The VMA admixture caused a slight decrease in strength determined after 28 and 128 days of maturation  and after 300 cycles of freezing and thawing (up to 9%) concerning concretes not containing VMA, i.e., S1 and S1.F. Strength losses may be due to slightly higher air content in hardened concrete containing VMA .t-test showed that the changes in compressive strength and RDMUPTT after 300 cycles of frost resistance are accidental. This means that the VMA admixture did not significantly affect the strength and frost resistance of unintentionally air-entrained concrete.The Student’s Unfortunately, the authors were unable to find any publications on the study of the effect of VMA admixture on the mechanical parameters of concrete.The intentional air-entraining of the concrete mix, which contained only a superplasticizer, caused the expected and commonly known effects. The positive effect was the improvement of the frost resistance of concrete, while the negative effect was the reduction in concrete compressive strength. This was confirmed by the results of tests of concrete S2.A and S2.A.V with the addition of AEA concerning the parameters of concrete S2 and S2.V without this admixture. As a result of adding AEA to mixtures S2 and S2.V, the air content increased from 2.1 and 2.5% to 5.0% . This di-A slight increase in strength was achieved in the case of concrete S2.A (3.3%) or a slight decrease (3.1%) for concrete S2.A.V—-RDMUPPT values were > 100% regardless of the number of cycles—-The weight loss of the specimens was negligible up to 0.1%.The concrete containing AEA met all the criteria for frost-resistant concrete after 300 test cycles:-Very high loss of compressive strength (49.3 and 32.6%), which excluded the frost resistance of concrete, turned into only a few percent decrease in strength or even a slight increase in strength after the frost resistance test—-RDMUPPT obtained for concretes without AEA changed into the opposite tendency, i.e., a continuous, although slight, increase in RDMUPPT—The trend for a continuous decrease in the value of The increased amount of air in the concrete mix, compared to the non-air-entrained concretes S2 and S2.V, resulted in the following:t-test comparing the mean compressive strength of concrete and the value of RDMUPTT after 300 cycles of freezing and thawing showed for concrete pairs S2 and S2.A, as well as S2.V and S2.A.V, that these concretes come from a population with different mean values. Thus, the effect of AEA admixture on frost resistance was significant.The Student’s -2 between S2 and S2.A concrete;By 18.7 N/mm-2 between S2.V and S2.A.V concrete.By 8.0 N/mmAs expected, the mean compressive strength of concrete after 28 days of curing was significantly lower than that of concrete without AEA:The loss of compressive strength of concrete with AEA after 28 days correlated with an over 3% decrease in the ultrasonic pulse velocity.After 128 days, the compressive strength in relation to non-air-entrained concrete was -2 in the cases of concretes S2 and S2.A;Lower by 14.3 N/mm-Almost identical for concretes S2.V and S2.A.V.-The relative increase in strength of S2.A air-entrained concrete was 31.1%, while for S2 concrete without AEA, it was 17.4%;-The relative increase in strength of S2.A.V air-entrained concrete was 11.5%, while for S2.V concrete without air-entraining admixture was 4.4%.The strength gain between 28 and 128 days of curing was significantly higher compared to concrete without AEA :-The ret-test showed the equality of the mean values in the population (despite the 16% difference). It follows that the admixture of VMA has no significant influence on this strength. The statistical tool also confirmed the non-obvious influence of VMA on the strength of concrete after 128 days of curing. In the case of a pair of concretes S2 and S2.V, the mean values can be considered different, indicating the existence of the VMA influence. However, this cannot be stated in the case of S2.A and S2.A.V concretes, where the mean strengths should be considered equal.The S2 and S2.V concretes were characterized by similar compressive strengths after 28 days of curing, which was proved by the statistical test for the equality of the mean values in the population. Similarly, in the case of S2.A and S2.A.V concretes, the Student’s As mentioned earlier, the authors did not find any information on the influence of the VMA admixture on concrete parameters other than rheological properties.The tests analyzed in publications ,7,50,53 The tests proved that air-entrained concrete is frost-resistant due to the side effect of the superplasticiser. However, this does not always have to be the case as there are many different types of superplasticisers with very different compositions, also with anti-foam admixtures. If the type of air-entraining superplasticizer were to be replaced, the porosity structure would be inadequate for preserving the frost resistance of the concrete. It should be emphasized that the necessity to use air-entraining to ensure the frost resistance is proved by the results of studies presented, for example, in the publication .Attention should be paid to the low number of tests of the mechanical properties of concretes containing admixtures. Research is mainly carried out on the influence of these admixtures on the rheological properties of concrete mixes.There are no findings regarding the impact of additional admixtures used in concrete to clearly state whether the modification through admixtures is neutral concerning concrete’s mechanical properties and durability. The effect of cement type and the negative effect of a retarding admixture on concrete frost resistance in the presence of deicing salts was found in tests described in the article . RetardiAn important and poorly understood parameter is the influence of the admixture dosage on the properties of hardened concrete.It is also crucial to correlate the results of concrete strength and frost resistance tests with destructive and non-destructive methods, facilitating the analysis of the influence of given admixtures during concrete maturation. This task is extremely complicated when the composition of self-compacting concrete contains pozzolanic additives that thicken the concrete structure during its maturation. Therefore, the analysis of the influence of admixtures on mechanical properties and durability seems to be an extremely complex issue and requires further research in this area.Destructive tests aimed at assessing frost resistance are carried out in a uniaxial state of stress. Many elements of concrete structures are in a complex state of stress. Therefore, the following question arises: does the state of stress affect the internal frost resistance of concrete? To the best of the authors’ knowledge, the first testing of frost resistance in a complex stress state was published in . It seem2, carried out in the range described in the article.The following conclusions concern the tests of self-compacting concrete with the mean compressive strength no less than 55 N/mmThe influence of admixtures and their combinations on internal frost resistance after 300 cycles of freezing and thawing and the compressive strength of concrete matured at room temperature was analysed.The second group of conclusions concerns the compatibility of measures and criteria for estimating the frost resistance of concrete with the methods used in these tests. Their confirmation may be the results of tests  obtainedThe superplasticizer based on polycarboxylic ethers unintentionally caused air-entraining to the concrete mix to about 8%. This resulted in the frost resistance of concrete after 300 freeze–thaw cycles. A potentially dangerous side effect of air entrainment was about 17% lower compressive strength compared to concrete with the same base composition, which contained a superplasticiser and did not demonstrate the above-mentioned negative effect.The addition of AFA to the unintentionally air-entrained concrete caused a decrease in the amount of air by about 5% in the concrete mix and about 2.5% of air voids in hardened concrete. The concrete with AFA still met all the frost resistance criteria used in tests. The decrease in air content did not result in the expected increase in the compressive strength. This effect may be due to the negative effect of the AFA admixture components  on cement hydration.The air-entrained concrete had the expected positive and negative effects. The air content increased to 5% in concrete mix and to near 4% in hardened concrete. According to the criterion of the change in compressive strength, the air entrainment of concrete mixtures caused the frost resistance of concrete, which was not frost-resistant. The negative effect was the 8–20% reduction in the compressive strength.The effect of VMA admixture was not evident. The influence of VMA in unintentionally and intentionally air-entrained concrete on internal frost resistance and compressive strength determined after 28 days of curing was insignificant. The influence on the compressive strength after 128 days of curing in non-air-entrained concrete was statistically significant.In the case of non-air-entrained concretes, the obtained frost resistance indexes indicated both a frost resistance and lack of frost resistance, depending on the assessment method and the corresponding criterion. The mentioned concretes did not meet the criterion of permissible loss of compressive strength; the decrease in strength after 300 cycles of the frost resistance test reached 50%.RDMUPTT was obtained, but the decrease was disproportionately low concerning the loss of concrete strength.The indicator in the form of the relative dynamic modulus of elasticity correctly described the damage caused by the impact of low temperatures only qualitatively. In the case of non-air-entrained concretes, a constant decrease in the value of There was no loss in weight of the non-air-entrained concrete specimens, despite a large reduction in strength. The criterion of sample mass change should only determine the resistance to surface damage caused by frost.Internal frost resistance, understood as resistance to degradation of the internal structure of concrete, as shown in this research, is best assessed using destructive methods. The decisive criteria for internal frost resistance should be the change in concrete strength and/or the static modulus of elasticity, which directly reflect the mechanical damage of concrete.


The dynamic behavior of a PPSRC beam–column joint is related to constraint effect, strength deterioration and strain rate effect. Then, it can be assessed by bearing capacity, stiffness degradation, displacement ductility and energy consumption. The results show that the increased strain rate causes growth in ring stiffness, bearing capacity and energy consumption of PPSRC beam–column joints. However, the influence of shear span-to-depth ratio on dynamic mechanical properties of PPSRC beam–column joints is more obvious than that of strain rate. Regardless of strain rate, the bearing capacity, initial stiffness, ring stiffness and energy consumption of PPSRC beam–column joints decrease as the shear span-to-depth ratio increases. Moreover, the ring stiffness under reverse direction is smaller than that the under forward direction at each displacement level. However, the stiffness degradation under a lower shear span-to-depth ratio is more obvious than that under a higher shear span-to-depth ratio. Moreover, the displacement ductility with a higher shear span-to-depth ratio is better than that with a lower shear span-to-depth ratio. Finally, the mechanical properties of PPSRC beam–column joints are affected by the extension length of partial steel plate, and the reasonable extension length of the partial steel plate in the column is affected by the shear span-to-depth ratio. Compared with traditional cast-in situ construction, a precast concrete structure possesses higher business competitiveness due to its environmental protection, economy and excellent mechanical properties . For exaResearchers were of great assistance in research into precast beam–column joints or connection. The conclusions were that precast specimens showed slightly reduced mechanical properties, including stiffness and energy consumption . DespiteBased on the difference in the connection method, precast concrete members can be connected at the site by wet connection or dry connection ,17. The With these considerations in mind, a new type of beam–column joint, i.e., precast and a partial steel reinforced concrete (PPSRC) beam–column joint was proposed for a precast concrete structure. To evaluate the feasibility of the PPSRC beam–column joint, cyclic loading tests were performed by authors in a previous paper to study the mechanical behavior of the PPSRC beam–column joint . CompareOn the other hand, multiple factors may affect the mechanical properties of the PPSRC beam–column joint, including the shear span-to-depth ratio, sectional characteristics, reinforcement detailing, concrete grade, the axial compression ratio, reinforcement anchorage type, and joint shear stress ,22. AmonAlthough a lot of research has been carried out to evaluate the effect of the shear span-to-depth ratio on the mechanical properties of RC members, the effect of shear span-to-depth ratio on the mechanical behavior of the PPSRC beam–column joint has been less investigated. Additionally, a comprehensive investigation on the dynamic behavior of the PPSRC beam–column joint under various shear span-to-depth ratios has not yet been carried out. The effect of the shear span-to-depth ratio on the dynamic behavior of the PPSRC beam–column joint is hence focused upon in this paper. Generally, experimental study is more suitable to assess the dynamic behavior of the PPSRC beam–column joint, but it is hard to realize in many cases. In this case, the finite element analysis is more suitable. Considered the constraint effect, strength deterioration and strain rate effect, a finite element model was first developed to assess dynamic behavior of the PPSRC beam–column joint. After a description of the experimental overview, the rationality of the finite element model was studied. The validated finite element model was then adopted to assess the dynamic behavior of the PPSRC beam–column joint. Finally, recommendations were made to design the reasonable extension length the of partial steel plate under various shear span-to-depth ratios.The finite element model was developed to the assess dynamic behavior of the PPSRC beam–column joint, where the characteristics of the cross-section, the reinforcement bars and steel plates properties are the same as that of specimens mentioned in a previous paper . The num(1)Under the influence of Poisson’s ratio, concrete will expand laterally under compression. However, the expansion deformation of concrete will be prevented due to the existence of stirrup reinforcements and steel plates, which have a certain constraint effect . If only(2)At present, the software ABAQUS is adopted by many scholars to simulate the mechanical properties of beam–column joints under cyclic loading. However, no descending segment existed in the obtained hysteretic curves ,32. As a(3)Concrete and steels are both rate-sensitive materials, which will exhibit various mechanical behaviors with conditions of various strain rates. The PPSRC beam–column joint is constituted of concrete and steel, so it is also rate-sensitive. When subjected to dynamic loadings, the response characteristics and damage mechanism of the PPSRC beam–column joint will show obvious differences from that subjected to static or quasi-static loadings . HoweverThe plastic damage model in the software ABAQUS may be adopted to simulate the mechanical properties of members under monotonic loading or cyclic loading. As mentioned above, the constraint effect should be considered due to the existence of stirrup reinforcements and steel plates. With this in mind, the stress–strain constitutive relationship for concrete in the plastic damage model will be established with the consideration of the constraint effect induced by stirrup reinforcements and steel plates. Extensive and mature research on the constraint mechanism of stirrup reinforcements and steel plates has been conducted by Mander and other scholars. Consequently, the stress–strain constitutive relationship for confined concrete can be established by referring to the published paper . In addiK). The formula for calculating the concrete stress (σ) in the Mander model is given by Reference [K). Before the stress–strain constitutive relationship for confined concrete is obtained, another problem is to obtain the effective lateral restraint stress according to the confined region. In light of the simplified restraint state of confined concrete, it can be divided into high restraint concrete, weak restraint concrete and unconfined concrete. Thus, the increasing factor of strength (K) should be calculated separately for different regional partitions, and the confined concrete in this paper can be divided into three types.For the confined concrete, the key to establish the stress–strain constitutive relationship is to determine the effective lateral restraint stress and increasing factor of strength (eference . The pubeference  will be (1)Partially restraint concrete (PRC) surrounded by I-steel flanges of the beam. The effective lateral restraint stress of the PRC is the linear superposition of restraint stress provided through steel flanges and stirrup reinforcements. In addition, the effective lateral restraint stress on the PRC can be given by Reference .(2)Highly restraint concrete (HRC) and partially restraint concrete (PRC) surrounded by cross-shaped steel of the column. The effective lateral restraint stress of the HRC and PRC can be calculated by Reference .(3)Partially confined concrete (PCC) surrounded by the stirrup reinforcements. The effective lateral restraint stress of the PCC provided through stirrup reinforcements of beam and column could be calculated as follows .x-direction and y-direction, respectively; ccρ is the longitudinal reinforcement ratio; cb is effective section width in x direction; cd is the effective section width in y direction; xρ and yρ represent the reinforcement ratios of the rectangular reinforced concrete member in the horizontal and vertical directions, respectively; x,hf and y,hf are yielding strengths supplied by horizontal and vertical reinforcement bars, respectively.cσ and cɛ are stress and strain under compression, respectively; cE is the elastic modulus for unconfined concrete; cα is coefficient corresponding to descending branch of the concrete stress–strain curve under uniaxial compression; c,rf is a typical value corresponding to concrete strength under uniaxial compression; c,rε is compressive peak strain corresponding to the typical value of uniaxial compression strength c,rf; cρ, cx and n are calculation parameters.For the unconfined concrete (UC), the stress–strain constitutive relationship mentioned in standard GB50010-2010 is adopted . The exptσ and tɛ are stress and strain under tension, respectively; td is damage evolution coefficient for concrete under uniaxial tension; tα is a parameter value corresponding to the descending branch of the concrete stress–strain curve under uniaxial tension; t,rf is a typical value corresponding to concrete strength under uniaxial tension; t,rε is tensile peak strain corresponding to the typical value of uniaxial tension strength t,rf; tρ and tx are calculation parameters.Following the provisions of the code GB50010-2010 , the expFor the PPSRC beam–column joint, the concrete in the column can be divided into four types, i.e., HRC, PRC, PCC and UC, while the concrete in the beam can be divided into three types, i.e., PRC, PCC and UC, which can be found from After the previously mentioned adjustments were made, the concrete stress–strain constitutive relationship of different regional partitions could be obtained based on the existing literature . The strd 0.5fcr .ρ, Poisson ratio μ, shear dilation angle Ψ, flow potential eccentricity Ε’, ultimate stress ratio of biaxial compression to uniaxial compression fα, the second stress invariant ratio of the compression meridian plane to tension meridian plane K1, viscosity parameter ν, can be found from Other material parameters of concrete including density eK, sK and cK represent the stiffness of the elastic stage, post-yielding stage and descending stage, respectively. The calculation method of the above stiffness is given by Reference [yP and Δy represent the yielding strength and the yielding displacement, while ΔB represents the peak displacement corresponding to the ultimate strength uP (yP = 0.8uP) [Since the amount of steel plates in the PPSRC beam–column joint core area is more than that of reinforcement bars, the stirrup reinforcements and longitudinal reinforcement bars of the PPSRC beam–column joint are assumed to be ideal elastoplastic materials that can simplify numerical computation. Before reinforcement bar yielding, the stress–strain is a diagonal line. After reinforcement bar yielding, the stress–strain relationship keeps a horizontal line, which can be found in eference . Moreove= 0.8Pu) .fcDIF) is calculated from the following formula [When subjected to dynamic loadings, the response characteristics and damage mechanism of the PPSRC beam–column joint will show obvious differences from that subjected to static or quasi-static loadings, so it is important to understand the dynamic behavior of the PPSRC beam–column joint. The basic reason lies in the strain rate effect that the mechanical behavior of structural materials changes as the strain rate changes. Thus, reasonable consideration should be given to the strain rate effect before establishing material stress–strain constitutive models. The aforementioned strain rate effect will be included in the plastic damage model of concrete, which is described by the following formula. When the concrete is under uniaxial compression, the dynamic increase factor ( formula .(12)DIFftDIF) is calculated from the following formula [When the concrete is under uniaxial tension, the dynamic increase factor ( formula .(14)DIFMore details of various parameters in the formulae mentioned above are shown in Reference .The yielding strength, ultimate strength and yielding strain of steel materials under dynamic loadings could be obtained by the dynamic constitutive model, which is proposed by Li and Li . The relMore details of various parameters in the formulae mentioned above are shown in Reference .Six specimens  were cast in which the section characteristic, longitudinal reinforcement bars and stirrup reinforcements were the same . The proThe concrete grade is C30, while the grades of the longitudinal reinforcement bar and stirrup reinforcement are HRB335 and HPB235, respectively. The grade of the steel plate is Q235b for the PPSRC beam–column joint. The selected strength of the materials meets the design requirements specified by GB50011-2010 and GB50010-2010 . The layThe loading apparatus of the exterior and interior beam–column joints are shown in Different finite element models of the PPSRC beam–column joint were established, as shown in Solid element C3D8R was used for the concrete and steel plate, and truss element T3D2 was used for reinforcement. The reinforcement and steel plate were embedded in concrete. The schematic diagram of mesh dividing for the PPSRC beam–column joint is shown in Comparison results can be found in Compared with experimental results, the ultimate bearing capacity and maximum displacement of finite element analysis results are almost consistent. It should be mentioned that the pinching effect of load-deflection hysteretic curves is rarely realized due to tie constraints between elements in the software ABAQUS. The pinching effect is caused by bond slipping; however, the bond slipping is not considered when tie constraints between elements are used. For specimen SE1, the steel plate was rusted before welding. After the test, the specimen SE1 was sectioned. It was found that the weld was destroyed. The above problem was not considered in the finite element analysis, which caused the discrepancy between the numerical solution and the experiment result. In addition, the changing trend of load-deflection hysteretic curves of numerical computation results is consistent when compared with the experimental results, and it illustrates the correctness of proposed finite element model again.For finite element software ABAQUS, the equivalent plastic strain and concrete tensile damage are related to the degree of crack development. Further efforts are made to illustrate the rationality of above-mentioned finite element model, and contours of equivalent plastic strain and concrete tensile damage are also given, which can be found in As mentioned earlier, the column was first destroyed due to the insufficient extension length of the partial steel plate in the column. According to the existing specifications , the colAnalysis results are given in −5, taking the average value of forward loading and reverse loading for example, the ultimate bearing capacity of finite element model FS4 (λ = 2.3) is 340.0 kN, while the ultimate bearing capacity of finite element model FS8 (λ = 4.0) is 149.2 kN. Through compared results, there is a conclusion that the ultimate bearing capacity of the PPSRC joint is reduced by 56.1%. For dynamic analysis with a strain rate of 1.25 × 10−2, taking the average value of forward loading and reverse loading for example, the ultimate bearing capacity of finite element model DFS4 (λ = 2.3) is 357.6 kN, while the ultimate bearing capacity of finite element model DFS8 (λ = 4.0) is 155.1 kN. There is a conclusion that the ultimate bearing capacity of the PPSRC joint is reduced by 56.6%. Regardless of the strain rate, the bearing capacity of the PPSRC beam–column joint decreases as the shear span-to-depth ratio increases. Moreover, another conclusion can be found that both yielding bearing capacity and ultimate bearing capacity of the PPSRC beam–column joint increase as the strain rate increases.The load-deflection skeleton curves of the PPSRC beam–column joint are given in i cycles, j represents the cyclic displacement level; i cycles.Stiffness degradation reflects an accumulation of damage. The ring stiffness can be used to study stiffness degradation of the PPSRC beam–column joint, which is expressed as follows .(22)Kji−5, compared with finite element model FS4 (λ = 2.3), ring stiffness of finite element model FS8 (λ = 4.0) decreases by 67.5% and 58.7%, when the displacement ductility coefficients (Δ/Δy) are equal to 0.5 and 7, respectively. For dynamic analysis with a strain rate of 1.25 × 10−2, compared with finite element model DFS4 (λ = 2.3), ring stiffness of finite element model DFS8 (λ = 4.0) decreases by 68.2% and 60.4%, when the displacement ductility coefficients (Δ/Δy) are equal to 0.5 and 7, respectively. Regardless of the strain rate, the ring stiffness of the PPSRC beam–column joint decreases as the shear span-to-depth ratio increases. However, stiffness degradation of the PPSRC beam–column joint under a smaller value of λ is more remarkable than that under a larger value of λ. Another conclusion is given through Eleven finite element models are analyzed to obtain the stiffness degradation of the PPSRC joint. The first cycle result of cyclic loading is calculated to assess stiffness degradation of the PPSRC joint, and the analysis results are given in μ∆). The following formula will be adopted to calculate μ∆ [u is ultimate displacement; ∆y is yielding displacement. ∆y in Equation (23) is obtained by the equivalent yield point determined on the skeleton curve. The “equivalent energy method” [u in Equation (23) is obtained from the descending section of the skeleton curve where the bearing capacity is reduced to 85% of the maximum value. The calculation results of displacement ductility coefficients are shown in Ductility performance is the property that allows the PPSRC beam–column joint to undergo a large deformation beyond the initial yielding deformation without abruptly losing its bearing capacity. The ductility performance of the PPSRC beam–column joint can be represented by the displacement ductility factor (ulate μ∆ .(23)μΔ= method”  is used λ increases. That is to say, the ductility performance of the PPSRC beam–column joint with a larger value of λ is better than that with a smaller value of λ.From Another main concern in the dynamic behavior of the PPSRC joint is energy consumption. When estimating the energy consumption capacity of the PPSRC joint, eleven models are analyzed to obtain the variation law of cumulative energy consumption of the PPSRC joint with different strain rates or shear span-to-depth ratios. The first cycle result of cyclic loading is calculated to assess the energy consumption of the PPSRC joint.−5, the cumulative energy consumption of finite element models FS4 and FS8 are 54.1 kN·mm and 23.1 kN·mm, where the values of λ are 2.3 and 4.0, respectively. Compared with finite element model FS4, the cumulative energy consumption of finite element model FS8 decreases by 57.3%. For dynamic analysis with a strain rate of 1.25 × 10−2, the cumulative energy consumptions of finite element models DFS4 and DFS8 are 57.5 kN·mm and 26.0 kN·mm, where the values of λ are 2.3 and 4.0, respectively. Compared with finite element model DFS4, the cumulative energy consumption of finite element model DFS8 decreases by 54.8%. When the value of λ remains constant, compared with finite element model FS6, the cumulative energy consumption of finite element models DFS6-1 and DFS6-2 increase by 4.5% and 11.4%, respectively. Therefore, the cumulative energy consumption of the PPSRC beam–column joint is larger under a larger value of strain rate. Regardless of strain rate, the cumulative energy consumption of the PPSRC beam–column joint is smaller under a larger value of λ.It can be found from As mentioned in the previous paper , the mosλ increases gradually with a variation amplitude of 0.1, and failure modes of the PPSRC beam–column joint under various values of λ would be obtained. Taking an extension length of the partial steel plate in the column equal to 870 mm as an example, contours of equivalent plastic strain corresponding to several representative values of λ are given, which can be found in To meet the existing specifications , the colλ, the concentration position of the equivalent plastic strain of the PPSRC beam–column joint also changes, and the equivalent plastic strain in the column decreases gradually. When the value of λ is smaller, concrete damage in the column is more serious; conversely, concrete damage in the beam and joint core area is more serious. Until the value of λ reaches 2.8, the equivalent plastic strain is concentrated in the beam and joint core area. Consequently, the reasonable extension length of partial steel plate in the column is 870 mm when the value of λ is greater than or equal to 2.8. Through further finite element analysis, the reasonable extension lengths of the partial steel plate corresponding to various values of λ are obtained, as given in With an increase in the value of The main object of this is to extend the application of the PPSRC beam–column joint mentioned in the previous paper to the precast concrete structure. For this purpose, further analysis of the dynamic behavior of the PPSRC beam–column joint was carried out. In the light of the previous statement, relevant conclusions can be summarized.(1)Ultimate bearing capacity and maximum displacement of numerical computation results are almost compatible with of the experimental results. Additionally, the changing trend of load-deflection hysteretic curves of numerical computation results is compatible with that of the experimental results. Moreover, the changing rule of equivalent plastic strain and concrete tensile damage of finite element analysis results is in good agreement with that of experimental results. Hence, the proposed finite element model can be utilized to assess the mechanical properties of the PPSRC beam–column joint.(2)Both the yield carrying capacity and the ultimate carrying capacity of the PPSRC beam–column joint increase as the strain rate increases. Furthermore, regardless of the strain rate, the ring stiffness of the PPSRC beam–column joint decreases as the shear span-to-depth ratio increases. The ring stiffness under the reverse direction is smaller than that under the forward direction at each displacement level, and the initial stiffness of the PPSRC joint is higher under a larger strain rate. However, stiffness degradation with a higher strain rate is more obvious under a larger displacement level. Moreover, the ductility performance of the PPSRC beam–column joint is rarely affected by strain rate. However, regardless of the strain rate, the displacement ductility factor of the PPSRC beam–column joint increases gradually as the shear span-to-depth ratio increases. Finally, the energy consumption of the PPSRC beam–column joint increases as the strain rate increases. Compared with finite element model FS6, the cumulative energy consumption of finite element models DFS6-1 and DFS6-2 increase by 4.5% and 11.4%, respectively.(3)Regardless of strain rate, the bearing capacity of the PPSRC beam–column joint decreases as the shear span-to-depth ratio increases. For quasi-static analysis or dynamic analysis, the ultimate bearing capacity of finite element model FS4 (λ = 2.3) is higher than that of finite element model FS8 (λ = 4.0). In addition, initial stiffness and ring stiffness of the PPSRC beam–column joints decrease as the shear span-to-depth ratio increases. However, stiffness degradation of the PPSRC beam–column joint is higher when the shear span-to-depth ratio is reduced. Moreover, the ductility performance of the PPSRC beam–column joint is better when the shear span-to-depth ratio is higher. Finally, the energy consumption of the PPSRC beam–column joint decreases when the shear span-to-depth ratio increases.(4)The mechanical properties of the PPSRC beam–column joint are affected by the extension length of partial steel plate in the column, and the reasonable extension length of the partial steel plate in the column is related to the shear span-to-depth ratio. When the extension length of the partial steel plate is insufficient, the concrete at the end of the partial steel plate in the column is crushed seriously, but the carrying capacity of the PPSRC beam–column joint does not decrease significantly. When the extension length of the partial steel plate in the column is adequate, the concrete damage in the beam and joint core area is more serious.


Received signal strength indication (RSSI) obtained by Medium Access Control (MAC) layer is widely used in range-based and fingerprint location systems due to its low cost and low complexity. However, RSS is affected by noise signals and multi-path, and its positioning performance is not stable. In recent years, many commercial WiFi devices support the acquisition of physical layer channel state information (CSI). CSI is an index that can characterize the signal characteristics with more fine granularity than RSS. Compared with RSS, CSI can avoid the effects of multi-path and noise by analyzing the characteristics of multi-channel sub-carriers. To improve the indoor location accuracy and algorithm efficiency, this paper proposes a hybrid fingerprint location technology based on RSS and CSI. In the off-line phase, to overcome the problems of low positioning accuracy and fingerprint drift caused by signal instability, a methodology based on the Kalman filter and a Gaussian function is proposed to preprocess the RSSI value and CSI amplitude value, and the improved CSI phase is incorporated after the linear transformation. The mutation and noisy data are then effectively eliminated, and the accurate and smoother outputs of the RSSI and CSI values can be achieved. Then, the accurate hybrid fingerprint database is established after dimensionality reduction of the obtained high-dimensional data values. The weighted k-nearest neighbor (WKNN) algorithm is applied to reduce the complexity of the algorithm during the online positioning stage, and the accurate indoor positioning algorithm is accomplished. Experimental results show that the proposed algorithm exhibits good performance on anti-noise ability, fusion positioning accuracy, and real-time filtering. Compared with CSI-MIMO, FIFS, and RSSI-based methods, the proposed fusion correction method has higher positioning accuracy and smaller positioning error. With the development of wireless communication technology, the demand for location-based services (LBS) has increased greatly. The complex indoor environment makes GPS ,2,3,4 siIEEE 802.11 protocol does not give specific processes or algorithms to generate RSSI. RSS refers to the MAC layer signal strength received by the client. Because RSS is coarse-grained information, it is often affected by multi-path effect and noise signal, and the location performance is not stable, so it can not meet the requirements of indoor precise location. In recent years, CSI ,11 can bIn Reference , CSI ampCurrently, most methods based on CSI fingerprints do not incorporate RSS information, thereby reducing the computing resources required for positioning. Therefore, this paper uses RSS and CSI, which are two kinds of information with different granularity, to realize regional location and precise location, respectively, and to make full use of the advantages of different granularity information. Compared with the distance estimation method, the complex indoor environment has less influence on fingerprint method. Based on the above reasons, this paper studies the indoor location method based on the hybrid fingerprint of RSS and CSI. Combining the respective characteristics of RSS information and CSI information, this paper proposes an improved fingerprint precise positioning algorithm based on RSSI and CSI. In the offline phase, the mobile terminal collects the RSSI signal and CSI signal from each AP in the known reference position. After denoising the original RSSI signal and CSI amplitude value by using the Kalman filter, the phase of CSI is preprocessed to build a more robust position fingerprint database. At the same time, to reduce the complexity of the fingerprint data and positioning error, we use the weighted k-nearest neighbor (WKNN) algorithm  to perfoThis paper proposes a novel cross-layer approach including MAC layer information and physical layer information that enables fine-grained indoor fingerprint location algorithm in OFDM-MIMO WLANs.The obtained RSSI value and CSI amplitude value are denoised, and CSI phase value is linearly transformed. The processed measurements information can express the difference of fingerprints between different locations.The proposed algorithm reduces the dimension of the amplitude and phase values of CSI, and constructs a fingerprint database that can map the location feature data.In this paper, an indoor fingerprint location method based on RSSI and CSI in high load AP environment is proposed. It improves the difficulty of getting RSS and CSI information of AP in high load WiFi channel due to beacon delay. The proposed method can be used in a high-load AP environment.The positioning accuracy of the proposed method in two typical indoor environments is high. This method is higher than several traditional localization algorithms, and it is a more accurate WLAN Indoor fingerprint location algorithm.The main contributions of this paper can be divided into the following:This article includes the following chapters: RSSI refers to the received signal strength received by the client, which belongs to the MAC layer and comes from each packet. The multi-path propagation of wireless signal refers to the reflection, diffraction, and scattering of electromagnetic waves on the propagation path. The signal received by the node does not come from a single path but from multiple paths. Due to the different path distances of electromagnetic waves, the arrival time of nodes is different, and there is phase difference. The positive and negative superposition of different phase differences will enhance or reduce the original signal, resulting in multi-path attenuation, which makes the indoor electromagnetic environment present regional and special. Therefore, the channel multi-path structure is unique for each location, which is called the RSSI position “fingerprint” ,20.WLAN vendors can privately define RSSI values. Through the description in the 802.11-2007 standard , we knowThe average value of RSSI within 1 s is obtained by averaging the instantaneous values of 8192 RSSIs. The average value of RSSI is calculated as follows:Power is sampled directly in time domain. Since most wireless signals are MW level, they are polarized and converted into dBm, which does not mean that the signal is negative.H appears in a complex form CSI data belongs to the physical layer information of wireless communication protocol. The physical layer (PHY) of 802.11 protocol  is the iN is the total number of paths propagated. Channel frequency response (CFR)  can be uSince CSI is the frequency response of multiple sub-carriers, it can accurately describe frequency selective channels. According to the Fourier transform of CIR and CFR, multiple propagation paths can be distinguished in time domain.RSSI is the superposition of multiple path signals, which is very unstable. In a certain range, the probability of RSSI coincidence in different locations is relatively large, which makes it difficult for RSSI to complete high-precision indoor positioning, and it is only suitable for rough estimation of positioning range. CSI is not the superposition of all the sub-carrier information, it describes the signal of multiple paths, has more characteristics, and contains the channel state information of multiple sub-carriers. The amplitude and phase of CSI sub-carriers in different positions are crossed, so single sub-carrier cannot be distinguished. But if we use the diversity of CSI frequency and all the sub-carrier data, through a certain algorithm, we can distinguish different locations. K reference points which are closest to the location point in space and calculates the location estimation value of the K reference points according to the coordinates of the K reference points. The basic distance space can be calculated as Equation  is a deterministic algorithm. It obtains the fingerprint of the first Equation .(5)dq=∑The weighted k-nearest neighbor (WKNN)  algorithTo ensure location accuracy, this paper proposes an indoor hybrid fingerprint location algorithm based on RSSI and CSI. Because of the influence of multi-path effect, AP loss, heterogeneous network interference, and other factors, the collected fingerprint data can not be directly used, and this paper will carry out the relevant data processing work. This part first introduces the structure of the indoor fingerprint positioning model. Secondly, it describes the process of RSSI and CSI data fusion after the establishment of the fingerprint database.The indoor fingerprint location method proposed in this paper includes two parts: offline phase and online phase. In the offline phase, a modified device supporting OFDM-MIMO is used to collect RSSI and CSI measurement data at the reference point. Then, according to the proposed method, the abnormal packets which significantly deviate from the whole in the continuous RSSI and CSI packets are removed. According to the location fingerprint generation method designed in this paper, the position fingerprint containing RSSI, CSI amplitude, and CSI phase information is generated. The fingerprint uses the characteristics of frequency diversity and space diversity of the Orthogonal Frequency Division Multiplexing (MIMO) system to obtain CSI and RSSI values on different antennas. In each sub-carrier, RSSI and CSI are aggregated in the unit of receiving antenna. At the same time, the anti-jamming ability and stability of the location fingerprint are further enhanced and the uniqueness of the location is better reflected, which helps to improve the accuracy of the location. Next, the location fingerprints generated in each reference location are collected to construct the location fingerprint map and database. In the offline phase, the coordinates of the target location are obtained by matching the fingerprint database. This section describes the fingerprint generation process of the fusion location method proposed in this paper. The features of the RSSI are its low characteristic dimension and easy obtainability, however, it also suffers from poor signal stability and low spatial resolution. On the other hand, the CSI retains the characteristics of fine signal granularity, high stability, high characteristic dimension, and high computational complexity. Based on the above characteristics, a fingerprint fusion localization method based on RSSI and CSI is proposed. For indoor environment, the multi-path effect is obvious and RSS is more unstable. There may be some abnormal values in the measurement results of RSSI packets. If these abnormal values are used as the received signal strength, the positioning results will greatly deviate. The indoor location algorithm based on fingerprint similarity comparison needs to take the whole RSS vector as a whole. The fluctuation and noise of an RSS signal will have a great impact on the overall comparison results. We first process the RSSI value using Gaussian filtering . The basIn this paper, the Dell notebook modified the wireless network card was used for data collection at Kyungpook National University (KNU), and the RSSI on different antennas was obtained. The detailed process of the experimental environment and data collection is described in detail in The algorithm can effectively eliminate the mutation data and noise fluctuation in RSSI fingerprint data. We use the aforementioned data processing method to uniformly process the RSSI values obtained in other indoor environments. The algorithm realizes the accurate and smooth output of RSSI values and is used to establish an accurate fingerprint database, which makes the subsequent positioning more accurate.The Wi-Fi signal using the 802.11n transmission protocol can use the OFDM modulation method to modulate the signal to each sub-channel for transmission and to extract CSI on each channel. The CSI data of physical layer is mainly used for wireless network optimization and it is generally difficult to access these data. In recent years, Inter and Atheros network card suppliers have processed some of their network card firmware programs and some relevant organizations have opened corresponding software development packages. We can modify the open-source driver of network card in Linux and WIN system and use debugging mode to obtain CSI data of some wireless network cards. The Intel5300 network card provides sub-carrier level channel measurement for OFDM system, convert the measured value into more abundant multi-path information, and provide more stable measurement value and higher positioning accuracy.p is the number of antennas at the transmitter; As mentioned above, all software and scripts to read and parse channel measurements are performed by the MATLAB. Finally, a channel matrix with 30 sub-carrier groups is obtained, that is, the 802.11n channel state information is acquired. By giving full play to the advantages of the frequency diversity and space diversity of the MIMO system, while using the characteristics of multiple receiving antennas, the location fingerprint can better reflect the uniqueness of the location. We aggregate CSI in units of receiving antennas under each sub-carrier:For each sub-carrier, the mean value of the two amplitudes obtained by the receiving antenna is calculated, so that the dimension of the amplitude becomes 30 dimensions. Among them, a is the slope of the received response phase. b is the offset. If the sub-carrier frequency is symmetric, then The existence of the error offset causes the original phase information to not be directly used. Assuming that the value of measurement noise After analyzing the trend of CSI phase, this paper proposes a data dimension reduction method.This method is easy to operate and reduces the calculation at the same time. Since the information contained in the adjacent sub-carriers is nearly similar, we remove the amplitude of the even-numbered adjacent sub-carriers according to this feature, and only preserve the phase information of the odd-numbered sub-carriers. Finally, the effective CSI obtained by dimension reduction can be used to establish offline CSI fingerprint database. Dimensionality reduction processing is carried out for the phase information of the two sub-carriers symmetric about the center sub-carrier, and the phase information from an antenna is reduced to 15 dimension:m represents the number of packets collected. i represents the number of antennas and s represents the number of APs, and, in this paper, t test points for fingerprint matching, and the coordinate value of the test point is By the aforementioned processing of RSSI, CSI amplitude, and CSI phase information, we obtain the fingerprints containing 2 × 1 dimensional RSSIs, 2 × 15 dimensional CSI amplitude, and 2 × 15 dimensional CSI phase information, respectively. The receiver of this paper is a laptop with ubuntu14.04.4 operating system and intel5300 wireless network card. The network card is attached with three dual-frequency external antennas of 2.4 G/5 GHz. The green dots in the figure indicate the positions of reference points. The accuracy of RSSI signal and CSI signal is the highest at a height of 1 m from the ground, so the distance between the AP antenna and the ground is 1 m. When collecting RSSI signal and CSI signal data, the tester holds a portable notebook device and stands at the reference point for data collection. The reference point receives signals from three APs. Each reference point collects RSSI data and CSI data for 30 min and saves them to the PC. The RSSI data and CSI data are extracted by MATLAB, and the original RSSI data and CSI data are filtered at the same time. Take the effective RSSI value and the effective CSI value to establish the database as the feature vector of the point. The experimental starts from the lower-left corner, and its coordinates are . The grid size of the fingerprint database is 1 m. In the corridor environment, fingerprint information of 24 locations are collected, and 27 locations are collected in the lobby environment. The performance of the algorithm is evaluated by the distance error between the estimated position of the reference point and the real position.In the indoor environment, there are many factors that affect the positioning results, such as the number of people in the positioning area and their status, static or moving, receiver location and antenna orientation, and the influence of other indoor equipment movements, etc. We consider these conditions that are difficult to control and evaluate the generality of the proposed algorithm. To weaken these external factors, the same set of location data is processed to compare the performance of the location algorithm.During the construction of fingerprint database, the number of samples makes a great impact on the positioning performance. For the similarity comparison method of fingerprint database, the location accuracy largely depends on whether the fingerprint samples in the fingerprint database can accurately describe the distribution of the overall fingerprint or not. For this experiment, each unit area is sampled for 5 min, and nearly 1000–3000 CSI samples can be sampled for each AP. In the case of the same environment parameters, we selected different numbers of sample sets for training to verify the existing indoor location method. We also investigated the influence of the different sample set number in the proposed fingerprint location method on the positioning performance. The sampling frequency of sampled data is equal to 1500 packets/s.In the positioning error analysis, cumulative distribution function (CDF), standard deviation, and average error were used to analyze the performance of the positioning method. In two indoor environments, the proposed method is compared with the RSSI-based fingerprint positioning system and two CSI-based fingerprint positioning systems (FIFS and CSI-MIMO). In the test process, WKNN is used as fingerprint matching algorithm and three APs are used to generate fingerprint. We use Euclidean distance to estimate the similarity measure between the reference point (RP) coordinates The CDFs of location distance error in the two scenarios are shown in It can be seen from the table, in terms of the average positioning error, the performance of the proposed method is about 1.171 m in the corridor environment, which is about 12.6% higher than CSI-MIMO and 36.9% higher than that of FIFS. The average positioning error of the RSSI-based method is about 2.122 m, it is lower than the positioning accuracy of the proposed method; In the lobby experimental scenario, the proposed method is about 1.094 m, which is 15.9% and 61.5% higher than CSI-MIMO and FIFS, respectively. The average positioning error of the RSSI-based method is about 2.078 m. Through the series of experiments, we confirmed that the method proposed in this paper was effective in improving the accuracy of positioning. The positioning method proposed in this paper can effectively improve the positioning accuracy by the following reasons. The reasons for the proposed algorithm to improve accuracy are as follows. Firstly, the fingerprints in the fingerprint database are integrated with RSS and CSI, which are not based on CSI or RSS alone; secondly, the fingerprint features are preprocessed effectively in the offline phase, and the integrity of the data is preserved; thirdly, WKNN is used to reduce the positioning error. In addition, since the proposed method performs the dimensional reduction for the fingerprint, its computational complexity is also improved over the CSI-MIMO and FIFS.In this paper, a hybrid fingerprint algorithm is proposed to improve the positioning accuracy of RSSI-based and CSI-based fingerprint location methods. In the offline phase, the amplitude values of RSSI and CSI are eliminated and filtered, and the phase value of CSI is introduced by linear transformation. This paper also proposes a method to reduce the fingerprint feature dimension of high-dimensional data CSI obtained in OFDM-MIMO system. Finally, combined with the effective RSSI, effective CSI amplitude value, and CSI phase value, a novel fingerprint database containing more abundant indoor location information was established. In the online phase, the fingerprint data is matched according to the WKNN algorithm, which effectively improves the positioning accuracy. This paper uses MATLAB to verify the effectiveness and superiority of the algorithm in two indoor environments. Compared with existing algorithms, the algorithm based on RSS and CSI hybrid fingerprints can improve positioning accuracy. At the same time, because additional hardware is not necessary for the proposed algorithm to perform positioning, its applicability is also high. Future research directions include the evaluation of the performance of the proposed algorithm in a three-dimensional indoor environment, an indoor laboratory environment with more obstacles and personnel flows.