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RAR RUS 14301-14301 Irkutsk National Research Technical University Kuz'min Mikhail Mike12008@yandex.ru Irkutsk National Research Technical University Kuz'mina Marina kuzmina.my@yandex.ru Irkutsk National Research Technical University Kuz'mina Alina zhuravlyova-alina@yandex.ru Production of Portland cement clinker from spent chamotte refractory lining Introduction. The cement industry is a major source of CO2 emissions, which highlights the need to implement circular economy principles, particularly the utilization of large-tonnage industrial wastes. Spent chamotte lining (SCL) from aluminum electrolyzers represents a significant environmental challenge – a Class IV hazardous refractory material containing fluorides and alkalis. The aim of this study was a comprehensive experimental assessment of the feasibility of technological integration of two types of waste – leached SCL and amorphous microsilica (MS) – into Portland cement clinker production as a replacement for traditional clayey raw material. Methods. The materials used included limestone, leached SCL, amorphous MS, and an iron-containing corrective sand. The raw mix composition was calculated and optimized using the Pearson's envelope method and solving a system of material balance equations with target values for the lime saturation factor (LSF = 0.90) and the silica ratio (SR = 2.3). Results and Discussion. Laboratory firing of pressed raw mix briquettes was conducted in a muffle furnace following a regime simulating the industrial cycle. The kinetics of decarbonation and phase formation were studied using Thermogravimetric Analysis methods with specifications. The phase composition of the clinker was determined by X-ray Diffraction Analysis, and its microstructure was examined using Scanning Electron Microscopy. The physico-mechanical properties of the obtained cement were tested according to standard methods. Conclusions. It was established that the introduction of a composite SCL+MS component (up to 14.5 % of the raw mix by mass) reduces the decarbonation temperature and the onset of alite (C3S) synthesis by 20–30 °C due to the combined effect of the high dispersity of MS and the residual mineralizing action of fluorides. The experimental clinker-based cement meets the requirements of PC 300 grade, demonstrating a 28-day compressive strength of 29.6 MPa, which is statistically indistinguishable from the control (29.8 MPa). Other critical parameters were evaluated for application which are: the equivalent alkali content (Na2Oₑq.) in SCL should not exceed 2.0–2.5 %, and its proportion in the raw mix can be 8–12 %. The results confirm the technical feasibility of utilizing hazardous waste to produce competitive cement with potential reductions in firing energy consumption. 1.Introduction The modern construction industry faces a global challenge, attempting to reconcile the growing demand for infrastructure with the need for a radical reduction in anthropogenic environmental impact. At the epicenter of this contradiction lies the cement industry – a titanic sector in scale, yet energy- and resource-intensive, responsible for 5–8 % of global CO2 emissions, where the majority of emissions are related to the irreversible process of limestone decarbonation (CaCO3 → CaO + CO2) [1, 2]. In light of the Paris Agreement goals and sustainable development principles, this situation has initiated a widespread search for innovative approaches that go beyond simple optimization of existing processes. The concept of a circular economy comes to the forefront, viewing industrial waste not as an inevitable evil but as potential "secondary resources" or "technogenic raw materials" for related industries, allowing for the simultaneous solution of disposal problems and reduced pressure on natural deposits [3, 4]. One of the most promising and actively studied directions is the partial replacement of primary raw materials (clay, shale, limestone) in the clinker raw mix with wastes containing the necessary oxides (SiO2, Al2O3, Fe2O3, CaO). Successful examples include the use of granulated blast furnace slag, coal fly ash from thermal power plants, nepheline slimes, and metallurgical dusts [5, 6]. However, the effectiveness and safety of such replacement directly depend on the chemical and mineralogical compatibility of the waste with the clinkerization technology, as well as the absence of critical impurities, such as chlorides or excessive alkalis, which can negatively affect the firing process and concrete durability [7, 8]. In the search for such synergistic solutions, the aluminum industry, which generates a range of specific and difficult-to-dispose wastes, is of particular interest. There is already positive experience in using fluorine-carbon-containing gas cleaning sludges as a fluoride mineralizer in cement plants [9]. It has been proven that fluoride ions (F⁻) can lower the temperature of liquid phase formation and reduce the viscosity of the melt in the CaO–SiO2–Al2O3–Fe2O3 system, thereby intensifying the synthesis of the main clinker mineral – alite (C3S) – and reducing specific fuel consumption [10, 11]. This experience was the first step in creating a technological symbiosis between aluminum and cement production. However, alongside these sludges, another large-tonnage and problematic material remains – spent chamotte lining (SCL) from aluminum electrolyzers. Millions of tons of this material are generated annually worldwide, classified as a Class IV hazardous waste due to significant content of mobile fluorides (up to 15 %) and soluble alkalis (Na2O, K2O) [12]. The lining's service life is 3–7 years, after which it is sent for costly landfill disposal or undergoes inefficient processing, posing a serious environmental and economic problem [13]. The key idea of this research is not merely the disposal of SCL but its deep technological integration into the cement production process after preliminary neutralization of the most hazardous components. We hypothesize that after hydrometallurgical leaching, used for fluoride recovery (e.g., in schemes for obtaining synthetic cryolite), SCL – which is essentially a fired high-alumina clay (main components: SiO2 and Al2O3) – can be considered as a source of an aluminosilicate component. However, its original chemical composition is typically characterized by a relative deficiency of silica and a significant excess of alumina compared to traditional clays, as well as the presence of residual alkalis after leaching [14]. This makes the direct use of SCL impossible without correcting the modular characteristics (silica ratio *n* and alumina ratio *p*) of the raw mix. To solve this structural problem, we propose the combined joint use of two types of technogenic raw materials: leached SCL and amorphous microsilica (MS). The latter is a finely dispersed (specific surface area 15–25 m2/g) waste from gas cleaning in the production of crystalline silicon or ferrosilicon, consisting of 85–98 % highly reactive amorphous silicon dioxide [15–28]. Thus, the research is aimed not at simple "disposal" of waste but at the targeted design of a new composite raw material component from them. In this composite, MS compensates for the SiO2 deficiency in SCL, while SCL, in turn, serves as a matrix-carrier for the volatile MS, preventing its losses during transportation and dosing. Furthermore, residual traces of fluorine in SCL may continue to perform the function of a mineralizer. The objective of this work is a comprehensive experimental assessment of the technological feasibility and practical expediency of such a replacement. The following tasks were addressed within the study: Chemical-mineralogical characterization of the initial wastes (leached SCL and MS) and traditional materials. Calculation and design of the raw mix composition using the "SCL+MS" composite to achieve the target clinker modular characteristics. Laboratory modeling of the firing process with a study of the kinetics of decarbonation and phase formation. Comprehensive analysis of the obtained clinker (phase composition, microstructure) and the Portland cement made from it (standard physico-mechanical properties) in comparison with a control produced by traditional technology. 2.Materials The basis for any modeling in cement technology is the accurate chemical composition of the components. We had four key materials at our disposal, each with its own specifics (Table 1). Table 1. Chemical composition of raw materials (wt. %). Component SiO2 Al2O3 Fe2O3 CaO MgO Na2O K2O SO3 LOI* Limestone 1.4 0.6 0.3 47.4 3.1 – – 0.1 46.5* Spent Chamotte Lining 59.3 32.0 3.0 0.7 0.6 2.0 0.15 0.3 2.5 Microsilica 92.5 0.8 0.6 0.3 0.5 0.40 0.40 0.1 4.6 Iron-containing Sand 28.7 5.4 57.3 3.3 2.8 – – 1.5 1.0   *Note: LOI – Loss on Ignition; for limestone, mainly CO₂.   Limestone served as the main source of calcium oxide (CaO). Leached SCL, after pretreatment, lost a significant portion of fluorine but retained the high alumina (Al2O3) content (32 %) characteristic of refractories and a moderate residual Na2O content (~2 %), which required consideration in the alkali balance. Its main drawback for cement raw mix purposes was a pronounced silica (SiO2) deficiency relative to alumina. To compensate for this deficiency, amorphous MS – an ultrafine powder with a content of reactive SiO2 exceeding 92 % – was introduced. Its high specific surface area predetermined both a potential influence on the mixture's reactivity and a possible increase in the water demand of the future cement. The fourth component was an iron-containing sand, the task of which was to adjust the alumina ratio and ensure the formation of the necessary amount of the aluminoferrite phase (C4AF). 2.1.Design of the Raw Mix Composition The process of designing a raw mix for cement clinker resembles solving a multi-parameter problem. The target values for the lime saturation factor (LSF = 0.90) and silica ratio (SR = 2.3) were set as constants, ensuring the production of clinker with optimal phase composition and hydraulic activity. The main difficulty was working with SCL. Analysis of its composition showed that in its pure form, it cannot serve as a clay analog due to the low SiO2/Al2O3 ratio. To visualize and solve this problem, the classic rule of mixtures – the "Pearson envelope" – was applied. This graphical method clearly showed that to bring the silicate component to the required level (~75 % SiO2), it is necessary to introduce MS in a ratio of 1:0.5 to SCL. Thus, a new, "synthetic" silicate component was created, representing a composite of two technogenic products. Its chemical profile (Table 2), including a reduced content of equivalent alkalis (Na2Oₑq. = 1.3 %), already met the suitability criteria. Table 2. Chemical composition of the modified silicate additive (SCL+MS) (wt. %). Compound SiO2 Al2O3 Fe2O3 CaO MgO Na2Oₑq. Content 75.0 16.0 1.5 0.35 0.27 1.30 Note: Na2Oₑq. = Na2O + 0.658K2O.   Subsequent calculation by solving a system of material balance equations [8] allowed for determining the exact proportions of all components in the raw mix. The final formulation consisted of 81.7 % natural limestone, emphasizing that the proposed technology does not represent a complete replacement of traditional raw materials, but rather a partial, yet significant (14.5 %) replacement of the clayey component. This is a realistic and pragmatic approach for potential industrial implementation. 2.2.Laboratory Modeling of the Firing Process The transition from calculation formulas to real material began with the preparation of a homogeneous raw mix and pressing it into wet briquettes (Fig. 1). Figure 1. Briquettes of pressed raw mix. Firing was carried out in a muffle furnace under a strictly controlled temperature-time regime, which served as a laboratory model of an industrial rotary kiln operation: from 100 °C to 800 °C – 45 min; from 800 °C to 1100 °C – 50 min; from 1100 °C to 1300 °C – 10 min; from 1300 °C to 1450 °C – 20 min. Key stages were: slow heating to remove free and chemically bound water, intensive decarbonation in the range of 700–900 °C, formation of intermediate oxide compounds, and finally, the culmination of the process – the synthesis of clinker minerals at 1450 °C. Rapid cooling of the obtained clinker nodules (Fig. 2) was necessary to fix the metastable high-temperature phases, primarily alite (C3S), which is standard practice in cement technology. Figure. 2. Obtained clinker samples. For a comprehensive characterization of intermediate and final products, an arsenal of modern physicochemical methods was used. Thermogravimetric Analysis (TGA/DTA) acted as a "real-time observer" of the process, allowing for the recording of mass loss during decarbonation and thermal effects accompanying phase transformations. X-ray Diffraction Analysis (XRD) allowed not only qualitative identification of crystalline phases in the clinker but also their quantitative assessment using the Rietveld method. Scanning Electron Microscopy (SEM) provided a unique opportunity to see the material's microstructure: the shape, size, and mutual arrangement of crystals, which directly correlates with the strength properties of the future cement. Standard physico-mechanical tests of cement paste and mortar became the final and most important criterion for success, translating scientific data into the language of practical construction standards (GOST). 3.Results and Discussion Comparative analysis of thermograms of the experimental and control mixtures revealed important differences (Fig. 3). Figure 3. Comparative thermograms (TGA/DTA) of the experimental and control raw mixes. The main endothermic peak, corresponding to the decomposition of calcium carbonate (CaCO3 → CaO + CO2), in the mixture containing SCL and MS, was shifted to a lower temperature region by 20–30 °C. This can be interpreted as a result of two factors. Firstly, finely dispersed MS, possessing an enormous specific surface area, creates an extensive contact zone with limestone particles, facilitating diffusion processes. Secondly, residual fluoride ions, preserved in SCL after leaching, may act as a catalytic mineralizing additive. It is known that even small amounts of fluorine contribute to the destruction of the crystal lattices of initial oxides and reduce the viscosity of the forming melt, thereby intensifying the reactions of solid-state and liquid-phase synthesis of calcium silicates [9]. This effect is also confirmed by the shift of the onset of the exothermic effect associated with alite (C3S) formation towards lower temperatures. Thus, the first important conclusion is that the introduction of the technogenic composite not only does not impair but potentially improves the kinetics of the firing process, promising direct energy benefits on an industrial scale. The obtained diffractograms, presented in Fig. 4, clearly demonstrate that the main qualitative composition of the clinkers is identical. Figure 4. X-ray diffractograms of the experimental and control clinker. In both cases, peaks characteristic of alite (C3S), belite (C2S), tricalcium aluminate (C3A), and tetracalcium aluminoferrite (C4AF) are clearly identified. However, quantitative calculation (Table 3) revealed nuances. Table 3. Phase composition of clinkers (wt. %), determined by the Rietveld method. Sample C3S (Alite) C2S (Belite) C3A C4AF Glass phase / Other Experimental 52 ± 2 25 ± 2 8 ± 1 12 ± 1 3 Control 56 ± 2 22 ± 2 7 ± 1 13 ± 1 2     In the experimental clinker, the proportion of alite – the most valuable and fast-hardening phase – was 4 % lower (52 % vs. 56 %), while the proportion of belite, which gains strength more slowly but more stably, was correspondingly higher. The explanation for this phenomenon can be found when examining the microstructure (Fig. 5). a b Figure 5. SEM micrographs (BSE mode) and EDS mapping of clinker samples. (a) Control clinker: prismatic alite (C₃S, light grey, 20–35 µm) with rounded belite (C₂S, darker grey) and interstitial phase (bright, Fe-rich). (b) Experimental clinker with SCL+MS additive: alite crystals (15–40 µm) show slightly irregular morphology; belite content visually higher. SEM micrographs show that alite crystals in the experimental sample have a slightly less regular shape and a larger size distribution (15–40 µm vs. 20–35 µm in the control). This may be related to changes in the rheological properties of the melt. Highly dispersed MS, actively interacting with the melt, may locally increase its viscosity. This creates kinetic barriers for the growth of large, ideal alite crystals and complicates the final stage of its formation from belite and free lime. Interestingly, energy-dispersive X-ray analysis (EDX) confirmed the hypothesis about alkali distribution: sodium primarily concentrated in the inter-crystalline glassy phase rather than entering the lattice of the main silicate minerals. This is a favorable scenario, as such immobilization reduces the risk of harmful alkali-silica reaction in concrete [6]. The compressive strength was determined at 28 days of age on a hydraulic press in accordance with GOST 310.4. Standard specimens made from the experimental and control cements were tested (Fig. 6). a b Figure 6. Process of testing cement specimens for compressive strength: (a) specimen installed in the grips of the testing machine; (b) general view of the hydraulic press during testing. The key confirmation of the new cement's quality is the compliance of its properties with standard requirements. The data presented in Table 4 and Fig. 7 allow for a definitive conclusion: the cement based on the experimental clinker fully meets the requirements of PC 300 grade.         Table 4. Properties of Portland cements based on experimental and control clinker. Characteristic Experimental Cement Control Cement Norm for PC 300 (GOST 31108) Specific surface, m2/kg 355 350 Not less than 300 Normal consistency, % 28.50 25.75 – Initial setting time, min 220 200 Not less than 45 Final setting time, min 430 470 Not later than 600 Compressive strength, MPa:       3 days 12.5 ± 0.8 14.1 ± 0.9 ≥ 12.0 7 days 21.3 ± 1.2 22.8 ± 1.3 ≥ 19.0 28 days 29.6 ± 1.5 29.8 ± 1.5 ≥ 28.0 56 days 34.2 ± 1.6 33.1 ± 1.5 ≥ 32.0   Some differences from the control sample are characteristic and explainable. The increased normal consistency (28.5 %) is a direct consequence of the presence of ultrafine MS, which requires more water for wetting. This is a technological nuance that must be considered when selecting water-reducing admixtures in concrete mix design. The kinetics of strength gain (Fig. 7) demonstrate a classic pattern for clinker with a slightly increased belite content. Figure 7. Variation of compressive strength with curing time (3, 7, 28, and 56 days). In the first three days, the strength of the experimental cement slightly lags, which correlates with the slightly lower amount of fast-reacting alite. However, by 7 days, the gap narrows, and by 28 days, the strengths become statistically indistinguishable. This vividly illustrates the compensatory role of belite: although its hydration proceeds more slowly, it continues for a long time, ensuring confident strength growth in the medium- and long-term perspective. Thus, a minor shift in the clinker's phase composition did not lead to a deterioration of its key strength characteristic. Comparison with previous studies. The observed reduction in decarbonation temperature (20–30 °C) due to the combined effect of fluoride residues and amorphous silica is consistent with the findings of 9. K. Vance et al. [9], who reported that fluoride ions lower the liquid phase formation temperature by 15–40 °C in cement raw mixes. Similarly, Katey O’Quinn et al. [11] demonstrated that fluoride-containing mineralizers enhance alite formation at lower temperatures. However, unlike previous studies that used pure fluoride salts, the present work achieved a comparable effect using residual fluorides in a waste material (SCL), which is more economically and environmentally attractive. The 28-day compressive strength of 29.6 MPa obtained in this study is slightly lower than the 32–35 MPa reported by Abdul,  W. et al. [27] for SCL-fly ash blends, but this difference is attributed to the higher alkali content in our SCL (2.0 % Na2O vs. 0.8 % in their study). Vuthaluru [19] also noted that alkalis above 1.5 % Na2Oₑq. can suppress alite formation, which agrees with our observed 4 % reduction in C3S content compared to the control. 4.Conclusion The conducted study, consistently from the calculation model to the testing of the finished product, proved the fundamental possibility of deep technological integration of wastes from aluminum and silicon production into the Portland cement manufacturing process. We did not merely add an inert filler but purposefully designed a new composite component (SCL+MS), which in quantities up to 14.5 % of the raw mix mass can fully replace traditional clay. The main conclusions of the work are of both scientific and practical application value: The combined use of leached SCL and MS allows for the mutual compensation of their shortcomings: MS compensates for the silica deficiency in SCL, while SCL serves as a matrix-carrier for finely dispersed MS. Residual fluorides in SCL and the high reactivity of MS have a positive effect on the firing kinetics, lowering the temperature of key reactions, which opens the way to fuel savings. Despite a slight modification of the phase composition (shift in the C3S/C2S balance) and the clinker's microstructure, the obtained Portland cement satisfies all regulatory requirements for PC 300 grade, demonstrating full competitiveness. For successful implementation, it is necessary to control the alkali level in the incoming SCL (Na2Oₑq. ≤ 2.0 %) and its proportion in the raw mix (8–12 %), as well as to account for the increased water demand of the cement when designing concrete mixes. Prospects for further research logically follow from the obtained results. The next necessary step should be pilot industrial trials on an operating rotary kiln, which will allow assessing the real impact on energy consumption, process stability, and emissions of volatile compounds. In parallel, an in-depth study of the durability characteristics of concrete based on the new cement is required, especially its resistance to freeze-thaw cycles and corrosive aggression. Future work should also include a comprehensive evaluation of concrete durability, including freeze-thaw resistance, sulfate attack, and alkali-silica reaction, as the presence of residual alkalis may pose long-term risks. In a broader context, this work is a clear example of implementing circular economy principles in heavy industry. It offers a specific, technically justified solution for two environmental problems simultaneously, transforming the costs of hazardous waste disposal into investments in the production of a demanded construction material. 10.34910/MCE.143.1 691.3 spent chamotte lining amorphous microsilica Portland cement clinker circular economy waste utilization fluorides alkalis mineralizer raw mix firing microstructure compressive strength https://engstroy.spbstu.ru/article/2026.143.1/

RAR RUS 14302-14302 University of Anbar Khalaf Khalaf kha22e1007@uoanbar.edu.iq

Ramadi, Anbar, Iraq

University of Anbar Aljanab Khalid kr_aljanabi@uoanbar.edu.iq

Ramadi, Anbar, Iraq

Shear strength and durability behavior of organic soils treated with recycled glass powder-based geopolymer Organic soil has many construction problems due to its being weak in engineering properties, such as low shear strength and high deformation or compressibility. This study's primary goal was to determine whether employing recycled glass powder-based geopolymer can enhance the engineering properties of organic soil through tests of durability and unconfined compressive strength (UCS). The impact of an alkaline activator solution on UCS and durability, as well as the effects of recycled glass powder (RGP) contents on maximum dry unit (MDU) and optimum moisture content (OMC), were also examined in this study. RGP-based geopolymer was used with organic soil to improve durability and compensate for reduced shear strength. The RGP was added with different percentages (5, 10, 15, 20, and 25 %) by dry weight of soil. Sodium hydroxide (NaOH) and sodium silicate (Na2SiO3) were used to prepare the geopolymer. First, sodium hydroxide with constant molarity (4M) was used with RGP to find the optimum mixture, then sodium hydroxide (SH) with sodium silicate (SS) (SH:SS = 72:28 and SH:SS = 50:50) with the same molarity was used with the optimum mix only. According to the findings, MDU weight increases as RGP content is added, but OMC decreases. Additionally, as the RGP content increases up to 20 %, the results demonstrate that the UCS increases. For the optimum mix (20 % RGP), the UCS increases by 29, 38, and 46 times, and the failure strain decreases by 31.4, 31, and 39.3 % with curing times of 7, 14, and 28 days at 65 °C, respectively, compared to the untreated soil. A durability test was conducted on compacted natural soil and stabilized organic soil with three different alkaline activator solutions 100:0, 72:28, and 50:50 for a curing time of 28 days at a curing temperature of 65 °C according to ASTM D559. Results showed that after 12 cycles of the wetting and drying cycles, UCS decreased by 20, 28.5, and 35.1 %, respectively. 1.Introduction Organic soil has several engineering problems due to its low shear strength, high compressibility, swelling, and shrinkage characteristics. The construction process presents a challenge for geotechnical engineers to address these issues. Today, Portland cement is a widely utilized material for soil stabilization. Still, cement manufacturing generates environmental impacts because it involves the significant release of carbon dioxide (CO2) emissions. Organic matter in the soil can reduce the reaction between cement and soil particles [1]. Replacing the natural soil layer with suitable soil from another site represents another method of organic soil stabilization [2]. As a result of this process, sometimes the project's cost may rise, particularly if the proposed location for the replacement soil is relatively far away. This has prompted researchers to explore alternative solutions. One of these methods involves soil stabilization with geopolymers. According to ASTM D2974, soil is classified as organic soil if the organic content exceeds 20 % [3]. Previous studies have investigated the engineering properties of organic soil, showing its high compressibility and low shear strength. Khairina et al. demonstrated that adding 10 % gypsum to organic soil with concrete waste increases the unconfined compressive strength (UCS) and reduces compressibility [4]. Adel et al. demonstrated that adding an amount of lime to organic soil, including both decomposed and non-decomposed samples, significantly affects their shear strength. The results showed that the cohesiveness values (c) increased by 5 % in non-decomposed samples and 7 % in decomposed samples with higher organic content [5]. Nath et al. evaluated the behavior of organic soil stabilized with fly ash as a function of strength. They found an increase in UCS with increasing fly ash amount due to the pozzolanic reaction of fly ash [6]. Ibrahim et al. demonstrated that increasing crushed waste concrete (CWC) to 50 % can increase organic clay's UCS values by 25 % [7]. Mohd et al. showed that adding lime and salt to organic soil increased the cohesion value from 7.1 to 23.6 kPa [8]. Some studies found that adding fly ash to organic soil increased the UCS and resilient modulus [9]. Moayedi et al. illustrated that adding 5 mol/L of sodium silicate (SS) to stabilized organic soil can increase the UCS values [10]. Habbi studied the organic soil's compressibility. The results demonstrated that an increase in organic content for all samples increases the compressibility characteristics (compression index, rebound index, coefficient of consolidation, and coefficient of secondary compression). The use of cement dust and fly ash has improved organic soil's compressibility [11]. Ali and Tatt studied that adding additives such as cement, lime, and fly ash to a mixture of organic soil improved its strength, particularly after the 7-day curing period [12]. Abbas et al. studied that additive of cement dust and fly ash with percentages (3, 6, and 9 %) by weight of organic soil improved compressibility characteristics [13]. Boobathiraja et al. studied that adding cement and lime in the range of 10–30 % as a percentage of dry soil mass caused an increase in the UCS of organic soil [14]. Rafizul et al. investigated how organic soils behave when mixed with cement, bentonite, and lime with different ratios of (5, 10, 15, 20, and 25 %) of the dry weight of organic soil. They found that MDU increased while OMC decreased as the admixture percentage increased [15]. Talib and Noriyuki developed another alternative binder using sugarcane bagasse ash (SCBA) for organic soil stabilization. Research demonstrated that combining SCBA with Portland cement enhanced the amount of UCS-stabilized organic soil [16]. As for improving the consolidation of organic soil. Thiyyakkandi and Annex showed that the consolidation coefficient decreased with increased organic matter [17]. Wardwell and Nelson showed the increase of organic content accompanied by a rise in the coefficient of secondary compression (Cα), causing an increase in the void ratio of soil [18]. Mustapa et al. showed that adding gypsum content with known percentages led to an improvement in the strength of organic soil. They found that any increased addition in gypsum content led to increased UCS values while the compressibility was reduced simultaneously [19]. The above literature review shows no application for organic soil stabilization using RGP-based geopolymers. The main aim of this study is to assess the effectiveness of using recycled glass powder-based geopolymer in improving organic soil engineering properties by conducting UCS and durability tests. Also, this study investigated the effect of RGP contents on MDU and optimum moisture content (OMC), as well as the effect of an alkaline activator solution on UCS and durability. 2.Methods and Materials 2.1.Soil It was collected from the agricultural area in Anbar Governorate, west of Iraq. Soil samples were collected from a depth (0.3) m. According to the Unified Soil Classification System (USCS), the soil was classified as low-plasticity organic silty clay (OL). Tables 1 and 2 show the physical properties and chemical composition properties of soil. Table 1. The physical and classification properties of soil. Property Soil Specification Liquid Limit (LL) (%) 44 According to ASTM D4318 Plastic Limit (PL) (%) 27 According to ASTM D4318 Plasticity index (PI) (%) 17 According to ASTM D4318 Specific gravity (Gs) 2.45 According to ASTM D854 Organic content (OC) (%) 20.8 According to ASTM D2974 Passing sieve #200 (%) 86 According to ASTM D422 Unified Soil Classification System (USCzS) OL According to ASTM D2487 Optimum moisture content) (%) 20 According to ASTM D698 Maximum dry unit) (KN/m3) 15 According to ASTM D698   Table 2. The chemical composition of soil by XRF. Chemical composition (%) SiO2 Al2O3 CaO Fe2O3 MgO Na2O K2O SO3 Mn Organic soil 39 20.91 20.4 5.74 9.28 1.24 1.31 1.10 0.08   2.2.Recycled Glass Powder The waste glass powder was collected from a waste landfill in Ramadi city. The glass was crushed using the traditional (metal mortar and pestle) tools. Then, it was sieved through sieve #200, and the particles finer than 75 μm were used as the base of the geopolymer. The glass powder specific gravity was determined to be 2.52, according to ASTM D854. The XRF test of RGP sample shows that its generally composed of SiO2, Al2O3, CaO, Fe2O3, MgO, etc. and it is generally composed of a high percentage of silica (SiO2), which is about 72.1 %. The XRF is conducted at the laboratories of Ministry of Industry and Minerals of Iraq. Table 3. Shows the chemical composition of RGP. Table 3. The chemical composition of RGP by XRF. Chemical composition (%) SiO2 Al2O3 CaO Fe2O3 MgO Na2O K2O SO3 Mn Glass powder 72.1 1.30 6.06 0.30 4.60 15.20 0 0.30 0   2.3.Alkaline solution This study used sodium hydroxide (SH) (NaOH) and sodium silicate (Na2SiO3) as alkaline activators with a constant concentration of 4M and their properties are listed in Tables 4 and 5, respectively. Table 4. The properties of (NaOH). Chemical formula Mass (g/mol) Purity (%) Density (g/cm3) pH NaOH 40 98.4 2.13 @ 20 °C 14     Table 5. The composition and properties of Na2SiO3. Na2O (%) SiO2 (%) Viscosity (N.s/m2) Specific gravity pH 13.7 33 800 1.534 12   2.4.Geopolymer It is an alternative binder instead of cement, made from reacted silica and alumina with an alkaline solution. It is used in many engineering applications, such as soil stabilization for instance. Geopolymer was developed as an eco-friendly alternative to Portland cement, as it is produced with less consumption of energy and reduces the emission of CO2. Geopolymers have many properties, such as flexibility, corrosion resistance, and being more resistant to environmental and climatic conditions, making them important materials in a variety of engineering applications. Many laboratory tests were achieved on untreated organic soil. On the other hand, the testing was conducted on organic soil mixed with 5, 10, 15, 20, and 25 % RGP to study the impact of RGP-based geopolymer on the UCS of the stabilized soil. Many specimens of natural soil mixed with 5, 10, 15, 20, and 25 % RGP were performed according to ASTM D698 by using the standard proctor test to obtain the MDU and OMC. To find the value of UCS for each mixture with different ratios of RGP, specimens were prepared at similar MDU and OMC values found from the standard proctor test. Also, a small plastic spilt mold with a hammer was used to achieve the processing of the specimen's compaction. As shown in Fig. 1, the plastic mold dimensions are 50 mm in inner diameter and 100 mm in height, while the hammer's weight is 2.5 kg, falling from 30.5 cm in height. Compaction processing was conducted in 3 layers, and every layer was compressed with 8 blows. Where layers and blow numbers were obtained to get a similar compaction effort (596 kN.m/m3) for the proctor test. At first, the different ratios of RGP+ soil (5, 10, 15, 20, and 25 %) by dry mass of soil were mixed to prepare testing specimens. The solution of the alkaline activator was prepared with a constant concentration of NaOH (4M), and after this, it was added to the mixture of soil and RGP. The specimens of untreated soil were tested directly, and other treated specimens were cured at 65 °C for 48 hours and then kept at room temperature of 25 °C for 7, 14, and 28 days. For each mixture and curing period, three specimens were prepared [20, 21]. For the durability test, alkaline activator solution in three different ratios of solution SH:SS represented by 100:0, 72:28, and 50:50 were used to prepare soil specimens. All these specimens were exposed to wetting and drying cycles; similarly, treated soil specimens were exposed to wetting, drying, and brushing cycles. Each cycle started with submerging the specimens for 5 hours in the distilled water, 42 hours in the dried oven (71±2 °C), and brushing with a wire scratch brush. At the end of each cycle, the specimens are weighed and measured in volume. As expected, all specimens lost weight with time. After completing 12 cycles, the specimen was put in the oven (110 °C) to dry it until the mass became constant, and the UCS was conducted on all specimens. Figure 1. Plastic spilt mold with dimension (50×100 mm). 3.Results and Discussion Compaction Tests The compaction test showed a relationship between dry density and moisture content for unstabilized (natural soil) and stabilized soil with different percentages (5, 10, 15, 20, and 25 %) of RGP, as shown in Fig. 2. The results show that as the RGP content ratio increases, MDU values increase and OMC values decrease. This may be attributed to the fact that finer particles of RGP fill the voids existing between soil particles [22]. This is similar to what was observed by the previous studies [23–25]. (a)        (b)                                                                     (c) Figure 2. a) The compaction curves of RGP-soil mixture, b) MDU versus RGP content, c) OMC versus RGP content.   Unconfined Compressive Strength 4.2.1. The impact of RGP content and curing period The UCS values of soil with geopolymer of many percentages of RGP content (5, 10, 15, 20, and, 25 %) and curing time 7, 14, and 28 days with fixed alkaline solution SH:SS = 100:0, molarity 4M at a curing temperature 65 °C are shown in Fig. 3. As expected, the values of UCS for all soil specimens stabilized with RGP geopolymer were more than that of the untreated soil for all three curing times. Also, this figure shows that the value of UCS increases with increasing RGP content up to 20 %, where this increase represented by 29, 38, and 46 times compared to untreated soil for 7, 14, and 28 days respectively. Figure 3. The values of UCS versus RGP content for different curing times 7,14 and 28 days at curing temperature 65 °C. The maximum value of UCS was obtained at 20 % RGP content due to the stronger bond between the soil particles and RGP geopolymer gel [26]. This is similar to what was observed in previous studies [27–29]. A slight decrease in UCS values above 20 % RGP content was observed. The additional amount of RGP may have adverse effects on the UCS. These effects might be caused by the substantial amount of RGP particles contacting the soil structure, which would reduce soil cohesiveness. RGP serves as a filler material rather than contributing to the geopolymer binder [29]. 4.2.2. Stress-strain behavior of RGP geopolymer-treated soil Fig. 4 illustrates the impact of RGP Geopolymer on the stress-strain behavior of treated soil for three curing times 7, 14, and 28 days. All treated specimens had a lower failure strain compared to untreated soil. Where the axial strain values of specimens treated with 20 % RGP decreased by 31.4, 31.5, and 39.37 % of curing times 7, 14, and 28 days. As seen in the behavior of treated soil closer to ductility with increasing RGP content, this may be returned to a delay in developing geopolymer bonds due to the low curing temperature. Similar studies demonstrated that treated soil with metakalin-based geopolymer developed UCS and ductility [27], and another explained that RGP-based geopolymer can improve soil ductility [29]. Figure 4. Axial strain (%) values versus RGP content for different curing times 7,14 and 28 days at curing temperature 65 °C. Durability According to ASTM D559, the durability test was conducted on all treated soil specimens prepared for this purpose. For the durability test, three different ratios of alkaline activator solution SH:SS represented by 100:0, 72:28, and 50:50 were used separately with 20 % RGP+80 % soil)to prepare two geopolymer specimens for each mixture. The durability test for all prepared specimens was tested by wetting and drying (w/d) cycles. After the end of 12 cycles, the loss in mass and change in volume were recorded and discussed, as shown below. 4.3.1. Volume change All specimens stabilized with RGP geopolymer have approximately changes (±1 %) in volume and survive all 12 w/d cycles. Whereas untreated soil specimens are destroyed within the first w/d cycle. Fig. 5 illustrates the natural soil and treated soil specimens before and after the w/d cycles. 4.3.2. Mass loss (%) The mass loss (%) for all treated soil specimens with the RGP geopolymer tested to the durability cycles is shown in Fig. 5. As shown in Fig. 6, it can be observed that a gradual increase in mass loss was observed until the fifth cycle for mixes treated with 20 % RGP+ (100:0) and 20 % RGP+ (50:50). After this, the mass loss approximately remained constant up to the twelfth cycle. Whereas a slight gradual increase after the fifth cycle for mix treated with 20 % RGP+ (72:28) up to the ninth cycle remained constant up to the twelfth cycle. The losses in mass for treated soil specimens for SH:SS = 100:0, 72:28, and 50:50 for 65 °C were 4.9, 6.65, and 8 %, respectively. In any case, if they were compared to untreated soil, the treated soil specimens behaved better durability in terms of mass loss. All the mass loss (%) for all treated soil specimens was limited according to American standards [25, 26]. (a)                                                                                      (b) (c)                                                                                      (d) Figure 5. Durability test (w/d cycles): a) natural soil during cycle No. 1, (b) natural soil after (10min) during cycle No. 1, (c) treated soil specimens during cycle No. 1, (d) treated soil specimens after cycle No. 12. Figure 6. Mass loss (%) versus No. of w/d cycles at 65 °C. 4.3.3. Strength loss The UCS of the stabilized soil specimens exposed to w/d cycles was tested after 12 cycles. Table 4 displays the UCS values before and after the durability test. This result indicates that a sudden reduction in strength values for all specimens stabilized with 20 % was 20, 28.5, and 35.1 %, respectively, for curing temperature 65 °C recorded at the end of 12 cycles. A similar result has been observed with [29, 30]. Additionally, several studies showed that the UCS values of the treated soil were negatively impacted by the durability test [31, 32]. In comparison to soil that had not been treated, the results were deemed to be highly significant. Table 4. Shows the results of UCS before and after durability (w/d cycles) for different soil mixtures. Mixture UCS before durability (MPa) UCS at the end of durability (MPa) Soil+20% RGP+(SH:SS=100:0) 9.41 7.5 Soil+20% RGP+(SH:SS=72:28) 8.12 5.8 Soil+20% RGP+(SH:SS=50:50) 8.01 5.2   4.Conclusion This paper aimed to study the behavior, shear strength, and durability of organic stabilized with RGP-based geopolymer. According to the results from the testing, the conclusions below can be found. When the RGP was added to the natural soil (organic soil), the MDU values increased and the values of OMC decreased. The results obtained from UCS tests for all specimens treated with RGP geopolymer demonstrated a significant increase in the shear strength of stabilized organic soil when the RGP content increased by more than 20 %. The strain values at failure decreased by 31.4, 31.5, and 39.37 % of the curing times 7,14 and 28 days, respectively, less than that of untreated soil, indicating a substantial effect of the RGP geopolymer additive on this parameter. The durability of all treated soil specimens was tested with wetting and drying cycles; all specimens survived 12 cycles. The volume change was approximately equal (±1), and the mass loss was 4.9 %, 6.65 %, and 8 % for treated soil specimens for SH:SS = 100:0, 72:28,and 50:50 at 65 °C, respectively, and it was found to be within the required limits. There was a reduction in strength values for all specimens stabilized with 20 % RGP represented by 20, 28.5, and 35.1 %, respectively, for SH:SS = 100:0, 72:28, and 50:50 at 65 °C. The strength values obtained after the wetting and drying cycles prove that the RGP geopolymer is a promising alternative solution of chemical stabilizers and a potential stabilizer and can be accepted for organic soil stabilizing. 10.34910/MCE.143.2 624 shear strength durability organic soil RGP geopolymer recycled glass powder unconfined compressive strength https://engstroy.spbstu.ru/article/2026.143.2/

RAR RUS 14303-14303 55875561800 0000-0002-8745-7059 Babol Noshirvani University of Technology Rezaei Sadegh S_Rezaei1366@yahoo.com

Babol, Mazandaran, Iran

0000-0002-8470-6160 Department of Civil Engineering, University of Science and Technology of Mazandaran Moradi Majid m.moradi@mazust.ac.ir

Behshahr, Iran

0000-0002-5918-8920 Department of Civil Engineering, Ayatollah Amoli Branch, Islamic Azad University Soleimani Kutanael Saman samansoleimani1616@yahoo.com

Amol, Iran

Effects of near-fault and far-fault earthquakes on the site response Investigation of previous earthquakes shows that the distance to the fault, from which the earthquake is sourced, is a paramount factor contributing to the site response and magnitude of the induced damages. In this research, equivalent linear and nonlinear methods were used to assess the effect of the earthquake field on the site response. Assessments included investigations of time histories of acceleration, velocity, displacement, as well as their peak values and response spectra. Records of the Bam earthquake acquired at two different stations were used for this purpose. Results showed that the peak values of the response spectrum induced by a near-field earthquake record occurred at higher frequencies than those seen in a far-field quake, with the nonlinear effects being more pronounced in the near-field earthquake record than in the far-field one. Additionally, the difference of the obtained responses from the nonlinear and equivalent linear methods was greater for the near-field earthquake record than for the far-field earthquake record. Finally, it is worth noting that the damage potential of an earthquake event cannot be adequately assessed unless the frequency content of the earthquake, soil effects, and structure stiffness are considered simultaneously.                                                                                                    1.     Introduction Earthquakes are among the most significant natural hazards humans have faced since their emergence on Earth. More than 5 million earthquake events occur each year, making it crucial to study every aspect of this phenomenon [1, 2]. A major characteristic of an earthquake that affects the induced damage and soil behavior is the distance to the quake-inducing fault. Based on the data on previous earthquakes, researchers have identified three types of quake events as near-field (within 20 km of the quake-inducing fault), mid-field (within 20–60 km of the quake-inducing fault), and far-field earthquake records (beyond 60 km of the quake-inducing fault) [3]. Near-field earthquake records are usually larger in magnitude than the far-field earthquake records. The near-field records exhibit intense pulse-like ground motions, which can be explained by the release of large amounts of energy in a short time upon faulting. This pulse-like ground motion imposes devastating amounts of energy on overlying structures at the start of the motions [4–6]. A near-field earthquake record generates higher frequencies than a far-field earthquake record because the closer distance to the source of the earthquake waves prevents the absorption of higher-frequency events, so that the resultant records contain higher frequencies than the records of far-fault areas [7–10]. Another characteristic of a near-field earthquake record is what is referred to as directivity. Pulse-like motions are particularly more pronounced in forward-directivity areas where the fault failure approaches at a velocity close to the shear-wave velocity. Another difference between the far- and near-field earthquake records is the peak vertical acceleration [11–15]. Typically, peak vertical acceleration is equal to two-thirds of the peak horizontal acceleration. However, studies on previous earthquakes have shown that the actual ratio is higher for near-fault areas and lower for the far-fault zones [16]. Very near-fault earthquake records (within 500 m of the fault) indicate substantial permanent ground displacement, which is a result of tectonic deformation of the ground in a process called the fling step. This deformation occurs during slippage along the fault plane and is therefore usually observed in the parallel component to the fault plane [17]. Considering the importance of the abovementioned topics, the present research was focused on evaluating the effect of the earthquake field on the site response with the help of equivalent linear and nonlinear methods. This evaluation included investigations of time histories of acceleration, velocity, displacement, as well as their peak values and response spectra. Records from the Bam earthquake, acquired at two different stations, were used for this purpose (Bam Station as near-field earthquake record and Ravar Station as far-field earthquake record). Despite extensive research on seismic site response and earthquake ground-motion characteristics, most previous studies have primarily focused on either near-fault ground motions, nonlinear soil behavior, equivalent linear analysis, or structural response independently. Limited attention has been given to a comprehensive comparative evaluation of near-fault and far-fault earthquakes using both nonlinear and equivalent linear approaches under identical soil conditions and real earthquake records. In particular, the combined investigation of acceleration, velocity, displacement, amplification behavior, and response spectra throughout soil depth has not been sufficiently addressed in earlier studies. Therefore, the present research aims to investigate the effects of near-fault and far-fault earthquakes on site response characteristics through nonlinear and equivalent linear analyses using real earthquake records. The study further evaluates how different seismic field conditions influence amplification behavior, spectral response, and depth-dependent ground-motion parameters, while also examining the role of soil nonlinearity in modifying seismic demand. Unlike previous investigations, this study provides an integrated assessment of seismic response characteristics together with their engineering implications for resonance behavior, structural vulnerability, and site-specific seismic design.                                                                                                        2.     Methods 2.1.               Input Ground Motion (Bam Earthquake) In the early morning (5:26:56 a.m. IRST) of Friday, December 26th, 2003, the city of Bam, Iran, was hit by a powerful earthquake. Fig. 1 shows the horizontal component of the studied earthquake for the Bam and Ravar Stations. As seen in the figure, the record at Bam Station (near-field) exhibits a peak horizontal acceleration of PHA = 0.777 while the corresponding figure to the Ravar Station (far-field) is PHA = 0.0126.   Figure 1. Horizontal acceleration records for the Bam earthquake at: a) Ravar Station; b) Bam Station. Fig. 2 exhibits velocity records for the Bam and Ravar Stations. As observed, the record for the Bam Station is clearly pulse-like at the start of the ground motion, while the record for Ravar Station does not exhibit such pulses.   Figure 2. Horizontal velocity records for the Bam earthquake at: a) Ravar Station; b) Bam Station. As explained in the Introduction, near-field earthquake records exhibit directivity. Fig. 3 indicates this fact. As seen in this figure, the component  of the horizontal record at Bam Station exhibits some pulses that are almost attenuated in the component   Figure 3. Horizontal acceleration records for the Bam earthquake: a) component L; b) component T. Fig. 4 shows the vertical acceleration of the studied earthquake for the Bam and Ravar Stations. As seen in the figure, the record at Bam Station exhibits a peak vertical acceleration of PVA = 0.994, while the corresponding figure to the Ravar Station is PVA = 0.006088 Moreover, the ratio of the peak vertical-to-horizontal acceleration was seen to be 1.28 (> 2/3 = 0.666) at Bam Station and 0.48 (< 2/3 = 0.666) at Ravar Station.   Figure 4. Vertical acceleration records for the Bam earthquake at: a) Ravar Station; b) Bam Station. Fig. 5 indicates the displacement records at Bam and Ravar Stations for the component  According to this figure, permanent displacements recorded at Bam and Ravar Stations were 2.8 and 0.0002 (~ 0) cm, respectively.   Figure 5. Horizontal displacement records for the Bam earthquake at: a) Ravar Station; b) Bam Station. Fig. 6 depicts the response spectrum for the records at Bam and Ravar Stations for a damping ratio of 5 %. For shorter periods (i.e., higher frequencies), the response spectra of the Bam Station exhibits higher values than those for the record at Ravar Station. The opposite was observed for longer periods. In general, far-field and near-field earthquake records are the controlling factors for the structures of long and short periods, respectively.   Figure 6. Response spectrum for a damping ratio of 5 %. 2.2.               Modeling In order to evaluate the site effect, Fig. 7 was considered as the base model for the soil layers. Four reference points (A, B, C, and D) were considered at the interfaces of successive layers, and the results were studied at these reference points.   Figure 7. Characteristics of soil layers. In this research, the effects of the earthquake and the soil were evaluated via two approaches, namely equivalent linear and nonlinear methods. The equivalent linear method uses linear properties for the elements. Obtained as average values over dynamic motion, these properties then remain constant during the ground motions. Accordingly, the phenomena that are driven by interactions among multi-frequency components encountered in a nonlinear material are actually omitted in an equivalent linear analysis. The equivalent linear method provides no information on irreversible deformation and permanent changes, as it barely models the vibrational motions. The so-called plastic flow is inappropriately modeled in the equivalent linear method [18–21]. In contrast, the nonlinear method can follow any predetermined nonlinear behavior of the material. Applying nonlinear rules for the material, mixing of different multi-frequency components can be naturally captured, and irreversible deformations and other permanent changes can be automatically modeled. Although this methodology can follow any stress-strain relation, its results are highly sensitive to the details of the constitutive models used [18–22]. Different steps of modeling by the nonlinear method in the PLAXIS software include general setting, geometry design, application of boundary conditions, definition of material properties, generation of element grids, establishment of initial conditions, and processing the computations. In this research, the Mohr–Coulomb constitutive model was implemented, with material damping approximated by the Rayleigh damping model, which assumes proportionality between damping and material mass and stiffness. Given that calculating the Rayleigh damping ratio requires the angular frequency in two vibration modes, the angular frequencies were calculated by modal analysis in the Abaqus software. Modeling by the equivalent linear method in the Deepsoil software goes through 5 steps: (1) configuring the analysis, (2) applying the properties of the soil layers and bedrock, (3) determining the input ground motion, (4) analyzing the model, and (5) producing the results. The most important part of an equivalent linear analysis is the proper choice of the diagrams of shear modulus and damping ratio, which shall be based on the studied soil layering.                                                                                    3.     Results and Discussion 3.1.               Acceleration Figs. 8 and 9 illustrate the time histories of acceleration produced by the nonlinear and equivalent linear methods, respectively, at the reference points under the influence of near-field and far-field earthquake records. As can be seen, the magnitude of the acceleration time history increases as one moves toward the surface. In general, it can be inferred that, given the lower shear-wave velocity and density of the material on the surface compared to the underlying materials and ignoring the damping and propagation decay effects, the principle of the conservation of elastic energy implies that the flow of energy shall remain unchanged, and this explains that the reduction in the shear-wave velocity and density of the soil tends to increase the magnitude of the associated ground motions. Moreover, when the earthquake waves reach the surface, a significant portion of their energy is reflected back to the crust, so that parts of the ground surface are simultaneously affected by the upward- and downward-propagating waves [23]. These two reasons can explain the increase in the ground motion from the bedrock to the ground surface. Of course, one should further consider the fundamental frequencies of the site and the ground motion with a focus on possible resonance. As can be seen from the results, the predicted increase by the equivalent linear method exceeds that by the nonlinear analysis. Indeed, the linear nature of the equivalent linear method leads to unreal resonance. It is further clear that the acceleration at the ground surface is higher in a near-field earthquake record than in a far-field earthquake record. This can be attributed to the attenuation of ground motion waves as one moves farther from the earthquake source. Another observation is that the time history of acceleration for a near-field earthquake record contains higher frequencies than a far-field earthquake record because the distance from the source of earthquake energy is insufficient to damp high-frequency events.   Figure 8. Time history of acceleration at reference points under the influence of a near-field earthquake record (Bam Station): a) nonlinear analysis; b) equivalent linear analysis. Figure 9. Time history of acceleration at reference points under the influence of a far-field earthquake record (Ravar Station): a) nonlinear analysis; b) equivalent linear analysis. Fig. 10 shows the Peak Horizontal Acceleration (PHA) as a function of depth for the near-field and far-field earthquake records using the equivalent linear and nonlinear analyses. As is evident from the figure, the peak acceleration from the equivalent linear analysis is higher than that from the nonlinear method. Indeed, with the equivalent linear methodology, the linear nature of the problem tends to exaggerate the result. Additionally, the deviation of the obtained PHAs from the nonlinear and equivalent linear methods was greater for the near-field earthquake record than for the far-field earthquake record. This is linked to the fact that the bedrock motion amplitude is larger in a near-field earthquake record (because of a shorter offset to the source of the earthquake) than in a far-field earthquake record. In fact, the motion of the bedrock dampens as one moves farther from the earthquake source, due to the effect of damping. As the bedrock acceleration increases, deformation of the soil layers increases, thereby intensifying the damping phenomenon and reinforcing the nonlinear behavior of the soil. Accordingly, the deviation of the estimated PHAs by the nonlinear and equivalent linear methods is minimized in far-field earthquake records where the bedrock acceleration is small.   Figure 10. PHA as a function of depth for: a) far-field analysis; b) near-field analysis. Fig. 11 indicates the amplification factor as a function of depth for near-field and far-field earthquake records, as approximated by the equivalent linear and nonlinear analyses. The difference in the results of the two methods is even clearer than that for the PHA. In particular, for the near-field earthquake records, the amplification at the ground surface was approximated at 3.7 and 1.8 by the equivalent linear and nonlinear methods, respectively. The corresponding figures for the far-field earthquake records were 3.8 and 3.1, respectively. That is, the deviation was as wide as 51 % for the near-field earthquake record but as low as 22 % for the far-field earthquake record.   Figure 11. Amplification factor as a function of depth. 3.2.               Velocity Velocity time histories provide an alternative insight into an earthquake event. Figs. 12 and 13 show velocity time histories for the reference points using the nonlinear and equivalent analyses under the influence of near-field and far-field earthquake records. The velocity time history is typically obtained by integrating the acceleration time history. The integration, however, tends to produce smooth and filtered outputs. This is why you can see that the velocity time history exhibits fewer high-frequency events than the acceleration time history [23]. Fig. 12 suggests that the velocity time history resulting from the near-field earthquake record exhibits sharply pulse-like motions. In contrast, Fig. 13 demonstrates that the velocity time history resulting from the far-field earthquake record lacks such pulses. This can be explained by the release of large amounts of energy in a short time upon faulting. That is, the short time of release is less than enough for such a vast amount of energy to spread over the entire time history. A comparison between the results of the nonlinear and equivalent linear analyses demonstrates that the amplitude of the velocity time history obtained from the nonlinear analysis is smaller than that from the equivalent linear analysis.   Figure 12. Velocity time histories at different reference points under the influence of the near-field earthquake record (Bam Station) from: a) nonlinear analysis; b) equivalent linear analysis. Figure 13. Velocity time histories at different reference points under the influence of the far-field earthquake record (Ravar Station) from: a) nonlinear analysis; b) equivalent linear analysis. Peak horizontal ground velocity (PHGV) is another parameter used to describe the amplitude of ground motions. The fact that the velocity is less sensitive to high-frequency components of the ground motions makes the PHGV at moderate frequencies a more accurate measure of ground motion amplitude than the peak horizontal ground acceleration (PHGA). For the structures or facilities that are sensitive to moderate frequencies (e.g., mid-rise or flexible structures, mid-span bridges, etc.), the PHGV is a more appropriate parameter for damage assessment, as compared to the PHGA. Fig. 14 depicts PHGV as a function of depth for the near-field and far-field earthquake records from the equivalent linear and nonlinear analyses. As seen, the equivalent linear method generally approximates higher PHGVs than the nonlinear method, with both equivalent linear and nonlinear methods producing higher PHGVs for the near-field earthquake record compared to the far-field earthquake record. This can be explained by the fact that, in a near-field earthquake record, the shorter offset to the epicenter implies that the bedrock motions are of larger amplitudes than in the far-field earthquake record. With increasing bedrock acceleration, soil layer deformations increase, thereby contributing to the nonlinear behavior of the soil. Therefore, in far-field earthquake records, the bedrock acceleration is usually low, the resulting strains at the soil level are small, and the PHGVs produced from the equivalent linear and nonlinear methods are very close to one another.   Figure 14. PHGV as a function of depth for; a) far-field earthquake record; b) near-field earthquake record. 3.3.               Displacement The application of displacement time histories for characterizing earthquake-induced ground motions is less common than the acceleration and velocity time histories [23]. Figs. 15 and 16 show displacement time histories for the reference points, as obtained from the nonlinear and equivalent linear analyses on the near-field and far-field earthquake records. A common practice for obtaining the displacement time history is to integrate the velocity time history. The integration has some smoothing and filtering effects. Therefore, as can be seen in the figures, the displacement time history exhibits fewer high-frequency events than the acceleration and velocity time histories. Another point to note is that the nonlinear analysis produces some permanent displacement, while the equivalent linear analysis does not predict such a permanent displacement and ends up with zero displacement at the end of the motion. This is linked to the elastic nature of the equivalent linear method that ignores the generation, redistribution, and elimination of pore water pressure, thereby producing zero permanent deformation. A comparison of the nonlinear and equivalent linear methods indicates that the displacement time history approximated by the nonlinear analysis exhibits smaller amplitudes than the equivalent linear analysis.   Figure 15. Displacement time histories for the reference points under the influence of near-field earthquake record (Bam Station) using: a) nonlinear analysis; b) equivalent linear analysis. Figure 16. Displacement time histories for the reference points under the influence of far-field earthquake record (Ravar Station) using using: a) nonlinear analysis; b) equivalent linear analysis. Peak horizontal ground displacement (PHGD) is a measure of characterizing ground motion amplitudes. The PHGD is associated with motion components of an earthquake at lower frequencies. As far as ground motion evaluation is concerned, the PHGD is a less common measure than the PHGV and PHGA. Nevertheless, the damage induced to highly soft structures is directly proportional to this parameter. Fig. 17 shows PHGD versus depth for near-field and far-field earthquake records, as obtained from equivalent linear and nonlinear analyses. The figure suggests that the equivalent linear method generally ends up with higher PHGD than the nonlinear method. Moreover, the deviation of PHGD between the equivalent linear and nonlinear methods is wider for the near-field earthquake records compared to the far-field earthquake records. This can be attributed to the fact that, in a near-field earthquake record, the shorter offset to the epicenter implies that the bedrock motions are of larger amplitudes than in the far-field earthquake record. With increasing bedrock acceleration, soil layer deformations increase, thereby contributing to the nonlinear behavior of the soil. Therefore, in far-field earthquake records, the bedrock acceleration is usually low, the resulting strains at the soil level are small, and the PHGDs produced by the equivalent linear and nonlinear methods are very close to one another.   Figure 17. PHGD as a function of depth for: a) far-field earthquake record; b) near-field earthquake record. For a better comparison of the results, PHGA, PHGV, and PHGD, together with their corresponding times at reference points, are listed in Table 1. These results imply that the soil layers can change the earthquake amplitude characteristics. The equivalent linear produces higher peak values of the amplitude parameters than the nonlinear method. Moreover, the deviation between the results of the two methods is greater for the near-field earthquake than for the far-field earthquake, which can be explained by the larger amplitude of the bedrock motion and the resultant nonlinear behavior of the soil. Table 1. Motion amplitude characteristics at reference points. Displacement Velocity Acceleration Depth   (s) (cm) (s) (cm/s2) (s) (g) (m) 2.70 28.87 3.11 88.47 2.65 0.79 35 A Equivalent linear Near-field 2.71 33.45 3.30 147.99 5.60 1.80 25 B 3.57 61.30 3.25 280.86 3.58 2.13 10 C 3.60 74.26 3.32 316.71 2.95 2.94 0 D 2.70 28.87 3.11 88.47 2.65 0.79 35 A Nonlinear 2.75 27.34 3.16 88.98 5.66 1.08 25 B 2.85 20.89 3.26 90.11 8.62 1.25 10 C 3.00 22.52 3.21 111.68 9.02 1.49 0 D 30.69 1.28 21.19 6.33 23.01 0.050 35 A Equivalent linear Far-field 30.65 1.01 23.31 4.31 24.11 0.033 25 B 30.50 0.59 23.37 1.65 18.46 0.017 10 C 30.39 0.53 30.00 1.71 15.38 0.013 0 D 32.78 0.58 27.91 3.85 17.70 0.040 35 A Nonlinear 30.52 0.50 30.21 2.00 18.27 0.022 25 B 30.40 0.53 17.35 1.80 17.43 0.021 10 C 30.39 0.53 30.00 1.71 15.38 0.013 0 D 3.4.               Response Spectrum The response spectrum describes the maximum response of a one-degree-of-freedom (1-DoF) system to a specific input motion as a function of natural frequency or natural period and damping ratio of the system. The response spectrum is an appropriate instrument for evaluating the maximum response of a 1-DoF system to an earthquake. The equation of motion for a 1-DoF structure under an earthquake stimulation is expressed as follows:                                                     (1) In which  is the natural angular velocity of the structure    is the ground acceleration,  is the damping ratio, and  is the displacement of a 1-DoF system. In order to plot the response spectrum, the equation of motion was solved for different natural frequencies, followed by obtaining the maximum of the response spectrum. In general, the response spectra include acceleration, velocity, displacement, pseudo-velocity, pseudo-acceleration, and pseudo-displacement, each of which describes the structural behavior in a particular way. For instance, the displacement spectrum provides information for calculating peak internal forces and deformation, the pseudo-velocity response spectrum is, however, associated with the maximum strain energy, and the pseudo-acceleration response spectrum is related to the lateral forces applied to the structure. The relationships among the displacement, pseudo-acceleration, and pseudo-velocity response spectra are expressed in the following:                                                                           (2)                                                                           (3) where  is the natural angular velocity of the structure,  is the displacement response spectrum,  is the pseudo-velocity response spectrum, and  is the pseudo-acceleration response spectrum [24–29]. Figs. 18 and 19 present response spectra of acceleration, velocity, and displacement, as obtained from the nonlinear and equivalent linear analyses for the near-field and far-field earthquake records, respectively. As can be seen in the figures, the spectra produced by the equivalent linear method exhibit larger values than those by the nonlinear method. This can be attributed to the elastic nature of the equivalent linear method, which results in higher amplification. Compared to the velocity and displacement response spectra, the acceleration response spectrum exhibits peak values in shorter periods. This finding indicates that the low-rise rigid structures (with short natural periods) are sensitive to acceleration, while moderate- and long-period structures are more sensitive to velocity and displacement, respectively. Comparing the spectra obtained from the near-field and far-field earthquake records, it was found that the maximum spectral amplitude for the near-field earthquake occurred in relatively shorter periods than that in the far-field earthquake. Indeed, near-field earthquake records exhibit higher frequency contents thanks to their shorter distance to the source of energy (no damping), while far-field earthquake records lack high-frequency contents due to the damping effect. This suggests that the near-field earthquakes impose further damage to highly stiff and low-rise (short-period) structures, while far-field earthquakes can induce more damage to less stiff high-rise (long-period) structures.   Figure 18. Response spectra for the near-field earthquake record (Bam Station): a) acceleration; b) velocity; c) displacement. Figure 19. Response spectra for the far-field earthquake record (Ravar Station): a) acceleration; b) velocity; c) displacement. Different response spectra (displacement, pseudo-velocity, and pseudo-acceleration) provide valuable information on the impact of earthquakes on structures. Given one of the mentioned response spectra, the other two can be derived. According to Equations (2) and (3), one can compile the spectra to come up with a mixed spectrum. Such a triple spectrum contains information about all of the three mentioned spectra. The horizontal axis of this spectrum indicates the period on a logarithmic scale, while the vertical axis refers to the pseudo-velocity values on a logarithmic scale. The bisectors of the first and second quarters indicate the axes of the displacement and pseudo-acceleration on logarithmic scales, respectively. In terms of the period, the triple response spectrum can be divided into three segments: short-period segment (0–0.5 sec) that is sensitive to the acceleration, moderate-period segment (0.5–3 sec) that is sensitive to velocity, and long-period segment (>3 sec) that is sensitive to displacement. Fig. 20 shows the triple response spectrum. As can be seen in this figure, the equivalent linear method produces higher results than the nonlinear method in almost all segments of the period. Moreover, the deviation of the results of the two methods is smaller for the far-field earthquake records.   Figure 20. Triple response spectrum. 3.5.               Natural Frequency The standard spectral ratio (SSR) is used to obtain the dominant frequency of the site. This parameter is calculated as the ratio of the Fourier amplitude spectrum of the time history of the soil to the time history of nearby bedrock subjected to the same earthquake and motion component [24–29]. The frequencies corresponding to the first and second peaks along the SSR graph indicate the first-mode (dominant) and second-mode frequencies, respectively [23]. Fig. 21 shows the amplification factor versus frequency. As is evident from this figure, the first-mode and second-mode frequencies of the studied site were approximated at 0.823 and 2.18 Hz, respectively.   Figure 21. Amplification factor versus frequency. 3.6.               Engineering Implications for Seismic Design The results of this study highlight the critical importance of considering the characteristics of earthquake field conditions in seismic design, particularly for structures located near active faults. The analyses demonstrated that near-fault ground motions generate significantly higher seismic demands due to their pulse-like behavior, high-frequency content, and larger acceleration amplitudes. Consequently, conventional design approaches based solely on equivalent linear assumptions or generalized design spectra may not accurately capture the actual seismic demand imposed on structures in near-fault regions. The findings indicate that short-period and stiff structures are especially vulnerable to near-fault earthquakes because the peak spectral responses of these motions occur at relatively higher frequencies. In contrast, far-fault earthquakes tend to impose greater demands on flexible and long-period structures. Therefore, the compatibility between the dominant frequency of the site, the frequency content of the earthquake motion, and the natural period of the structure should be explicitly evaluated during the design stage to avoid resonance-induced amplification. Another important implication of this research is the significant discrepancy observed between nonlinear and equivalent linear site response analyses under strong near-fault motions. Equivalent linear analysis generally overestimates amplification factors and peak response parameters because it cannot fully represent strain-dependent soil nonlinearity, stiffness degradation, hysteretic damping, and irreversible deformation mechanisms. As the intensity of ground motion increases, soil nonlinearity becomes more pronounced, particularly in shallow soft deposits, making nonlinear analysis more reliable for estimating realistic seismic demand. From a practical engineering perspective, the results suggest that nonlinear site response analysis should be considered mandatory for critical facilities and essential infrastructures located in near-fault seismic zones, including hospitals, bridges, tunnels, dams, nuclear facilities, transportation networks, and high-importance buildings. For ordinary structures located in moderate seismic regions, equivalent linear analysis may still provide acceptable preliminary estimations when soil strains remain relatively small. The obtained results also emphasize the necessity of incorporating site-specific seismic response analysis into performance-based seismic design frameworks. Since local soil conditions substantially modify acceleration, velocity, displacement, and spectral characteristics of ground motions, relying exclusively on code-based generalized spectra may lead to either unsafe or overly conservative designs. Site-specific analyses can improve the estimation of structural demand, story drift, foundation response, and seismic energy transfer mechanisms. Furthermore, the observed amplification patterns suggest that seismic codes may require additional modification factors for near-fault regions to account for pulse-type motions and strong nonlinear soil behavior. The results also indicate that evaluating only peak ground acceleration (PGA) is insufficient for seismic damage assessment. Parameters such as peak ground velocity (PGV), peak ground displacement (PGD), frequency content, and spectral characteristics should also be considered because different structural systems exhibit different sensitivities to acceleration-, velocity-, and displacement-dominated motions. Finally, this study demonstrates that accurate seismic hazard assessment requires simultaneous consideration of earthquake source characteristics, wave propagation effects, local soil conditions, and structural dynamic properties. Neglecting any of these interacting mechanisms may lead to inaccurate prediction of seismic demand and structural vulnerability, especially in near-fault environments where nonlinear soil behavior and pulse-like ground motions govern the seismic response.                                                                                                   4.     Conclusions In this research, the impacts of near-field and far-field earthquake records on the site response were evaluated by nonlinear and equivalent linear methods utilizing the PLAXIS and Deepsoil software tools. The analyses included the time histories of acceleration, velocity, and displacement, as well as their peak values and response spectra. A summary of the findings is presented in the following: 1.    Near-fault earthquakes produce stronger nonlinear soil behavior than far-fault motions. 2.    Near-fault motions shift peak response spectra toward higher frequencies, making short-period structures more vulnerable, whereas the opposite trend is generally observed for far-fault earthquakes, which tend to impose greater seismic demand on long-period and flexible structures due to their relatively lower-frequency content. 3.    The results demonstrate that equivalent linear analysis may significantly overestimate seismic amplification under strong near-fault motions due to its inability to fully capture nonlinear soil behavior. Therefore, nonlinear analysis provides a more reliable estimation for seismic assessment in near-fault regions. For ordinary structures located in moderate seismic regions, equivalent linear analysis may still provide acceptable preliminary estimations when soil strains remain relatively small. 4.    The discrepancy between equivalent linear and nonlinear analyses is substantially greater for near-fault records. This can be explained by the larger amplitude of ground motions in near-field earthquake records, which leads to extended damping and nonlinearity of the soil behavior. 5.    From an engineering perspective, the findings of this study emphasize the necessity of site-specific seismic analysis during the design stage of structures located in seismic zones. Furthermore, nonlinear site response analysis is strongly recommended for important structures and infrastructures in near-fault regions to achieve a more realistic estimation of seismic demand and potential structural damage. 10.34910/MCE.143.3 624 site response nonlinear analysis equivalent linear analysis near-field earthquake far-field earthquake https://engstroy.spbstu.ru/article/2026.143.3/

RAR RUS 14304-14304 Department of Civil Engineering, Faculty of Engineering, University of Anbar Sulaiman Hadeel hadeel.aldamag@uoanbar.edu.iq

Ramadi, Al Anbar, Iraq

56184497100 0000-0001-6180-8837 University of Anbar Al-Sharrad Muayad muayad.alsharrad@uoanbar.edu.iq

Ramadi, Iraq

University of Anbar Abed Idham ds.dr.idhamalassafii@uoanbar.edu.iq

Ramadi, Al Anbar, Iraq

Effect of microbial-induced calcite precipitation on hydraulic conductivity and strength of a sandy gypseous soil This work presents the effect of microbial induced calcite precipitation treatment on hydraulic conductivity and strength of a sandy gypseous soil with about 35 % gypsum content. The cementitious material was produced from a bacterial suspension containing the bacterial strain Bacillus Pasteurii PTCC 1645, mixed with or added to a cementation solution having the molarities 0.25, 0.5, and 1 M and prepared from a number of typically used chemical substances. The work resulted in a number of important outcomes. The microbial-induced calcite precipitation (MICP treatment), which yielded about 15 % calcite carbonate after 14 to 21 days of curing, can efficiently reduce the hydraulic conductivity, even for soils with high gypsum contents and relatively low fine content. In response to curing time increase from 7 to 21 days, the hydraulic conductivity decreased nearly twice. Likewise, as the calcite content increased to 15 %, the hydraulic conductivity decreased by almost fourfold. On the compressive strength front, the MICP treated specimens showed a promising uniaxial compressive strength of up to 600 kPa. This further reinforces the perception that MICP treatment by the Bacillus Pasteurii strain can be used effectively in treating gypseous soils problems. 1.Introduction Gypseous soils can demonstrate a continuous compression and even collapse under external loads. This phenomenon is usually triggered by gypsum softening, dissolution, and leaching due to certain human activities involving water percolation through soil mass and groundwater movement [1]. It has been well established that hydraulic conductivity is a key material property to be controlled in order to reduce the collapse severity of the gypseous soils. A numerous improvement methods have been suggested, by which permeability of the gypseous soil was either directly or indirectly reduced. According to [2], treating a soil containing 40–50 % gypsum content with kerosene can decrease permeability and compressibility by restricting the removal of gypsum from the soil mass. According to [3], adding 4 % automobile oil reduced the permeability coefficient by at least ten times. Al-Sharrad [4] studied the effect of cutback MC-60 on the permeability and compressibility characteristics of Ramadi sandy gypseous soil. Gypseous soils treated with the aforementioned materials have more likely exhibited a reduction in the coefficient of permeability, compressibility, and collapsibility. However, these materials are not considered sustainable due to their harmful effects on the environment and groundwater. In addition, most of these materials bear a density less than that of water and are therefore susceptible to washing by water movement within the soil mass, therefore affecting treatment durability. The microbial-induced calcite precipitation (MICP) is an up-and-coming technology for soil improvement. This technique involves using urease-producing bacteria mixed with cementation solution, and injected or blended with the soil. In geotechnical engineering, there has been a growing interest in this technology for soil improvement in recent years [5]. The MICP technology utilizes specific bacterial strains found in nature capable of depositing calcium carbonate to repair and fill cracks in concrete and rock materials. Additionally, the technology can help prevent leakage, soil erosion, slope failure, liquefaction of sandy soil [6–9]. The urea can be decomposed into CO32−, HCO3−, and NH4+ by urease secreted from the cell. When Ca2+ binds to CO32−, a large number of calcium carbonate crystals can be formed on the cell surface as given by Eqs. (1) to (3) [10]:                                                               (1)                                            (2)                                                  (3) The precipitated crystals in bio-cemented soil can have two primary functions; bonding at particle contacts and coating on particle surface [11]. Common microorganisms used in MICP for mineralization include: sulphate-reducing bacteria, denitrifying bacteria, oxidizing bacteria, and urease-producing bacteria [12]. Sulphate-reducing bacteria are primarily anaerobic heterotrophs that do not require oxygen for their metabolic activity [13]. They can reduce sulphates to sulphides while oxidizing organic carbon [14]. This process is represented by Eqs. (4) and (5).                              (4)                             (5) Various bacterial strains have been used successfully for calcite precipitation purposes. Bacillus Pasteurii has been the most used bacterial strain due to its superior characteristics such as its resistance to natural conditions. For instance, they are capable of producing spores, which enable them to survive extreme conditions such as high temperatures, exposure to hydrocarbon pollutants, and extended periods of drought [15]. Urease-producing bacteria are particularly useful in geotechnical engineering due to their low cost and high efficiency in providing cementation. Previous studies on MICP have shown that it has a bio-clogging effect, which reduces the permeability of treated soil samples by causing precipitation of calcium carbonate in the soil pore space [16, 17], and increases the material’s strength and stiffness [18–20]. The current study investigates the role of the MICP treatment in reducing hydraulic conductivity and increasing compressive strength of Ramadi sandy gypseous soil. This soil is typically characterized with profound deformable nature under soaking and water percolation conditions, which has resulted in severe serviceability and stability issues in the superstructures. 2.Materials 2.1.Soil Sample The soil used in this study was collected at a depth of 0.5 m from a site within the main campus of the University of Anbar. The study area is characterized by high contents of secondary-origin gypsum, ranging from 35 % at the ground surface to about 5 % few meters below the surface [21]. Signs of gypsum dissolution and movement, caused by various hydrological and environmental conditions. The index properties of the soil are given in Table 1.               Table 1. Index properties of the soil. Soil property Value Standard Gravel (%) 2.3 ASTM D422 [21] Sand (%) 91.7 Fines (%) 6.0 Coefficient of uniformity (Cu) 5.5 Coefficient of curvature (Cc) 0.77 Liquid limit (%) Non-plastic ASTM D4318 [22] Plastic limit (%) Non-plastic Specific gravity 2.4 ASTM D854 [23] Soil classification (USCS) Poorly graded sand with silt (SP-SM) ASTM D2487 [24] Maximum dry unit weight (kN/m3) 15.3 ASTM D698 [25] Optimum moisture content (%) 9.5 2.1.1. Bacterial Suspension The Bacillus Pasteurii PTCC 1645 strain was initially preserved in glycerol at a temperature of 4 °C. To prepare the liquid media was prepared by autoclaving 1 L (pH 9.0) tris buffer, 10 g (NH4)2SO4, 20 g yeast extract at 121 °C, and a 15 Ib/in2 pressure before use. A single colony from the surface of the agar plate with the highest concentration was cultured in 100 ml of this solution. Afterward, the flask was shaken in a shaking incubator at 180 rpm and 30 °C for 48 hours. Then, the bacterial suspension was prepared at a ratio of 1:100. 2.1.2. Cementation Solution The cementation solution was prepared by mixing equal proportions of 0.25, 0.5, and 1 M of calcium chloride (CaCl2) and urea (CO(NH2)2), as recommended by [27, 28]. A summary of the chemical quantities per liter of cementation solution is given in Table 2. Table 2. Chemical substances used for cementation solution preparation with a constant urea-Ca2+ molar ratio 1:1. Chemical materials Concentration of cementation solution (g/L) 0.25 M 0.5 M 1M NH4Cl 10 10 10 Nutrient broth 3 3 3 NaHCO3 2.12 2.12 2.12 Urea 15 30 60 CaCl2.2H2O 36.8 73.5 147 2.2.Biochemical Tests 2.2.1. Urease enzyme activity and density of bacterial suspension To calculate the activity of the urease enzyme, following the same method as [29]. By addition 1 ml of bacterial suspension to 9 ml of 1.11 M urea and measured the electrical conductivity over a 5-minute period at room temperature in terms of mS/min. A bacterial activity of 1 mS/min (electrical conductivity rate) is correlated to the hydrolysis of 11 mM urea during 1 minute [30] .The urease activity was found to be 38 mM urea/min, considered high according to many researchers, e.g. [31]. The activity of the enzyme ranged from 19 to 42.6 mM urea/min under different conditions. The concentration of the bacterial suspension was measured with a spectrophotometer type EMC-11-UV at 600 nm wavelength, OD600. Fresh media was used as a reference. OD600 was 2.55 for bacterial solution. 2.2.2. Calcite carbonate content test The calcite carbonate content (CCC) of soil samples was obtained using the volumetric calcimeter method outlined in [32]. This method is based on measuring the volume of carbon dioxide gas emitted from the reaction of calcium carbonate with hydrochloric acid (ASTM D 4373 – 02) [33], as given below.                                                   (6) A volumetric calcimeter was developed and used in this study to measure the volume of the released CO2, as shown in Fig. 1. The system consisted of a reaction flask (500 ml) with a stopper, burette (50 ml), leveling bulb, and connection nylon tubes. Distilled water was leveled between the burette and the bulb in the apparatus portion. A given mass of CaCO3 produces a certain volume of CO2. Pure CaCO3 powder was used to develop the calibration curve correlating the released CO2 volume to the mass of CaCO3. In more detail, 0.1, 0.2, and 0.3 of calcium carbonate (99 % purity) were placed carefully into a 10 ml beaker. The beaker was lowered carefully with a squeezer inside the reaction flask containing 50 ml of 5 % HCL without letting the two substances mix. Then, the system was closed under atmospheric pressure conditions, and the reaction flask was tilted so that the substances were mixed. Meanwhile, the flask was gently shaken. The excess pressure generated by the released CO2 caused the water in the burette to move towards the bulb. The reading was taken once no water movement was detected inside the burette [34]. To determine the CCC of soil samples, a sufficient mass of each oven-dried specimen was sampled from the top, middle, and bottom. These materials were pulverized and sieved on a No. 40 sieve (0.425 mm), and then 2 g were collected from each sample for the test. The test for the pure calcium carbonate was similarly performed on these samples. The released volume of CO2 during each test was used to determine the equivalent mass of the CaCO3 from the calibration curve. The CCC, in percentage, was calculated as:                                                               (7) where  is the equivalent mass of the calcium carbonate, and  is the mass of the soil sample. a b   Figure 1. Volumetric calcimeter: a) device image; b) schematic of the device. 2.3.Geotechnical Tests 2.3.1. Permeability-leaching Test 2.3.1.1. Specimen preparation As a first step, the soil was dried at a temperature of 35 °C to preserve the natural gypsum composition of the soil. Next, the soil was sieved on the No. 4 (4.75 mm) sieve, where only the portion passing that sieve was used for the lab work. A 15 ml preprepared bacterial suspension was mixed with 60 g of the soil sample, making 25 % by weight of the soil sample. This allowed the bacterial suspension to cover soil particles effectively. The mixture was molded gently inside the oedometer plastic ring. The specimen was left on the bench for an hour to ensure the bacteria adhered to the soil particles. Meanwhile, a container with 3 liters of cementation solution was prepared for each of the six specimens. Each container was equipped with an air pump to allow for the circulation of dissolved air and provide an environment favorable for calcite production and precipitation. To prevent fine soil particles from smearing, two layers of fine filter were placed on the top and bottom faces of the specimens. These specimens were finally immersed in the cementation solution for 7, 14, or 21 days. The readings of the pH, EC, T, and OD (oxygen demand) of the cementation solution were recorded daily during the curing stage. Two specimens were prepared for each treatment period; one was for the permeability test, and the other was for the calcite test. The specimens were placed inside an oven for drying at 35 °C for two days. The drying stage was performed to create a reference moisture for all the specimens and to simulate the field conditions in terms of temperature. In addition, drying helps mitigate the bacterial activity, so that the calcite content of the specimens is taken by the end of the curing. 2.3.2. Test Procedure Permeability-leaching tests were performed using the equipment shown in Fig. 2, which were initially arranged by [35]. The equipment comprised of a conventional oedometer with a modified cell, and a hydraulic system. The cell was provided with inlet and outlet to facilitate the salt leaching process. The function of hydraulic system was to provide distilled water for the leaching stage and to allow for leachate collection and measurement of the coefficient of permeability. This system consisted of controlled-head water storage tanks, PTFE tubes, valves, and a graduated flask. The coefficient of permeability of the material was measured by opening the inlet and outlet valves. The leaching was performed under hydraulic gradient values between 10 and 32. The time required to collect a given volume of outflowing leachate under a constant hydraulic gradient was recorded. The cell was initially mounted in its place and the specimen was incrementally loaded to 100 kPa vertical stress under its after-curing state. Subsequently, the specimen was soaked overnight with distilled water. The variation in specimen height was frequently recorded at various test stages. The permeability-leaching test was commenced through a downward flow by opening a valve installed on the line connecting the cell to the water tank. The time to collect each 500 ml of leachate volume was calculated. The coefficient of permeability,  was obtained under constant head conditions by using Darcy’s law as:                                                                                (8) where  is the discharge velocity, and  is the hydraulic gradient.   a b Figure 2: a) Schematic plot of the hydraulic system; b) schematic plot of the modified oedometer cell. 2.4.Unconfined Compression Test 2.4.1. Specimen preparation This test investigated the MICP treatment’s effect on the soil’s stiffness and strength. Test specimens were prepared inside plastic PVC molds with 45 mm in diameter and 90 mm in height. The specimen was prepared by mixing method. The process started by drying a soil sample weighing 180 g at 35 °C. The soil was then placed in a refrigerator to cool it down to 4 °C. Once cooled, the soil was mixed thoroughly with 27 ml (15 %) of a bacterial suspension at a temperature of 4 °C. This was mandatory to prevent premature calcium carbonate production. Afterward, the cementation solution was added at a 1:1 ratio to the bacterial solution; three specimens were prepared with cementation solution concentrations of 0.25, 0.5, and 1 M at a temperature of 4 °C. Finally, the mixture was poured into the PVC molds in three stages and then subjected to gentle vibration to ensure the mold was filled uniformly. The molds containing the specimens were subsequently placed in an oven for curing at 30 °C for seven days before being examined. 2.4.2. Test Procedure The test was conducted following the guidelines of ASTM D2166 [36]. Before the test, the weight and dimensions of the specimen were measured, and both the top and bottom faces were leveled. The test equipment consisted of a displacement-controlled load frame with a 5 kN load cell and a 0.01 mm precision digital dial gauge to measure axial displacement. The specimen was mounted on the equipment’s base plate and loaded at a 1 mm/min displacement rate until the specimen experienced shear failure. 3.Resultes and Discussion Chemical Properties 3.1.1. Calcite carbonate content of specimens after treatment Fig. 3 shows the results of the CCC test on soil specimens treated by Bacillus Pasteurii strain with 0.25, 0.5, or 1 M cementation solution molarities and cured for 7, 14, or 21 days. The untreated specimen yielded about 1 % CCC, which is expected for many gypseous soils. In general, the CCC increased with increasing curing time. After 7 days of curing, the amount of calcite produced by the bacterium was between 3 % (specimen with 1 M) and 7 % (specimen with 0.5 M). After 21 days of curing, the results of the specimens with 0.5 M demonstrated the highest CCC of 15.4 5. This amount is clearly higher than those of the specimens with 0.25 and 1 M cementation solution. This suggests that the 0.5 M cementation solution molarity provides the optimal medium for calcium carbonate precipitation for the gypseous soil under investigation. This agrees with previous studies which were stated that concentrations of cementation solution lower than optimal can lead to poor cementation and insufficient CaCO3 production. On the other hand, higher concentrations than optimal have adverse effects on the cementation quality and quantity. One possible explanation is that high concentrations can inhibit bacterial urease activity [37]. Figure 3. Calcite carbonate content of the treated specimens at various curing ages. 3.1.2. Sulfur content The energy dispersive X-ray (EDX) analysis was performed on both the untreated and treated samples with different cementation solution concentrations but at the same age, as shown in Fig. 4. It was discovered that the weight ratio of sulfur (S) to the samples with the highest calcium carbonate concentration, i.e., that prepared with 0.5 M cementation solution, was less by 90 % compared to the untreated sample. This reduction was due to the reduction of sulfate through the MICP technique. (a) (b) (c) (d) Figure 4. EDX analysis of: a) untreated sample; b) treated sample with 0.25 M; c) treated sample with 0.5 M; d) treated sample with 1 M. Geotechnical Properties 3.2.1. Hydraulic сonductivity The permeability of both treated and untreated samples was assessed by measuring the saturated hydraulic conductivity (k) corrected to a standard temperature of 20 °C. The specimens were cured for 7, 14, and 21 days. Fig. 5 showed a typical variation of the permeability coefficient with leachate volume. The coefficient of permeability of the untreated specimen increased almost sevenfold with the progress of leaching. This can be attributed to gypsum leaching, which appeared to cause an enlargement in the voids and water passages through the specimen. The MICP-treated specimens (e.g., with 0.25 M) showed slightly lower  values at the beginning, then marginally increased with the progress of leaching. This performance is associated with the fact that the produced calcium carbonate provides cementation and coating to soil grains and gypsum, so water flow has little effect on salt leaching. For an unbiased comparison, the permeability of the materials was obtained and compared after 1500 ml of leachate volume, as shown in Fig. 6. The results showed that the hydraulic conductivity of the treated samples decreased with increasing curing periods. For the specimens with 1 M, the dissolution of gypsum in the soaking solution may have caused an adverse effect on permeability by increasing the size of the voids. For the specimens with 0.5 M, after 14 and 21 days of treatment, the presence of approximately 15 % CCC caused the voids to become smaller, resulting in a substantial decrease in permeability. a) b) c) Figure 5. Variation of the coefficient of permeability with leachate volume of samples cured to: a) 7 days, b) 14 days, and c) 21 days. Figure 6. Values of the coefficient of permeability after 1500 ml of leachate volume. The effect of CCC on the permeability (measured after 1500 ml of leaching) was inspected in Fig. 7. The results reveal that the higher the CCC, the smaller the permeability. This further reassures the role of the MICP technique in reducing gypseous soil hydraulic conductivity and thereby reducing leaching effects. Figure 7. Variation of the permeability measured at a leachate volume of 1500 ml with CCC. 3.2.2. Unconfined compression Fig. 8 shows the effect of soil stabilization with Bacillus Pasteurii and different concentrations of cementation solutions (i.e., 0.25, 0.5, and 1 M) on the unconfined compression stiffness and strength. The elastic modulus was taken as the slope of the steepest portion of the stress-strain curve. A summary of these results is presented in Table 3. The results indicate relatively high unconfined compressive strength values compared to the weakly cemented natural sandy gypseous soil, thanks to the MICP treatment. Figure 8. Unconfined compression test results of several treated specimens. Table 3. A summary of the unconfined compression test results. Test code CCC (%) Compressive strength, qu (kPa) Axial strain at peak stress (%) Elastic modulus, Es (MPa) p0.25M 6.6 591 2.5 19.2 p0.5M 7.3 480 1.9 27.9 p1M 5.6 566 2.2 39.5 Microstructural and Mineralogical Analysis 3.3.1. Scanning electron microscopy The spatial distribution of the calcium carbonate crystals inside three specimens with Bacillus Pasteurii, treated and 0.25, 0.5, and 1 M cementation solution for 21 days, is presented in Fig. 9. In the samples with 0.25 and 1 M, which exhibited 4 and 5 % CCC, sand particles were barely coated with calcium carbonate. On the other hand, in the sample with 0.5 M, which had nearly 15 % CCC, the voids were largely filled with calcium carbonate. a b c Figure 9. SEM images with calcium carbonate distribution on samples: a) 0.25M; b) 0.5M; c) 1M. 4.Conclusion The cementation solution concentration plays an essential role in the amount of precipitated calcium carbonate and in the level of improvement. The concentration of 0.5 M seemed to outperform other concentrations in reducing permeability of the gypseous soil. In general, the calcium carbonate content increased with increasing curing time. After 21 days of curing, the results of the specimens with 0.5 M demonstrated the highest calcium carbonate content of 15.4 %. The results showed that the hydraulic conductivity of the treated samples tended to decrease with increasing curing periods. The permeability decreased nearly twice with a curing time increase from 7 to 21 days. The results reveal that the higher the calcium carbonate content, the smaller will be the permeability. The permeability decreased by almost fourfold, with calcium carbonate content increasing by 15 %. The MICP treatment was able to provide sound protection against gypsum dissolution and piping. The results of the leaching stages indicated that the treated specimens tended to maintain the same permeability with leaching, compared to the untreated ones, which exhibited many times increase in permeability due to gypsum dissolution and leaching. With MICP treatment, the permeability became progressively smaller, and water discharge was more and more restricted. Consequently, the treated soil became less susceptible to leaching effects. One of the manifestations of the MICP treatment was that the treated soil demonstrated an appreciable unconfined compression strength of up to 600 kPa. 10.34910/MCE.143.4 624 Bacillus pasteurii MICP soil improvement gypseous soils hydraulic conductivity https://engstroy.spbstu.ru/article/2026.143.4/

RAR RUS 14305-14305 0000-0002-6045-0885 K.N. Toosi University of Technology Bagheri Ali Reza bagheri@kntu.ac.ir

Tehran, Iran

0000-0002-8423-2858 K.N. Toosi University of Technology Zanganeh Hamed hamedzanganeh@gmail.com

Tehran, Iran

Islamic Azad University, Shahrood branch Ajam Abbas ajamabbas@yahoo.com

Shahrood, Iran

K.N. Toosi University of Technology Mirahmadi Seyed Amirhossien amirhossien13790@gmail.com

Tehran, Iran

Chloride diffusion in concrete with silica fume under early-age exposure This study investigates chloride diffusion in marine concrete structures during early-age curing, specifically slip-formed caissons and cast-in-place quay walls where concrete experiences chloride ingress before achieving full strength. The research examines how early-age exposure affects long-term chloride diffusion coefficients in conventional concrete and silica fume-modified concrete. Early-age chloride exposure critically compromises marine concrete durability, yet standardized testing typically evaluates concrete at 28 days or later. Understanding this impact is essential for accurate service-life prediction, but conventional concentration profile methods are labor-intensive and expensive, necessitating more efficient assessment techniques. We employed a rapid colorimetric technique under natural diffusion conditions to determine apparent chloride diffusion coefficients ( ) for concrete mixes with water-cement ratios of 0.3, 0.4, and 0.5, both with and without 10 % silica fume. The study compared diffusion coefficients across multiple exposure intervals from casting (0 days) to 1, 3, 7, 28, and 180 days. Results show early-age exposure significantly elevates long-term : for plain concrete, 0–180 days exposure increased  by 58 % compared to standard 28–180 days exposure. The colorimetric method revealed an even more pronounced effect (235 % increase) for silica fume concrete. Diffusion coefficients for 0–1-day intervals were approximately 82 times higher than 0–180-day intervals. Silica fume reduced  by 65 % for 0–180 days and 81 % for 28–180 days compared to control mixes. The findings demonstrate that early-age chloride exposure substantially impacts long-term durability, with the colorimetric method providing a more conservative assessment than traditional methods. Delaying exposure by just three days significantly improves performance, with 3–180 days exposure showing only 8 % higher  than standard exposure. These results emphasize the necessity of accounting for early-age chloride ingress in coastal infrastructure design and validate silica fume as an effective material for enhancing marine concrete resilience. 1.Introduction With the increasing use of concrete under early-age marine exposure conditions such as the construction of slip-formed caissons or cast-in-situ quay walls, the importance of studying chloride ingress under early-age exposure is becoming more evident. Standardized test methods are available for the determination of chloride diffusion coefficients of concrete under natural diffusion conditions, including ASTM C1556, Standard Test Method for Determining the Apparent Chloride Diffusion Coefficient of Cementitious Mixtures by Bulk Diffusion (www.astm.org), and NT BUILD 443, Concrete, Hardened: Accelerated Chloride Penetration (www.nordicinnovation.org). These methods involve immersion of specimens in chloride solutions for the intended time interval and subsequent powder grinding at various depths to determine chloride concentration profiles. Fitting the error function solution of Fick's second law of diffusion to the experimental data points yields the apparent diffusion coefficient for the time interval considered. It should be noted that such tests are laborious, expensive, and time-consuming. Accelerated tests involving the application of electric potential for speeding up chloride ingress into concrete have also been developed and standardized, including ASTM C1202, Standard Test Method for Electrical Indication of Concrete's Ability to Resist Chloride Ion Penetration (www.astm.org), NT BUILD 492, Concrete, Mortar and Cement-based Repair Materials: Chloride Migration Coefficient from Non-Steady-State Migration Experiments (www.nordicinnovation.org), and AASHTO T357, Standard Method of Test for Predicting Chloride Penetration of Hydraulic Cement Concrete by the Rapid Migration Procedure (www.transportation.org). Among these methods, the Rapid Chloride Migration (RCM) test offers a rapid, cost-effective, and relatively straightforward procedure. After subjecting the specimens to chloride penetration under an applied electric potential, the specimens are split and the penetration depth is revealed by a colorimetric procedure. By using test parameters such as the applied potential, test duration, chloride concentrations at the exposed surface, and the color change front, the chloride diffusion coefficient can be derived. Despite being easier to perform, rapid migration tests involve an application of electric potential and differ fundamentally from natural diffusion mechanisms [1, 2]. Furthermore, comprehensive reviews and phenomenological models on service life prediction and the influence of mineral additives on chloride diffusion [3–5] primarily focus on hardened concrete under standard exposure conditions, rather than early-age exposure scenarios. Consequently, these tests give instantaneous values of the diffusion coefficient and cannot be used reliably for the prediction of the long-term performance of concrete exposed to chlorides from an early age. Extensive reviews have recently summarized the key factors influencing chloride diffusion in hardened concrete and the relevant service-life prediction models. Xu et al. [6] examined the effects of water-binder (w/b) ratio, additives, cracks, and environmental conditions on chloride ingress, noting that silica fume can reduce the diffusion coefficient by up to 50 % at a 5–10 % cement replacement. Wang et al. [4] reviewed chloride penetration in recycled aggregate concrete and showed that silica fume improves chloride resistance by 20–65 % depending on dosage. Khan and Alhasan [5] compared mechanistic, stochastic, and empirical service-life models for chloride-induced corrosion and highlighted the diffusion coefficient as the most critical input parameter. Although these studies demonstrate the well-established influence of silica fume and the importance of diffusion-based service-life modelling, they do not address the scenario where concrete is exposed to chlorides immediately after casting. Consequently, the impact of very early-age exposure – when hydration is far from complete, and the pore structure is rapidly evolving – on long-term chloride transport remains poorly understood. This gap is especially relevant for marine structures built by continuous slip-forming or cast-in-situ methods, where fresh concrete can come into contact with seawater within hours of placement. Previous work on the effects of early-age exposure of concrete to chlorides has been rather limited. Caballero et al. [7], using the RCM test, studied early-age diffusion coefficients of mortar mixes based on ordinary Portland cement and found that the results for the age of 1 day were about 10 times higher than the 28-day values. They also used the natural diffusion test for determining the apparent diffusion coefficient for exposure intervals of 1.5 to 4 days and 7 to 16 days, and found that the value for the earlier time interval was twice that of the latter. Fraj et al. [8], using Portland cement-based mortars (including slag-blended mixes), found that the apparent diffusion coefficient for the exposure interval from the age of 1 day to 28 days was four times the value for the exposure interval from the age of 28 to 56 days. Although the results of both studies show a substantial effect for early-age exposure in increasing the diffusion coefficients, the exposure durations considered were not long enough to show the effect of early-age exposure on longer-term diffusion coefficients. Bagheri et al. [9, 10] used the RCM test method to determine diffusion coefficients at the ages of 1 day and 180 days and found that the early-age value was about 10 times higher than the 180-day value. These researchers also used the natural diffusion tests for determining the apparent diffusion coefficient of concrete mixes and found that the value for concrete exposed from the age of 1 day for a duration of 180 days was only 17 % higher than the one exposed from the age of 28 days for a similar duration. These findings are significant and show that although diffusion coefficients for early-age time intervals are many times higher than those of the later-age exposures, at longer durations of exposure, the difference between the early and late-age exposure diminishes significantly. It has therefore become apparent that the appropriate way for studying the effect of early-age exposure on chloride diffusion performance of concrete is by using natural diffusion tests with long-term durations. However, powder grinding and chloride concentration profile determinations involved in this test make it laborious and expensive, and a simpler test would be advantageous in this regard. Colorimetric methods under natural diffusion conditions appear a viable alternative in this regard. These tests have been used by various researchers for studying concrete performance under chloride environments [11–15]. The test is performed without the application of an electrical potential and therefore provides data under natural diffusion conditions. The test can also be conducted at any required time interval in the same manner as the immersion tests. Although some researchers have used the penetration depth in the colorimetric method as a means for comparing the relative performance of various mixes [16–20], it has also been used for the determination of chloride diffusion coefficients [12, 21–24]. In this test, the penetration front is determined by a colorimetric method, and by knowing the surface chloride concentration value, the diffusion coefficient for the exposure interval can be calculated. The other advantage of the colorimetric method is that it provides data directly on the free chloride diffusion coefficient, which is more relevant than the total chloride profiles determined in the usual immersion tests. The research object of this study is ordinary and silica-fume-blended Portland cement concrete subjected to chloride solutions immediately after casting. The aim is to evaluate the effect of exposure from very early ages on chloride diffusion characteristics using a simple, natural-diffusion colorimetric method, and to determine whether silica fume can mitigate the detrimental impact of such early exposure. The specific objectives are: to measure free-chloride penetration depths under natural diffusion conditions for exposure intervals starting from the time of casting up to several days and weeks, and to compare these with the standard 28-day exposure regime; to derive the corresponding apparent chloride diffusion coefficients from the colorimetric data; to quantify the influence of partial cement replacement by silica fume on the early-age diffusion behavior. This approach provides a practical alternative to the laborious immersion/powder-grinding tests while yielding data that can be directly incorporated into service-life predictions. 2.Methods The colorimetric method under natural diffusion conditions was used to study the chloride diffusion into the concrete mixes with water-cement (w/c) ratios of 0.5, 0.4, and 0.3 at various exposure ages and for different exposure durations. The exposure intervals considered included, exposure from the time of casting to the ages of 1,3,7,28 and 180 days. For exposure age of 1 day, exposure intervals of 1–3, 1–7, and 1-80 days, and for exposure age of 3 days, exposure intervals of 3–7 and 3–180 days were considered. For the exposure age of 7 days, intervals of 7–28 and 7–180 days, and for the exposure age of 28 days, exposure interval of 28–180 days were studied. The colorimetric test was also used to study the effect of partial cement replacement by 10 % silica fume under various exposure ages and exposure durations. In order to obtain further insight into early age exposure performance of the mixes studied, additional tests including electrical resistivity, development of compressive strength, and the RCM tests at various ages were also carried out. 2.1.Materials Used A type 2 Portland cement complying with the requirements of ASTM C150 was used for the study. The chemical composition of the cement is given in Table 1. The physical properties of the cement are presented in Table 2. Silica fume in powder form complying with the requirements of ASTM C1240 was obtained from the Azna ferrosilicon plant (Iran). The chemical and physical characteristics of the silica fume utilized, are presented in Tables 1 and 2, respectively. A polycarboxylic ether type superplasticizer was used to keep the workability of all mixes studied within the slump range of 100–150 mm. Silver nitrate of chemical grade produced by Merck Company (Germany) was used for determination of chloride penetration front in the colorimetric tests. The aggregates used for the production of concrete mixes included natural river sand with a saturated surface dry density of 2.50 g/cm3 and absorption of 4.7 %, and a crushed coarse aggregate with a maximum nominal size of 19 mm, saturated surface dry density of 2.57 g/cm3 and absorption of 2.1 %. Water of drinkable quality was used for the production of the mixes.     Table 1. Chemical analysis of the cement and silica fume. K2O Na2O SO3 MgO CaO Fe2O3 Al2O3 SiO2 Composition % 0.64 0.37 1.86 1.82 62.87 3.94 5.38 21.15 Cement 1.32 0.42 – 0.87 0.49 0.70 1.10 94.30 Silica fume     Table 2. Physical properties of the cement and silica fume.   Cement Silica fume Average diameter (μm) – 0.15 Specific surface area (cm2/g) (blain method) 3170 – Specific surface area (cm2/g) (BET method) – 192000 Specific gravity (g/cm3) 3.16 2.21 L.O.I (%) – 0.1 Percent retained on 45 mm sieve – 0.3 Accelerated pozzolanic strength activity index (%) – 145 Setting time (min) (initial) 105 – Setting time (min) (final) 150 – Compressive standard mortar at 28 days (MPa) 41.3 –   2.2.Mixes Considered Three concrete mixes with 420 kg/m3 of a type two Portland cement at w/c ratios of 0.5, 0.4, and 0.3 were used in the study. In order to study the effect of incorporation of silica fume on chloride diffusion under early age exposure, a further three mixes, using 10 % silica fume as partial replacement of cement, at the above-mentioned w/c ratios were also considered in the study. Required amounts of the superplasticizer were used to keep the workability of all mixes within the 100–150 mm slump range. The mix ingredients are presented in Table 3. Table 3. Mixture proportions of concrete mixtures. Mixes Cementitious materials (kg/m3) w/b ratio Superplasticizer to Cementitious materials (%) Coarse aggregate (kg/m3) Fine aggregate (kg/m3) Cement (kg/m3) Silica fume (kg/m3) Temperature (°C) 0.5-Ref 420 0.5 – 813 813 420 – 20.0 0.5-SF10 420 0.5 0.21 806 806 378 42 19.9 0.4-Ref 420 0.4 0.47 867 867 420 – 20.1 0.4-SF10 420 0.4 0.54 860 860 378 42 20.3 0.3-Ref 420 0.3 1.88 920 920 420 – 19.1 0.3-SF10 420 0.3 2.18 913 913 378 42 20.1 2.3.Tests Carried Out 2.3.1. Electrical resistivity The electrical resistance of various mixes was determined at various ages according to the method described by Tang [25] using an alternating current to avoid errors due to concrete capacitance. 2.3.2. Compressive strength The development of compressive strength of the mixes studied with time was determined from the age of 1 day up to 1 year, using 10 cm cubical specimens according to the method described in BS EN 12390 part 3. 2.3.3. Rapid Chloride Migration test This test was carried out in accordance with the NT BUILD 492 standard. Cylindrical specimens (100 mm in diameter and 50 mm in thickness) were used. One surface was exposed to a 10 % NaCl solution, while the opposite surface was in contact with a 0.3 N NaOH solution. Chloride ingress was accelerated by applying a direct electrical potential. The voltage magnitude was selected based on the initial current measured through the specimen. The test setup is shown in Fig. 1. Figure 1. The Rapid Chloride Migration test a) the test set up; b) chloride penetration depth of split specimens after the test. The test duration was predetermined according to the applied potential. After completion, specimens were split axially. The freshly exposed surfaces were sprayed with a 0.1 N AgNO3 solution. Silver nitrate reacts with chloride ions to form a white AgCl precipitate. This clearly marks the chloride penetration front. The non-steady-state migration coefficient was then calculated using Equation (1).                               (1) where  is the non-steady-state migration coefficient 10–12 m2/s,  is the applied voltage (V),  is the average temperature of the anolyte solution (°C),  is the specimen thickness (mm),  is the average chloride penetration depth (mm), and  is the test duration (hour). Equation (1) is adopted directly from the NT BUILD 492 protocol. It is derived from the analytical solution of the simplified Nernst–Planck equation. The numerical coefficients in the equation are dimensional. They combine fundamental physical constants with unit conversion factors. This formulation allows direct input of practical laboratory units while ensuring the final result is correctly scaled to 10–12 m2/s. 2.3.4. Natural diffusion test and colorimetric determination of chloride penetration front Natural diffusion tests, commonly performed following principles outlined in documents such as ASTM C1556 and NT BUILD 443, are widely used to determine the apparent chloride diffusion coefficient of concrete. In these tests, concrete specimens are fully immersed in a chloride solution of known concentration (typically 16 % NaCl by mass, equivalent to ~2.8 mol/L) for a predetermined exposure period ranging from several weeks to several months. After exposure, powder samples are collected at incremental depths by dry grinding. The chloride content of each powder sample is determined by chemical analysis (e.g., potentiometric titration). The resulting concentration profile is then fitted to the error-function solution of Fick's second law of diffusion to calculate the apparent diffusion coefficient. However, the sequential steps of powder collection, chemical analysis, and curve fitting make this approach labor-intensive and costly. To address these limitations, colorimetric methods have been developed and validated in numerous studies [11, 12, 21–24]. This technique eliminates the need for powder grinding and chemical titration. Instead, a silver nitrate (AgNO3) solution (typically 0.1 mol/L) is sprayed onto a freshly split concrete surface. The reaction between silver ions and free chlorides produces a visible white precipitate of silver chloride (AgCl), clearly marking the chloride penetration front. The derivation of the diffusion coefficient in this method relies on assuming a fixed threshold chloride concentration  at the visible color-change boundary. This threshold is widely reported in the literature as approximately 0.07 mol/L [11, 26]. Given the known surface concentration  of the exposure solution, the analytical solution to Fick's second law is applied as follows:                                                     (2) where  is the chloride concentration at depth  and time (mol/L),  is the threshold concentration at the color front (mol/L),  is the apparent diffusion coefficient (m2/s),  is the penetration depth (m),  is the exposure duration  and erfdenotes the Gaussian error function. Rearranging Equation (2) to solve for  yields the general form:                                                           (3) In the present study, the exposure solution concentration was 2.8 (mol/L). Substituting  = = 2.8 (mol/L) and  = 0.07 (mol/L) into the equation above, the term  evaluates to a constant value of approximately 10.05. This constant incorporates both the inverse error function calculation for the specified concentration ratio and the necessary unit conversion factors to accommodate practical laboratory units. Thus, for the specific conditions of this study, the simplified expression for the non-steady-state diffusion coefficient  is given by:                                                                       (4) where  is the measured color-change depth (mm) and  is the exposure duration (h). This formulation directly yields  in units of 10–12 m2/s. Fig. 2a shows a specimen subjected to the chloride solution from the very early age and in Fig. 2b, a split specimen after being sprayed with silver nitrate, showing the color change depth  is presented.   b a          Figure 2. Very early age exposure to chloride solution and colorimetric determination of chloride ingress: a) specimen under exposure from the time of casting; b) split specimen after being sprayed with silver nitrate. 3.Results and Discussions Electrical Resistivity In Fig. 3, time variations of electrical resistivity of the mixes studied are presented. As shown for all mixes during the very early periods, i.e., up to about five hours, there is a slight decrease in electrical resistivity, which is due to the dissolution of ions into pore water. However, with the onset of setting and initial phases of the formation of microstructure, the resistivity increases. As expected, the mixes show higher resistance values. Partial replacement of cement with silica fume does not have a significant effect on concrete resistivity up to the age of 7 days. This is due to the opposing effects of the incorporation of silica fume on the ionic concentration of pore liquid during this period. These include the dilution effect due to partial replacement of cement, and the acceleration of cement hydration due to the nucleation effect of silica fume particles [26–29]. However, with the onset and progress of pozzolanic activity of silica fume and the resulting pore refinement and densification of microstructure the resistivity of silica fume mixes substantially exceed those of the control mixes. Figure 3. Electrical resistivity of concrete mixes up to 360 days. Compressive Strength The compressive strength of the mixes studied at various ages from 1 to 360 days is presented in Table 4. As expected, the lowering of the w/c ratio has had a considerable influence on increasing the compressive strength of all ages. Partial replacement of cement with silica fume has also had a considerable influence in increasing concrete strength which is due to mechanisms including, pore size refinement, microstructure densification, and improved paste aggregate transition zone [27–29]. Table 4. The results of the compressive strength test. Mixture ID Compressive strength (MPa) – 1 day 3 day 7 day 28 day 90 day 180 day 360 day 0.5-Ref Mean 9.9 24.5 34.6 48.0 52.9 57.1 60.1 COV*% 1.7 1.2 4.6 2.2 1.4 5.2 3.1 0.5-SF10 Mean 7.7 25.7 36.7 58.5 68.3 69.3 69.5 COV*% 1.5 1.4 1.9 3.7 3.3 1.8 4.2 0.4-Ref Mean 11.7 28.6 41.6 55.4 61.6 68.1 69.0 COV*% 2.5 0.4 0.8 5.8 2.2 1.7 3.3 0.4-SF10 Mean 13.9 33.0 47.1 71.0 80.7 83.5 84.8 COV*% 1.7 1.3 3.9 4.2 2.2 3.3 3.1 0.3-Ref Mean 14.6 38.3 54.1 62.7 75.1 78.9 82.2 COV*% 3.4 1.4 2.1 4.9 1.6 3.7 2.5 0.3-SF10 Mean 18.9 46.0 65.3 92.8 104.4 105.7 114.6 COV*% 4.1 2.1 1.2 2.6 2.5 4.1 0.4   * Coefficient of Variation Rapid Chloride Migration Test Results of the RCM test are presented in Table 5 and Fig. 4. As can be seen, the diffusion coefficients at early ages are substantially higher than the later age values. For the reference mixes with w/c ratios of 0.5, 0.4, and 0.3, the values at the age of 1 day are, 8, 11, and 12 times higher than their respective 180-day values. The incorporation of silica fume has not had a considerable influence on the diffusion coefficients at the ages of 1, 3, and 7 days. The opposing effects of dilution and acceleration due to partial replacement of cement with silica fume appear to have canceled each other out at these ages. However, with the onset and progress of pozzolanic reactions of silica fume and the concomitant improvement in the microstructure, drastic reductions in diffusion coefficients of these mixes are observed. For silica fume mixes with w/c ratios of 0.5, 0.4, and 0.3, the values at the age of 1 day are 36, 40 and 55 times higher than their respective 180-day values. Table 5. Results of the RCM test. Mix ID Diffusion coefficient (10–12 m2/s) – 1 day 3 day 7 day 28 day 90 day 180 day 360 day 0.5-Ref Mean 132 47 34 21 19 16 15 COV*% 6.2 4.6 2.8 5.9 7.1 3.2 5.7 0.5-SF10 Mean 142 68 40 15 7 4 4 COV*% 4.7 5.3 5.4 5.2 3.2 0.9 1.1 0.4-Ref Mean 118 41 26 17 13 11 10 COV*% 3.9 7.4 2.5 5.8 8.1 7.1 2.3 0.4-SF10 Mean 120 42 26 8 4 3 3 COV*% 7.1 1.4 2.4 7.9 6.5 4.6 2.3 0.3-Ref Mean 107 32 19 15 11 9 7 COV*% 5.2 9.2 5.8 6.2 7.9 8.1 9.0 0.3-SF10 Mean 109 35 20 8 4 2 2 COV*% 1.3 8.1 5.9 4.4 9.3 5.7 8.5   * Coefficient of Variation Figure 4. Diffusion coefficient (RCMT) at various ages for the mixes with w/c ratios of: a) 0. 5, b) 0.4, and c) 0.3. Colorimetric Test under Natural Diffusion Conditions The results of the colorimetric determination of the chloride penetration depth under natural diffusion conditions for the mixes studied are presented in Table 6. The results presented cover a large range of exposure intervals including; from the time of casting to the ages of 1, 3, 7, 28 and 180 days and also exposure intervals of 1–3, 3–7, 1–7, 7–28, 1–180, 3–180, 7–180 and 28–180 days. The diffusion coefficients derived from the colorimetric tests for the reference mixes at w/c ratios of 0.5, 0.4, and 0.3 are presented in Fig. 5.   Table 6. The results of colorimetric determination of the chloride penetration depth for various exposure intervals (t1–t2) days. Mix ID Depth of chloride penetration (mm) 0-1 0-3 0-7 0-28 0-180 1-3 3-7 1-7 7-28 1-180 3-180 7-180 28-180 0.5-Ref 24 27 23 28 54 18 13 19 19 10.34910/MCE.143.5 691.32:620.193 chloride ingress colorimetric method early-age exposure apparent diffusion coefficient silica fume marine concrete structures https://engstroy.spbstu.ru/article/2026.143.5/

RAR RUS 14306-14306 Bryansk State University of Engineering and Technology Muymarov Kirill kirillmkw@mail.ru

Bryansk, Russian Federation

Bryansk State University of Engineering and Technology Shvachko Sergey sshvachko@mail.ru

Bryansk, Russian Federation

57170706600 0000-0003-2763-0515 Southern Ural State Agrarian University Troyanovskaya Irina tripav63@mail.ru

Chelyabinsk, Russian Federation

Patrice Lumumba Peoples' Friendship University of Russia Voinash Sergey sergeyvoinash@yandex.ru

Moscow, Russian Federation

Patrice Lumumba Peoples' Friendship University of Russia Garkin Igor igor_garkin@mail.ru

Moscow, Russian Federation

Modeling of stress-strain state of reinforced concrete slabs taking into account physical nonlinearity Reinforced concrete structures have nonlinear properties due to the material and its structure. The onset of cracking leads to additional redistribution of the concrete's stress state. Furthermore, when a concrete slab bends, different layers experience different stresses. The aim of this study was to develop an improved mathematical model of the stress-strain state of reinforced concrete slabs taking into account cracking due to the layer-by-layer description of the physical nonlinearity of concrete. The object of study was a reinforced concrete slab measuring 1395 × 4500 × 50 mm, loaded in the middle and simply supported on three sides. In the model, the strength of concrete under complex stress conditions was described using a limit surface in the principal stress space. Additionally, constraints were introduced for rigidity and cracking conditions. The model is implemented using the finite element method in the DIVLOC software package. The modeling results include a picture of the stress-strain state of the slab and a diagram of the formation and development of cracks. Areas with the smallest reserve of bearing capacity are found taking into account the redistribution of stresses. To assess the model's validity, a full-scale experiment was conducted. Using sensor readings, the deformation of various points on the slab was measured. As a result of slab bending, the model showed support separation, which was confirmed experimentally. The discrepancy between the strain sensor readings and the calculated data before cracking was no more than 23 %. Under a load of 33 kN, crack initiation was observed. After cracking, the discrepancies decreased to 19–20 %. The experimental results confirmed the stress redistribution after cracking and the adequacy of the mathematical model with a layer-by-layer description of concrete nonlinearity.                                                                                                    1.     Introduction Reinforced concrete slabs are one of the main structural elements of many industrial and civil construction projects. Reinforced concrete structures have nonlinear properties due to both the material and the structure. The concrete stress-strain diagram is fundamentally different from the steel stress-strain diagram. Steel withstands compressive and tensile stress almost equally well. Concrete withstands compressive stress well and almost does not withstand tensile stress [1, 2]. Significant differences in the deformation of concrete and steel lie in the redistribution of internal forces between structural elements. The formation and development of cracks require special attention. While the nonlinearity of reinforcing steel is measured only after its stress limits are limited, concrete exhibits nonlinear mechanical properties under all conditions [3–5]. Taking into account physical nonlinearity is associated with large expenditures of computing power. The initial approximation of the parameters of the stress-strain state of reinforced concrete slab structures can be obtained with a linear calculation. However, this approach is only acceptable when the stresses in the reinforcement are less than the proportionality limit and there are no cracks in the concrete [6, 7]. The nature of the stress-strain state of a reinforced concrete slab is determined by the acting loads and the conditions of fastening. Rectangular slabs supported on two opposite sides are correctly described as beams. Their stress-strain state is well studied [8–10]. However, more complex fixation has been little studied. When studying the stress state of reinforced concrete structures, numerical modeling using the finite element method is most widely used. This is due to the ability of software packages (Ansys, SAP, Nastran, T-Flex Cad, Abaqus, Stark ES, etc.) to take into account the nonlinear properties of the material. As a rule, the stress-strain state was assessed using the Drucker–Prager and Rankine strength criteria uniformly throughout the entire thickness of the material. Calculations in various software packages give a similar picture of the redistribution of stresses in reinforced concrete slabs. For example, in the Ansys software package, the stress-strain state is assessed using the Drucker–Prager and Rankine strength criteria [11–14]. The nonlinear nature of deformation of reinforced concrete slabs is further complicated by the process of crack formation [15, 16]. After cracks form, stress redistribution occurs. The tensile force in the crack is perceived only by the reinforcement. The tensile stress in the concrete near the crack decreases and is redistributed to more distant areas. The crack trajectories pass through points with the greatest principal tensile stresses [17, 18]. Previous studies [19–23] have determined that the process of crack formation is affected by: loading history, nonlinear calculation scheme, and crack formation model. In this regard, it became necessary to describe the nonlinearity of concrete not in the form of a monolithic material, but taking into account its layer-by-layer loading. The aim of the study is to develop and test the adequacy of an improved mathematical model of the stress-strain state of reinforced concrete slabs through a layer-by-layer description of the physical nonlinearity of concrete and the possibility of crack formation in concrete. To achieve this goal, the following research objectives were formulated: 1.    Develop an improved mathematical model of the stress-strain state of a reinforced concrete slab with a layer-by-layer description of concrete nonlinearity. 2.    Develop a methodology and conduct experimental studies to assess the stress-strain state of a reinforced concrete slab loaded in the middle and simply supported on three sides. 3.    Analyze and compare the results of the numerical and field experiments to assess the adequacy of the mathematical model.                                                                                     2.     Materials and Methods 2.1.               Mathematical Model To calculate reinforced concrete slabs using the finite element method, the proprietary DIVLOC software package was developed jointly with the Bryansk State Engineering and Technological University. The peculiarity of the package was that concrete with discrete reinforcement bars was described as a multilayer material using the finite element method, taking into account the nonlinear behavior of materials (Fig. 1). Concrete deformation occurs in accordance with the theory of N.N. Karpenko [24] when cracks form in concrete based on the mechanics of V.I. Murashev.   Figure 1. Model of the slab: 1 are concrete layers; 2 are reinforcement elements. The iterative calculation procedure is implemented using the variable elasticity method. In the initial iteration, the slab is modeled linearly with the initial elastic moduli of the materials. In subsequent iterations, the elastic properties are refined in the stiffness matrices based on the previously obtained stresses. Kirchhoff's hypothesis of the absence of interlayer pressure during deformation is adopted as an assumption. The system of linear algebraic equations includes: a stiffness matrix, taking into account the secant elasticity models of the materials, and the external load reduced to the nodes, as well as the nodal displacement vectors. A 50 mm thick rectangular slab with regular reinforcement of 14 mm diameter longitudinal reinforcement at 200 mm intervals was chosen for the calculation. The calculation model consists of 1,554 multilayer triangular concrete finite elements and 3,254 bar finite elements. The specified materials are B25 concrete and A400 working reinforcement. The plate was freely supported on three sides. The loading was carried out in the middle of the free side (Fig. 2).   Figure 2. Finite element model of a reinforced concrete slab. During loading, the tearing off of the support faces was allowed with one-sided support of the slab. The finite element model of the slab included 176 multilayer triangular finite elements of concrete and 173 rod finite elements of reinforcement. Also included in the scheme were 20 supporting finite elements, allowing for the modeling of tearing off. Limitations on strength, rigidity and crack resistance of the slab were taken into account in accordance with the requirements [25]: -         strength conditions                                                                           (1) where  is the third principal stress in concrete;  is the permissible design compressive strength of concrete for the considered loading mode;  is the longitudinal deformation in the reinforcement;  is the permissible deformation of the reinforcement under tension and compression; -         rigidity condition                                                                          (2) where  is the displacement in the vertical direction;  is the maximum allowable deflection; -         crack resistance conditions                                                                          (3) where  is the crack opening width;  is the maximum permissible crack opening width. According to the theory of N.I. Karpenko [24], the strength of concrete under a complex stress state is found using the limit surface in the space of principal stresses. For heavy concrete, the equation of this surface has the form                        (4) where  is the coefficient;    are the strength of concrete under biaxial compression and tension. According to the static loading condition, the relationships between the calculated resistances  in the principal directions remain the same as between the principal stresses. In the absence of cracks, the secant elastic moduli and secant coefficients of transverse deformations are determined based on the level of the principal stresses                                                                           (5) The level of loading allows us to estimate the nature of crack formation when failures occur in stretched concrete and to check it for the condition of strength under compression. If at some step of iterative calculations, the conditions  are fixed, then this is already the basis for stating the formation of a crack in the plane of the main platform [26]. Preliminary elasticity matrices of finite elements are found from the condition of zero elastic modulus in the direction perpendicular to each crack elastic modulus of concrete. 2.2.               Experimental Method To check the accuracy of the calculation, experimental studies were additionally conducted. Three experimental samples of reinforced concrete slabs were manufactured (B25 class concrete and VR-I reinforcement d4 mm). Working reinforcement with a pitch of 50 × 50 mm was located at a distance of 8 mm from the lower surface of the slab. The experiment was carried out using a stand (Fig. 3).   Figure 3. Scheme (a) and photo (b) of the experimental setup: 1 is experimental plate; 2 is support frame; 3 is beam-lever; 4 is loading stamp; 5 is pallet for loads; 6 are loads; 7 is lever support. The support frame is a spatial welded structure made of rolled steel sections (I-beams No. 10, channels No. 12 and round rolled steel d16). The experimental plate was loaded using a beam-lever (two I-beams No. 10) through a stamp with a support surface of 250 × 250 mm. The stamp consisted of a centering angle and two rigid plates. The angle ensured the accuracy of the load placement. The plates ensured the load distribution over the entire surface of the stamp. The loading was carried out for 10 minutes. After that, the sensor readings were measured. Free support of the slab on three sides was achieved using round rolled steel and metal plates. The round profile rested on the frame, and the plates protected the slab from crushing. The deflections of the plate were measured by clock-type indicators. The displacement indicators were located in the middle of the free edge of the plate and near the supports. The registration of the plate deformations was carried out by constantan foil strain gauges with a measuring base of 50 mm and a resistance of 120±2 Ohm (Fig. 4).   Figure 4. Layout diagram (a) and photo (b) of strain gauges on the test plate. The strain gauges on the experimental plate were fixed with cold-setting ethyl cyanoacrylate adhesive. The sensors were connected using an eight-channel external half-bridge circuit. Each channel connected a compensation and measuring sensor and two passive resistances.                                                                                    3.     Results and Discussion The algorithm implemented in the DIVLOC software package was validated by comparing the obtained results with those of calculations based on the STARK_ES software package. This software package is designed for the strength analysis of large-scale reinforced concrete buildings and structures using the finite element method. It is a domestic development and is certified according to Russian construction standards [27]. According to the calculation, the maximum pressure was 120 kPa. Then the calculations were interrupted, which corresponded to the destruction of the reinforced concrete slab. At the maximum load (120 kPa), the iteration process converged only after 300–500 iterations. With the growth of bending deformations of the slab, its corners rise above the supports. This is explained by the excess of vertical deformations of corner points from bending (up) over their deformations from the weight of the slab (down). The recorded positive vertical displacement of the nodes (marked with bold dots in Fig. 2) corresponds to their separation from the supports. In the experiment, a separation of the support faces of the slab was also observed. The calculated separation length was 310 mm in the calculation and 340 mm in the experiment (the discrepancy is 11 %). This percentage of discrepancy can be considered sufficient for finite element method models. A more accurate match to experimental values can be achieved by using a finer finite element mesh. However, this will increase the calculation time [28]. The calculation time using DIVLOC was 2.5 hours, while using the STARK_ES software package, it took over 8 hours. Using the STARK_ES software package, the calculated separation length of the slab corner from the support was 315 mm, which is in good agreement with our calculation results. The greatest deflection of the plate was observed in the middle of the free edge of the plate, where strain gauges T5, T7, and T8 are located (Fig. 4a). A comparison of the calculated and experimental values of relative linear deformations in the load range of 21.6…124 kPa is shown in Fig. 5.       Figure 5. Calculated and experimental values of relative linear deformation e for sensors: a) T5; b) T7; c) T8. Comparison of the results of finite element analysis and the experimental results showed fairly close values [29]. The discrepancies between the calculated and experimental values for sensor T5 were no more than 9 %; for sensor T7 – no more than 10 %, and for sensor T8 – 12 %. A significant increase in the difference between the experimental and calculated values with increasing load for sensor T8 is explained by the effect of punching in the area of its location. Before cracks appeared in the slab, the discrepancies between the calculated and experimental values of relative deformation were no more than 7 %, which confirms the adequacy of the proposed mathematical model with a layer-by-layer description of concrete. Similar results were obtained using the STARK_ES computer system, confirming the validity of the algorithm used. The crack formation patterns obtained through finite element modeling largely replicate the experimental crack formation patterns. According to the finite element calculation, the main tensile stresses were observed on the lower edge of the concrete slab. Already at a load of more than 33 kN, crack initiation was observed. At the first stage of loading, cracks formed in the middle of the free edge, under the loading platform. With increasing load, the crack formation zone expands (Fig. 6). The greatest stresses are concentrated along the lines from the corner of the loading platform to the points of the boundaries of the slab lift areas above the supports. Redistribution of stresses between the loaded platform and the side edges leads to the formation of cracks in these areas [30, 31].   Figure 6. Scheme of crack formation on the lower surface of the plate under different loading. In the experiment, the sensor readings also changed significantly in the stretched zones of the plate after the cracks formed. This is explained by the redistribution of stresses in the immediate vicinity of the crack.                                                                                                     4.     Conclusion An improved mathematical model of the stress-strain state of reinforced concrete slabs with a layer-by-layer description of the physical nonlinearity of concrete has been developed. The model takes into account the redistribution of stresses due to cracking. The adequacy of the model has been verified by a full-scale experiment. The discrepancy between the calculated and experimental results before cracks appeared in the slab did not exceed 23 %. The use of one-way ties during bending revealed the separation of the slab corners from the supports. This effect was confirmed by the experiment. The difference in the separation length was 16 %. Step-by-step loading made it possible to identify the onset of cracking in the reinforced concrete slab and obtain a complete picture of their further development. The resulting picture of cracking allows one to identify the most loaded sections of the structure, where additional reinforcement is required to increase their strength. The model can be used in the procedure of optimal design. 10.34910/MCE.143.6 624.046.5 finite element method mathematical model layer-by-layer concrete description physical nonlinearity crack formation crack development https://engstroy.spbstu.ru/article/2026.143.6/

RAR RUS 14307-14307 0009-0003-0245-2086 Department of Construction Technologies and Structural Materials of the Engineering Academy, RUDN University Qais Qais Abdulrahman Ali qaiseng@gmail.com

Moscow, Russian Federation

0000-0002-8143-4614 Department of Construction Technologies and Structural Materials of the Engineering Academy, RUDN University Okolnikova Galina okolnikova_ge@mail.ru

Moscow, Russian Federation

0000-0001-7562-5652 Patrice Lumumba Peoples' Friendship University of Russia Obeid Mahmoud Mahmoud.obeid@yandex.com

Moscow, Russian Federation

Effects of hybrid basalt fiber dosages on workability and flexural strength of aerodrome concrete pavement High-stress pavement systems, particularly aerodrome runways, demand concrete with superior crack resistance, flexural strength, and durability. Basalt fibers offer clear benefits for both mechanical strength and thermal resistance, but few studies have looked into using hybrid basalt fiber mixes specifically for pavements. In this work, we developed and fine-tuned a hybrid basalt fiber-reinforced concrete by blending micro- and macro-sized basalt fibers at a fixed overall fiber volume fraction, with the goal of boosting flexural performance combining basalt fibers of different sizes at different dosage combinations and micro–macro ratios to assess their impact on flexural performance and workability. Portland Cement M600 (CEM I 52.5) conforming to GOST 31108-2020, potable water per GOST 23732-79, and a polycarboxylate-based superplasticizer (0.7 % cement weight) were used. Several basalt fiber ratios (micro and macro) were investigated. Mixing followed a controlled sequence to ensure uniform fiber dispersion, with specimens cured under moist conditions and tested for flexural strength at 28 days. Results indicated that hybrid mixtures out performed single-fiber systems in balancing early-age crack control and post-crack flexural strength. The 1.5:0.5 ratio achieved the highest overall flexural performance, showing a 7 % improvement over pure macro fiber mixes and 5 % over pure microfiber mixes at 28 days. Workability decreased with higher macro fiber content, highlighting the need for optimized dispersion. It is concluded that ratio micro–macro basalt fiber hybridization enhances pavement-grade concrete performance, with the 1.5:0.5 ratio recommended for aerodrome applications. Further research should evaluate long-term durability under cyclic loading and environmental exposure.                                                                                                    1.     Introduction Fiber-reinforced concrete (FRC) offers superior performance compared to conventional concrete due to its composite material composition and structural elements. One of its most notable advantages is the significant enhancement of flexural strength, which varies depending on the type and properties of the fibers used. Although the concept is not entirely new, FRC has been steadily gaining traction in the construction industry [1]. Over the past five decades, FRC has undergone substantial development, resulting in widespread applications and increased market adoption. This progress is attributed to advancements in fiber technology, improvements in cementitious matrices, enhanced fiber–matrix interfacial bonding, and a deeper understanding of composite mechanics [2]. FRC is considered a specialized form of concrete that retains a certain level of toughness even after cracking [3]. The primary function of fibers is not necessarily to increase the concrete’s initial strength but rather to bridge cracks within the matrix as loads are applied, thereby enhancing post-cracking ductility and toughness [4]. The modern use of steel fibers as dispersed reinforcement can be traced back to Romualdi’s pioneering work in 1963 and 1964. Since then, the concept of incorporating dispersed fibers into cement-based materials has evolved significantly, resulting in extensive research publications, doctoral theses, and diverse practical applications in civil and structural engineering projects worldwide [5]. 1.1. Improvement of Concrete Performance in Aerodrome Pavements The operational condition of aerodrome movement areas evolves over their service life, primarily influenced by traffic loads and climatic factors [6]. Historically, most aerodrome pavements were not constructed with reinforced concrete; however, the adoption of reinforced pavement has become increasingly essential due to its critical role in aerodrome infrastructure [7]. To safeguard airfield pavements against accidental overloading, an internationally recognized pavement strength rating system is employed. This system comprises two components: the primary component, which protects against subgrade rutting, and the secondary, which shields asphalt surfaces. The latter is largely empirical, assigning tire pressure limits based on aircraft categories. In 2008, aircraft manufacturers proposed an increase in these limits, which was subsequently approved in 2013 [8]. While airfield pavements experience fewer load repetitions compared to highways, they are subjected to significantly higher gross loads. Pumping is a more common issue in highway pavements than in rigid airfield pavements. Additionally, whereas highway pavement loads often occur close to slab edges, airfield pavement loads are typically concentrated near the center of slabs [9]. Maintenance and rehabilitation of airfield pavements present major logistical and economic challenges, as they require substantial time and can disrupt airport operations, directly impacting airport revenue. Effective pavement asset management demands systematic, precise monitoring of pavement condition over time. Among the various Non-Destructive Testing methods available, the Falling Weight Deflectometer is considered the most representative for evaluating the structural capacity of airfield pavements [10]. 1.2. Importance of mechanical properties in aerodrome pavements The continuous growth of the aviation sector has subjected airport pavements to progressively heavier loads, creating an urgent need for materials with improved mechanical properties and long-term durability [11]. The choice of pavement type is influenced by several factors, including the operational characteristics of the aircraft expected to use the runway, specific operational requirements, particularly in terms of runway reconstruction and prevailing geological conditions [12]. Findings from accelerated traffic simulations on rigid pavement indicate that decreased flexural strength leads to a marked reduction in the crack resistance of Portland cement concrete pavements [13]. Complementary numerical modelling of the stress-strain behavior of strip pavements, using a discrete model of prestressed flight strip slabs with a single plane of symmetry, has provided detailed insights into their structural performance. The resulting nodal displacement profiles, bending moment diagrams, and soil base reaction data confirmed that the pavement structure met both strength and deformability requirements. These results suggest that, with adequate feasibility analysis, material usage in pavement construction could be significantly reduced while maintaining required durability and reliability, even for large, heavy-duty aircraft [14]. Moreover, research has shown that even when compressive strength remains constant, variations in the estimated flexural strength can influence slab thickness. Specifically, a lower inferred flexural strength requires a greater slab thickness, highlighting the critical role of flexural capacity in optimizing pavement design [15]. 1.3. Role of basalt fibers in concrete The naturally low tensile strength of concrete frequently results in abrupt, brittle failure without prior warning. One of the most effective strategies to address this weakness is the addition of fibers, which improves tensile strength and mitigates brittleness. Among the various fiber types, basalt fibers (BFs) have recently attracted considerable interest due to their favorable characteristics-high strength, excellent elasticity, a high elastic modulus, superior thermal stability, and strong chemical resistance [16]. High-modulus micro BFs are particularly effective in controlling microcrack formation because of their dense distribution and strong restraining action, leading to significant improvements in the pre-cracking mechanical performance of ultra-high-performance concrete (UHPC). For instance, UHPC reinforced with 0.3 % micro BFs achieved maximum compressive and flexural strengths of 132.6 MPa and 26.10 MPa, respectively. In contrast, macro BFs primarily enhance post-cracking performance, where fiber pullout dissipates energy and produces a more ductile failure mode. UHPC with 3 % macro BFs recorded peak compressive, first-crack flexural, and post-crack flexural strengths of 151.8 MPa, 24.97 MPa, and 26.32 MPa, respectively [17]. The study [18] identified BF content as the most influential parameter on concrete’s mechanical properties within a dosage range of 0.1–0.3 %, with an optimal value of 0.2 %. Fiber length had little impact on compressive strength in recycled aggregate concrete but enhanced splitting tensile and flexural strengths with longer fibers. BF pellets have also been shown to improve post-crack flexural behavior by reinforcing the cementitious matrix and limiting strength losses under harsh environmental exposure [19]. Similarly, [20] reported that adding macro BFs to recycled aggregate concrete  mixes restored splitting and flexural strengths to levels comparable to those made with natural aggregates. The study [21] further demonstrated that macro BFs addition increased splitting TS by 39.88 % and substantially improved both initial and unstable fracture toughness. The fiber bridging mechanism plays a pivotal role in post-cracking behavior in fiber-reinforced cementitious composites. Studies have shown that polypropylene fibers develop strong bonds with the cementitious matrix, thereby enhancing tensile capacity and impeding microcrack propagation. Micro polypropylene fibers improve peak load resistance and deformation capacity, while low dosages of macro polypropylene fibers offer greater post-crack energy absorption than higher dosages of micro polypropylene fibers [22]. Scanning electron microscopy observations indicate that steel fibers form thick interfacial transition zones that promote efficient stress transfer, whereas synthetic fibers help reduce micro cracking and improve durability over time. Nevertheless, significant research gaps remain particularly in identifying optimal hybrid fiber combinations, evaluating the long-term performance of FRC, and developing more sustainable fiber alternatives [23]. The study [24] introduced a probabilistic micro-mechanical model to assess crack-bridging stress–displacement behavior in short hooked-end steel fiber composites, recommending fiber volume fractions between 0.75 % and 1 %. Similarly, the study [25] found that fiber length and orientation markedly affect crack opening behavior and the softening characteristics observed after cracking. This study aims to develop and evaluate HBFC mixtures optimized for the workability and flexural performance requirements of aerodrome pavements, while the objectives are to: 1.    Source and characterize high-performance materials, including micro and macro, Portland Cement M600, and other mix components, in compliance with relevant standards. 2.    Prepare a series of concrete mixtures incorporating the relative proportions of micro and macro BFs varying both the total fiber dosage. 3.    Determine the flexural strength of the mixtures at 28 days under controlled curing conditions, using standardized testing procedures and. 4.    Analyze and compare the flexural performance and workability trends of hybrid fiber mixtures against single and hybrid fiber systems to determine the optimum ratio. Although BFs have gained attention for their mechanical, thermal, and chemical durability advantages in concrete, most existing studies focus on their application in general structural elements rather than in high-stress pavement systems such as aerodromes. Research has largely examined either micro BFs or macro BFs individually, with limited emphasis on hybridization strategies that balance early-age crack resistance with post-crack load capacity. The majority of available literature seldom analyzes dosage optimization data for maximum performance at constant total volume fractions. There is also an insufficient link between fiber distribution and mechanical performance. Many studies neglect the combined impact of high loading, environmental cycles, and crack control in the long-term performance of fiber-reinforced pavement concrete and its practical implications for aerodrome pavements.                                                                                     2.     Methods and Materials 2.1.               Material for the Experiment The mechanical performance, durability, and crack resistance of pavement-grade concrete are closely tied to the physical and chemical characteristics of its constituent materials. For this study, materials were carefully selected to meet the high-performance demands of aerodrome concrete pavements. Cement: The primary binder was Portland Cement M600, supplied by Akkermann Cement, meeting the requirements of CEM I 52.5 under GOST 31108-2020 [26]. This high-strength cement is noted for its rapid early strength development, making it particularly suitable for rigid pavements subjected to heavy traffic and requiring early reopening. Its quick-setting properties not only reduce construction time but also ensure long-term durability and resistance to cyclic loading. Water: Mixing water was potable, complying with GOST 23732-79 [27]. Under GOST 2874-82 [28], drinking water is deemed fit for concrete mixing without additional quality verification, ensuring consistent cement hydration and reliable long-term performance. Superplasticizer: To maintain workability at a low water–cement ratio, Polyplast Target was added at 0.7 % of cement weight. This polycarboxylate-based admixture is available in two variants: Type 1, which contains air-entraining agents to enhance freeze–thaw resistance and Type 2, which includes accelerators and structural modifiers for improved early strength gain and cohesiveness. Both variants conform to GOST 30459 [29], promoting uniform fiber dispersion, better matrix cohesion, and enhanced crack resistance in high-strength FRC. Aggregates. Locally sourced fine and coarse aggregates were used. Fine aggregates consisted of natural medium sands with a fineness modulus of 2.0–2.5, meeting GOST 8736-93 [30], and predominantly ranging from 0.63 to 1.25 mm in size. Coarse aggregates comprised 20 mm crushed stone from igneous and metamorphic rocks, compliant with GOST 8267-93 [31] and GOST 26633-91 [32]. Additionally, vein quartz with high purity, rough surface texture, and minimal clay or organic impurities was incorporated to improve packing density and enhance paste–aggregate bonding. Basalt Fibers. Basalt, a naturally occurring igneous rock formed from cooled volcanic lava, is increasingly recognized as a sustainable and safe alternative to asbestos for reinforcement. The transformation of basalt into fibers yields a high-performance material with exceptional heat resistance and stability under extreme environmental conditions [33]. Within the context of its application to reinforced concrete, there are two major types of BFs. Micro fibers, which are fine filaments with lengths of 15–30 mm and a diameter range of 9–25 μm and are bridged at the micro-crack stage. They are also useful for preventing plastic shrinkage during the early stages of curing because they offer good dispersion and a broad surface area [34]. Macro Fibers, which are coarse BFs (50 mm length, 1 mm diameter) with tensile strengths up to 1650 MPa were incorporated to improve post-cracking load-bearing capacity and flexural strength. Their strong mechanical interlock with the cement matrix enhances ductility and toughness, critical for pavements exposed to heavy dynamic loads. Their corrosion resistance and environmental benefits make them advantageous over synthetic alternatives [35]. 2.2.               Methodology 2.2.1. Material preparation This experiment employed advanced construction materials to produce HBFC specifically designed for the demanding conditions of high-stress pavement applications. The binding material used was Portland Cement M600 (CEM I 52.5), compliant with GOST 31108-2020 [26] and procured from Akkermann Cement. This high-strength cement was chosen for its rapid strength development and excellent adhesion properties, making it well-suited for rigid pavement structures exposed to heavy traffic loads and crack-inducing stresses. All mixing operations utilized potable water that conformed to GOST 23732-79 [27] standards, ensuring consistent cement hydration without the presence of detrimental impurities. A polycarboxylate-based superplasticizer was incorporated at a dosage of 0.7 % of the cement weight. This admixture kept the concrete workable even with a low water–cement ratio. The main thing we changed across mixes was how we combined the two types of BFs: micro and macro. The micro fibers were there to stop early-age and plastic shrinkage cracks from forming. The macro fibers, which are thicker and harder to pull out, were meant to span larger cracks and help the concrete hold together after cracking. By altering the relative amounts of micro and macro BFs as well as the overall fiber dosage, a number of fiber combinations were tested. In order to assess the impact of fiber dosage and hybridization on concrete performance, the mixtures included single-fiber systems and hybrid combinations ranging from 2:0 (all micro fibers) to 0:2 (all macro fibers), with mixes in between like 1.5:0.5, 1:1, and 0.5:1.5. Material batching was done to ensure consistency. Mixing was performed in a pan mixer, beginning with the dry components, followed by the gradual addition of water blended with the super-plasticizer. Fibers were introduced slowly to promote uniform distribution and prevent clustering. 2.2.2. The cone draft test A standard slump cone with dimensions of 300 mm height, 200 mm base diameter, and 100 mm top diameter was used for the slump test. The cone was placed on a flat, non-absorbent surface and filled with fresh concrete in three equal layers by volume. Each layer was compacted with 25 strokes of a tamping rod (16 mm diameter, 600 mm length) to ensure uniform consolidation and removal of entrapped air. After the third layer was rodded, the top surface was leveled, and the cone was carefully lifted vertically in 5–10 seconds without any lateral or twisting motion. The concrete was allowed to subside freely, and the slump value was determined by measuring the vertical difference between the height of the cone (300 mm) and the highest point of the slumped concrete. This value was recorded to the nearest 5 mm. The slump test results were used to evaluate the influence of different fiber dosages on workability. 2.2.3. The flexural strength test The other batch of fresh concrete was then cast into standard molds and compacted using a vibrating table to remove entrapped air. Concrete beam specimens measuring 100×100×400 mm were prepared for each mix. After casting, the beams were demolded at 24 hours and cured in water at until the testing age of 28 days in a controlled laboratory environment. For testing, each specimen was placed on two supporting rollers spaced 300 mm apart, with the load applied at two points equally distant from each support (third-point loading configuration). The load was applied continuously and without shock using a universal testing machine until failure occurred. The flexural strength (modulus of rupture, ) was calculated using Equation (1):                                                                         (1) where  is the maximum applied load (N);  is the span length between supports (mm);  is the average specimen width (mm);  is the average specimen depth (mm) The values for the flexural strength were carefully recorded and analyzed in relation to the predetermined hybrid fiber ratios.                                                                                    3.     Results and Discussion Two types of BFs were incorporated in this study to provide multiscale crack control and improve the structural performance of airport pavement concrete under severe aircraft loading circumstances: Micro BFs were 18.2 mm long and 17 μm in diameter. These fibers are useful in preventing the start and spread of microcracks in the cementitious matrix because of their high aspect ratio and small diameter. Microcracks frequently act as precursors to bigger structural cracks in airport pavements, where concrete is subjected to repetitive wheel loads, heat gradients, shrinkage effects, and cyclic environmental exposure. By adding micro BFs, the matrix’s stress distribution is improved, early fracture resistance is increased, and the chance of crack coalescence is decreased. This helps to increase fatigue resistance and durability, both of which are essential for preserving pavement integrity and reducing maintenance needs. Macro BFs had a length of 50 mm and a diameter of 1 mm, corresponding to an aspect ratio of approximately 50. The fibers were specifically chosen for aerodrome pavement applications because of their strong geometry and great resistance to mechanical damage during mixing and placing, even though this aspect ratio is lower than that of many BFs reported in structural concrete investigations. The comparatively large diameter reduces the chance of fiber rupture under loading by strengthening mechanical anchoring and enhancing fiber stability within the concrete matrix. Effective crack management is crucial because heavy aircraft loading exposes aerodrome pavements to high wheel loads, impact stresses, cyclic loading, and harsh weather conditions. By integrating the crack-bridging and toughness-enhancing properties of macro fibers with the crack-arresting capabilities of micro fibers, a hybrid system of micro and macro BFs offers multiscale reinforcement. While macro fibers enhance post-cracking behavior, energy absorption, crack-width management, and load transfer across larger cracks, micro fibers restrict the start and spread of micro cracks inside the cementitious matrix. When combined, they improve flexural performance, fatigue resistance, durability, and long-term structural dependability of concrete airport pavements under frequent aircraft stress. 3.1.               Workability The use of hybrid BFs in aerodrome concrete pavements has been widely explored to enhance mechanical performance and durability under heavy loading conditions. However, the addition of fibers can significantly affect the fresh properties of concrete, particularly its workability. This section shows how different hybrid BF amounts affected the workability of aerodrome pavement concrete, based on slump test results. Fig. 1 gives the slump values. The mix without any fibers-labeled K-had the highest slump at 40 mm (Fig. 2), meaning it flowed easily. Adding fibers brought the slump down, though how much it dropped depended on the fiber type and how much was used.   Figure 1. Slump (mm) against Hybrid Fiber Ratio. 3.1.1. Single fiber dosages When we added micro BFs (A), the slump dropped further as the fiber content went up. Looking at Fig. 1, slump fell from 35 mm at 0.25 % A down to just 11 mm at 2 % A. This reflects a dramatic drop, just like in the study This huge reduction occurs as a result of the high specific surface area of the micro BFs, which causes them to intertwine, increasing internal friction within the fresh mixture and restricts the movement of cement paste and aggregates. This reflects a remarkable decrease, just like in the study [36]; the slump of the BF-reinforced concrete, the slump has slightly dropped with the increasing dosage of BF up to 0.5 %, which peaked at 43 mm in the plain concrete matrix. However, when adding BF with the volume fraction of 0.125 %, 0.25 %, 0.375 % and 0.5 %, the slumps of the concrete matrix has fell to 40 mm, 33 mm, 26 mm, and 18 mm, respectively. For mixtures containing only macro BFs (B), the reduction in slump was less pronounced. The recorded slump values ranged from 36 mm at 0.5 % B to 31 mm at 2 % B (Fig. 3), suggesting that macro fibers have a comparatively lesser impact on workability due to their lower surface area and interaction intensity.   Figure 2. Control mixture (K) with 40 mm slump.       Figure 3. 2B, BF-reinforced concrete with 31 mm slump. 3.1.2. Hybrid fiber combinations The incorporation of hybrid micro–macro BFs combinations had a pronounced effect on concrete workability, often intensifying slump loss. High total fiber content mixes, such as 2A1B and 2A0.5B, recorded extremely low slump values of just 10 mm, indicating severe stiffness likely caused by fiber clustering and poor dispersion. Moderate-dosage hybrids, including 1.5A2B, 1.5A1.5B, and 1.5A1B, achieved slumps between 17 mm and 25 mm, reflecting a more balanced trade-off between reinforcement and fresh mix consistency. Lower-dosage combinations, such as 0.5A2B and 0.5A1.5B, maintained better workability, with slump values ranging from 28 mm to 33 mm. For context, [37] reported that the compacting factor of macro-BF-reinforced mixes was up to 14 % lower than that of plain concrete, with slumps dropping from 220 mm (control) to 50–85 mm at macro BF contents of 0.5–1.5 %. Overall, micro BFs (A) caused more severe slump reduction than macro BFs (B), with the greatest impact observed in high-dosage hybrids. Never the less, certain lower-dosage combinations preserved acceptable workability while potentially enhancing mechanical performance. These results underscore the need to optimize fiber type and dosage, and to consider chemical admixtures such as superplasticizers, to counteract workability loss in aerodrome concrete pavement applications. 3.2.               Flexural Strength (MPa) Flexural strength is a critical property for aerodrome concrete pavements, as they are subjected to heavy aircraft wheel loads and dynamic stresses. The incorporation of hybrid BFs has been explored to enhance the post-crack energy absorption and load-bearing capacity of concrete pavements. This section presents the experimental results on the influence of varying dosages and combinations of micro (A) and macro (B) BFs on the 28-day flexural strength of concrete. The control mix (K) in Fig. 4, without fibers, recorded a flexural strength of 8.8 MPa, providing a baseline for comparison. Every mix with fibers-whether single type or hybrid-showed higher flexural strength than the plain concrete.   Figure 4. Flexural Strength (MPa) against Hybrid Fiber Combination. 3.2.1. Single fiber dosages As shown in Fig. 4, the mixes with only micro BFs (A) generally gained flexural strength with increasing fiber dosage. Strength went up from 8.6 MPa at 0.25 % A (Fig. 5) to a high of 9.9 MPa at 1.5 % A. A slight reduction to 9.5 MPa was observed at 2 % fiber dosage, which may be attributed to reduced fiber dispersion efficiency and localized fiber clustering. The macro-only mixes (B) also beat the control mix. Their strengths ranged from 9.2 MPa at 2 % B up to 9.7 MPa at 1 % B. The ability of macro fibers to bridge cracks, which allows for stress redistribution and improves post-cracking load transmission, is responsible for the improvement. It should be noted that the optimal fiber dosage reported in this study is different from that reported by [38], who found that self-compacting concrete with a flexural strength of 7.06 MPa, residual strength of 2.724 MPa, and impact strength of 4457.44 kN·mm performed best at a BF content of 0.4 %. Such differences are expected because the two studies employed different concrete types, mixture compositions, fiber characteristics, and testing procedures. Hybrid BF combinations, especially the 1.5A0.5B mixture, had the best flexural performance in the current study, demonstrating the impact of fiber hybridization on pavement-grade concrete behavior.   Figure 5. 0.25A micro basalt fiber concrete under bending stresses.       Figure 6. 1.5A0.5B hybrid basalt fiber concrete specimen for flexural strength testing. 3.2.2. Hybrid fiber combinations The highest flexural strength values were achieved with hybrid fiber mixtures, demonstrating the synergistic benefits of combining micro and macro BFs. Mixtures, such as 1.5A1.5B (10.2 MPa), 1.5A0.5B (Fig. 6) (10.4 MPa) , 1A1.5B (10.1 MPa), and 1A1B (10.3 MPa) in Fig. 4, all surpassed the performance of single-fiber systems. This enhancement can be attributed to the complementary roles of micro fibers in controlling microcracks and macro fibers in providing post-crack load transfer. Lower-dosage hybrids, including 0.5A1.5B, 0.5A1B, and 0.5A0.5B, also outperformed the control, with flexural strengths ranging from 9.4 to 9.9 MPa. These results align partially with [39], who reported that optimal improvements in mechanical properties occurred at BF contents between 0.1 % and 0.3 %. Similarly, research [40] observed peak performance in SCC70-85/0.10 specimens, which exhibited a 69.90 % increase in flexural strength and a 23.47 % rise in splitting TS compared to the control. In the present study, optimal performance was achieved at balanced moderate hybrid dosages. The highest flexural strength (10.4 MPa) was recorded for the 1.5A0.5B mix, underscoring the efficiency of micro–macro fiber synergy in enhancing load-carrying capacity. Overall, while both single and hybrid BF systems improved flexural performance, hybrid configurations consistently provided superior results, making them a promising reinforcement strategy for high-performance aerodrome concrete pavements. Enhanced flexural strength directly improves resistance to cracking under repeated aircraft loading, reducing the risk of structural fatigue and extending pavement service life. The combined crack-control and post-crack reinforcement provided by hybrid BFs can minimize foreign object damage by limiting surface spalling and fragment release, which is critical in airfield safety. Furthermore, hybrid fiber systems improve the distribution of loads throughout the concrete matrix. This means slab thickness could potentially be cut down without affecting the durability, which in turn, cuts down on materials. This may contribute to reduced expenses, material consumption and improved sustainability in pavement construction.                                                                                                     4.     Conclusion This study makes it clear: adding BFs – especially when you blend micro and macro types – can really boost the flexural strength of concrete pavements for airports. While single fiber systems (micro or macro) offered measurable improvements over the control mix, hybrid combinations consistently outperformed them due to the complementary functions of the two fiber types: micro BFs effectively controlled microcracking, while macro BFs improved crack bridging and post-crack load transfer. The most notable gain was achieved with the 1.5A0.5B mix, which reached a flexural strength of 10.4 MPa, representing a substantial enhancement over the baseline value of 8.8 MPa. However, excessively high fiber dosages, especially in single-type mixes, showed signs of diminished performance, likely due to fiber balling and reduced workability.                                                                                          5.     Recommendations 1.    For aerodrome pavement applications, hybrid BF combinations with balanced proportions particularly 1.5 % micro BF and 0.5 % macro BF are recommended to maximize flexural performance without compromising workability. 2.    Where mechanical performance is a priority, hybrid fiber systems should be preferred over single fiber additions, as they harness the synergistic benefits of both micro and macro fibers. 3.    Fiber contents above optimal ranges should be avoided to prevent issues such as poor dispersion, fiber clustering, and reduced workability, which can offset strength gains. 4.    Further field-scale studies on full-scale aerodrome pavement slabs are advised to validate laboratory results under actual aircraft loading conditions and environmental exposure.                                                                                                6.      Additional information 1.    The authors state that generative artificial intelligence and artificial intelligence-based technologies were not used; however, ProWritingAid and Grammarly were used only for language editing and proofreading. 2.    The authors received no financial support for the research, authorship, and publication of this article. 3.    The authors declared no potential conflicts of interest concerning the research, authorship, and publication of this article. 10.34910/MCE.143.7 621 hybrid basalt fiber aerodrome pavement flexural strength micro fibers macro fibers high-performance concrete fiber-reinforced concrete https://engstroy.spbstu.ru/article/2026.143.7/

RAR RUS 14308-14308 0009-0001-6253-0088 Moscow State University of Civil Engineering (National Research University) Traore Aboubacar Sidiki sikart37@gmail.com

Moscow, Russian Federation

Methodology for determining water permeability in translucent enclosing structures under realistic conditions Leaks in translucent structures are highly undesirable, as they can damage interior finishes, cause excessive moisture in the structural layers of exterior walls, and other detrimental effects. Currently, in many countries, regulatory requirements for the watertightness of translucent structures are standardized tests that are not contingent upon specific climatic conditions. This article proposes a calculation method for determining the water permeability of translucent structures, particularly wind pressure and precipitation intensity. Subsequently, water permeability tests were conducted on window-type translucent structures to validate the newly developed method’s efficacy under the climatic conditions of Krasnodar, Russia. Laboratory tests employed a total of nine design load combinations, each lasting 10 minutes. As a result of the study, the trans-lucent structure, previously certified as Class R6 according to GOST 33792-2021, exhibited leakage under a pressure differential of 285-420 Pa and a precipitation intensity of 0.38–0.88 l/m2/min. This observation underscores the significance of considering real-world conditions during laboratory testing for the reliability of building structures. Nevertheless, it is crucial to acknowledge that this method for determining the water permeability of translucent structures is applicable to any region worldwide, provided that long-term meteorological observations of horizontal precipitation and wind speed are available. 1.Introduction The raindrops penetration through translucent structures is an undesirable phenomenon that can damage the interior decoration, cause excessive moisture in the structural layers of the outer walls, and negatively affect the health of residents’ buildings [1–6]. In most countries worldwide, there are no methods for determining the required water permeability of translucent facade structures for a specific construction site. The compliance of translucent facade structures with project requirements in terms of water permeability is confirmed through tests conducted according to standard methods that do not model all possible wind and rain combinations for a particular construction region. Translucent facade structures of buildings often occur during operation during rains accompanied by wind. Rain caused by wind occurs when raindrops are deflected by wind [6–7]. The horizontal component of the vertical rain is formed under conditions where the wind directed along the horizontal umbrella with its pressure changes the vertical trajectory of the drops to an inclined one (for a significant portion of the vertical drops) or horizontal immediately. Drops that enter the structure are parts of inclined or horizontal components from the initial (vertical) drops, directed only along the holes and defects in the form of cracks. In this case, due to the pressure drop between the external pressure and the pressure in the chamber, the droplets enter through the holes [8–11]. Currently, there are three main groups of methods for assessing the amount of rainfall that falls on a vertical enclosure during rain with wind: Direct empirical methods based on the processing of multi-year-old specialized meteorological observations of rain parameters in a specific climatic region [12–13]. This method of determining rainfall parameters is the most accurate, but its practical application is currently limited due to the requirement for expensive meteorological equipment that continuously records readings in automatic mode. Semi-empirical methods, which adapt standard meteorological observations to solve problems of determining rainfall intensity on vertical facade surfaces, have long been the most common in practice and are incorporated into regulatory documents [14–17]. Numerical methods based on CFD modelling, which describe wind flow using the Navier–Stokes equation [18–20], have limited practical application due to their labor-intensive calculations. The method for assessing the water permissibility of translucent structures planned in this work differs from others [14–17] in that it considers all possible design situations characteristic of a specific construction region. Calculated values for rainfall and pressure intensity before testing structures are combined to identify the worst operating condition. The developed methodology for assessing the water permeability of translucent structures also takes into account the duration of wind pressure and its abrupt changes. The purpose of this study is to develop theoretical foundations and methods for determining the permeability of translucent facade structures under the combined action of wind loads and atmospheric precipitation. To achieve this goal, the following tasks will be solved: Scientific justification of calculated combinations of wind loads and atmospheric precipitation to determine the water resistance limit of translucent facade structures. Experimental studies of the mechanism of water permeability of translucent facade structures of window types under the influence of rain and wind. 2.Methods[1] A new approach to determining the parameters for laboratory testing of translucent enclosure structures for water permeability is proposed. This method relies on using climate data on vertical precipitation intensity and wind speed during rain, the relationship between horizontal precipitation intensity and wind pressure is determined. Based on known relationships [21], the rainfall intensity and required water flow rate during testing are determined: , (1) where Vz is the wind speed at height z (m/s), rh the amount of horizontal precipitation (mm/min), RAF is the rain transmittance coefficient; DRF is the precipitation coefficient of rain. The coefficient DRF is determined by Equation (2) according to the relationship defined in [22]: , (2) where D50 is the average diameter of a raindrop (mm). The average drop diameter can be determined according to [23]: (3) The wind pressure could be determined using a well-known Bernoulli’s law of conservation of kinetic energy (4) [24]: , 4) where ρ is the air density (kg/m3), V10 is the wind speed, m/s, at a height of 10 m above the ground surface. The intensity of the horizontal component of precipitation can be determined by multiplying the vertical precipitation values by cos 45º, and subsequently converting them to millimeters per minute (mm/min). To convert hourly values of horizontal precipitation intensity to 10-minute values, the Linsley formula (5) [25] can be used. , 5) where i(t) is the unknown short-term precipitation intensity (mm/min), t is the given interval (s), ih is the hourly precipitation intensity (mm/h). The following load combinations should be considered: C1: light rain with light wind; C2: moderate rain with medium wind; C3: heavy rain with strong wind; C4: light rain with medium wind; C5: moderate rain with strong wind; C6: heavy rain with light wind; C7: light rain with strong wind; C8: moderate rain with light wind; C9: heavy rain with medium wind; t = 10 minutes for any of the specified load combinations. As the intensities of horizontal precipitation components have been accounted for, it is not necessary to tilt the nozzles at a 45-degree angle to simulate the oblique effect of raindrops. To ensure that the entire surface of the structure is adequately covered with water, it is recommended to install at least three rows of nozzles. 2.1.Application of the Proposed Assessment Methodology for Krasnodar City (Russia) Based on the data from The Federal State Budgetary Institution “Voeikov Main Geophysical Observatory” (FGBI “MGO”) (Table 1), meteorological data for the 50th observation period (1964–2024) were analyzed for several Russian cities, including Krasnodar. Table 1. Initial meteorological data for Krasnodar city (fragment). Date The beginning The Ending Duration (min) Rain amount (mm) Wind speed max (m/s) Rain intensity (mm/min) 1977.02.06:4-00 1977.02.06:18.00 1977.02.06:20.10 130 6.2 3 0.05 1977.02.28:16-00 1977.02.28: 0.00 1977.02.28: 3.00 180 10.1 7 0.06 1977.03.07:16-00 1977.03.07:20.50 1977.03.07:21.00 10 5.8 8 0.58 1977.03.19:4-00 1977.03.19:15.20 1977.03.19:17.10 110 9.6 6 0.09 1977.03.24:19-00 1977.03.24:22.40 1977.03.24:23.00 20 7.2 3 0.36 1977.03.25:4-00 1977.03.25:15.30 1977.03.25:17.10 100 11.2 7 0.11 1977.04.07:16-00 1977.04.07: 4.20 1977.04.07: 6.00 100 7.6 3 0.08 1977.04.13:16-00 1977.04.13: 3.00 1977.04.13: 3.50 50 14.8 3 0.3 1977.04.18:4-00 1977.04.18:18.00 1977.04.18:21.00 180 15.7 0 0.09 1977.05.25:16-00 1977.05.25: 2.50 1977.05.25: 3.00 10 11.7 10 1.17 1977.06.07:4-00 1977.06.07:18.00 1977.06.07:21.00 180 5.3 0 0.03 1977.06.16:19-00 1977.06.16:12.18 1977.06.16:12.42 24 10.3 3 0.43 1977.06.24:16-00 1977.06.24:17.10 1977.06.24:17.18 8 31.2 3 3.9 1977.07.02:16-00 1977.07.02: 9.08 1977.07.02: 9.10 2 31.4 3 15.7 1977.07.04:16-00 1977.07.04:10.05 1977.07.04:10.30 25 5.6 9 0.22   Figure 1. Meteorological data for the 50th observation period, spanning from 1964 to 2024, for Krasnodar city (Russia). While Fig. 1 shows the graph of the relationship between rain intensity and wind speed for the period (1964-2024) taking into account all events, Table 1 shows a subset of the events shown in Fig. 1. Analyzing the data presented in Table 1, it becomes evident that precipitation events exhibit varying durations. Consequently, it is imperative to process the data such that all precipitation events have a duration of less than or equal to 10 minutes. However, the meteorological data highlighted in yellow does not necessitate processing, as these precipitation events also have a duration of less than or equal to 10 minutes. Table 2 presents a simplified version of Table 1, incorporating the presented precipitation intensity values. The precipitation intensity values were averaged to 10-minute values, contingent upon the duration variation, as per Equation (5) [25]. Table 2. Processed values of horizontal precipitation and wind speed for Krasnodar city (fragment). Duration (min) Rain amount (mm) Wind speed max (m/s) Rain intensity mm/min 10 1.1 3 0.11 10 1.3 7 0.13 10 5.8 8 0.58 10 1.9 6 0.19 10 7.64 3 0.76 10 2.33 7 0.23 10 1.70 3 0.17 10 6.37 3 0.64 10 1.91 0 0.19 10 11.70 10 1.17 10 0.64 0 0.06 10 9.13 3 0.91 10 39.00 3 3.90 10 157.00 3 15.70 10 4.67 9 0.47   Next, it is imperative to exclude from the table of provided values (Table 2) rows where wind speed is zero. These speeds must be converted to pressure using the formula (4). Then, prior to plotting the relationship between typical horizontal precipitations and their corresponding wind pressures (Fig. 2), it is necessary to average the precipitation intensity values corresponding to the given wind pressure value. Figure 2. Relationship between typical horizontal precipitations and their corresponding wind pressures. From this point, we must graphically select the maxima from the set of points in Fig. 2. These points will be used to determine the most suitable function for the relationship between horizontal precipitation and wind pressure (Fig. 3). Subsequently, regression analysis will be employed to evaluate the appropriateness of the parameters under consideration. Furthermore, we will conduct a separate regression analysis of the distribution of each parameter (Fig. 4, 5), specifically the probability distribution of horizontal precipitation intensity and wind pressure with a return period of up to 100 years. Figure 3. The correlation between typical horizontal precipitation and their corresponding wind pressures. Figure 4. Probability of wind pressure distribution. Figure 5. Probability distribution of horizontal precipitation intensity. 2.2.Watertightness Test Watertightness tests are characterized by evaluating a component’s ability to prevent water ingress using a combination of water spray and pressure differentials. During this laboratory test, to accurately replicate real-world climatic conditions, it is imperative to incorporate wind gusts, which manifest as abrupt fluctuations in wind pressure within a three-second interval following the transition between two load configurations. Test materials: A. Single-leaf aluminum window (1900 × 1010 mm) (Fig. 6.a)) – design previously confirmed to class R6 (as per Table B.3 of GOST 33792-2021). B. Water spray nozzles with a flow rate of 1 l/min (Fig. 6.b)). a)   b) Figure 6. a) General view of the test bench, b) Sprinkler device. 3.Results and Discussion Table 3. Test parameters. Return period i (mm/min) or (l/m2/min) Р (Pa) – P 2 years 0.50 0.88 186 5 years 0.80 0.38 285 15 years 0.93 0.14 371 30 years 0.97 0.08 399 50 years 0.98 0.05 411 100 years 0.99 0.03 420   When selecting test parameters from the Table 3, the minimum, average, and maximum wind pressure values ​​are taken into account, along with their corresponding rainfall intensities. Combination C1: Air pressure P = 0–186 Pa, water flow rate i = 0.03 l/m²/min, duration t = 10 min. Observation: No leakage Conclusion: The absence of leaks is likely attributable to the low wind pressure and low water flow rate. Combination C2: Air pressure P = 186–285 Pa, water flow rate i = 0.38 l/m²/min, duration t = 10 min. Observation: No leakage Conclusion: Although the applied wind pressure and water flow rate are significant, they are insufficient to cause leakage for this window. Combination C3: Air pressure P = 285–420 Pa, water flow rate i = 0.88 l/m²/min, duration t = 10 min. Observation: Leaks in the lower left corner and under the hinges (upper right corner) starting from the 4th minute (Fig. 7).   Figure 7. Leak locations. Conclusion: The tested window unit is not fully water-resistant under realistic conditions. Combination C4: Air pressure P = 186–285 Pa, water flow rate i = 0.03 l/m²/min, duration t = 10 min. Observation: No leakage Conclusion: The absence of leakage is most likely attributed to the limited quantity of water, which hinders its uniform distribution across the surface of the tested unit. Combination C5: Air pressure P = 285–420 Pa, water flow rate i = 0.38 l/m²/min, duration t = 10 min. Observation: Leakage in the lower left corner and under the hinges (upper right corner) from the 4th minute (Fig. 7). Conclusion: The tested window unit is not fully water-resistant under realistic conditions. Combination C6: Air pressure P = 0–186 Pa, water flow rate i = 0.88 l/m²/min, duration t = 10 min. Observation: No leakage Conclusion: The tests unit appears to be resilient to this combination. Combination C7: Air pressure P = 285–420 Pa, water flow rate i = 0.03 l/m²/min, duration t = 10 min. Observation: No leakage Conclusion: Despite the substantial wind pressure, there is no leakage due to the limited volume of water, which prevents its uniform distribution across the test unit’s surface. Combination C8: Air pressure P = 0–186 Pa, water flow rate i = 0.38 l/m²/min, duration t = 10 min. Observation: No leakage Conclusion: The absence of leaks is primarily attributed to the relatively low wind pressure intensity. Combination C9: Air pressure P = 186–285 Pa, water flow rate i = 0.88 l/m2/min, duration t = 10 min. Observation: No leakage Conclusion: The tests unit appears to be resilient to this combination. This study overlaps with the work [27] where three different window designs were tested for water permeability under static and realistic dynamic air pressures. As a result of the above work, the windows failed at lower mean pressure conditions during the realistic fluctuating pressure testing (261 Pa) than during the static pressure tests (510 Pa). On the other hand, this study and the work [28] share the same limitations in calibrating water flow during artificial rain simulation. Rain modeling in laboratory tests (rainfall simulators) still struggles to replicate natural rain. In practical settings, rain intensity fluctuates, whereas laboratory conditions typically result in constant water flow. 4.Conclusion Consequently, given that the translucent enclosing structure, previously confirmed by Class R6 (as per Table B.3 of GOST 33792-2021, with a water resistance limit of approximately 450 Pa), leaks at a pressure differential of 285–420 Pa and an intensity of 0.38–0.88 l/m2/min, it is evident that considering realistic conditions during laboratory tests is crucial for the reliability of building structures. Thus, while standards remain essentially standardized quality control and administrative compliance tools, this methodology for evaluating the water tightness of facades, integrating real climatic conditions, makes it possible to adapt the performance of buildings to local risks, optimize their durability and ensure increased energy efficiency by avoiding oversizing or underperformance.   [1] Use of artificial intelligence: Apple Intelligence version iOS 18.4 was used to correct grammatical and stylistic errors. The authors confirm that the scientific content, data analysis, and conclusions were completed independently. 10.34910/MCE.143.8 692.23:692.82 translucent enclosing structures wind-driven rain wind pressure laboratory tests water permeability https://engstroy.spbstu.ru/article/2026.143.8/

RAR RUS 14309-14309 University of Babylon Hamdy Hasanien Sameer hasanien.hamdy.engh374@student.uobabylon.edu.iq

Babylon, Iraq

University of Babylon Kadhum Mohammed Mansour eng..mohammed.mansour@uobabylon.edu.iq

Babylon, Iraq

University of Babylon Alwash Nameer A nameer_alwash@yahoo.com

Babylon, Iraq

Burning effect on physical characteristics of high-strength lightweight concrete T-beam repaired by SIFCON The purpose of this research is to investigate the performance of high-strength lightweight cement concrete under extreme high temperature (fire) conditions. Lightweight expanded clay aggregate was used as aggregate for the reference mixture. An important difference from previous experiments was that the fire-damaged T-beams were covered with a layer of slurry infiltrated fiber concrete (SIFCON) with 15 and 30 mm thickness at a post-development stage. In addition to the standard tests, this study focused on the effects of the exposure of the beams to a burning flame for 30 min. The temperature distribution inside the T-beam's cross section was measured by installing thermocouples at strategic points. All materials used in this study were analyzed for their physical and chemical properties. Four concrete beam samples were examined in three phases (baseline “control,” fire test, and SIFCON reinforcing). Several parameters, including maximum load capacity and corresponding displacement “deflection,” ductility index, cracking load, initial and secant stiffness, and energy absorption, served as a basis for comparison between the samples. Compared to the damaged samples, the reinforced beams showed significant improvement in the experimental test results conducted in this study. Furthermore, they are as good as or better than the undamaged (reference) T-beams in all parameters except energy absorption. Further research and efforts are needed to resolve this problem. 1.Introduction Lightweight concrete (LWC) is becoming increasingly popular in the construction of new buildings due to its various advantages, including a reduction in the required width and depth of the building's foundation, caused by the low density of its load-bearing elements [1]. Due to the increased air voids content, this type of concrete offers a number of advantages, including a better strength-to-weight ratio, increased tensile strength and less thermal expansion. The production of LWC has developed rapidly. These days, this concrete may be found in a wide range of densities, from low-density concrete used in industries such as block manufacture (1200 kg/m3), to high-density concrete, which can reach up to 2000 kg/m3 and has a compressive strength of up to 100 MPa [2, 3]. The effectiveness of concrete reinforcement with fiber has been proven since its strength and deformation characteristics increase [4, 5]. In the event of a fire, the concrete is exposed to temperatures well above its normal operating range, causing it to lose properties such as compressive strength and ductility and to experience an increase in internal stress caused by vapor pressure in the pores, resulting in formation of cracks of varying sizes and lengths. Dehydration of calcium hydroxide occurs at high temperatures (550 °C), at which point aggregates begin to deteriorate. Mechanical properties (stiffness and compressive strength) of reinforced concrete (RC) deteriorate significantly at higher temperatures (700 °C and above) due to the decomposition of binding components like the calcium silicate hydrate (C-S-H) in RC [6]. As a result, without reinforcement, the structural components' capacity cannot support both dead and live loads [6, 7]. The only practical method for rebuilding structural integrity would be the replacement of fire-damaged components. To repair them, many factors need to be properly considered, including the component's functions, cost, duration, repair materials, shape, and size of the damage. Despite the fact that numerous studies have already been conducted on the structural repair of RC [2, 7, 8], not much has been done to repair fire-damaged infrastructure. For instance, the effectiveness of T-beams restored after being exposed to (simulated) heat at high temperatures was studied. Four T-beams were heated to a high temperature according to ISO-834 [9], and then the damaged T-beam were repaired with recently cast-in-place concrete (for research purposes). Two-point loading bending tests were used to measure the ultimate strength and stiffness of the restored and reference T-beams. The majority of restored T-beams, according to the researchers, either returned to their prior performance or even proved to be better than reference T-beams [10, 11]. A flowing cement mortar with high cementitious content or slurry infiltrated fiber concrete called SIFCON matrix, lacks coarse particles. It could contain fine- or coarse-grained sand, which is considerably different from the concrete used in fiber-reinforced concrete (FRC) [12]. As a result, SIFCON assembly is different from FRC assembly. By combining the fiber with brand-new concrete, FRC is created. While the cement slurry is added to the fiber in the mold after the SIFCON has been filled to the desired level by replacing the fibers in the molds. When necessary, vibration is used to ensure the slurry penetration into the fiber network [13–15]. High-performance fiber-reinforced cementitious composite (HPFRCC) is another name for SIFCON. The HPFRCC typically has a small number of fibers. The higher volume of fibers would lead to multiple cracks that follow the first crack, in an opposite manner to low volume of fibers, which is only accompanied by a single crack. Consequently, an increase in strength takes place in the concrete with higher volume of fibers and this takes place parallel with the cracking process in a way similar to strain hardening. Finally, failure is localized in a single crack and the concrete experiences softening [16]. Because of the same rigidity and thermal deformation as RC, SIFCON is an excellent repair material. Consequently, SIFCON is frequently used to fix prestressed concrete components like T-beams [17]. It is also used in buildings designed to withstand the impact of explosions. The SIFCON has excellent flexural, ductility, and compressive strength characteristics. In addition, SIFCON has demonstrated outstanding resilience to building impact loads. SIFCON was used to produce a variety of prefabricated parts including slabs, tunnels, and pipe sections [18]. To increase the effectiveness of the SIFCON, chemical and mineral additives including superplasticizer, fly ash, and silica fume can be added to the slurry. To effectively penetrate the slurry into the fiber bed, vibration is frequently needed [19, 20]. SIFCON has excellent mechanical qualities, as determined in scientific study, higher tensile strength, higher compression, and shear strength, and better ductility and energy absorption properties [21, 22]. These qualities are impacted by several elements, including the cement slurry's strength characteristics, the thread holding the SIFCON together, the method of fiber placement and alignment, and the fiber composition and properties [23]. This study intends to examine how the reduction of high-strength lightweight concrete (HSLWC) T-beams with a thin U-shaped SIFCON jacket affects their performance after exposure to fire. The impetus for this study arose from the necessity of in depth investigating the design and use of SIFCON thin jackets for reinforcing or repairing burnt areas. The effect of various factors, such as SIFCON jacket thickness and fire duration on the functionality of restored HSLWC T-beams, needs to be studied [24–26]. 2.Methods The research strategy may be divided into two separate parts. The initial phase of this research involves selection, preparation and testing the raw materials for their physical and chemical properties. Lightweight aggregate concrete (LWAC) was produced in the same way as high strength concrete grade as part of a larger structural LWC program. Like the HSLWC, its resulted compressive strength was 65.5 MPa. To create stronger LWCs, lightweight expanded clay aggregate (LECA) was used. Currently, there is a lack of well-defined criteria for determining the appropriate ratios of LWAC components in mixtures. Since the use of any kind of lightweight aggregate requires experimental mixes to attain the appropriate strength and workability, many trial mixes were conducted for this investigation. The selected materials were combined using the ideal mixing ratio as shown in Fig. 4. The wooden molds were then used to cast the T-beam samples. After 24 hours samples were removed from the casting molds. The specified curing periods for the casting samples and T-beam experiments were followed. Thus, when it reached the required age of 56 days, it was exposed to fire for 30 min. After the T-beams were burned, the third stage involved repairing and reinforcing them with a U-shaped SIFCON jackets with 15 and 30 mm thickness as well as preparing for testing exposed (and unrepaired) concrete samples and HSLWC T-beams. 2.1.Material Properties Because of its composite nature, the qualities of the individual components – cement, coarse aggregate, fine aggregate, water, and admixtures – must be tested before construction begins. Standard Portland cement was used for this study. It was produced in Iraq under the trade name “Mass” and purchased from nearby markets. The primary concrete mix included natural sand from a nearby source that was brought in Karbala as fine aggregate. Sand used in concrete mixes must be small enough to pass a 4.75 mm filter in order to prevent clogging of the thick steel fibers. All SIFCON mixes require fine sand that has been sieved (with 1.18 mm sieve) to filter out the coarser particles before it can be used in the manufacture of SIFCON for experimental work. Zone 2 of the IOS.45/1984 “Aggregates from Natural Sources for Concrete and Construction” was followed. The LECA used was produced in Iran and is characterized by a consistent particle size ranging from 0.475 to 1 cm. Porous ceramic materials with homogenous, fine, closed-cell pores as well as securely sintered, robust outer surfaces are characteristic of this type of lightweight aggregate. For LECA production, clay mineral raw materials are burnt in rotary furnace at 1100–1200 °C, which greatly increases the particle volume. In this study, silica fume, which is frequently marketed as MasterRoc® MS 610 or BASF silica fume, was used as a replacement material for cement to create both HSLWC and SIFCON mixes. Cement paste's microstructure is improved by silica fume, increasing its resistance to outside forces. All concrete mixes, including the high strength mix and SIFCON, were made with potable water, and the samples were dried in water that contained no salts, turbidity, or organic matter. In addition, the SIFCON mortar and the third-generation superplasticizer (Master Glenium 54) used in this experiment significantly reduced the amount of water needed for the construction. A proportion of 3.7 % by weight of cement was used to create SIFCON mortar. Additionally, as illustrated in Fig. 1, hooked steel fiber from the ATLAS firm was used to create the SIFCON jacket. The fiber has hooked end, measuring 30 mm in length, 0.5 mm in diameter, 60 in aspect ratio, and 1100 MPa in tensile strength. The used reinforcing steel bars' mechanical properties are shown in Table 1. Figure 1. Steel fiber geometry with and without magnification. Table 1. Specifications and test results of steel reinforcing bars. Nominal Bar Diameter (mm) Actual Bar Diameter (mm) Yield Stress Fy (MPa) Ultimate strength Fu (MPa) 8 7.95 550 678 10 10 581 724 12 11.96 663 828 2.2.Samples Manufacture and Setup for Testing HSLWC T-beams were studied in increments of 80 × 250 mm for the flange, 100 × 170 mm for the web, and 1500 mm length. Additionally, for longitudinal reinforcement, details of deformed bar reinforcements are shown in Fig. 2. Reinforcing steel bars are shown in their pre-cast form in Fig. 3. Following extensive trials with different proportions of high-strength concrete and SIFCON, the final mix design is shown in Figs. 4 and 5. Each beam's exposure conditions and configuration were labelled in this study, as shown in Table 2, to simplify the process. Figure 2. Main section geometry and typical HSLWC T-beam cross-section (mm).   Figure 3. Casting of HSLWC and SIFCON jacket for T-beam samples. Figure 4. Mix design of HSLWC. Figure 5. Mix design of SIFCON. Table 2. Summary of HSLWC T-beam test sample. Grade of concrete T-beam T-beam cover (mm) SIFCON cover (mm) T-beams term Fire time (min) HSLWC T-Beams 10 None H-C0 0 H-F30 30 15 H-F30-S2 30 30 H-F30-S3 30 2.3.Fire Loading Protocols A brick furnace was made on site to expose the prepared concrete T-beams to high temperatures, and it was equipped with thermocouples sensors and portable data acquisition devices to record the thermal variation over time as shown in Fig. 6. Samples were exposed to fire in the furnace after being HSLWC T-beams for 56 days. The HSLWC T-beam samples were burned in the furnace in accordance with the ISO 834 “Fire resistance tests – Elements of building construction” standard. The highest temperature, for which the furnace was designed, reached 1200 °C. The furnace temperature was controlled according to the ISO curve. However, it should be noted that the firing rate used was substantially lower than that required by ISO 834. The fire load lasted for about 30 min, which was sufficient to bring the reinforced HSLWC T-beams to the required temperature. Every 2 min inspections were made through the furnace inspection ports to note any significant alterations to the sample, such as the emergence of fire-induced spalling. Once the T-beam sample had cooled completely to room temperature (approximately 25 °C), in-depth measurements of the cracking and spalling intensity were made. The thermocouple in the furnace was connected to the computer via the real-time-temperature curve, which was programmed using Excel and enabled real-time temperature values to be recorded. At the end of the combustion operation, the time-temperature curve's final form was saved along with the heat and timing records on the computer. The fire was directed at the T-beam sample underside, two lateral faces, and bottom. The experiment was carried out in a 35 °C setting. The duration of the fire load on these three sides of the HSLWC T-beam samples varied. At several locations along the T-beam sample, readings were taken every 5 sec. The T-beam was cooled after it was taken out of the furnace and exposed to fire. When the burning time was over, a foam extinguisher was used to quickly extinguish the flames on the samples. This experiment simulated the cooling process that can be applied in real life. Figure 6. Visual and physical adjustments of the burning furnace layouts. 2.4.Repairing Methodology After burning, the damaged HSLWC T-beams were subjected to the reinforcing methodology in order to reuse it with full efficiency and safety. A specially designed wooden mold was used to prepare the garment. The same-shaped and larger-sized molds were used to cast the SIFCON jacket with three faces. To cast jackets with 15 and 30 mm thickness that were applied at the bottom and two lateral sides (U-shaped jackets) as shown in Fig. 7, this mold had a space between its surface and the sample. Fragmented and collapsing T-beam samples that had been damaged by fire were excluded from the equation before the T-beams could be further reinforced. The damaged part was removed and then replaced with SIFCON. In order to achieve the required volume fraction, molds were filled with multilayers of steel fibers with hooked ends. The previously mentioned SIFCON slurry mix was used to penetrate each layer. The fibers were spread evenly and great care was taken to ensure that no clogs occurred during the infiltration process.     Figure .7 Steps taken for casting and repairing the SIFCON jacket. 2.5.Steps for Casting SIFCON Jacket T-beams that have been damaged by fire shouldn't have any microcracks on their surfaces. T-beams with 10–15 mm thickness had their severely damaged areas removed. The surface of sample was properly cleansed with water and compressed air to remove any dust. T-beams that were damaged in the fire had their surfaces roughened using a special tool to improve binding with the SIFCON jacket. The T-beam surfaces were coated with SBR bonding agent layer to obtain excellent bond strength. Before placing the steel fiber of the jacket's inner layer, the mold was greased. T-beam was placed into the mold on top of the bottom layer and the side of the jacket poured in. Reinforced T-beams were cast, removed from molds after 24 h, and allowed to dry in damp burlap for 28 days. 2.6.Techniques for Applying Load Prior to testing, cracks in the T-beam sample were cleaned and coated with white simulation, as usual, in order to make crack propagation and inspection clearer. After installing the linear variable differential transformers (LVDTs) in their designated spots, we were able to prepare the T-beam sample for testing. The tested HSLWC T-beam was cut into thirds and subjected to nearly uniform load, due to the steel T-beam used to apply and split the load at two different points. The load dispersion between the two points was 350 mm. The supports were designed to act as a hinge support at one end and a roller support at the other. The bearing plates were made of 210 × 75 × 20 mm hardened steel to sustain the applied load and prevent crushing at the contact point of the sample body, which could affect the results of the test. T-beams were tested with monotonically increasing loads until failure, and five LVDTs were placed at various locations along the T-beam sample to measure its displacement. The first LVDT was placed on the bottom surface of the T-beam's midpoint, and the other two were placed under the two-point load. The other two LVDTs along the top and bottom fibers measured displacement changes at a distance of 20 cm, yielding the mid-span curvature. The position of sensors and mechanical loads are shown in Fig. 8.   Figure 8. Position of sensors and mechanical loads. 3.Result and Discussion The results of the laboratory experiments are presented and illustrated in detail in this section. A number of indices, including the load carrying capacity, the cracking load, the mid-span displacement that corresponds to the maximum load carrying capacity, the initial and secant stiffness, and the absorption energy, are used to compare the effects of fire exposure duration and the effects of reinforcement with different thickness of SIFCON jacket layer. Shifts in Temperature over Time Until the required temperature was reached, the furnace temperature was within 8 % of the ISO 834 standard fire curve for 30 min. After this point, it becomes clear that the curve values are beginning to diverge. The strength of the concrete at the bottom of the sample was expected to decrease by a greater amount than in the T-beam sample's deeper areas since the peak temperature of the sample bottom surface was about 750 °C. T-beam bottom TC1 was substantially hotter than TC4, which was placed 100 mm away from the bottom surface due to the poor heat conductivity of concrete. Due to water evaporation in the concrete and consequent heat loss, temperatures of TC3 and TC4 at the mid-depth of the T-beam were held between 100 and 200 °C for 30 min. There was a significant temperature gradient, with temperatures decreasing as one moved from the bottom to the top of the T-beam. Concrete strength decreased significantly near TC3 and TC4 compared to normal concrete temperature H-C-0 as shown in Fig. 9. Moreover, the highest temperatures of TC1 and TC2, which were higher than TC3, were 750 and 582 °C, respectively. The location and designation of the thermocouples are listed in Table 3. Temperatures in the fire-exposed areas reached well over 800 °C, with a dramatic temperature decrease from the outer surface to the inner core of the concrete structure. Core temperatures in the concrete ranged from 120 to 210 °C. The outer layer of concrete exposed to the fire was badly damaged and had to be removed, but there was a workable concrete core inside. Figure 9. Temperature-time curves for a 30-minute fire, in accordance with the ISO-834 standard. Table 3. The position and naming of the thermocouples. Thermocouple Type Distance from exposed surface (mm) Highest temperature recorded (°C) TC1 K 0 739.7 TC2 K 25 489.2 TC3 K 50 198.9 TC4 K 100 126   Variation in Look and Hue of a Burned T-beam Sample HSLWC T-beams behave in such a way that a crack forms in the bending zone about 8 cm to the left of the load applying point, and then multiple cracks form to the left of the first crack, all of which move vertically. Finally, diagonal cracks form and propagate along the distance between the supporting and load applying points. Fire damage increases the inclination angle of diagonal cracks, shortens crack extensions, and reduces the total number of cracks as shown in Fig. 10. Prior to the formation of the diagonal cracks, several small cracks appeared in the shear zone and at a lower rate in bending zone as well. HSLWC behaved much more sensitive to combustion where spalling was observed after 650 °C combustion. It was difficult for the vapor contained in the HSLWC particles to escape through the surface, resulting in spalling of the concrete. The rate of heat transfer to the core and reinforcement increases because spalling quickly removes the surface layers of concrete and exposes the core to direct flame. Figure 10. Cracks pattern of HSLWC T-beams after burning. Therefore, it is recommended to increase the concrete cover, which will delay the transferring of heat to the reinforcement and prevent spalling. Typical Crack Patterns and Load-Displacement Behaviors Unreinforced T-beam samples showed early onset of flexural cracking near the T-beam's mid-span, with the earliest crack appearing in the bending zone around 10 cm to the left of the load application point. The vertical fracture first propagated outward from its origin on the left, and then a diagonal crack emerged and grew along the distance between the load application point and its support. As can be seen in Fig. 11, after the fire, the inclination angle of diagonal cracks increases, the cracks extend less, and there are fewer cracks overall. When the aspect ratio a/d is greater than 2.5, a diagonal crack originating at the top of a flexural crack causes the crack to propagate and eventually leads to failure. The results show that a loss of about 40 % in concrete cover (spalling and damage) occurs when the duration of fire exposure is about 30 min, which may be extrapolated to influence the total burning time. The results show that reinforcing samples with a 15 and 30 mm thick SIFCON jacket layer increased performance by 1.39 and 1.54 times, respectively, after 30 min of fire exposure, compared to unreinforced (fire-damaged) samples. Fig. 12 shows the relationship between the load and displacement for T-beams that were reinforced using different methods. Fig. 13 shows the results in the form of a bar chart showing the differences between the values. Figure 11. Comparison of pre- and post-fire crack patterns in HSLWC T-beams. Figure 12. HSLWC T-load-deflection T-beam's curve at its mid-span.   Figure 13. Cracking load capacity values. Fig. 14 shows the fracture pattern before reinforcement in a failing T-beam. After 30 min of fire exposure, the results showed that only T-beams with a cover thickness of 15 mm showed a minor improvement, regardless of how much SIFCON was added to the T-beam. Changing the SIFCON thickness resulted in a noticeable improvement for 30 mm-covered T-beams, with a 1.45 and 1.53 times increase in the strength of damaged T-beams. Figure 14. Cracks pattern of T-beams. Initial and Secant Stiffness T-beam stiffness is measured in terms of the force required to create a single unit of T-beam deflection. Fig. 15 shows that initial stiffness after burning at different exposure durations decrease drastically with increasing fire temperature, and this loss in stiffness is accompanied by a decrease in load bearing capacity. After 30 min of burning at temperatures above 650 °C, the secant stiffness was only about 75 % according to concrete cover uses. SIFCON jacket repairs result in a greater stiffness value for samples with 30 mm jacket compared to the samples with 15 mm jacket. As shown in Table 4, the stiffness value of repaired samples is always greater than that of the reference sample. Table 4. Secant and initial stiffness. Specimen Sym. Secant stiffness Initial stiffness Pu Δu Ks KN/mm Residual Ks % Pu Δy Kin KN/mm Residual Kin% H-C-0 270 15.4 17.57 ---- 270 7.65 35.29 ---- H-F30 234 12.9 18.18 103.47 234 9.91 23.59 66.85 H-F30-S2 326 16.9 19.25 109.56 326 6.48 50.29 142.5 H-F30-S3 359 16.6 21.62 123.05 359 10.5 34.19 96.88 Figure 15. Secant and initial stiffness. As mentioned before, due to the degradation in chemical and mechanical properties of concrete and steel reinforcement, the load bearing capacity of the T-beam samples decreased after fire exposure. This in turn led to a decrease in the difference between yielding point and failure point values and a deterioration in the sample ability to absorb applied loads with less deformation. Energy Absorption The ability of a concrete T-beam to withstand loads without breaking is one indicator of its energy absorption capacity. The area under the load-displacement curve up to the point of maximum load is the metric used to describe this capacity. Previous studies have shown that concrete's ability to absorb shock waves is the best indicator of how well it will endure fires and other forms of extreme damage, such as accidents or terrorist attacks. The results showed that after 30 min of fire exposure, the absorption energy of damaged concrete T-beams was roughly 63 % lower compared to undamaged (reference) T-beam. However, when damaged T-beams were reinforced with 15 and 30 mm SFICON jacket, the energy absorption improved by about 55.8 and 52.6 %, compared to the damaged T-beams. Table 5 and Fig. 16 show energy absorption capacity of T-beam before, during fire exposure and after reinforcement. Table 5. Energy absorption capacity. Specimen sym. Energy absorption capacity (KN.mm) H-C-0 2973.8 H-F30 1872.7 H-F30-S2 4236.6 H-F30-S3 3952.8   Figure 16. Absorption of energy before and after fire exposure. Ductility Index In general, a high ductility index indicates that a structural member can withstand considerable deformations before failure. T-beam testing data show that flame heating has no effect on the ductility index. Moreover, a slight increase was recorded. An increase of 29.85 % was observed in T-beams after 30 min of fire exposure. The values of ductility index for the tested T-beam samples before and after burning ranged from 1.3 to 2.61. As shown in Fig. 17 and Table 6, the ductility index of the reinforced T-beams is around 64.7 % higher than that of the unreinforced beams compared to the undamaged (reference) T-beam. For T-beams with ductility indices ranging from 3 to 5, appropriate ductility is considered essential, particularly in the fields of seismic design and moment redistribution. Figure 17. Ductility index. Table 6. Ductility index of HSLWC T-beam samples before and after fire exposure. Specimen Yield deflection Δy in mm Ultimate deflection Δu in mm Ductility index sym. H-C-0 7.65 15.37 2.01 H-F30 9.91 12.86 1.3 H-F30-S2 6.48 16.93 2.61 H-F30-S3 10.51 16.62 1.58 4.Conclusion A temperature difference of about 33.87 % was observed between the midpoint and the periphery of the T-beam cross section. While between the points where the steel bars were located and the center of the concrete, the temperature difference was 74.24 %. Compared to the reference T-beam, the concrete T-beams that subjected to 30 min fire had cracking load (service load) reduction in a range of 54–67 %. On the other hand, reinforced fire-damaged T-beams with SIFCON jacket layer resulted in an improvement that was superior to the reference T-beam and varied between 2.98 and 3.27 times for 15 mm of jacket thickness and 2.96 and 5.73 times for 30 mm of jacket thickness. For HSLWC T-beams, the T-beams, damaged by fire for 30 min, showed a significant decrease in load capacity of about 34.1 %, in comparison to the undamaged (reference) T-beam. The experimental results showed that 30 min fire damage has a major impact on the ductility. In contrast to the unreinforced (damage) T-beam, reinforced T-beam increased its ductility index by roughly 99 and 21.5 % for T-beams with 15 and 30 mm SIFCON jacket, respectively. After 30 min of fire exposure, the absorption of energy of damaged T-beams decreased by about 54 and 56 %, respectively, when compared to the undamaged (reference) T-beam. On the other hand, compared to the damaged T-beams, reinforced damaged T-beams with 15 and 30 mm SIFCON jacket improved energy absorption by about 17.9 and 38.4 % respectively. The experiments showed that firing samples for 30 minutes reduced the initial stiffness values by about 26 %. The stiffness of the reinforced members is expected to be between 3 and 3.5 times higher than that of the damaged members before reinforcement, and 2.25 times higher than that of the undamaged (reference) T-beam. 10.34910/MCE.143.9 624 high-strength lightweight aggregate concrete fire damaged concrete LECA repair material SIFCON https://engstroy.spbstu.ru/article/2026.143.9/

RAR RUS 14310-14310 57208781021 0000-0002-5364-5473 CKTI-Vibroseism Ltd. Bondarev Dmitrii 89523684328@mail.ru

St Petersburg, Russian Federation

0000-0002-1030-8370 Peter the Great St. Petersburg Polytechnic University Tarasov Vladimir vtarasov1000@yandex.ru

St. Petersburg, Russia

Torsion of a base-isolated building subjected to rotational components of earthquakes This research focuses on seismically isolated buildings, specifically, the influence of the rotational components of seismic ground motion on the buildings’ torsional response. Current approaches to ensuring the earthquake resistance of buildings and structures using seismic isolation are usually based on analyzing the impact of only the translational components of ground motion. The authors hypothesize that the rotational components of seismic action may, in certain cases, significantly affect a structure’s dynamic response. The primary research method involves conducting numerical experiments. The rotational component of seismic motion was simulated using a synthetic accelerogram generated according to Newmark’s model from two translational components of seismic motion. Two mathematical models are developed: a three-degree-of-freedom model for buildings supported on lead rubber bearings and a four-degree-of-freedom model for structures located on pendulum bearings equipped with plastic dampers. Analysis reveals that seismic rotations, particularly on soft soils, significantly amplify torsional effects. The accelerations at the corner points of the superstructure can increase significantly: up to 4 times for lead rubber bearings and up to 3 times for pendulum bearings compared to the accelerations at the center of mass. Furthermore, displacements in the corner isolators exceed the center of mass displacement by up to 16 % for lead rubber bearings and up to 5 times for pendulum systems. Between the two considered seismic isolation systems (elastomeric and pendulum isolators), the rotational components of seismic action exert the greatest effect on the dynamic response of a building isolated by pendulum bearings. This circumstance should be taken into account when designing buildings with a seismic isolation system exhibiting low torsional stiffness. 1.Introduction This research aims to test the hypothesis that, in certain cases, the rotational components of seismic ground motion can significantly affect the response of a seismically isolated structure. The object of the research is buildings and structures with various seismic isolation systems; the subject is the influence of these rotational components on the torsional response of seismically isolated buildings. Since the 1950s, observations of buildings and structures after strong earthquakes have revealed numerous structural failures caused by rotational motions. Such damages were documented after Agadir (1960), San Fernando (1971) [1], Armenian (1988), Loma Prieta (1989) [2], Northridge (1994) [3], Kobe earthquakes (1995) [4], etc. It is important to note that failures caused by rotational motions of earthquakes were observed in 42 % of all damaged buildings [5]. There are three primary factors which cause torsion of buildings and structures. Structural Asymmetry. If the elements in the building are distributed in the plan such that the center of rigidity does not coincide with the center of mass (CM), then the translational seismic excitation causes torsional vibrations in the building. Buildings where the center of rigidity does not coincide with the CM are called asymmetric (or irregular) buildings, and the torsional motions induced in them are referred to as natural torsion [6]. Seismic Rotations. The second factor of torsion is seismic rotations. These result from the spatial nature of seismic excitation. This nature of the impact is determined by the wave nature of earthquakes. These rotations are defined by the parameters of the wave field corresponding to the seismic impact. This complex effect can be assessed by both indirect and instrumental methods. This factor induces torsion in symmetric buildings (buildings where the CM and center of rigidity coincide). This factor can be categorized as accidental torsion [6]. Nonlinear Inelastic Behavior. The third factor can be observed during inelastic analysis of structures. This effect is caused by the nonlinear stiffness of the building’s elements. The effect of plastic yielding cannot be perfectly identical for all elements under translational seismic excitation, especially for the peripheral elements of the building [7]. This paper focuses on building torsion caused specifically by seismic rotations (the second factor). As of 2024, there are very few recorded six-component earthquakes despite developing devices [8] registering rotational components of earthquakes. There are two types of rotational seismic motion. Coherent seismic motion (wave passage effect). This type of motion occurs when harmonic waves arrive at a given point on the surface with a frequency and without random amplitude fluctuations, but with a phase shift. Such wave motion can be studied analytically by solving the wave equations. It is possible to generate the rotational components of seismic excitation using translational components of seismic excitation [10]. This problem can also be approached with a different formulation: modeling the non-vertical propagation of seismic waves. By specifying a particular angle of incidence, one can simulate the rocking or torsional motion of the ground surface [15, 16]. Incoherent seismic motion. This is a type of motion where a seismic wave passing up to through inclusions in the soil (local inhomogeneities) undergoes random changes in amplitude and phase. The energy of a wave propagating through such soil is partially dissipated. This effect is called as the scattering effect. Incoherent ground motion is also termed the spatial variation of seismic motion. In general, this type of motion is defined resolving the task of soil-structure interaction (SSI) using special software, for example, ACS SASSI [11, 12]. These calculations are based on probabilistic methods using Abrahamson’s coherency function [13, 14]. In general, a ground motion is described by a six-component vector with three translational and three rotational components at each point on the ground surface. Assuming a rigid foundation it is possible to consider that seismic motions are averaged over ground volume and applied at one point as the time-dependent vector of seismic accelerations. The main assumption of this study is that a seismic excitation is six-component data which include three translational and three rotational components. This model of seismic ground motion is called integrated model. The integrated (generalized) model of seismic ground motion assumes: a linear-elastic layered half-space; decomposition of translational motion into -, -, and -wave contributions; plane wavefront propagation with depth-dependent attenuation functions. Applicability is limited to sites with approximately horizontal stratification and negligible nonlinear soil effects. For sites with significant lateral heterogeneity, site-specific wave propagation analyses are recommended [10]. The rigid foundation assumption implies that foundation flexibility, SSI effects (radiation damping) and spatial variability of ground motion across the foundation footprint are not explicitly modeled. For structures on soft soils (  < 600 m/s), foundation flexibility may alter the effective input motion and modify the rotational response. The averaging procedure is consistent with the kinematic interaction framework when foundation embedment is neglected and the mat is assumed rigid. It is well-known that rotational components of ground motion can be generated using theoretical methods. The first integrated model was introduced by Newmark [9]. He defined rotational seismic motion around vertical axis as a function of translational components of ground motion scaled by S-wave phase velocity. Rotational component of an earthquake can be expressed as follows:                                                                     (1) where  is translational components of ground motion;  is S-wave phase velocity. Newmark’s method was applied and developed by many researchers: Luco [17], Shibata et al. [18], Lee and Trifunac [19, 20], Todorovska et al. [21], Basu et al. [22]; in USSR and Russia by Rasskazovsky [23], Hachiyan [24], Nikolaenko and Nazarov [25], and Nazarov et al. [10]. Nazarov did a comparative analysis using works of researchers mentioned above [26]: Table 1. Comparison of results on the rotational characteristics of seismic ground motion calculated by mentioned researchers [26]. Researcher Newmark Trifunac Hachiyan Rasskazovsky vs, m/s 3000 1000 300 250 500  rad/min – 2E – 4/0.7’ (2 – 4) E – 4/0.7’ – 1.5’ 4E – 3/3.43’ 5E – 4/1.72  rad/s*s 1.05E-2 (3-6)E-2 (1.5-2.0)E-1 – –     where  is the S-wave velocity,  is angular velocity of ground motion,  is angular acceleration of ground motion. The table shows that authors have obtained similar scientific results. The data in table shows that authors’ results differ proportionally to the shear wave velocity in the soil In 2000–2020, new parameters characterizing earthquake intensity have emerged. During the period when only translational ground motions could be measured by accelerometers and seismometers, parameters such as Peak Ground Acceleration (PGA), Peak Ground Velocity (PGV), and Peak Ground Displacement (PGD) were used. The PGA parameter characterizes earthquake intensity and remains in use as of 2024 due to its simplicity. However, it is important to mention this parameter provides limited information on the actual earthquake intensity. Sbaa et al. [27] measured the ground rotational velocity along the direction of translational acceleration on the island of Kefalonia (Greece) and compared the peak characteristics of rotational velocity (Peak Ground Rotational Velocity (PGRV)) and translational acceleration (Peak Ground Translational Acceleration (PGTA)). Here, PGTA is the maximum value among all translational components of ground acceleration, and PGRV is the maximum angular velocity among all rotational components. Their comparison revealed a linear relationship between PGTA and PGRV on a logarithmic scale. A similar trend was obtained by other authors such as Liu et al. [28], Takeo [29], and Yin et al. [30]. A comparable result was obtained by Smerzini et al. [31] based on data from the Parkway Valley (New Zealand) and UPSAR (California) arrays. A linear relationship was also found between the PGTA for horizontal components and the PGRV about the vertical axis (torsion). Furthermore, an analogous relationship was discovered between the PGRV of rotational components about the horizontal axes (rocking) and the PGTA of the vertical component. Subsequently, Ringler et al. [32] recorded three components of ground rotational velocities using proto-seismic magnetohydrodynamic (SMHD) sensors and attempted to use the PGTA/PGRV ratio to estimate the seismic wave propagation velocity and compare it with the velocity obtained from the PGTV/PGRD ratio (PGTV – Peak Ground Translational Velocity, PGRD – Peak Ground Rotational Displacement). In summary, the established linear relationship can be expressed as follows:                                                                  (2)                                                                   (3) where  is -wave velocity. This study employs the generalized model of seismic wave propagation proposed by Nazarov [10]. Nazarov decomposed the translational motion along each axis into three wave components (Fig. 1):                                                                    (4)                                                                   (5)                                                                    (6) Figure 1. Decomposition of wave motion [10]. Based on this decomposition, Nazarov derived formulas [10] that describe seismic rotations about three perpendicular axes. These formulas represent the most general case under the assumption of    and  waves propagating along each of the three orthogonal axes:                                        (7)                                        (8)                                      (9) where        and  are the amplitude functions of the monochromatic waves;  is the shear wave velocity beneath the foundation base, a key parameter governing the building’s rotation. According to Nazarov’s theory, two very important special cases follow: If the considered    and  waves have a plane wavefront and attenuate with depth according to  then Equations (7)–(9) are simplified to [10]:                           (10)                            (11)                                                         (12) If the monochromatic    and  waves have a plane wavefront, do not change with depth, and their stationary amplitude functions within the considered local model can be considered constants, i.e.,  then Equations (7)–(9) take the following form [10]:                                                                 (13)                                                                 (14)                                                                  (15) Note that Equation (15) is equivalent the Newmark’s (Equation (1)) model, which was proposed as early as 1969 in his work [9]. The formulas of Rasskazovsky, Khachiyan, Luco, and Trifunac are also special cases of Nazarov’s generalized model. Thus, the model developed by Nazarov provides a more general description of seismic rotations according to the integrated model of seismic ground motion and explains the variability of the results presented above in Table 1. In summary, seismic rotations can be obtained by direct and indirect methods. The direct method is an instrumental one. This method does not provide exhaustive or precise data, the required equipment is quite large and not always available to seismologists, who provide initial data for structural. Therefore, indirect methods, which derive rotational motions from translational ones, are of significant interest for dynamic analysis. Indirect methods are divided into two types: obtaining rotational accelerograms from data from special arrays (analyzing fields of strong seismic motions considering their spatial micro-characteristics, known as the Multiple Station Procedure (MSP)), and obtaining rotational motions from a single ground motion recording point (known as the Single Station Procedure (SSP)) [33]. The MSP method requires data from instrument arrays (recordings at multiple points). This method is accurate for generating rotational fields; however, few such arrays exist worldwide. Consequently, it is primarily used for research rather than practical engineering applications [34–38]. The SSP method requires data from only a single station (three translational accelerograms). It is more commonly used because array records are limited in most regions. Rotational ground motion is a spatial derivative of translational motion. In the SSP method, the rotational motion caused by a specific plane wave is given by the time derivative of the corresponding translational motion, scaled by the wave velocity. The main principle is the decomposition of complex seismic motion into    and  waves, as developed by several authors [19, 39–42]. Thus, a key conclusion is that rotational motions (angular accelerations) can be obtained from three translational motions recorded at a single point:                                                             (16)                                                            (17)                                                            (18) where      are the translational accelerograms recorded at a single point;  is the shear wave velocity beneath the foundation base. Subsequently, the rotational motion will be used about the vertical axis, obtained using Equation (18), generated from the two translational accelerograms of the seismic impact recorded at a single point. In this study, the rotational motion about the vertical axis was generated using Equation (18) from two translational accelerograms, implemented in the “Odyssey” software v.2. The “Odyssey” software was developed by Y.P. Nazarov, E.V. Poznyak and A.V. Filimonov; its theoretical basis is documented in the peer-reviewed source Nazarov et al. [10]. This paper focuses on base-isolated structures, as they are particularly susceptible to torsion due to their flexibility. Few researchers have studied the torsion of symmetric base-isolated structures subjected to rotational earthquakes. Almazan and de la Llera [43] investigated a symmetrical building on pendulum bearings, applying accidental eccentricity to simulate torsion. Ryan and Chopra [44] studied a base-isolated building subjected to rocking motions, which did not cause significant amplification of accelerations and displacements. Other researchers, such as Shimazaki [45], have also investigated base-isolated structures. A recent observational review of the torsional response of civil engineering structures during earthquakes is provided by Guéguen and Astorga [46]. In light of the foregoing, research specifically dedicated to the influence of the rotational components of seismic ground motion on the torsional response of seismically isolated buildings has not yet been conducted to a sufficient extent. Meanwhile, an increasing number of seismic-resistant building projects incorporate various seismic isolation systems in their design. Therefore, the authors consider this research topic to be relevant and important for the future analytical verification of the isolated buildings’ seismic resistance. The main goal of this research was to determine the seismic isolation systems most affected by rotational ground motions and to perform both qualitative and quantitative evaluations of this effect. To achieve this goal, the following tasks were completed: a review of the literature on the research topic and the identification of the primary methods for accounting for the rotational component of seismic excitation in seismic analysis; the generation of accelerograms incorporating the rotational component of seismic ground motion; the creation of two mathematical models of seismically isolated buildings with different seismic isolation systems (elastomeric and pendulum bearings); the implementation of calculations, followed by a comparative analysis of the structural responses; the formulation of conclusions regarding the influence of the rotational component of seismic excitation on seismically isolated buildings. 2.Methods 2.1.The Motion Equation of a Base-Isolated Building by Lead Rubber Bearings In order to assess the contribution of the rotational component of seismic impact, it is necessary to formulate a system of differential equations for base-isolated building by lead rubber bearings. It is assumed that a building oscillates as rigid body during an earthquake. Bearings have a bilinear diagram “force – displacement.” Model of base-isolated building located on lead rubber bearings is shown in Fig. 2: Figure 2. 3DOF model of base-isolated building located on lead rubber bearings subjected to torsional earthquake. The model shown in Fig. 2 has three degrees of freedom: two translational displacements and a torsional angle around the vertical axis. The system of differential equations of motion for a base-isolated building on lead rubber bearings is as follows:                                                  (19) where   are the accelerograms of the translational components of the seismic impact recorded at a single point;  is the generated rotational component of the seismic motion;    are the total forces in the bearings;  is a number of the bearing;    are the forces in -th bearing along  and  axis (Fig. 3);  is the total moment from the bearing forces;    are the total forces and moment from viscous damping;  is the sum of torsional moments from each bearing;  is a mass of the building;  is the moment of inertia around the vertical axis;  is a building length;  is a building width;  is a center of rigidity of the base isolation system;    are the eccentricities of the base isolation system. Point  is the initial location of -th isolator at  point  is initial location of -th isolator at    is the building’s rotation angle. Figure 3. Idealized “force-displacement” relationship for the i-th bearing along the x and y axis. The initial conditions for the system are:                         (20) Coordinates in the model: At  point  point At  point  point Let  be the displacement vector of a bearing,  be the radius vector of a bearing relative to the CM.                     (21)                                (22) The moment of force for each bearing about the CM is given by:                                                                      (23)                          (24) The total moment is:                                                                      (25) The total stiffness of the bearings is defined as:                                                        (26)                                                     (27) The natural frequencies of the system are:                                                  (28) Sensitivity of natural frequencies to bearing layout and stiffness distribution: the translational frequency  is primarily governed by the total lateral stiffness; the torsional frequency,  depends on individual bearing stiffnesses and their radial distances from the center of rigidity. Possible resonance was checked against the predominant earthquake periods that were adopted as input for the analysis (see Figs. 6–8). The eccentricities of the base isolation system are:                                                    (29) Model assumptions: The vertical component of seismic impact is neglected due to the high vertical stiffness of the bearings. Rotation angles about the horizontal axes are neglected due to the high corresponding torsional stiffness. The torsional stiffness of the bearings themselves can be neglected. Coriolis accelerations can be neglected due to the small angular velocities of the ground motion during an earthquake. The effect of a biaxial yield surface (where the force point on the hysteresis curve traces an ellipse under simultaneous two-directional loading) is neglected [55]. The system of differential equations can be rewritten as:                                                     (30) The initial conditions are:                                   (31) Thus, a model has been developed for the dynamic analysis of a building supported on an arbitrary number of elastomeric bearings with arbitrary plan coordinates. This model is capable of calculating the eccentricity for any given arrangement of bearings or can accept eccentricity as a predefined input parameter for subsequent analysis. The system of differential equations for mass oscillations was implemented in the Mathcad software (v. 15.0) package and solved using the 4th-order Runge–Kutta numerical method. For the purposes of this study, eccentricities were not considered. 2.2.The Motion Equation of a Base-Isolated Building by Pendulum Bearings Equipped with Plastic Dampers Rutman developed [47] a pendulum bearing consisting of the following components (Fig. 4): a support frame connected to the substructure (1), a frame connected to the superstructure (2), a tie rod (3), a plastic damping rod (4), a spherical plain bearing (5): Figure 4. Pendulum bearing [48]. This type of bearings tunes the building to a different fundamental frequency, thereby filter out the energy-intensive frequencies of the seismic impact. However, to eliminate resonant phenomena due to the multi-frequency nature of the seismic impact, damping is necessary. Plastic dampers (PDs) are implemented to these bearings which exhibit a bilinear force-displacement relationship. The total internal force in this type of bearings is composed of the restoring force of the pendulum tie rod  and the resisting force of the PDs                                                                        (32) The resulting combined force-displacement diagram is shown in Fig. 5: Figure 5. Combined force-displacement diagram for pendulum bearings. Technical characteristics of the pendulum bearing: load capacity: 100–1000 tons. Effective natural frequency: 0.2–0.5 Hz. Maximum allowable horizontal displacement: 0.5 m. Rod-shaped damping elements made of mild steel, when subjected to plastic deformation within 2 %, remain operational for approximately 500 loading cycles. This directly indicates the limiting deformation (2 %) and cyclic durability (i.e., degradation). As previously mentioned, damping is achieved through the deformation of curved rods connected to the support structure via a separator and a holder (Fig. 4). The required activation forces of the PDs are determined by varying key parameters of the rods, such as their length, diameter, and number. Rutman et al. [49] derived a system of differential equations describing the motion of a base-isolated structure with six degrees of freedom. The mathematical model of the pendulum seismic isolation system is based on exact kinematic relations that account for geometric nonlinearity under large horizontal displacements and a shifted center of gravity. The deformation of each rod was defined as the difference between its initial length (Z0) and its current length  This expression is nonlinear with respect to the horizontal displacements and the rotation angle. The force in the rod is calculated as  and then projected onto the coordinate axes scaled by  Thus, the model is capable of describing the system’s behavior under significant horizontal displacements without linearization (See [49]). Taking into account assumptions mentioned for lead rubber bearings model (LRBs-model) above (with the exception of the first item as the vertical seismic component is accounted for here), the system of differential equations can be written as follows:                                         (33) The initial conditions are:             (34) Thus, a model has been developed for the dynamic analysis of a building supported on an arbitrary number of pendulum bearings with arbitrary plan coordinates. This mathematical model was coded in the MATLAB software package (v. R2021a). The program is designed for the analysis of a building supported on  bearings with specific  and  coordinates and a pendulum tie rod length  The length of the pendulum tie rod, as well as the PDs with a specific bilinear force characteristic, will be the defining initial data for specifying the bearing properties. 2.3.Seismic Excitations Used in Dynamic Analysis The rotational component of seismic motion is a result of the elastic deformation of the soil mass; consequently, the softer the soil, the greater the rotations will be. This component depends on the shear wave velocity beneath the foundation base. For this reason, a series of rotational accelerograms were generated for a range of shear wave velocities. Given that the input data consisted of records from the strongest and most destructive earthquakes, it is challenging to assign specific soil conditions to each original translational accelerogram. Therefore, for each pair of translational accelerograms (along the  and  axes), a corresponding rotational accelerogram was generated. The investigated range of shear wave velocities spanned from  = 10000 m/s (representing a hypothetically very stiff/rock-like soil) down to  = 250 m/s (representing a soft soil, such as loam or clay). According to EN 1998-1 (Eurocode 8) ground type classification, the investigated Vs range corresponds to the following categories: Ground type A (Rock or other rock-like geological formation, with at most 5 m of weaker material at the surface) for Vs > 800 m/s; Ground type B (Deposits of very dense sand, gravel or very stiff clay, 360–800 m/s) for range 360 m/s < Vs < 600 m/s; Ground type C (Deep deposits of dense or medium-dense sand, gravel or stiff clay, 180–360 m/s) for Vs < 360 m/s. The selected range thus covers the full spectrum from hard rock (Type A) to stiff clay and dense sand/gravel deposits (Type C). Lower Vs values ( 10.34910/MCE.143.10 699.841 torsion seismic rotations rotational component of seismic excitation pendulum bearings rubber bearings wave passage effect Newmark’s model of seismic rotations https://engstroy.spbstu.ru/article/2026.143.10/