Three different types of concrete, i.e., normal concrete, barite, and magnetite containing concrete, were prepared to investigate this study. The radiation attenuation was calculated by studying the dose absorbed by the concrete and the linear attenuation coefficient. Additionally, artificial neural network (ANN) and gene expression programming (GEP) models were developed for predicting the radiation shielding capacity of concrete. A correlation coefficient (R), mean absolute error (MAE), and root mean square error (RMSE) were calculated as 0.999, 1.474 mGy, 2.154 mGy and 0.994, 5.07 mGy, 5.772 mGy for the training and validation sets of the ANN model, respectively. Similarly, for the GEP model, these values were recorded as 0.981, 13.17 mGy, and 20.20 mGy for the training set, whereas the validation data yielded R = 0.985, MAE = 12.2 mGy, and RMSE = 14.96 mGy. The statistical evaluation reflects that the developed models manifested close agreement between experimental and predicted results. In comparison, the ANN model surpassed the accuracy of the GEP models, yielding the highest R and the lowest MAE and RMSE. The parametric and sensitivity analysis revealed the thickness and density of concrete as the most influential parameters in contributing towards radiation shielding. The mathematical equation derived from the GEP models signifies its importance such that the equation can be easily used for future prediction of radiation shielding of high-density concrete.Concrete is an economical and efficient material for attenuating radiation. The potential of concrete in attenuating radiation is attributed to its density, which in turn depends on the mix design of concrete. This paper presents the findings of a study conducted to evaluate the radiation attenuation with varying water-cement ratio ( The harnessing of energy released during nuclear reactions can be rightly called an important milestone in technological development. Over time, nuclear technology has found its way into several fields; medical science is one of them. Nuclear technology entails the emission of radionuclides such as gamma rays, X-rays, and neutrons. These radionuclides pose a serious risk to all living things, particularly human beings. Nuclear radiation has the potential to destroy living cells, the building blocks of human beings, hence warranting shielding against their destructive action ,2. Prote3 [3 to 2600 kg/m3 [The material selection for radiation shielding is mainly dependent on the emissions source, type, and the material’s weight . A numbe3  as compa00 kg/m3 . Density00 kg/m3 ,30,31,3200 kg/m3 ,36,37,38Numerous studies in the past have been conducted to investigate the performance of heavyweight concrete (HWC) based on industry requirements and applications. Most of these investigations, however, have focused on exploring the mechanical and shielding performance of HWC based on the type of aggregate used ,25,39,40w/c) ratio is also an important factor contributing to the strength and radiation shielding properties of heavy weight concrete. Lotfi et al. [w/c ratio significantly reduces the compressive strength of heavy weight concrete, while the mechanical and radiation shielding behavior of concrete has been found to improve with decreasing w/c ratio. Yang et al. [Water-cement  is an effective tool for assessing the concrete performance while considering the effect of multiple parameters such as composition of ingredients, water cement ratio, and quantity of additives ,49,50,51w/c ratio, cement quantity, and slump value were selected as the control factors and compressive strength and linear attenuation coefficient were considered as the quality responses. At the end, optimal values of mixture with consideration of multiple quality characteristics are obtained and verified.In this study, the ANN method was used to develop a model by using our own experimental data that evaluates the concrete mixes’ performance against radiation without compromising the mechanical properties of concrete. High radiation shielding ability could be achieved with the materials having relatively high density . In the 3), conforming to ASTM C-33, was used as coarse aggregate in concrete, whose particle sizes ranged from 9.5 mm to 25 mm. The gradation curve of the coarse aggregate obtained from sieve analysis (ASTM C136) is presented in Crushed stone, calcareous in nature  are mathematical based models working on the analogy of the human brain. ANN was started with the concept of the brain which solves computational problems in different ways as compared to conventional computers. A neural network encompasses three layers of immensely equivalent distributed processors such as input, hidden, and output layer. There are multiple factors that impact the neuron quantity in each layer. The number of neurons in the output and input layer is determined through modeling the relevant parameters in the layers. The number of neurons present in the hidden layer is a variable that must be chosen to achieve a suitable output response . In ordeFor the development of ANN models, the data presented in The input data shown in w/c ratio is evident, reflecting a linear reduction of compressive strength with an increase in w/c ratio from 0.30 to 0.45. The variation in strength with change in w/c ratio is consistent with a number of previous studies [w/c ratios and is presented in w/c ratio up to 0.40, followed by a decrease. The maximum value of the attenuation coefficient is obtained at w/c equal to 0.40. w/c ratio of 0.40 may be attributed to higher concrete density. So, it can be inferred from the test results that gamma rays can be attenuated either by using lighter materials with an increased thickness or heavier materials with optimum thickness. Normal concrete can be used as a useful material for gamma-ray shielding if it is used at a w/c ratio at which concrete has maximum density. The results are in accordance to the literature related to different materials used for shielding against radiation; specifically, studies that used high density constituent in concrete, significantly increased the attenuation coefficient [The results of compressive strength for the three types of concrete investigated in this study are shown in  studies ,66. The fficient ,33,37,38The developed ANN and GEP models were evaluated using statistical indices, i.e., the values of R, MAE, and RMSE, provided in x-axis, and the predicted values were plotted on the y-axis. Many researchers in previous studies used the slope of the regression line as a statistical evaluation procedure for studying the performance of AI models [While investigating the performance in terms of regression slope, experimental values of the radiation absorbed were plotted on the I models ,64,71. PI models ,74. It wThe model statistical assessment was further enhanced through the error analysis and the tracing of experimental results by the predictions made from the ANN and GEP models. The results relating to this analysis are presented in It is obvious from the above analysis that ANN performs better in terms of accuracy; however, the GEP model has interpreted acceptable results. The beauty of the GEP model is lying in the fact that it furnishes a simple mathematical equation, which can be used for predicting a new data set, without using a computer program. The disadvantage of the ANN model is its black-box nature. You must retrain the model with the data used originally in order to predict the new data. Equations are given as follows (Equations (2)–(5)), obtained from the GEP model which can be used for predicting the radiation dose absorbed for a given sample of concrete whose input parameters are known.Sensitivity and parametric analysis of the developed model is the evaluation of the trained model on the entire new dataset. The sensitivity analysis shows which input variable is more important in furnishing the magnitude of the target variable, and the parametric analysis depicts the trend in contributing towards the output variable. For this purpose, a simulated dataset was created such that one input variable was varied between its extreme values, whereas the other variables were kept constant at their average values. The simulated dataset was created for the three types of concrete investigated in this study. The simulated dataset was tested on the trained ANN model owing to the superior performance of the model. The results are shown in w/c ratio of 0.40–0.42 for normal and barite containing concrete, and 0.45 for magnetite-containing concrete. The increase in thickness and density also improved the radiation shielding depicting polynomial variation. Maximum radiation shielding was observed for the maximum compressive strength investigated in this study. It is highly recommended to consider these input parameters and their effect on radiation shielding structures intended to resist radiation especially atomic power plants.The parametric study revealed that maximum radiation is absorbed at w/c ratio were observed showing least contribution in radiation shielding.The sensitivity analysis  showed tw/c ratio in order to achieve a higher density without affecting strength properties. For normal and barite-containing concrete, the optimum water/cement ratio was observed as 0.40–0.42. Using an optimal w/c ratio would decrease the wall thickness required for radiation shielding in therapy bunkers and atomic reactors, indirectly saving cost. Increasing the w/c ratio was found to reduce the compressive strength.The density of material and the thickness of concrete samples are the two important factors that attenuate the quantity of gamma radiation. Increasing the thickness and density of concrete improves its radiation shielding ability. Normal concrete is the most commonly used material in construction. Therefore, it is recommended to use such a The AI models developed in this study showed close agreement between experimental and predicted results; however, the ANN model developed for predicting radiation shielding manifests outperformed the GEP model. The simple mathematical relationship produced from the GEP model signifies its importance because it can be used in the future to predict radiation shielding of new data without using any computer program.The results obtained from the parametric analysis showed agreement with the experimental results. The thickness and density of concrete were found to be the most influential parameters in determining the shielding ability of concrete.This study examined the shielding capability and mechanical properties of concrete at variable water-to-cement ratio, thickness, density, and compressive strength. For this purpose, three different types of concrete, i.e., normal concrete, barite, and magnetite-containing concrete, were cast and tested for compressive strength and radiation shielding. Moreover, ANN and GEP models were developed to predict radiation shielding of concrete. The following results were drawn from this study:


The widespread use of aerated concrete in construction has led to the emergence of many types and compositions. However, additional research should fill theoretical gaps in the phenomenon of gas release during the formation of the structure of aerated concrete. Based on theoretical analysis and experimental studies, the article proposes a mathematical model of the swelling process based on the physicochemical laws of convection and molecular diffusion of hydrogen from a mixture and the conditions of swelling, precipitation, and stabilization of the mixture. An improved method for the manufacture of aerated concrete is proposed, which consists of introducing cement pre-hydrated for 20–30 min into the composition of the aerated concrete mixture and providing improved gas-holding capacity and increased swelling of the mixture, reducing the average density of aerated concrete up to 29% and improving heat-shielding properties up to 31%. At the same time, the small dynamics of a decrease in the strength properties of aerated concrete were observed, which is confirmed by an increased structural quality factor (CSQ) of up to 13%. As a result, aerated concrete has been obtained that meets the requirements of environmental friendliness and has improved mechanical and physical characteristics. Economic efficiency is to reduce the cost of production of aerated concrete and construction in general by about 15%. The study’s relevance is due to the current scientific lack of research on the fundamental nature and substantiation of mathematical and physical models to form promising cellular concrete. This material fully meets the world’s requirements for energy efficiency and energy saving. It is a suitable material for improving its porous structure with the help of formulation and technological factors to obtain the most efficient building structures with a minimum cross-section and minimum thermal conductivity. In terms of cost characteristics, non-autoclaved cellular concretes significantly outperform autoclaved competitors due to the significantly reduced cost of production and manufacture of such concretes and less environmental impact. From the point of view of technological and recipe factors, there are quite a lot of studies of non-autoclaved and autoclaved aerated concrete ,33,34,35Studies ,3,4 are It is known that the recycling of aerated concrete is widely used as raw material in the production of aerated concrete products and structures ,7,8,9,10Studies of the influence of various fibers and microsilica on lightweight concrete’s mechanical properties (compressive and bending strength) are also of great importance ,14,15,162 microdust on the strength properties of samples of autoclaved aerated concrete. Based on the results of the studies, it was found that the complex additive affects the process of hydration of cellular concrete. Namely, it leads to calcium hydro silicates of the tobermorite group (C–S–H). The compressive strength of aerated concrete samples containing a complex additive increased by 52%, and the tensile strength in bending by 62% compared with the strength characteristics of samples of the control composition without the additive.Complex additives are also used in aerated concrete technology. In , the autIn other studies ,21,22,23Investigation of dependences and modeling parameters of the behavior of AAC products in terms of wind load , materiaSeveral works ,33,34,35Diffusion phenomena that occur during swelling, as a result of which part of the hydrogen is removed from the cellular concrete mixture, are the consequence of defect formation and lead to an increase in the average density of cellular concrete and a decrease in the quality of products. Therefore, the creation of conditions under which the diffusion phenomena of the intumescent mixture are manifested to a lesser extent makes it possible to achieve relatively better characteristics of the material structure.The research plan is presented in a structural–logical block diagram .This work aims to optimize the technological process for the manufacture of aerated concrete products using injection technology at the molding stage, ensuring a decrease in the average density and an increase in the uniformity of material properties. This goal is achieved by deepening the theoretical understanding of the processes of formation of a cellular structure and by optimizing the kinetics of processes occurring during swelling and improving on this basis the technology for manufacturing aerated concrete products, improving the means of controlling the properties of materials.The working hypothesis of the work is formulated as follows: the intumescent aerated concrete mixture meets the optimal conditions for the manufacture of aerated concrete with desired properties, which ensures the coincidence in time of the start of coagulation of new cement formations and the start of intensive gas release by the aluminum blowing agent.Based on the mathematical model, it is necessary to calculate an environmentally friendly, economic non-autoclaved aerated concrete that meets the requirements of the UN global ESG agenda for environmental protection, has an improved structure and improved energy-efficient and energy-saving properties, and better mechanical characteristics.This section lists the characteristics of the raw materials used in the experimental studies. The study of the processes of formation of a cellular structure, the determination of the optimal compositions of cellular concrete, and the physical and mechanical properties of the obtained materials were carried out on cement–sand mixtures.When carrying out the experiments, Portland cement of the CEM I 42.5N brand produced by JSC Novoroscement  was used. Quartz sand produced by Arkhipovsky Quarry OJSC  was used as a fine aggregate, the physical characteristics of which are presented in Aluminum powder PAP-1 produced by OOO SKIF  was used as a blowing agent. The physical characteristics and chemical composition of aluminum powder are shown in The compressive strength was determined on 100 mm × 100 mm × 100 mm cube samples following the requirements of GOST 10,180 “Concretes. Methods for strength determination using reference specimens” . The aveThe thermal conductivity of aerated concrete was determined under the requirements of GOST 7076  on sampl-Technological equipment—installation for the production of foam concrete and aerated concrete GBS-250 manufactured by METEM ; ball planetary mill “Activator-4M” ;-Testing equipment—hydraulic press MIP-25 ;-Measuring instruments—metal measuring ruler 500 mm ; laboratory scales HT-5000 ; caliper ShTs-I-250-0.05 ; thermal conductivity meter ITP-MG4  b; viscomThe study used:To determine the parameters of the aerated concrete mixture and due to the lack of necessary methods, there was a need for special instruments and methods for studying gas release, swelling, and other characteristics described in this section of the work. The device PGV-2A  operates in automatic control mode. The device parameters are registered by a multipoint automatic potentiometer of the KSP-4 type . The volume of the reaction vessel is 2–3 L, the measured volume of the evolved gas is up to 3 L.The device PGV-2A a consistOn the front control panel of the PGV-2A device, there are controls for internal pressure control, stirring rate control (ACU), and temperature control (TCU) of the reaction medium, as well as the control of the movement of the variable measuring capacitance (MCU).i…p with a time interval of no more than 15 s, the process, and device parameters are recorded: the temperature of the substance tB(i), the temperature of the vapor–gas medium above the substance ti)2, the volume of concrete mix in the container VB(i).Using the PGV-2A device, the parameters of the swelling kinetics are determined as follows. First, the test substance is placed in a reaction container installed in the device. Then a thermocouple is introduced into the substance, and the device is sealed. After that, for time points 1, 2, 3…KB(i), the gas diffusion coefficient D(i), the gas evolution of tB(i), for time points (i) is carried out according to the following formulas:3; 3; 3; 3; 3/(g × deg); 3 [After the completion of the process, the calculation of the parameters of the swelling kinetics of the substance—the swelling coefficient ), g/cm3 ,34,35.-Revealing the fundamental-applied connection between the processes of gas release and structure formation of aerated concrete with the performance characteristics of the hardened composite;-Verification of technological and operational efficiency when using partially hydrated cement in the production of non-autoclaved cellular concrete with improved structural and operational characteristics.The study considers the fundamental aspects that occur at the level of interaction of various media during gas release and the formation of the aerated concrete structure. The mathematical models of all these processes have been developed. It is proposed to consider aerated concrete mixtures as a system of finite elements, for which one gas bubble is taken. Furthermore, using the apparatus of mathematical physics, the equations of molecular diffusion, and modeling the process of gas release in the emerging aerated concrete, two main hypotheses can be tested:3 is used as the reaction medium, the temperature of the reaction medium and the stirring rate are maintained constant at a given level [Several processes should first be modeled from the point of view of mathematical physics and then wholly or partially reproduced in the laboratory in a natural experiment. To determine the parameters of the kinetics of gas evolution, it is necessary to stabilize the conditions of the experiment. For this purpose, milk of lime with a density of 1.05–1.2 g/cmen level ,34,35.t2(i) is recorded, and the internal volume of the device pV is changed. After the end of the gas evolution reaction, the values of the volume of released hydrogen  phase with aluminum particles having an oxide layer and covered with a stearin film has an induction period that depends on the rate of development of the reactive surface of aluminum particles. The hydrogen released as a result of the reaction diffuses from the surface of a part of aluminum into the liquid phase, saturating it. Due to the high concentration of hydrogen, gas bubbles form at the surface of the particles. At the same time, hydrogen migrates into the depth of the liquid phase and into entrained air bubbles, which are always present in real mixtures. Hydrogen migration also proceeds to the surface of the mixture and into the surrounding atmosphere. A significant hydrogen concentration gradient can explain the predominance of molecular diffusion through the mixture surface on the mixture surface. Supersaturation of the liquid phase with hydrogen is the result of a significant partial pressure of hydrogen in bubbles of a small radius, as well as an insufficient surface of the existing bubbles for the diffusion of molecular hydrogen into them. Achieving the maximum rate of molecular diffusion of hydrogen from the mixture is a conditional transitional moment between the induction period and the intense swelling of the mixture.The swelling period is characterized by an intensive increase in the volume of the aerated concrete mixture up to a certain maximum value. The phenomena that take place during this period can be explained by the high rate of the gas formation reaction, the increase in the radius of gas bubbles, and their surface area. The limiting factor for swelling is the interpore wall’s structural and rheological kinetic characteristics. A decrease in molecular diffusion is a consequence of a decrease in supersaturation of the liquid phase with hydrogen and saturation of the mixture with gas bubbles. During the period of maximum intensity of swelling, sound emission of the mixture is observed, which indicates the beginning of the formation of defects in the interpore walls in the form of cracks and holes. This moment corresponds to the minimum diffusion of gas through the mixture. The subsequent intensive removal of gas from the mixture is a consequence of the convective diffusion of vapor and hydrogen through defects. The damping of swelling can be explained by convective diffusion of the gas, which reduces the pressure in the bubbles of the mixture. When the gas pressure in the bubbles is balanced and the pressure required to deform the interpore wall, the mixture stops swelling.The period of precipitation is characterized by a decrease in the volume of the mixture and intense convective diffusion of the vapor–gas mixture from it (gas breakthrough). These phenomena proceed at a variable speed. The sedimentation of the mixture occurs due to the deformation of interpore partitions under the forces of the hydrostatic pressure of the overlying layers. The settling decreases as the internal gas pressure in the bubbles, the resistance stress of the interpore walls to compression, and the hydrostatic pressure of the overlying layers of the mixture are balanced.The stabilization period is characterized by the absence of a decrease in the volume of the mixture and the high diffusion of gas from it. The phenomena of this period are similar to the phenomena of the previous one. Full stabilization of the mixture is achieved under the condition that the stress of resistance of the interpore walls to collapse exceeds the pressure of the overlying layers. The period of precipitation may be absent if the condition of stabilization of the mixture is met immediately after the period of swelling. The swelling process can be considered completed after the end of gas diffusion through the surface of the mixture.The considered phenomenological concepts of swelling are the basis of the model of this process ,34,35.Further, based on ,34,35, tThe leading indicators characterizing the dispersed phase are the gas content, disperse composition, and chemical composition of the gas phase. Gas bubbles in cellular concrete are not monodisperse. The average size of the bubbles and their polydispersity largely depend on the specific conditions of production, the rheological and surface properties of the interpore substance, and many other factors. Cells of different sizes in aerated concrete have different values of excess surface energy and therefore have different solubilities or vapor pressures. As a result, in polydisperse systems, particles are redistributed in size in the direction of their enlargement, and the thermodynamic limit of this redistribution is the division of the disperse system into two layers. During swelling, cells in aerated concrete can be enlarged in two ways: coalescence and molecular transfer of gas from small cells to large ones. The simultaneous action of these two mechanisms is also possible.The stability of gas emulsions with respect to coalescence processes is determined by the interaction energy of gas bubbles and the strength of the two-sided film upon their contact. Therefore, it depends on several conditions: the properties of the dispersion medium and the dispersed phase, the nature of the emulsifier used, the presence of impurities, temperature. The phenomenon of coalescence in the aerated concrete mixture, apparently, prevails at the initial stage of swelling, when the size of the bubbles and the rheological properties of the interpore wall  are still small.In gas-filled disperse systems containing bubbles of various sizes, the size of the bubbles is redistributed due to diffusion mass transfer. The mechanism of this phenomenon is based on the fact that the vapor pressure of small bubbles is greater than that of large ones. The thermodynamic regularities of formation, growth, and distribution of bubbles show that bubbles are more stable, the larger they are. The gas in small bubbles dissolves since the gas concentration in the liquid phase of the material of the interpore wall is lower than the equilibrium one. In contrast, with respect to the largest bubbles, the same liquid phase of the interpore substance is supersaturated, and the gas dissolved in the liquid phase is released into large bubbles. In this case, the largest bubbles grow due to the dissolution of small ones and partially due to the liquid phase of the interpore substance. As a result, the gas concentration in the liquid phase decreases, and the critical size of the bubbles, which are in equilibrium at a given gas saturation of the liquid phase, continuously increases. If gas formation occurs during a chemical reaction in the interpore substance, then the degree of gas supersaturation in the liquid phase reaches large values, significantly exceeding the equilibrium concentrations for small and large bubbles. Therefore, it can be assumed that bubbles of different sizes grow at different rates in an intumescent aerated concrete mixture, and growth is more intense for larger ones.R is the average cell radius.The gas porosity is:R and the minimum thickness of the interpore partition kN, can be represented by the following formula:The dependence of the gas porosity of aerated concrete on the average pore radius R of the cell, and the coordination number kNBased on Equations (11) and (12), we obtain the dependence of the minimum thickness of the interpore wall V and the number of cells in the aerated concrete mix N are known, then with an average cell radius R, the average value of the thickness of the interpore wall If the batch volume pD of the interpore substance is equal toThe minimum thickness of the interpore partition during swelling of the aerated concrete mixture has a certain critical value, upon reaching which, it is possible to form holes in the interpore partition. This critical thickness depends on the dispersion of the interpore substance and is equal to 3–5 diameters of the coarse component. If we characterize the dispersion of the interpore substance by the specific surface, then the average particle diameter N0 is the total number of cells in the mixture (layer).However, in natural materials, the thickness of the partitions is much greater than the critical minimum thickness of the interpore partition Considering that as a result of cement hydration  of the volume of the gas bubble.D is the molecular diffusion coefficient; The difference in gas concentrations in the liquid phase leads to the molecular transfer of matter. According to Fick’s first law, the diffusion process is described by the dependence :(18)dmS The rate of substance transfer at a given temperature and pressure is proportional only to the concentration gradient near the interface.The value of the concentration derivative in Equation (21) at a fixed interface is determined from the solution of the molecular diffusion equationThe solution of Equation (19) under the initial and boundary Conditions (20) makes it possible to determine the concentration gradient at the bubble boundaryDependences (18) and (21) the mass flow of gas through a single area, which is determined by the process of molecular diffusion in a liquid, can be foundC∞(τ) and C0(τ), Equation (25) takes the formWith a time-varying gas concentration in liquid In the case of a vapor–gas bubble, the rate of its growth or dissolution depends, in addition to diffusion, on heat transfer, which is described by the control of heat transfer during liquid evaporation or vapor condensation. The equilibrium vapor pressure (vapor pressure) over a concave liquid surface (with radius R) is lower than for a flat interface. It can be determined from the Kelvin–Helmholtz relation, which for the case −5 cm, the saturation vapor pressure above the meniscus in the capillary is equal to the saturation vapor pressure over a flat surface with an accuracy of 1%. For the entire set of bubbles in the aerated concrete mixture, the amount of gas released into the bubble is equal toFor capillaries with a radius greater than 10Swelling of the mass of aerated concrete mixture occurs as a result of deformation of the interpore wall under the action of gas pressure in the cells, and the sediment is the result of deformation of the interpore material under the action of hydrostatic pressure from the overlying layers of the aerated concrete mixture.P0 is atmospheric pressure; Ph—hydrostatic pressure from the overlying layers of aerated concrete mixture; Pmn is the pressure required for plastic deformation of the interpore wall; Pv is the pressure caused by the limited swelling of the mixture in the mold and the constraint of cell movement.According to the theory of the energy of shape change of a plastic body, the specific energy of shape change for any point remains constant in the plastic state of matter. Based on this, when deforming an array of aerated concrete, you can write the following expression for the pressure of the vapor–gas medium in the cells:The condition of swelling and settling of an aerated concrete mixture and any elastic-plastic system can be justified by the position of the problem of motion stability. The effect of the loss of stability of the interpore partition with an increase in the internal pressure in the cell is the appearance of swelling deformations that occur when a certain critical value of the internal pressure in the cell is exceeded, that is:When the mixture settles, there is a loss of stability of the interpore wall, which occurs under the action of the hydrostatic pressure of the overlying layers when the conditionτ0 behave like a solid body, and when these stresses are exceeded, they irreversibly flow with a strain rate dv/dy due to the plastic viscosity of the mixture and can be described by the Shvedov–BinghamCellular concrete mixtures and their interpore partitions under applied stresses not exceeding the limiting shear stress In an utterly plastic state of a polydisperse medium with spherical inclusions, the pressure causing such a state is expressed by the dependenceThe formula determines the critical value of swelling pressure:The pressure in the bubble from the action of surface energy forces at the bubble–interstitial wall boundary is determined by the formula:mnγ is the average density of the interpore wall; σ is the surface tension of the liquid at the phase boundary; H is the height of the aerated concrete mixture; h is the height from the bottom of the mold to the layer under study; g = 9.81 m/s2.The hydrostatic pressure from the overlying layers is:The presented mathematical model ,46,47,48G(j), the limiting shear stress of the interpore substance τ0(j), and the temperature of the mixture T0 was constant and equal to 40 °C.For this purpose, the conditions of the process of swelling of the aerated concrete mixture were modeled, under which the time-varying parameters were the outgassing of the gasifier 5 cm3.Mixing volume S0 = 2.5 × 103 cm2.Sectional area of the array Volume of gas saturation of the mixture (nuclei) φ = 0.27%.P0 = 1,013,250 dynes/cm2.Atmospheric pressure −5 cm2/s.Molecular diffusion coefficient D = 4.8 × 10H = 1.1618 × 10−10 (cm3/cm3) × (cm2/dyne).Henry coefficient kPn = 76,196.4 dynes/cm2.Partial pressure of water vapor 2.Surface tension of water σ = 70 erg/cmmn = 1.762 g/cm2.Average density of interpore substance γW/T—mixture ratio = 0.5.3.Density of water T = 2.874 g/cm3.The average density of the solid phase 𝜌Nk = 12.Coordination number of cells 2.Free fall acceleration g = 980 cm/s−4 cm.The thickness of the diffuse film δ = 10Number of layers i = 10.The number of analyzed time intervals j = 40.τ = 60 s.Time interval Δ∞C(0) = 0.The initial concentration of hydrogen in the liquid phase is −2.The average initial radius of steam–air bubbles (nuclei) of the mixture is R = 10−9 s;Coefficient M = 10−3 cm.The minimum critical thickness of the interpore wall at the beginning of the process per cell −3 cm.The minimum critical thickness of the interpore wall 20 min after mixing the mixture with water The initial data for the calculation according to the model were also:Swelling modeling was carried out for six experiments, differing in the moment of the beginning of the gas evolution of the blowing agent in the mixture.An analysis of the simulation presented in The observed inhomogeneity of the properties of the expanded aerated concrete mixture depends on the correspondence between the kinetics of microstructure formation of the interpore substance and the gas release of the blowing agent, and decreases with a shift at the beginning of the kinetics of the blowing out of the blowing agent, in the region of stabilization of the rheological properties of the interpore wall.The simulation of the swelling of aerated concrete mixture made it possible to identify two practical directions for implementing the provisions of the hypothesis: the first is the use of a blowing agent with a long induction period, the second is the use of pre-hydrated cement as a binder.The interpore wall of the aerated concrete mix consists of a multi-component substance. The change in the rheological characteristics is determined mainly by the kinetics of the structure formation of the binder.To study the swelling processes of aerated concrete mixtures, of particular interest is the initial period of structure formation of the binder, and the period of intense hydration, coinciding in time with the stage of formation of the cellular structure.τ0), plastic viscosity (η), and plastic strength (mP) in time equal to the swelling period (0–80 min) was studied.To assess the kinetics of the rheological properties of the material of the interpore wall of the aerated concrete mixture, the change in its ultimate shear stress (spS = 3000 cm2/g) were mixed with water (W/T = 0.5), for 3 min. The mass (at t = 35 °C) was placed in a viscometer and, upon reaching a given point in time, the values τ0 and η were determined. The experiment was repeated 3 times. The results of the experiment are shown in The test procedure was adopted as follows. Raw materials (Portland cement and ground sand −2 Pa×s) 2 on their surface, and the appearance of coagulation bonds between the particles of the hardening system  b. The cug system a,c, whicτ0 and Pm stabilize in the period of 20–40 min is explained by the saturation of the liquid phase of the Ca(OH)2 interpore substance, fine-grained cement neoplasms, and the appearance of a binder film of hydrated neoplasms on the surface of the grains, which prevents the development of structure formation of the cement system. The instability of the parameters of the hydration kinetics of cement in the initial period, and the impossibility of operational control of hydration, leads to a change in the kinetics of swelling of the aerated concrete and the heterogeneity of the final properties. It is possible to reduce the influence of the instability of the initial period of structure formation on the process of swelling of the aerated concrete mixture, if the gas release of the blowing agent begins during the period of stabilization of the properties of the cement system. This can be achieved by introducing pre-hydrated cement into the aerated concrete mixture or by holding the mixture until the blowing agent is introduced.The fact that the values of The alignment characterizes the traditional casting technology in a time of three kinetic phenomena—intensive hydration of the binder, changes in the rheological properties of the interpore material, and the gas evolution reaction of the aluminum blowing agent, which have a decisive influence on the swelling kinetics and physical and mechanical properties of aerated concrete. The study on the phenomenological model, carried out in the previous section, revealed that if the outgassing occurs during the period of intensive hydration of the binder (up to 30 min from the start of mixing), then the swelling kinetics is unstable, and a slight change in the outgassing parameters, rheological, and other properties lead to significant changes in the swelling process.To achieve increased physical and mechanical properties, an optimal combination of the kinetics of hydration phenomena, microstructure formation of the interpore wall, and gas release is necessary. To create favorable conditions for swelling, cement previously mixed with water and aged for a given time, was introduced into the composition of the aerated concrete mixture as its component. At the same time, the process of cement structure formation reached the stage of coagulation of hydrate neoplasms, and the rheological properties stabilized.Preliminary studies of the influence of the water-cement ratio W/C (0.3–0.6) on the regularities of the kinetics of the rheological properties of the cement paste showed that the time for the start of stabilization of the limiting shear stress with an increase in W/T increases from 17 to 24 min. For the convenience of work in further experiments, W/C = 0.5 was taken.As a result of tests b, it wasThe results of swelling of an aerated concrete mixture a,b of thbR is compressive strength, MPa; avρ is average density, kg × m3.To assess the effectiveness of the pre-hydration time of the binder on the mechanical and physical characteristics of aerated concrete, the coefficient of constructive quality (CSQ) ,52 was c3) and thermal conductivity by 31%, as well as an increase in CSQ, is achieved with a pre-hydration time of 20–30 min. At the same time, according to the CSQ indicator, it is noticeable that the dynamics of strength reduction in this pre-hydration time interval is the smallest CSQ is 7–13% higher compared to other time intervals.The values of the average density of aerated concrete and its compressive strength  show thaA further increase in the pre-exposure time is impractical since it worsens the quality of the structure. Thus, the determination of the adequate time of preliminary hydration of cement at a given material strength can be determined from the corresponding values of its average density and thermal conductivity.In order to assess the contribution of the study to the base of world science, it is necessary to determine its place in comparison with the results obtained by other authors. The study has a theoretical and applied character and consists of two main aspects. The first is the filling of research gaps, expressed in the study of the very nature of the process of outgassing and modeling of these processes to obtain more accurate theoretical knowledge and develop existing ideas about the processes occurring during the formation of the microstructure of aerated concrete. The second aspect is the filling of technological deficiencies, expressed in the determination of quantitative and qualitative aspects and values of the recipe and technological parameters that affect the quality of the final material—non-autoclaved aerated concrete of a new level, and obtaining effective building structures, buildings, and structures from them. In comparison with the researchers who previously carried out work to determine the nature of the formation of the aerated concrete structure, in particular with the works ,35, moreBased on theoretical analysis, experimental studies, and the mathematical model of the swelling process, which take into account the convective and molecular diffusion of hydrogen from the mixture and the conditions of swelling, precipitation, and stabilization of the mixture, the increase in the uniformity of the level of swelling of the aerated concrete mixture was developed.An improved method for the manufacture of aerated concrete is proposed, which comprises preliminarily hydrated for 20–30 min cement into the composition of the aerated concrete mixture. The method provides an improvement in the gas-holding capacity and an increase in the swelling of the mixture, a decrease in the average density of aerated concrete up to 29%, and an improvement in heat-shielding properties up to 31%. At the same time, the smallest dynamics of the decrease in the strength properties of aerated concrete were observed, which is confirmed by a large CSQ of up to 13%.Aerated concrete has been obtained that meets the requirements of environmental friendliness and economic efficiency, and has improved mechanical and physical characteristics. The effectiveness of the use of production waste in the form of partially hydrated cement in the compositions of such aerated concrete has been proven, thereby reducing the cost of production of aerated concrete and construction in general, amounting to about 15%.Thus, the environmental effect of our proposals is to reduce the burden on the environment through the use of waste-free technology. Such technology is the addition of partially hydrated cement, i.e., a waste from aerated concrete production, in a new production. At the same time, the environmental effect develops into an economic one, which is expressed in a reduction in the cost of raw materials, which is especially important for manufacturers.


The distributions of antibiotic prescriptions by geography, antibiotic class, and prescriber specialty are similar in the US Centers for Medicare and Medicaid Services (CMS) Part D Prescriber Public Use Files and IQVIA Xponent dataset. Public health organizations and healthcare systems can use these data to track antibiotic use and guide antibiotic stewardship interventions for older adults. The Centers for Disease Control and Prevention (CDC) Core Elements of Outpatient Antibiotic Stewardship highlight the importance of tracking and reporting of clinician prescribing. Proprietary databases, such as IQVIA Xponent, have been used for tracking antibiotic use at the national level and identifying opportunities for improving prescribing practices, but require funding and have not been compared with other data sources that characterize antibiotic prescribing. Stakeholders can use prescription data from the Centers for Medicare and Medicaid Services (CMS) at low to no cost to support antibiotic stewardship activities.In 2014–2016, the highest rates of outpatient antibiotic prescribing were observed in adults 65 years and older; 30% of antibiotic prescriptions in this population are considered unnecessary.Adults 65 years and older, as well as individuals under 65 with certain medical conditions, are eligible to enroll in Medicare insurance coverage. Approximately 94% of adults 65 and older are enrolled in Medicare and 72% have Part D prescription coverage.The CMS provide three Part D Prescriber PUFs that are publicly available and contain information on drug utilization: Geography-Drug, Provider, and Provider-Drug datasets. In 2018, IQVIA Xponent captured ∼92% of the outpatient prescriptions that were dispensed by retail pharmacies in the United States. IQVIA then uses a proprietary projection methodology to estimate 100% of outpatient prescriptions.IQVIA Xponent has been used to describe national outpatient antibiotic prescribing.We determined the antibiotic data elements available and assessed the level of suppression of prescription claims by comparing the overall volume of antibiotic prescriptions in each dataset to the national level of the Geography-Drug dataset in 2018. We compared the distribution of antibiotic claim counts by US Census region, antibiotic class, and prescriber specialty when available. The Geography-Drug, Provider, and Provider-Drug datasets were stratified by state. The Geography-Drug and Provider-Drug datasets were stratified by antibiotic class and agent.We limited the comparison of CMS Part D Prescriber PUF and IQVIA Xponent to adults aged ≥65, included only oral antibiotics available in both datasets and excluded non–US states . We used the Geography-Drug dataset at the state level for comparison since data could be stratified by age, region, and antibiotic class with minimal suppression. This activity met the requirements of public health surveillance as defined in 45 CFR 46.102(l)(2).Across the CMS Part D Prescriber PUF datasets, the number of outpatient antibiotic prescriptions ranged from 64.6 million in the national level of the Geography-Drug dataset to 44.5 million in the Provider-Drug dataset Table . The GeoFor adults aged ≥65 years, the number of oral antibiotic prescriptions was lower in the CMS Part D Geography-Drug dataset at the state level (N = 48.4 million) compared to the IQVIA Xponent dataset (N = 57.6 million). The proportion of antibiotic prescriptions by region and antibiotic class varied by <2% across both datasets Table . Stratif CMS Part D Prescriber PUFs are publicly available and readily accessible to public health organizations and healthcare systems.The distribution of prescriptions by geography, antibiotic class, and prescriber specialty in the CMS Part D Prescriber PUFs are similar to the distributions in the national IQVIA Xponent dataset. Furthermore, the CMS Part D Prescriber PUFs have been used previously to describe national and regional outpatient antibiotic prescribing trends. The Geography-Drug dataset can be used to describe annual prescription trends by antibiotic class and agent among older adults enrolled in Medicare Part D but cannot be used to provide prescriber feedback. The Provider dataset can be used to describe antibiotic prescription trends by geographic region (including state and city) and provider specialty. Although antibiotic class and agent cannot be described in the Provider dataset, it can be used to assess prescriber-level total antibiotic volume with the least analytic manipulation. The Provider-Drug dataset provides the most detail at the prescription level. However, it has the highest level of data suppression and its complexity requires more analysis to describe prescriber-level prescribing practices compared to the Provider dataset. Individualized feedback provided to clinicians on antibiotic prescribing practices, especially when including comparison with peers, has been shown to be effective at reducing antibiotic prescribing in high-volume antibiotic prescribers. The Provider dataset may be most suitable for public health organizations and healthcare systems to provide prescriber feedback.The CMS Part D Prescriber PUFs include unique data characteristics that must be considered to determine which dataset best aligns with program goals and stewardship interventions.There were differences in antibiotic volume between the CMS Part D Prescriber PUFs and IQVIA Xponent. IQVIA Xponent is projected to 100% of the retail market, whereas Part D prescription claims cover ∼75% of Medicare beneficiaries. Also, prescription claim counts <11 are suppressed in CMS Part D Prescriber PUFs, which has a larger impact on total antibiotic volume at the prescriber level; up to one-third of prescriptions and prescribers are suppressed in different CMS Part D Prescriber PUFs based on the level of aggregation.The CMS Part D Prescriber by Provider dataset provides readily available data for public health organizations and health systems to assess antibiotic prescribing among adults 65 years and older and to identify prescribers for peer comparison audit and feedback interventions.


The mechanical strength, thermal stability, thermal performance, and microstructure of Qtech T26 blast mitigation polyurea (T26 polyurea) were studied using quasi-static and dynamic mechanical experiments, thermogravimetric experiments, differential scanning calorimetry (DSC), scanning electron microscopy (SEM) experiments, and contact explosion and non-contact explosion experiments with polyurea-coated reinforced concrete slabs. Additionally, the energy dissipation mechanism of the coating was analyzed. The blast mitigation ability and blast mitigation mechanism of T26 polyurea-coated reinforced concrete slabs were investigated by analyzing the macroscopic morphology of reinforced concrete slabs with or without coatings and the contact explosion simulation of polyurea-coated reinforced concrete slabs. The results showed that T26 polyurea exhibited a certain strain rate effect. Its initial thermal decomposition temperature reached 286 °C, and its thermal stability was good. After carbonization, carbon slag can form and adhere to the structural surface. The glass transition temperature Tgs of the soft segment was −44.9 °C, and the glass transition temperature Tgh of the hard segment was 36.5 °C, showing a certain amount of microphase separation morphology. After the explosion test, there was a small pit on the front surface of the coated reinforced concrete plate, and there was no damage on the back surface. The integrity of the plate was good. The uncoated reinforced concrete slab had a large crater on the front of the explosion surface, and the back of the explosion surface experienced explosion collapse, concrete crushing, and an overall loss of stability. The numerical simulation results showed that the failure mode of the coated plate was consistent with the test. The kinetic energy conversion rate of the uncoated reinforced concrete plate was 87.27%, and the kinetic energy conversion rate of the coated reinforced concrete plate was 95.36%. The T26 coating improved the kinetic energy conversion rate of the structure and improved the blast mitigation ability of the reinforced concrete plate structure. Polyurea is a kind of polymer material formed by the rapid cross-linking of isocyanate components and amino compounds that has excellent mechanical properties ,2 and whIn addition, the good blast mitigation effect of polyurea in explosion protection is closely related to its excellent mechanical properties and strain rate effect . ThroughGiven the limitations of the field explosion test, other relevant research is based on the use of ANSYS/LS-DYNA software for numerical simulation. Amini  used numPolyurea protective coating has been studied in terms of anti-explosion, but there is little analysis on the influence of the performance of polyurea material on its blast mitigation. The explosion process is complicated. The explosion will produce high temperatures and strong shock waves that are scattered around. In the explosion protection, the coating material should not only withstand the high temperature and high heat, but also resist the tensile and tearing effects caused by the explosion loads. Therefore, the thermal properties and mechanical properties of coating materials are the basic conditions for their blast mitigation effect. In this regard, for blast mitigation, T26 polyurea was selected in this paper. Starting with the characteristics of the material, the basic mechanical properties and thermal properties of T26 polyurea at different strain rates were studied to understand the molecular stability of T26 polyurea at high temperatures and predict the blast mitigation ability of the material. On this basis, through the contact explosion test and non-contact explosion test of T26 polyurea-coated reinforced concrete slabs and the numerical simulation of reinforced concrete slabs with or without polyurea coating under contact explosion, the damage of reinforced concrete slabs with or without polyurea coating was compared, and the energy absorption and energy dissipation characteristics of T26 polyurea under explosion load were analyzed. The microstructure and the failure mode of the cross-section of T26 polyurea coating after the explosion were observed. The failure mode of the coating under explosion load was studied to verify the blast mitigation ability of T26 polyurea.−3 and has the characteristics of low density, as shown in T26 polyurea is a kind of blast mitigation polyurea material optimized via the traditional polyurea formula. The density of T26 polyurea is below 1 g · cmThe concrete strength grade was C40 with the reinforcement spacing at 150 mm and the diameter at 10 mm, while the protective layer thickness was 15 mm and the size of the reinforced concrete slab was 1000 mm × 1000 mm × 300 mm. The reinforcement was as shown in Good adhesion between the T26 coating and the concrete substrate is crucial. Before spraying, an epoxy-modified polyurethane primer should be applied to the surface of the substrate . The seaReinforcement concrete slabs sprayed with T26 were, after seven days of maintenance, placed on the restraint frame. The explosion pit had a side excavation depth of 0.5 m and a width of 0.7 m on the back explosion surface, and explosives with a TNT dosage of 1.4 kg were placed on the upper surface of the reinforced concrete plate for the explosion test. The schematic of the experimental setup is shown in −1, 0.01 s−1, and 0.1 s−1. The tensile test was carried out until the samples were broken.The T26 polyurea samples were cut into a dumbbell shape using a tablet punching machine  and 1.4 nm (1 kV), the acceleration voltage is 0.1–30 kV, the electron gun uses a tungsten filament lamp, and the magnification is 25–1,000,000 times.ANASYS software was used for the modeling, and LS-DYNA software was used to calculate the model. Calculation models included steel bars, concrete slabs, explosives, air, and polyurea materials. A Lagrange grid and hexahedral element were used in the model grid. The fluid–solid coupling algorithm (ALE) was used in the grid, and the non-reflective normal boundary conditions were set at the boundary. The polyurea material was modeled using a shell element, the steel was modeled using a beam element, and the concrete slab was modeled using a solid element. In addition, the coating and concrete automatically had single-sided contact, and the common node model was used between steel and concrete. The reinforced concrete slab model size was 1000 mm × 1000 mm × 300 mm, and the bottom had fixed support using double reinforcement. The explosive was a cylindrical TNT with a radius of 50 mm and height of 110 mm, and the dosage was 1.4 kg. The air was evenly divided into 1.5 cm grids.After establishing the model of contact explosion between uncoated and T26-coated reinforced concrete slabs in ANSYS, the output file was set as an LS-YDNA file format. The relevant parameters in the output file were modified, including coating thickness and output time, and the coating thickness was 10 mm, the output time was 1000 μs. The modified file was post-processed in LS-YDNA software to obtain the relevant simulation results.For polyurea, the elastic-plastic model named MAT_PIECEWISE_LINEAR_PLASTICITY  was usedJohnson–Holmquist–Cook model  was usedThe reinforcement model was MAT_PLASTIC_KINEMATIC . It is aThe air was described by the MAT_NULL material model and linear polynomial state equation EOS_LINEAR_POLYNOMIAL. The air model parameters are as shown in The explosive model was MAT_HIGH_EXPLOSIVE_BURN, and the EOS_JWL equation of state was selected. The detailed parameters of the above material model can be found in the LS-DYNA user manual . The exp−1 to 0.1 s−1, the stress of the material increased with the increase in the strain rate. Thus, T26 polyurea showed a good strain rate effect at a low strain rate.The stress–strain curves of T26 polyurea at a low strain rate are shown in −1 was higher than that at the strain rate of 11.37 s−1. The accurate stress–strain curves of T26 polyurea were nonlinear at a high strain rate. With the increase in true strain, the true stress increased, and when the strain rate increased, the true stress also increased, indicating that T26 polyurea presented a good strain rate effect. T26 polyurea showed good mechanical strength at a high strain rate. Therefore, during the explosion, the material can continuously improve its strength to resist explosion shock load and enhance the blast mitigation ability of the composite structure with the increase in explosion load strength.The strain rate effect of the material under a high strain rate was further studied. The true stress-strain curve of the material under a high strain rate was obtained by filtering the data collected by the acquisition instrument, as shown in The DSC curve of materials in the temperature range from 30 °C to 700 °C is shown in The explosion environment is a high-temperature environment, which requires the high-temperature adaptability of materials. The TG and DTG curves of T26 polyurea coating are shown in In addition, it can be seen from the DTG curve in The failure modes of uncoated reinforced concrete slabs after contact explosion are shown in The failure modes of the reinforced concrete slabs coated with T26 after contact explosion are shown in The failure modes of the reinforced concrete slab coated with T26 after the explosion with an explosion distance of 50 mm are shown in The T26 polyurea coating after explosion damage was divided into section area I, explosion source center area II, and coating edge area III, and the coatings in the three regions were cut for microscopic morphology observation, as shown in The micro-morphology of T26 polyurea coating was enlarged by 4000 times in different regions after the explosion. The surface of the section area was torn in different degrees, the shape of the damage was scaly, the surface arrangement was disordered and uneven, and there were more tearing layers and a small amount of brittle failure. It can be seen that the polyurea coating melted in some areas under the high temperature caused by the explosion, and the strong shock wave caused the tensile failure of the polyurea coating. At the end of the explosion, the instantaneous decrease in temperature led to the transformation of polyurea from a highly elastic state to a glass state, and the broken polyurea solidified into flakes attached to the surface of the section, as shown in The stress nephograms of the front, back, and side of the uncoated reinforced concrete plate at time t = 1000 μs are shown in The stress nephograms of the front, back, and side of the coated reinforced concrete plate at time t = 1000 μs are shown in In summary, a T26 polyurea coating can improve the blast mitigation ability of reinforced concrete slabs, which played a key role in the blast mitigation protection of reinforced concrete slabs. The numerical simulation and explosion test damage diagram of T26 polyurea are shown in 5 J. Additionally, the kinetic energy change trend of the coated reinforced concrete slab was similar, and when the time t = 29.96 μs, the peak value was 2.12 × 105 J. Compared with the uncoated reinforced concrete slab, the peak of kinetic energy shifted and decreased by 65.42%, indicating that the presence of coating absorbed part of the energy and weakened the kinetic energy of the reinforced concrete slab, as shown in 5 J. Although the internal energy of the coated reinforced concrete slab changed little, showing a trend of increasing first and then decreasing slightly, the maximum absorption of internal energy was 3.26 × 105 J. In summary, the explosion shock energy was greatly attenuated after passing through the T26 coating. The coating can reduce the kinetic energy and internal energy of the reinforced concrete slab by absorbing a large amount of the energy generated by the explosion, and ultimately improved the ability of the reinforced concrete slab to resist the explosion.An explosion can instantly produce high temperatures and strong kinetic energy that is spread around in the form of waves that penetrate reinforced concrete slabs to cause local or overall damage. When the blast wave propagates from the face surface blast of the reinforced concrete slab to the back blast surface of the reinforced concrete slab, the main failure modes of the plate are explosion pits, explosion collapse, explosion penetration, and explosion punching ,24. The In order to further explore the energy absorption of the T26 coating, the kinetic energy, internal energy, and kinetic energy conversion rate of the face surface blast coating, back blast surface coating, and the reinforced concrete slab were shown in (1) Compared with uncoated reinforced concrete slab, the T26-coated reinforced concrete slab had a minor damage degree and higher structural integrity under a 1.4 kg TNT explosion load, and the T26 polyurea had significant explosion protection ability.(2) The explosion protection forms of the coating of the face surface blast and back blast surface were different. The T26 coating on the face surface blast was melted and perforated under explosion load. After melting, the coating formed a surface of carbon slag attachment, which played a role in coating and heat insulation. The T26 coating prolonged the action time and dissipation time of the explosion load by absorbing the energy of the explosion shock wave. By coating the concrete structure, the back blast surface coating restrained the explosive debris to resist the residual shock wave and reduced the secondary damage.(3) In terms of energy conversion and dissipation, the kinetic energy and internal energy of the uncoated slab were larger than those of the coated slab under the same explosive load. The kinetic energy conversion rate of the uncoated reinforced concrete slab was 87.27%, and that of the coated reinforced concrete slab was 95.36%. The T26 coating improved the kinetic energy conversion rate of the structure and dissipated part of the kinetic energy into internal energy, thus weakening the transfer of explosive energy and improving the blast mitigation ability of the reinforced concrete slab structure.


The legacy of the ‘SL > SS principle’, that a single or a few large habitat patches (SL) conserve more species than several small patches (SS), is evident in decisions to protect large patches while down‐weighting small ones. However, empirical support for this principle is lacking, and most studies find either no difference or the opposite pattern (SS > SL). To resolve this dilemma, we propose a research agenda by asking, ‘are there consistent, empirically demonstrated conditions leading to SL > SS?’ We first review and summarize ‘single large or several small’ (SLOSS) theory and predictions. We found that most predictions of SL > SS assume that between‐patch variation in extinction rate dominates the outcome of the extinction–colonization dynamic. This is predicted to occur when populations in separate patches are largely independent of each other due to low between‐patch movements, and when species differ in minimum patch size requirements, leading to strong nestedness in species composition along the patch size gradient. However, even when between‐patch variation in extinction rate dominates the outcome of the extinction–colonization dynamic, theory can predict SS > SL. This occurs if extinctions are caused by antagonistic species interactions or disturbances, leading to spreading‐of‐risk of landscape‐scale extinction across SS. SS > SL is also predicted when variation in colonization dominates the outcome of the extinction–colonization dynamic, due to higher immigration rates for SS than SL, and larger species pools in proximity to SS than SL. Theory that considers change in species composition among patches also predicts SS > SL because of higher beta diversity across SS than SL. This results mainly from greater environmental heterogeneity in SS due to greater variation in micro‐habitats within and across SS habitat patches (‘across‐habitat heterogeneity’), and/or more heterogeneous successional trajectories across SS than SL. Based on our review of the relevant theory, we develop the ‘SLOSS cube hypothesis’, where the combination of three variables – between‐patch movement, the role of spreading‐of‐risk in landscape‐scale population persistence, and across‐habitat heterogeneity – predict the SLOSS outcome. We use the SLOSS cube hypothesis and existing SLOSS empirical evidence, to predict SL > SS only when all of the following are true: low between‐patch movement, low importance of spreading‐of‐risk for landscape‐scale population persistence, and low across‐habitat heterogeneity. Testing this prediction will be challenging, as it will require many studies of species groups and regions where these conditions hold. Each such study would compare gamma diversity across multiple landscapes varying in number and sizes of patches. If the prediction is not generally supported across such tests, then the mechanisms leading to SL > SS are extremely rare in nature and the SL > SS principle should be abandoned. I.et al., et al., World Conservation Strategy.Conservation decision‐making relies on a combination of local knowledge and general rules or principles  or several small (SS) patches. Early reviews of these empirical studies showed a lack of support for the principle. In particular, Simberloff & Abele , p. 48 fWikipedia entry for ‘SLOSS debate’ concludes that “[t]he general consensus of the SLOSS debate is that neither option fit[s] every situation and that they must all be evaluated on a case to case basis.” The SLOSS debate has therefore largely disappeared from the ecological literature: Google Ngram Viewer indicates that the proportional occurrence of the term ‘SLOSS debate’ peaked in 2006 and has declined steadily since  or the landscapes . These are summarized below and in Table et al., et al., et al., et al., et al., et al., Despite the fact that most researchers have shelved the SLOSS debate, its legacy remains in practice, because many conservation agencies continue to prioritize protection of large, contiguous areas of habitat, while small patches of natural habitat are less likely to be protected  AND (“single large” OR “single‐large” OR “SLOSS”), refined by research area to environmental sciences and biodiversity and conservation. We retained all papers presenting SLOSS predictions, whether based on formal theory or verbal arguments. Although SLOSS is specifically about species richness, most of the predictions related to SLOSS are based on single‐species models and mechanisms i) patches are far apart; (ii) the matrix is hostile and leads to very high dispersal mortality; (iii) the species avoid entering the matrix ; or (iv) the species have very low innate mobility. As small patches are expected to have smaller populations than large patches, they should have higher extinction rates from demographic stochasticity. The persistence of any given species on a set of isolated patches will then be driven by the size of the largest patch et al., et al., sensu Taylor et al., et al., When movements among patches are common, population processes are generally predicted to lead to SS > SL Table . SS shouet al., The species pool available to colonize SS is also expected to be larger than the species pool available to colonize SL. If potential colonists can arrive at a patch from nearby habitat of the same type within a given distance of the patch , then the species pool available to colonize a set of habitat patches (SS or SL) will depend on the total area of that same habitat type within their local landscapes. This total area of potential donor habitat is expected to be larger for SS than SL because the total edge length of SS is larger than the total edge length of SL, making the sum of the local landscapes larger for SS than for SL Fig. . Along w(3)All of the SLOSS predictions discussed so far derive from assumptions about how extinction/mortality and colonization/immigration dynamics interact with sizes of individual patches and with sets of patches. In general, SL > SS is predicted when extinction dominates these dynamics, except when spreading‐of‐risk plays an important role in population dynamics. SS > SL is generally predicted when colonization/immigration dominates the dynamics. Considering these factors together, Ovaskainen  predicteet al., et al., A different set of SLOSS theory asks how the number of patches  is expected to affect beta diversity. Perhaps the simplest or null theory is the ‘geometric effect’, based on a cookie‐cutter analogy  decreasing inter‐patch movement potentially leading to SL > SS, and (ii) increasing across‐habitat heterogeneity and decreasing species overlap leading to higher beta diversity and SS > SL i) arguments based on population processes generally predict SL > SS when between‐patch movements are assumed to be rare, such that variation in local (patch) extinctions dominates the extinction–colonization dynamic; (ii) an exception to this occurs where spreading‐of‐risk plays a large role in population persistence, leading to a prediction of SS > SL; (iii) arguments based on population processes generally predict SS > SL when between‐patch movements are assumed to be common such that variation in colonization dominates the extinction–colonization dynamic; and (iv) consideration of beta diversity and across‐habitat heterogeneity generally leads to predictions of SS > SL. Therefore, SLOSS predictions can be largely characterized by the combination of three variables: the frequency of between‐patch movements; the role of spreading‐of‐risk in landscape‐scale population persistence; and the level of species clumping indexed as across‐habitat heterogeneity. These are the three axes in Fig. The major features of SLOSS predictions and data to date are illustrated in Fig. all of the following are met: between‐patch movements are rare, the role of spreading‐of‐risk in landscape‐scale population dynamics is low, and across‐habitat heterogeneity and species clumping are low, reducing the role of beta diversity i) the frequency of between‐patch movements, (ii) the degree to which spreading‐of‐risk is important for landscape‐scale population persistence, (iii) the level of across‐habitat heterogeneity; and (iv) gamma diversity over different landscapes characterized by SS versus SL. Note empirical tests will measure across‐habitat heterogeneity rather than spatial clumping of species because estimating the spatial distribution of multiple species over multiple landscapes  have more or fewer species than few large patches . In addition, when SLOSS is evaluated using subsets of intermixed patches, the link between the data and several of the mechanisms in Table  SL Fig.  includes SL Fig. , rather et al., versus landscapes with SL  than large ones, e.g. due to different ownership of different patches  dissipation of transient positive fragmentation effects caused by a crowding effect on small patches following patch creation  sufficient time for any extinctions to play out x hold.’ Such conditions have been suggested  habitat is rare, i.e. patches – both large and small – are far apart relative to the dispersal range of the species group, (ii) habitat is spatially homogeneous, and (iii) the matrix is hostile . The groups of species selected should be those assumed to have low innate mobility, and those for whom spreading‐of‐risk likely plays a minor role in population dynamics, i.e. stronger competitors under bottom‐up control that are not subject to frequent local disturbances et al., et al., As indicated in Table et al. et al., Here we emphasize that a single study on a particular species group in a particular region cannot answer the question ‘are there consistent, empirically demonstrated conditions that lead to SL > SS?’ SL > SS was conceived and is used as a general principle. We know it is not universally valid, because most empirical studies do not support it. However, it may still apply in general when certain conditions hold, specifically the combination of low between‐patch movement, low spreading‐of‐risk, and low across‐habitat heterogeneity. Testing this prediction will require multiple studies on a range of taxa and regions that match these conditions , Fahrig  habitat aggregation , (ii) aggregation of environmental conditions , and (iii) connectivity . They predict maximum species coexistence under the combined conditions of low habitat aggregation (SS), high across‐habitat heterogeneity, and high between‐patch movement frequency. It therefore appears that the SLOSS cube hypothesis is compatible with general metacommunity theory, although a more formal evaluation is needed.We note that SLOSS predictions Table  and meta, et al. , p. 8 suet al.'s  proposed . Habitat loss is the main cause of species declines, and so habitat preservation and restoration are the top priorities for biodiversity conservation. If, in a particular situation, a choice is presented between conserving one large patch versus several small patches, but the small patches have much less habitat in total, then the decision should be to conserve the large patch. For example, in the Steigerwald forest in Southern Germany there is an ongoing discussion about establishing a national park of 10000 ha versus protecting a set of smaller areas of about 5000 ha in total. Here, the large national park would probably be more effective for biodiversity conservation, because the total habitat preserved would be twice that of the set of small patches.We emphasize that SLOSS is explicitly not about the role of habitat amount. Rather, it is about the influence of the pattern or configuration of a given amount of habitat  versus number of patches in the landscape, for landscapes within each of 32 studies included in the main analysis in Watling et al. (g et al. .Click here for additional data file.


D/t) and the tensile strength of the FRP (ffrp) were set as the input sets. The existing models were compared with the test data. In addition, artificial neural networks (ANNs) and support vector regression (SVR) were used to predict the mechanical behaviour of FRP-confined circular concrete columns. The study showed that the predictive accuracy of the compressive strength in the existing models was higher than the peak compressive strain for the high dispersion of material deformation. The predictive accuracy of the ANN and SVR was higher than that of the existing models. The ANN and SVR can predict the compressive strength and peak compressive strain of FRP-confined circular concrete columns and can be used to predict the mechanical behaviour of FRP-confined circular concrete columns.The prediction and control of the mechanical behaviours of fibre-reinforced polymer (FRP)-confined circular concrete columns subjected to axial loading are directly related to the safety of the structures. One challenge in building a mechanical model is understanding the complex relationship between the main parameters affecting the phenomenon. Artificial intelligence (AI) algorithms can overcome this challenge. In this study, 298 test data points were considered for FRP-confined circular concrete columns. Six parameters, such as the diameter-to-fibre thickness ratio ( Fibre-reinforced polymers (FRPs) are widely used in composite structures and for structural strengthening owing to their light weight, high strength, and good corrosion resistance ,4,5,6,7.In FRP-confined circular concrete columns, the core concrete is subjected to triaxial compression under axial loading, which improves the bearing capacity and ductility of the members and subsequently reduces the section size and self-weight of the members ,9,10,11.D/t), the compressive strength of the core concrete (fco), the strain corresponding to the compressive strength of core concrete (εco), the tensile strength of FRP (ffrp), the elastic modulus of FRP (Efrp), and the ultimate tensile strain of FRP (εfrp) on the axial compressive mechanical behaviours of FRP-confined circular concrete columns and proposed their axial compression constitutive models. Fardis studied the influences of the section size and compressive strength of core concrete on the axial compressive mechanical behaviours of FRP-confined circular concrete columns and proposed a corresponding axial compression constitutive model based on the test results [Researchers have extensively investigated the axial compressive mechanical behaviours of FRP-confined concrete columns. They have studied the influences of the diameter-to-fibre thickness ratio  and support vector regression have attracted the most attention ,36,37,38ANNs are mathematical models that simulate the neural frame of a human to process complex information. They are widely used for data prediction ,40. Liu Support vector regression (SVR) is a regression model developed by Vapnik , who intD/t, fco, εco, ffrp, Efrp, and εfrp were set as input sets. Based on the established database, the forecast accuracy of the existing axial compression constitutive model for FRP-confined circular concrete columns was evaluated and analysed. ANN and SVR models were developed, and the forecast accuracy of the axial compressive mechanical behaviours of the FRP-confined circular concrete columns was evaluated and analysed using the ANN, SVR, and the existing axial compression constitutive models. Finally, based on the intelligent algorithm model, the affecting key factors were analysed using expanded parameters. Finally, the key factors affecting the axial compressive mechanical behaviours of the FRP-confined circular concrete columns were analysed based on an intelligent algorithm.ANNs and SVR have been successfully applied in the field of architecture and achieved ideal results ,48,49,50D/t, fco, εco, ffrp, Efrp, and εfrp on the axial mechanical behaviour of FRP-confined circular concrete columns. Detailed information on the main parameters is presented in The database relied on 298 specimens of tested data obtained from 13 studies ,56,57,58D/t, fco, εco, ffrp, Efrp, and εfrp are shown in D/t was mainly distributed in the range of 0–500. The minimum fco was 9.9 MPa, the highest was 136.3 MPa, and the data between 50 MPa and 100 MPa were the highest. The εco was concentrated in the range of 1500–3000 με. The ffrp in the range of 2000 MPa–4000 MPa was up to 65%. Most data on the Efrp were distributed in the range of 200–300 GPa. The data points of the εfrp in the range of 4.5 × 104–5 × 104 με were the least, and maximum data points were in the range of 3 × 104–4.5 × 104 με.The range of the R2), the mean square error (MSE), the mean absolute percentage error (MAPE), and the integral absolute error (IAE) were used to evaluate the predictive accuracy of the models. R2 reflects the correlation between the independent and dependent variables. The closer R2 is to 1, the higher is the correlation between the predictive value and the actual value. The MSE reflects the average error. The lower the MSE, the smaller the error between the predictive value and the actual value. MAPE reflects the degree of data dispersion. The smaller the MAPE, the more the predictive value converges to the actual value. Additionally, the IAE reflects the predictive accuracy. The smaller the IAE, the higher the predictive accuracy of the data. All the indices are often used to evaluate the predictive accuracy of the neural network model [iC is the predictive value of the compressive strength or ultimate compressive strain (MPa/με);  is the average value of the actual value of the compressive strength or ultimate compressive strain (MPa/με); n is the number of data points. is the average value of the predictive value of the compressive strength or ultimate compressive strain; and To evaluate the predictive accuracy of the models of the axial compressive mechanical behaviours of the FRP-confined circular concrete columns, the regression coefficient  for the predictive accuracy of the compressive strength of the above models are listed in R2 is above 0.5. The Lam model [R2 of up to 0.83 and the lowest average error and a small dispersion.The evaluation indexes  of the predictive accuracy in the peak compressive strain of all the models. It can be observed from The predictive accuracy of the compressive strength and peak compressive strain by the existing axial compressive constitutive model of FRP-confined circular concrete columns is low and that of the peak compressive strain is especially poor. Therefore, a new predictive model is urgently required to predict the axial compressive mechanical behaviour of FRP-confined circular concrete columns.An ANN is an information processing system that simulates the structural and functional characteristics of a biological neural system . It incl3; and the learning accuracy is 4 × 10−7.A MATLAB-based program with a graphical user interface (GUI) was developed to train and evaluate the ANN model. The ANN model divided the established database into two parts: 80% for training  and 20% for testing . According to the predictive target, there are six and one nodes in the input and output layers, respectively; the momentum rate is 0.5; the learning cycle is 10MSE of the compressive strength and peak compressive strain is the lowest, and R2 is the highest. The predictive accuracy of the ANN model was the highest. Therefore, when predicting the compressive strength and peak compressive strain, the number of nodes in the hidden layers in the ANN model was 10.The number of nodes in the hidden layer plays a vital role in the predictive accuracy of an ANN. To determine this, the predictive accuracies of different numbers of nodes in the hidden layers were compared and analysed. The influence of the number of nodes in the hidden layers on the predictive accuracy of the compressive strength is shown in The SVM is an intelligent algorithm for general classification problems, first proposed by Boser in 1992 . Unlike g is the key parameter of the RBF which can affect the smoothness of the function. The larger the g, the better the predictive effect of the training set.For the SVR model, the established database was divided into two parts: 80% for training and 20% for testing. The SVR model involves three parameters: ε (insensitive loss function), C (regularised constant), and g (kernel coefficient). In SVR, the main goal is to obtain a function that differs at most ε from the actual targets for all training data, while being as flat as possible . The smaTo determine the optimal values of ε, C, and g in the SVR, each value is tested in a certain space on the premise of specifying the step. Then, based on the flow of the SVR algorithm, the parameter values of the SVR with optimal accuracy are derived: ε = 0.01, C = 20, and g = 0.3. The flow of the SVR algorithm is illustrated in Based on the established database, the comparison between the ANN and SVR models for the predictive results of compressive strength and peak compressive strain are shown in R2 of the compressive strength and peak compressive strain is up to 0.96 and 0.94, respectively. In conclusion, the SVR model proposed in this study can provide an approximate basis for revising and unifying the compressive strength and peak compressive strain formulas for FRP-confined circular concrete columns.Among the existing axial compressive constitutive models for FRP-confined circular concrete columns, the Lam  and FardD/t, fco, ffrp, Efrp, fcc/ fco, and εcc/εco on the axial compressive mechanical behaviour of FRP-confined circular concrete columns. While analysing the influence of each parameter, the values of the other parameters were set as the average value of each parameter in the established database.An ANN was used to accurately analyse the influence of D/t on the compressive strength and peak compressive strain of the FRP-confined circular concrete columns is shown in D/t of the specimen. When the D/t increased from 200 to 1000, the compressive strength decreased from 130 MPa to 60 MPa and the peak compressive strain decreased from 3 × 104 to 104. When the D/t increases and the section size of the core concrete remains unchanged, the fibre thickness decreases and the force of constraint it can provide decreases, thus reducing the bearing capacity and ductility of the specimens [The influence of pecimens ,75,76,77Efrp on the compressive strength and peak compressive strain of the FRP-confined circular concrete columns is shown in Efrp, whereas the peak compressive strain is negatively correlated with the Efrp. When the Efrp increases from 40 GPa to 200 GPa, the compressive strength increases from 90 MPa to 150 MPa, and the peak compressive strain decreases from 2.5 × 104 to 1.5 × 104. When the Efrp increases, the elastic deformation resistance, the brittleness of the specimens, and the bearing capacity of the specimens increase, and the ductility decreases [The influence of the ecreases ,78,79.ffrp on the compressive strength and peak compressive strain of the FRP-confined circular concrete columns is shown in ffrp. When ffrp increases from 800 MPa to 4000 MPa, the compressive strength increases from 50 MPa to 250 MPa, and the peak compressive strain increases from 8 × 103 to 4 × 104. When ffrp increases, the force of the constraint provided by the FRP increases, and the bearing capacity and the ductility of the specimens are improved [The influence of improved ,80,81.fco on the compressive strength and peak compressive strain of the FRP-confined circular concrete columns is shown in fco, while the peak compressive strain of the FRP-confined circular concrete columns is negatively correlated with fco. When fco increases from 40 MPa to 100 MPa, the compressive strength of the FRP-confined circular concrete columns increases from 90 MPa to 160 MPa, and their peak compressive strain drops from 1.6 × 104 to 4 × 103. When fco increased, the overall strength, brittleness, and the bearing capacity of the specimens increased, and the ductility decreased [The influence of ecreased ,83,84.fcc/fco is negatively correlated with fco, while εcc/εco is positively correlated with εco. When fco increases from 40 MPa to 100 MPa, fcc/fco drops from 2.5 to 1.5. When εco increases from 3000 εcc/εco increases from 4 to 5. When fco increases, its ductility decreases, and the restraint of FRP on the core concrete weakens. Additionally, when εco increases, its ductility increases. The restraint effect of FRP on core concrete is strengthened.The influence of the mechanical behaviours of the core concrete on the FRP-confined circular concrete columns is shown in This study evaluated the existing axial compressive constitutive model of FRP-confined circular concrete columns and established a predictive model for the axial compressive mechanical behaviours of FRP-confined circular concrete columns based on ANNs and SVR. The main conclusions are as follows.(1)D/t, fco, εco, ffrp, Efrp, and εfrp on the axial mechanical behaviours of FRP-confined circular concrete columns were considered.A database of the axial compressive mechanical behaviours of FRP-confined circular concrete columns was established from the relevant published literature, which included 298 datasets. The effects of (2)Comparing and analysing the existing axial compressive constitutive model of FRP-confined circular concrete columns, the Lam model  exhibite(3)Comparing and analysing the existing axial compressive constitutive models of FRP-confined circular concrete columns, the Fardis model  exhibite(4)The ANN and SVR models can be used to predict the axial mechanical behaviours of FRP-confined circular concrete columns. Their predictive accuracy was much higher than that of the existing axial compressive constitutive model of FRP-confined circular concrete columns, and SVR had the highest predictive accuracy.(5)D/t is positively correlated with the compressive strength, whereas fco, ffrp, and Efrp are negatively correlated with the compressive strength of the FRP-confined circular concrete columns. The ffrp is positively correlated with the peak compressive strain, whereas D/t, Efrp, and fco are negatively correlated with the peak compressive strain of FRP-confined circular concrete columns.An intelligent algorithm was used to analyse the parameters of the axial mechanical behaviour of FRP-confined circular concrete columns. The analysis results show that