Resistance Model Study On Spherical Cavity-Expansion Model For The Penetration Of Reinforced-Concrete Targets

Being as the important anti-impact protective material,reinforced-concrete is widely used in civil buildings and military infrastructures,such as building construction,dam,protective structure,weapon and ammunition dumps,etc.When these important structures are targeted,it is the main concern that how to effectively destroy them or how to perform their protective functions.Different from plain concrete,the penetration resistance of the projectile during the penetration process should be determined by both the concrete and reinforcing bars.In general,the strength of reinforcing bars and mesh spacing also must affect the final results of penetration/perforation.In summary,although some different analytical models had been established on the penetration of the reinforced-concrete targets,most of them treated the reinforced concrete as an equivalent plain concrete.Even if some scholars considered the effects of the restriction effect of reinforcing bars and the direct-impact resistance,a convincing,effective and reliable research method still has not been established for the limitation of models.Based on the dynamic cavity expansion model,the theory model,numerical simulation and penetration test have been done for reinforced-concrete target in this paper,the main contents includes:Firstly,the factor of reinforcing bars is introduced into the dynamic cavity expansion theory.Based on the elastic-plastic response penetration model of plain(i.e.,unreinforced)concrete proposed by Forrestal and Tzou,a dynamic spherical cavity-expansion penetration model for reinforced-concrete targets is developed with the consideration of the circumferential restriction effect derived from reinforcing bars in the crushed region.And the results show that the present theoretical model has inclusiveness to the plain concrete model of Forrestal and Tzou.Then the theoretical solution and simplified calculation formula of cavity radial stress for the incompressible and compressible reinforced-concrete are achieved by introducing the reinforcement ratio,i.e.,the volume fractions of rebar in the concrete targets.When the volume reinforcement ratio is 6%,the increment of radial stress reaches 14.4%and 9.91%for the incompressible and compressible model,respectively.The radial stress increases with the increasing reinforcement ratio,which indicates that the the reinforcing bars has restriction effect on the concrete,meanwhile,the increase of the radial stress becomes larger with the increasing of cavity expansion velocity.The main function of reinforcing bars in concrete is to sustain tension,so it has strong constraint effect on the concrete in cracked region.In order to improve the penetration model,an improved dynamic cavity expansion model includes the restriction effect of reinforcing bars in cracked region has been established.And the theoretical solution of cavity radial stress for the incompressible and compressible reinforced-concrete are achieved.The results shows that:the radial stresses of elastic-cracked-crushed model are smaller than that of elastic-crushed model at low initial velocity,this is consistent with the results of plain concrete.Combine with the analysis of concrete strength and reinforcement ratio,the engineering model on the penetration of reinforced-concrete targets was constructed.Compared with the experimental data and empirical formulae,the penetration resistance model of reinforced-concrete target can better reflect the two important characteristic indexes:the acceleration time and penetration depth of the projectile during the penetration process.In the actual penetration problem,the projectile diameter is generally greater than the spacing of the reinforcing bars,the projectile inevitably hits the reinforcement directly during the penetration process.Therefore,the resistance model of the projectile directly hitting the steel bar in the cavity region was established,and the engineering analytical model of the penetration resistance of the reinforced-concrete target is obtained.A damping function is presented to describe the restriction effect of single layer reinforcing bars on surrounding concrete,and thus the penetration resistance calculation model of multi-layers reinforced-concrete targets is established.Compared with the test data of penetration depth,the validity of the theoretical model is verified and further discussed.Later,in view of the response regions of concrete,formed during penetration,have important significance for the penetration resistance and concrete damage.Based on the existing theoretical model of dynamic cavity expansion for reinforced-concrete,the calculation method of the region size in concrete at different speeds is proposed,and the influence of the reinforcement ratio and the concrete strength on the size of each region is discussed.The LS-DYNA is used for the simulation of rigid projectile penetration into concrete target.Based on the two threshold value of concrete ultimate compressive strain and ultimate tensile strain,the cavity expansion response regions of concrete target are identified and the size of each concrete response region in penetration process is obtained.The effect of the volumn ratio and spacing of steel on the crushed and cracked regions are analyzed.Last,Test of 156mm caliber oval projectile penetrating into reinforced-concrete target is carried out.With the pre-arranged pressure sensors,the pressure of concrete,at different positions of the target,were obtained during the penetration.Combined with numerical simulation,the damaged region of concrete and the stress states of steel bars at different positions are analyzed,which provides some support for the hypothesis of the previous theoretical analysis.Considering the meso-scopic structure of concrete,the reason and possible affecting factors of ballistic trajectory deflexion of rigid projectile penetration into concrete target are analyzed.Regarding the deflection angle of projectile as an index,the quantitative discussions on the influence coming from the meso-scopic factors of concrete(aggregate random distribution,aggregate strength,mortar strength,etc.),the ratio of projectile diameter/largest aggregate diameter and the striking velocity of projectile are conducted.According to the analysis of the ratio of projectile diameter/largest aggregate diameter,it concludes that the meso-scopic and homogeneous FEM models may be applicable for the different cases of concrete penetration simulation,respectively.