The article presents a comparative analysis of the impact of the addition of steel and polypropylene fibers on the properties of the concrete mixes and hardened concrete used in the concrete floor industry. The behavior of concrete intended for floors is different from conventional structural concrete because it is formed horizontally; until now, the effect of steel and polypropylene fibers on the properties of concrete formed horizontally has not yet been fully understood. Therefore, the aim of this article is to examine this issue and compare the behavior of concrete modified with steel and polypropylene fibers in concrete that is formed horizontally. The following properties of fresh concrete mixes were analyzed: consistency, the content of air-voids, and bulk density. Consequently, the following properties of hardened concrete were analyzed: compressive strength, bending tensile strength, and brittleness. It was confirmed that steel and polypropylene fibers have a different type of effect on the properties of fresh concrete mixes and hardened concrete. Finally, a combined economic and mechanical analysis was performed. Horizontally formed concrete is commonly used in civil engineering. It is especially used in floors, which are one of the most important construction elements in buildings. An important problem regarding horizontally formed concrete is the heterogeneity of its mechanical properties. Previously conducted research  shows thFloors are very often very expensive and difficult to make ,2. In orThe properties of concrete mainly depend on the ingredients of the concrete mix and the used additives ,7,8. To Concrete formed horizontally is usually reinforced with reinforcement bars or meshes; however, the method of reinforcing these elements differs significantly from other structural elements  . Neverth3. In order to estimate the influence of these fibers on the concrete, it was decided to add the fibers while repeatedly increasing their dosage by 2.5 kg/m3. It should be emphasized that a lower addition of steel fibers (20–30 kg/m3) is used in floor concretes than in construction concretes (40–80 kg/m3) , cmf—the compressive strength of the concrete [MPa].In order to determine the mechanical properties of the concrete with the addition of fibers, destructive tests (concrete compressive strength test and concrete bending tensile strength) were conducted exactly after 28 days after molding the specimens. Tests of the compressive strength of the concrete were performed on cubic samples (15 cm × 15 cm), whereas tests of the bending tensile strength of the concrete were performed on beam samples (15 cm × 15 cm × 60 cm). The compressive strength was investigated using an endurance machine . After the storage time (28 days), the samples were placed in the jaws of the machine, and then the load was applied at normal speed until the sample was destroyed. The destructive force was recorded. The test was performed on at least 6 samples of the same test series. The bending tensile strength was also investigated using an endurance machine. Samples were placed in special jaws , and then the load was applied at the standard speed until the sample was destroyed. The destructive force was again recorded. The test was performed on at least 4 samples of the same test series in order to ensure the appropriate number of results for statistical purposes. All the tests were performed in a laboratory at Wroclaw University of Science and Technology. Based on the conducted destructive tests, the value of brittleness (B) was determined according to Equation (1):Brittleness is an indicator that describes how the destruction of material looks under the influence of an acting load. The higher the brittleness, the more the concrete is damaged in an unsigned and catastrophic manner . In turn, the lower the brittleness, the more visible the damage in the concrete is . Generally, brittleness B is a parameter that describes the relationship between the basic mechanical properties of concrete. If the brittleness ratio is greater than 0.125 (–), then the concrete is very brittle.3 of polypropylene fibers changes the consistency of the concrete mixes from the S4 consistency class to S3. Similar results were achieved in research [research . The addDifferences in the consistency of the concrete mix modified with fibers may be related to the absorption of water by the fibers. The surface of fiber during mixing requires being surrounded by the cement paste, which reduces the amount of free water in the mix. It can also be caused by the accumulation of fibers—the shape of the fibers causes them to be stuck, and therefore there is an irregular distribution of the number of fibers in the concrete mix. The addition of fibers to the concrete mix also causes them to wedge against the aggregate grains, which prevents their free arrangement in the concrete mix. Some researchers investigated the impact of the length or shape of fibers on the consistency of concrete mixes . Longer 3 of steel fibers changes the content of air-voids in the concrete mixes by 2% when compared to the reference concrete. Similar results were observed in studies [ studies ,38, in w studies . In turnThe differences in the content of air-voids in the concrete mixes with the addition of fibers are related to the fact that the addition of any material with a non-spherical shape causes an increase in the content of air-voids in the mixes. This is due to the fact that there is a reduction of the self-compacting properties of the mixes, which is caused by this additive (resulting from gravity forces). The distribution of air-voids and the orientation of the fibers inside the mix is affected by several parameters . Moreover, some researchers believe that the addition of steel fibers results in the formation of larger air-voids, which is due to the fact that these fibers are often contaminated. The highest content of air-voids in the mixes modified with steel fibers is related to the hooked-ends of these fibers. The polypropylene fibers have a different shape (continuous), and therefore do not have such a significant impact on the content of air-voids in the concrete mix when compared to the steel fibers.Slight changes in the bulk density of the fiber-modified concrete mixes are related to the low weight of the fibers when compared to the weight of the concrete (fiber weight is less than 1% of the weight of concrete). Evaporating water causes a greater change of density if fresh concrete and hardened concrete are compared. Such a change in the density is 3–4 times bigger than the change of density caused by fibers.fcm of the concrete with the addition of steel (red line) and polypropylene (blue line) fibers when compared to the reference concrete (black dashed line).fcm of the concrete with different types and contents of fibers. The compressive strength of the concrete modified with the addition of fibers is lower than the strength of the reference concrete (even by 10%). Moreover, the compressive strength of the concrete modified with fibers does not significantly change when the content of the fibers increases. The compressive strength of the concrete with steel fibers is lower than the concrete without fibers (reference). The compressive strength of the concrete modified with polypropylene fibers is similar to the reference concrete. The hardened concrete modified with polypropylene fibers has a higher compressive strength than the concrete mixes with steel fibers (on average by 20%). The compressive strength of the concrete modified with polypropylene fibers is more or less stable (nonsignificant changes of ca. +/− 5%), but the compressive strength significantly decreases with the addition of these fibers in an amount higher than 3.5 kg/m3. The compressive strength of the concrete modified with steel fibers is also quite stable (nonsignificant changes of ca. +/− 5%), but the compressive strength significantly decreases with the addition of these fibers in an amount higher than 30 kg/m3. It can be seen that for both types of fibers, the addition of too many fibers causes a decrease in the compressive strength of the concrete. A significant increase in the compressive strength of the concrete (when compared to the reference concrete) was only observed in the case of the polypropylene fibers (with a content of 3–3.5 kg/m3). Steel fibers are most often added to concrete in an amount of 20–40 kg/m3. In these studies, the authors added the steel fibers in an amount of 20–32.5 kg/m3 in order to investigate the effect of an increased addition (a repeated increase by 2.5 kg/m3) of the fibers on the properties of concrete. The producers of polypropylene fibers indicate that in terms of the influence on the properties of concrete, the addition of 4 kg/m3 of these fibers corresponds to an addition of 35 kg/m3 of steel fibers. Based on this, the authors decided to investigate the addition of 1.5–4.0 kg/m3 of fibers (a repeated increase by 0.5 kg/m3) in order to compare the results obtained for both types of fibers.In the research presented in paper , the res3—steel fibers and 3.5 kg/m3—polypropylene fibers), there is a significant difference in the number of fibers of a particular type  The compressive strength value is also dependent on the number of large air bubbles in the concrete. As shown in the literature [Differences in the compressive strength observed in the case of adding both types of fibers may be related to the changes in consistency, which was induced by adding the fibers. Moreover, the random arrangement of fibers can cause the dissolution of research results. It may also be important that for the most optimal amount of fibers  and polypropylene (blue line) fibers when compared to the reference concrete (black dashed line).fctm of the concrete with different types and contents of fibers. Generally, the bending tensile strength of the concrete modified with the addition of fibers is comparable with the strength of the reference concrete. Moreover, the bending tensile strength of the concrete modified with fibers does not significantly change when the content of the fibers increases. The bending tensile strength of the concrete with steel fibers is higher (average 8%) than the concrete without fibers (reference). The bending tensile strength of the concrete modified with polypropylene fibers is lower (on average by 8%) than that of the reference concrete. The bending tensile strength of the concrete modified with steel fibers is higher than the bending tensile strength of the concrete mixes with polypropylene fibers . The bending tensile strength of the concrete modified with polypropylene fibers is variable (changes of ca. +/− 20%), but with the addition of fibers in an amount higher than 2.5 kg/m3, the bending tensile strength significantly decreases. The bending tensile strength of the concrete modified with steel fibers is quite stable (nonsignificant changes of ca. +/− 10%), but for testing the contents of the fibers (20–32.5 kg/m3), no optimal content was found. It can be seen that for the polypropylene fibers, the addition of too many fibers to the mix causes a decrease in the bending tensile strength of the concrete. A significant increase in the bending tensile strength of the concrete (compared to the reference concrete) was observed only for the 3.5 kg/m3 content of polypropylene fibers. Similar results were obtained in research [research . As the research ,22, in wThe differences in the bending tensile strength observed for both types of fibers may be related to the diameter of the fibers. It is a fact that the pull-out strength of a single fiber is related to its diameter. The higher bending tensile strength value for the concrete modified with steel fibers can be related to the higher Young’s modulus value of these types of fibers. During the research, it was observed that the tested types of fibers have different destruction behavior. Bending tensile strength depends on the shape, length and type of fibers, but also on their interaction with the aggregate and matrix in the concrete. Concrete beams with the addition of steel fibers do not fall apart during destruction, and the fibers are not pulled out of the concrete. The opposite can be said for polypropylene fibers. During element destruction, polypropylene fibers are pulled out of the concrete, and the beam falls apart.Concrete properties are usually interrelated. This means that the mechanical properties of concrete  depend on the properties of the concrete mix . This influence must be especially considered in concrete with added fibers, as the fibers can influence these properties. It is well known that the shape, type and length of the fibers influence the properties of the concrete mix. The influence of the tested fibers on the properties of the concrete mix is presented below and compared with the properties of the hardened concrete.In order to analyze the properties of the concretes with the addition of steel and polypropylene fibers, their costs and mechanical properties were determined and then compared. In the mechanical analyses, the compressive strength and bending tensile strength were compared. In the economic analyses, the cost of preparing all the investigated series was calculated and compared.The mechanical performance of concrete is the most important criterion. To compare the mechanical performance of all the investigated concrete series, the mechanical performance ratio MPR was determined.Based on the MPR determination, mechanical performance analysis was performed. The results of the analysis are shown in Cmixes was calculated.The economic performance of concrete is an important aspect that is often compared and analyzed. To compare the economic performance of concrete modified with steel or polypropylene fibers, economic performance analysis was performed. To analyze the economic properties, the effective cost ratio ECR was used. In the first step, the cost of all research series Based on the costs of concrete mixes, the effective cost ratio ECR was calculated.The results of the economic performance analysis are shown in In research concerning steel fibers , it can Generally, it can be seen that the cost of steel fibers is related to their type , shape, dimensions and the season of the year. The cost of polypropylene fibers is not as variable as steel fibers. Using recycled fibers can reduce the cost of concrete. The cost of concrete mix ingredients  depends on the part of the world and the access to raw materials.The choice of concrete mix for construction elements should always be well thought out. The addition of fibers to the concrete mix could be an interesting idea for improving the properties of concrete; however, it should be stated that the addition of fibers to concrete mixes is quite expensive. In order to decide on the type and contents of added fibers, combined economic and mechanical concrete performance analysis was performed. The results of the analysis are shown in When summing up the results of the conducted analysis, two mechanical properties of concrete—compressive strength and bending tensile strength—were compared regarding the cost of the concrete—The performed analysis allows concrete mixes to be divided according to their mechanical and economic performance. (1)Lower cost and higher strength, MPR ≥ 100% and ECR ≤ 130%;(2)Higher cost and higher strength, MPR ≥ 100% and ECR ≥ 130%;(3)Lower cost and lower strength, MPR ≤ 100% and ECR ≤ 130%;(4)Higher cost and lower strength, MPR ≤ 100% and ECR ≥ 130%.It can be seen that most of the series are in area 4 (the worst from the point of view of a designer), and none of the series show properties that would qualify it to be included in area 1 (the best from the point of view of a designer). The concrete modified with polypropylene fibers (5 series) has better properties when compared to the concrete modified with steel fibers.The consistency of the fresh concrete mixes modified with the addition of polypropylene fibers is denser when compared to both the mixes modified with the addition of steel fibers and the reference mix,The addition of fibers to the concrete mix leads to an increase in the content of air-voids in the mix when compared to the reference mix. In the case of the analyzed changes in the dosage of fibers, the concrete mixes with the addition of steel fibers have a higher content of air-voids when compared to the concrete mixes with polypropylene fibers,The addition of fibers to the concrete mix does not cause significant changes in its bulk density,The compressive strength of the concrete modified with fibers is on a similar level or even lower when compared to the strength value of the reference mix. In the case of the analyzed changes in the dosage of fibers, the addition of the polypropylene fibers to the concrete mix leads to nonsignificant changes in the value of compressive strength, whereas the addition of steel fibers to the concrete mix leads to a decrease in compressive strength when compared to the reference concrete,3 of polypropylene fibers, an improvement of the concrete’s bending tensile strength when compared to the reference concrete was observed,The addition of steel fibers to concrete leads to an improvement in its bending tensile strength. For the amount of 2.5 kg/mThe concrete modified with the addition of polypropylene fibers has better brittleness properties than the reference concrete and concrete modified with steel fibers,The addition of polypropylene fibers to concrete is economically much more sensible than the addition of steel fibers. However, it should be noted that both types of fibers have worse mechanical properties when compared to the reference concrete.The performed research and analyses allow the following conclusions to be drawn:It should also be stated that the reason that fibers are added to concrete is the fact that they prevent the cracking of floors. For this dosage, civil engineers cannot expect any improvement in the compressive strength and bending tensile strength. To achieve this goal, higher contents should be implemented, which is not commonly used in concrete designed for floor purposes.


The present work aimed to study the effects of temperature changes and concrete creep on I-shaped steel–concrete composite continuous girder bridges during construction and operation processes. This study combined structural health monitoring data, an ANSYS finite element simulation, and the age-adjusted effective modulus method to obtain the variation laws of temperature and internal force in composite girders. Moreover, a temperature gradient model was proposed that is suitable for bridges in Hebei, China. In addition, a concrete creep experiment under unidirectional axial compression was performed using concrete specimens prepared from the concrete batch used to create the composite girder. The long-term evolution laws of the deflection and internal force of the composite girder were obtained by predicting the concrete creep effect. The measured data showed that the temperature variation trends of the steel beam and concrete slab were characterized by a sinusoidal curve without a temperature lag. The heating rate of the concrete slab was higher than the cooling rate. The prediction results showed that the internal force changes in the composite girder were characterized by three stages. The stress changes in the composite girder during the first 10 days were significant and the stress charge rate of the concrete slab, the steel girder and the shear stud can reach 5%–28%. The stress change rate decreased continuously during 10–90 days. The stress changed slowly and smoothly after 90 days. This research can provide feedback and reference for structural health monitoring and service safety control of similar I-shaped steel–concrete composite bridges. Steel–concrete composite girder bridges are becoming increasingly popular with increasing bridge spans and advantages in terms of reliable performance, reasonable cost, and structural rationality. However, some shortcomings of these structures need to be solved, including the stress redistribution caused by ambient temperature changes and concrete shrinkage and creep. Therefore, the time-dependent effects and the evolution law of structural performance during bridge construction and operation periods should be studied, which is beneficial to the further promotion and application of composite girder bridges .First, the maximum stress caused by temperature changes can reach 20%–30% of the allowable stress, which cannot be ignored ,5. Chen The theories describing the stress–strain constitutive relationship caused by concrete creep include the aging theory (creep rate method), elastic creep theory (superposition method), elastic aging theory (flow rate method), secondary effect flow theory, and age adjustment effective modulus method ,16,17,18In addition, the significances of the long-term monitoring of bridges are as follows: (1) the difference between the monitored experimental results and the numerical model for prediction analysis of bridges can be identified to correct the model. The corrected model can be further applied in the subsequent analysis of the mechanical behavior of the bridges. (2) The bridges are monitored for the long term to ensure their safety. This can provide a steady foundation for superior behavior of bridges in their life cycle and meet the requirement of the long-cycle design idea. (3) The monitored experimental results of the mechanical behavior of the bridges in a complicated and variable environment may create a new research issue. Therefore, long-term monitoring of the bridges is important for the development of investigation of the bridges.In this paper, the effects of temperature changes and concrete creep on I-shaped steel–concrete composite continuous girder bridges were studied. This study combined field monitoring data, an ANSYS finite element (FE) simulation, and the age-adjusted effective modulus method to obtain the variation laws of temperature and internal force of the composite girders. Moreover, a temperature gradient model suitable for bridges in the Hebei region of China was proposed. In addition, a concrete creep experiment under unidirectional axial compression was carried out using concrete material from the batch used to create the composite girder. Then, concrete creep curves under 28-day loading were obtained. The long-term evolution laws of the deflection and internal force of the composite girder in response to concrete creep were predicted.The background project is located in Baoding city, Hebei Province in China, and the first west segment of the bridge is shown in The I-shaped steel–concrete composite continuous girder was used in the superstructure of the bridge. The north and south side girders are symmetrical relative to the road centerline. The cross-section of the northern half of the composite girder is shown in The regulations of the temperature gradient model in the codes of every country are different because the selection of the temperature gradient model is related to the bridge type, cross-section form, sunshine conditions, and geographical location. In this paper, the temperature distribution law of a multiple I-steel composite girder was obtained based on field-measured data, and the most unfavorable temperature gradient mode was determined. Moreover, the transverse gradient model of temperature was proposed, which can guide structural designs.The measured temperature changes in the composite girder in Sections S4 and S6 from May 1 to May 8 of 2018 are shown in The measured strain changes in the composite girder in Sections S4 and S6 in one day are shown in The variation laws of the internal forces of the concrete slab and steel beam in Section S6 along with temperature changes in one day were analyzed, as shown in The variation laws of the internal forces of the concrete slab and steel beam in Section S4 along with temperature changes in one day are shown in The temperature of the concrete slab is characterized by a large transverse gradient because of the bridge direction and environmental shielding. However, the Chinese code specifies only the transverse temperature effect of the wide box girder without cantilevers. Therefore, the suggested temperature gradient model for composite girder bridges in the Hebei Province of China was proposed by processing the temperature monitoring data with a guaranteed rate of 95%.The transverse distribution of the concrete temperature in Section S4 is shown in The maximum differences in the girder temperatures during each day were extracted as shown in The temperature gradient model for the composite girder bridges in Hebei, China, was proposed with a guaranteed rate of 95%. A temperature gradient of 4 °C/m was adopted for the height range from the bottom of the steel beam to the junction of the flange and web. A temperature gradient of 20 °C/m was adopted for the height range from the junction of the flange and web to the top of the concrete slab. Moreover, the temperature gradient in the pavement could be specified according to the Chinese code. In addition, the heat diffusion and conduction in the girder changed along the transverse direction because of the different boundary conditions, which resulted in the transverse gradient of the temperature. A transverse gradient of 3 °C/m could be adopted. The proposed temperature gradient model can be referenced during the design process.The stress redistribution in composite girders is difficult to solve by theoretical analysis alone because of the complexity of concrete creep and the property differences between steel and concrete. The variation laws of girder deflection and stress caused by concrete creep were studied based on field monitoring data, concrete creep experiments, and numerical models. The expander was added into the concrete of the composite bridge to eliminate the shrinkage effect. Little concrete shrinkage strain was observed in the shrinkage tests of concrete batches. Therefore, only the concrete creep effect was taken into account in the below-mentioned discussion.A concrete creep experiment under unidirectional axial compression, including two ordinary concrete specimens and two steel fiber reinforced concrete specimens, was carried out using specimens made from the same batch of materials as the actual bridge. The dimension of the concrete specimens was 100 mm × 100 mm × 300 mm. The average value was taken from the 28-day creep data of the two concrete specimens. Moreover, two compensation specimens were designed to offset the deformations caused by the hydration of cement, external temperature, and humidity, including concrete condensation, hardening shrinkage, drying shrinkage, and temperature expansion.The load on the composite girder during the normal use stage was approximately 40% of the ultimate load, which was selected as the load in the test. The 28-day compressive strength of the ordinary concrete specimen was 55.60 MPa and the 28-day compressive strength of the steel fiber reinforced concrete was 48.40 MPa.t0 was 28 days.A picture of the concrete creep experiment is shown in C, as shown in Equation (1):εc(t) is concrete creep strain at time t, σ(t) is concrete stress at time t.According to the definition of creep degree function C of the ordinary concrete and the fiber-reinforced concrete were obtained and shown in The curves of the creep degree function A0, A1, and m are the parameters that can be regressed by experimental results, which are shown in t0 is the initial loading age of concrete, which is 28 days for the concrete of the bridge.A parameter regression was performed by utilizing a large number of experimental data with high prediction accuracy. A simplified fitting formula of creep degree function was proposed based on the measured data:A comparison between the fitting results of the simplified formula and the experimental data for the creep degree function is shown in The aging coefficient was used to consider the effect of concrete aging on the final creep value based on the age-adjusted effective modulus method ,34,35,36ε is as follows:t0; φ is creep coefficient at time t with loading time t0, which can be calculated by Equation (4):The sum of elastic strain and creep strain of concrete φE is the age-adjusted effective modulus. The age-adjusted effective modulus φE can be expressed as follows:χ is the aging coefficient, which ranges from 0.5 to 1.0 and is generally chosen as 0.8.According to the integral mean value theorem, Equation (3) can be converted into the following form:According to the proposed creep degree function and the Dischinger method, the aging coefficient can be expressed as follows:The elaborate FE model of the bridge established in ANSYS is shown in 5 MPa, the Poisson’s ratio of steel is 0.3, and the density of steel is 7850 kg/m3. The Poisson’s ratio of concrete is 0.2, and the density of concrete is 2500 kg/m3. The age-adjusted effective modulus method was used to simulate the concrete creep effect of the composite girder bridge. The 28-day Young’s modulus of the concrete (3.65 × 104 MPa) was measured by testing specimens made from the same batch of concrete material.The Young’s modulus of steel is 2.06 × 10The FE model was verified based on the monitoring data of structural deformation and stress during the concrete pouring process. The pouring dates of each segment are shown in The concrete construction process was simulated based on the FE model by locking and activating the concrete slab elements of each pouring segment in sequence using the life-and-death element method.A comparison between the calculated and measured deflections of the steel beams at the middle of each span is shown in Comparisons between the calculated and measured girder strains in Sections S4 and S6 are shown in The deflection monitoring data within two months after bridge completion were used to verify the FE model. Comparisons between the calculated and measured deflections in Sections S2 and S6 are shown in The abovementioned FE model was used to predict the long-term evolution of the structural performance of the composite girder bridge. The prediction results of girder deflection under self-weight are shown in The concrete creep significantly affected the stress redistribution between the steel beam and concrete slab. The girder stress changes in Sections S4 and S6 were predicted as shown in The stress in the concrete slab in the negative moment zone of the composite girder decreased under the influence of concrete creep. Over time, the steel beams participated more in bearing the load. The concrete slab in the positive bending moment zone was continuously involved in load-bearing, and the compression part of the steel beam decreased gradually. The internal force in the lower flange of the steel beam in the positive moment region still increased due to the stiffness reduction in the negative moment region. In addition, the stress variation in the composite girder was characterized by three stages. The stress variations during the first 10 days were the most significant, the stress change rate decreased continuously during days 10–90, and the stress changed slowly and smoothly after 90 days.Beam elements were used to simulate the stud to consider the interfacial slip. The internal force changes in the studs of the same column at the first and second spans were predicted under concrete creep. The bending moment of the lower end of the stud after 28 days of concrete pouring under self-weight is shown in (1)The daily temperature variations in the composite girder and the corresponding influence law were studied. The temperature variation trends of the steel beam and concrete slab were characterized by sinusoidal curves without temperature lag. In addition, the heating rate of the concrete slab was higher than the cooling rate. The rates of heating and cooling of the concrete slab first increased and then decreased. Moreover, the suggested temperature gradient model for composite girder bridges in the Hebei Province of China was proposed with a guaranteed rate of 95% by processing the maximum temperature difference during a single day.(2)A concrete creep experiment under uniaxial compression was carried out using the same batch of concrete material as that used for the bridge. A creep degree function of concrete was obtained. The concrete creep effect of the composite girder bridge was predicted by integrating the age-adjusted effective modulus method and FE model. The accuracy of the numerical analysis was verified by comparing the calculated and monitoring results of girder deflections and strains. The prediction results show that the internal force of the concrete slab in the negative bending moment zone decreased, and the stress of the steel beam increased gradually. The concrete slab in the positive bending moment zone was continuously involved in load bearing. The compression part of the steel beam decreased gradually. However, the internal force of the lower flange of the steel beam in the positive bending moment zone still increased because of the stiffness reduction in the negative moment zone.(3)The internal force change in the composite girder was characterized by three stages. The stress changes during the first 10 days were significant, the stress change rate decreased continuously during days 10–90, and the stress changed slowly and smoothly after 90 days. The bending moment change in the stud along the longitudinal direction was characterized by a sinusoidal distribution. The stud bending moment was the largest in Section S3. The stud bending moment near the 3rd pier section increased gradually as a result of concrete creep, and the stud bending moments in the other sections decreased gradually.In this study, we focused on the influence of time-dependent effects on an I-shaped steel–concrete composite continuous girder bridge, including temperature changes and concrete creep effect. The field monitoring data and FE simulation were combined. The main contributions of this paper are as follows:


Recurrent miscarriage is one of the complications of pregnancy in which the potential role of immunologic factors has already been mentioned. Here, two young women with recurrent miscarriage were consulted in the infertility center. The diagnosis of immunoglobulin G4 (IgG4) deficiency was made through the reduction of IgG4 Ig levels and normal total IgG titer. Considering this abnormality, intravenous Ig 200 mg/kg was started monthly, and they both had successful pregnancies. Little is known about IgG4 deficiency in women with recurrent miscarriage. IgG4 deficiency should be taken into account in these patients. It is expected that these results will shed further light on the feasibility of intravenous Ig for women with recurrent miscarriage. PRECIS: Heterotopic pregnancy treated with vNOTES procedure. The etiology of RM in up to 50% of cases is genetic. Thyroid disorders have a disputed role in RM, and investigations for thyroid-stimulating hormone and thyroid antibodies are strongly recommended in RM. Searching for uterine malformations should also be considered as a part of diagnostic examinations of couples with RM. There is a doubtful association between hereditary thrombophilia and acquired thrombophilia or Antiphospholipid syndrome with miscarriage. Antiphospholipid syndrome is diagnosed through the persistent presence of antiphospholipid antibodies and vascular thrombosis; the role of alloimmune mechanisms remains poorly understood,2,3. The role of immunologic factors has already been mentioned for reproductive failure in patients with RM. A normal pregnancy induces some changes in antibody formation; increased level of immunoglobulin M (IgM) at the early phase of a primary immune response and IgE antibodies in some mothers with a genetic background. At the late phase of primary immune response or after chronic antigen exposure, antibodies switch to IgG; IgG4 in particular have received special attention,5.Recurrent miscarriage (RM) is considered as ≥2 fetal losses before 24 weeks of gestation, affecting an estimated 1-3% of women in their reproductive age. It is classified as primary RM without a previous viable pregnancy and secondary RM with one or more pregnancies,7. IgG4 deficiency is the most common immunodeficiency subclass. A deficiency can be identified as a level >2 SD less than age-matched reference values accompanied with a normal total IgG level. Some patients with decreased IgG4 are asymptomatic, but several groups present with recurrent respiratory infections. IgG4 deficiency has been noted in some primary immunodeficiency disorders such as Wiskott-Aldrich syndrome, IgM deficiency, ataxia telangiectasia, and mucocutaneous candidiasis. Other disorders with IgG4 deficiency are Down syndrome, immune thrombocytopenia, lupus erythematosus, and growth hormone deficiency. Monthly intravenous immunoglobulins (IVIG) are the mainstay of treatment for symptomatic patients with IgG subclass deficiencies,10. There are scant data on abnormal Ig subclasses in women with RM. Due to pregnancy loss and its repetitive nature in women, and even its emotional impact on men, there is a need for studies on the etiologic factors of RM. Little is known about IgG4 deficiency in women with RM. We report two young women with primary RM and IgG4 deficiency who became pregnant after IVIG therapy.IgG4 accounts for approximately 5% of total IgG in the serum of adults and is unable to activate the classic complement pathway and antibody-dependent cell-mediated cytotoxicity. IgG4 uniquely plays as a blocking antibody with anti-inflammatory properties; therefore, it is known a as a rule-breaker antibody2. Her menstrual cycles were regular . The results of hormonal investigations revealed normal gonadotropin levels, implying regular ovulatory cycles. Transvaginal ultrasound of the pelvis showed a normal uterus and ovaries. Based on her history and laboratory features, a diagnosis of unexplained RM was made. Evaluation of blood parameters revealed white blood cells (WBC) 8200 cell/mm3, hemoglobin (Hb) 14.3 g/dL, and platelets 264000/mm3. The laboratory tests for diabetes, hyperprolactinemia, and vitamin D deficiency were normal. Antinuclear antibody and anti-dsDNA levels were measured using enzyme-linked immunosorbent assay with a negative result. The other antibody identification studies are shown in ®, Germany) was started with 200 mg/kg monthly with the diagnosis of antibody deficiency; she became pregnant after two months. Subsequently, the woman had a successful pregnancy and her infant was delivered at 37 weeks of gestation with a normal Apgar score.A 24-year-old Caucasian woman, gravida 2 parity 0, with a history of two miscarriages was seen in Isfahan Fertility and Infertility Center affiliated to Isfahan University after five years of marriage. The ages of miscarriage were 8 weeks and 10 weeks’ gestation. She was not a smoker, she had no significant past medical history and was not on any long-term medications. Her physical examination was normal with body mass index (BMI) of 26.6 kg/m2. Transvaginal ultrasound revealed no anomalies of the uterus and ovaries. The initial complete blood count revealed WBCs of 10.300 cell/mm3, Hb of 12.9 g/dL, and platelets of 35.7000/mm3. Laboratory investigations were performed to exclude diabetes mellitus and prolactin deficiency. The levels of antibodies in the serum are shown in A 27-year-old woman with a history of eight miscarriages in the second trimester was referred from Isfahan Fertility and Infertility Center affiliated to Isfahan University. Her age at marriage was 17 years. She had regular menstrual cycles since the age of 13 years. There was no history of smoking and other diseases. At the time of her referral, her BMI was 26.8 kg/m. A normal pregnancy is associated with increased levels of interleukin (IL)-10 and IL-4 related to Th2 type, whereas some miscarriages are associated with high levels of interferon-gamma and IL-12 related to Th1 type. In normal pregnancy, secretion of IL-4 causes the plasma cells to switch to the production of IgG4, whereas in miscarriage, elevated levels of interferon-gamma inhibits the process of switch to IgG4. Wilson et al. study showed that women with RM had significantly low levels of total IgG and IgG subclasses 1, 2, 3, and 4 compared with normal pregnant women. IgG4 is an antibody with unique biologic properties. There is evidence for the beneficial effect of IgG4 in allergic disease by inhibiting mast cell degranulation and impairing anti-tumor immunity in malignant melanoma; however, the mechanism of IgG4 in normal pregnancy is not fully understood. IgG4 generally induces a tolerance mechanism in allergic immunotherapy; therefore, it may play an important role in maternal tolerance to the fetus and maintenance of pregnancy. A new clinical study by Piccinni et al. suggests that the local production of leukemia inhibitory factor (LIF) is necessary for embryo implantation and it can be up-regulated by IL-4 and progesterone. We think IgG4 may contribute to LIF production; low level of IgG4 followed by miscarriage. The level of IgG4 in our two cases was very low. It is notable that as many as 10-15% of normal people have IgG4 concentrations below the limit of detection. A prominent feature in the CD markers of our patients was the decreased the ratio of CD3CD4 T cells to CD3CD8 T cells. A normal CD4:CD8 ratio in pregnant adults is not 2:0; Ghafourian et al. investigated different types of T-cell subsets in 25 women with RM. Compared with normal, the proportion of CD3CD8 T cells was significantly higher in women with RM. IVIG was administered for the treatment of our cases with successful results, similar to Abdou et al. study. The mechanism of IVIG in the treatment of women with RM is the modulation of immune cells. A recent study found that IVIG increased the regulatory T cells and diminished Th 17 responses in RM. Although we did not measure post-treatment IgG4 levels in our patients, it could explain the possible beneficial effect of IVIG on the increased levels of IgG4 in women with RM and deficiency of IgG4. We recommend IgG4 subclass determination in the initial evaluation of women with RM. We need a deeper understanding of the role of IgG4 in pregnancy; it is expected that these results will shed further light on the feasibility of IVIG for women with RM.This study presents two women with low levels of IgG4 and primary RM. After treatment with IVIG, they had successful pregnancies. To date, there have been very few reports of IgG4 deficiency in women with RM


The early-age performances of cement-based mixtures are governed by cement hydration reactions. As a matter of fact, the heat generated during the setting and hardening phases due to the hydration processes increases the temperatures within the concrete elements while it starts developing its mechanical properties. These thermal stresses can cause the premature cracking of the cementitious matrix and undermine the long-term durability of the whole concrete element, especially in the case of massive structures where the dissipation of generated heat is more difficult. It is worth highlighting that the kinetics of cement hydration is mainly governed by the mixture composition; on the other hand, the heat generated during the setting and hardening is also influenced by the geometry of the element and/or its curing conditions. In this context, this study presents a numerical procedure intended to simulate the hydration reactions, and hence scrutinize the development of concrete properties at the early-age. Specifically, considering the variation of several factors, such as concrete strength class, element size and curing conditions, a comprehensive parametric analysis is presented herein, leading to the proposal of a simplified approach for both predicting the time evolution of the concrete mechanical performances at the early-age and mitigating the risk of premature cracking. The heat generated during the setting and hardening phases of cement hydration increases the temperature within the concrete elements and, consequently, it can result in cracking phenomena that compromise the long-term durability performance of concrete structures . GeneralTherefore, nowadays, with the diffusion of high-performance cementitious composites, the cracking risk in concrete at the early-age is no longer limited to the case of massive structures ,7,8. As On the other hand, the setting and hardening processes developing in cement-based mixtures can be monitored by analyzing the hydration kinetics which can be scrutinized by the so-called degree of hydration and, at the same time, the latter can be correlated to the development of the relevant physical and mechanical performance of the resulting composites ,12.In principle, the degree of hydration, which is measured by the heat generated in the hydration reaction, can be easily determined only in the case of reactions developing under adiabatic conditions, as, in that case, the generated heat is proportional to the temperature development within the concrete mixtures . ConversIn this context, the present work firstly summarizes a numerical procedure that is capable of simulating the time evolution of the early-age temperature development also cured in non-adiabatic conditions: this modelling/identification procedure can be used to simulate the time evolution of the degree of hydration of a concrete by considering various boundary conditions .The implementation of the proposed modelling approach allows to implement an “implicit” verification procedure for cracking phenomena occurring during the hydration processes. Moreover, since the degree of hydration represents the evolution of the microstructure formation, it can be correlated to the development of the associated mechanical properties, such as the compressive/tensile strength and the elastic modulus ,19.Based on these assumptions, a parametric analysis is proposed by considering the variation of the following parameters: concrete mix design, structural element geometry and boundary conditions . In principle, these parameters lead to control and prevent the cracking risk by optimizing the following aspects: cement-based mixture composition , casting procedure and the use of heat-insulating formwork for the entire duration of the casting maturation.3S, C2S, C3A and C4AF) in Portland cement present different kinetics. For these reasons, it is a common practice to also define the degree of hydration (αh) as a general indicator  of the hydration processes occurring in concrete mixtures during setting and hardening [As a matter of principle, the development of the hydration reactions in cement-based mixtures represent a complex problem in concrete technology since the hydration degree of individual phases  can be also defined as the ratio between the amount of heat Q(t) produced up to the time t, and the heat Qmax potentially produced by the reaction of the total amount of cement [On the other hand, as it is well known, the time evolution of the degree of hydration αf cement :(1)αh(t)Consequently, the cement hydration results in a heat transfer process and then a transient temperature field T. It is worth mentioning that, in most of the relevant cases of massive concrete structures  , the temc is mass per unit volume, cc is the specific heat, λc is the thermal conductivity coefficient and qc is the rate of heat production of the cement, expressed as follows:The T field developing in a 1-D domain can be described by the following equation:c and then Q cannot be easily predicted as they depend on the actual temperature developed inside the concrete sample.The analytical expression of qa(t) [*a,max (<Qmax) is the actual amount of heat produced at the end of the reaction (in adiabatic conditions), whereas τ and β control the curve shape. Therefore, the rate of heat production qa(t) can be easily defined by introducing the expression of Qa(t) given by Equation (4) within the rate definition provided by Equation (3). However, the quantity qc is generally not equal to qa(t) because different temperatures develop inside curing concrete under different boundary conditions. Nonetheless, an analytical relationship can be stated between qc and qa(t) by considering the well-established Arrhenius principle [However, the following heat production function has been proposed in the case of adiabatic conditions and denoted as Qa(t) :(4)Qa(t)rinciple , and theR is the initial room temperature (or ambient temperature). The boundary condition depends on the border between the curing concrete sample and the external environment.The initial and boundary conditions are needed to solve this problem. The initial condition can be generally written as follows:p and λp are the thickness and the thermal conductivity of the insulating layer. Conversely, if the concrete is cured in “isothermal” boundary conditions at a room temperature TR , the following boundary conditions should be considered:In the case of non-adiabatic conditions, the following relationships can be imposed to guarantee the continuity of heat flow throughout the insulating layer and the external environment:, with the boundary conditions in Equations (6) or (7), can be employed to simulate the time evolution of T within the concrete element. The resulting theoretical simulation of the temperature field Tth can be symbolically denoted as follows:qr contains the following set of parameters listed below:The solution of the integral-partial-differential Equation (2)qr:-R) can be assumed “a priori” according to the direct measurements;the reference temperature  are evaluated as a function of the mixture composition;the “thermal” properties of the concrete  with the boundary conditions of Equations (6) or (7)) are based on the procedure proposed by Martinelli et al. [The values obtained for each mixture for i et al. , in whici et al. .This section presents the simulation approach proposed for the assessment of the key mechanical performance of cement-based mixtures based on the hydration modelling procedure.h controls the key relevant mechanical properties of concrete during the hardening phase [c), Young modulus (Ec) and tensile strength (fct), are reported below [c (αh = 1), Ec (αh = 1) and fct (αh = 1) represent the asymptotic theoretical maximum values for compressive strength, elastic modulus and tensile strength, in the ideal case of complete hydration (αh = 1). On the other hand, α0 is the so-called critical hydration below which no relevant strength gain is achieved. The parameters A, B and C represent numerical values depending on the type of cement employed within the mixtures.As a matter of principle, it is widely recognized that the degree of hydration αng phase . Specified below :(10)fc; (ii) geometry of the concrete element ; (iii) thermal insulation characteristics  during the setting and hardening phases; and (iv) the environmental conditions .The formulation of the numerical procedure outlined in In this context, a comprehensive parametric analysis is proposed in this study by considering the variation of each parameter. All the analyses proposed in the present research will be executed on three representative mixture compositions and, then, for each mixture, the other parameters  will be varied. Specifically, a variable mixture composition is realized by designing three concretes with the strength classes C25/30, C35/45 and C50/60 in accordance with the Eurocode 2 . 3) in order to ensure also the desired workability . Then, three different types of Portland cement, labelled CEM IV/B 32.5, CEM II/A-LL 42.5R and CEM I 52.5R in accordance with the EN 197-1: 2011 [ck): 32 MPa for C25/30, 45 MPa for C35/45 and 60 MPa for C50/60 [These mixtures are designed by keeping the water-to-cement ratio constant , as well as the maximum size of the aggregates  and the free water amount . The calibration is based on the best fits of the values proposed by the Italian guidelines on structural concrete production [In accordance with the hydration model described in oduction : the resoduction . MoreoveOn the other hand, in order to propose an assessment of the mechanical performance at the early-age, the numerical parameter presented in the Equations (10)–(12) should be defined.0, which represents the end of the setting phase and the start of hardening [Regarding the parameter αardening , in the ardening . Regardiardening  considerardening  assume tFinally, for the tensile strength, parameter C assumes numerical values ranging from 0.46 and 0.88 .0, A, B and C are calibrated  with the aim to obtain the best fit of the curves of the Equations (10–12), with the corresponding curves  proposed by the fib Model Code 2010 [fib Model Code [0, A, B and C are summarized in In the present research, the aforementioned parameters αode 2010 . In ordedel Code  with theOnce the concrete mixture’s composition is defined, the numerical procedure proposed in the previous section can be employed for simulating the time evolution of the temperature within a concrete element. For instance, Moreover, these simulations lead to identifying the profile temperatures within the concrete elements during the setting and hardening phases. As a matter of fact, max) in the center of the concrete element as well as the maximum gradient of temperature between the several layers of the element (ΔTmax): these values, as expected (due to the hydration kinetics), are more significant for the C50/60 mixture (containing CEM I 52.2R) and this is more pronounced when the concrete element’s geometry increases .The figures highlight that, already during the first 48 h, the cement hydration lead to the achievement of the maximum temperature rising , on the cracking risk occurring in structural concrete elements during the setting and hardening phases.The geometry of the structural element plays a fundamental role on the temperature developed inside the mixture due to the cement hydration. For instance, in the case of massive structures, such as slab foundations of multi-storey buildings and retaining walls of considerable height, due to the low thermal conductivity of the concrete, the external layers of the structural elements prevent the dissipation of the generated heat during the hydration from the center towards the outside, causing a significant increase in the temperature. The cortical layers settle on lower temperatures than those that occur in the heart of the structure, giving rise to a thermal gradient, which can determine the appearance of the critical crack patterns.-Ambient temperature set to 20 °C;-Absence of thermal insulation protection;-Variable thickness between 0.50 and 1.50 m.For the parametric analysis, the following input parameters were considered for simulating the concrete behavior of the mixture considered in this research:Further, in the light of the results obtained in the previous subsection, it is clear that the attenuation of the thermal gradient in massive structures can be pursued through a reduction of the gap between the maximum temperature achieved within the core of the element and the outer layers of the elements that are in direct contact with the external ambient: this could be also obtained by adopting a protection of the outer layers through an adequate thermal insulation system. As a matter of fact, by adopting insulation systems, the dissipation of heat towards the environment is limited, increasing the temperature of the heart but significantly decreasing the thermal gradient, which causes cracking.(i)p = ∞);Absence of thermal insulation p = 0.125 W/mK) realized with wooden formwork;Intermediate thermal insulation system p = 0.065 W/mK) realized with fir-mineralized wood bonded with Portland cement formworks. For both the thermal insulation systems, an equal thickness of the formwork’s panel  is considered.High thermal insulation system . Conversely, the thermal gradient between the core and the cortical layers is reduced. Therefore, the application of a thermal insulation system for the protection of the cast mixture leads to mitigate the thermal cracking risk only in some cases and for certain thicknesses and types of cements.In addition to the measures aimed at reducing the development of the hydration heat that directly affects the concrete components or the technological aspects, another factor that also has a key influence on the formation of thermal cracks is the environmental condition.R = 0 °C) to hot (TR = 35 °C) climates. Further, in this case, the other input parameters are considered as “invariant”: element’s thickness of 1 m and absence of thermal insulation protection. The results of the simulations are reported in Therefore, in this subsection, a parametric analysis is conducted considering the variation of the ambient temperature, going from cold : these values could be then compared with the thermal stresses generated during the hydration.In this context, It can be seen, therefore, that the “grid” of the degree of hydration  corresponds to the “grid” of the key mechanical performances by considering Equations (10)–(12) defined in In fact, the results reported in both Then, for a given concrete mixture, it is noted that, as the thickness increases, in the center of the element, the temperature increases  and consFinally, although, for the sake of brevity, all the parametric analysis figures are not reported herein, the simulations highlight that the mechanical properties are strictly related to the temperature and consequently, their development is faster when the ambient temperature increases and/or when thermal insulation systems are employed for protecting the mixture curing.the proposed model is capable to simulate the time evolution of both the temperature and degree of hydration in concrete during the setting and hardening phases of the hydration processes;the proposed 1-D flow and hydration model turns out to be a useful tool for assessing the cracking risk due to thermal stresses;the parametric analysis proposed herein allows to quantify the influence of key parameters affecting the thermal crack formations, such as the geometry of the element, the type of formwork employed for the thermal protection and the ambient temperature;the figures derived from the parametric analysis can be employed as simplified design abaci for the optimization of both concrete mixtures as well as the construction phases aimed at mitigating the thermal cracking risk: similar simulations can be performed for other types of mixtures leading to a more comprehensive set of data that can be used for practical aspects;the model can be easily employed also for estimating the time evolution of mechanical properties such as the compressive strength, the tensile strength and the elastic modulus: this represents the first step toward a more advanced simulation tool for the “direct” verification of thermal crack formations.This study presented a numerical procedure for simulating the effects of generated hydration heat in hardening concrete. Considering the variation of the several factors, the simulations lead to propose a simplified procedure for mitigating the cracking phenomena. The following conclusions deserve to be highlighted:Finally, as a further step of the present research, the proposed approach can be applied in the case of relevant case studies and, moreover, the numerical procedure can be implemented also to the 3-D domain in order to be proposed for a wide range of possible applications.


To remove the necessity of the tranceive phase assumption for CSI‐EPT and show electrical properties maps reconstructed from measured data obtained using a standard 3T birdcage body coil setup.The existing CSI‐EPT algorithm is reformulated to use the transceive phase rather than relying on the transceive phase assumption. Furthermore, the radio frequency (RF)‐shield is numerically implemented to accurately model the RF fields inside the MRI scanner. We verify that the reformulated two‐dimensional (2D) CSI‐EPT algorithm can reconstruct electrical properties maps given 2D electromagnetic simulations. Afterward, the algorithm is tested with three‐dimensional (3D) FDTD simulations to investigate if the 2D CSI‐EPT can retrieve the electrical properties for 3D RF fields. Finally, an MR experiment at 3T with a phantom is performed.From the results of the 2D simulations, it is seen that CSI‐EPT can reconstruct the electrical properties using MRI accessible quantities. For 3D simulations, it is observed that the electrical properties are underestimated, nonetheless, CSI‐EPT has a lower standard deviation than the standard Helmholtz based methods. Finally, the first CSI‐EPT reconstructions based on measured data are presented showing comparable accuracy and precision to reconstructions based on simulated data, and demonstrating the feasibility of CSI‐EPT.The CSI‐EPT algorithm was rewritten to use MRI accessible quantities. This allows for CSI‐EPT to fully exploit the benefits of the higher static magnetic field strengths with a standard quadrature birdcage coil setup. The acquired conductivity and permittivity can be used as a contrast mechanism, especially the conductivity of tissue has been shown to have potential as a biomarker in oncologyElectrical properties tomography (EPT) is an MR‐based technique aiming at measuring the electrical properties (conductivity and permittivity) of tissues. This is achieved in a non‐invasive manner through MRI‐based mapping of the circularly polarized magnetic component , gradient‐EPTB1+ field. While the magnitude of the B1+ field is measurable with MRI, the phase is not accessible. To overcome this limitation, the measurable transceive phase is used. From this, the transmit phase is derived as half of the transceive phase, which is known as the transceive phase assumption (TPA). However, this assumption is only valid at low field strengths and for symmetrical objects, where the polarization remains circular. For more complex structures, nonsymmetrical objects, or multiple tissue interfaces, these conditions are not met, and the assumption is not valid.Furthermore, CSI‐EPT reconstructions have two major limitations. First, CSI‐EPT requires knowledge of the incident RF electric and magnetic fields. These are the RF fields of the empty transmit coil, that is, when an object/patient is not present. These RF fields can only be obtained through electromagnetic simulations and will vary from coil to coil. Second, similar to the derivative‐based MR‐EPT approaches, the CSI‐EPT reconstruction algorithm is formulated in terms of the complex B1+ and formulate the CSI‐EPT algorithm in terms of only the magnitude. This has been done in Ref. [B1+,To reconstruct the tissue parameters, essentially two options can be followed. The first option is to discard the phase information of the  in Ref.  and has  in Ref. . While tB1+ magnitude and the transceive instead of the transmit phase, both measurable with MRI, without relying on the transceive phase assumption, which was until now a cornerstone of MR‐EPT reconstruction methods. Furthermore, CSI‐EPT reconstructions require knowledge of the background RF‐fields. These are obtained from electromagnetic simulations which require inclusion of the RF‐shield. We will show that supplying the CSI‐EPT algorithm with the correct incident fields is necessary to obtain the correct electromagnetic properties. These RF‐shields are especially important for reconstructions from realistic MRI measurements, as these fields are only accessible via simulations. Thus, we numerically incorporate this RF‐shield to mimic the realistic MRI scenario. Using these proposed changes, we will present the first reconstructions of the electrical properties of a phantom with MRI acquired data using CSI‐EPT.Therefore, in this work, we reformulate the CSI‐EPT algorithm to use the 22.1Ez is the z‐component of the total electric field and χ is the contrast with respect to free space which is defined as ρ as the position vector, ε0 and εr as the permittivity in vacuum and relative permittivity, respectively, σ is the conductivity and ω is the angular Larmor frequency. Reconstructing the contrast is the goal of this method since the electrical properties can directly be calculated once the contrast is known. The contrast and contrast source are the two parameters that are iteratively updated in CSI‐EPT. This is realized by minimizing the cost functional presented in Ref. [l ≥ 1 indicates a summation over various transmit channels including linear combinations such as a standard quadrature drive, ηS,D are normalization factors for the data functional (first term on the right‐hand side of (3)) and object functional (second term on the right‐hand side of (3)). It should be noted that in MRI the domain where the object is located, D, is the same as the location where the data are collected, S. Furthermore, GS+ and GD are integral operators that map the contrast source to the scattered B1+ field, B1+,sc, and the scattered electric field, Ezsc, respectively. These integral operators are given by k0 and c0 are the wavenumber and the speed of light in vacuum, respectively. The spatial derivatives with respect to x and y are indicated with ∂x,y. The source locations are defined by ρ′ and G^(ρ‐ρ′) is defined as the 2D free‐space Green’s function, which is given by H0(2) is the zeroth‐order Hankel function of the second kind.In this section, we reformulate the CSI‐EPT algorithm as described in Ref. . We star in Ref.  given byB1+ field is not directly accessible through measurements. What can be measured is the so‐called transceive phase ϕ±. This transceive phase consists of the transmit phase ϕ+ and receive phase ϕ‐ according to B1+ field in terms of the transceive phase as n.The problem with the cost functional given by (3) is that the phase of the 90∘ phase difference between the two ports) and this creates a circularly polarized B1 field that is efficient in tipping the spins. In receive mode, the birdcage coil is switched to a receive state which means the 90∘ phase difference becomes a ‐90∘ phase difference. This results in a counter‐rotating circularly polarized field that is efficient in receiving the signal. This receiving state of the birdcage coil is called reverse quadrature or anti‐quadrature. This mode of the transmit coil creates different RF fields. The incident RF fields in reverse quadrature display a simple phase shift for a birdcage coil setup compared with forward quadrature, but the scattered fields are inherently different which is why the TPA is not valid when these scattered fields are comparable in magnitude to the incident field.In this section, the electric and magnetic RF fields are the fields encountered in the receive state of the birdcage coil. During transmission, the birdcage coil is fed in quadrature mode  at iteration n, is defined as Ezinc, the incident electric field during reception, is modeled together with B1‐,inc for an empty coil, that is, in reverse quadrature mode for a birdcage coil. Since the incident fields for the transmit state are already modeled for each port, the incident receive fields are acquired by driving these ports in reverse quadrature.To compute the scattered receive field at each iteration, we use B1+ data. The new pseudo code is shown below with a dagger (†) indicating the quantities in the receive state of the birdcage coil. Furthermore, the Polak‐Ribière update directions can be found in Refs. [By adding the receive phase as an extra unknown into the minimization problem, the minimization becomes more difficult and the computation time is increased since the number of required integral operations is increased to obtain the receive phase. However, the TPA is no longer required to reconstruct the contrast from the in Refs. , 30 and in Refs. .2.2Inside every MRI system, there is an RF‐shield present. The purpose of the RF‐shield is to screen external RF signals from the MRI signal. The RF‐shield changes the RF‐fields produced by the transmit coil, and as previously stated, the incident electric and magnetic RF‐fields are required as input for the CSI‐EPT algorithm. Therefore, including the RF‐shield in the model that simulates these incident RF‐fields is required. The copper RF‐shield can be approximated by a perfect electrically conducting (PEC) material.G^(ρ‐ρ′)→G^ and this results in a significant increase in computation time because the integrals in Equations  can no longer be computed using the fast Fourier transform, but instead have to be computed using a convolution.In Ref. , the RF‐z‐direction. From there, we follow Ref. [d is the distance from the mirror source to the center of the birdcage coil, RPEC is the radius of the RF‐shield, and RS is the distance from the center of the RF‐shield to the source.To avoid a severe increase in the computation time of the CSI‐EPT algorithm, we implemented the RF‐shield for the incident fields numerically using mirror currents. At the location of the PEC, the tangential electric field should be zero. To accomplish this for the circular RF‐shield, we assume that it is infinitely long in the low Ref. , where a3First, CSI‐EPT was used to reconstruct tissue parameters based on simulated data. Simulations allow knowledge of the ground truth EPs, thus benchmarking the accuracy of the reconstruction algorithm. Subsequently, first CSI‐EPT reconstructions were performed from MRI measurements in a phantom.3.1The performance of the modified CSI‐EPT scheme is tested first by the use of 2D line source simulations in Matlab . The contrast that is used for these simulations is shown in Figure 3.1.1The incident electric and magnetic fields were computed with and without the RF‐shield included using the setup that is shown in Figure 3.1.2B1+ amplitude and transceive phase are separately corrupted with white Gaussian noise using realistic SNR valuesB1+ amplitude and transceive phase are acquired using two different measurements each with a corresponding noise set.B1 maps and corrupting both the real and imaginary parts separately. From one pair of corrupted real and imaginary values, the B1+ amplitude was extracted. The other pair of real and imaginary values was corrupted with a different noise set and used to construct the transceive phase. In all the simulations, total variation regularization was used during the minimization, as described in Ref. [The effects of the transceive phase on the original CSI‐EPT algorithm, using the TPA, and the newly proposed transceive phase corrected (TPC) CSI‐EPT algorithm are investigated for 3T and 7T. In all the simulations, both the  in Ref. .Errσ defines the mean absolute error in the conductivity, σtrue is the original conductivity of the phantom, σrecon is the reconstructed conductivity, and N is the number of voxels within the region indicated by the black box.To obtain a measure of the quality of the reconstructed electrical properties, the mean absolute error is computed. This is performed within a region of the phantom as indicated by the black box in Figure Ez,Bx and By components. Before using measured data, we want to characterize the error that is made by using this 2D assumption.After these 2D line source simulations, a 3D FDTD simulation package  is used to investigate the effects of the 2D assumption that is used in this version of the CSI‐EPT algorithm. This assumption states that in the center plane of the transmit coil the RF‐fields have only the B1+ magnitude and transceive phase with the phantom in the simulation are used as inputs for the CSI‐EPT algorithm.For these simulations, the same phantom as for the 2D line source simulations was constructed, the specifications are shown in Figure 3.2Finally, CSI‐EPT reconstructions from MRI measurements using a 3T system  were performed to show the potential of this method on in vivo data. Since there is no ground truth available with measurements, unlike the simulations, the CSI‐EPT reconstructions are compared to the standard Helmholtz‐based EPT method, where a 7‐point kernel is used.21∘C. For the background, 2.5 gr/L was added resulting in a conductivity of 0.41 S/m at 21∘C.For the measurements, a phantom was constructed with the same dimensions as the phantoms shown in Figure B1+ amplitude.An AFI sequence was used to obtain the A vendor‐specific algorithm  was used to convert the receive phase measured with the head coil to the body coil.B1+ amplitude and the phase difference between the two ports of the birdcage coil were extracted from the log file created by the scanner.To correctly model the incident RF fields, the μ) and standard deviation (σ) are given for the reconstructions of the measured data. These values are computed for the two different compartments of the phantom. Since standard Helmholtz MR‐EPT is not able to reconstruct the boundaries properly,Finally, the mean (4The effect of the mirror currents is shown in Figure CSI‐EPT reconstructions from the 2D line source simulations at different field strengths are shown in Figure B1+ magnitude and transceive phase are shown. From the line plots, we can see the impact of the noise at lower field strengths, because of the lower sensitivity, and the TPA at the higher field strengths. When the TPC CSI‐EPT algorithm is used, the higher intrinsic sensitivity at the higher field strengths can be utilized.This is further illustrated in Figure Figure The bottom plot of Figure Figure Finally, since the newly proposed method also reconstructs the receive phase during the minimization process, it is possible to compare this reconstructed phase from the measurement with the 2D line source simulated one. This together with the comparison between the 2D simulated transceive phase and the measured transceive phase is shown in Figure 5B1+ magnitude and the transceive phase. Furthermore, we showed that with this formulation we can derive the true B1‐ fields rather than the relative B1‐, which is reconstructed by using one transmit channel as a reference. Furthermore, we included a numerical implementation of the RF‐shield resulting in more realistic incident RF‐fields that are used as input for CSI‐EPT. Ultimately, with this work, we demonstrated for the first time the feasibility of CSI‐EPT conductivity reconstructions from MRI measurements at 3T. These results ultimately confirm the reduction of boundary errors and less noise compared to Helmholtz EPT as is always claimed from simulated results.In this work, we reformulated the CSI‐EPT algorithm in terms of MRI accessible quantities, that is, the The solution to the RF‐shield was proposed to model the incident RF‐fields correctly. Another solution to implement the RF‐shield into the CSI‐EPT scheme has been proposed in Ref. , where iThe TPA is valid at lower field strengths, as a result, we can reason that the error in the reconstruction from Figure With the standard CSI‐EPT algorithm and standard Helmholtz EPT, there was a trade‐off for the field strength to use when measuring with a standard birdcage setup. At lower field strengths, the sensitivity is poor, while at higher field strengths the TPA is not valid. With the TPC CSI‐EPT, this trade‐off is no longer present since TPC CSI‐EPT is not affected by the invalidity of the TPA. Therefore, the increased SNR and inherent sensitivity of 7T for a regular widely available standard quadrature setup can be exploited. As a limitation of this work, MRI measurements were only performed at 3T and not at 7T because the specifications of transmit coil at 7T are not available. As shown in Figure In each of the eight reconstructions, in Figure Ex, Ey, and Bz components that are not taken into account in this 2D CSI‐EPT algorithm. This is the cause of the underestimation of the conductivity, as can be seen by the plot at the bottom of Figure Figure z‐direction for the length of the phantom. This was done to keep the assumption that the RF‐field is 2D valid in the center slice of the birdcage coil. In Ref. [The phantom has a contrast that is invariant over the  In Ref. , the effnth iteration to alleviate the additional computational effort. Further, the increase in computation time can be managed by using some form of a hybrid method, where either 2D CSI‐EPT or a deep learning approachPossible solutions for the underestimation of the dielectric properties are to formulate the CSI‐EPT algorithm for 3D RF fields. However, this will significantly increase the computation time of the algorithm. Currently, the reconstructions are obtained within 1 minute of computation time using an i5‐6600k processor compared to multiple hours for 3D CSI‐EPT.From the reconstruction of the measured data in Figure From the TPC CSI‐EPT, we can also extract the reconstructed transmit and receive phase as shown in Figure Ultimately, the presented methodology enables the use of CSI‐EPT for higher field strengths with a standard birdcage setup and as a result of the reformulation to MRI accessible quantities, it could also move to be used for in vivo EPT.6B1+ amplitude and transceive phase can serve as input data instead of the complex B1+ field. Due to this reformulation, the transceive phase assumption, which is not valid at high field strengths, is not necessary anymore. This allows for CSI‐EPT to fully exploit the benefits of the higher static magnetic field strengths with a standard quadrature birdcage coil setup.In this work, the CSI‐EPT algorithm was reformulated such that the Finally, in this work, the first MRI acquired data CSI‐EPT reconstructions are shown and illustrate a significant improvement over the standard Helmholtz MR‐EPT reconstructions. Moreover, we observed that CSI‐EPT can reconstruct the boundaries between different dielectric properties and that it is robust with respect to realistic SNR values.


With the development of concrete technology, the tendency to combine different materials with each other to achieve a greater efficiency and durability of structures can be observed. In the modern construction industry, various materials and techniques are increasingly being combined in order to achieve e.g., an increased resistance to dynamic impacts of a structure, or an increased scope of work of a selected constructional element, which translates into a significant increase in the energy of destruction. Thus, hybrid elements, known as composite ones, are created, which consist of concrete and reinforcements. This study examined the influence of the preparation of the concrete surface on the behavior of high-performance, self-compacting, fiber-reinforced concrete (HPSCFRC), reinforced with carbon fibers (CF) using a cement matrix. In the general lamination processes, this is preformed using epoxy resin. However, epoxy resin is sensitive to relatively low temperatures, and therefore the authors attempted to use a cement matrix in the lamination process. When connecting hardened concrete with a fresh concrete matrix or mixture, the type of the concrete surface is significant. In this research, three types of concrete surfaces e.g., unprepared, sanded and grinded were considered. All of the surfaces were examined using a 3D laser scanner, to determine the Abbott-Firestone profile material share curve. In this research, cylindrical concrete specimens were reinforced with one, two and three layers of laminates. They were then subjected to a uniaxial compressive test. The results of tests showed that the use of cement matrix in the lamination process, due to its low efficiency, should not be applied when reinforcing concrete elements with a high compressive strength. Moreover, the grinded surface of concrete showed the best cooperation with CF reinforcement.  Composites  are materials that are consciously constructed of two or more materials and which have properties other than individual constituent materials. Fiber reinforced polymer (FRP) composite can be defined as a polymer which is reinforced with fiber. The use of FRP in civil engineering is becoming more and more common in relation to strengthening existing and newly designed structures. This is due to the many advantages of materials from this group of polymers. The most important advantages of FRP materials are its: high Young modulus, strength to weight ratio, resistance to aggressive environments, good fatigue properties, low lifecycle costs, electromagnetic transparency and low thermal conductivity ,4,5,6,7.In civil engineering, intensive growth in the design of structures manufactured by self-compacting concrete (SCC) has been observed ,9. The uCarbon fibers (CF) are the most often used to strengthen engineering structures, and are characterized by good thermal and chemical resistance. Working temperature is one of the most important criteria for choosing a given type of fiber to reinforce a composite material. For example, the properties of carbon fibers do not change in a non-oxidizing atmosphere to 2000 °C, unlike glass or aramid fibers ,19. CarbCFRP still remain a new tendency in the design process. The role of the matrix in the laminate can be played by epoxy resin, and sometimes by the cement matrix . Due to It has been proven many times that CFRP can protect the structure of concrete  and compIn most of the analyzed literature, researchers do not provide detailed information on surface preparation, and often provide basic information that the concrete surface has been cleaned and dusted before the lamination process. Only a few works provide information concerning the method of preparing a concrete surface. In most cases the surface was not prepared using any technological treatment, or was treated using grinding. The lack of morphological characteristics of the concrete surface in many scientific papers inspired the main author of this work to analyze the impact of surface preparation on the efficiency of reinforcing concrete elements with carbon fibers. Due to the plastic behavior of epoxy resins in low temperatures, the authors tried to answer the question of whether a cement matrix could be reasonably used in the lamination process of high-performance concrete. The paper analyzes three types of the most common concrete surfaces: unprepared, sanded and grinded. In summary, the main purpose of the work is to indicate the optimal concrete surface intended for reinforcing when using FRP materials.3), river sand as fine aggregate (650 kg/m3), diabase as coarse aggregate (1000 kg/m3), superplasticizer Sikament FM6 (17.5 kg/m3), Sika Fume addition as microfiller (60 kg/m3) and water from waterworks (160 kg/m3). The water to cement (w/c) ratio was equal to 0.32. The steel micro-reinforcement (78 kg/m3) had the form of steel oar-shape fibers with a length (l) of 30 mm and an outer diameter (d) of 0.3 mm  and grinded (G) in each group, and the remaining 12 samples had an unprepared surface (U). The samples were then reinforced with 1, 2 and 3 layers of carbon fibers—4 samples for each series. The samples were marked as follows: U/S/G-1:3-1:4. For example, S-2-4 means a fourth concrete sample with a sanded surface, reinforced with two layers of carbon fibers using cement matrix. Samples S-1, S-2, S-3 and S-4 are the reference samples, and not reinforced in any way.2), effective thickness (0.167 mm), ultimate elongation at the break (1.7%), tensile strength (4900 MPa) and Young’s modulus (230 GPa). In the case where the samples were reinforced with more than one layer, a pre-cut CF mat was prepared, to ensure the appropriate length of the reinforcement. For samples reinforced with one layer, 364 mm of CF reinforcement was used. For two and three layers, 678 mm and 992 mm were used, respectively. The height of the CF was 200 mm. The specimens were laminated with high performance cement matrix during the dry lay-up process. The content of the cement matrix was as follows (by mass): cement type I 52.5 R: Sika Fume HR: Water: Plasticizier Sikament FM 6, which was equal to 100:30:40:10. The compressive strength of the cement matrix was 64 MPa. Firstly, the whole concrete sample was embedded in the cement matrix, and then a CF mat was applied to the concrete surface, which was covered with a cement matrix using a brush, while trying to soak and infiltrate the CF. The thickness of the cement matrix was about 4 mm. The lamination process was carried out at a temperature of 24 °C, and a humidity of 65% ± 5%. The samples reinforced with the cement matrix were tested 28 days after lamination.A carbon fiber (CF) overlap of 50 mm was provided for each sample. The properties of the CF according to manufacturer are as follow: density  based on the method of laser triangulation, which involved measuring the deformation of the line produced by the laser beam. The distances between individual points located on the tested surface were measured with a stepper motor-driven camera, thanks to which, measurements can be made with an accuracy of 15 µm in profiles spaced 10 mm apart. The laser has a compact structure, and therefore tests can be carried out in both laboratory and field conditions. The device assigns three coordinates to each measuring point, describing its location on the test surface. The measurement data file is saved in asc format. The result of the scan is a virtual 3D image of the morphology of the surface being examined. The image was analyzed in order to obtain the values of the parameters that describe the surface morphology .Profile elevation zone;Profile core zone;Profile recess zone.The profile material share curve is the curve that illustrates the profile material share at a certain level c (most often expressed as a percentage) as a function of distance c from the line passing through the highest point of the profile, and which is parallel to the average line. This curve is also called the Abbott-Firestone curve ,49,50,51pk;Average height of high mid elevations above the core of the roughness profile—reduced height of Rk;The depth of the middle part of the profile, determined by a simple linearizing material share curve—depth of the roughness core Rvk pits.Average depth of deep pits under the roughness core—reduced depth of RThe following parameters of the material share curve of the surface roughness profile are distinguished :Average mr1 corresponds to the upper limit of the core of the profile, while the material fraction Rmr2 corresponds to the lower limit of the core. The Rt is the distance between the highest and the lowest point on the surface roughness profile.The material fraction RIn order to characterize the surface of the concrete, an additional three cubic samples of HPSCFRC with dimensions equal to 10 cm × 10 cm × 10 cm were made. The first sample had an unprepared surface (sample U1—mr1) and lower (Rmr2) core boundaries are similar for the unprepared and grinded surfaces. In the case of the sanded surface, it should be noted that the material proportion corresponding to the upper limit of the core is more than half, and the lower limit of the core has the lowest value with regards to the other two surfaces. The roughness core depth Rk is the most important parameter that says a lot about the nature of the surface. When analyzing the samples macroscopically, it could be clearly stated that the unprepared surface has the smallest roughness, followed by the grinded surface, with the sanded surface having the largest roughness. Scanning studies confirmed this fact by providing The Abbott-Firestone curve for the unprepared, sanded and grinded concrete surfaces is presented in The depth of the middle part of the profile was the smallest for the unprepared surface, and was, on average, 0.21 mm, whereas, for the sanded and grinded surface, it was 0.6935 mm and 0.3556 mm, respectively. The average depth of deep cavities under the roughness profile core was the greatest for the sanded surface (0.3884 mm), decreasing for the grinded surface (0.3427 mm) and reaching the lowest value for the unprepared surface (0.1142 mm). The average height of high mid elevations above the core of the roughness profile was 0.09805 mm, 0.166 mm and 0.1228 mm for the unprepared, sanded and grinded surfaces, respectively. In summary, it can be stated that the highest roughness was found in the sanded surface, and the smallest in the case of the unprepared surface. The grinded surface in this respect is in between the other two. The roughness profile parameters are presented in Detailed results for the samples reinforced with cement matrix are presented in In the case of samples reinforced with two layers of CFRP, a slight increase in compressive strength was observed, and it amounted to 88.69 MPa, 83.67 MPa and 94.79 MPa for the unprepared, sanded and grinded samples, respectively. This means that there is an increase in strength, when compared to non-reinforced concrete, by 10%, 4% and 18%, respectively. The standard deviation of the compressive strength was the lowest for the samples with a sanded surface and amounted to 1.95 MPa. It was higher for the grinded surface (11.89 MPa)-and the unprepared surface (5.44 MPa). The axial deformability of the samples at the moment of the failure of the specimens was equal to 0.0081, 0.0080 and 0.0088 for the concrete with the unprepared, sanded and grinded surface, respectively. The average lateral deformability of the samples was 0.0033, 0.0033 and 0.0038, respectively. For the samples with the grinded concrete surface, the obtained average axial deformation was higher by 9% and 10% when compared to the samples with the unprepared and sanded surfaces. The average transverse deformation was also higher—a 15% increase was recorded for the concrete with a grinded surface, when compared to the samples with the unprepared and sanded surfaces.For the samples reinforced with three layers of CFRP, a variable value of compressive strength was also found for the samples with the unprepared, sanded and grinded surfaces, and it amounted to 86.34 MPa, 81.82 MPa and 95.57 MPa, respectively. This means that there is an increase in strength when compared to non-reinforced concrete by 7%, 2% and 19%, respectively. The standard deviation of the compressive strength was greatest for the samples with the grinded surface. There was also no change in the average value of the compressive strength of the samples with the sanded surface. The average axial deformability of the samples at the time of failure was equal to 0.0091, 0.0084 and 0.0098 for the concrete with the unprepared, sanded and grinded surfaces, respectively. The lateral deformability of the samples was equal to 0.0036, 0.0035 and 0.0041, respectively. For the grinded surface, the average axial deformability was by 8% and 17% higher than for the samples with the unprepared and sanded surfaces. The average transverse strains were also higher—a 14% and 17% increase for the concrete with the grinded surface was noted, when compared to the samples with the unprepared and sanded surfaces.A macroscopic analysis of the failure of the samples reinforced with one layer of carbon fibers is presented below. In the case of CFRP layers in the amount of more than one, the damage had a similar course, and the adhesion between the first layer of reinforcement and the concrete surface is crucial for the failure process. In all the cases, the overlap was cut. All the samples after the tests are presented in In the case of the samples with the unprepared surface, it should be noted that the adhesion of carbon fibers to a high-performance cement matrix is similar to the adhesion of this matrix to the concrete surface. The better adhesion of the cement matrix to the concrete surface can be observed in the case of the sanded surface. Only a negligible part of the cement matrix remained glued to the carbon fibers—some of them remained on the high-performance matrix during the failure . LocallyIn the case of the grinded surface, similar phenomena were observed as for the unprepared surface, with the proviso that in this case these phenomena were more dispersed and did not occur on large surfaces. To sum up, the best cooperation of external reinforcement with a concrete core was demonstrated for the grinded concrete surface. The surface of high-performance concrete is a specific surface, which is due, among other reasons, to its high tightness and low open porosity. Hence, low cement adhesion to the unprepared surface may occur. In the process of strengthening the samples using the considered method, their surface, after the application of the reinforcement, was subjected to some pressure in order to achieve a better infiltration of the fibers. This pressure was made manually by the same person for all the samples. In the case of the sanded surface, it was possible to locally squeeze the fresh cement matrix from the deeper troughs of this surface, which after unloading resulted in the creation of an empty space between the carbon fiber mats and the deeper part of the surface, possible affecting the results. The grinded surface, which has a higher roughness than the unprepared surface, and a smaller roughness than the sanded surface, could have been subjected to the best combination of all the surface types considered, which was confirmed by the results of the compressive strength of the samples.The best cooperation of external CF reinforcement with a concrete core was obtained for the grinded concrete surface. The surface of HPSCFRC is a specific surface, due to, among other reasons, its high tightness and low open porosity, when compared to normal performance concrete. Therefore, there could be a low cement mortar adhesion to the unprepared surface. In general, the strength of concrete increases as the number of reinforcing layers increases. However, this regularity was only obtained for the grinded concrete surface. Surface roughness and its morphology significantly affect the obtained results. The lack of preparation of the concrete surface before lamination or too big differences in the height of the surface profile (as in the case of the sanded surface) leads to low cooperation between carbon fibers and the HPSCFRC surface. The most optimal preparation process of concrete substrate is grinding. Given the high cost of CF reinforcement, it is not recommended to use cement matrix, due to low strengthening efficiency, when reinforcing high-strength concrete.