In order to study the axial compression performance for composite hollow column of steel fiber, high-strength lightweight aggregate concrete and angle steel, the axial compression tests were carried out on five composite hollow columns of steel fiber, high-strength lightweight aggregate concrete and angle steel with the variation parameters of hollow ratio  and the form of opening (round hole and square hole). The failure phenomena and failure forms of the specimens were observed, and their stress–strain curves were measured, and the axial bearing capacity formula suitable for composite hollow column of steel fiber, high-strength lightweight aggregate concrete and angle steel was established. The following conclusions may be obtained from the test results: the axial compression performance for the composite hollow columns of angle steel is influenced by the hollow ratio and opening form greatly. The axial compression performance for composite hollow columns of steel fiber, high-strength lightweight aggregate concrete and angle steel is almost close to that of composite solid columns when the hollow ratio is low; The higher the void ratio, the more the cracks at the surface of the concrete, some transverse cracks appear, the peak load decreases by about 5–38%, and the deformation ductility coefficient increases gradually; The deformation ductility coefficient of round-hole hollow column is lower than that of square-hole hollow column. Based on the test, the finite element software ABAQUS is used to simulate the SCAH column. The correctness of the model is verified via the comparison between the numerical simulation results and the test results. At the same time, the stress nephogram of concrete and steel at different stages and the stress nephogram at concrete restraint state are simulated. According to the finite element simulation results, Mander model is used to calculate the axial compression bearing capacity of composite hollow column of angle steel. The high calculation accuracy and suitable for popularization can be obtained. On the one hand, the high-performance concrete shall be used to minimize the own weight of the building. The structure may be reduced effectively via replacing the ordinary concrete with the high-strength lightweight aggregate concrete at the same strength grade5. However, the brittleness of concrete increases significantly along with the gradual increase of the strength grade of high-strength lightweight aggregate concrete6. It can be found that the crack resistance, ductility energy consumption and the brittleness may be improved effectively by adding the steel fiber to the lightweight aggregate concrete7. On the other hand, it is to optimize the structural form and change the beam column section. It is found that the hollow column with holes at the column section can effectively reduce the own weight of the structure9. The hollow column is widely used in the building structure and pier due to small own weight, huge anti-bending and torsional stiffness.Along with the development of high-rise and long-span buildings, the structural weight of buildings is becoming larger and larger. The research shows that reducing the own weight of buildings can greatly reduce the impact of strong earthquakes on buildings, the amount of materials and the project cost, so as to obtain sustainable environmental economic benefits and environmental social benefits11 studied the axial compression performance of reinforced concrete hollow columns and found that the bearing capacity, ductility and deformation capacity of reinforced concrete hollow columns were poor. Al-Gasham et al.12 studied the axial compression performance of self-compaction concrete hollow columns with hollow ratio of 0.0%, 2.3%, 9.0% and 20.3%, and found that the ultimate load, stiffness and toughness of self-compaction concrete hollow columns were lower than those of solid columns, while the ductility was higher than that of solid columns. Concerning the change of section form of reinforced concrete column, Liang et al.14 focused on the research and investigation of the restraint effect of reinforced concrete solid columns with circular and square sections, reinforced concrete hollow columns with outer circle and inner circle sections, outer square and inner square sections under axial compression load. It was found that the restraint effect of reinforcement in solid columns and hollow columns on concrete deformation was different to a great extent, and the restraint effect of reinforcement in outer circle and inner circle, outer square and inner square concrete hollow columns was also different, and the difference was caused by the change of concrete expansion and confining pressure distribution on the cross section. To sum up, the following conclusions may be obtained that the own weight of the structure can be reduced and the ductility of the structure can be increased effectively via the increase of void ratio, while the bearing capacity is reduced, and the restraint effect of the reinforcement on concrete is different due to different opening methods.In recent years, a series of researches on the axial compression performance of hollow column via the changes of hollow ratio and section form have been conducted by the scholars at home and abroad. Concerning the change of void ratio, Han et al.15 when compared with the reinforced concrete columns at various section types, which can improve the axial compression performance of hollow columns of reinforced concrete. Hwang et al.16 studied the axial compression performance of the built-in angle steel composite column and found that the axial bearing capacity and deformation capacity of the test column were good, and sufficient lateral constraints were formed on the concrete in the core area via the angle steel and welded stirrups. Kim et al.17 studied the bearing capacity of built-in angle steel and high-strength concrete column and found that when the contribution and restraint efficiency of steel were high, the built-in angle steel and high-strength concrete column was still equipped with a large bearing capacity after the protective layer was peeled off because the strength of concrete in the core area remained unchanged after the angle steel yielded. On the basis, the paper aims to achieve a higher ultimate bearing capacity, deformation performance and better ductility of composite hollow column of steel fiber, high-strength lightweight aggregate concrete and angle steel with the purpose of reducing the own weight of the structure and improving the performance of reinforced concrete hollow column via replacing the ordinary concrete with steel fiber and high-strength lightweight concrete, and substituting the longitudinal reinforcement and stirrup with angle steel and batten plate respectively.Moreover, it can be found via the research that the composite column of angle steel concrete is featured with the advantages of high bearing capacity, good ductility and convenient constructionP·O 42.5 cement. The applicability can be seen in Table Grade-I fly ash, loss on ignition is 0.6%, water content is 0.52%, water demand ratio is 95%.2 content is 97.1%, water content is 0.5%, water demand ratio is 120%.Micro silica powder, loss on ignition is 3.7%, SiORiver sand, the particle grading is zone II medium sand, and the fineness modulus is 2.7.3, cylinder pressure strength is 17.7 MPa and 1 h water absorption is 8.1%, as shown in Fig. Crushed Stone shale ceramsite, particle size is 5–10 mm, bulk density is 1015 kg/mQ235 grade angle steel and flat steel. The material properties of the steel are tested according to ASTM E-8 standard. The performance parameters can be seen in Table 5 MPa, as shown in Fig. End hook type steel fiber, length is 13 mm, tensile strength is 1070 MPa and elastic modulus is 2 × 10Naphthalene B2 high-efficiency water reducing agent, water reducing rate is 19%.18, so it is widely used in practical projects, while there are a few relevant studies on the application of steel reinforced concrete columns19. Therefore, the high-strength lightweight aggregate concrete with strength grade of LC60 is used for the test in the paper, and the mix ratio can be shown in Table 20, which can effectively improve the overall performance of the test column and reduce the spalling degree of the concrete protective layer. Considering the workability of concrete, the steel fiber at 39 kg/m3 is added into the high-strength lightweight concrete in the paper.It is found that high-strength lightweight aggregate concrete has good structural benefits21 show that the hollow ratio influences the mechanical performance of hollow columns greatly. In practical application, controlling the hollow ratio within 36% can ensure the safety of members. The research results of Al-Gasham et al.22 show that the void ratio of outer square and inner circle self compacting concrete hollow columns increases from 0 to 25.8%, the strength and stiffness of the test columns decrease, while the ductility increases slightly. The research results of Al-Ajarmeh et al.25 show that the strength and ductility of GFRP reinforced concrete hollow columns are higher than those of reinforced concrete hollow columns. When appropriate parameter design is adopted, the bearing capacity of GFRP reinforced concrete hollow columns is higher than that of GFRP reinforced concrete solid columns. Considering that the smaller hollow ratio has slight effect on the weight reduction of hollow columns, the construction difficulty is increased, the bearing capacity and ductility of hollow columns are reduced greatly at the larger hollow ratio, the hollow ratio in this test is taken as 0, 15%, 16%, 32% and 36%.The research results of Ji et al.Five SCAH column specimens have been made. The cross-sectional dimension of the column is 250 × 250 mm, the hollow diameter of round hole is 110 mm and 160 mm respectively, the hollow side length of square hole is 100 mm and 150 mm respectively, and the thickness of protective layer is 20 mm. The angle steel adopts Q235 steel with side length of 30 mm and thickness of 4 mm; The batten is made of Q235 flat steel with the thickness of 6 mm, the spacing of 150 mm and the height of 750 mm. The cross section is shown in Fig. Concrete Structure Test Method Standard (GB/T50152-201226), the method of force control to load step by step is used in the test. At the beginning of loading, the load of each level is 1/10 of the estimated Pu (Pu represents the peak load) and the load is maintained for 2 min; When the load reaches the estimated 0.8 Pu, the load of each level is 1/20 of the estimated Pu, and the load is held for 2 min; When the load drop section is close to 0.6Pu, It is loaded continuously and slowly until the specimen is finally damaged and the loading is stopped. Figure 5000 kN hydraulic testing machine is used for loading test. According to Pu–0.6 Pu of the peak load, some narrow and short vertical cracks begin to appear at the end of the cylinder; With the gradual increase of load strength, the number of longitudinal cracks is also increasing, while the cracks extend slowly to the middle of the specimen and the width and depth of cracks increase gradually under the restraint and obstruction of batten plate; The load reaches about 0.6 Pu− 0.8 Pu of the peak load, and the crackling sound and skin blasting phenomenon appear successively at the surface of the column; After the load reaches the peak load, the through longitudinal splitting cracks and transverse cracks emerge rapidly on the column surface at a speed visible to the naked eye; the loading is continued. When the load is reduced to 0.6 Pu of the peak load, the angle steel of all specimens buckles obviously, some batten plates bulge out, and the concrete is crushed and damaged in different degrees. At the corner of the bottom of the column, some concretes are crushed and peeled off, and the loading is stopped. The typical failure mode of the specimens is shown in Fig. At the initial stage of loading, the specimen lies in the elastic stage, the concrete is compressed longitudinally without obvious crack on its outer surface. When the load reaches about 0.3With the increase of the hollow ratio coefficient of the hollow column, the damage degree of the outer surface of the hollow column with circular hole is weakened, and the damaged section moves down from 2/3 to 1/3. It is because the wall thickness gradually decreases along with the increase of the hollow ratio. In the later stage of loading, the stress distribution of the section is uneven, and the transverse strain in the middle of the four sides of the hollow column is gradually greater than the corner strain. The transverse expansion of concrete becomes more and more obvious with the increase of the load, the non-uniformity of the whole force of the hollow column is amplified, resulting in the destruction of the section near the loading end; The opening form is a hollow column with square holes, and the damage phenomenon is basically the same as the damage degree.The constraint at the end of the hollow column is very small, so the damage at the end of the concrete is relatively serious. According to the stress nephogram simulated by finite element, the stress at the end of the concrete is more concentrated, it can be seen that the number and width of cracks at the end of the sample increase, and continue to extend to the middle of the sample. However, the end restraint of solid concrete column is well, and the specimens are mainly destroyed in the middle.The load-deformation curve of the specimen is shown in Fig. –3). Before the longitudinal angle steel reaches the yield strain, the strain of the longitudinal angle steel gradually increases with the increase of void ratio under the same load. Due to the obvious corner effect of the inner wall of the hollow column with square hole, the longitudinal stiffness of the high-strength lightweight aggregate concrete hollow column is weakened, so that the longitudinal angle steel strain of the square hole hollow column is greater than that of the round hole hollow column with the same hollow rate.Load-angle steel longitudinal strain (P-ε) curve of the specimen can be shown in Fig. The load-concrete transverse and longitudinal strain curves of the specimen  can be shown in Fig. 27, as shown in Fig. The ratio of ultimate deformation and yield deformation is defined as the deformation ductility coefficient, the deformation corresponding to 0.85pu in the descending section of the load-deformation curve is taken as the ultimate deformation, and the yield deformation of the specimen is determined by the equal energy methodThe high-strength lightweight concrete is obtained from the full stress–strain curve test  represents the stress in the z-axis. The positive value is tensile stress and the negative value is compressive stress. It can be seen from Fig. It can be seen from Fig. It can be seen from Fig. Von Mises stress is the fourth strength theory (such as Eq. ). AccordThe specimen enters into the elastic–plastic stage (AB) along with the increase of the load, and the yield stress (328 MPa) is reached within the full length of the angle steel, while the batten stress is about 160–300 MPa with the failure to reach the yield stress. At this time, the Mises stress of the middle batten of the specimen is significantly greater than that of the end batten, and the Mises stress of the batten at the connection with the angle steel is significantly greater than that near the center point of the batten.The specimen enters into the descending section (BC) along with the development of the loading, the radial deformation of concrete increases rapidly, the tensile stress of batten plate increases, and finally it reaches the yield stress. Most of the specimens yield to the second and fifth battens.It can be seen from Fig. 28 is established for stirrups restraining ordinary concrete square columns. The lateral restraint effect of stirrups on core concrete and “arch effect” of effective restraint area and rectangular restraint are considered. Considering whether the bearing capacity calculation of angle steel restrained high-strength lightweight aggregate concrete is applicable, the model is verified below:Mander modelFor the specimen with small void ratio, the compressive strength formula of triaxial confined concrete is shown in Formula :4\documeFor the specimen with large void ratio, the compressive strength formula of biaxial confined concrete is shown in Formula :5\documeNote: the test specimen with hollow ratio less than 16% is considered as small hollow ratio, otherwise it is the specimen with large hollow ratio.29; In the formula: In the formula:  formula , and theIn the formula:  formula , and the formula .10\documBased on the superposition principle, the axial compression bearing capacity of composite hollow column of steel fiber, high-strength lightweight aggregate concrete and angle steel can be calculated according to formula :12\documIn the formula: Since the test results may be affected by the defects in the test loading, it is necessary to increase the reduction factor of 1.2. According to Table The ends of SCAH-2–SCAH-5 are damaged severely, the cracks extends from the ends to the middle of the specimen, and the width increases. The column end of SCAH-1 is well constrained, and the failure of the specimen is mainly focused in the middle.The peak load of composite hollow column of steel fiber, high-strength lightweight aggregate concrete and angle steel decreases significantly and the ductility increases along with the increase of void ratio; Under the same void ratio, the deformation ductility coefficient of hollow column with round hole is slightly lower than that of hollow column with square hole; The peak load of round hole is higher than that of square hole under large void ratio; Compared with the solid column, the hollow column with square hole at the hollow ratio of 16% has no great influence on the bearing capacity and ductility, and the ductility is better than the solid column.The bearing capacity and load-longitudinal deformation curves obtained by finite element simulation are in good agreement with the experimental values. In the elastic stage, the compressive stress of concrete is less than − 20 MPa, and the angle steel and batten plate do not reach the yield stress; In the elastic–plastic stage, the maximum compressive stress of the concrete core area of the specimen with small void ratio increases significantly (up to − 60 MPa), while the compressive stress of the concrete of the specimen with large void ratio increases slightly (about − 30 MPa), and the yield stress is reached in the full length of the angle steel, but the batten still does not reach the yield stress; In the descending section (BC), the compressive stress of the concrete surface of the specimen is small (about − 6 to − 13 MPa), and even a small tensile stress (0–8 MPa) occurs. The radial deformation of the concrete increases rapidly, and some battens reach the yield stress.The influence of angle steel skeleton on concrete strength is considered in Mander model, and then the superposition calculation is conducted. It is safer to calculate with the method for the calculated value is less than the test value, and the calculation accuracy is high.The influence of different void ratios and opening methods on the axial compressive properties of composite hollow column of steel fiber, high-strength lightweight aggregate concrete and angle steel is researched in the paper. Combining lightweight aggregate concrete with hollow column, the dead weight of the specimen is greatly reduced, and the finite element simulation is conducted. The bearing capacity of SCAH is calculated by three methods, and the following conclusions may be drawn:


G2P) model for applications of genomic prediction and the realized trait and performance differences in the TPE for the genotypes that are the prediction targets. The strength of this MET-TPE relationship is usually assumed to be high, however it is rarely quantified. To date investigations of genomic prediction methods have focused on improving prediction accuracy within MET training data sets, with less attention to quantifying the structure of the TPE and the MET-TPE relationship and their potential impact on training the G2P model for applications of genomic prediction to accelerate breeding outcomes for the on-farm TPE. We extend the breeder’s equation and use an example to demonstrate the importance of the MET-TPE relationship as a key component for the design of genomic prediction methods to realize improved rates of genetic gain for the target yield, quality, stress tolerance and yield stability traits in the on-farm TPE.A major focus for genomic prediction has been on improving trait prediction accuracy using combinations of algorithms and the training data sets available from plant breeding multi-environment trials (METs). Any improvements in prediction accuracy are viewed as pathways to improve traits in the reference population of genotypes and product performance in the target population of environments (TPE). To realize these breeding outcomes there must be a positive MET-TPE relationship that provides consistency between the trait variation expressed within the MET data sets that are used to train the genome-to-phenome ( Plant bApplication of genomic prediction technologies has emerged as a major theme of breeding program design in the 21st Century . Here we22.1ΔG ) from one cycle (L) of a breeding program, following application of a selection strategy  used as training data sets , an equation for trait genetic gain within the TPE, based on selection decisions made using predictions from G2P trait information obtained from METs , can be given as:The breeder’s equation, as represented in equation (1), quantifies the per cycle rate of change of the trait mean value for the RPG . HoweveriMET is the selection differential applied to phenotypic and G2P prediction information obtained from analyses of the MET training data sets, as for i in equation (1), ra(MET) is the prediction accuracy for the selection units based on applications of the training data available from the MET, as for ra in equation (1). In equation (2) the σa term of equation (1) is replaced by the product of two terms ra and σa(TPE) . The term ra is the genetic correlation between the additive genetic effects estimated by applying G2P models developed using the MET training data sets, and the additive genetic effects for the trait targets required for realized trait performance in the TPE. The term σa(TPE) represents the relevant target additive genetic variation for the traits within the TPE. Thus, the ra term of the extended breeder’s equation provides a quantitative measure of the impact of the MET-TPE alignment for the prediction of additive genetic variation for traits in the TPE, and thus for predicting their contributions to genotype performance in the TPE. The ra can range from +1, with good MET-TPE alignment, to -1, with poor MET-TPE alignment. Additional forms of equation (2) can be given, for example for prediction at the level of the total genotypic trait performance level. Equally equation (2) can be further extended to examine the contributions of quantitative trait loci (QTL) and combinations of haplotypes and specific QTL to the additive or total genotypic variance for multiple traits in the RPG for the TPE.Two of the terms in equation (2) are equivalent to terms in equation (1): Applying the extended form of the breeder’s equation given in equation (2), statements can be made regarding the design of genomic prediction strategies based on applications of equation (1).ra → +1 and equations (1) and (2) will converge to the same form of the breeder’s equation, as given in equation (1); in this case the σa of equation (1) converges to the σa(TPE) of equation (2). However, if there is GxE interaction and divergence in environmental composition between the MET and the TPE, ra < +1 can occur, diminishing prediction accuracy for the TPE. Under such circumstances it can be expected that realized genetic gain in the TPE will be lower than predicted when based on studies confined to pursuing G2P modelling algorithms for improved prediction accuracy within the bounds of the MET training data sets; in this case the σa of equation (1) can diverge from the σa(TPE) of equation (2). Whenever there is historical evidence that realized genetic gains in the on-farm TPE are lower than the predicted gains, the magnitude of ra should be investigated to quantify its potential impact on the expected realized prediction accuracy that can be achieved in the TPE based on prediction accuracy derived from the training data available through the MET.Firstly, if the environmental composition of the MET is an accurate sample of the environmental composition of the TPE then it can be expected that Secondly, whenever there is evidence of GxE interactions within the TPE, including GxExM interactions, and there is the potential for divergence between the environmental composition and trait data obtained from current METs and those expected for the future TPE, as is often projected for the influences of climate change , the extra and determination of the genetic and environmental factors contributing to ra < +1. The effects of climate change on the environmental composition of the TPE and associated changes in trait contributions to yield and GxE interactions for current and future cropping systems represents one clear area for urgent consideration in the design of METs to address the MET-TPE alignment  component of equation (2). The first considers a familiar theoretical example from the study of crossover GxE interactions  term from equation (2). Here we consider the genotypic correlation rg between weighted average yield of the two genotypes between the MET and the TPE, where the weights are based on the frequencies of occurrence of the two environments in the MET and the TPE  of the average performance of the two genotypes in the MET and the TPE is plotted against the frequency of Env_1 in the MET and the TPE. The genotypic covariance is the numerator of the genetic correlation rg term of equation (2) and is used here in place of rg to smooth out the response surface for illustration purposes. The shape of the response surface for the genotypic covariance  , approaches 0  and of ra(MET) from equation (2), is demonstrated for any prediction method within the confines of the MET training data set.Secondly, as the frequencies of the environments within the MET and the TPE deviate from 0.5 towards 1.0 for Env_1 and towards 0.0 for Env_2, or towards 0.0 for Env_1 and towards 1.0 for Env_2, then the influence of the MET-TPE alignment becomes increasingly important. When there is good MET-TPE alignment of the environment frequencies the genotypic covariance is positive and the crossover GxE interaction is less problematic for selection decisions  term of equation (2) for a range of wheat MET-TPE alignment scenarios for north-eastern Australia  between the MET and TPE  and prediction of average grain yield in the TPE based on average grain yield estimated from the MET  between the estimates of weighted average grain yield for the 15 genotypes between the MET and TPE for all MET-TPE alignment combinations. We then plotted the rg against the frequency of environment-type E1 in the MET and TPE to generate a simulated rg genotypic correlation response surface for all MET-TPE alignment configurations  between the simulated MET and TPE alignments ranged from a high value of 0.90 to a low value of -0.07  response surface for the wheat example has interesting features. Firstly, there is a relatively broad plateau of high rg values for many of the MET-TPE alignment scenarios. This plateau of high rg values occurred for scenarios where the frequency of the water-sufficient environment-type E1 was higher than 0.5 in both the MET and TPE  is degraded from the high levels of the plateau  for prediction of average grain yield for the TPE based on average gain yield obtained for the MET was intermediate  = 0.70 for MET f(E1) = 0.41, f(E2) = 0.59 and for TPE f(E1) = 0.31, f(E2) = 0.69. Thus, the MET-TPE alignment for the empirical example was located on the rg response surface  levels, but still above the precipice where the rg value is severely degraded. This empirical realization of MET-TPE alignment is just one of the many possible scenarios that can occur as the frequencies of environment-types change between the MET and the TPE  this MET-TPE alignment disconnect can result in low realized genetic gain under the on-farm conditions of the TPE, even when high prediction accuracy, based on ra in equation (1) or more explicitly ra(MET) in equation (2), is demonstrated for genomic prediction methods evaluated within the confines of the MET. The extended form of the breeder’s equation, introduced here as equation (2), provides a framework to remove this disconnect and to support design of prediction-based breeding strategies that take aim at the TPE by emphasizing the influence of the MET-TPE alignment on realized genetic gain for the on-farm TPE  , rather than assuming ra = +1, as is the case for the traditional form of the breeder’s equation.Design of breeding programs, and crop improvement strategies in general, to take aim at the crop productivity requirements of the TPE is critical to both accelerate and achieve realized genetic gain on-farm that contributes to closing yield gaps , improvifarm TPE . Here weWe have introduced and demonstrated the utility of the extended form of the breeder’s equation through applications to a theoretical and empirical example. In summary the following key points were presented.Theoretical considerations: We extended the breeder’s equation, introducing the genetic correlation ra to explicitly incorporate and quantify the relationship between a MET and the TPE, as a framework for designing METs to take aim at the TPE. Three further considerations are important: (1) the traditional form of the breeder’s equation assumes that the genetic correlation ra = +1; (2) in the presence of GxE interactions the genetic correlation ra can be decomposed to take into account the genetic variance-covariance structure among the environment-types within the TPE  can be applied to the continuum of selection units of interest to breeders, extending from the level of sequence information, accounting for QTL and chromosomal haplotypes, to total multi-trait, multi-QTL predicted genotypic performance or breeding value obtained for any G2P model that is derived from relevant training data sets that can be generated from METs together with augmented data sources from specialized phenotyping facilities cilities .G2P information for traits, that is available from the environment-types sampled in the MET training data sets, by their frequencies of occurrence and relative importance in the TPE  in terms of the more recent TPE characterization (TPE sets . This prTPE sets  and so wFuture research: The extended form of the breeder’s equation is particularly relevant as a framework for the design of breeding strategies to target climate resiliency to address the impacts of climate change on the environmental composition of the short, medium, and long-term future diverse geographical TPEs expected for our global agricultural systems ( systems . Future  systems .mark.cooper@uq.edu.au.The data analyzed in this study is subject to the following licenses/restrictions: The dataset utilized in the examples was obtained from previous studies, as cited within the article. The dataset can be obtained from the corresponding author. Requests to access these datasets should be directed to MC conceived and wrote the manuscript. Ideas that contributed to the manuscript came from collaborative research conducted by MC, CG, CM, TT, OP. All authors contributed to the article and approved the submitted version.


Misuse of antibiotics has been associated with poor knowledge, attitude and practice (KAP). Therefore, this study aimed to assess if KAP of prescribers and dispensers could drive irrational use of antibiotics among children in Tanzania.A convergent parallel mixed-methods study design that employed quantitative and qualitative approaches was conducted in 14 regional referral hospitals (RRHs). A total of 108 participants, prescribers [54] and dispensers [54] working with the pediatric population in the respective regions participated in a quantitative survey, by filling the standard questionnaire while 28 key informant interviews were conducted with in-charges of units from the pharmacy and pediatric departments. Two key informants (prescriber and dispenser) were selected from each RRH.p = 0.53, those with positive attitudes were 31.5% and 81.5%, p < 0.001 and poor practices were among 70.4% and 48% p = 0.0312 respectively. Among prescribers, 14.8% agreed and strongly agreed that prescribing antibiotics that a patient did not need does not contribute to resistance. Moreover 19% disagreed to prescribe antibiotics according to local guidelines. Among dispensers, a-quarter of the dispensers thought individual efforts to implement antibiotic stewardship would not make a difference, 17% agreed and strongly agreed that antibiotics can treat viral infection and 7% agreed and strongly agreed antibiotics can be stopped upon resolution of symptoms. From qualitative interviews, both participants displayed an adequate understanding of multi-contributors of antibiotic resistance (AR) including polypharmacy, community self-medication, among others. Regardless, both professions declared to prescribed and dispensed antibiotics according to the antibiotics available in stock at the facility. Furthermore, prescribers perceived laboratory investigation took a long time, hence wasting their time. On the other hand, Dispensers reported not to provide adequate instruction to the patients, after dispensing antibiotics.Overall, among prescribers and dispensers, there was adequate knowledge; 81.5% and 79.6%, Both prescribers and dispensers had adequate knowledge, few prescribers had positive attitudes and the majority had poor practices. Few dispensers had poor attitude and practice. These findings highlight the need to provide adequate training on antimicrobial stewardship and enforce regulation that foster appropriate medical practice.The online version contains supplementary material available at 10.1186/s12913-022-08359-7. Antibiotic resistance (AR) is rampant and is considered a global health threat of the twenty-first century . CurrentThe irrational use of antibiotics is a major factor fueling the development of AR . AccordiEvidence from research agrees that one way to address antibiotics resistance (AR) is to consider the vital role played by healthcare professionals, especially prescribers and dispensers , as theyn = 2802) in one of the largest study in 14 referral regional hospitals in Tanzania, whereby only 10% and 16% of parents had good knowledge and positive attitudes, and the majority (82%) had poor practices on rational use of antibiotics for children [Moreover, although parents are believed to be a determining factor for appropriate or inappropriate use of antibiotics among children, their practices and most of what they know or do not know concerning antibiotics is influenced by health care workers. This is evidenced by findings from parents  of prescribers and dispensers and its influence on antibiotic use among children to fill the gap of evidence on antibiotic use among children in Tanzania Mainland.A hospital-based cross-sectional design using convergent parallel mixed-methods  was conducted in 14 RRHs in Tanzania Mainland between June and September 2020. Two RRHs from each zone were selected to represent seven administrative zones in Tanzania Mainland. Selection of hospitals were based on regional socio-economic activities  such as Purposive sampling was used to select participants for both quantitative and qualitative studies. For the quantitative data, all prescribers and dispensers working in RRH pediatric and pharmacy units respectively with at least a diploma level education were assessed upon signing the informed consent form. Prescriber with diploma were 8(15%), and dispensers with diploma were 25(46%). For the purpose of triangulation of the study population, participants in charge of the units in pediatric and pharmacy departments who had at least two years of experience in the administrative role were recruited to participate in the qualitative study. In this case, two informants (dispenser and prescriber) were recruited from each RRH to participate in the key informant interview. To limit response bias, the informants who participated in the qualitative study were excluded from participating in the quantitative study.A prescriber with a diploma is one level below a medical doctor (Bachelor's degree), during the study period, prescription was restricted according to the facility level, in which capacity to do culture and sensitivity was one of the criteria. Therefore, a diploma holder working at a RRH could prescribe all levels of antibiotics as a medical doctor would. A diploma in pharmacy or a pharmaceutical technician is one level below pharmacists (bachelor's degree holder). They assist pharmacists in compounding and dispensing activities in a pharmacy. In cases where both a pharmacist and technician are present, the pharmacist will review prescriptions, communicate with physicians for queries, and counsel patients, whereas the technician will mainly perform packaging, labeling, and compounding tasks. However, due to a shortage of healthcare workers in our country and many other LMICs, technicians may assume some pharmacist's responsibilities in centers where there are few or no pharmacists. This may also involve querying and making recommendations to physicians, although they are most often required to consult senior colleagues first, such as the head of department, or any pharmacist that can possibly be reached within a reasonable time. Their contribution to antimicrobial stewardship is therefore significant, whether that be in the form of assisting pharmacists or taking more pronounced, empowered and leading roles where pharmacists are not available.A total of 108 prescribers (54) and dispensers (54) were assessed for the quantitative study. For qualitative data, 28 in-depth interviews among the 28 Prescribers and Dispensers in charge of the pediatric unit and pharmacy unit respectively were done.Two different 5-point Likert scale structured questionnaires for dispensers and prescribers were adopted from the previous study , 14 afteA semi-structured interview guide was developed following a comprehensive literature review. The questions were focused on knowledge of antibiotics, AR, and antibiotic stewardship. Also, the questions evaluated the attitude of prescribers and dispensers towards antibiotic stewardship, activities to fight against AR and continuing education of antibiotic resistance as means of fighting against AR. Furthermore, effort done by prescribers/dispensers in reducing AR, and antibiotic stewardship activities were assessed. Lastly, their recommendation on what could be improved in order to reduce AR and ways to accelerate the implementation of antibiotic stewardship was questioned. A total of 28 key informant interviews were conducted with prescribers and dispensers who were in charge of pediatric units using a semi-structured interview guide to explore what drives the irrational use of antibiotics. All interviews were conducted in Swahili language a native local language for both researchers and participants. Interviews were audio-recorded to capture the information provided by the participants. During the interview process field notes on verbal and non-verbal aspects were taken to complement the audio recorded information. Each interview lasted between 25 and 45 min.p-value of less than 0.05 was the measure of statistical significance.Open Data Kit  was used in data collection. Collected data were exported to Microsoft Excel Sheet  then to statistical package for social sciences version 25  for coding and data analysis. For KAP, the scores were 1 for correct and 0 for wrong or uncertain/neutral responses on individual questions, respectively. The scores for poor knowledge was 0–40%, moderate knowledge was 50–70% and good knowledge was 80–100%. The scores for negative attitude was 0–40%, uncertainty or sometimes was 50–70% and positive attitude was 80–100%. The percentage score for practice was either poor or good if the score was 0–70% or 80–100%, respectively. Categorical variables such as age, sex and education level were presented using frequencies and percentages. The Association of demographic variables, education level, experience and KAP between prescribers and dispensers was computed using Chi-square test. The The audio recorded interviews and FGDs were first transcribed verbatim. The transcripts and field notes were read and re-read by six researchers to be familiar with the data and understand the participant`s accounts before the coding process. Thematic analysis was conducted following procedures delineated by Braun and Clarke . Team-ban = 41) had age between 26–35 years, similarly to dispensers 51.9% (n = 27), p = 0.0692. Most of the prescribers were graduates/ medical doctors 75.9% (n = 41) while for dispensers the majority were diploma holders/ pharmaceutical technicians 46.3% (n = 25), p < 0.001. Most of the participants in both groups 68.5% (n = 37) each, p = 0.01074 had the experience of 1 to 5 years of working with the pediatric population (Table Most of the prescribers 75.9% n = 4 had age n = 44) and dispensers 79.9% (n = 43), p = 0.5278 had a good knowledge about antibiotics use in children. Regarding the attitude, 31.5% (n = 31.5) of the prescribers and 81.5% (n = 44) of the dispensers, p < 0.001 had positive attitudes. Poor practice was observed in the majority of the prescribers 70.4% (n = 38) while 51.9% (n = 28) of dispensers, p = 0.0312 had good practice  Fig.  used antIn total 28 key informants (14 prescribers and 14 dispensers) were interviewed from 14 RRHs in Tanzania Mainland. Participants’ characteristics are summarized in Table .Table 3CPrescribers and dispensers stated that they have adequate knowledge on the basics of antibiotics use in pediatric patients and the cause of AR. Their knowledge included but was not limited to correct knowledge on the group of antibiotics to be used in pediatric patients. They added that the adequate knowledge influenced how they interacted with the patients and thus influenced the rational use of antibiotics among the patients.“…Patients should receive the prescribed right dosage, at the right time and at the recommended time interval …… for example; appropriate dose is when a patient takes one tablet three times a day and dosage is when a patient takes some tablet per day for 5 days……” (Prescriber 3),“…I normally explain to my patients how to appropriately use antibiotics… Also, I explain to them the possible side effects when given antibiotics……” (Dispenser 20)Participants of this study expressed knowledge on the multi-level contributors of antibiotics resistance in pediatrics. They stated that antibiotic resistance is contributed by patients’ behavior on antibiotics’ use, health care providers themselves, and hospital management.… In the community, there is self-medication… a patient visits a community outlet and requests for a certain antibiotic without any investigation or being attended by a health care provider (Dispenser 2)Prescribers also contribute to antibiotic resistances through polypharmacy …… Sometimes a patient is given two or three different antibiotics for treating the same infection for the purpose of increasing hospital income…… (Prescriber 3)… Sometimes in hospitals when antibiotics are about to expire, prescribers are instructed to prescribe them to patients even when there is no clear indication, for example, it has happened mostly with meropenem… (Prescriber 4)Participants of this study expressed that adequate knowledge on the impacts of antibiotics resistance influence the antibiotics prescription and thus antibiotics use. The latter was expressed as knowledge on cost implication of antibiotics resistance and knowledge on antibiotics resistance as a burden to the patients.“…Antibiotic resistance is a major concern as it increases cost of treatment and causes complications …. It is a threat to human health and economy; therefore, I think we should take action now.” (Prescriber 2)“Resistance is problematic to neonates, the first line drugs such as ampicillin plus gentamicin do not respond to neonatal sepsis…the second line drug, like ceftriaxone is very expensive but yet increased resistance to ceftriaxone is reported…” (Prescriber 11)Participants felt that continued training is crucial to improve antibiotics dispensing practices and thus essential in fighting antibiotics resistance. The participants stated that the training helps to improve decision making, influence the behavior of the prescribers/ dispensers, improve the component of dispense-patient communication, knowledge on antibiotic resistance and improves the dispenser's confidence.“Training helped me to understand the drug interactions……which in turn has helped me to change my prescribing behavior to reduce the spreading of drug resistance…… (Prescriber23)…Training has helped me in decision making and in educating my colleagues……dispensing is not only about issuing medication but providing instruction to patients on how to use the medication because a slight mistake may harm the patients…….”. (Dispenser 17)Participants of this study stated that to address antibiotic resistance, it is crucial to have adequate laboratory investigations for coming up with a definite diagnosis before initiating antibiotics. For them laboratory investigations including culture and sensitivity whenever possible were seen to influence rational use of antibiotics and thus reduce antibiotic resistance.“High quality laboratory investigations should be conducted prior to antibiotic prescription. For example, when a child has a fever or stomach ache and the doctor suspects UTI, an appropriate laboratory should be conducted to guide antibiotic prescription ……”( Prescriber 3)“Culture and sensitivity tests play a key role in reducing the burden of antibiotic resistance. As it helps in isolating the bacteria responsible for a particular medical condition before the prescription of antibiotics……” (Dispenser 3)Some participants stated that some of the laboratory investigations are time-consuming and thus they tend to avoid them. For that case they stated that time-consuming investigations challenge the prescribers on which decision to take and often prescribe empirically.“I normally receive culture and sensitivity test results at least after 72 h …sometimes the patient needs urgent treatment, I therefore initiate antibiotics …… (Prescriber 23)“……prescribers think ordering culture and sensitivity tests is a waste of time as it takes a long time to get the results…………they see it as a disturbance to ask the patient to return after 48 hours for culture and sensitivity results…” (Dispenser16)Participants felt that private health facilities were profit-oriented and thus their main focus was not on good outcomes of the patients. They further added that private health facilities were more likely to have poor quality laboratory investigations as their focus was profit-making other than the outcomes of the patients.“…………. Probably the problem is with Accredited Drug Dispensing Outlets (ADDOs) shops because the patient goes direct and presents his or her symptoms and gets the medications, so it will depend on the knowledge of the dispenser. But remember those are business people so even when a patient complains of flu who may just need paracetamol or cetirizine if the patient requests for amoxicillin they will dispense…………” (Prescriber 3)“….. Sometimes when parents take their children to private laboratories……most of the private laboratories lack integrity. Even if there are no reagents to diagnose the infection, they will take the sample and release the results” …. (Dispenser 23).Participants stated that health facilities contribute to antibiotic resistance through the management pressure that focuses on raising hospital income. They also reported that political pressure and being forced to prescribe based on the available stock contributed to antibiotic resistance.“Sometimes the hospital management forces us to dispense strong antibiotics without a laboratory test. Sometimes we advise prescribers and they understand but in most cases, we are forced to dispense, if you resist you will be blamed for allowing expensive antibiotics to expire…” (Dispenser 23)Sometimes…. amoxicillin/clavulanic acid are out of stock, and we receive calls from pharmacies that only certain antibiotics are available… so whoever comes we prescribe what is available, just like that. (Prescriber 2)Some of the dispensers interviewed in this study stated that some health care providers' practices contribute to the increase of antibiotic resistance. They mentioned some of the practices to include spending less time with patients and thus giving inadequate instruction on the use of antibiotics to the patients.“Dispensers contribute to AR because they don’t provide enough education to patients before dispensing antibiotics….”. (Dispenser16)Participants viewed patients as a good contributor to the increase in antibiotic resistance. They stated that some patients do not complete the prescribed dose even if they are instructed to complete the dose by a health practitioner. Further-more some patients request for incomplete doses as a result of financial limitations.“you may prescribe the correct antibiotic but they (patients) will not complete the dose,… after feeling good, they stop taking the drug ……” ( Prescriber 8)“…. probably because of financial constraints, some patients come with a prescription of a certain antibiotic requesting half a dose ….” (Dispenser 11)Participants of this study highlighted the strategies towards reducing antibiotics resistance that included sustainable continued development education for health professionals, adherence to professional practice in provision of antibiotics, practicing antibiotic stewardship activities and continuous provision of health education to patients on antibiotic use.“So we try to educate mothers not to self-medicate children at home, rather visit nearby health care facilities…………so we educate them on irrational uses of medicines”. (Prescriber 19)“I usually educate patients on rational uses of antibiotics… I provide appropriate instructions on how to use the medicines ….” (Dispenser18)We conducted this study to assess if KAP of prescribers and dispensers could drive irrational use of antibiotics among children in Tanzania. The overall knowledge was found to be adequate in both quantitative and qualitative findings, for example, most of the respondents were aware that misuse of antibiotics can trigger antibiotic resistance. Similar to other reports, knowledge on rational use of antibiotics, the existence of AR and its contributors did not seem to be the issue with majority of healthcare workers , 28 rathAlthough few, some prescribers were observed to have poor knowledge on antibiotics. For example, 24% of the prescribers admitted to having a hard time selecting the right antibiotics, 19% were unsure if AR is a worldwide problem and 7.4% didn’t think they ought to know the resistance pattern of the antibiotic before prescribing it. According to Tanzanian treatment guidelines, selection of antibiotics should be informed by culture and sensitivity , the reaFrom qualitative interviews, participants displayed adequate knowledge on multi-contributors AR and AR impact to the community. Community self-medication of antibiotics was mentioned as one of the main contributors of antibiotic resistance among others. According to Byrne et al., antibiotic use in the community is 4 times that of a hospital set up and most of these antibiotics are being accessed without prescription . In the Moreover, this study found some positive attitudes toward antibiotic use for children. Prescribers and dispensers believed that workshops and training on the rational use of antibiotics is one of the ways of fighting against antibiotic resistance. This is similar to other studies conducted elsewhere , 35. HowApart from the majority, a few prescribers (14.8%) agreed and strongly agreed that prescription of unnecessary antibiotics to a patient does not cause any harm. According to Rezal et al., prescribers tend to prescribe un-required antibiotics in order to avoid more serious superinfection that they might have missed . FurtherPerspectives from qualitative findings on attitude emphasized on the importance of laboratory investigation to guide rational prescription and dispensing of antimicrobials however prescribers had concerns on these investigations taking a long time and hence wasting of their time and bringing disturbance to the patients. According to Polage et al., in Ghana at least 90% of physicians rarely or never ordered laboratory tests because of time constraints . AlthougDespite good knowledge and some positive attitudes, we found poor practice, especially among prescribers whereby about 36% of prescribers agreed and strongly agreed to prescribe antibiotics according to the availability of the antibiotic at the facility. Similarly in Uganda prescriptions were based on availability, not suitability . DespitePoor Practices among Dispensers were attributed by 29% who sometimes dispensed antibiotics without prescription and 7% and 6% who often and almost always did this. Non-prescription antibiotics are becoming common despite antibiotics being prescription only , 45. An Findings from a qualitative survey, pointed out patients not receiving adequate instruction from dispensers. Antibiotic dispensing without instructions may lead to wrong self-dosages and inappropriate dosing intervals that might harm the patients . This isThis study was limited to prescribers and dispensers and how they drive irrational use of antibiotics among children, although other health professions such as laboratory scientists and nurses could have some influence on this practice as well. Nonetheless, this does not take away from the fact that findings presented in this study are a representation of the situation in referral regional hospitals in Tanzania. Further studies should aim to study hospital facilities at lower levels and include other health care professions that could have influenced the decision to prescribe or dispense.This study found an adequate knowledge, some positive attitude, and poor practice on appropriate antibiotic use and AR for children among prescribers and dispensers. Poor practice was linked to shortage of facilities such as non-functioning laboratories, un-availability of reagents, inadequate number of healthcare providers, limited training on antibiotics use and antibiotics resistance, patients' behaviors (sharing of prescription and incomplete dose), and poverty, among others. This study recommends re-training and instigation of measures to ensure sustainable implementations of antibiotics stewardship programs in regional referral hospitals in Tanzania. Furthermore, regulatory bodies should conduct regular audits on systems influencing antibiotics misuse in RRH to identify loopholes of misconduct and systemic weaknesses that could be fueling the irrational use of antibiotics among children in the country.Additional file 1. Dispensers responses on individual questions.Additional file 2. Prescribers responses on individual questions.


In this paper, to study the development of load-carrying capacity and long-term creep performance of reinforced concrete beams under different corrosion patterns, the rate-dependent model of concrete is used as the basis to consider the creep development process from the meso-scale level. The porosity mechanics method is used to simulate the generation and penetration process of corrosion products. Three corrosion conditions are set: bottom longitudinal reinforcement corrosion, top longitudinal reinforcement corrosion and all reinforcement corrosion. The corrosion rate is used as the variable in each corrosion condition. The results show that: (1) the greater the corrosion rate in all conditions, the lower the bearing capacity. In addition, the corrosion of top longitudinal reinforcement causes the damage form of the beam to change to brittle damage; (2) the creep coefficient decreases with the increase in corrosion rate in all working conditions, but the main factor for this phenomenon is the obvious increase in initial deformation. Consequently, it is not suitable to follow the conventional creep concept  for the development of plastic deformation of damaged members. It is more reasonable to use the global deflection to describe the long-term deformation of corrosion-damaged members. Reinforced concrete structures are widely used in houses, tunnels, ports, and other infrastructure construction. These RC structures located in the coastal area are in a complex environment coupled with corrosion influence and load effect. Rust of reinforcement bars in concrete causes internal micro-cracks and cumulative damage. Corrosion not only reduces the elastic modulus and ultimate bearing capacity of structure members but also makes the structure deformation increase and then affects the long-term creep performance of the structure.There are few research results about the influence of rust cracking on the creep development of reinforced concrete members. Cao  conducteThrough the self-developed multi-scale model of material structure, the coupling analysis of the hydration process, material transport, structural durability deterioration and mechanical property deterioration of concrete materials is realized ,5. The cAs mentioned before, research on the creep development of rust-damaged members is relatively limited, and the only studies available usually only consider the effect of the corrosion rate on the mechanical properties of the beams. In this paper, based on the concrete material rate-dependent model considering the time course effect of creep, coupled with the analysis of corrosion product entity generation and infiltration process, the changes of load-bearing capacity and creep long-term performance of reinforced concrete beams under different rust expansion and cracking modes are investigated. The influence law of rust rate and rust morphological characteristics on the creep properties of steel and concrete structures is explored in depth.K and plastic strain pε. K is the ratio of the number of remaining intact elements after damage to the number of initial elements, and pε is the plastic deformation of the plastic parts of each Maxwell element. The damage coefficient K and plastic strain pε represent the damage degree and plastic deformation of the material, respectively, which determine the change in elastic modulus and plastic strain of concrete materials.Based on the author’s previous research, the rate-type elastic-plastic damage constitutive model of concrete material is shown in The basic mathematical expression of the elastic-plastic damage mechanical model of concrete is shown in Equation (1).Φ represents the tendency of plastic deformation to increase and decrease in the development of life history, while the second term κ is linear creep.vC is the intrinsic creep time, representing the speed of linear creep development; limC is the creep coefficient at infinite time.The influence of the damage coefficient and plastic strain is expressed by the rate-type formula, see Equation (2), where the first term is the time history change in plastic deformation , and the second term is the cumulative deformation and damage of cyclic action . The creep constitutive of concrete is proposed based on the above elastoplastic damage mechanical model of concrete. The calculation formula of creep can be obtained by considering the linear creep of concrete into the creep constitutive model, as shown in Equation (3). The first term is the time history law of plastic deformation of concrete material, which reflects the nonlinear creep of concrete material. The corrosion products can be regarded as two different phases. Between them, the solid phase rust products accumulate at the corrosion interface. However, the liquid phase rust products have fluidity . The corsV, as shown in Equation (5).D represents the diameter of the original reinforcement; γ represents the volume loss rate of reinforcement, which is related to the corrosion rate. α represents the volume expansion rate of the corroded product relative to the corroded part of the original reinforcement.When the steel corrosion product is free to expand without restraint, the diameter of the steel bar and its composition can be expressed asThe free expansion strain of the reinforcement rust composition can be expressed asG is the modulus of solid phase corrosion product; The average modulus of the corrosion system is defined in Equation (8), and the corresponding rust expansion stress can be obtained through free expansion strain and average modulus, as shown in Equation (9):3), 3), and n is the porosity in the system.The behavior of liquid phase corrosion products in concrete should be analyzed based on multiphase pore medium mechanics, as shown in p is the pore pressure (N/mm2) caused by the pore medium. i = j and 0 when I ≠ j. l is the unit normal vector of the crack plane.When the concrete is not cracked, the pore pressure can be regarded as isotropic. After the concrete cracks, the pore pressure is anisotropic because the plane where the cracks are located cannot be transversely transmitted. Therefore, the stress tensor i,mmu are the second partial derivatives of skeleton displacement with respect to time (m/s2); ig is the component of gravitational acceleration along vector i (m/s2); i,mw and i,mmw are the first partial derivatives (m/s) and second partial derivatives (m/s2) of the displacement of the pore medium relative to the skeleton with respect to time, respectively. ik is the permeability of corrosion products.Due to the fluidity of liquid phase corrosion products, the dynamic equilibrium equation should be used to describe the interaction between pore medium and skeleton:p itself is constrained. According to its deformation degree, the pore pressure p can be obtained asThe liquid phase rust products will produce volume expansion, which will cause pore media to squeeze the pore wall (skeleton) and cause pore pressure (rust expansion stress). At the same time, the pore pressure β is related to the corrosion rate of reinforcement, which can be calculated as follows [icorr is the corrosion rate of reinforcement (μA/cm2).In an environment saturated with pore water and rich in chlorine, the crystallization rate of rust products   follows :(15)β=0.k of the pore medium composed of liquid phase corrosion products. Relevant studies show that when concrete cracks under load, the k value will increase [i, j, k> is the coordinate axis direction in the orthogonal coordinate system, and j and k are parallel to the crack plane; ik is the transmission rate (m/s) of the liquid phase corrosion product in the i direction. −10 cm/s.Due to the existence of liquid phase rust products, the rust products will be transmitted from the reinforced concrete interface to the surrounding cracks and concrete micropores . From thincrease .(16)ki=In this paper, the reinforced concrete beam is taken as the research object, and the material parameters used in the calculation model established are the same as those of the test specimen . The speIn this paper, the calculation process of the static load test after the corrosion of the reinforced concrete beam is as follows: specimen curing → steel corrosion reaches preset corrosion rate → static load loading until failure. The loading form is controlled by displacement, and the rate is 8.33 mm/h. The calculation process of the creep development test for RC beams after corrosion is as follows: specimen curing → steel corrosion reaching preset corrosion rate → static load holding, and the load holding level is 20% (22 kN) of the ultimate bearing capacity of RC beams. The calculation process can be seen clearly in As shown in The strain results of partial corrosion calculation are visualized as shown in The research on beam creep after rusting is relatively scarce, and the above contents confirm that the rate-type creep constitutive and the model considering corrosion crack and corrosion product penetration adopted by the authors have high accuracy in describing creep development and corrosion expansion. Therefore, the author intends to further study the creep properties of corroded beams and explore the influence of rust expansion and cracking on creep.It can be seen from the foregoing that the damage caused by the corrosion of steel bars in different positions is different. The creep property degradation caused by rust corrosion is mainly due to the internal damage of concrete caused by rust expansion, so it is necessary to clarify the specific influence of crack damage in different parts on concrete creep. This section mainly explores the influence of different rust cracking modes on the creep characteristics of reinforced concrete beams.It can be seen from Wp is creep deflection under load; eW is instantaneous elastic deflection; α represents the speed of linear creep development; β represents the creep coefficient at infinite timeThe long-term deflection of the beam is calculated by Equations (17) and (18). According to β had no obvious regularity. The regularity of the characterization of integration of α decreases with the increase in corrosion rate, and the creep coefficient is explained through the ductility in this paper, as mentioned before, but in fact, the creep coefficient is the ratio of elastic strain and plastic strain after the sustained load, and this conventional definition is used to describe traditional material creep characteristics. However, the creep coefficient used in material science is introduced in the structure in many pieces of research. The elastic strain at the moment of material loading corresponds to the instantaneous deformation at the moment of structure loading. However, for pre-damaged members, the deformation at the moment of loading is not elastic, so it is biased to use the concept of creep in this case. This is also the fundamental reason that the creep coefficient of the damaged component decreases with the increase in the initial damage. The author thinks that the quantitative index of the long-term deformation of the damaged component needs to be further improved, and the previous creep concept cannot describe the deformation characteristics of the damaged component.Only from the data regularity of observation, t = Wp + WeW can be known from the aforementioned Equation (18), as in Equation (19). In actual engineering structures, the members are basically all of the rust, and the relationship between the rust rate and deflection curve can be obtained by fitting a curve, where ζ is the corrosion rate. In order to facilitate the calculation of β take uncorroded members 0β, the fitting results are shown in Equations (20) and (21). The fitted curves and the predicted effect of the deflection curve model are shown in At present, it is more suitable for damaged members to directly study the overall deformation of the member caused by the coupling of its durability damage and sustained load, and the total deflection deformation (1)In this paper, the time history effect of creep was considered based on the rate-type constitutive model, and the generation of rust expansion cracks and the penetration phenomenon of rust products were fully considered in the calculation of rust corrosion. The three-dimensional rust expansion and cracking modes caused by different rust corrosion conditions were simulated more realistically, and a logical connection was established with subsequent mechanical properties.(2)According to the calculation and observation of the ultimate bearing capacity of the beams with different corrosion forms, the corrosion of the longitudinal bars at the top reduces the strength of the concrete in the compression zone, which leads to a decrease in the strengthening section of the fracture curve of the members and causes the brittle failure mode of the reinforced concrete beams. The corrosion of the longitudinal bars at the bottom causes the reinforcement to work in advance and reduces the mechanical properties of the tensile bars. The ultimate bearing capacity of the beam decreases gradually with the increase in the corrosion rate of the longitudinal bars at the bottom.(3)By observing the load-bearing deformation of beams with different corrosion forms, it is found that the creep coefficient of RC beams decreases with the increase in corrosion rate. This phenomenon is mainly caused by the obvious increase in initial instantaneous deflection caused by corrosion, which does not mean that corrosion is conducive to the creep of beams. In addition, this phenomenon indicates that it is not easy to use the traditional concept of creep  for the load-bearing deformation of corroded, damaged members, and it is more reasonable to use the global deflection to describe the long-term deformation of corroded, damaged members.(4)For future research on damaged members, this paper argues that the global deflection should be used reasonably to describe the performance degradation of members, where the damage study includes rust damage, fatigue damage, etc. The coefficient of creep was originally used in materials research and migrated to structural research. The creep coefficient is only suitable for the study of sustained load at undamaged times. For the creep of damaged members, it is recommended to directly use the absolute amount of plastic deformation at the sustained load for the description.


Ultrasonic testing (UT) is an important method for concrete, and ultrasonic pulse velocity is commonly used to evaluate the quality of concrete materials in existing studies. The ultrasonic pulse velocity of concrete materials is affected by many factors; therefore, it is necessary to establish a quantitative prediction model for the ultrasonic pulse velocity of concrete materials. Based on the multiscale homogenization method, concrete material is divided into different scales of homogenized materials, namely cement paste, mortar, and concrete. Then, a multiscale ultrasonic pulse velocity model is established through a combination of elasticity formulation and the hydration model. At the three scales of cement paste, mortar, and concrete, the elastic parameters and ultrasonic pulse velocity were predicted with the water-to-cement ratio of 0.35, 0.5, and 0.65, respectively. The ultrasonic pulse velocity of concrete with different water-to-cement ratios and different ages were measured in the test and predicted by the model. The results show that the predicted value of ultrasonic pulse velocity is within the error range of ±1.5% of the measured ultrasonic pulse velocity, suggesting that the established prediction model of ultrasonic pulse velocity can reliably predict the velocity change in concrete materials. Ultrasonic testing (UT) is a commonly used concrete testing method, with advantages including fast testing speed, convenient operation procedure, and a non-destructive nature. The strength and other parameters of concrete can be evaluated based on its ultrasonic pulse velocity (UPV) ,2,3. It In order to optimize the evaluation of concrete performance based on ultrasonic pulse velocity detection, it is necessary to study the ultrasonic pulse velocity prediction model of concrete materials. However, the ultrasonic pulse velocity of concrete is affected by various factors, such as the properties of materials , mix proThe mathematical model for predicting ultrasonic pulse velocity of concrete has been established by analysis of multiple influencing parameters . FurtherIn this study, based on the multiscale homogenization method and the elasticity formulation of homogenized multiphase material, a multiscale ultrasonic pulse velocity model for multiphase concrete material was established. Combined with the prediction of hydration process, the elastic modulus and ultrasonic pulse velocity could be predicted by the model in three-scale homogenized materials of cement paste, mortar, and concrete. The accuracy of the prediction model was verified by comparing the measured ultrasonic pulse velocity with the predicted value of the model. Based on this prediction model, the change of ultrasonic pulse velocity during the hydration process of concrete can be calibrated for future studies. Moreover, the concrete damage parameters can be introduced based on the established model for calculating the ultrasonic pulse velocity of concrete, which provides a theoretical basis for the study of ultrasonic pulse velocity of concrete damage.Based on the elastic theory of homogeneous and isotropic materials, the formula for the correlation of elastic parameters such as ultrasonic pulse velocity and elastic modulus can be obtained through the derivation of the theoretical formula. The ultrasonic wavelength used in concrete ultrasonic testing is larger than the size of the discontinuities existing inside concrete. Therefore, the ultrasonic waves do not interact with these inhomogeneities, and concrete can reasonably be regarded as a homogeneous material . The corK, G, and ρ of the concrete first.However, concrete is a composite of different components, the overall properties of which cannot be directly determined when viewed as a homogeneous material. Therefore, we need to determine the K, G and ρ, or the effective properties of multiscale multiphase concrete composite . In this paper, the iterative homogenization method is used in concrete such a multiphase material to predict the parameters of K and G at different scales.The focus is then on how to predict The homogenization method describes the overall elastic properties of representative volume elements (RVE) at different scales. The size of the representative volume unit defined within it needs to be much smaller than the overall analysis, and the characteristic length of the inhomogeneity in the unit needs to be much smaller than the size of the unit. In this scheme, the material in the RVE can be considered as uniform at the statistical level . The elaAccording to the homogenization method, RVE selected at different scales can be regarded as uniform, so that the elastic parameters of cement-based materials at each scale are calculated according to the theory of micromechanics. Since each component is considered isotropic, the homogenized material is isotropic as well.r, respectively; r, respectively; and Combined with research results of micromechanics on the elasticity formulation of homogeneous multiphase materials, the authors in  summarizThe elastic modulus and Poisson’s ratio can be calculated according to the following Equation (3):P and shear compliance Q are determined by the shape and elastic properties of each phase in the material. In this study, it is considered that each component exists in a nearly spherical state in undamaged concrete. According to Berryman [P and shear compliance Q are calculated considering spherical inclusions, as seen in Equation (4):The compressibility Berryman , the comAccording to Equations (2)–(5), the compressibility and shear compliance of homogeneous media at different scales can be obtained, depending on a suitable iteration scheme.Three scales are considered in concrete materials: (1) cement paste composed of CSH skeleton and pore substances; (2) mortar composed of cement paste and fine aggregates; and (3) concrete composed of mortar and coarse aggregates. The Mori-Tanaka scheme  and selfUsually, the Mori-Tanaka scheme defines a medium as reference medium, which has a large volume fraction in the mixture. The self-consistent scheme takes each medium as the reference medium for step-by-step iterative calculation, which is suitable for a closer volume fraction of each phase. Significantly, it leads to different values being substituted in Equation (4) when different schemes are used. Thus, the self-consistent scheme is used for cement paste due to its complex components, including more overlaps among the components and more pores. Obviously, using the Mori-Tanaka scheme for mortar is more suitable because the volume fraction of cement paste is so large that it can be considered as the main body, and the fine aggregate as spherical inclusions. In the same way, the mortar can be considered as the main body and the coarse aggregate as spherical inclusions in the concrete level. We chose the Mori-Tanaka scheme for concrete. The prediction of elastic parameter and ultrasonic pulse velocity in this paper refers to the above selection of the iterative scheme.2O), hydrates (hyd), and air voids as functions of the hydration degree ξ and the water-to-cement ratio w/c are:ξ is the hydration degree; w/c is the water-to-cement ratio; The RVE of cement paste consists of unhydrated cement clinker, water, hydrates, and air voids ,29,30,39ξ is the hydration degree and w/c is the water-to-cement ratio. The hydration degree evolves with age, influenced by the water-to-cement ratio, aggregate properties, and so on. In order to evaluate the proportion of each component in the composites, we need a scheme to predict the hydration degree.The maximum hydration degree is affected by the water-to-cement ratio. If the water-to-cement ratio is below 0.42, the cement clinker cannot be fully hydrated. The hydration degree reaches the maximum when the water is exhausted. If the water-to-cement ratio is larger than 0.42, the maximum hydration degree is equal to 1 when the cement clinker is fully consumed ,39. The ξ with a specific water-to-cement ratio can be quantified. Different hydration processes with water-to-cement ratios of 0.35, 0.5, and 0.65 are shown in With the calculation of pore distribution and hydration heat by the DuCOM model , the incObviously, the hydration degree shows a notable acceleration since initiation, and a slight increase in the hydration degree was found in the stable period. Based on the analysis of the predicted results, the mixture with a larger water-to-cement ratio has a higher hydration degree at the same age before the process is ended.At the scale of cement paste (Level II), the prediction of ultrasonic pulse velocity requires correlation parameters of clinker, water, hydrates, and air voids to predict the elastic parameter, as shown in K, shear modulus G, elastic modulus E, and Poisson’s ratio υ of homogenized material and phase were calculated by the model with the self-consistent scheme. The correlation curves between different parameters and the hydration degree are shown in According to Equations (2)–(5), bulk modulus At the same degree of hydration, a higher water-to-cement ratio shows a lower bulk modulus, shear modulus, and elastic modulus. With the growing hydration degree, the bulk modulus, shear modulus, and elastic modulus of the cement paste all show an increasing trend, and the differences between these parameters also increase gradually. For cement paste with a high water-to-cement ratio in the initial stage of hydration, the shear modulus and elastic modulus increase from around 0, which is also close to the corresponding parameters of water. Poisson’s ratio decreases with the increase of the hydration degree, and Poisson’s ratios of cement paste with different water-to-cement ratios approach 0.25 when the hydration is completed.The ultrasonic pulse velocity (UPV) of the cement paste can be calculated using Equation (1) with the elastic parameters. The UPV of cement paste as a function of the hydration degree is shown in The predicted ultrasonic pulse velocity of the cement paste also increases with the degree of hydration, displaying the same trend as the bulk modulus, shear modulus, and elastic modulus. In the case of a high water-to-cement ratio, the initial value of the wave speed is about 1.5 km/s, which is close to the ultrasonic speed in water. When the hydration is completed, the influence of the water-to-cement ratio on the final UPV is generally linear with a negative correlation. The influence on the initial UPV is more sensitive when the water-to-cement ratio is less than 0.4. Once the water-to-cement ratio is greater than 0.4, its increase has little effect on the initial UPV. The main influencing factor on the final UPV is the proportion of hydrates in the cement paste. When the volume fraction of water, which mainly affects the initial UPV, is larger in the mixture, the ultrasonic pulse velocity will continue to approach the ultrasonic pulse velocity in water.Considering different schemes, the predicted results are shown in When the ultrasonic pulse velocity model upgrades to mortar and concrete, the volume fraction of the aggregate in each scale material should be determined. According to the mix proportion and density of the aggregate, the volume fraction can be calculated using Equations (11) and (12).The quantified prediction of the mortar and concrete also requires the elastic parameters of the cement paste, while the required physical parameters of the aggregate are shown in The parameter can be given for the prediction of ultrasonic velocity, which is calculated according to the commonly used mix proportion, as shown in w/c ratios, which are shown in The calculated results indicate that the whole cement paste is taken as one phase in the two-phase material composed of cement paste and fine aggregate. According to the established prediction model, the curves of the elastic modulus and Poisson’s ratio of mortar are predicted with the Mori-Tanaka scheme, as shown in The overall trend of the predicted curve is consistent with the predicted results of the cement paste. Compared with cement paste, the elastic modulus and ultrasonic pulse velocity of mortar are larger, while the Poisson’s ratio is smaller at the same hydration degree.According to the preceding homogenization process of mortar scales, the mortar is considered one phase to the composite, considering the concrete as a two-phase material consisting of mortar and coarse aggregate. With the calculating parameters of the concrete scale shown in The predicted results for the elastic modulus, Poisson’s ratio, and UPV of concrete as functions of the hydration degree are shown in The overall trend of the predicted curves is consistent on the three scales of cement paste, mortar, and concrete. However, the aggregate, occupying the bulk of the volume, has stable properties and basically unchanged relevant parameters with the hydration process. This means that with the progress of hydration, the differences between the prediction values of the elastic modulus, Poisson’s ratio, and ultrasonic pulse velocity corresponding to different water-to-cement ratios are decreasing. Due to the addition of the aggregate phase, the ultrasonic pulse velocity of the homogenized materials at the scale of mortar and concrete increases at the same degree of hydration, compared with the scale of cement paste. In the case of the same water-to-cement ratio from the initial stage of hydration to completed hydration, the change of ultrasonic pulse velocity is also smaller than that of the cement paste scale.To verify the accuracy of the multiscale ultrasonic pulse velocity prediction model, a validation experiment was designed.w/c ratios . Ordinary Portland cement with a grade of P.O 32.5 was used. The fine aggregate used for the concrete was local river sand with a fineness modulus of 2.3 and a relative density of 2.65. The coarse aggregate used for concrete was local limestone, with sizes of 5–20 mm and a relative density of 2.62. The hydration degree of the three concrete mixtures at the ages of 7 days and 28 days were predicted by the DuCOM model, which is shown in Three series of concrete specimens were prepared with two different target ages (7 and 28 days) and three different The concrete specimens with dimensions of 100 mm × 100 mm × 100 mm were demolded after 48 h. Each sample was placed in water to cure at curing room temperature  for 7 days or 28 days.The specimens and UPV testing tools are shown in The “ZBL-U5200” device was adopted to measure the UPV of the concrete specimen. The measurement of UPV was carried out immediately after the specimen left the curing condition to ensure the stability of its moisture content and other states. The transducers were placed on two parallel surfaces of the specimen, with the Vaseline coupling between the transducers and the specimen. Five measuring points were designed on two parallel surfaces, with three instances of measurements on each measuring point. The ultrasonic pulse velocity detection test adopts the direct transmission, as shown in The testing results of the UPV are shown in With the increase of age, the ultrasonic pulse velocities of groups A, B, and C showed an overall increasing trend. At the same age, the ultrasonic pulse velocity of the specimens in the low water-to-cement ratio group was significantly higher than that in the high water-to-cement ratio group. The error bar shows that the standard error of the measured value of each specimen in the test was also controlled within a reasonable range.According to the experimental material parameters, the elastic modulus and UPV of concrete can be predicted based on the multiscale ultrasonic pulse velocity prediction model, as shown in It can be observed that the trend of ultrasonic pulse velocity is consistent with that of the hydration degree. In the early stage of hydration, due to severe hydration reaction, the ultrasonic pulse velocity and elastic modulus increase rapidly, reaching about 80% of the maximum value within 5 days of age. The development trend then slows down. At 28 days of age, the speed is extremely slow or even remains unchanged.For concrete at the same age, the ultrasonic velocity of those with a water-to-cement ratio of 0.55 is the smallest, which develops to about 4300 m/s at 28 d. The ultrasonic velocity of concrete with a water-to-cement ratio of 0.37 is the highest, which finally develops to about 4500 m/s. Although concrete with a high water-to-cement ratio has a higher degree of hydration at the same age, its elastic model and ultrasonic pulse velocity values are still lower than those of low water-to-cement ratio concrete. Therefore, the mix design has a great influence on the elastic parameters and ultrasonic pulse velocity of the concrete material.Comparing the predicted results with the measured results, as shown in The standard deviation of the measured values of each group is marked in The predicted ultrasonic pulse velocity values highly fit with the measured values, showing a satisfactory agreement. If the required parameters are available, the elastic parameters and UPV of the multiphase cement-based material can be predicted by this multiscale ultrasonic pulse velocity model.With more experimental data, further research will be able to verify the applicability of this new calculation model in other cases.w/c ratios in Ye’s study, compared with the measured results.According to Ye’s study , the ultw/c ratios. In addition, the effect of the different cement materials’ properties provided in the paper also leads to some random errors. In general, the multiscale ultrasonic pulse velocity model exhibits a good predictive capacity when it is adapted to predict the ultrasonic pulse velocity of concrete.The results indicate that the predicted UPV of concrete is close to the measured UPV, especially after reaching a high hydration degree. It is thought that the air entrapped in the fresh cement paste is the reason for random error in the initial stage, which is more pronounced in the case of high In this paper, a multiscale ultrasonic pulse velocity model for multiphase concrete materials is established based on the homogenization approach combined with the model of the hydration process. During the hydration process, the elastic parameters and ultrasonic pulse velocity of cement paste, mortar, and concrete can be predicted by the model. The accuracy of this model is verified by concrete ultrasonic testing and other research data.Based on the multiscale homogenization method and the elasticity formulation of homogenized multiphase materials, a multiscale ultrasonic pulse velocity model is established which can predict elastic parameters and ultrasonic pulse velocity during the hydration process, according to material parameters, mixture, and age.In this model, the iterative calculation of elastic parameters requires different schemes at different scales. The self-consistent scheme is applied at the scale of cement paste, while the Mori-Tanaka scheme is used at the mortar and concrete scales.The elastic parameters and ultrasonic pulse velocity at three scales of cement paste, mortar, and concrete were predicted by this model with the water-to-cement ratios of 0.35, 0.5, and 0.65, respectively. At the scale of cement paste, the volume fraction of water and the proportion of hydrates are the main influencing factors of the initial ultrasonic pulse velocity and final ultrasonic pulse velocity, respectively. At the scale of mortar and concrete, the aggregates make the influence of the water-to-cement ratio gradually decrease as hydration progresses, with the large volume fraction and stable nature.According to the experiments detailed in this paper, the relative error of the measured ultrasonic pulse velocity and the predicted value is within ±1.5%. According to Ye’s study , the ult