R2) is also the largest. The new model is suitable for fitting the stress–strain curve of concrete under uniaxial compression under various deteriorating forms, and the degree of fit between the constitutive prediction curve and the measured curve is high. It can be seen from the fitting results of the new model parameters that the ductile deformation capacity of concrete decreases first and then increases slightly, which is inconsistent with the law of gradual deterioration of strength. There is a minimum moment of ductility deformation capacity of concrete (MDC). The MDC of O-C40 concrete is about 114 freeze–thaw cycles, and the MDC of O-C50 concrete is about 116 freeze–thaw cycles; the degree of fit between the constitutive prediction curve and the measured curve is high. We hope that the improvement mentioned offers valid reference to the study of ductile deformation characteristics and failure process of compressed concrete under different deterioration forms.In order to study the ductile deformation characteristics and failure process of plain concrete under uniaxial compression, this paper proposes a new constitutive model. The new model was used to fit and analyze the constitutive curve of concrete under uniaxial compressive under various degradation forms and was compared with the traditional constitutive models. Finally, the new model was used to quantitatively analyze and predict the stress–strain curve of concrete in different degradation periods of a set of freeze–thaw measured data. The results show that, compared with the traditional constitutive model, the new model is simple in form and has few parameters, and the numerical value of the parameter can reflect the ductile deformation capacity of concrete. The fitting curve of the new model has the highest fitting degree with the measured stress–strain curve of concrete, and the goodness of fit ( Concrete material is one of the most important materials in the world. It is known as being “food for construction industry”. For the past 40 to 50 years, at the early stage of engineering design, the initial investment cost of the project was often emphatically considered. However, the influence of engineering environment on concrete durability is ignored ,2. As a The uniaxial compressive stress–strain curve of concrete is a comprehensive macroscopic reaction of the basic characteristics of compressed concrete , which cIn the past few decades, some experts and scholars have proposed various constitutive models to analyze the uniaxial compression stress–strain curve of concrete ,18. ThesBased on the previous research results, this paper finds that the piecewise constitutive model is easier to accurately fit constitutive curve of uniaxial compression, the polynomial equation is suitable for fitting the ascending curve, and the rational fraction equation is suitable for fitting the descending curve. In view of this, based on the model of , this paf is the stress in the constitutive model of concrete under uniaxial compression, and ε is strain.Reference  proposedIn order to meet the actual needs of the project, reference  carried However, there are some differences between the fitting results of this equation and the measured curves; for instance, the peak of the curve is discontinuous, and the descending section curves of different concrete are very different.prε is the peak strain, and uε is the strain corresponding to 0.85prf (peak stress) in the falling section. In Equation (2), c1, c2, c3, and c4 can be obtained. Substituting parameters mentioned above into Equation (3) can get the fitting curve of Equation (3). The fitting degree of the measured curve and the fitting curve can be observed intuitively by putting them in a graph, or by the goodness of fit (R2).In order to improve the fitting ability of the stress–strain full curve of concrete, reference  used theWhen  proposedm of the model is fitted. Through the experimentation, reference [In order to introduce the damage variable into the constitutive model to characterize the degradation of concrete materials, reference  establiseference  proved teference  is an emm = pr/fpr))1/, Reference  proposedβ1 and β2 are material parameter that depends on the shape of the stress–strain curve. Reference [β1 and β2 can be obtained by calculation. When 0 ≤ ε ≤ εpr, by substituting the value of parameter β1 into Equation (5), the fitting result of the rising curve can be obtained, and the value of parameter β2 adopts the same method can get the descent curve when εpr ≤ ε. prf′ is the maximum stress, usually considered as the concrete strength and usually determined in accordance with ASTM C 39, “Standard Test Method for Compressive Strength of Cylindrical Specimens”. Moreover, εpr′ is the strain corresponding with prf′. Since the prism specimen is adopted in this paper, in order to ensure that the peak stress and the peak strain of the fitting curve are equal to the values of the measured curve, the peak stress prf is used to replace prf′ and the peak strain prε to replace εpr′.In Equation (6), eference  points oa after fitting the ascending segment of the stress–strain curve of concrete (the curve before the peak stress). The second equation can obtain the value of parameter b after fitting the descending segment of the stress–strain curve of concrete (the curve after the peak stress). By substituting the value of parameter a into the first equation, the fitting result of the rising curve can be obtained, and the value of parameter b adopts the same method. This constitutive model is widely used at present, as shown in Equation (7).Reference  proposedy = prf/f, x = prε/ε. Parameters a and b have clear physical and geometric meaning [a value range from 1.5 to 3 and the parameter b values range from 0 to positive infinity, while the parameter a value may also be less than 1.5 or even negative. If a is smaller or b is larger, such as a is 0 and b is 10, the curve will be steeper, and the surrounding area under the curve will be smaller, indicating that the plastic deformation capacity and ductility deformation capacity of the concrete will be smaller, the material will be brittle, the failure process will be rapid, and the residual strength will be lower. On the contrary, the damage of concrete is slow and the residual strength is high. Therefore, the parameters a and b can be used to compare or measure the differences in the mechanical properties of concrete.In Equation (7),  meaning : Under nThe theoretical description of the full curve of  is shownx = 0, y = 0;(1) x(2) 0 ≤ x = 1, y = 1, dy/dx = 0, the curve is a single value peak;(3) x(4) x(5) x→ ∞, y→ 0, dy/dx→ 0; (6) x ≥ 0, 0 ≤ y ≤ 1.(7) x = 0, y = 0; x = 1, y = 1; x = 1, dy/dx = 0).At present, most of the constitutive models are unified full curve equations for the ascending curve and the descending curve. However, it is difficult to choose a single curve equation with simple form which can satisfy the geometric conditions of the constitutive curve and adjust the exact shape of the curve according to different concrete, so the form of the new constitutive model is piecewise. Reference  proposedc4 is zero, the equation has the same form as Equation (7) when c1, c2, and c3 are zero. The equations are shown in Equations (8) to (10):Because Equation (3) contains four parameters, in order to get a single parametric equation, one of the four parameters needs to be zero; when y = prf/f, x = prε/ε. Combing with x = 0, y = 0; x = 1, y = 1; x = 1, dy/dx = 0, Equations (8)–(10) can be transformed into Equations (11)–(13):In Equations (8)–(10), x = 0, dy/dx = 1.5 + 0.5c, we get the following:Taking Equation (12) as an example, when O, E = df /dε|x=0 is the initial tangent elastic modulus of concrete, N/mm2; and PE = pr/εprf is the peak secant modulus of concrete, N/mm2.In Equation (14)Equation (15) can be obtained from Equation (14):c has a clear physical (geometric) meaning—the ratio of the initial tangent modulus to the secant modulus times 2 minus 3. It can be seen that x ≤ 1, 2y/dxd2 = −6(0.5 + 1.5c)x + 12cx2 < 0, the available range of c is as follows: By condition (2), when 0 ≤ c, the fitting curve of Equation (12) can be obtained by substituting the fitting result of c into the equation. The corresponding relationship between the different value of parameter c and the curve shape before the peak stress is shown in c > 1, y > 1.0, in the local area of the rising curve, part of the stress is higher than the peak stress before the peak point, which obviously violates the actual situation. When −1/3 < c < 1, there is an inflection point on the curve, but the inflection point and the curvature are not obvious. When c < −1/3, with the decrease of c, the curvature of the curve increases gradually, and a large deformation will occur under small stress. The shape of the uniaxial compression curve of concrete can reflect the mechanical properties of concrete, so there is a certain relationship between the value of parameter c and the mechanical properties of concrete. By fitting the ascending section of the stress–strain curve based on Equation (12), and then getting the value of the parameter a, and the value of parameter a can reflect the ductile deformation capacity of concrete. Equation (12) is derived from Equation (7) and it contains only one parameter c, so it can be known from c has a clear physical meaning: If c is smaller, the curve will be steeper and the surrounding area under the curve will be smaller, the plastic deformation capacity and ductility deformation capacity of the concrete will be smaller, the failure process will be rapid, and the residual strength will be lower. In contrast, the ductility deformation capacity of concrete and residual strength will be higher. Therefore, the mechanical properties of concrete can be measured by the numerical value of parameter c.In c in Equation (11) is meaningless. Using Equation (11) to fit the ascending section of the stress–strain curve can get the value of the parameter c. The mechanical properties of concrete represented by parameter c are the same as Equation (12); the range of c is as follows: By using the same method, it can be concluded that the parameter c has a clear physical (geometric) meaning—the ratio of the initial tangent modulus to the secant modulus is reduced by 2 and then multiplied by −0.5. Using Equation (13) to fit the ascending section of the stress–strain curve can get the value of parameter c. The mechanical properties of concrete represented by parameter c are the same as Equation (12); the range of c is as follows:It can be seen that Reference  designedThe concrete specimens are cast in a size of 100 mm × 100 mm × 300 mm, and the freeze–thaw test is performed according to the “Test method for long term performance and durability of ordinary concrete” (GB50082-2009). Each freezing-and-thawing cycle is completed within 2 to 4 h; the melting time is more than 1/4 of the time of a freezing-and-thawing cycle. The central temperature of concrete specimens at the end of freezing and thawing is −18 ± 2 °C and 5 ± 2 °C, respectively. Dynamic modulus of elasticity and mass of concrete specimens are measured every 50 freezing-and-thawing cycles, as shown in prx = ε/ε, pry = f/f, u = εu/εprx) are used in the figure. Put the measured curve and the calculated curve or fitting curve in the same graph, so that their fitting degree can be observed. In order to prevent the accidental results of the fitting results, 50, 100, and 150 cycles of freeze–thaw cycles were conducted on ordinary C50 concrete. The results of stress–strain curves are shown in R2) is less than 0.94; the fitting results are quite different from the measured curve, which is also difficult to reflect the deformation and failure process of concrete under compression. The fitting results of [sults of   is always higher than 0.96, and the fitting results always have a high integration degree with the measured curve. The fitting curve of the new model two is always surrounded by the fitting curve of [2GR is only 0.94, and the minimum value is as low as 0.85, so the fitted result has severely deviated from the measured curve; the minimum value of 2NR of the new model two is 0.95, which is higher than the maximum value of 2GR and always keeps a high integration degree with the measured curve. There is almost no negative stress area in the fitting results, which is more in line with the reality. In summary, the new model two proposed in this paper has a high integration degree to the measured curve of concrete, and almost no negative stress areas appear and is more in line with actual.It can be seen from model of  and the model of ) was lesmodel of  decreasecurve of . In the curve of  has negaIn order to explore the applicability of the new model to the stress–strain curve of concrete under uniaxial compression under other state of deterioration, four groups of measured data of concrete under different deterioration situations were selected, which are high temperature failure, dry–wet cycle failure, freeze–thaw cycle failure, and high temperature failure after freeze–thaw cycle ,28,29,30The fitting curve of the new model has a high degree of integration with the measured curve. The goodness of fit of the new model is greater than that of the model of  and the Therefore, this paper uses Equation (19) to fit and analyze the measured stress–strain curve in c is the parameter in the fitting equation of the ascending curve (the curve before the peak stress), which can be obtained by fitting the curve before the peak stress; and b is the parameter in the fitting equation of the descending curve (the curve after the peak stress), which can be obtained by fitting the curve after the peak stress.Here, c and b of the measured curve in The stress–strain curve of concrete under uniaxial compression is the most basic constitutive relation, which can fully reflect the strength, toughness, and ductile deformation of concrete materials, etc. Equation (19) is used to fit the constitutive curve of concrete under uniaxial compression; the value of the parameter can be used to reflect the mechanical properties of concrete by fitting the value of parameters, and can also study the evolution law of mechanical properties of concrete through the change of parameters. The fitting parameters c of AE-concrete is gradually decreased, parameter b is gradually increased, the curve becomes increasingly steep –(23): In order to obtain the stress–strain curve of concrete in any deterioration period, and then to predict and study the mechanical properties of concrete, and also to explore the corresponding freeze-and-thaw times of the MDC, the relationship among the peak stress, the peak strain, parameters prf is the peak stress of concrete; prε is the peak strain of concrete; b and c are model parameters; and N is the number of freezing and thawing.In Equations (20)–(23), According to Equations (20)–(23), the constitutive curve of freeze–thaw concrete in any deterioration period can be predicted. It can be seen from c of O-C40 concrete is −3.865 and the corresponding number of freeze–thaw cycles is 111.42, the maximum value of the parameter b is 11.735 and the corresponding number of freeze–thaw cycles is 118.63, indicating that the MDC of the ordinary C40 concrete is about 111–118 times of freezing and thawing. According to Equation (21), the maximum value of the parameter b is 5.636, and the corresponding number of freeze–thaw cycles is 115.86, indicating that the MDC of the O-C50 concrete is about 116 times of freezing and thawing. According to Equation (20), the minimum value of the parameter In the study of this paper, the MDC only appears in ordinary concrete, but this phenomenon does not occur in air entraining concrete. The reason is that the ordinary concrete deteriorates faster; the compressive strength of O-C40 concrete and O-C50 concrete suffering 100 cycles of freezing and thawing decreased by 0.48 and 0.40, respectively, compared with that of unfreezing–thawing concrete, while that of AE-C40 concrete and AE-C50 concrete suffering 400 cycles of freezing and thawing decreased by 0.19 and 0.17, respectively, compared with that of unfreezing–thawing concrete. Therefore, the MDC usually occurs when the sample is damaged seriously, at this moment, the ductile deformation capacity of concrete is the weakest, the damage process is the fastest, and the concrete instantly break into several larger test blocks. Therefore, in practical engineering, we should not only pay attention to the change of concrete strength, but also the MDC, because once the concrete is destroyed when its ductility is the weakest, the damage speed of concrete is difficult to control and the loss is immeasurable. At present, the MDC can only be obtained by using the computing method in this paper. In the future, the research of the construction curve should pay attention to this aspect of the MDC, and it is also important to develop a more accurate forecasting methods for the MDC.It can also be found in In this paper, a new constitutive model of concrete under uniaxial compression was proposed, and its fitting characteristics and advantages were compared with traditional constitutive models. The applicability of the new model to the uniaxial compressive stress–strain curve of concrete under various degradation forms was verified, and the new model was used to quantitatively analyze and predict the stress–strain curve of concrete in different degradation periods. From the research in this paper, the following conclusions can be obtained:R2) is also the largest. The predicted curve of concrete obtained by the new model coincide with the measured constitutive curve.(1) Compared with traditional constitutive models, the new model is simple in form and has few parameters; the parameter value can reflect the ductility and deformation of concrete. The fitting curve of the new model has the highest fitting degree with the measured stress–strain curve of concrete, and the goodness of fit ((2) The new model is suitable for fitting the stress–strain curve of concrete under uniaxial compression under various deteriorating forms. For concrete with good mechanical properties, the fitting results of the new model are almost seamless with the measured results. For concrete with poor mechanical properties, the fitting results of the new model can still maintain a high degree of the goodness of fit with the measured results, and the fitting results are basically free of stress less than zero. Therefore, the fitting results of the new model are more accurate.(3) The quantitative analysis results of the measured curve show that the ductile deformation capacity of concrete does not decrease with the deepening on the deterioration of concrete, but decreases first and then increase slightly. This phenomenon is often seen in concrete with serious deterioration, and the conclusion is also obtained by using the model of  to quant(4) By collating the quantitative analysis results of the measured constitutive curve, it can be concluded that there is the MDC in the process of concrete deterioration. The MDC of O-C40 concrete is about 114 freeze–thaw cycles, and the MDC of O-C50 concrete is about 116 freeze–thaw cycles.


Thanks to the achievements in sanitation, hygiene practices, and antibiotics, we have considerably improved in our ongoing battle against pathogenic bacteria. However, with our increasing knowledge about the complex bacterial lifestyles and cycles and their plethora of defense mechanisms, it is clear that the fight is far from over. One of these resistance mechanisms that has received increasing attention is the ability to enter a dormancy state termed viable but non-culturable (VBNC). Bacteria that enter the VBNC state, either through unfavorable environmental conditions or through potentially lethal stress, lose their ability to grow on standard enrichment media, but show a drastically increased tolerance against antimicrobials including antibiotics. The inability to utilize traditional culture-based methods represents a considerable experimental hurdle to investigate their increased antimicrobial resistance and impedes the development and evaluation of effective treatments or interventions against bacteria in the VBNC state. Although experimental approaches were developed to detect and quantify VBNCs, only a few have been utilized for antimicrobial resistance screening and this review aims to provide an overview of possible methodological approaches. Humanity′s history is a continuous battle between us and microbial pathogens and for the most part, we were on the losing side with bacterial and viral infections being among the major causes of morbidity and mortality worldwide. Thanks to the development and improvement of sanitation, hygiene practices, and especially the discovery of antibiotics and vaccinations since the early 20th century, deaths from infectious diseases have declined markedly which can be considered one of the biggest success stories in human history . HoweverDuring the last decades, a plethora of antibiotic resistant bacterial genotypes have been reported and as a result, research has intensified to identify novel antibacterial agents and antibiotics ,10,11. WIn order to preserve viability and adaptability in constantly changing environmental conditions, bacteria have developed various mechanisms for switching from a vegetative to a metabolically inactive, but highly resistant and persistent state. The most studied type of such cellular dormancy is sporulation of sporogenous bacteria, while in recent years, the viable but non-culturable (VBNC) state for many bacterial pathogens has gained more attention ,14,15,16This widespread, or almost universal, occurrence of bacterial cellular dormancy can lead to serious diagnostic and safety problems. Bacteria in the VBNC state represent a diagnostic challenge, due to the simple fact that the majority of current tests are either entirely culture based or need at least one cultivation step, thus failing to detect non-growing VBNC cells ,20,21,22Although antimicrobial resistance is generally recognized as one of the major challenges posed by VBNC cells, the overall number of studies investigating this effect remains sparse. It is our opinion that the main reason for this is the technical and experimental difficulty of investigating antimicrobial resistance of dormant cells in a quantitative way. Therefore, this article aims to provide an overview of the currently available approaches, which could be used for antimicrobial effectivity testing of bacteria in the VBNC state.In addition to the special case of sporulating bacteria, there are a few different manifestations of phenotypic plasticity in microbes resistant to traditional antibiotic therapy: L-forms , persister cells, and VBNC bacteria . While iVibrio (V.) cholerae -2-deoxy-D-glucose (2-NBDG), which is comparable to glucose, to measure the active cell metabolism ,165. HowAdenosine triphosphate (ATP) is the energy source for metabolic activities in all living organisms and can be used as a viability indicator ,24. ManyThe application typically involves the addition of a reagent to lyse cells and release ATP, which, in the presence of luciferase, reacts with the substrate, D-luciferin, to produce light. The light intensity is then measured as relative light units (RLU), which is interpreted as a measure of ATP concentration ,169. It de novo ATP production of five different pathogens  in the VBNC state, to plate count during exposure to different heat stress and demonstrated that the ATP production of VBNC cells was in agreement with the plate count of culturable bacteria. On a laboratory scale, this approach can be used to determine the minimum ATP inhibitory concentration, which is a VBNC-MIC testing approach  for VBNC cells. Using this approach, the authors could demonstrate that bacteria in the VBNC state showed elevated tolerance levels against antibiotics, as well as disinfectants, while no differences were found in regard to heat stress. As the authors only compared MIC and MAIC results, but did not determine the minimal bactericidal concentration (MBC), it cannot be completely excluded that MBC and MAIC coincide.For this reason, in the VBNC research ATP is a popular biomarker for microbial viability as it is a fast, cheap, and easy approach to distinguish the viable from dead cells ,27,170. approach . After iApplicability for antimicrobial effectivity testing:de novo ATP production is able to qualitatively detect metabolically active cells including viable and VBNC cells. VBNC cells are defined by a significant de novo ATP production without the occurrence of culturable cells. The approach is not able to detect viable and VBNC cells at the same time from the same sample and dead cells are not actively detected, but rather inferred by the reduced de novo ATP production. The utilization of the de novo ATP production as a viability indicator offers the chance to perform a high throughput end-point screening for antibiotic and antimicrobial effectivity testing based on the de novo ATP production high-throughput in a similar setup as the established micro-broth dilution assay. Especially the fact that the de novo ATP production is a universal viability parameter for all bacterial species, makes the methodological approach very promising, as it should be readily transferable to other target organisms without additional adaptations. The approach is not dependent on the successful resuscitation of the target organisms, but as is the case for cell proliferation assays  to measure the uptake of the molecule through the cell membrane via an active electron transport system. Metabolically active cells reduce tetrazolium to a red-fluorescent formazan that accumulates within the cells and is detectable by microscopy or cytometry. The same principle can be measured using CTC, which is reduced to red-fluorescent 3-cyan-1,5-ditolyl formazan (CTF) [There are different fluorescence staining methods available to measure the metabolic activity via an active efflux pump system, enzyme activity, or an intact membrane potential . Emersonan (CTF) ,172,173.an (CTF) ,66. An ean (CTF)  using than (CTF) ,165.The different fluorescence staining methods can easily be detected by fluorescence microscopy and/or flow cytometry . In addiLin et al.  and Guo They found that CTC flow cytometry characterizes the essential viability of VBNC cells although CTC is only involved in a small part of the respiratory chain and reflects only the redox ability of the electron transport chain. Overall, the authors could demonstrate the effectiveness of their methodological approach to perform antimicrobial effectivity testing against bacteria in the VBNC state ,181.Applicability for antimicrobial effectivity testing:The methodological approach based on detecting the respiratory activity and membrane potential can be used to quantify viable as well as VBNC cells. By combining the approach with plate count methods, the amount of culturable as well as VBNC cells can be quantified from the same sample. In combination with additional staining methods , the approach can be used to accurately distinguish and quantify viable, dead, and VBNC cells. The combination of flow cytometry and fluorescent dyes for the detection of the respiratory activity and membrane potential offers the potential to perform antimicrobial effectivity testing of VBNC cells. In contrast to ATP detection methods, this approach can obtain quantitative results and is not susceptible to the possible regrowth of culturable cells.Limitations:A considerable disagreement exists to the exact value of this method for the analysis of environmental samples . One of In recent years, the awareness about the viable but non-culturable state of bacterial pathogens has dramatically increased and the fact that bacteria in the VBNC state are not visible for routine, growth based detection methods led to the development of novel analytical methods. The majority of methodological approaches determines at least one of the generally accepted viability parameters such as resuscitation, membrane integrity, metabolic activity, or a combination thereof. Thanks to these new methodological approaches, it was discovered that, due to their low metabolic activity and cellular changes in the VBNC state, bacteria have a drastically increased tolerance against antibiotics, as well as antimicrobials and that the methodological approaches could be utilized for antimicrobial effectivity testing against VBNCs.The majority of methodological approaches were originally developed with a clear focus on the rapid and cost-effective detection of VBNC pathogens and high-throughput methods for antimicrobial effectivity testing are still rare. However, it is our opinion that the relevance of the topic will facilitate their development. As reviewed in this article, there have been several different methodological approaches in order to investigate the tolerance and resistance of VBNC cells, measuring one viability parameter . Based on their underlying experimental principles and the currently available literature, each of the methodological approaches has certain advantages, as well as limitations and for antimicrobial effectivity testing the respective method has to be chosen carefully .What also becomes clear from the current literature is a lack of comparative studies regarding the respective methods and their respective outcomes. To the best of our knowledge, there are no studies yet available which perform tolerance testing of bacteria in the VBNC state with different experimental approaches. Given the relative novelty of many of the developed methods this is not surprising, but we would highly encourage researchers to increase the collaboration on this topic. The aim should be to establish standard protocols or guidelines regarding VBNC tolerance testing and how they could ultimately complement existing and well-established procedures for culturable bacteria. Furthermore, standard protocols are needed to assess the impact of decontamination effectiveness against VBNC cells when novel decontaminating technologies are available. The application and development of new methods to further investigate the VBNC state and its tolerance is very important to generate new efficient intervention methods to ensure water and food safety to reduce public health risks.


The HIV/AIDS incidence rates have decreased in African countries although the rates are still high in Sub-Saharan Africa. Our study aimed to examine the long-term trend of the overall HIV/AIDS incidence rates in four countries of the central region of Africa, using data from the Global Burden of Diseases (GBD) 2019 study. The Age–Period–Cohort statistical model analysis was used to measure the trends of HIV/AIDS incidence rates in each of the four countries. HIV/AIDS incidence rates decreased slowly in Cameroon (CAM), Chad, and Central African Republic (CAR), but considerably in the Democratic Republic of the Congo (DRC) from 1990–2019. HIV/AIDS incidence rates in the four countries were at their peaks in the age group of 25–29 years. According to the age relative risks, individuals aged between 15 and 49 years old are at high risk of HIV/AIDS incidence in the four countries. The period and cohort relative risks have decreased in all four countries. Although CAM recorded an increase of 59.6% in the period relative risks (RRs) between 1990 and 1999, HIV/AIDS incidence has decreased dramatically in all four countries, especially after 2000. The decrease of the period RRs (relative risk) by nearly 20.6-folds and the decrease of the cohort RRs from 147.65 to almost 0.0034 in the DRC made it the country with the most significant decrease of the period and cohort RRs compared to the rest. HIV/AIDS incidence rates are decreasing in each of the four countries. Our study findings could provide solid ground for policymakers to promptly decrease HIV/AIDS incidence by strengthening the prevention policies to eliminate the public health threat of HIV/AIDS by 2030 as one of the targets of the Sustainable Development Goals (SDGs). The human immunodeficiency virus (HIV) is known as the virus that affects the immune system, causing a disease called the acquired immunodeficiency syndrome (AIDS) . Until tIn 2019, the Central and the West African countries registered almost five million people who were living with HIV/AIDS . The RepMany studies on HIV/AIDS and AIDS-related diseases in that region of Africa have focused generally on the incidence, mortality, and prevalence amongst the populations aged between 15 and 49 years old. However, there is no study revealing the association of age, period, and cohort relative risks to HIV/AIDS incidence in those four countries. The relative risks induced by age, period, and cohort are still unclear in CAM, CAR, Chad, and DRC. Therefore, our study aims to address and elucidate these limitations through comprehensive analysis to evaluate the impact of age, period, and birth cohort relative risks on HIV/AIDS incidence in the respective countries by examining the long-term trend of HIV/AIDS. The national level of estimates and the patterns of HIV/AIDS incidence rates might help to assess the impact of HIV/AIDS prevention policies and re-think strategies to improve the outcome of HIV/AIDS prevention policies.All HIV/AIDS incidence estimates from 1990–2019 and the population data used in this study were extracted from the Global Burden of Diseases (GBD) 2019 for all four countries . Estimatp-value set at p ˂ 0.01 for statistical significance. Despite the APC analysis advantages, APC possesses limitations such as the uncertainty principle and identifiability problems [HIV/AIDS incidence rates were evaluated through an age–period–cohort model analysis. The age effects represent different risks during different periods of life. Period effects indicate the population-large exposure at a specific point of time, and different risks in different birth cohorts are mainly reflected by cohort effects ,17. To iproblems . The uncproblems . The ideWe used the APC Web Tool  software in our statistical analysis, and RStudio version 1.3.959 2009–2020 to realize our graphics.The trends of crude and age-standardized HIV/AIDS incidence rates in the four countries displayed similar declining patterns . In 1990The cohort RRs of HIV/AIDS incidence in CAM, the CAR, Chad, and the DRC are represented in p ˂ 0.01.The Wald tests demonstrated statistical significance for the net drifts, the local drifts, the age RRs, the period RRs, and the cohort RRs at In our study, we investigated the long-term trend of HIV/AIDS incidence from 1990 to 2019 in four countries of the central region of the African continent using an age, period, and cohort statistical model. Compared to existing researches, our study is the first to examine the association of age, period, and cohort relative risks to HIV/AIDS incidence in Cameroon (CAM), the Central African Republic (CAR), Chad, and the Democratic Republic of the Congo (DRC) from 1990 to 2019. Our findings revealed that HIV/AIDS incidence decreased in CAM, the CAR, Chad, and the DRC from 1990 to 2019. However, HIV/AIDS incidence rates in CAR during 1990 and 2019 were the highest compared to the other countries, and between 1990 and 2000, the HIV/AIDS incidence rates in CAM rose before declining until 2019. In CAM, the first national strategic plan was drafted from 2000 to 2005 to fight the increase in HIV/AIDS incidence in the country . TherefoThe net drift, which represents the overall annual percentage changes of the adjusted age group over time, and the local drifts, which are the annual percentage change in each age group, were all below zero in all four countries. According to the net drift value of each country, HIV/AIDS incidence of the adjusted age group decreased the most overtime in the DRC compared to CAM, the CAR, and Chad. Although all countries had negative values for the annual percentage changes in each age group, some age categories recorded upward behavior. The age groups of 55–69 years in CAM, 60–74 years in the CAR, 70–79 years in Chad, and 25–34 and 60–79 years old in the DRC have seen their annual percentage changes elevating slightly compared to each respective previous age group. This finding might be because of the following facts. On one hand, all four countries had a similar socio-cultural background mainly because of their geographical location. Sexual practice with multiple partners is common in CAM, the CAR, Chad, and the DRC . Socio-dHIV/AIDS incidence rates were at the peak in the age group of 25–29 years old in all four countries. According to the age relative risks (RRs) associated with HIV/AIDS incidence, the population aged between 15–49 years old in the CAR, Chad, the DRC, and CAM are at higher risk of HIV/AIDS incidence. The association of individuals aged from 15–49 years old to the risk of HIV/AIDS incidence had been discussed in other studies ,31. The The period and cohort RRs of HIV/AIDS incidence of the four countries all displayed decreasing patterns in trends. The trend of period RRs in CAM showed an upward behavior from 1990 to 1999 before decreasing until 2019, and the period RRs in the DRC decreased the most compared to the other countries (nearly 20.6-folds from 1990 to 2019). The cohort RRs in CAM, the CAR, Chad, and the DRC have all decreased significantly to nearly zero from the cohort born in 1915 to 2004. In the cohort born before 1955, the cohort RRs decreased dramatically compared to the cohort born after 1955. The fact that period effects can have some influence on some age groups and people from different birth cohort during separated years can also influence the period association, their separate interpretation tends to be relatively difficult . TherefoOur study had some limitations. First, our research did not discuss any subgroup of HIV/AIDS or gender specificity. The second constraint is related to the age–period–cohort analysis (identifiability and uncertainty principle). These parameters could not be avoided because the interpretation of results from an individual’s level does not necessarily equate to the interpretation at the population level. However, many other studies have been conducted using the web tool APC model as we did in our study ,47,48. TIn summary, although HIV/AIDS incidence has decreased over the last three decades in Cameroon, the Central African Republic, Chad, and the Democratic Republic of the Congo, the decrease is not sufficient because the disease called the acquired immunodeficiency syndrome (AIDS) caused by HIV/AIDS remains one of the leading causes of death in all four countries. Young adults aged from 15 to 49 years are at high risk of HIV/AIDS incidence according to our analysis. More strategic policies regarding public health, the health care system, and poverty alleviation should be implied by national and international organizations to control the sexual behavior of this age category. Massive campaigns about sexual education for health care practitioners and the populations, especially about HIV/AIDS prophylaxis, should be organized on a regular basis. This approach could help to significantly decrease the HIV/AIDS incidence in Cameroon, Chad, the Central African Republic, and the Democratic Republic of the Congo.


This paper investigates the influence of non-uniform corrosion in the transversal direction of the steel reinforcement on the cracking propagation of the concrete cover. An analytical model is proposed for the prediction of the corrosion-induced cracking performance. Both the thick cylinder theory of the concrete and the effect of transversal non-uniform corrosion of the steel reinforcement are involved by considering the corrosion layer of the corrosion products and a layer of concrete with the corrosion products filled with the pores. A three-stage corrosion-induced cracking of the concrete is proposed: corrosion without expansive stress to the concrete, corrosion with expansive stress to the adjacent concrete, as well as the corrosion-induced cracking of the concrete. By considering the non-uniform corrosion of the steel reinforcement and the tensile stress induced by the volumetric expansion of the corrosion products, the cracking initiation resulting from the non-uniform corrosion was involved in the prediction model. The models were also validated by the experimental results from both the corroded specimens and the existing literature, which would be helpful for the evaluation of the existing reinforced concrete constructions in the marine environment. Corrosion of steel reinforcement is usually considered as one of the most important factors for the deterioration of reinforced concrete (RC) elements , which tThe corrosion products accumulate at the zone of the steel-concrete interface. However, the volume of the corrosion products is about 2–6 times larger than that of the original steel . The corLiu et al.  proposedIn the first stage, Michel et al.  investigFor the second stage and the third stage, the research mainly focuses on the development of the volumetric expansion stress between the steel-concrete interface and the propagation of the cracking process of the concrete cover . The theAs for the third stage, the corrosion-induced cracks happen to the concrete cover and extended to the surface of the concrete cover gradually. Lu et al.  investigIn this paper, the cracking path of the concrete cover induced by the non-uniform corrosion of the steel reinforcement will be studied. A typical model of non-uniform corrosion will be involved. The Timoshenko  theory wAccording to the authors’ previous investigations on the corrosion of the steel reinforcement embedded in the RC beams exposed to a chloride environment for a long period of 26–28 years, the non-uniform corrosion occurred almost throughout the span of the length. More detailed information could be found in the published literature ,23. FiguThe typical corrosion morphology of Melchers & Val’s model was adopted in this investigation. The corrosion morphology of Melchers & Val’s model will be adopted to analyze the mechanical performance of the corrosion-induced cracking of the concrete cover based on the knowledge of a thick-walled cylinder . As inveCLD, and the depth of the concrete with the pores filled with the corrosion products was marked as CFD. Zhao et al. [CLD and CFD are usually considered to be 100 μm and 180 μm, respectively. The relationships of the values could be deduced as follows:CFD and CLD, as shown in According to Zhao et al. , the layo et al.  also proCFD, which could be treated as the area of the corrosion products with the equivalent depth of The area of the concrete filled with the corrosion products could be deduced by the pores of the concrete with the depth of w/c is the ratio of the water to cement.CFD as shown in In the first stage, the corrosion occurs to the steel reinforcement gradually. Part of the corrosion products take the place of the corroded zone of the steel reinforcement. However, as the volume of the corrosion products is about 2–6 times of the steel reinforcement [cpA as follow:The area of the corrosion zone o et al. .Then the area of corrosion products that migrate into the concrete from the steel-concrete interface during the stage I could be deduced as follows:In this stage, stress happened to the concrete adjacent to the steel-concrete interface, which was induced by the volumetric expansion of the corrosion products, as shown in CPD, which could be deduced as follows:The stress could be treated as the contribution of the corrosion products layer with the depth of CPD could be expressed as follows:According to Equations (7) and (8), CPD as follows:The hoop strain of the concrete corresponding to the corrosion zone could be expressed with the help of the radial displacement corrp corresponding to the corrosion zone could be evaluated according to Timoshenko [During the uncracked stage II, the corrosion pressure moshenko . In the sr along the radius direction at stage II;sr at stage II;sr along the radius direction;1c is the external radius of the cylinder.crr, as shown in The corrosion-induced crack happened to the concrete cover and developed gradually from the steel-concrete interface to the surface of the concrete. According to Tepfer , the cylThe whole pressure stress induced by the corrosion products is mainly contributed by the cracked section As for the external section of the non-cracked cylinder, the elastic stress The contribution of the non-cracked section of the concrete could be achieved based on the equilibrium condition of the cracked cylinder as follows:r.The stress of the concrete in the corrosion-induced cracked section is exerted in a nonlinear way. The stress in the cracked concrete can be deduced from the radial pressure, which was deduced by Den et al.  as folloa, b are the coordinates of the intersection point of the two softening lines. According to Bazant and the other available literature [w is the width of the corrosion-induced crack; It should be noted that the soften branch is considered for the concrete’s constitutive tensile law. Den et al.  proposedterature ,32,33,34w and the radius r, the total elongation of the generic ring in the concrete cover was assumed to be constant, as proposed by Van [r can be deduced by:n is the number of corrosion cracks.In order to make clear the relationship between the width of the corrosion-induced crack d by Van . The hooThe stress The radial displacement of the concrete can be calculated by the integration of the hoop strain as follows:The width of the corrosion-induced crack The corrosion-induced crack in the concrete cover was simplified to be in linear shape and the length As a result, the morphology of the corrosion-induced cracks of the concrete cover could be deduced according to the non-uniform corrosion of the steel reinforcement.The predicted results of the corrosion propagation of the steel reinforcement are conducted based on the theoretical method, as described in the previous section. The results of the previous experimental tests were retrieved from the available literature and then analyzed with the proposed theoretical model in order to make the validation of the theoretical model.The corrosion degree corresponding to the corrosion-induced cracking of the concrete cover was collected by Andrade et al.  and Vu eIn fact, if the prediction results were deduced based on the uniform corrosion rather than the pitting corrosion of Melchers’ model, the experimental results were then compared, as shown in The relationships of the width of the first visible surface cracking in the concrete cover and the radial loss of the steel reinforcement due to the corrosion were also investigated by Andrade et al. . The preIt could be found that the results predicted by the proposed prediction model matched well with Andrade et al.’s experimental results . When thThe compression stress between the steel-concrete interface could be deduced based on the proposed theoretical model. During Stage II, the corrosion compression was almost in linear relationship with the develop of the corrosion. However, the increase of the corrosion compression got reduced gradually during Stage III. The reason could be due to the fact that the inner cracks in the concrete cover could release the restraint for the deformation, and then the compression stress induced by the volumetric expansion of the corrosion products could be reduced even though the compression stress was still far smaller than the ultimate stress.The displacement happened to the concrete in the steel-concrete interface gradually once the volumetric expansion stress of the corrosion products was induced. The propagation of the corrosion-induced crack in the concrete cover can also be investigated in this section based on the proposed prediction model. Before the corrosion-induced cracking happened to the surface of the concrete cover, the width and the length of the corrosion cracks in the inner concrete cover were assessed based on the pitting depth of the corrosion of the steel reinforcement. The results are shown in According to Moreover, the width of the corrosion-induced cracks developed in a much more significant way than that of the length. (1)A new predicted model about the cracking propagation of the concrete cover induced by the non-uniform corrosion of the steel reinforcement was proposed based on Melchers’ model and the thick cylinder theory. The predicted results were validated by the experimental results.(2)The corrosion compression to the concrete was increased in a linear way at first. However, the appearance of the corrosion-induced cracks could release the compression significantly, even though the value was far smaller than the ultimate stress.(3)With the propagation of the corrosion, the width and the length of the corrosion-induced crack were developed in a non-linear way in the concrete cover. The pitting depth of 6 μm would lead to an inner crack with a length of 20 mm and a width of about 2 μm in the concrete cover.The cracking performance of the concrete cover induced by the corrosion of the steel reinforcement was investigated in this paper. The thick cylinder theory was applied. The corrosion morphology of Melchers’ model was also involved in the theoretical analysis. The following conclusions could be drawn:


L-Met, a new methionine (Met) source, has been commercially available for duck diet formulation. The bioavailability of L-Met is greater than DL-Met for growth performance in duck. The present study estimated the Met requirement of starter Pekin ducks from 1 to 21 days of age by supplementing crystal L-Met to formulate the diets at different ME levels. The results suggested that the Met requirement of starter Pekin ducks was affected by dietary ME levels. The data potentially provide theoretical support for the utilization of crystalline L-Met in duck production.Tremendous improvements have been made in the duck commercial industry, especially in aspects such as the increase of body weight and shortening of the production cycle. Meat duck production has been increasing annually worldwide. Improvements in precise nutrition were crucial for ducks to improve growth efficiency and reduce diet costs. Currently, L-Met was supplemented to yield six diets according to different supplemental levels . The results showed that the body weight (BW) and average daily weight gain (ADG) were increased (p < 0.05) with increasing dietary Met levels. Dietary ME levels changed from 11.54 to 12.52 MJ/kg increased the BW and ADG (p < 0.05) as well as decreased the average daily feed intake and feed to gain ratio (p < 0.05). As the dietary Met level increased, leg muscle yield increased (p < 0.05). Conversely, increasing the dietary ME level decreased the leg muscle yield (p = 0.0024) and increased abdominal fat (p < 0.001). Meanwhile, the concentrations of total cholesterol (TCHO), high-density lipoprotein cholesterol (HDLC), and low-density lipoprotein cholesterol (LDLC) in plasma were decreased (p < 0.05) when the ME levels of diets changed from 11.54 to 12.52 MJ/kg. Meanwhile, the plasma TCHO and HDLC concentrations decreased (p < 0.05) as dietary Met levels increased. Based on the linear-broken line model, the dietary Met requirement of starter Pekin ducks from 1 to 21 days of age for optimal ADG were 0.362%  at 11.54 MJ ME/kg and 0.468%  at 12.52 MJ ME/kg, respectively, when crystal L-Met was supplemented to formulate the diets. This suggested that the Met requirement of starter Pekin ducks was affected by dietary ME levels. The data potentially provide theoretical support for the utilization of crystalline L-Met in duck production.A 2 × 6 factorial experiment was conducted to determine the influences of dietary metabolizable energy (ME) and methionine (Met) levels on growth performance, carcass traits, and plasma biochemical parameters of starter Pekin ducks from 1 to 21 days of age. A total of 600 one-day-old male Pekin ducklings were randomly assigned to 12 groups (six replicates each group and eight ducks per replicate) in a 2 × 6 two-factor arrangement. The basal Met levels of two basal diets (11.54 and 12.52 MJ/kg ME) were 0.31 and 0.29%, respectively. The crystalline  Meat duck production has been increasing annually worldwide over the decades . The preDL-Met is usually supplemented to balance the duck Met requirement of ducks. Theoretically, chemically synthesized DL-Met supplemented in the diet is a racemic mixture of equivalent D- and L-Met. L-Met could be incorporated directly into the body with approximately 100% bioavailability, but D-Met must be converted to L-Met before the incorporation into protein [L-Met, a new Met source, has been commercially available for duck diet formulation. The bio-efficacy of L-Met was approximately 1.4 times relative to DL-Met for the growth performance of starter ducks [L-Met supplementation.Methionine (Met), usually the first limiting amino acid for ducks ,3, plays protein . Currenter ducks  as well Metabolizable energy (ME) is an index to evaluate energy levels in duck diets. High ME levels in broiler diet resulted in a reduction of feed intake , which mL-Met), was conducted to evaluate the effects of dietary ME and Met levels on growth performance, carcass characteristics, and plasma biochemical parameters of starter Pekin ducks from 1 to 21 days of age. At 1 day of age, a total of 750 male Pekin ducklings (from the Pekin Duck Breeding Center of CAAS) were weighed individually, and the birds with lowest (below 50 g) and highest (above 70 g) body weight were removed. Finally, a total of 600 male Pekin ducklings (56.1 ± 0.7 g) were selected from the remaining ducklings. Then, these birds were randomly divided into 12 treatments with 6 replicates each and 8 birds per replicate according to similar pen body weight . Each plastic-floor pen (length 2 m × width 0.75 m × height 0.4 m) served as a replicate, and the experiment lasted for 3 weeks (ducklings from 1 to 21 days of age). Pelleted feed and water were available ad libitum, and the water was provided by the drip-nipple water supply line. During the experimental period, the temperature was kept at 32 °C from 1 to 3 days of age and then reduced gradually to approximately 22 °C thereafter until 21 days of age in the duck house. The lighting was kept continuous (24 h) throughout the whole study.All experimental procedures of the present study were permitted by the Animal Care and Use Committee of Institute of Animal Sciences, Chinese Academy of Agricultural Sciences (CAAS) . A 2 × 6 factorial experiment, using 2 dietary ME levels  and 6 supplemental Met levels  according to 6 supplemental levels  at the expense of rice hull  [Two basal diets  were formulated to be Met-deficient with varying percentages of corn, soybean meal, and wheat bran . Then, eice hull . The forice hull . The basice hull . The cry22-2012)  for starAt 7, 14, and 21 days of age, all ducks were fasted overnight (10–12 h) for the accuracy and reliability of growth performance; then, the body weight (BW) and diet consumption of the ducks in each pen were measured. Average daily weight gain (ADG), average daily feed intake (ADFI), and feed/gain (F/G) were calculated of birds at different stages . The ADFI and F/G were corrected for mortality. ME and Met intake were determined according to the ME and Met concentrations in diets and ADFI. Meanwhile, the ME and Met conversion were calculated according to the formula [2 inhalation and were immediately bled. The breast muscle, leg muscle (deboned and peeled), and abdominal fat were all separated manually, and their weights were recorded. The yields of breast muscle, leg muscle, and abdominal fat were determined as the following equation:At 21 days of age, all ducks were fasted overnight (10–12 h) for the accuracy and reliability of carcass traits, and two ducks with close to the average body weight were randomly selected from each pen. Then, the selected ducks were weighed and euthanized by COg for 15 min at 4 °C to obtain the plasma samples. The plasma samples were stored at −20 °C for further analysis. The plasma concentration of triglyceride (TG), total cholesterol (TCHO), high-density lipoprotein cholesterol (HDLC), low-density lipoprotein cholesterol (LDLC), alanine transaminase (ALT), aspartate transaminase (AST), total protein (TP), albumin (ALB), uric acid (UA), glucose (GLU), and alkaline phosphatase (ALP) were measured based on a spectrophotometric method using an automatic analyzer  with corresponding kits  based on their specifications.At 21 days of age, all ducks were fasted overnight (10–12 h) before blood collection for the accuracy and reliability of plasma biochemical parameters. Before duck euthanizing, the heparinized blood of two ducks selected for carcass traits measuring was collected using heparin sodium-anticoagulant tubes from the wing vein and centrifuged at 1300 × p < 0.05) between dietary ME or Met level, Duncan’s multiple comparison tests were used to compare differences among means. Based on main effects, polynomial contrasts were performed to assess the linear and quadratic responses of dietary Met levels on dependent variables. In the present study, the linear broken-line regression analysis [The data were analyzed as a 2 × 6 factorial experiment design by the two-way ANOVA with GLM procedure . The replicate (pen) was considered to be the experimental unit for growth performance, while each duck was considered to be the unit for carcass traits and plasma biochemical parameters. The main effects of dietary ME level, Met level, and their interaction of each parameter was evaluated. Results were presented as means with the pooled standard error of the means (SEM). In the case of significant treatment , while the ADFI (p = 0.0035) and F/G (p < 0.001) were decreased when dietary ME changed from 11.54 to 12.52 MJ/kg. Dietary L-Met supplementation increased the BW at 21 days and ADG from 1 to 21 days of age (p < 0.05) in both ME levels diets. The ADFI was linearly increased (p < 0.05) as dietary L-Met supplementation. Compared with ducks fed 11.54 MJ ME/kg diet, birds fed 12.52 MJ ME/kg of diet had the greater ME intake (p = 0.0014), and the lower ME conversion (p < 0.001), Met intake (p = 0.0023), and Met conversion (p < 0.001). The Met intake (p < 0.001) and Met conversion (p < 0.001) of ducks as increased dietary Met supplementation (As is shown in entation .p > 0.05) at the beginning of the trial (day 1), while the birds fed 12.52 MJ ME/kg diet had higher (p < 0.05) BW at day 14 and day 21. Similarly, the ADG of ducklings from 8 to 14 days and 15 to 21 days of age fed 12.52 MJ ME/kg diet as greater (p < 0.05) than birds fed 11.54 MJ ME/kg diet. During the whole study period, dietary ME level drove to reduce the ADFI and F/G (p < 0.05) of ducks at each stage . As dietary L-Met supplementation, the ducks at 7 days, 14 days, and 21 days had all greater BW compared to birds fed diets without L-Met supplementation. The ADG and ADFI of ducklings at the first two weeks  increased as dietary L-Met supplementation increased.The growth performance of starter Pekin ducks during different stages  was investigated . The BW p = 0.0024) and the abdominal fat (p < 0.001) was increased when the dietary ME level rose from 11.54 to 12.52 MJ/kg. As dietary L-Met supplementation increased, the leg muscle yield was increased (p < 0.05). In addition, dietary L-Met supplementation resulted in a tendency to increase breast muscle yield (p = 0.0904) and a decreasing tendency for abdominal fat (p = 0.0767) although this was not significant.The effects of dietary ME and Met levels on the carcass characteristics of starter Pekin ducks at 21 days of age are shown in p = 0.0002), HDLC (p = 0.0005), and LDLC (p = 0.0287) in plasma were decreased when the ME levels of diets increased from 11.54 to 12.52 MJ/kg (p < 0.05) as dietary L-Met supplementation increased (p > 0.05) by dietary ME or Met levels (The concentrations of TCHO (52 MJ/kg . The plancreased . The plat levels .L-Met) at 11.54 MJ ME/kg, and 0.468%  at 12.52 MJ ME/kg, respectively, when crystal L-Met was supplemented to formulate the diets. The dietary Met requirement of 0.468% at 12.52 MJ ME/kg was greater (p < 0.05) than 0.362% at 11.54 MJ ME/kg by Student t-test analysis.The Met requirements of starter Pekin ducks were estimated by the regression model . Based oL-Met  by the corn and soybean meal to formulate the low- or high-energy basal diet. Both basal diets were Met-deficient  for starter Pekin ducks to investigate the growth responses. In our study, growth depression was observed when ducklings fed both Met-deficient basal diets, and BW and ADG of birds were improved after feeding diet supplemented crystalline L-Met . Similar–4% by thL-Met , which mL-Met , which sL-Met , which iCarcass characteristics have been considered as crucial response indicators to evaluate dietary energy and amino acid status in poultry diets such as yields of breast muscle, leg muscle, and abdominal fat ,13,22,25Plasma or serum biochemical parameters are reflection of the nutrient metabolism condition in ducks. Plasma TCHO mainly comes from diets or was synthesized in the body. Due to the similar proportion of formula for both basal diets , the difference of plasma TCHO concentration observed in the present study  was a reL-Met, not DL-Met, was supplemented to formulate the experimental diets in the current study. The bio-efficacy of L-Met to DL-Met ranged from 120 to 140% for the growth performance of young ducks from 1 to 14 days of age [L-Met relative to DL-Met were 134% of Pekin ducks from 1 to 21 days of age by the linear ratio-slope regression [L-Met for starter ducks was 1.2 to 1.4 times that of DL-Met, which might be the main factor resulting in the lower Met requirement in our study. Considering the utilization efficiency and costs of crystal L-Met, the supplementation of L-Met in duck diet might be reasonable and economic. Therefore, the results provided the data for the application of crystalline L-Met in the duck diet.Several regression models, such as quadratic polynomial ,7,37, lis of age . Similargression . That isL-Met) at 11.54 MJ ME/kg and 0.468%  at 12.52 MJ ME/kg, respectively, when crystal L-Met was supplemented to formulate the corn–soybean meal type diets. This suggested that the Met requirement of starter Pekin ducks was affected by dietary ME levels. The data potentially provide theoretical support for the utilization of crystalline L-Met in duck production.In conclusion, the growth performance, carcass traits, and plasma biochemical parameters could be regulated by dietary ME or Met levels in starter ducks. Based on the linear broken regression model, the dietary Met requirement of starter Pekin ducks from 1 to 21 days of age for ADG was 0.362% (0.052% supplemental


Proteus mirabilis is responsible for dire clinical consequences including septicaemia, urinary tract infections and pneumonia, but is not a species previously known to enter VBNC state. We suggested that stress‐induced P. mirabilis can enter a VBNC state in which it retains virulence. P. mirabilis isolates were incubated in extreme osmotic pressure, starvation, low temperature and low pH to induce a VBNC state. Resuscitation was induced by temperature upshift and inoculation in tryptone soy broth with Tween 20 and brain heart infusion broth. Cellular ultrastructure and gene expression were examined using transmission electron microscopy (TEM) and quantitative real‐time polymerase chain reaction (qPCR), respectively. High osmotic pressure and low acidity caused rapid entry into VBNC state. Temperature upshift caused the highest percentage of resuscitation (93%) under different induction conditions. In the VBNC state, cells showed aberrant and dwarf morphology, virulence genes and stress response genes (envZ and rpoS) were expressed (levels varied depending on strain and inducing factors). This is the first‐time characterization of VBNC P. mirabilis. The ability of P. mirabilis pathogenic strains to enter a stress‐induced VBNC state can be a serious public health threat.Pathogenic bacteria can enter into a viable but non‐culturable (VBNC) state under unfavourable conditions.  We also studied different P. mirabilis VBNC‐inducing factors and resuscitating conditions. To the best of our knowledge, this is the first‐time characterization of VBNC P. mirabilis.We suggested that 22.1P. mirabilis clinical isolates were recovered from patients in Kasr Al‐Aini Hospital, Cairo, Egypt. Approvals from the research ethics committees of the hospital and the faculty of Pharmacy, October University for Modern Sciences and Arts, Giza, Egypt were obtained prior to conducting the study. Two isolates, P6 and P7, were recovered from urinary tract infections, and the isolate, coded P3, was recovered from wound infection. Written consents were obtained from all participants in the study.Three 2.2P. mirabilis strains were grown overnight in tryptone soy broth (TSB) at 37°C with shaking. The culture was centrifuged at 5000 rpm for 10 minutes at 5°C, and pellets were washed twice by sterile saline solution. The resulting pellets were resuspended in sterile deionized water, and the cell concentration was adjusted to be equivalent to McFarland 0.5 (1.5 × 108 CFU/mL). A volume of 400 µL was used to inoculate 40 mL of the induction medium, in a 50‐mL falcon tube, to reach a final density of approximately 106 CFU/mL. Different induction media were used to create different stressful conditions for isolates: (a) deionized water, for starvation and low osmotic pressure stress; (b) deionized water + NaCl (0.9%), for starvation stress; (c) deionized water + NaCl (0.9%) at pH 5, for starvation and acidic condition stresses; (d) deionized water + NaCl (4%), for starvation and high osmotic pressure stresses, and (e) deionized water + NaCl (7%), for starvation and high osmotic pressure. Each induction condition was done in duplicate, and tubes were incubated at 4°C, without shaking and in dark. Culturability on TSA was assessed every week in duplicate plates, and time required for loss of culturability was recorded. Test of culturability was done by testing the growth of 1 mL of culture, and then, when no growth is detected, 10 mL of culture was centrifuged and resuspended in 1 mL and repeated subculture was done. Heat killed bacteria at 100°C for 15 minutes were used as control cells.The VBNC state induction was done according to Pinto et al 2.3® System (Promega). Extraction was done according to the manufacturer's instructions. RNA was stored in RNase‐free water and then stored at −80°C until use. RNA quantity and quality were measured at wavelengths 260 and 280 nm using ND‐1000 spectrophotometer (NanoDrop Technology). RNA quality was also tested by agarose gel electrophoresis. The RNA samples were treated with RNase‐free DNase I (New England Biolab). Samples were confirmed to be free of genomic DNA by 40 cycles of conventional PCR using 16S rRNA primers . After confirming the absence of genomic DNA by agarose gel analysis, ~l µg DNase‐treated RNA was subjected to reverse transcription using the SensiFastTM cDNA synthesis kit (Bioline) following the supplier's directions  temperature upshift, (b) inoculation in TSB with added nutrients of Tween 20 (3% v/v) and (c) inoculation in low‐nutrient medium BHI (1/8 concentration).Resuscitation by temperature upshift was performed according to Zeng et al 10 mL medium was inoculated with 20 µL from the VBNC suspension. The inoculated media included the following: TSB with added Tween 20 and low‐nutrient medium BHI (1/8 concentration). Inoculated media were incubated at 37°C for 72 hours, and then, the appearance of turbidity indicated resuscitation of VBNC cells and regaining of the culturability of VBNC cells.2.6rpoS and envZ), virulence genes  and genes for cell division (ftsZ). Expression in VBNC cells was compared to control cells. The primers were designed using the complete genome sequence of P. mirabilis (HI4320) obtained from the NCBI database (NCBI accession no. https://www.ncbi.nlm.nih.gov/nuccore/NC_010554). Primers for the qPCR used in the current study .We studied the change in gene expression of the following genes: stress response genes . All reactions (20 μL) were performed using three technical replicates. Each reaction mixture contains 100 ng cDNA and 400 nmol/L primers per reaction. The RT‐PCR cycling conditions were as follows: one cycle with 95°C for 2 min; then 40 cycles of denaturation at 95°C for 5 seconds, annealing at 55°C for 10 seconds, and extension and fluorescent data collection at 72°C for 20 seconds. A dissociation curve was generated at the end of each reaction. In all qPCR runs, negative controls without template were run in parallel. The 16s rRNA gene (housekeeping gene) was selected as the internal control based on the results of BestKeeper® software tool.P. mirabilis potential VBNC as compared to their levels in the control cells unexposed to stress  grown in BHI medium and incubated for the late exponential phase. Only genes with a relative 2−∆∆C value above 1.0 or below 1.0 were considered significant. [Correction added on 17 February 2020: 2∆∆C has been changed to 2−∆∆C in the preceding sentence.]Quantitative real‐time reverse transcription polymerase chain reaction (qRT‐PCR) was performed by Applied Biosystems StepOne2.7The structures of control, VBNC and resuscitated cells were investigated using transmission electron microscope (TEM). Cells were harvested by centrifugation, and the bacterial pellets were washed three times with PBS. Cell fixation and processing steps were performed according to the method described in Henriques et al.2.8Results of three replicates were analysed for statistical significance with PRISM 5 (GraphPad). A one‐way analysis of variance (ANOVA) was performed. Data comparisons were performed using Bonferroni's correction for multiple testing.3The samples were exposed to different VBNC induction conditions which include a combination of either acidic or osmotic pressure in addition to both cold and starvation stresses. The number of weeks taken by each of the three samples to enter in the VBNC state varied from 14 to 26 weeks according to the inducing condition , virulence genes , autoinducers coding genes (luxS) and the gene coding for septum formation during division (ftsZ). Gene expression was normalized relative to the 16S rRNA gene. The ftsZ gene expression was down‐regulated in all VBNC cells . Up‐regulation was observed in strain 6 under the conditions of water, NaCl 4% and NaCl 7%, by 10‐, 2‐ and 10‐fold. In strain 3, significant up‐regulation (2.9‐fold) was observed only in the presence of water, whereas down‐regulation was observed in presence of all other conditions. Significant down‐regulation for the envZ gene was observed under all conditions except the acidic conditions, at which the envZ expression was significantly up‐regulated (1.5‐ to 2‐fold). The expression of the fliL gene coding for basal flagellar protein varied depending on the condition inducing the VBNC state. While the acidic pH caused significant down‐regulation in fliL gene expression, the high osmotic pressure (4% NaCl) caused a significant up‐regulation of the fliL gene expression (an increase of 1.7‐fold in strains 3 and 7 and an increase of 9‐fold in strain 6). The expression of the gene zapA coding for metalloprotease protein was variable depending on strains and conditions inducing VBNC. Significant down‐regulation was observed under all conditions with strain 3 and in the presence of high salt concentrations (4% and 7%) in strain 7. The zapA gene was significantly up‐regulated in isolate 6 under all conditions. The luxS gene coding for autoinducer 2 (AI 2) was generally down‐regulated in all tested isolates under most conditions  after 182 days. Upon TEM examination of the VBNC cells, cells were aberrant shaped, smaller in size and more rounded than control cells. They had thicker cell walls with condensed dark cytoplasm attached to the cell wall Figure C. Resusc4P. mirabilis VBNC state.The VBNC state is a potential public health hazard in the environment,P. mirabilis were cold temperature (4°C) and starvation accompanied by: low osmotic pressure (deionized water); high osmotic pressure (deionized water + 4 or 7% NaCl); acidic pH (deionized water + 0.9% NaCl at pH 5); and isotonic pressure (deionized water + 0.9% NaCl). The entry of P. mirabilis (starting count 1.5 × 106 CFU/mL) into the VBNC state under cold conditions (4°C) was more rapid than at room temperature (25°C), and the maximum time required for loss of culturability was 26 weeks at 4°C and over than 65 weeks at 25°C (data not shown). The rapid entry into VBNC state at 4°C could be attributed to the inability of the cells to detoxify lethal peroxides produced under stressful conditions, because cold incubation prevents catalase activity and its de novo synthesisIn our study, the conditions used for inducing the VBNC state in Proteus mirabilis showed more rapid entry (20 weeks) into the VBNC state compared to the E coli O157:H7 in a study P. mirabilis to combined stressful factors lead to more rapid entry (P < .01) into the VBNC state than exposure to single factor as detected in E. coli by Muela et alProteus sp was found to survive in marine environments due to their halotolerance trait attributed to the polyphosphate kinase encoded by the ppk gene,Campylobacter jejuni were found to exhibit decreased ability to enter the VBNC state,P. mirabilis isolates into the VBNC state was confirmed by detecting the continuous expression of the 16S rRNA and rpoS genes in tested strains after losing their culturability. RNA detection was used because the half‐life of RNA is 3‐5 minutes and its continuous expression is an indication of continuous viability of bacteria that have lost their culturability.rRNA and Rpos genes were used as viability indicators as they are both housekeeping genes that need to be continuously expressed in living cells. The expression of 16S rRNA remains consistently high in viable cell indicating its validity as a viability indicator. Conversely, the gene is absent in dead bacterial cells after 48 hours of treatment. The rpoS gene is similarly absent in dead cells. This confirmatory method for entry of bacterial cells into the VBNC state was previously used in other studies.rRNA genes were not detected after 48 hours from heat treatment at high temperature for 15 minutes as found by McKillip  et alRpoS gene was not detected in dead cells as detected by Liu et al The entry of the P. mirabilis strains than the low‐nutrient medium. This result is in contrast to what was reported by Bloomfield et alSeveral factors play roles in the ability of bacteria to resuscitate from the VBNC state. These factors include the particular strain used and the conditions that can induce the VBNC state and/or resuscitationP. mirabilis include adhesins, motility, biofilm formation, immunoavoidance, toxins and nutrient acquisition.ftsZ), stress response regulators (rpoS and envZ), virulence traits (zapA and fliL) and autoinducer (AI‐2) production (luxS). On assessing the relative expression of ftsZ gene under different induction conditions, the expression of this gene in the tested VBNC cells was reduced by variable folds according to the stress conditions and strains. Down‐regulation of ftsZ expression in VBNC bacteria was previously observed.P. mirabilis (P6) incubated in deionized water (containing 0.9% NaCl at 4°Cfor 182 days) revealed that VBNC cells appear aberrant and smaller in size than normal and resuscitated cells with condensed cytoplasm at the poles of the cells, condensed chromosomal DNA and intact cytoplasmic membrane. Upon resuscitation, the bacteria increased back to the normal size. The aberrant and dwarfing shapes were also observed in the VBNC cells of Vibrio parahaemolyticus,Vibrio vulnificus,Listeria monocytogenes,Yersinia pestis Helicobacter pylori.The virulence factors known to be involved in pathogenesis of ducer AI‐ productirpoS and envZ) under these conditions to determine its role in stress resistance. The envZ gene controls the outer membrane protein (Omp), and thus, it has a role in controlling membrane porins and sensing the change in environmental stimuli. Some studies suggested that envZ gene is vital for entry into the VBNC state and that any mutations in this gene could inhibit the entry into this state but does not affect the survival under the VBNC‐inducing conditions.envZ gene, which is part of osmoregulating system EnvZ‐OmpR, was down‐regulated under all tested condition except in samples incubated in acidic deionized water where it is up‐regulated (1.6 to 8 folds) compared to normal cells. These results indicate that envZ gene has no role in cell survival under VBNC state except under acidic conditions and this observation was also noticed in a study carried by Kaeriyama et al E coli, where envZ controlled porins were up‐regulated under low osmotic pressure (0.5% NaCl) at acidic pH. Stress δs factor, coded by rpoS gene, controls the production of trehalose, which acts as a protective osmolyte, and is associated with persistence in the VBNC state.rpoS gene expression occurs at two levels: transcriptional and translational. There are differences between factors inducing rpoS gene transcription and those inducing rpoS mRNA translation into δs factor. RpoS gene transcription into rpoS mRNA is induced by reduced growth rate and is negatively controlled by cAMP‐CRP,s factor is induced by osmotic pressure and high cell density.rpoS gene was variable under combined effects of starvation with high osmotic pressure and acidic conditions. Gene expression was down‐regulated in strain 3 compared to normal cells while up‐regulation occured in strains 6 and 7. VBNC‐induced cells incubated in water microcosm showed up‐regulation in rpoS expression. The down‐regulation in rpoS gene in strain 3 might explain the lower percentage (44%) of resuscitation in this strain under different resuscitating conditions compared to strains 6 and 7, in which percentages of resuscitation were 64 and 67%, respectively.The entry of bacterial cells into the VBNC state provides them with necessary resistance to unfavourable stress conditions.fliL) and metalloprotease (zapA). Bacterial motility increases under high osmotic pressures V. vulnificus. Conversely, the expression of fliL gene was down‐regulated in all tested strains under acidic pH, which lead to reduction in flagella formation and motility as reported by Soutourina et alThe ability of pathogenic bacteria to retain their virulence factors in the VBNC state is strain‐dependent.Proteus mirabilis encodes a metalloproteinase, serralysin (ZapA), which was shown to cleave secretory immunoglobulins and antimicrobial peptides and hence establishing urinary tract infections.zapA is expressed at low levels in vivo, a P. mirabilis zapA mutant is less efficient than wild type at colonizing the urine, bladder and kidneys in murine infections.P. mirabilis retained its metalloproteinase virulence traits during the VBNC state.Proteus mirabilis possesses a luxS homologue and produces AI‐2, which can mediate interactions between species.luxS gene was observed in all tested strains under VBNC conditions. However, AI‐2 does not likely contribute to pathogenicity,luxS expression in biofilm formation.luxS gene under different VBNC‐inducing conditions in our study might indicate a reduced ability of VBNC cells for biofilm formation.P. mirabilis can enter the VBNC state under several conditions of starvation, extreme osmotic pressure, acidity and low temperature. The time required for entry into a VBNC state is dependent on the inducing condition and the bacterial strain. Removal of the cold stress by temperature upshift on VBNC cells lead to successful bacterial resuscitation. Bacterial cells under the VBNC state showed aberrant dwarf morphology and returned back to their normal shapes after resuscitation but with relatively smaller sizes as compared to normal cells. Gene expression was variable under different conditions and the continuous expression of virulence trait‐coding gene indicated that bacterial cells can retain some of their virulence properties under the VBNC state.In conclusion, The authors declare no competing financial interests.Dr Reham Wasfi, Dr. Ghada R. Abdellatif, Dr. Hisham M. Elshishtawy and Dr. Hossam M. Ashour contributed to the design of the study, performance of experiments, analysis of the results and writing of the manuscript.


X-ray diffraction (XRD), thermogravimetry (TG), and differential scanning calorimetry (DSC) were used to analyze the change in mineral composition over time. The microstructure was also studied by scanning electron microscopy (SEM) and energy dispersive spectrometry (EDS). The results showed that significant expansion and great loss in compressive strength did not occur in concrete if the content of SO3 lay below 1.5% and 3% in fine and coarse aggregates, respectively. The concentration of sulfate ions in concrete was not enough to form new a phase of gypsum. During the process of internal sulfate attack, the content of gypsum decreased and the content of ettringite increased. Ettringite was the main reason for the expansion damage of concrete. Additionally, the fracture mode of internal sulfate attack on concrete was the crack extension from gypsum to paste; finally, the aggregate separated from the paste.Damage to concrete structures with gypsum-contaminated aggregate occurs frequently. Aggregates in much of the southern part of China are contaminated with gypsum. Therefore, in this study, the effects of using different quantities of gypsum-contaminated aggregate on the expansion and compressive strength of concrete were investigated over a period of one year. Two groups of concrete were designed with the gypsum-contaminated aggregate containing different parts of fine and coarse aggregate, respectively. The SO Internal sulfate attack (ISA) on concrete is a reaction between sulfates present in the original mix of concrete and the calcium aluminate in cement and water, which can show signs of deterioration . In the concrete . In the concrete , and somconcrete . A large3A content in Portland cement and the susceptibility of concrete to sulfate attack, and cements with limited C3A content were introduced to the market. These cements are used in the concrete that is exposed to moderate and severe sulfate concentrations [42− > 8000 mg/L [The mechanism of external sulfate attack (ESA) has been studied for many years. Sulfate is supplied by seawater, groundwater, and industrial wastewater. Sulfate ions react with ionic species of the pore solution to precipitate ettringite, gypsum, or thaumasite . The majtrations ,9. The strations . The devtrations . Normall000 mg/L . Thaumas000 mg/L . The tha000 mg/L .3 content in fine and coarse aggregates. It is stipulated in GB/T14684 and GB/T14685 that the SO3 content in fine and coarse aggregates shall not exceed 0.5% and 1%, respectively. Samarai proposed a 0.1% expansion as a safe margin for finding the allowable sulfate level [Compared with the sulfate ions that penetrate into concrete by diffusion for ESA, there is a higher concentration of sulfate ions in concrete for ISA. The hazard is illustrated in the materials which cause higher tensile stress, leading to spalling and disruption of concrete structures . For exate level . Accordite level . BecauseIn this paper, the influences of the dosage of gypsum aggregate on the compressive strength and expansion performance of concrete were studied. The types of reaction products in the process of internal sulfate attack were also studied.P·II 52.5 Portland cement conforming to Chinese National Standard GB175 was used in this study and its chemical composition is shown in In our experimental program, there were two types of concrete specimen: 100 mm by 100 mm by 100 mm and 75 mm by 75 mm by 280 mm. They were demolded a day after casting and cured in water at 20 ± 2 °C. The cube samples were used to determine the compressive strength of the concrete with different amounts and sizes of gypsum. The prism specimens were used for the ultrasonic and expansion test of concrete at different ages. 3 content  in the concrete. The grain size curves of fine and coarse aggregates are shown in The gypsum-contaminated aggregate was crushed into gypsum sand (<4.75 mm) and gypsum stone (5–20 mm). Part of the normal fine and coarse aggregate was replaced with gypsum-contaminated aggregate in the mixture of concrete, to get five levels of SOL0, L, and tL represent the initial length, effective length of 250 mm, and testing length at different ages, respectively.An expansion test was conducted using three specimens per mix. The reference points used to measure the dimensional variations of samples were placed on the 75 mm by 280 mm sides that were in contact with the lateral sides of the molds. As shown in The compressive strength of the concrete cubic specimen was examined at the ages of 28, 60, 90, 150, 210, and 240 days by using a compressive-testing machine with a loading rate 0.5–0.8 MPa/s. The machine for testing compressive strength is shown in The ultrasonic velocities, which describe the material internal damage, in specimens at different ages were tested, by fixing the launcher and receiver transducer firmly on the two sides of the specimen (75 mm by 75 mm), in accordance with the “Technical specification for inspection of concrete defects by ultrasonic method” (CECS 21: 2000). The machine used to test the ultrasonic pulse velocity is shown in 2 atmosphere.To get the complementary mineral information, mortar specimens were subjected to XRD and TG–DSC analyses at different ages. The mortars cut from the concrete samples were immersed in absolute ethyl alcohol for 12 h to terminate hydration, before being vacuum dried at 60 °C for 24 h, and then ground into powder. The test powders were passed through an 0.08 mm sieve. The XRD data were collected in the range of 10°–70°, 2θ at a counting time of 15 s/step, and a divergence slit of 1°. TG–DSC data were obtained from 50 to 950 °C at a rate of temperature increase of 10 °C/min in a NIn order to investigate the morphology of concrete under internal sulfate attack, a fractured fresh piece of concrete was sampled, hydration terminated, and vacuum dried. Then, the dried sample was embedded in a low-modulus epoxy, polished using progressively smaller grids, coated with a gold-palladium coating, and investigated using JSM-7600F SEM.The pore solution in concrete was expressed directly with a compressive-testing machine whose final pressure value was 2000 MPa at a speed of 2 MPa/s. Then, the sulfate concentration in this pore solution was tested by inductive coupled plasma emission spectrometer (ICP). 3 presented a significant increase in expansion for 360 days. There was a little expansion when the SO3 content in sand was 1.5%, and the expansions of the specimen was less than 0.1% in 360 days. Meanwhile, specimens containing SO3 less than 1.5% showed no expansion. 3 content in coarse aggregate was less than 3%. The average expansion increased obviously as the SO3 content increased to 5% and 7%. The final measured expansions for the specimens containing 5% and 7% SO3 were 0.1401% and 0.3602%, respectively, at 360 days. The expansion data in 3 content.For the samples with gypsum-contaminated coarse aggregate, no significant variation was observed, when the SO3 contents are bigger than the limit established in several standards, such as GB/T14684 an GB/T14685 in China.Several studies recommended 0.1% expansion as a safe margin for determining the maximum percentage of sulphate than can be present in a mixture without causing any significant degradation . Based o3 increased. It was evident that with 0.5–1.5% SO3 in sand, the initial compressive strength of concrete decreased by 25%. Additionally, 3–7% SO3 in sand led to a loss in the initial compressive strength of samples of about 38%. The compressive strength of all specimens with gypsum-contaminated aggregate increased first and then decreased with the curing age. As shown in 3 content in sand of less than 1.5% is relatively safe. 3 in coarse aggregate, only the strength of the G7 specimen increased—from 30.2 to 33.3 MPa in 28 days—before reducing to 14.2 MPa at 360 days because of the expansion properties shown in 3) had less effect on the compressive strength of concrete relative to the initial strength of the reference.For the samples with SOThe internal damage of specimens under internal sulfate attack was tested by ultrasonic pulse velocity, and the results are presented in To detect the existence of gypsum in mortar during the internal sulfate attack, while avoiding the effects of quartz and dolomite peaks in the XRD, the XRD results from 5° to 20° are shown in 3 in sand at 56, 240, and 360 days. The peaks of ettringite (E), portlandite (P), and gypsum (G) are highlighted in the graph. The results indicate that the mortar in concrete had no gypsum when the SO3 content in the sand was less than 1.5% at 56 days. Note that there were apparently no peaks corresponding to gypsum in the FG3 specimen at 240 days. Moreover, for the FG5 and FG7 samples, there was also a certain amount of gypsum in mortar until 360 days. It was clear that during the process of ISA, the gypsum in concrete could be dissolved.3 in coarse aggregate at 360 days. It is worth mentioning that all concrete with gypsum coarse aggregate incorporated had gypsum for 360 days during the internal sulfate attack. This provides evidence that the dissolution rate of gypsum in gypsum-contaminated aggregate with bigger particle size is relatively slower.3 content was less than 3% in sand. For the higher contents of SO3 in FG5 and FG7, the new gypsum phase would be formed by the dissolution of SO3. To solve these problems, the TG–DSC analysis of FG7 specimen was researched. 2O3·3CaSO4·32H2O), gypsum (CaSO4·2H2O), and portlandite (Ca(OH)2), respectively. During heating from 80 to 120 °C, 26 mol of water will be removed from AFt [4·2H2O and Ca(OH)2  to form gypsum in solution [solution . Howeversolution . Additio3 in sand. 3 in sand at 120 and 240 days. It is shown that with the development of ISA, the fracture firstly extended from the gypsum to the paste. Then, the crack extended around the sand, and finally, the sand separated from the paste completely. SEM was applied to observe the microstructure of mortar with 5% SO3 content in aggregate, the concrete expansion increased, and the compressive strength decreased. However, if the SO3 content was lower than 1.5% and 3% in fine aggregate and coarse aggregate, respectively. Although, the expansion was not obvious, and the compressive strength of samples was above the initial strength of the reference specimen. The critical values of SO3 content in fine and coarse aggregate were found to be 1.25% and 3%, respectively. At values above these harmful expansion and large strength loss appear.With an increase in the SO42− dissolved more easily when the particle size of aggregate was smaller. When the SO3 content in the sand was less than 1.5% at 56 days, all the gypsum was dissolved. That was the reason why the expansion of specimens with a smaller SO3 content (1.25% for fine aggregate and 3% for coarse aggregate) was not significant.SO3 content was less than 7% in aggregate. For the internal sulfate attack, the main reaction product is ettringite, which causes the expansion of specimens.The concentration of sulfate ions in the pore solution of concrete was not enough to form a new phase of gypsum when the SOThe fracture mode of internal sulfate attack was the crack extending from gypsum particles to paste, which made the aggregate separate from the paste.In this paper, only TG–DSC was used to analyze the content of major phases, and no other methods were combined. This paper only studied the changes in compressive strength and expansion performance of concrete containing gypsum aggregates for 360 days. To study whether it is safe to use gypsum aggregates in concrete, other durability tests are needed. In addition, there has been lack of evaluation on methods that can be used to determine the safe dosage of gypsum aggregate in concrete at home and abroad, which will be the focus of our follow-up work.The deterioration process of concrete exposed to internal sulfate attack was investigated. The main conclusions are as follows: