Investigation On The Performance Of Concrete And Reinforced Concrete Against Rigid Projectile Impacts Using 3D Meso-scale Method

As one of the most common building materials,concrete has been widely used in both civil and military fortifications.The dynamic response of concrete and reinforced concrete(RC)under projectile penetration attracts more attentions in recent years.The resistance mechanism of concrete and RC under impact loading has been studying by previous scholars by fitting experiments data,theoretical analysis and numerical simulations.Much research has been conducted in an attempt to propose a model predicting the anti-penetration property of concrete or RC targets.Concrete or RC is a typical composite material and the penetration resistance is effected by the internal structure.Much mesoscopic models of concrete has been established,however,the majority of these models in existing literature were used to investigate the influence of mesoscopic factors on static and dynamic mechanical properties of concrete under low strain rate.There are significant deficiencies in the studies on the numerical simulations of mesoscopic concrete,especially RC,against projectile impacts.In this study,the penetration resistance of concrete and RC against projectile impacts are studied quantitatively by using a 3D meso-scale method.The main research areas are introduced as follows:Based on the 3D Voronoi tessellation,the negative factors in the initial Voronoi polyhedra,such as short edge and sharp corner,are eliminated by programming language in Matlab.The shrinking algorithm is proposed and used to generate graded aggregates.And the meso-scale concrete model with high volume fraction of aggregates is created by sinking algorithm.The verifications on aggregate convexity and intersection among aggregates are avoided in this method.Thus,compared with some other traditional methods,it is more efficient,especially for concrete model with higher aggregates content.A simple and effective intersection detection is used for aggregate-reinforcement to create the meso-scale RC model.The penetration process of rigid projectile impacts RC model is simulated by LS-DYNA.Compared with existing test data,the numerical model is accurate for predicting the interaction between projectile and concrete target.By measuring the deflection angle of projectile during the penetration process,the effects of some factors on ballistic stability are investigated quantitatively by using the 3D meso-scale concrete model and the critical values of these factors affecting the deflection angle of projectile are obtained.These factors focus on the impact velocity,projectile shape and calibre-radius-head(CRH),the ratio of projectile body length to diameter,aggregate strength,mortar strength,the aggregates volume fraction and the ratio of aggregate size to the diameter of projectile.The effects of mortar strength,aggregate strength,maximum size and volume fraction of coarse aggregate on penetration resistance are quantitatively studied by using 3D meso-scale modelling.The relationships between four factors and penetration resistance of concrete target are given,respectively.The applicable condition of the homogeneous assumption and the upper bounds of aggregate size and volume fraction that affect the penetration resistance are determined with respect to the aggregate configurations.The factors dominating the penetration resistance of concrete target are investigated and it is found that the sensitivity of penetration resistance to aggregate size is lower than other mesoscopic factors,i.e.,mortar strength,aggregate strength and volume fraction.In addition,a formula incorporating the effect of multi-factors is proposed to predict the DOP of rigid projectile penetration into concrete target mixed with coarse aggregates.The proposed formula,which considers the effects of the mesoscopic factors on the penetration resistance,can give better predictions of DOP into concrete targets.Based on the validated meso-scale model of RC,numerical studies are conducted to study the influences of reinforcements on the penetration resistance of slabs under various impact positions and reinforcement configurations,focusing on the diameter of reinforcement,reinforcement content,size of reinforcing meshes,distribution location(front,middle and rear),buried depth of the first layer,interlayer spacing and the number of reinforcing layers.The conclusions are drawn that the effect of impact positions on residual velocity of projectile can be ignored when the ratio of the reinforcing meshes size to projectile diameter is less than 0.4;the penetration resistance of RC target is more sensitive to the distribution location of reinforcements and the number of reinforcing layers than the buried depth of the first layer and interlayer spacing of reinforcing meshes.For RC where the reinforcement content is less than 2%,the effects of these factors on anti-penetration performance of RC slabs are not obvious when the projectile velocity is over 600 m/s.In addition,the optimal solution of increasing reinforcement content is given from the perspective of the engineering protective.Finally,the validations of numerical perforation results on ballistic limit are assessed by comparing with some empirical formulae.By the energy evolution analysis of each part during the perforation process,the results show that the distributed aggregate also is an important factor affecting the penetration resistance of RC.