Review on Empirical Studies of Lo...
International Journal of Sustainable Construction Engineering & Technology 71 Review on Empirical Studies of Local Impact Effects of Hard Missile on Concrete Structures Ismail Abdul Rahman*1, 2Ahmad Mujahid Ahmad Zaidi, and 1Qadir Bux alias Imran Latif, *1Faculty of Civil and Environmental Engineering, 2Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia 86400 Parit Raja, Johor, Malaysia *Corresponding E-mail: *1 email@example.com Abstract Concrete is basic construction material used for any kind of structure. However, in most vital and local structures such as nuclear plants, Power plants, Weapon Industries, weapons storage places, water retaining structures like dams, and also local industries, & etc., concrete structures have to be designed as defensive structures to provide protection against any accidents or knowingly generated incidents such as dynamic loading, dynamic local impact damage and global damage generated by kinetic missiles (steel rods, steel pipes, turbine blades, etc.). The impacting missile (projectile) can be classified as ‘Hard’ and ‘Soft’ in nature, depending upon the implication of its deformation with respect to the deformation of target. ‘Hard’ missile impact can generate both local impact damage and also overall dynamic global damage of concrete structure. This paper only provides the review of previous empirical studies related to our study and can be used for making design recommendation and design procedures for determining the dynamic response of the target to prevent local and impact damage. Keywords: Empirical Study, Local Impact Effects, Hard missile, Concrete
International Journal of Sustainable Construction Engineering & Technology 72 1.0 INTRODUCTION Over the years, concrete is very commonly used construction material for the military and civil applications to protect structures from local and explosive impact loads. For the designing of high-quality protective structures it is crucial to have a good knowledge about behavior of concrete against impact or explosive loading conditions. Projectile may be exists in a long diversity with fluctuation in sizes, shapes, velocity, weight, density, such as bullets, fragments, tornado, terrorist bombing, etc. The projectile may be classified as ‘Hard’ and ‘Soft’ depending upon deformability of projectile with respect to target’s deformation. Deformation of hard missile is considerable smaller or negligible compared with target’s deformation. Almost in all cases hard missiles are considered as non – deformable or rigid. However, ‘Soft’ missile deforms itself considerably well as compared to target’s deformation. Interest is focused on local damage and global response of target deformation caused by ‘Hard’ missiles considering failure criteria, contact mechanics, material model, and parametric analysis (velocity of missile, distance b/w missile and target, weight of missile, size and shape of missile, angle at which missile attacks on target, density of missile and target, thickness of structure, strength of concrete and reinforcement of concrete). Local impact effect consists mainly four process: (i) Spalling of concrete (ejection of material from front face or impacted face), (ii) scabbing of concrete (peeling off of material from back face or opposite side of impacted face of target), (iii) Missile Penetration into target (displacement of missile into the target), and (iv) Perforation of the target (full penetration beyond target). The local impact effect of hard missile on concrete structures can be studied by three ways, (i). Empirical Studies (predict empirical formula based on experimental data), (ii). Analytical Studies (create formula based on physical laws and compared with experimental data), and (iii), Numerical Simulation (based on computer based material model generate results and compared with experimental data). This study is based on numerical simulation with the help of finite elements. This paper only provides the review of previous empirical studies related to our study. 2.0 LOCAL IMPACT EFFECTS There’re two breed of impacts occurs at target, when it is subjected to projectile. First one is local impact and other one is explosive impact. The damage caused by projectile with its physical parameters, not because of explosion is known as local impact damage. Local impact effect is further briefly sub-divided in below explained processes: Radial Cracking: When projectile colloids with concrete target with certain velocity, it results radial cracks originated from the point of impact within the target in every direction.  Spalling: The ejection of material of target from front face (impacted face) due to impact of hard projectile is called spalling. Spalling produces spall crater in the surrounding area of impact. Spall crater is the total damaged portion of peeling off material from target on impacted face. [1, 58] Penetration: Penetration is defined as the digging of missile into the target body afar from the thickness of spall crater. The lengthwise measurement of dig is called penetration depth. [1, 58]
International Journal of Sustainable Construction Engineering & Technology 73 Cone cracking & Plugging: During penetration missile colloids with rear border of target and generates curved shear cracks in the shape of bell plug is called cone cracking. And than missile continues penetrating through target, it forces plug and shears-off the surrounding material of target is called plugging. This process generates rapid change into the behavior of target.  Scabbing: Ejection of target material from back face of target is called scabbing. [1, 58] Perforation: Perforation means complete passage or complete crossing of projectile through the target. It causes missile to extend penetration hole through scabbing crater and exit from the rear face of target. [1, 58] Figure.1. Explains the local impact phenomena caused by hard projectile. (a) Penetration, (b) Cone cracking and Plugging, (c) Spalling, (d) Radial cracking (i) front face and (ii) back face, (e) Scabbing, (f) Perforation, and (g) Global phenomena. 3.0 EMPIRICAL STUDY REVIEW Empirical formulae for designing of protective concrete structure against local impact effects of hard missile are below discussed in detail in both measuring systems (S.I Units and F.P.S Units). These formulae are verified with original formulae. The notations and symbol used in this paper for the calculation of local impact effects are shown in table: Table 1. Notation of terms used in paper. Symbol Description x Penetration depth e Perforation limit hs Scabbing limit E Modulus of elasticity of projectile Es Modulus of elasticity of Steel M Mass of projectile d Diameter of projectile h Height of projectile nose R / Rs Radius of projectile nose H Thickness of cone plug Ho Thickness of the target ft Tensile strength of target
International Journal of Sustainable Construction Engineering & Technology 74 fc Unconfined compressive strength of target r Percentage of reinforcement (both ways of reinforcement) A Aggregate diameter vo Projectile impacting velocity N Nose shape factor Ψ Caliber-radius-head D Caliber density of projectile f’c Ultimate compressive strength of target K / kp Target penetrability factor 3.1 Modified Petry Formula [1,58] The most commonly formula used to predict various components of local impact effects of hard missile on concrete structure in USA was modified Petry formula. It is the oldest of available empirical formulae, and developed originally in 1910. According to Petry the penetration depth x (inches) can be predicted as: ⎟ ⎟ ⎠ ⎞ ⎜1 ⎜ ⎝ ⎛ + = 215,000 log10 12K p Vo2 Ap x (1) This equation was derived from the equation of motion which states that the component of drag-resisting force depends upon square of the impacted velocity, and the instantaneous resisting force is constant. In above equation, Ap represents the missile section pressure (psi). Kp is concrete penetrability co-efficient, it depends upon the strength of concrete and on the degree of reinforcement. It equals to 0.00426 for normal reinforced cement concrete, 0.00284 for special reinforced cement concrete (front and rear face reinforcement are laced together with special ties), and 0.00799 for massive plain cement concrete. The modified Petry formula – I suggested by Q.M. Li in S.I unit is: ⎟ ⎟ ⎠ ⎞ ⎜1 ⎜ ⎝ ⎛ + = 19,974 log10 3 Vo2 d M k d x (2) The above listed both formulae are famously known as Modified Petry formula - I. it is suggested that k value for normal reinforced cement concrete 0.000339, 0.000226 for special reinforced cement concrete, and 0.000636 for massive plain cement concrete. The relationship b/w k and Kp is equals to k = 0.0795Kp. Later on, Amirikian  suggest revised value for Kp for the account of variation in concrete strength. He suggests that Kp is a function of concrete strength, as shown in figure.2.2. With the revised Kp value this formula known as modified Petry formula – II. Amirikian also suggests that the perforation limit (e) can be calculated by formula based on penetration depth (x). d x d e 2 = (3) and scabbing limit (hs)
International Journal of Sustainable Construction Engineering & Technology 75 d x d hs 2.2 = (4) Figure. 2. Variation of concrete penetrability Kp with the unconfined compressive strength of concrete (fc). 3.2 Ballistic Research Laboratory (BRL) Formula [1, 9-11, and 58] For the calculation of penetration depth (x) of concrete impacted by hard missile, Ballistic Research laboratory (BRL) was suggested a formula in 1941 [12, 13], and its modified expression was given by [1, 9 10]: 0.2 3 427 ⎟ ⎠ ⎞1.33 ⎜ ⎝1000 ⎛ ⎟d ⎠ ⎞ ⎜ ⎝ ⎛ = c Vo d M f d x (F.P.S) (5) 0.2Vo1.33 3 3 1.33×10 c d M f d x ⎟d ⎠ ⎞ ⎜ ⎝ ⎛ = − (S.I) (6) Chelapati et al.  suggested perforation limit (e) can be calculated based on above calculated penetration depth (x) by: d x d e 1.3 = (7) And for scabbing limit (hs), modified BRL formula is [1, 14]: d x d hs 2 = (8) 3.3 Army Corp of Engineers (ACE) Formula [1, 13, 15 and 58] Before 1943, The Ordnance Department of the US Army and Ballistic Research Laboratory (BRL) done many experimental works on local impact effects of hard missile on concrete structure, based on those results Army Corp of Engineers developed the ACE formula: 0.5 282.6 0.215 3 + ⎟ ⎠ ⎞1.5 ⎜ ⎝1000 ⎛ ⎟d ⎠ ⎞ ⎜ ⎝ ⎛ = c Vo d M f d x (F.P.S) (9)