Damage analysis of POZD coated square reinforced concrete slab under contact blast

Wei Wng ,Qing Huo ,Jin-cho Yng ,Jin-hui Wng ,Xing Wng ,Wei-ling Go

a Key Laboratory of Impact and Safety Engineering,(Ningbo University),Ministry of Education,Ningbo,315211,Zhejiang,China

b Institute of Defence Engineering AMS,PLA,Luoyang 471023,China

c Institute of Advanced Energy Storage Technology and Equipment,Ningbo University,Ningbo,315211,Zhejiang,China

Keywords:Contact exposion Square reinforced concrete slab POZD coating Numerical simulation

ABSTRACT High efficiency,environmental protection and sustainability have become the main theme of the development of the protection engineering,requiring that the components not only meet the basic functions,but also have chemical properties such as acid and alkali corrosion resistance and aging resistance.Polyisocyanate-oxazodone(POZD)polymer has the above characteristics,it also has the advantages of strong toughness,high strength and high elongation.The concrete slab sprayed with POZD material has excellent anti-blast performance.In order to explore the damage characteristics of POZD sprayed concrete slabs under the action of contact explosion thoroughly,the contact explosion test of POZD concrete slabs with different charges were carried out.On the basis of experimental verification,numerical simulation were used to study the influence of the thickness of the POZD on the blast resistance of the concrete slab.According to the test and numerical simulation results that as the thickness of the coating increases,the anti-blast performance of the concrete slab gradually increases,and the TNT equivalent required for critical failure is larger.Based on the above analysis,empirical expressions on normalized crater diameter,the normalized spall diameter and normalized spall diameter are obtained.

1.Introduction

Disasters such as terrorist attacks and large-scale industrial explosions have always been potential threats to the people's wellbeing.At the same time,they have also launched new challenges to protection projects.Traditional concrete is widely used in various building structures due to its low cost.However,traditional concrete has many disadvantages,such as weak tensile strength,poor toughness and high brittleness.Many researchers have been looking for ways to improve the blast resistance of concrete components.

Concrete slab components are not only the main force-bearing components of the building structure,but also the primary target of various terrorist attacks and military strikes.Therefore,researchers from various countries have never stopped exploring how to improve the blast resistance of typical components like concrete slabs.Li et al.[1,2]used ultra-high performance concrete and ordinary concrete to conduct contact explosion tests.Through the quantitative analysis of the spalling distribution and size of concrete slabs of different materials,an empirical method for evaluating the anti-blast performance of concrete slabs is proposed.Morishita et al.[3,4]investigated the influence of the arrangement of steel bars,concrete strength and charge on the damage degree of concrete slabs under contact explosion.Based on the test results,a standard for evaluating damage levels was established.Yamaguchi et al.[5,6]expected to achieve the purpose of improving the antiblast performance by adding polyethylene fiber to concrete,from the perspective of reducing reflected tensile waves.The results showed that PEFRC can improve anti-explosion by reducing the spall damage.Through the analysis of the test data,it is proposed a formula can evaluate the pit depth of the PEFRC board under thecontact explosion load is established.Ichino et al.[7]investigated the blast resistance of two-stage concrete(TSC)panels by contact explosion tests,and the failure mode under different maximum diameter of coarse aggregate and type of coarse aggregate conditions,as well as the relationship between the critical spalling amount and the thickness of the plate.Feng et al.[8]modified the parameters of the original Karagozian and Case concrete(KCC)model in LS-DYNA,then the dynamic response of rubberized concrete under explosive load is studied by numerical simulation.Maazoun et al.[9]based on the explosion test,then a new method was used to study the explosion resistance of carbon fiber reinforced polymer concrete slabs.Yu et al.[10]conducted a contact explosion test of basalt fiber-reinforced polymer(BFRP)bar reinforcement concrete slabs under different equivalents of TNT,according to the test results,the damage level is divided,and the damage threshold is compared with the existing empirical formula.

Lu and Silva[11,12]studied the feasibility of using new composite materials to improve one-way reinforced concrete slabs by using carbon fiber and steel fiber reinforced polymers to reinforce concrete slabs.Ohkubo[13]and Wu[14]investigated the reinforcement effect of fiber sheets on concrete slabs by tests,the results show the blast resistance of reinforced slabs is significantly improved.Wang[15,16]studied the influence of geometric effects on the damage degree of the slab by the contact explosion test of concrete slabs of different sizes.Based on the experimental results proposed that the damage error caused by the geometrical effect relative to the prototype can be corrected.In recent years,powerful numerical simulation technology has been applied to simulate the dynamic response of reinforced concrete under explosive loads[1,17—19].

Bending shear failure and spalling failure are common failure modes of reinforced concrete structures under explosive loads.When the failure mode is bending failure,the reinforced concrete structure will appear steel bar yield fracture and concrete crushing.in this process,a large amount of energy will be absorbed,thereby reducing the damage to personnel and equipment,so bending damage is the most desirable for people.Low and Hao[20]studied the shear and bending response mechanisms of singledegree-of-freedom concrete slabs under explosive loads with two loosely coupled SDOF systems.

Concrete spalling is another failure mode of concrete slabs.McVay[21]studied the influence of factors such as plate thickness and proportional distance on concrete spalling by a large number of experiments,on this basis,an empirical formula for predicting concrete spalling was established according to the test data.In the UFC guidelines[22],An example were taken into to analyze the critical load of concrete structure spalling when resisting the explosive load in detail,and established concrete spalling failure criteria.Foglar and Kovar[23]studied the influence of fiber content and concrete strength on the blast resistance of large-size reinforced concrete slabs with test and numerical simulation,the research results show that fiber-reinforced concrete has excellent anti-blast performance.However,when comparing the test data with the UFC guidelines,they found that only ordinary reinforced concrete slabs were consistent with the peeling curve and failure curve of the UFC guidelines.

With the continuous advancement of material technology,new composite materials with excellent properties have begun to attract people's attention.In order to improve the resistance of the structure under explosive loads extremely,a large number of researchers have begun to get involved in the field of new material reinforcement[9,24—28].Because of the good ductility,toughness and strength of polyurea material,the use of polyurea coating to strengthen concrete members can make up for the shortcomings of concrete,thereby improving its anti-blast performance significantly[25,29].Shi et al.[26]studied the anti-blast performance of polyurea-woven glass fiber mesh composite reinforced RC slabs by experiments and numerical simulations,the results show that because of addition of woven glass fiber mesh,enabling explosive load transferred immediately,thereby transforming the concrete slab from shear failure to bending failure,in that way,which improved its anti-blast performance effectively.Polyurea material has broad application prospects in improving the blast resistance of concrete components.However,there are few reports on Polyisocyanate-oxazodone(POZD)polymer coated square reinforced concrete slabs under contact explosion.

In order to study the mechanism of Polyisocyanate-oxazodone(POZD)polymer in improving anti-knock performance,This paper used 2000 mm×2000 mm×150 mm concrete slabs to carry out a contact explosion test.Before the start of the test,different thicknesses of POZD polymer will be sprayed on the back of each concrete slab.The experiment was carried out by placing 0.4 kg—3.6 kg trinitrotoluene on the center point of the sprayed POZD polymer concrete slab.According to the test results,the influence of the coating thickness on the pit size of the front blast surface,the peeling area of the back blast surface and the diameter of the punching hole is analyzed.At the same time,on the basis of experimental verification,numerical simulation is used to supplement the experimental conditions.Based on the above analysis,an empirical formula for predicting the size of the opening pit on the front blast surface,the spalling area of the back blast surface,and the diameter of the punching hole were established,providing data support for polyurea materials to improve the anti-knock performance.

2.Experiment setup

2.1.Introduction to POZD coating

POZD material(polyisocyanate-polyisocyanate-oxazolone)is a new type of composite polymer material produced by the catalytic oxidation of isocyanate groups and epoxy resin.It has multiple characteristics like anti-explosion,anti-corrosion,wear-resisting,waterproof,etc.Which has great development potential in the military and civilian fields.

Polyurea is a type of polymer material formed by the gradual polymerization of isocyanate components(-N=C=O)and aminoterminated substances(-NH).The microstructure of polyurea is a block copolymer composed of alternating soft and hard segments.Its soft section is in a highly elastic state at room temperature,with low modulus,good flexibility,and a random curl shape.The hard segment is in a glassy state at room temperature,with high modulus and poor plasticity.The alternating inlay of soft and hard segments gives the material higher strength and modulus.The difference in thermodynamic properties between the soft and hard segments,as well as the forces between complex molecular chains such as hydrogen bonds,make the material present a complex multiphase system,a unique microphase separation morphology of polyurea is formed.The unique microstructure gives it the characteristics of impact resistance,aging resistance and corrosion resistance,it has been widely used in national defense and civilian fields.After special processing,polyurea can be sprayed on the substrate.Due to its special chemical properties,a uniform polyurea elastomer coating can be formed on the substrate in a short time,thereby protecting the structure.

Although the matrix of POZD material is polyurea,in addition to having the characteristics of polyurea material,it is also different from polyurea.On the basis of polyurea,POZD material has significantly improved its tensile resistance by introducing new substances into R material.The addition of linear unbranched chainand oxazolidinyl group makes POZD material not only have high ductility,high toughness and high strength,but also have the advantages of low hardness.It is in a flow-plastic state at room temperature,which provides convenience for the processing and spraying of POZD materials.The figure Fig.1 provides the scanning electron micrographs of polyurea and POZD,the fracture of polyurea material is smooth and neat,while the fracture of POZD material shows filamentous and viscous fracture.

In terms of environmental protection,as an environmentally friendly polymer material,POZD material has incomparable advantages over other polymers,mainly in the following aspects:a.Spraying POZD material adopts 100% solid content raw material formula,without any volatile ingredients;b.During the construction process,POZD materials have no organic solvent volatilization,production and construction do not pollute the atmospheric environment,and do not affect the health of production and construction personnel.It is a green and environmentally friendly coating;c.There is no volatilization of flammable and explosive substances in production and construction,which can effectively eliminate the potential safety hazards of flammable and explosive.It is a safe-to-use coating;d.After the POZD material is solidified,its basic performance is stable in a normal temperature environment,no harmful substances are volatilized,and no peculiar smell is generated.

Compared with ordinary organic polymer elastomers,POZD materials have outstanding mechanical properties.Table 1 shows the parameter comparison between POZD materials and traditional polyurea materials,it can be found from the table that the tensile strength of POZD material is 56.25% higher than that of ordinary elastomer materials,the elongation at break increased by 16.25%,the adhesion of concrete has also increased by about 17%,other performances have also been improved to a certain extent.

2.2.POZD reinforced concrete slabs

The size of the reinforced concrete base plate used in the experiment is 2000 mm×2000 mm×150 mm,among them,the steel bar HRB400Φ14@200×200 is arranged in two layers,the thickness of the protective layer is 15 mm,and the selected concrete strength grade is C40,as is shown in Fig.2.Before the start of the test,the thick t of 4 mm,6 mm,8 mm and 12 mm POZD coatings were sprayed on the back explosion surface of the base plate,number the test pieces as P1—P4 respectively.

Fig.3 shows the test device,by placing the processed test piece on the prefabricated steel support,the underside of the board is presented in an empty state.The equivalent of TNT used in the test is 0.6 kg—3.6 kg.Since the mass of each piece of TNT is 200 g,from the perspective of safety,the amount of each charge is an integer multiple of 200 g.A single piece of TNT is a cube of 25 mm×50 mm×100 mm.Choose the appropriate combination method according to the charge required for the test.The combination of charge under different working conditions is shown in Fig.4.A single piece of TNT is pasted with transparent tape and bound firmly to form a group charge placed in the geometric center of the POZD concrete slab.The height of the explosive core of the group charge from the plate is h,and the explosive is detonated by the electronic detonator.The test was carried out 5 shots in total,as shown in Table 2.

Table 1The mechanical properties of POZD materials and traditional polyurea materials.

Table 2Experimental program.

3.Numerical simulation modeling

The explicit nonlinear finite element program LS-DYNA is used to simulate the overall structural deformation of reinforced concrete slabs and local concrete slabs.It has been proved to be effective in geometric modeling and impact analysis to study its damage and damage through three-dimensional numerical models(Zhao and Chen[30],Li et al.[1,31],Wang et al.[16,32]).

3.1.Material model

The dynamic response of reinforced concrete structures under strong dynamic loads is a complicated process.Therefore,the strain rate effect must be considered when choosing a concrete constitutive model.The material model of the concrete material in this paper is the 72RW3(Mat_Concrete_Damage_Rel3)material model in LS-DYNA software.The concrete material model 72RW3 is the third version of the Karagozian and Case(K&C)model.This model contains strain rate and damage effects,uses three shear failure surfaces,and is a plastic-based material model.Which can automatically generate required parameters based on unconfined compressive strength of concrete[33,34].

Since the material model of the steel bar must have the ability to respond to strain rate sensitivity,Therefore,the reinforcement in the numerical simulation is represented by the MAT_PLASTIC_KINEMATIC material model[35].

Due to the test results of the mechanical properties of POZD materials,the strength is significantly increased at high strain rates,so the dynamic response of POZD at high strain rates should be shown out,including elasto-plastic deformation during explosion loading,and yield during fracture Guidelines.

In this study,the POZD material is represented by the MAT_-PIECEWlSE_LINEAR_PLATICITY material model of LS-DYNA,which is a multi-line segment elastoplastic material model.This model can define the fracture strain value and input the stress underdifferent strain rates.The strain curve can well simulate the response process of elastic-plastic materials.The input stress-strain curve is shown in Fig.5.This series of curves is taken from the stress-strain curve at different strain rates measured by the US Air Force Laboratory of polyuria.

Fig.1.SEM of polyuria and POZD materials(500×).

POZD material has a complicated microstructure,its dynamic response under explosive load is also more complicated.The conventional stress-strain curve is difficult to describe its dynamic response process.Since POZD material is a kind of polymer material produced by the catalytic reaction of isocyanate group and epoxy resin based on polyurea.The main difference between POZD material and polyurea is that POZD material introduces heterocyclic compounds,functional fillers and chain extenders into the R material component,which improves the tensile properties and tearing properties of the material,however,POZD materials and polyurea materials have similarities in the molecular framework structure.Therefore,a special stress-strain curve was used,this series of stress-strain curves is based on the measurement of polyurea under different strain rates by the US Air Force Laboratory[36].In this paper,the tensile failure of POZD is defined as 0.85.

Because explosives instantly release a large amount of heat and accompanied by high-temperature and high-pressure gas generation,the high-deflagration Jones-Wilkins-Lee(JWL)equation of state(EOS)is considered when selecting the material model of the explosive.Air is regarded as a non-viscous ideal gas,which is described by the NULL model and the LINEAR_POLYNOMLAL polynomial equation of state,as shown in Zhao C F[30].

Fig.3.Testing arrangement.

3.2.Finite element model

The arbitrary Lagrangian Euler(ALE)method in LS-DYNA can effectively reflect the interaction between air and structure,so that fluid and solid are coupled with each other,and can better simulate the interaction process of explosion shock wave and structure.The numerical simulation model is shown in Fig.6 and Fig.7.

The division form and size of the element play a vital role in the damage of the structure,and it also affects the calculation accuracy and time to a large extent.Therefore,in order to optimize the calculation model,two different grid sizes were used in the model according to the calculation requirements.The element size near the center area of the plate is 5 mm×5 mm,and the element size near the boundary is 20 mm×20 mm.The total number of reinforced concrete floor slabs and air model units is 2216364.The erosion algorithm was used to describe the damage of the board.After comparing the numerical simulation results with the test,the erosion criterion of 0.01 can describe the damage of the board more accurately.

This criterion is also used in Ref.[31].

3.3.Comparison of damage characteristics and numerical values with experimental results

The damage of the slab under 4 different tests are shown in Figs.8-12.It can be seen from the figure that the impact of theshock wave has caused varying degrees of damage on the explosion-facing surface of the plate.However,due to the effect of POZD coating on the back explosion surface of the slab,the degree of concrete shedding has been effectively contained,and the POZD coating on the back explosion surface played a role in the bottoming of the concrete debris and shock waves generated by the explosion.In this way,the damage of the concrete slab is greatly reduced,and the greater the thickness of the coating,the more obvious this phenomenon.

Fig.2.Schematic diagram of POZD concrete specimen.

Fig.4.Diagram of charge combination mode.

The damage results between the experiment and the numerical simulation of the 4 mm POZD coating slab P1-1 under 0.6 kg TNT charge contact explosion was shown Fig.8.Numerical simulation results were in good agreement with experimental results.In Fig.8a,the concrete slab shows punching damage after the explosion.One steel bar in each direction is exposed but not broken.In Fig.8b,the reinforced concrete slab is also damaged by the contact explosion and punching.In Fig.8c,since POZD material has high elasticity and toughness,its combination with concrete makes the slab have the characteristics of both concrete and POZD material.This special structure plays an important role in absorbing the shock wave generated by the reflected stretch wave on the back of the board.Therefore,there is no concrete spalling and collapse on the back of the concrete slab.The POZD coating only produces a certain range of bulging deformation,but it is not damaged.

Fig.5.Stress-strain curve for polyurea at various strain rates.

The numerical simulation result of the back of the slab is shown in Fig.8d.There is also small bulging deformation in the center of the coating.The slab exhibits punching damage,and the POZD coating is not damaged.A crater with a diameter of about 332 mm appeared on the explosion face of the slab while experiment is 338 mm,and the diameter of the breach area is 450 mm while experiment is 455 mm.The bulging height of the POZD coating is 65 mm while experiment is 70 mm,and the diameter of bulging area is 650 mm while experiment is 750 mm.

The experimental and numerical simulation results of the damage area of reinforced concrete slabs P2-1,P3-1 and P4-1 are shown in Figs.9-11.According to the numerical simulation results,the failure mode of the board was punching failure as shown in Figs.9b—11b,which is consistent with that shown in Figs.9a—11a.The POZD coating produced a certain range of bulging deformation and not damaged which can be observed in Figs.9c—11c on the bottom surface of the slab.The damaged area on the bottom surface of the plate calculated by numerical simulation is shown in Figs.9d—11d.The diameters of the POZD bulging areas were approximately 990 mm,1000 mm and 1150 mm.At the same time,the numerical simulation shows that the diameter of the damaged area is 680 mm,800 mm and 1000 mm,which are slightly smaller than the experimental damage diameters.The slabs all exhibit serious damaged,while the POZD coatings have no damage,the bulging phenomenon only appeared in the central area.

When the thickness of the POZD coating is 12 mm and the charge is 3.6 kg,in the test results,due to the impact of the shock wave,a pit with a diameter of about 385 mm emerged on the explosion face of the plate,as shown in Fig.12.The entire concrete slab was penetrated,and the POZD coating was torn into a nearly 113 mm hole,as shown in Fig.12 a and c.When comes to numerical simulation model,a penetration occurs in the geometric center position of the slab,the surface pit diameter is 380 mm,and a hole with a diameter of about 220 is formed at the POZD coating.Take the results of the numerical simulation and the experiment for comparison,there is no tearing of the POZD coating in the numerical simulation model.

Fig.6.Three-dimensional finite element model.

Fig.7.1/4 Three-dimensional numerical model.

Fig.8.Comparison of test results and numerical simulation results P1-1(4mmPOZD-0.6 kg TNT).

Fig.9.Comparison of test results and numerical simulation results P2-1(6mmPOZD-1.8 kg TNT).

Fig.10.Comparison of test results and numerical simulation results P3-1(8 mmPOZD-2kg TNT).

Fig.11.Comparison of test results and numerical simulation results P4-1(12 mmPOZD-3 kg TNT).

Fig.12.Comparison of test results and numerical simulation results P5-2(12mmPOZD-3.6 kg TNT).

The main reason is the unevenness of POZD spraying during the test,or there were same gaps in the adhesion between the POZD coating and the concrete slab,under the explosive load,tearing occurred from the weak point of the POZD coating.The numerical simulation results are under ideal conditions,and the unevenness of the POZD coating and the adhesion between the coating and the concrete slab are not considered,and the numerical model uses ideal fixed constraints,while the concrete is in the experiment,theslab adopts the constraint condition of approximate fixed support.Therefore,there is a certain difference in the damage effect between the numerical simulation results and the test results.Although there is a certain difference between the numerical simulation and the experimental phenomenon,the damage area appearing on the surface of the board is consistent with the experiment.In general,the numerical simulation results and experimental results of POZD coating damage have high credibility.

The experimental results and simulation results were list in Table 3.Although the damage parameters of the numerical simulation seem to be less serious than the experiment,the error is acceptable in engineering.There may be two reasons for this errors:one is that the calculation time is not enough to cause deformation.The other is the difference in boundary conditions.Through the above analysis,the parameters and simulation methods used in this article are effective.

Table 3Comparison of results from simulations and tests.

4.Discussion on POZD coating thickness

The explosive loads are generated by the explosion of 0.6—3.6 kg TNT explosive located in the center of the slabs.The thickness of the POZD coating is from 4 mm to 12 mm.After numerical simulation and contact detonation test,the damage and destruction of reinforced concrete slabs were observed in detail.As shown in Fig.13,the diameter of crater C,spalling S and breach D are measured.

According to the quantitative analysis of the measurement results,the thickness of the POZD coating has a greater impact on the diameter of crater C,spalling S and breach D.An empirical formula to determine whether the stress wave will cause concrete spalling of reinforced concrete slabs is proposed by McVay[21].Morishita et al.[3,4]proposed a formula for evaluating the damage of concrete slabs under contact explosion based on McVay's formula.The formula are defined as follows(the unit is m/kg):

Fig.13.Measuring size of external damage.

According to our previous research[37],the charge amount is another important factor for the failure mode of the concrete slab.Using formulas(1)~(3)to determine that the critical amount of concrete spalling is about 400 g.At this time,normalize the charge and plate thickness to get T/Wis 0.204 m/kg,with the concrete peeling off,the board will appear"crater and spall"phenomenon.With the increase of the charge,the concrete slab begins to transition from pitting to perforation and punching.The critical dose of perforation and punching is about 600 g,and the corresponding T/Wis 0.2 m/kg.After comparing the numerical simulation results with the test results,our judgment was verified.But the diameter of the crater C,the spall S,and the breach D are not analyzed.In this chapter,according to the function of the proportional thickness C/T with T/Wof conventional concrete under the action of contact explosion proposed by Morishita et al.[3,4],on the basis of considering the thickness of the POZD coating,the relationship between the diameter of the crater C,the spall S,and the breach D and the thickness of the POZD coating and the amount of charge were fitted respectively.Because the effect of the explosive stress wave on the surface of the concrete slab will be completed in a very short time,the coating on the back will not be able to take effect,so the size of the diameter of the crater C has nothing to do with the POZD coating.The empirical formula for predicting the diameter of the crater C proposed in this paper is applicable to the crater size of other conventional concrete slabs under contact explosion.But the spall S,and the breach D will be protected by the POZD coating.The elastic modulus and elongation of the POZD coating are higher than that of the ordinary polyurea coating.If the empirical formula established in this article is used to predict the spall S and the breach D,the predicted result will be too small.The last section of this chapter analyzes the protection mechanism of POZD coating on reinforced concrete slabs.

4.1.The diameter of the crater C

The theoretical analysis is introduced into the numerical simulation and test results.Because the explosion impact loading on the front surface of the slab is completed in a very short time,the incident wave crushes the concrete slab on the front surface in a very short time to produce pits until it is perforated.

The POZD coating on the back explosion surface cannot absorbthe incident wave in time,so the POZD coating cannot protect the concrete on the front explosion surface,that can only protect the backburst surface by absorbing the reflected stretch wave.According to the analysis results,normalize the measured crater diameter and the plate thickness T to obtain a fitting with scaled concrete thickness T/W.The fitting result is shown in Fig.14,and the fitting formula is as follows:

4.2.The diameter of the spall S

Due to the complex microstructure of the POZD coating,and at the same time,the combination of the coating and the concrete slab makes its dynamic response under the action of the explosion shock wave much more complicated than that of the simple concrete slab.POZD coating has the characteristics of tensile resistance and high toughness,which makes the dynamic response time of the concrete slab under explosive load prolonged.In this process,the coating absorbs a large amount of energy generated by the explosion,and the thicker the coating,the more energy it absorbs,and the stronger the hindering effect on the peeling of the back blast surface of the board,and the anti-explosion performance of the board is improved eventually.Based on numerical and test results,the relationship between the spall diameter and height of the POZD coating thickness with TNT mass is shown in Fig.14.It can be found that under the same conditions,the thickness of the POZD coating has a good inhibitory effect on the area of the spalling area,and the spalling area is negatively correlated with the thickness of the POZD.

According to numerical results and test results,the relationship between the normalized spall diameter S/T and the scaled concrete thickness T/Wand the POZD thickness is given by data fitting shown in Fig.15.The fitting formula is as follows:

Fig.14.Relationship between scaled concrete thickness and normalized crater diameter.

4.3.The diameter of the breach D

After combing and analyzing the results of experiments and numerical simulations,it is found that as long as T/W>0.2 m/kg,the concrete slab and POZD coating will be perforated as a whole,and the thickness of POZD and the diameter of the perforation are negatively correlated.When the thickness of the POZD coating is constant,increasing the charge will increase the diameter of the hole.The relationship between the normalized spall diameter H/T and the scaled concrete thickness T/Wand the POZD thickness is given by data fitting shown in Fig.16.The fitting formula is as follows:

4.4.Protection mechanism of POZD coating

The shock wave generated by the contact explosion propagates in the concrete slab and the POZD coating.When it propagates to the back explosion surface,a reflected stress wave will be formed.The reflected stress wave σcan be given by the incident stress waveσ[38]:

Where ρis the density of the concrete,cis the propagation speed of the stress wave in the concrete,ρand care the density of the POZD coating and the propagation velocity of the stress wave in the POZD,respectively.When the reinforced concrete slab has no POZD coating,the relationship between the reflected stress wave σon the back and the incident stress wave σas follows:

The ratio of the magnitude of the reflected stress wave under thetwo conditions η as follows:

Fig.15.Relationship between scaled concrete thickness and normalized spall diameter.

Fig.16.Relationship between scaled concrete thickness and normalized breach diameter.

Due toρc<ρc,So η<1,the addition of the POZD coating makes the reflected stress of the shock wave on the backburst surface reduced to a certain extent.

When the POZD coated concrete slab produces plastic hinge,the bending moment Mis defined as[39]:

Where Eand εare the elastic modulus and strain of the POZD coating,d is the thickness of the POZD-coated concrete slab,dis the thickness of the protective layer of the steel bar,ρis the ratio of the thickness of the POZD coating to the total thickness,andσis the maximum stress before yielding,ρis the reinforcement ratio of the concrete slab.If the reinforced concrete slab has no POZD coating,the bending moment Mwhen plastic hinge is generated is defined as:

The bending moment ratio m under the two conditions is

Since the elastic modulus Eof the POZD coating is greatly improved compared to ordinary polyurea materials,From Eq.(12),the bending moment ratio m>>1,the ability of the concrete slab to resist the bending moment of the explosive stress wave has been significantly improved.In addition,the high elasticity and strong flexibility make the POZD coating can absorb the energy generated by the explosion effectively,at the same time,it can delay the action time of the stress wave,and the POZD coating can restrain the splashing of concrete debris.

5.Conclusions

By applying experimental and numerical simulation methods to study the influence of POZD coating on the anti-explosive performance of the plate,the failure mode of the plate is analyzed based on the results of the experiment and numerical simulation.The influence law of POZD thickness and charge on the surface pit,center perforation and back fall off is analyzed parametrically.The following conclusions are drawn.

(1)On the back explosion surface of the slab,the degree of concrete falling off due to the effect of the POZD coating is effectively contained,and the POZD coating has a bottoming effect on the concrete debris and shock waves generated by the explosion.In this way,the damage of the concrete slab is greatly reduced,and the greater the thickness of the coating,the more obvious this phenomenon.

(2)The test results are basically consistent with the numerical simulation results.The numerical simulation model can simulate the damage characteristics of concrete slabs under different thicknesses of POZD coatings effectively.According to the results,the dynamic response process and damage mechanism of the POZD sprayed concrete slab were analyzed in detail.

(3)The relationships between normalized crater diameter C/T,the normalized spall diameter S/T and normalized spall diameter H/T with thickness of the POZD coating and scaled thickness of the slab are established.Based on the above analysis,empirical expressions on normalized crater diameter,the normalized spall diameter and normalized spall diameter are obtained which considered both the thickness of the POZD coating and scaled thickness of the slab.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

The authors acknowledge the financial support from National Natural Science Foundation of China(Grant Nos.11302261 and 11972201).This paper is also supported by the project of Key Laboratory of Impact and Safety Engineering(Ningbo University),Ministry of Education.The project number is CJ202011.