After the calibration of the computational models, a parametric study is then conducted to assess the influence of the FRP axial stiffness (thickness and modulus of elasticity) on the interfacial normal and shear stresses. The numerical analysis results show that increasing the thickness or the elastic modulus of the FRP strengthening affects the efficiency of the FRP bonding and makes it susceptible to earlier debonding failures. A tapering technique is proposed in wet lay-up applications since multiple FRP layers are often required. It is shown that by gradually decreasing the thickness of the FRP strengthening, the concentration of stress along the plate end can be reduced, and thus, the overall strengthening performance is maximized. The tapering is successful in reducing the bond stress concentrations by up to 15%, which can be sufficient to prevent concrete rip-off and peel-off debonding failure modes. This article contributes towards a better understanding of the debonding phenomena in FRP-strengthened elements in flexure and towards the development of more efficient computational tools to analyze such structures.This article examines numerically the behavior of prestressed reinforced concrete slabs strengthened with externally bonded reinforcement (EBR) consisting of fiber-reinforced polymer (FRP) sheets. The non-linear finite element (FE) program Abaqus The need to increase service loads, changes or updates in design codes, design errors or aging make the strengthening of reinforced concrete elements necessary. Due to several advantages over more traditional techniques, externally bonded reinforcement (EBR) in the form of fiber-reinforced polymers (FRP) has gained a special interest in strengthening applications of reinforced concrete (RC) structures ,2,3,4. TPrevious research indicates that EBR FRP strengthening can increase the flexural capacity of elements in both service and ultimate conditions ,6,7,8. HIn order to prevent debonding failures at the end anchorage of a plate or sheet of an EBR FRP-strengthened slab a, severaSeveral models/guidelines exist to predict the bond behavior of FRP-concrete systems, but they are still unable to give accurate predictions ,7. This Past studies have adopted different approaches to simulate debonding phenomena. For example, smeared and discrete approaches can be used to simulate cracking and debonding in plain and FRP-strengthened concrete structures ,27. OtheThis article examines numerically the end-plate behavior of prestressed concrete slabs strengthened in flexure with EBR FRP sheets. This is achieved by using previous data from four-point bending tests on EBR FRP-strengthened prestressed concrete slabs. Non-linear FE analyses was first performed to calibrate computational models of the strengthened slabs. Subsequently, a parametric study was conducted to assess the influence of the FRP axial stiffness  on the normal and shear interfacial stresses. The article also provides some recommendations to enhance the capacity of FRP bonded to prestressed concrete slabs, as well as to improve the effectiveness of FRP plate bonding techniques. This article contributes towards a better understanding of the debonding phenomena in FRP-strengthened elements in flexure and towards the development of more efficient computational tools to analyze such structures. 2  were used as flexural bottom reinforcement. Such tendons complied with the ASTM A421 [Five prestressed concrete slabs tested previously by the authors  were tak2 b. Four fSTM A421  specificft, of 1.4 mm, was used to strengthen the slabs’ soffit. The FRP sheets were bonded with the slabs in an upside-down position, as shown in PS-EBR-1-250-TP: EBR CFRP-strengthened slab, strip width 250 mm, tapered at one end anchorage (tapering length = 250 mm).PS-EBR-2-100-TP: EBR CFRP-strengthened slab, strip width 100 mm each, tapered at one end anchorage (tapering length = 250 mm).PS-EBR-1-250 and PS-EBR-2-100: same as above but without tapering.PS-C: unstrengthened control slab.One layer of carbon FRP (CFRP) strip with single or double layouts, having a thickness fE = 200 GPa, Poisson ratio = 0.29, ultimate strength fuf = 2590 MPa and rupture strain εfu = 0.015, as given by the manufacturer. The FRP was bonded to the slabs’ soffit using a two-part epoxy adhesive bonding agent. The properties of the epoxy resin reported by the producer were modulus of elasticity mE = 5 GPa, tensile strength mf = 20 MPa and Poisson ratio = 0.35. The slabs were cast using C30 concrete with a mean compressive strength of cf = 30.8 MPa, tensile splitting strength crf = 3.6 MPa and modulus of elasticity cE = 22 GPa, which were calculated according to fib Model Code [The properties of the CFRP were modulus of elasticity The five slabs were subjected to monotonic load until failure. The mid-span deflection behavior of the slabs was monitored using vertical displacement transducers located at the soffit. As expected, the ultimate failure of the slabs was controlled by debonding of the CFRP sheets at the free end anchorage for all of the strengthened specimens. ® FE software [®. The internal reinforcement was modeled using 1D elements and is embedded in the concrete matrix, , ode 2010 .For CFRP-strengthened specimens with tapering CFRP sheets at the end anchorage (PS-EBR-1-250-TP and PS-EBR-2-100-TP), it was found that plate end bonding failure was well prevented, and instead, multiple intermediate cracks induced interfacial debonding failures i.e., . This isThe results in ft = 0.7, 1.4, 2.0 and 4.0 mm), whereas fE = 150, 200 and 250 GPa). The results in these figures indicate that, as fE increases, the overall stiffness of the slab also increases, and less deflection is recorded . recorded b. When tmax) and shear stress (S11) of the concrete–adhesive interface of the CFRP-strengthened slabs without end-tapering (PS-EBR-250) and with end-tapering (PS-EBR-250-TP). In these plots, the thickness of the CFRP varied from 1.0 to 1.4 mm in PS-EBR-250-TP to compare with the 1.4 mm of CFRP in PS-EBR-250. The development of the principal stresses in the FE model can be used to identify the concentration of stresses in the concrete, CFRP sheets and adhesive resin. As a failure ratio of 0.037 was used , a diagonal crack in the concrete would occur when the tensile stress in the concrete (at the end of the plate) reaches its ultimate strength. However, the full composite action is assumed in this modeling exercise, which makes the analysis run completely until a compressive failure of concrete occurs. At this point, the maximum tensile stress in the CFRP sheets can be used to examine the effectiveness of the FRP strengthening before the beam starts to develop diagonal cracking, loses its composite action and eventually fails due to FRP debonding  are used to investigate the principal and shear stresses of the slabs and the FRP plates. ft = 1.4 mm) is considered. The concentration of these stresses is found to be the cause of debonding due to rip-off or peel-off. Conversely, the tapering reduces the principal stresses (by up to 15%) and shear stresses (by up to 10%) along the anchorage length, thus, re-distributing stresses towards the beam mid-span. Therefore, tapering is extremely successful in reducing the stresses by up to 15%, which can be sufficient to prevent concrete rip-off and peel-off FRP debonding failures.In all CFRP-strengthened prestressed slabs, the ultimate failure was controlled by debonding of the CFRP sheets at the end anchorage. End debonding failure and intermediate crack-induced interfacial debonding failure were observed in the slabs without and with tapered CFRP sheets, respectively.The results from the tests showed that an end tapering technique improved the ultimate load by up to 5% compared to slabs without tapering. The tapering also prevented end debonding failure by allowing multiple interfacial debonding failures.For CFRP-strengthened slabs, the FE models predicted better the results compared to unstrengthened specimens up to a load level of approximately 75% of the ultimate load. However, the numerical predictions showed approximately 20–25% fewer deflections at ultimate loads. Further research is necessary to achieve better predictions at ultimate loads.Results from a parametric study showed that increasing the thickness or the elastic modulus of the CFRP strengthening sheets can affect the efficiency of the FRP plate bonding technique, thus, making it susceptible to potential premature debonding failures.The FE results confirmed that a tapering technique at the end anchorage of the CFRP sheets can increase the capacity of a CFRP strengthening system. For the CFRP-strengthened slabs analyzed in this study, the end tapering reduced the stresses by up to 15%, which can be sufficient to prevent concrete rip-off and peel-off debonding failures. Nonetheless, further numerical analyses are necessary to extend the validity of these observations to other structural elements strengthened with EBR CFRP sheets.This article numerically examines the behavior of prestressed reinforced concrete slabs strengthened with EBR CFRP sheets in flexure. Computer simulations based on finite element (FE) analysis were conducted on five specimens tested previously by the authors to investigate stress concentrations in the slabs, as well as at the CFRP–concrete bonded interface. The simulation is then used to carry out a parametric study that shows that increasing the thickness or the elastic modulus of the FRP plate affects the efficiency of the FRP plate bonding. Further analysis investigated the efficiency of tapering the EBR FRP on reducing the stress concentrations at the end anchorage to the strengthening system. Based on the results of this study, the following conclusions can be drawn:


In this work, we present an analysis of natural fine aggregates’ influence on the properties of ultra-high-strength concrete. The reference concrete mix was made of natural sand with the addition of fly ash and microsilica. It was assumed to obtain concrete with a very high strength without the addition of fibers and without special curing conditions, ensuring the required workability of the concrete mix corresponding to the consistency of class S3. The reference concrete mix was modified by replacing sand with granite and basalt aggregate in the same fractions. Five series of concrete mixes made with CEM I 52.5R cement were tested. Experimental investigations were carried out regarding the consistency of the concrete mix, the compressive strength, the flexural strength and the water absorption by hardened concrete. A comparative analysis of the obtained results indicated significant improvement in the concrete strength after the use of basalt aggregate. The strength of the concrete series based on basalt aggregate, BC1, allowed it to be classified as ultra-high-performance concrete. Concrete based on sand, SC1, was characterized by the lowest compressive and flexural strength but obtained the best workability of the mix and the lowest water absorption. The results presented in the paper, show a significant influence of the type of aggregate used on the mechanical and physical properties of ultra-high strength concrete. High-performance concretes (HPCs) and ultra-high-strength concretes (UHSCs) are predominantly used to produce small architectural elements such as facades, etc. However, these materials are increasingly being used in large volumes to construct structural elements of bridges, tunnels, runways, etc. . The useThe design and analysis of the mechanical and physical properties of HSCs and UHPCs are the subjects of various studies. A significant portion of these studies concerns concretes made with the use of steel or composite fibers. Kusumawardaningsih et al. in ,4 showedThe use of UHPCs is limited due to the technological difficulties in their production and the high costs, especially of the constituent materials. As Zhao and Bo showed in , casting2, which has a compressive strength of 150–300 MPa and a tensile strength of 10–20 MPa. Experimental investigations on the use of basalt aggregate in high-strength concrete mixes, which were conducted by Kishore et al. and presented in [At the beginning of the 20th century, Donza et al. in  conducteented in , Li et aented in . The obtUltra-high-strength concrete mixes are characterized by a very high density, which significantly reduces their workability. Chemical admixtures partially overcome this problem, but have limited uses. A dense consistency makes it difficult or even impossible to use concrete in elements with a complex reinforcement structure. Complex internal structures usually require the use of modified cement mortar, instead of concrete. An example of such a solution was presented by Małek et al. in . The useThis paper presents the results of research devoted to the development of a concrete recipe that enables high and very-high-strength concrete to be obtained while maintaining the required consistency of the concrete mix. The analyzed concrete mixes were formulated with the intention to be used in the manufacturing of concrete elements containing spatial reinforcement, with a high density of reinforcement bars and small sized reinforcement meshes, which are the subject of the patent description . TherefoTightness is a characteristic feature of UHSCs, which increases the durability of the structure. Therefore, in the paper a test which allows for a preliminary assessment of concrete resistance to water penetration under the influence of atmospheric pressure was performed. Studies with similar scopes were presented by Golda and Kaszuba  and by DThe tests were carried out for five series of concrete mixes using CEM I 52.5 R Portland cement and fine aggregate to 2 mm. The series of concrete mixes differed in the type of aggregate and the amount of cement that was in them. One series of samples was prepared based on pit sand, two based on granite aggregate and the other two based on basalt aggregate.White Portland cement CEM I 52.5R (c);Fine aggregate—pit sand, granite, and basalt with fractions of 0.125–0.25 mm, 0.25–0.5 mm, 0.5–1.0 mm and 1–2 mm;Fly ash (fa);Microsilica (ms);Polycarboxylate admixture;Pure laboratory pipeline water (w).The materials used for the tests are as follows:Cement CEM I 52.5 R with one of the highest compressive strengths available on the market was used to the tests. The compressive strength of cement after 2 days of maturation is 44 MPa and after 28 days it is 72 MPa. In each of the tested series of concrete, the same fly ash additive was used to ensure an increase in the workability of the concrete mixes. The fly ash used was characterized by fineness below 12% and, loss on ignition below 5% and was certified according to the EN 450–1 standard . The det3 for concretes BC1 and BC2 as well as GC1 and GC2 is the same, i.e., 6%. All of the recipes maintained the same water–cement ratio w/c = 0.33, water–binder ratio w/b = 0.26 and the consistency class S3. Moreover, to improve the workability of the concrete mixes, fly ash was used in proportion of fa/c = 0.167. Microsilica in proportion of ms/c = 13.3 was used to improve the tightness of concrete and increases its strength. The concrete mixes’ compositions are given in To investigate the influence of the type of aggregate on the physical and mechanical properties of high-strength concrete, first the composition of the primary SC1 mix based on sand was developed. The main aim during the design of the SC1 mix was to obtain high strength parameters while maintaining the required consistency class of the mix. The required consistency class was determined as plastic, which corresponded to class S3 according to the slump test. Class S3 is defined as the consistency for which the cone fall is between 100 and 150 mm. Then the primary mix was modified by replacing sand with granite and basalt aggregate The GC1 and BC2 concrete mixes are equivalents of SC1 mix made on granite and basalt, respectively, including the volume density of the aggregates. Moreover, two additional concrete mixes GC2, and BC1 were analyzed. The GC2 concrete composition was correlated with the proportion of BC2 concrete, and the BC1 concrete composition was correlated with the GC1 concrete composition in a similar way. The difference in the amount of cement used in relation to 1 mThe slump test following EN 12350–2  was usedTest to determine uniaxial compressive strength were carried out on cubic samples of 100 mm side dimensions using a MEGA 6-3000-150 (PW-MEGA) automatic hydraulic press with a maximum compressive load of 3000 kN. The samples were tested with a constant rate of loading within a range between 0.5 and 0.7 MPa/s. The initial load was 30 MPa for each tested specimen. Tests to determine compressive strength were carried out for concrete recipes SC1, GC1, GC2, BC1 and BC2 after 2, 7 and 28 days of concrete maturation following the EN 12390–3 standard . Three rcff—the flexural strength of the concrete (MPa);F—the maximum load (N);l = 120—the distance between the supporting rollers (mm);d1 = 40, d2 = 40—the lateral dimensions of the specimen (mm).The flexural strength of concrete was tested in a center-point loading scheme following the EN 12390-5 standard . The tesiw—the parameter of water absorbability by hardened concrete in the i-th sample (%);i-th sample after 20 h of curing (g);i-th sample after 28 days of curing (g).The water absorption by hardened concrete was investigated by comparing the mass of samples before insertion into the water and instantly after their removal from the water. The tests were carried out on three cubic samples of 100 mm side dimensions for each of the concrete series of SC1, GC1, GC2, BC1 and BC2. After being cured for 20 h, the concrete samples were weighed and placed in water at a temperature of 20 °C. For 28 days, the concrete samples were conditioned in water at a temperature of 20–22 °C. To provide the proper water circulation, a minimum of 20 mm of space was left between the samples, and between the surface of the curing tank. After 28 days, the specimens were removed from the water and reweighed. The measurements of the samples’ masses were made with an accuracy of 0.01 g using an electronic balance. The parameter of water absorbability by hardened concrete was determined under the formula:The results presented in The results of the compressive strength tests are shown in cmf,28), which was determined to be 100%. After two days of maturation, the compressive strength of the SC1 concrete was 71% ctmf,28, while for the BC2 series concrete, it was 69% cmf,28, and for the GC1 concrete, it was only 47% cmf,28. After 7 days of maturation, the proportions of compressive strength were similar for all the series of concrete. The strength of the SC1 concrete was 82% cmf,28, and the strength of the GC2 concrete was 80% cmf,28. The proportion for the GC1 and BC1 concretes was the same, which was 76%, while the lowest value was found for BC2 concrete, which was 73%.The impact of aggregate type on the development of compressive strength in relation to the maturation time of the concrete was also analyzed. cfmf,28), which was determined to be 100%. On the 7th day of maturation, the flexural strength of the BC1 concrete was 79% cfmf,28, and the flexural strengths of the BC2 and GC2 concrete were 76% cfmf,28. The greatest decrease in the flexural strength after early maturation was observed in the SC1 concrete, for which the flexural strength was 66% cfmf,28.cfα = 0.145 characterized the GC2 concrete. For the SC1 concrete, the value of the coefficient was cfα = 0.137. The lowest values of the cfα coefficient were achieved for concretes based on basalt aggregate, i.e., BC1 and BC2, the values of which were cfα = 0.119 and cfα = 0.126, respectively.The results of the tests conducted indicate that it is possible to create high-strength concrete while maintaining the S3 consistency class allowing its use in structures containing spatial reinforcement. When the concrete mix consistency was tested, the SC1 concrete made from sand was characterized by the highest degree of plasticization. The use of basalt aggregate reduced the plasticity of the concrete mix. However, the greatest reduction in plasticity was observed after the use of granite aggregate. Comparing the cone fall obtained for the GC1 and GC2 concrete series, it was found that with an increasing amount of aggregate in the concrete mix, its consistency became less plastic. A similar phenomenon was observed in the case of concretes made of basalt aggregate.The analysis of the test results shows that the type of aggregate used had a significant influence of on the compressive strength of concrete. Base concrete SC1 made from sand had the lowest compressive strength after 28 days. Replacing sand with granite aggregate in the GC1 series concrete resulted in an increase in compressive strength by 9%, while the use of basalt aggregate increased the strength of theBC2 concrete by 28%. The influence of the type of aggregate was also visible when changing its amount in the concrete mix. Concerning concretes made with granite aggregate, concrete from the GC1 series had 7% higher compressive strength after 28 days than the GC2 concrete containing an increased proportion of aggregate, while in the BC1 and BC2 concretes, which were made from basalt aggregate, there was only a 1% Difference. The test also showed that the most significant delay in the early-age compressive strength was on GC1 concrete made from the granite aggregate. This phenomenon was particularly evident on the second day of concrete maturation.cfα coefficient can be treated as a measure of the ductility of concrete. Similar coefficient was used by Liu et al. in [cfα coefficient in concretes made from granite and sand indicated the better adhesion of these aggregates to the cement matrix. For concretes made from basalt aggregate, this coefficient was the smallest among the series of concrete mixes analyzed.Concrete based on basalt aggregate had the highest flexural strength after both 7 and 28 days, while the concrete made from sand had the lowest flexural strength value. Comparing the flexural strength to the compressive strength, the highest value was obtained in concretes made from granite aggregate. The t al. in  and by Wt al. in . An incrThe type of aggregate significantly affects the water absorption by hardened concrete. Concretes made from basalt aggregate were characterized by water absorption rates more than 20% higher than those made from the sand. The highest water absorption rate was found in concretes made from granite aggregate.Although the concrete mixes contained a significant amount of Portland cement, their very high strength properties allowed for a considerable reduction in the cross-sectional dimensions and mass of structural elements, which will lead to a reduction in the carbon footprint.A comparative analysis of the presented solutions was carried out with the solutions found in the literature. The analyzed concrete mixes were made with the use of CEM I 52.5 R Portland cement. The composition of the MC1 (HPC) concrete mix presented by Máca et al. in  was comp3 of concrete in each series.3 of concrete mix. The BC2 concrete is characterized by the highest compressive strength among the concrete mixes analyzed. Its strength was 3% higher than the compressive strength of the MC2 (3-900) concrete; however, it requires the use of 121 kg less cement per 1 m3 of concrete.The compressive strength of the MC1 (HPC) concrete was 14% higher than that of the SC1 concrete, but it required the use of 246 kg more cement for 1 mLow cement consumption;No need to use special curing conditions;Use of waste additives such as fly ash;The consistency that enables the use of concrete in an element with a complex reinforcement system.The following features distinguish the presented concretes in comparison with conventional concretes:3 and with the addition of microsilica and fly ash allowed concrete with a compressive strength exceeding 150 MPa, while maintaining S3 consistency to be obtaining. Obtaining such a level of compressive strength in concrete did not require special care conditions or the addition of fibers.The use of basalt aggregate in a concrete mix made with CEM I 52.5 R Portland cement below 600 kg/mThe water demand of an aggregate and its quantity affected the consistency of a concrete mix. Increasing the amount of crushed aggregate in a concrete mix reduced its plasticity. In the recipe obtained for very-high-strength concrete based on sand or granite as a natural fine aggregate, changing the aggregate to basalt increased the compressive strength of concrete by 28%, which allowed it to be classified as ultra-high-strength concrete.Concrete made from sand had the lowest compressive strength among all of the concrete mixes analyzed. The achieved strength allowed it to be classified as very-high-strength concrete. The SC1 concrete mix was characterized by the highest degree of plasticization. The flexural strength was almost 14% of the compressive strength of the concrete. This concrete was characterized by the lowest water absorption rate.Concrete made based on granite aggregate was characterized by the lowest degree of mix liquefaction and the lowest early-age compressive strength. However, after 28 days, the GC1 concrete had a compressive strength 9% higher than that of the SC1 concrete. The flexural strength of the GC1 concrete was 13% of the compressive strength, and of the GC2 concrete—of 14.5%. This concrete was characterized by the highest water absorption rate, which was caused by the absorption of granite aggregate.Concrete made from basalt aggregate was characterized by the highest strength throughout the entire maturation period. This applied to both compressive and flexural strength. The strength of the BC1 concrete allowed it to be classified as ultra-high-strength concrete. The liquefaction of the mix was slightly lower than the consistency of the concrete mix made from sand. Water absorption rate was greater than that of concrete made from sand by no more than 25%.The following conclusions can be formulated from the research conducted:


The tests revealed that frost resistance, determined in all-sided testing directions, of concrete modified with 6%, 9%, and 12% of bottom ash added by weight of cement corresponds to strength grade F100. Such concrete can be used in construction works.The aim of this study is to investigate the effect of municipal solid waste incineration bottom ash from a cogeneration plant on the physical and mechanical properties and durability of cement concrete. Part of the cement in concrete mixtures tested was replaced with 0%, 3%, 6%, 9%, and 12% by weight of municipal solid waste incineration bottom ash. Concrete modified with 6% of bottom ash had a higher density (2323 kg/m The recycling of bottom ash from the incineration of municipal solid waste (MSW) in cement-based materials is one of the trends in the development of a circular economy. The use of MSW has a unique potential to support sustainability while preserving natural resources. Greenhouse gas (GHG) emissions in cement manufacturing are very high, accounting for about 8% of the global carbon dioxide . BA was obtained from the cogeneration plant, where municipal waste is incinerated at a temperature of ~1100 °C. The ash was stored for one year in the Klaipėda regional landfill in Dumpiai under natural conditions. Afterwards, it was dried at 105 °C and ground in a ball mill. BA had the bulk density of 0.91 g/cm3 and the particle fineness  of 4.0%. The bottom ash is attributed to Class F, as the total SiO2 + Al2O3 + Fe2O3 content exceeds 70%.The following binding materials were used: commercial Portland cement CEM I 42.5 R (containing 95–100% of clinker) produced by AB Akmenės cementas, Naujoji Akmenė (Lithuania); and bottom ash from a cogeneration power plant UAB Gren Lietuva, Klaipėda (Lithuania). The chemical composition of the cement and bottom ash (BA) is given in 0/2 fraction sand with the particle size distribution given in 3) was used as a coarse aggregate in the tests (50%—5/8 fraction and 50%—11/16 fraction).5/16 fraction granite crushed stone  Crackstop F6 Adfil NV (Belgium) with a density of 0.905 kg/dm3 and pH value 5.6 at T = 20 °C.Superplasticiser Master Glenium ACE 560 (SP) MBCC Group, Master Builders Solutions (Poland), was used in the mixes. It is a high-performance liquid admixture based on the new generation of polycarboxylate ether polymers, with a density of 1.06 g/cmTap water was used to prepare the samples.The cement content in the concrete mixes varied up to 12%. The maximum ash content was chosen by taking into account the data already presented by other authors , who poi15 specimens were cast for each concrete mix. Concrete cubes with the dimensions of 100 × 100 × 100 mm were cast in reusable stainless-steel moulds. Concrete pastes were compacted on the laboratory vibrating table . The formed specimens were stored for one day in covered moulds, then demoulded and cured according to LST EN 12390-2. Three specimens from each batch were used to test the durability, and the physical and mechanical properties of concrete.The compressive strength of concrete specimens was determined according to EN 12390-3 with a hydraulic press ALPHA 3-3000S test machine . Three specimens of each mix were tested at 7 and 28 days of curing. The density of hardened concrete was determined according to EN 12390-7, the density of compacted fresh concrete was determined according to EN 12350-6, the slump was determined according to EN 12350-2, and the flow was determined according to EN 12350-5. Ultrasonic pulse velocity was determined using a Pundit 7 instrument (converter frequency = 54 kHz) calculating the ultrasonic pulse velocity  according to the literature . To deteaP) (capillary pores), the total porosity (tP), and the closed porosity (uP) (air pores) of concrete. The open porosity was calculated from the following Equation (1):W is water absorption after 48 h, %; ρ is the density of concrete, g/cm3, wρ is the density of water, g/cm3. The total porosity was calculated from the following Equation (2):tρ is the density of concrete, kg/m3; pρ is the specific density of concrete, kg/m3.The porosity parameters of concrete were determined by measuring water absorption kinetics according to the methodology presented in GOST 12730.4-78. This method is used to describe the open porosity :The frost resistance of concrete using the all-sided testing direction was tested using the Rumed 3301 climate chamber  in order to determine the effect of freezing and thawing (FT) cycles on the compressive strength of concrete when different amounts of fly ash were used in concrete mixes. The durability of concrete specimens was determined after 28 days of curing according to the requirements of LST 1428-17. According to the accelerated frost resistance test, water saturated specimens are subjected to cyclic freezing in air and thawing in water. For the accelerated test, the specimens are soaked in 3% aqueous sodium chloride solution (NaCl). The frost resistance class F100 corresponds to the resistance to 20 FT cycles. Prior to the FT test, the saturated specimens are removed from the water bath and placed in such a manner that the water can drain from them. After 2–4 h following the removal of the specimens from the water bath, the control specimens are tested for their initial compressive strength according to LST EN 12390-3. The remaining concrete specimens are placed in the freezing chamber. The specimens are air frozen for at least 2.5 h. The temperature in the centre of the freezing chamber are (−18 ± 2) °C during freezing. After determining the frost resistance, the specimens are removed from the freezing chamber and placed in the bath of aqueous NaCl salt solution at (18 ± 5) °C. The specimens are kept in the bath for at least (2 ± 0.5) h. The all-sided frost resistance of concrete specimens is determined not only by measuring the compressive strength but also by the mass loss. If, after the required number of FT cycles, the loss in compressive strength of concrete specimens does not exceed 5% and/or mass loss of the concrete specimens does not exceed 3%, the concrete is considered to have passed the frost resistance test. Two freeze–thaw cycles per day were carried out with the tested specimens. After 100 cycles, the specimens were crushed and the loss in strength and mass was calculated.3. As expected, the density of fresh concrete decreased due to the loss of internal moisture [Slump and flow tests were carried out in order to determine the effect of bottom ash on the consistency of the fresh concrete. The results obtained using a constant water/binder ratio of 0.55 are shown in moisture . All cemThe properties of hardened concrete depend on the constituents of the concrete mix and their proportions. When bottom ash is used in the concrete mix, it is important to determine the effect of ash on the properties of hardened concrete. In this work, concrete specimens were tested by changing the ash content in the mix. Control concrete specimens without ash were used as the reference. The addition of different amounts of fly ash to the mix resulted in concrete that varied not only by density but also by compressive strength values.3. The average density values obtained in the experimental tests vary within a narrower range: the average density of specimens B0 was 2318 kg/m3, the average density of specimens B3 was 2264 kg/m3, the average density of specimens B6 was 2323 kg/m3, the average density of specimens B9 was 2271 kg/m3, and the average density of specimens B12 was 2315 kg/m3. It should be noted that specimens B6 had a denser structure because their density values were the highest. The obtained results show that the addition of bottom ash at 3% causes a 2.3% drop in density. When 9% of ash is added into the mix, the drop in density becomes less significant at only 2.0%. The tests results show that bottom ash does not have a significant effect on the density of concrete. Similar results were reported by Abubakar [3, respectively.The results given in Abubakar ; the repThe variation in the ultrasonic pulse velocity (UPV) values in relation to the ash content is shown in The UPV is the most consensual in situ and non-destructive test to evaluate the quality of concretes. In this work, the compressive strength of concrete specimens was determined after 7 and 28 days of curing. The average compressive strength values obtained in the experimental tests are shown in The results of further tests show  is required.


Component errors limit the scaling of programmable coherent photonic circuits. These errors arise because the standard tunable photonic coupler—the Mach-Zehnder interferometer (MZI)—cannot be perfectly programmed to the cross state. Here, we introduce two modified circuit architectures that overcome this limitation: (1) a 3-splitter MZI mesh for generic errors, and (2) a broadband MZI+Crossing design for correlated errors. Because these designs allow for perfect realization of the cross state, the matrix fidelity no longer degrades with increased mesh size, allowing scaling to arbitrarily large meshes. The proposed architectures support progressive self-configuration, are more compact than previous MZI-doubling schemes, and do not require additional phase shifters. This removes a key limitation to the development of very-large-scale programmable photonic circuits. Fabrication errors limit the scaling of programmable photonic circuits. Here the authors show how a broad class of circuits can be made asymptotically fault-tolerant, where the effect of errors remains controlled regardless of the circuit’s size. N × N reconfigurable feedforward linear circuit. This device, typically constructed with a compact mesh of Mach–Zehnder interferometers , the effect of errors grows with mesh size, meaning that, in practice, even modestly sized circuits cannot be programmed to high accuracy. Motivated by this challenge, a large body of recent work has focused on “correcting” hardware errors by global optimization10, self-configuration18, or local correction20. For conventional MZI meshes, correction reduces errors by a quadratic factor19; however, the effect of errors still grows with mesh size and poses a fundamental limit to the scaling of these circuits.Large-scale programmable photonic circuits are opening up radical new possibilities for optics. Of key importance in many devices is the universal multiport interferometer, which functions as an ors Fig.  are a cr22, but suffer from large chip area and the need for many crossings. A complementary approach is to stick to conventional geometries2, but insert redundant MZIs to realize the full range of splitting ratios even in imperfect hardware25. This solves the scaling problem, but at the cost of a 1.5–2× increase in the number of splitters and phase shifters. The resulting effects on chip area (particularly on emerging high-speed platforms where phase shifters have a large footprint27), waveguide length (which affects insertion loss and latency28), and electronic complexity  make this option unappealing.To overcome this limit, various alternative mesh architectures have been proposed. Non-compact structures such as binary trees avoid the extreme splitting-ratio requirements24, and do not require additional phase shifters. Moreover, the proposed architectures support progressive self-configuration17, allowing for error correction even when the hardware errors are unknown. This work will enable the development of freely scalable, broadband, and compact linear photonic circuits.In this paper, we propose two mesh architectures that achieve the same perfect scaling without significant added complexity: a 3-splitter MZI that corrects all hardware errors Fig.  and an MThis paper is structured as follows: first we introduce the formalism of error correction in MZI meshes, focusing on the self-configuration approach. Splitting ratios are visualized as points on the Riemann sphere, where forbidden regions emerge as a result of hardware imperfections; these regions are centered at the poles (bar- and cross-state), where the probability density is at a maximum. To avoid this unfortunate coincidence, our architectures “rotate” the Riemann sphere to move the forbidden regions away from this peak, so that a larger fraction of MZIs are perfectly realized. Based on this concept, we introduce the 3-splitter MZI, which can correct arbitrary errors by rotating the forbidden regions to the equator. Using a benchmark optical neural network, we show that this modified MZI mesh is >3× more robust to hardware errors, enabling accurate inference in a regime where standard interferometric circuits struggle. Finally, we introduce the MZI+crossing, which flips the poles of the Riemann sphere. While this design is only robust against correlated errors, it has the added advantage of broader intrinsic bandwidth. For both architectures, we compare the matrix fidelity to the standard MZI to demonstrate the scaling advantage of both schemes.17. Figure 1, where the procedure is more straightforward. The transfer matrix for this system is a product of a phase screen D and a sequence of 2 × 2 unitaries W:Tmn is the nth MZI of the mth rising diagonal.To correctly configure an MZI mesh in the presence of errors, one uses a nulling method based on physical measurementsW in order to diagonalize the “target” matrix X = UW†. For every step, we add one 2 × 2 unitary to W, performing the update W → TmnW, which right-multiplies the target matrix Tmn is chosen to null a specific matrix element v → 0 :i, j) element of X is implemented by inputting the field jth column of W†) and adjusting the MZI parameters  to zero the output power at the ith port. If all nulling steps are performed exactly, the mesh will perfectly realize the target matrix U (see Methods and Supplementary Section We program the mesh using a sequence of steps (Givens rotations), which build up mn† Fig. . The 2 ×mentclass2pt{minimα, β in Fig. s where perfect nulling is impossible  or bar (s = ∞) state.Mathematically, nulling involves setting the  splitting ratio ble Fig. . It is able Fig. , highligs. The overall error is the quadrature sum of all such residuals.If in a given nulling step 29, we sample target matrices randomly over the Haar measure31 and consider an uncorrelated Gaussian error model 〈α〉rms = 〈β〉rms = σ.For linear photonic circuits, two important fidelity figures of merit are (1) the coverage 19. The coverage N ≳ 1/σ2, error correction will be ineffective and the mesh cannot realize most matrices at high fidelity. Thus, even with error correction, hardware imperfections set a fundamental scaling limit for standard MZI meshes.Analytic expressions for 2/3 (Eq. ) decreass = 0  solves this problem by eliminating the forbidden regions altogether24, but at the cost of added optical and electrical complexity. Here, we take the alternative approach of displacing the forbidden regions away from the cross state. This can be performed by placing a third splitter at the input of the MZI, as shown in Fig. η = π/4) maps the bar and cross states to s = ±i .The main challenge limiting error correction here is that the forbidden regions overlap with the peak of the probability distribution, which clusters tightly around the cross state = 0 Fig. 29. This  ±i Fig. . This cas∣ ∈ [0, ∞), and can thus function as a high-contrast optical switch32. However, forbidden regions are still present for the 3-MZI, which implies that for some configurations, the relative phase of the splitter N ≳ 64, the matrix error is approximately 1–2 orders of magnitude lower with the 3-MZI. Moreover, the 3-MZI exhibits more favorable error scaling, with the error remarkably decreasing with mesh size as N → ∞, matrices can be programmed perfectly.This “3-splitter MZI” (3-MZI) can therefore access the complete range of splitting-ratio magnitudes ∣ods (Eq. ), takes s = ±i, where the forbidden regions are centered29. This probability decreases exponentially with the distance from the triangle’s base (see Methods for details). Therefore, although the mesh has N(N − 1)/2 MZIs, only O(N) contribute significantly to the matrix error under self-configuration. A naïve estimate assuming uncorrelated errors would give This non-intuitive effect arises from the fact that, under the Haar measure, only a small fraction of MZIs have significant probability density near sult Eq. .σth ∝ N−1/2, in contrast to the N−3/2 dependence seen for the conventional mesh. Consequently, errors are perfectly correctable under a much broader range of circumstances, as shown in Fig. A second benefit to the 3-MZI is its higher threshold for perfect error correction. One obtains this threshold by computing the coverage ods, Eq. ). This i5. Scaling remains the major challenge to constructing practical optical neural networks, as large mesh sizes (N > 100) are required to achieve a significant advantages over electronic hardware, and such large meshes are especially susceptible to fabrication errors. A recent numerical study showed that even with state-of-the-art process tolerances, hardware errors can significantly degrade DNN inference accuracy33, a difficulty that has spurred investigations into alternatives to the MZI mesh, which all have their own limitations37.To highlight the significance of this error reduction, consider as a concrete example deep neural network (DNN) inference on coherent optical hardware. A DNN is a sequence of layers, consisting of linear synaptic connections and nonlinear neuron activations. An emerging application of photonics seeks to use optical interference to accelerate this process, encoding neuron activations in coherent optical amplitudes, while a programmable MZI mesh implements the synaptic weights and activations are performed with an all-optical or electo-optic nonlinearity38 are preprocessed by a Fourier transform and cropped to a window of size 2 and electro-optic nonlinearities for the activation . For small σ, this is recovered using error correction19. However, many broadband coupler designs47 trade bandwidth for fabrication sensitivity and are in practice very sensitive to process variations, meaning larger splitter errors σ ≳ 5% are common. In this moderate-error regime, error correction alone is not sufficient and the network shows reduced accuracy, a problem that becomes more pronounced as the size N increases. Moving to the 3-MZI architecture overcomes this limitation, enabling effectively error-free inference  even out to very large splitter errors σ ≈ 10–15%, far beyond what is likely to be encountered in practice.This accuracy is plotted in Fig. 48, errors are correlated in practice. This is especially true for broadband couplers based on multimode interference (MMI)43, subwavelength gratings45, and asymmetric designs47, all of which are highly dependent on the device geometry, which can vary slightly from run to run. Moreover, even with perfect 50:50 couplers, the splitting ratios are still wavelength-dependent. Operating the mesh away from its design wavelength leads to correlated device errors, so sensitivity to these errors is closely tied to the operational bandwidth of the device.For generic, uncorrelated component errors the 3-splitter MZI is well-suited. However, since the correlation lengths of process variations tend to be larger than a single MZIμ for all splitting ratios: α = β = μ. In a standard MZI, the bar-state forbidden region (around s = ∞) disappears since ∣α − β∣ = 0, while the cross-state region  remains in place  mesh by performing the nulling procedure on target unitaries, obtaining ind (Eq. ):4\documses (Eq. ), so thaα − β∣ that arise from local fluctuations in waveguide dimensions. The effect of such errors is analyzed in Supplementary Section α − β∣ ≪ μ and differential errors are insignificant for mesh sizes up to at least N = 512.Ultimately, the scalability of the MZI+X architecture is limited by differential errors ∣σk is a Pauli matrix. For the cross state (θ = 0), the errors μ add up constructively, while for the bar state (θ = π), they cancel out . Most crossings in large meshes are close to the cross state, which leads to constructive addition of the errors in the standard MZI mesh. However, for the MZI+X, the input ports of each MZI are exchanged, so the physical MZIs are close to the bar state where the errors cancel out. The resulting uncorrected matrix error is (see Methods):53. All beamsplitters are dispersive, and this dispersion leads to a correlated wavelength-dependent splitter error, which can usually be expanded to first order μ ≈ (dμ/dλ)Δλ. Two important wavelength-dependent figures of merit are (1) the tuning range, which refers to the range of λ over which the mesh can be programmed to a given accuracy, Fig. As an added bonus, the MZI+X design also reduces the effect of errors in the absence of correction. To see how, we can make an analogy to Bloch-sphere rotations. The transfer matrix of a standard MZI is (up to a phase factor) the product of four rotations:mentclass2pt{minimS21; scattering into the forward-facing port leads to a perturbation γ ≪ 1, and the forbidden region is still far from s = 0. In-plane crossings in silicon can achieve sub-40 dB crosstalk suppression (γ < 0.01) with insertion losses well below 0.1 dB58. Unlike directional couplers, crossings are inherently broadband; the insertion loss and crosstalk depend only very weakly on λ, so any crossing imperfections can be treated as (correctable) wavelength-independent errors that do not affect the bandwidth enhancements of the MZI+crossing scheme. In addition to the forward-scattered light, a 90° crossing will scatter light into the backward-facing port. Back-reflected light can be subsequently reflected in other crossings, leading to a spurious signal that interferes with the forward-propagating light. Provided that the phases of reflected beams are random, these add in quadrature: with amplitude γ2 and O(N2) scattering paths, we expect this to induce an O(Nγ2) error, which may be uncorrectable and set a limit on scaling. However, if this effect is small, gradient-based methods or iterative self-configuration may enable correction of these errors.Real crossings have a small amount of nonzero crosstalk, quantified by the S-matrix element 59, and “perfect” photonic circuits, which require a larger number of photonic and electronic components24. This paper has introduced two designs for programmable circuits that strike a tradeoff between these extremes, as shown in Fig. As photonic circuits grow larger, error tolerance becomes increasingly important. Many techniques exist to manage hardware errors, but all involve a tradeoff between accuracy and complexity. At opposite poles lie “zero-change” error correction, which has limited scalabilitydecreases with size. Our design choices are motivated by the elegant theory of self-configuration by matrix diagonalization17, where splitting ratios are set to successively zero the off-diagonal elements of the target unitary. By visualizing the MZI state on the Riemann sphere, we can intuitively understand the increased error robustness of our designs in terms of “rotating” the forbidden regions away from the peak probability density. This leads to a several-orders-of-magnitude reduction in post-correction errors compared to the standard MZI mesh. The ability to achieve near-perfect and freely scalable MZI meshes with less complexity than the MZI-doubled designs24  removes a major roadblock to the realization of very-large-scale nanophotonic systems.The main insight from this paper is that, by adding a single passive component (either a splitter or a waveguide crossing) to the MZI, we can recover behavior that is asymptotically perfect—that is, the average normalized matrix error 32. Likewise, the near-cancellation of correlated errors in the MZI+crossing architecture explains the 62 may allow this imperfect cancellation to be made exact, further improving the bandwidth (and multiplexing capabilities) of linear photonics.An interesting direction for future work is to explore to what extent multiport interferometers can be made robust to imperfections in the absence of error correction. For example, previous studies of 3-MZI splitters have noted a wavelength-independent coupling ratio for certain parameter choicess = T11/T12. Specifically, any two unitaries are equivalent up to output phases, i.e., s can be visualized on the Riemann sphere /(1 + z) (which inverts to x + iy = 2s/(1 + ∣s∣2), z = (1 + ∣s∣2)/(1 − ∣s∣2)).A generic 2 × 2 complex-valued matrix has eight degrees of freedom, and a 2 × 2 unitary has four. However, the space of 2 × 2 unitaries can be divided into equivalence classes based on the splitting ratio ere Fig. , where tL2) norm Ordinarily, the distance between matrices is defined as the Frobenius  map to the standard polar coordinates, i.e., A common parameterization is X . Each nulling step zeros a single element, increasing the size of the zeroed-out off-diagonal region. Nulling steps are performed in a particular order to ensure that zeroed-out elements remain zero after all subsequent steps17. In a given step, if nulling cannot be achieved perfectly, the “zeroed-out” region of matrix X is left with a residual of magnitude:s is the closest physically realizable value, and P(s) of target splitting ratios, a function of the distribution of target unitaries, and (2) the locations and sizes of the forbidden regions, a function of the specific mesh implementation . For the Haar measure, P(s) depends on an MZI’s location in the mesh; for a given Tmn it takes the following form29:Pmn(s)dμ(s) = 1. Note that, under Eq.  ≈ P(s±) inside each The forbidden regions U31 and the distribution of hardware errors α, β. We calculate the mean residual 〈r2〉 by averaging Eq. (P(s). This is simplified in the case of small hardware errors, because the forbidden region is correspondingly small and where we can assume P(s) is approximately constant:qmn = 〈∣u∣2 + ∣v∣2〉, where  are the highlighted in green in Fig. qmn = (n + 1)/(N + 1 − m).The normalized matrix error 19 and global optimization10 (which has a much longer convergence time), is presented in Supplementary Section A detailed description of the nulling algorithm, including a comparison to the local methodα〉rms = 〈β〉rms = σ, the forbidden regions are  symmetric, with moments For the uncorrelated Gaussian perturbation model with 〈s = 0 term, where Pmn(0) = n/4π. Considering only this term, we calculate:N. Likewise, the top forbidden region dominates the matrix error, so we evaluate Eq. , so we cannot convert the sums to integrals. We first perform the summation over n, which converges rapidly due to the 1/2n+1 factor (approximating the upper bound to infinity because of the rapid convergence), followed by summation over m. We find the normalized error:γe ≈ 0.5772.For the MZI mesh, the coverage expression Eq.  is dominuate Eq.  includinwing Eq. , the covying Eq. , the mea in Eqs.  arise beα = β = μ. In this case, there is only one forbidden region, which for the MZI is centered at s+ = 0, with R+ = 4μ. The coverage and matrix error for the standard MZI can then be calculated from Eqs. (s+ → ∞. Only the MZIs in the bottom row of the triangle (n = 1) contribute to the sums in Eqs. α = β = μ in Eqs.  and 14)α = β = μ in Eqs.  vanishess+ = ∞, with R+ = 4μ. Only the MZIs in the bottom row contribute to the sum, because the probability distribution Eq. , the norm of the matrix error is:θ = 0. For the MZI+crossing Δλ, the tuning range and bandwidth can be calculated from the expressions for As before, we use the residual formula Eq.  to calcution Eq.  vanishesing Fig. , we findmentclass2pt{minimN is the DNN’s inner layer size. The signal from this window (N input neurons) passes through two optical layers, with unitary connectivity realized with rectangular meshes. The activation function at the inner layer is realized electro-optically: a fraction of each output field is tapped off and sent to a detector, whose photocurrent modulates the remaining output light39, implementing the activation function:α is the power tap fraction, g is the modulator response, and ϕ is the phase at zero power. Here, we choose α = 0.1, g = π/20, and ϕ = π, so that f(E) approximates a leaky ReLU in the right power regime. Models of sizes N = 64 and N = 256 were trained using the NEUROPHOX package40.The optical neural network model is based on the architecture described in ref. 63. Figures All simulations were performed using the MESHES package, an open-source simulator for feedforward photonic circuits that can account for hardware imperfectionsSupplementary InformationPeer review file


With the aim of investigating the response of concrete to the dual effect of accidental fire high temperatures and possible induced impacts due to falling fragmented or burst parts or objects, an experimental work is conducted in this study to explore the influence of exposure to temperatures of 200, 400 and 600 °C on the responses of concrete specimens subjected to impact loads. Cylindrical specimens are tested using the recommended repeated impact procedure of the ACI 544-2R test. Three concrete mixtures with concrete nominal design strengths of 20, 40 and 80 MPa are introduced to represent different levels of concrete strength. From each concrete mixture, 24 cylinders and 12 cubes are prepared to evaluate the residual impact resistance and compressive strength. Six cylindrical specimens and three cubes from each concrete mixture are heated to each of the three levels of high temperatures, while the other six cylinders and three cubes are tested without heating as reference specimens. The test results show that the behavior of impact resistance is completely different from that of compressive strength after exposure to high temperatures; the cylindrical specimens lose more than 80% of the cracking and failure impact resistance after exposure to 200 °C, while impact resistance almost vanishes after exposure to 400 and 600 °C. Concrete compressive strength is found to be effective on the unheated impact specimens, where the higher-strength cylinders retain significantly higher impact numbers. This effect noticeably decreases after exposure to 200 and 400 °C, and vanishes after exposure to 600 °C. Concrete is one the construction materials that is known for its adequate safe endurance when subjected to high-temperature exposures. Compared to metallic constructions, concrete structural members can last for a longer time under the catastrophic destruction of accidental fires. However, the degradation of the material’s microstructure is inevitable, which is directly translated into strength losses and unfavorable serviceability issues . TherefoConcrete is significantly affected by high-temperature exposure when the temperature exceeds 400 °C; below this temperature, strength losses are recoverable and damages can be controlled, and the rehabilitation of the structure becomes the favorable choice. When concrete is subjected to temperatures lower than 200 °C, its compressive strength keeps close to the original unheated strength, either slightly higher or slightly lower ,2. The sImpact resistance is the ability of the material or the structural member to withstand low- or high-speed impact forces within a very short period of time. The impact resistance of concrete can be evaluated using different testing techniques. One of the most common test methods to evaluate the impact performance of concrete is the drop-weight impact test. In this test, a specific mass is left to drop freely from a specific height and the structural response of the tested element is recorded in terms of impact force, deflection, vibration and possibly strain. Such a type of test is an expensive one and is intended to be performed on moderate- to large-scale test structural elements (beams or slabs), and is a very useful technique to study structural response under the effect of heavy falling objects ,27,28,29The ACI 544-2R  repeatedAs introduced in the brief literature survey, the ACI 544-2R has been adopted recently by several research works to cost-effectively explore and compare the impact energy absorption capacity of concrete mixtures. The simple test procedure is used to evaluate the effect of the incorporation of different materials on the response of concrete under impact loads. However, all of the reviewed works considered the normal ambient environment conditions, while very limited research works ,66,67,68The experimental work of this research included preparing three concrete mixtures with three levels of design grades: M20, M40 and M80. These concrete mixtures were designed to achieve 28-day compressive strengths of 20, 40 and 80 MPa, respectively. The per-cubic meter weights of cement, water, fine aggregate and coarse aggregate of the three concrete mixtures are listed in 2/kg. Crushed gravel with a maximum size of aggregate of 12.5 mm with the gradings shown in ® ViscoCrete 5930-L  super plasticizer to achieve the required mixture workability, while there was no need for this material in the M20 and M40 concrete mixtures.Ordinary Portland cement type 42.5 from Mass Cement Plant, Sulaimaniya, Iraq was adopted in all concrete mixtures with a specific gravity of 3.15 and a specific surface of 368 mThe furnace shown in The repeated impact testing procedure recommended by the American Concrete Institute ACI 544-2R  was follPrevious works ,62,76 ha2 into CaO, which was accompanied by the drying and shrinkage of cement gel particles due to the liberation of water, which increased the porosity and deteriorated the strength [The compressive strength test was the only mechanical control test adopted in this study to discuss the quality of the concrete mixtures. As preceded in the previous section, cube specimens were cast, cured and heated under the same conditions of the impact cylindrical specimens. The responses of the compressive strength of each of the three concrete mixtures with low, normal and high design strengths with temperature are shown in strength . Becausestrength ,7,79.The weight loss of the cube specimens shown in The effect of the design strength of the impact specimens on their cracking and failure impact resistance decreased with temperature increase, as explicitly revealed in The deterioration of the impact resistance of the three concrete mixtures M20, M40 and M80 with temperature is separately depicted for Ncr in The excessive deterioration of the repeated impact resistance of the heated specimens is attributed to the induced stresses and stress distribution in the microstructure under the effect of each single impact blow. The compressive impacts concentrated on the center of the specimen’s top surface via the steel ball were diagonally spread across the subsurface layers as multidirectional tensile stress waves that affected the microstructure within a very short period of time. Hence, tensile shocking waves were transferred along all diagonal directions of the specimens. As the heated specimens were already weakened due to the induced thermal stresses that affected the strength of the cement paste, aggregate particles and the bond between them, the action of the shocking tensile waves noticeably accelerated the microstructural degradation and the specimen fracturing. It should be mentioned that the behavior of heated concrete under tensile stresses (splitting tensile test and bending test) is different from that under compressive stresses; several previous studies have reported a faster deterioration of the tensile strength of concrete compared to compressive strength ,7,14,80.It should be noticed that although all concrete mixtures strongly deteriorated after high-temperature exposure, the higher strength concrete exhibited higher percentage losses than the lower-strength concretes. Samples of the final patterns of the tested cylindrical specimens are shown in Oppositely, the specimens heated to higher temperatures were noticeably cracked before testing due to the effect of temperature loss and the other chemical changes occurred within the concrete microstructure after exposure to 400 and 600 °C. Therefore, the surface and the interior structure of the specimens were weakened to a degree that changed their failure patterns to those shown in Regardless of their original strength, the compressive strength of the concrete cubes exposed to a temperature of 200 °C was in general higher than the original unheated strength, where a strength gain of 2.5 to 9% was recorded for the tested specimens. On the other hand, exposing the cubes to a temperature of 400 °C decreased the strength by no more than 20%, while a strength reduction of not less than 40% was recorded for cube specimens heated to 600 °C;The impact resistances of the impact specimens increased with the increase in the mixture’s compressive strength. Compared to the M20 specimens, the cracking and impact numbers of the M40 specimens  increased by approximately 72%, while the M80 specimens (with an 80 MPa design strength) retained higher cracking and impact numbers by more than 460%, compared to the M20 specimens;Owing to the degradation of the cement matrix, aggregate particles, and the interfacial bond, the effect of the design compressive strength on the impact resistance of the heated specimens decreased as temperature increased. For instance, the percentage increase in the failure impact resistances of the M80 specimens over the M20 ones decreased from 464% before heating to 140 and 68% after exposure to 200 and 400 °C, respectively. The influence of the original strength faded after exposure to 600 °C, where all concrete mixtures cracked and failed after approximately one impact blow;Owing to the different types of induced stresses, the deterioration in the impact resistance was much higher than that of the compressive strength. The specimens lost more than 80% of their cracking and failure impact resistances after exposure to only 200 °C, while the impact resistance was almost vanished after exposure to 600 °C. For instance, the failure impact numbers of the three concrete mixtures decreased by 80.1 to 91.6%, 92 to 97.6% and 97.8 to 99.5% when exposed to 200, 400 and 600 °C, respectively;Exposing the impact cylindrical specimens to 200 °C did not cause noticeable thermal effects on the surface of the specimens, while a noticeable thermal cracking was visually clear for specimens heated 400 °C, and was more obvious on the surfaces of specimens heated to 600 °C. Therefore, the failure patterns of the cylindrical specimens exposed to 200 °C were similar to those of unheated cylinders with two, three or four diagonal cracks and insignificant central fracturing. This was different for specimens heated to 400 and 600 °C with larger surface fracturing and non-uniform surface cracking;The failure of specimens heated to 400 and 600 °C was not affected by the original concrete strength of the specimens, while this effect was clear for the unheated specimens. As the higher-strength specimens (M80) contained higher amounts of cement, their microstructures were stiffer with lower porosity compared to the lower-strength specimens. As a result, the M80 specimens could withstand much higher impact blows concentrated on the central area of the top surface of the specimens, which caused a larger surface central fracturing zone compared to the M40 and M20 specimens;The available literature on this topic is very limited; therefore, we recommend extending the presented work using different concrete mixtures that include frequently used additives and fibers. For instance, the influence of cementitious materials such as silica fume and fly ash on the impact response of fired specimens could be investigated in future works. Other concrete mixtures with high cementitious material content such as high-performance concrete might behave differently under such kinds of dual thermal and impact loading.With the aim of evaluating the residual repeated impact responses of different grade concrete after exposure to high temperatures, cylinders and cube specimens from three concrete mixtures  were tested before and after exposure to 200, 400 and 600 °C. From the experimental records obtained in this study and within the limitations of the adopted parameters, the following conclusions can be drawn:


In IgG4-related disease, the relationship between pathological findings and relapse has not been well established. This study aimed to identify the clinical and pathological predictors of disease relapse in IgG4-RD.n = 71) were enrolled between January 2011 and April 2020; all cases were pathologically confirmed. The clinical and pathological features were recorded in a database at baseline and each follow-up visit. Patients were followed up at least once a month via outpatient clinic examinations and telephone calls. Univariate and multivariate Cox regression analyses and receiver operating curve (ROC) analysis were used to identify the predictors of disease relapse and to assess their predictive value.Patients with newly diagnosed IgG4-RD , IgG ≥ 20.8 g/L , IgG4-RD responder index (RI) ≥ 9 , and severe IgG4+ plasma cell infiltration . A prognostic score developed using three of the identified predictors  showed good value for predicting impending relapse .Over a median follow-up of 26  months, 3/71 (4.2%) patients died. Of the remaining 68 patients, 47 (69.1%) patients had achieved clinical remission and 21 (30.9%) had suffered relapse at the last follow-up. The independent predictors of relapse were IgG4 ≥ 6.5 g/L  ≥ 9, and severe IgG4The online version contains supplementary material available at 10.1186/s13075-022-02792-z. Among 68 patients with IgG4-RD, 21 (30.9%) suffered relapse during continuous treatment.+ plasma cell infiltration.Independent predictors of relapse were high IgG4, IgG, and IgG4-RD RI and severe IgG4A prognostic score developed using three of the identified predictors showed good predictive value.+ plasma cell infiltration, storiform fibrosis, and obliterative phlebitis [IgG4-related disease (IgG4-RD) is a newly recognized systemic autoimmune disease that can involve the pancreatobiliary tract, retroperitoneum/aorta, head and neck region, and salivary glands . The etihlebitis , 3.Relapse is common in IgG4-RD, occurring in 24–54% of patients after reduction of glucocorticoid dose . The 2-yAlthough the pathological diagnostic criteria for IgG4-RD have been established –21, the A total of 71 consecutive patients with newly diagnosed IgG4-RD were enrolled for this prospective study between January 2011 and April 2020 at the Zhongshan Hospital of Fudan University, Shanghai, China. Some patients visited our department directly while others were referred to us from various departments such as gastroenterology, pneumology, otolaryngology, general surgery, and urology. The patients were first classified as probable or definite IgG4-RD using the 2011 Japanese Comprehensive Clinical Diagnostic Criteria . Those iEnrolled patients were followed up through outpatient visits and/or telephone calls every month until disease relapse, death, or the end of the study (November 2020). All patients completed at least 6 months of follow-up. Demographic data, clinical features, laboratory examination results, pathological findings, imaging data, medical treatments, and disease outcomes were recorded in a database at baseline and each visit.This study was approved by the Ethics Committee in Zhongshan Hospital of Fudan University (B2013-115(3)) and conformed to the ethical guidelines of the 1975 Declaration of Helsinki. Written informed consent was obtained from all patients.The immune scatter turbidity method was used to detect the serum IgG4 level. All tests were performed using a Siemens BN II automatic protein analyzer in our hospital laboratory, with a limit of 0.08 g/L.For the first 3 years, all patients underwent salivary gland ultrasound once every 3 months, chest and abdominal computed tomography (CT) scan once every 6 months, and/or head, neck, and abdominal magnetic resonance imaging (MRI) once every 6 months. Additional imaging examinations were performed if there was suspicion of reactivation. After the first 3 years, ultrasound was performed once every 6 months and CT once a year.+ and IgG+ plasma cells were determined by manually counting the cells in five high-power fields (HPF) with a magnification of 400× under an optic microscope and calculating the average; the IgG4+/IgG+ plasma cell ratio was then calculated [A total of 75 tissue samples were collected from the 71 patients and sent to the pathology department of our hospital. Sections were stained with hematoxylin and eosin (HE), elastic tissue stains, and immunohistochemical stains (including for markers of IgG and IgG4). The immunohistochemical antibodies used were rabbit monoclonal anti-IgG4 antibody  and rabbit polyclonal anti-IgG antibody A0423, Dako). The numbers of IgG43, Dako. 2 per month), azathioprine (1–2 mg/kg/day), mycophenolate mofetil (500–750 mg twice a day), or rituximab .Treatment was started with a glucocorticoid (prednisone), with or without an immunosuppressor agent. The dosage of prednisone was 0.6–0.8 mg/kg/day for the first 4 weeks; the daily dose was then gradually reduced by 5 mg every 2 weeks in the first 3 months and by 5 mg every month during the remaining follow-up period. The maintenance dose was 0.1–0.2 mg/kg/day. Patients with risk of irreversible organ damage or signs of multiorgan involvement also received single-agent immunosuppressor therapy with cyclophosphamide (0.6/mDisease activity was monitored using the IgG4-RD responder index (RI) , measureRemission was defined as a decline in IgG4-RD RI score by 50% and reduction in glucocorticoid dose to less than 0.2 mg/kg/day without relapse throughout the follow-up period , 25–27.Relapse was defined as progressive disease or recurrence of clinical symptoms or imaging findings after remission, with or without elevation of the serum IgG4 level , 25.The following potential predictors of relapse were investigated: age, sex, medical history, clinical characteristics, laboratory findings, and pathological features.t-test, the Mann–Whitney U test, the Kruskal–Wallis test, and the chi-square test were used, as applicable, for comparison between groups. The optimal cut-off values were determined by the receiver operating curve (ROC) analysis, and the area under the curve (AUC) was used to assess the predictive value of identified factors and the combined factors. Based on the fact that heavier infiltration was observed in lacrimal and salivary glands and lymph nodes than in visceral organs [p < 0.05 was considered statistically significant. A predictive score for disease relapse was established using a multivariate Cox proportional hazard model . Both the p value and the clinical importance were concerned when the predictors were incorporated into the model [Normally distributed continuous variables were summarized as means ± standard deviation and non-normally distributed variables as medians and interquartile ranges. Categorical variables were summarized as frequencies and percentages. The independent two-sample Student’s l organs , 28, we he model , 30. StaA total of 71 patients  were enrolled. Table Over a median follow-up of 26  months, 3/71 (4.2%) patients died; the causes of death were infection (at 2 months), disease progression , and cerebral infarction (at 8 years). Of the remaining 68 patients, 13 (19.1%) received continuous glucocorticoid monotherapy, and 55 (80.9%) received continuous glucocorticoid plus immunosuppressor therapy. By the end of follow-up, 21/68 (30.9%) patients had relapsed, with a median time to relapse of 10 (6–30) months; the remaining 47/68 (69.1%) patients had sustained remission during a median follow-up of 17 (7–45.5) months. There was no significant difference in the therapy between the relapse patients and the remission patients.A total of 75 tissue samples were obtained from the 71 patients. While 67 patients received biopsy at only one site, 4 patients received both organ biopsy and lymph node biopsy. The 75 tissue samples  IgG4+ plasma cell/HPF. In 73.3% (55/75) of samples, the ratio of IgG4/IgG-positive cells was ≥40%; the median ratio was 40% (33–56%). The IgG4+ plasma cell infiltration was significantly more severe in samples from the head and neck region  than in samples from the viscera : 90 (43–200) IgG4+ plasma cells/HPF vs. 45 (20–79) IgG4+ plasma cells/HPF, respectively (p = 0.010). The number of IgG4+ plasma cells per high-power field for each organ is shown in Supplementary Table 2, Additional file Marked lymphocyte and plasmacyte infiltration was seen in all samples. All samples had >10 IgG4Obliterative phlebitis and fibrosis were seen in 30.7% (23/75) and 78.7% (59/75) samples, respectively. Other pathological manifestations are shown in Supplementary Table 3, Additional file p = 0.045), higher IgG4-RD RI (p = 0.038), higher serum IgG4 (p = 0.026), and higher serum IgG (p = 0.011) at baseline; moreover, they had significantly lower baseline serum triglyceride (p = 0.046), total cholesterol (p = 0.005), low-density lipoprotein (p = 0.030), and complement 4 (p = 0.019) levels.Table + plasma cell infiltration , and lower prevalence of lymphoid follicle formation (p = 0.048). However, the prevalence of other pathological characteristics , IgG4 ≥ 6.5 g/L , IgG4-RD RI ≥ 9 , total cholesterol < 3.56 mmol/L , serum triglycerides < 0.97 mmol/L , low-density lipoprotein < 2.09 mmol/L , and severe IgG4+ plasma cell infiltration  were all associated with disease relapse. Number of involved organs ≥ 2, C4 < 0.19 g/L, and lymphoid follicle formation were not associated with relapse.In univariate Cox regression , IgG ≥ 20.8 g/L , IgG4-RD RI ≥ 9 , and severe IgG4+ plasma cell infiltration . The Cox proportional hazard model identified three factors for incorporation into the predictive model: IgG4-RD RI ≥ 9 (p = 0.026), severe IgG4+ plasma cell infiltration (p = 0.007), and IgG ≥ 20.8g/L (p = 0.056). Though the predictor IgG was not statistically significant, it was also incorporated into the predictive model due to its importance in clinical practice [CI) of this predictive model increased from 0.736 (0.610–0.861) to 0.806 (0.695–0.917).In multivariate Cox regression Table , the facpractice . Upon adAUC (95% CI) for IgG, IgG4-RD RI, and severe IgG4+ plasma cell infiltration were 0.708 (0.572–0.845), 0.652 (0.514–0.791), and 0.712 (0.578–0.847), respectively. Thus, a predictive score was created by assigning 1 point for the presence of each of the three predictive factors; thus, the total score could range from 0 to 3. A score of ≥2 had sensitivity and specificity of 83% and 70%, respectively, for predicting the risk of relapse.Figure Figure + plasma cell infiltration. A prognostic score created using three of these risk factors  showed good value for predicting the risk of relapse.The present study aimed to identify the clinical and pathological characteristics that predicted the risk of relapse in patients with IgG4-related disease. The independent predictive factors of disease relapse included IgG4 ≥ 6.5 g/L, IgG ≥ 20.8 g/L, IgG4-RD RI ≥ 9, and severe IgG4High IgG4-RD RI score and high IgG4 level have been found to be associated with relapse in previous studies also , 32, 33.Recent studies have investigated whether the 2019 ACR/EULAR classification criteria  and the + plasma cells per high-power field was significantly higher in tissues from the head and neck than from the viscera .Previous studies on IgG4-RD have found that the degree of infiltration by IgG4-positive plasma cells differs between organs , 28, wit+ plasma cell infiltration is one of the characteristic pathological manifestations of IgG4-RD. The pathogenesis of IgG4-RD remains unknown. Th2 cytokines  production can lead to IgG4 hyperproduction in B cell. IL-21-secreting Tfh cells could help germinal center formation and promote the differentiation from B cell to plasma cell. Several studies have demonstrated that the number of plasmablasts is positively correlated with disease activity and that the appearance of distinct plasmablast clones is associated with relapse of IgG4-RD [+ plasma cell infiltration and disease activity or relapse is not well established.Marked IgG4 IgG4-RD , 37. How+ plasma cell infiltration was found to be independently associated with disease relapse. In clinical practice, based on the findings of previous studies, patients with IgG4-RD are considered to have a low risk of relapse if they have single-organ involvement, low serum IgG4 level, and low IgG4-RD RI. However, our results suggest that those with a large number of IgG4+ plasma cells in the biopsied organ should also be considered to be at risk.In this study, severe IgG4+ plasma cell infiltration) shows promise for predicting the risk of relapse. Therefore, we suggest that, for patients with a prognostic score of 2 or 3, maintenance treatment including steroid-sparing drugs is required. Meanwhile, patients with a score of 1 or 0 only need the initial course of steroids, and long-term treatment can probably be avoided.The prognostic score that we created using three predictive factors . The elevation of total IgG might be due to elevated IgG1 [The IgG4-RD RI score comprises the sum of organ sites’ scores plus the serum IgG4 concentration score . Thus, tted IgG1  and/or I+ plasma cell infiltration, and high serum IgG4 level [Zhang et al. classified IgG4-RD into two types according to the clinicopathological characteristics: a proliferative type and a fibrotic type . Some feG4 level , 39. TheIn the present study, different from our previous research , all patSome limitations of this study must be acknowledged. The sample size was small, and all patients were from Shanghai or its peripheries in east China. However, a sample size of 71 was more than the calculated sample size of 63 for this diagnostic test (if sensitivity and specificity were both 0.8 ± 0.1). In addition, a selection bias may also exist because patients who had not received biopsy or resection were excluded. Therefore, whether our findings are applicable to all patients with IgG4-RD needs to be clarified in future research. In this study, we used the 2012 version of IgG4-RD RI and not the modified IgG4-RD RI published in 2018 ; this mi+ plasma cell infiltration appear to be independent predictors of relapse. The prognostic score created using three of the identified predictors  could be a useful clinical tool to identify patients at high risk of relapse.In patients with IgG4-RD, IgG4 ≥ 6.5 g/L, IgG ≥ 20.8 g/L, IgG4-RD responder index (RI) ≥ 9, and severe IgG4Additional file 1: Supplementary Table 1. Demographic and clinical features of the patients (n = 71). Supplementary Table 2. Summary of the 75 tissue samples and the number of IgG4+ plasma cells per high-power field for each organ. Supplementary Table 3. Pathological features in the 75 tissue samples. Supplementary Table 4. Baseline patients’ characteristics stratified by relapsed status. Supplementary Table 5. The hazards ratio (HR) and diagnostic efficiencies of factors associated with IgG4-RD relapse by univariate analysis. Supplementary Table 6. The relapse rates in the patients with different prognostic score at 1, 2, 3, and 5 years. Supplementary Table 7. Relationship between the three risk factors and relapse at 3 years.Additional file 2: Supplementary Figure 1. A. Lymphocyte and plasma cell (△) infiltration ; B. storiform fibrosis  ; C. IgG4+ plasma cell ; D. eosinophilia infiltration ; E & F. obliterating phlebitis . Supplementary Figure 2. A-D. Retroperitoneum tissue (×100): A. (H&E) Marked lymphocyte and plasma cell (→) infiltration and fibrosis (△); B. (H&E) lymphoid follicle formation (→); C & D. serial sections of IgG+ cell and IgG4+ cell . E-H. Submandibular gland (×100): : E. atrophic glandular acini and glandular ducts (circle) with marked lymphocyte and plasmacyte infiltration and fibrosis (H&E); F. genetic centre formation (H&E); G & H. serial sections of IgG+ cell and IgG4+ cell . Glomerular sclerosis (circle) with lymphocyte and plasmacyte infiltration ; J. lymphocyte and plasma cell scattered within fibrosis; K. typical storiform fibrosis. I-K .


Results show that the influences of foamed concrete on the blast resistance of RC walls are jointly decided by the stress drop caused by impedance effect and exponential attenuation and the stress rise caused by high-speed impact compression. The coating thickness mainly affects the foam concrete’s fragmentation degree and stress attenuation. A lower critical coating thickness exists in foamed concrete-coated RC walls. The blast resistance of the RC wall will decrease when the coating thickness is less than that value. The lower critical coating thickness is related to the intensity of blast load and the energy absorption capacity of foamed concrete, and it can be predicted by monitoring the explosive stress and energy incident to the RC wall.How to effectively reduce the damage of frequent accidental explosions and explosion attacks to existing walls is an important concern of the blast resistance field. In the present study, the influence of the foamed concrete (density 820 kg/m The frequent accidental explosions and explosive attacks in recent years often cause large-scale damage to buildings, accompanied by huge casualties and economic losses ,2. The RFoamed concrete is a lightweight porous building material, which can be constructed by cast-in-place or masonry, with the advantages of low price, simple maintenance, and suitability for large-scale application . At presThickness is one of the important structural parameters of foamed concrete cushions, and the influence of thickness has always been a concern. Nian et al.  analyzed3, water-cement ratio 0.4) on the blasting damage of a 120 mm RC wall was studied through blast experiments, numerical simulations, and shock wave theory. The influence of coating thickness on the stress distribution on the front side, the incident energy, and the spalling size on the back side of RC walls were discussed. The research results are expected to guide the engineering application of foamed concrete cushioning layers.In this paper, the cushioning effect of foamed concrete (density 820 kg/m3) was prepared from cement, water, and foaming agent. The masses of the three materials were 800 kg, 320 kg, and 4 kg, respectively. The cement was ordinary Portland cement (P. O 42.5). The foaming agent was a kind of commercial polymer composite cement foaming agent. To produce foam, the foaming agent was diluted with water at a ratio of 1:40 by volume. The foamed concrete , the RC wall is in a critical spalling state under this working condition. Three blast experiments were carried out for three types of RC walls, namely, the wall uncoated (SW), the wall coated with 10 mm foamed concrete (10 mm FC + SW), and the wall coated with 20 mm foamed concrete (20 mm FC + SW). SW was taken as the reference that corresponds to the spall damage mode of the wall. The explicit nonlinear finite element program LS-DYNA was used to simulate the deformation and damage of the RC walls under blast loading ,20. As sAir can be regarded as an ideal gas, which was described using the NULL (MAT_009) constitutive model and the LINEAR_POLYNOMIAL (EOS_001) equation of state . The preThe initial parameters and detonation pressure of TNT explosive were described using the HIGH_EXPLOSIVE_BURN (MAT_008) constitutive equation and the JWL (EOS_002) state equation . The calAn RHT (MAT_272) model was used to analyze concrete structures subjected to impulsive loadings . Considevariants . The damaterials . The maiA PLASTIC_KINEMATIC (MAT_003) model was adopted to describe the reinforcement. This model considers the strain rate effect of materials and is suitable for calculating the deformation of beam elements under high pressure and high strain rate . The maiTable 5The CRUSHABLE_FOAM (MAT_063) model was characterized the compressibility of foamed concrete through volumetric strain . The strAs the damage mainly occurs in the mesh refinement area, the grid size of the refinement area was set as 8 mm, 10 mm, and 12 mm respectively, and the horizontal damage sizes of the foamed concrete and the RC wall for the 20 mm FC + SW wall experiment are calculated. The results are shown in When the blast load interacts with the RC wall, the wall is subjected to a compression wave on the loading surface while subjected to a tensile wave on the free surface . Given tThe initial state parameters of the impact point among the blast wave, foamed concrete, and RC wall can be calculated through the mirror inversion method . The solThe intersection points among the state lines of the blast wave, foamed concrete, and concrete represent the initial state parameters of the interface. When the materials are determined, the initial state parameters are only related to the intensity of blast load. Under the same blast load, the initial stress of foamed concrete is lower than that of concrete. When the blast load increases , the initial stress will increase. The propagation and attenuation of blast waves in foamed concrete are very complex. On the one hand, under the high-speed impact, foamed concrete will be compacted, and the transmitted stress will rise rapidly; on the other hand, the fragmentation process of foamed concrete will absorb energy and reduce stress . The thiIn the simulation results, taking the loading center of the explosion wave as the origin (tion (7) :(7)σ=σ0⋅The stresses under different coating thicknesses were dimensionless, and the attenuation law of normalized stress at different locations was fitted using Equation (7). As shown in Nian et al.  and Li eWang et al.  analyzedTian et al.  and WangThe volume of foamed concrete crushing and RC wall spalling zones was calculated according to the experimental and simulation results. The calculation results are shown in The critical coating thickness in this paper is obtained under the critical blasting spall of a 120 mm RC wall, which is the minimum thickness of the foamed concrete cushion. When a smaller stand-off or a larger charge mass is used, the critical coating thickness will increase correspondingly due to the increase of incident stress and energy . In addi3, water-cement ratio 0.4) on the blast resistance of a 120 mm RC wall. The results of this work can provide a reference for the blast resistance designs of any type of RC walls and panels. The main conclusions are as follows:(1)The influences of foamed concrete coating on the blast resistance of RC walls include: Due to the impedance of foamed concrete is low, the initial stress of the structure is reduced; after high-speed compression, foamed concrete enters the compacted state, and the stress on the surface of RC wall increases significantly when the coating thickness is insufficient; and the fragmentation process of foamed concrete absorbs the energy of stress wave, and the transmitted stress gradually attenuates.(2)Coating thickness is one of the important factors that affect the attenuation of the blast wave in foamed concrete. The attenuation of stress is exponential with the increase of coating thickness. The attenuation index increases with the increase of load intensity.(3)Foamed concrete coated RC wall has a lower critical coating thickness. When the thickness of foamed concrete is less than that value, the blast resistance of the RC wall decreases; when it is greater than that value, the blast resistance of the RC wall is gradually improved as the coating thickness increases. The lower critical coating thickness can be predicted by monitoring the explosive stress and energy incident to the RC wall.(4)For the given 120 mm RC wall, the lower critical thickness of the foamed concrete coating to enhance the blast resistance is 15 mm. In the blast resistance design, the coating thickness of foamed concrete should not be less than the lower critical thickness, and the optimum coating thickness can be determined by comprehensively considering the blast resistance, economy, and space.This paper studied the influence of the coating thickness of foamed concrete (density 820 kg/m