Asian Journal of Civil Engineering https://doi.org/10.1007/s42107-018-0064-x
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ORIGINAL PAPER
Design strategies for fragment and projectile penetration into steel and concrete structural elements using CONWEP Graeme McKenzie1 • Bijan Samali1 • Chunwei Zhang1 • Eric Anciche1 Received: 2 April 2018 / Accepted: 4 July 2018 Springer Nature Switzerland AG 2018
Abstract Designers who design structures to mitigate against blast loadings (Remennikov 2007) have another duty and that is to design for the effects of fragmentation not only caused from bulk explosives, but also impact from projectiles. Impact causes damage to a structure and inevitably results in debris from penetration and perforation (breach) of the structural elements. This debris is in fact the result of the damage outcome to a structure either from the blast loading or projectile impact. Fragmentation (Bangash 2006) is the end result of the blast waves impacting the structural elements resulting in scabbing and spall both of which manifest themselves in the production of fragmentation. This fragmentation is propelled outwards at velocity causing supplementary damage to the structure, adjoining structures and individuals caught near the fragmentation. Those designing for fragmentation must consider many parameters from the geometry of the impacted structural element, to the velocity of the fragments, the weight of the fragments and the range of the fragments. As has been said the fragments cause damage and the designers overall duty is to design to mitigate against damage and death or injury to individuals. The pool of worldwide knowledge on this topic is growing exponentially particularly as the need arises with weapons of high velocity and sophisticated projectiles of extreme lethality and range. Keywords Penetration Perforation Scabbing Spalling Primary fragmentation Secondary fragmentation
Introduction When either a military projectile or a bulk explosive impacts a structural component of steel, concrete, glass, wood, soil, rock, etc., both primary and secondary fragments can be generated. They can be projected away from the structural element impacted at high velocity thus making them capable of damaging not only the element impacted, but also adjoining structures and causing death or injury to those caught within the range of the fragments. & Graeme McKenzie
[email protected] Bijan Samali
[email protected] Chunwei Zhang
[email protected] Eric Anciche
[email protected] 1
Centre for Infrastructure Engineering, Western Sydney University, Locked Bag 1797, Penrith, NSW, Australia
This situation makes it mandatory for those designing against blast loadings to structures to also design for and against fragmentation. Those structural elements most likely to be susceptible to ballistic attack can be strengthened by the application of fibre reinforced polymers (FRP) (Razaqpur et al. 2007) or sprayed on polyuria coatings (Wade and Wayt 1996) both of which do not stop fragmentation occurring but confine the fragments and spall thus stopping it from flying off at velocity causing further damage and death or injury to those nearby. Apart from the application of FRP’s and similar products the geometry of structures and structural components such as their thickness can prevent penetration although this only prevents fragmentation occurring at the rear face in the case of concrete but not necessarily from the impact face where spall usually occurs and fragmentation is produced. One of the best design strategies that can be employed against fragmentation is the same as that employed by designers to mitigate structural damage from either air bursts (spherical blasts) or ground bursts (hemispherical bursts) and that is to try and keep the point of
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detonation of the explosion as far as possible away from the structural element that is to be impacted by the blast wave. It is no different in the case of a projectile impacting a structural element and so causing fragmentation. In other words, the greater the range of the projectile being fired at a structure the less likely fragmentation may occur and even if it does the number of effective fragments generated will likely be reduced. Accordingly, the level of damage will also be reduced. So, the incorporation of range (R) into the structural design to cater for fragmentation is critical. Another factor that needs to be addressed during the design phase is to consider the material type that will be impacted. In the case of concrete the higher the strength of the concrete the greater the capacity of the concrete to not only reduce the fragmentation produced, but also effect both penetration and perforation of the any structural concrete element. In the case of steel structural elements the ‘‘Brinell Hardness’’ (Hill et al. 1989) plays a part in whether steel elements will be perforated and gives a designer an idea as to the likely structural performance of the steel element in relation to whether it will produce fragments as a result of a projectile impact. The higher the hardness value the less likely that the steel will be perforated as so fragmentation may be reduced. CONWEP software (Hyde 1991) is used at the end of this paper to consider certain scenarios (Zukas et al. 2002) and to detail the outputs in relation to fragmentation. Penetration and perforation (Smith and Hetherington 1994) are investigated for a variety of materials and outcomes from the application of projectiles and bulk explosives.
•
•
•
employed against a structural element the impact causes stress waves to pulsate through the element in the form of a compressive wave until it becomes a tensile wave reflecting off the rear surface of the element. This effect then causes a scab (Zhou et al. 2008) to form depending on the toughness of the element. Under certain conditions this scab can be dislodged and projected outwards at velocity. Spall Spalling (Tabatabaei et al. 2013) can produce many fragments that fly off from the rear face at velocities that can cause injury or death to those nearby. This process is called spall. Primary fragmentation Primary fragmentation (Baera et al. 2016) is produced from the metal casing of exploding military ordnance thus for expediency and simplicity sake is termed in the form of a common shaped ‘‘cylinder’’ with a uniform case thickness (Fig. 1). This overcomes the problem in trying to cater for the many uncertain factors involved such as fragment shape, mass, and velocity as well as the type of explosive and casing type used in the military ordnance. Secondary fragmentation Unlike adopting a standard fragment shape considered in the primary fragmentation case one is forced with secondary fragmentation (Baera et al. 2016) to consider the many uncertainties involved with fragment shape, size, and velocity as a result of the explosion. To design against secondary fragmentation the worst case loading scenario must be considered.
Terminology To understand fragmentation, one must understand the terminology used in relation to it. The following are the main terms that need to be understood. •
•
•
•
Debris The shattered fragmented structural elements resulting from the application of a blast loading to a structure are termed debris. This debris can then in turn be utilized as secondary fragments because of a further blast loading to a structure. Penetration Penetration (Smith et al. 2014) is the distance a fragment has travelled into a structural element, Perforation Perforation (Li and Tong 2003) is the complete penetration of structural element resulting in the fragment completely passing through it (breaching). Scabbing When a projectile strikes a target or a bulk explosive is
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Fig. 1 Standard primary fragment shape (Hetherington and Smith 2014)
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•
Primary fragmentation Primary fragment shape
• All military ordnance casings are scored to form standard or uniform fragments of known weight but for design purposes the standard design fragment shape as in Fig. 1 above is adopted.
Primary Fragment Mass Using a confidence level of CL B 0.999 and the standard shape the fragment mass can be estimated using the following equation: Wdf ¼ MA2 ln2 ð1 CL Þ;
ð1Þ
where Wdf design fragment weight (kg), MA fragment distribution factor, CL confidence level. tc 1=3 MA ¼ Btc5=6 di 1þ ð2Þ di where B = explosive constant (Mott Scaling Constants), tc = average thickness (mm), di= average inside diameter of casing (mm).
Primary fragment velocity The initial velocity of fragments (Kennedy 1970) are produced when a cylindrical casing shatters and this event is a direct function of the explosive output (Bulson 2002) resulting from detonation and the explosive charge weight (kg) and the casing weight (kg). Therefore, the initial velocity of fragments is calculated as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffi W=Wc 0 vop ¼ FS 2E ; ð3Þ 1 þ 0:5W=Wc pffiffiffiffiffiffiffi where vop initial velocity of primary fragment (m/s), 2E0 Gurney energy constant, FS factor of safety (1.2), W design charge weight = FSWact(m/s), Wact actual quantity of explosive material (kg), Wc weight of metal casing (kg).
•
Determine the distance from the centre of detonation (explosive centre) to the position of the potential fragment. Determine the size, shape, structural constraint and orientation of the potential fragment. Determine the potential fragment velocity as detailed in Eq. 3 above.
Simplified to a 3-step function to assist design the blast loading is represented by an idealized time loading in Fig. 2 below. It represents the rise of the peak pressure then its decay over time that results from the diffraction of the blast wave around the object, the rarefaction waves across the front of the object causing a reduction in density unlike compression that increases density and lastly the drag loading.
Unconstrained fragments When fragments are not attached to an object that is impacted by a blast wave they are picked up and thrown at velocity away from the blast site. The concept of being not attached assumes that no energy is expended having to break the object free, that the object will not deform and gravity will not affect velocity with the objects acceleration outwards at velocity away from the blast site. For unconstrained fragments far from the charge they are defined far from the charge if the objects are located at a distance more than 20 times the radius of the explosive (encased in a metal casing or free as with a bulk explosive). Equation 4 allows the fragments velocity to be calculated:
Secondary fragmentation To gauge the damage or potential damage caused by secondary fragmentation one needs to undertake the following steps during any design phase: •
Define the actual blast loading impacting a structural element by determining such parameters as initial pressure (MPa), peak pressure (MPa) impulse (MPamesc), range (m) and time (mesc). Fig. 2 (Bulson 2002)
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Vðtd Þ ¼
Ztd
A id ; M
ð4Þ
0
where V velocity (m/s), td load duration (msec), A area of object facing blast (mm2), M mass of object (kg - msec/ mm), id total drag and diffraction (MPa - msec/kg1/3).
Constrained fragments
In the case of primary fragments Eq. 7 can be simplified as follows. Assume: A 0:78 ¼ ðfor mild steel fragments) Wf W 1=3 f qa = 0.00071 (kg/mm3), CD = 0.6. Resulting in: 0:004
Vs ¼ v 0 e A constrained secondary fragment is formed when it breaks away from its parent object and is thrown out at velocity away from the detonation source. The impulse applied to the object minus the impulse required to break the fragment free dictates the fragments velocity. Equation 5 allows the velocity to be calculated: I Ist ¼ Mvo ;
ð5Þ
where I total blast impulse applied to the fragment (MPa msec), Ist impulse required to free the fragment from the support (MPa msec).
Fragment design parameters Fragment trajectory, velocity upon impact and the angle at which the fragment impacts the target (angle of obliquity) influence the impact the fragment has on a structural component. For design a zero angle of obliquity is assumed as the actual angle of obliquity is rarely known.
Fragment final velocity Drag forces over distance dictate the velocities of individual fragments so the greater the distances the lower the velocity at which a fragment impacts a structural element. US doctrine says that for objects close to a detonation (Tran 2007) such as distances of less than 20ft (6.1 m) (Defence 2008) delay in velocity can be ignored. For objects of greater distance fragment velocity is calculated from Eq. 6: Vs ¼ v0 e½12kv Rf ;
Rf 1=3 W f
ðm/s)
Fragment trajectory Because it is difficult to predict the trajectory of fragments due to the fragments irregular shapes and differing mass simplified fluid dynamic force prediction methods are normally adopted. Once both primary and secondary fragments velocities are known it is necessary to establish when they hit the ground or what range applies. The fragments are generally large irregular masses that are controlled by drag forces resulting in most methods ignoring the lift forces from the irregular shapes and calculating accelerations he drag forces. The fragment range prediction graph Fig. 3 below is then used to calculate the range R (m) as follows: Using Fig. 3 the non-dimensional velocity can be calculated from the abscissa as follows: ½v ¼
12qo Cd AD v2o ; Mg
A q CD ; Wf a
ð6Þ
ð7Þ
where Wf fragment weight (kg), WAf fragment form factor, qa specific density of air (kg/mm3). Fig. 3 (Ngo et al. 2007)
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ð9Þ
where qo mass density of the medium through which the fragment travels (kg msec2/mm2), AD drag area (mm2), g gravity (9.81 m/s2). Again, using Fig. 3 the dimensional range [R] can be found from the ordinate and then the equation rearranged as in Eq. 10 to find the maximum range R:
where Vs final fragment velocity (m/s) at distance of interest (Rf), v0 initial fragment velocity (m/s), Rf distance from the centre of detonation (m), kv velocity coefficient and: kv ¼
ð8Þ
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R¼
M½R ðmÞ 12qO Cd AD
ð10Þ
Fragment impact damage All structural elements are susceptible to fragment strike and the damage sustained can range from small to substantial. For individuals the same applies, but a fragment strike in this case can cause death of injury. Fragments can either penetrate or perforate (pass through) an object and both events depend on factors such as the mass and material strength of the fragment, the initial velocity of the fragment, the final velocity of the fragment as it strikes, the angle at which the fragment strikes the object and the range of the fragment from the point of detonation to the object. In some cases, the fragment might not penetrate or perforate an object because the material strength of the object causes the fragment to be deflected away from the object thus causing another object to be impacted.
THOR equation for penetration into miscellaneous materials
Fragments penetration of a thin metal target can be calculated based on the thin metal structural elements material and the fragment properties with penetration a surety if the fragment velocity is greater than the limit velocity (Vso). The limit velocity can be calculated as follows: pffiffiffiffiffiffiffiffi rt qt V50n VSO ¼ ; ð14Þ qf where rt target yield stress (MPa), qt target density (kg/ m3), qf fragment density (kg/m3), V50n non-dimensional limit velocity (m/s) (calculate h/a and determine V50n from Fig. 4, h target thickness (mm), a fragment radius. Fragment penetration into mild steel structural elements is based on simplified assumptions with the primary assumption being that the fragment shape is a cylinder with a rounded leading edge plus the steel has a ‘‘Brinell Hardness’’ (Tabor, 2000) of less than 150. Steel with greater hardness will produce more conservative results. The depth of penetration for mild steel impacted by armour piercing steel fragments can be calculated as follows: x ¼ 0:30Wf0:33 Vs1:22 ðmm)
The military has developed ‘‘THOR’’ equations (Qian et al. 2005) explicitly for use by the military, but they can be used for commercial purposes if limitations are kept in mind. The equations apply to small fragment sizes into objects or targets for miscellaneous materials. The equation for minimum thickness of a steel plate to resist perforation by a mild steel fragment is as follows: 1C5 C C1 þ7C2 þ3C3 C 3 C4 C2 10 2 C2 t¼ mf VS ðcos ;ÞC2 ; ð11Þ Af where t fragment penetration (m), mf fragment mass (kg), Af presented area of fragment (m2), Vs impact velocity (m/ sec), O impact angle relative to normal from tangent (rad), C1 - C10 empirical THOR constants. Two important equations are for the calculation of residual velocity and residual mass for fragments once they impact a structural element. The equation for residual velocity is as follows: Vr ¼ Vs 10ðC1 þ7C2 þ3C3 Þ ðtAf ÞC2 mCf 3 ð1= cos ;ÞC4 VsC5 ;
Steel structural elements
ð15Þ
The depth of penetration for mild steel impacted by mild steel fragments can be calculated as follows: x ¼ 0:21Wf0:33 Vs1:22 ;
ð16Þ
where x depth of penetration (mm), Wf fragment weight (kg), Vs striking velocity (m/s).
Concrete structural elements When a concrete structural element is impacted by a fragment a crater (Leppa¨nen 2002) forms on the surface of the concrete of an irregular size due to the impulse imparted to the concrete by the fragment. For fragment velocities more than 300 m/s the fragment will penetrate
ð12Þ
where Vs residual velocity of fragment after perforation (m/ sec). The equation for residual fragment weight is as follows: mr ¼ mf 10ðC6 þ7C7 þ3C8 3Þ ðtAf ÞC7 mCf 8 ð1= cos ;ÞC9 VsC10 ; ð13Þ where mr residual mass (kg).
Fig. 4 Non-dimensional limit Velocity V’s non- dimensional thickness for ‘‘Chunky’’ fragments (Baker et al. 2012)
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beyond the crater, but if the fragment deforms on impact the size of the crater well be smaller and in some cases the crater will not form at all. On the opposite side to the fragment impact spallation may occur because of the impact compression wave travelling through the structural element to its opposite face and then reflecting of the free surface thus causing tensile stresses in the free face. Once the tensile stresses exceed the compression stresses spall occurs (Xu and Lu 2006). Spall can occur all the way through to the reinforcing steel. For armour piercing fragment penetration into concrete ¨ beyli et al. 2007) the maximum penetration into mass (U concrete can be calculated from the following equation: For Xf 2d :
pffiffiffiffiffiffiffiffiffiffi Xf ¼ 4:0103 KNDd 1:1 Vs0:9
ð17Þ
For Xf [ 2d : pffiffiffiffiffiffiffiffiffiffi Xf ¼ 4:0106 KNDd 1:2 Vs1:8 þ d
ð18Þ
where Xf maximum penetration into armour piercing pffiffiffiffi fragment (mm), K penetration constant (K = 12.91/ fc0 , N nose shape factor (Fig. 1), D caliber density (Fig. 1), d fragement diameter (mm). For a standard primary fragment and concrete strength of 30 MPa Eqs. 17 and 18 can be expressed in terms of fragment diameter (mm) as follows: For Xf 2d
ð19Þ
Xf ¼ 2:86103 d 1:1 Vs0:9 For Xf [ 2d 6 1:2
Xf ¼ 2:0410 d
Vs1:8
þd
ð20Þ
The equation in terms of fragment weight is as follows: For Xf 2d Xf ¼ 1:92103 Wf0:37 Vs0:9 For Xf [ 2d Xf ¼ 1:32106 Wf0:4 Vs1:8 þ 0:695Wf0:33
ð21Þ
ð22Þ
For concrete strengths more than 30 MPa an estimate of fragment penetration can be estimated by multiplying results above by the square root of the concrete strengths: sffiffiffiffiffi 30 0 Xf ¼ Xf ; ð23Þ fc0 where Xf0 max penetration by armour piercing fragment into concrete with compressive strength of fc0 (mm). For non-armour piercing fragment penetration into concrete can be calculated from the following equation that considers the metal hardness values in Table 1: Xf00 ¼ K3 Xf ;
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ð24Þ
Table 1 K3 Values for metal types (Tabor 2000)
Type of material
K3
Arm or piercing steel
1.00
Mild steel
0.70
Lead
0.50
Aluminium
0.15
where Xf00 maximum penetration by non-armour piercing fragment (mm), K3 constant to account for fragment metal hardness (see Table). For concrete to prevent perforation as a function of the maximum penetration into massive concrete the following equation applies: Tpf ¼ 1:13Xf d0:1 þ 1:311d
ð25Þ
where Tpf minimum concrete thickness to prevent perforation by design fragment (mm), Xf maximum fragment penetration into massive concrete structure (mm). If a fragment perforates a concrete structural element (Leppa¨nen 2005) then individuals behind it could be injured so it is essential to know the residual or exit velocity to gauge the hazard that exists. The following equation calculates that velocity: For Xf 2d " 2 #0:555 vr Tc ¼ 1 vs Tpf
ð26Þ
For Xf [ 2d 0:555 vr Tc ¼ 1 vs Tpf
ð27Þ
where Tc concrete thickness up to Tpf, vr residual velocity of fragment as it leaves the element (m/s). Concrete spall is a function of the fragment penetration depth and so the following equation gives the minimum concrete thickness to prevent spall: Tsp ¼ 1:215Xf d0:1 þ 2:12d
ð28Þ
where Tsp minimum concrete thickness to prevent spall by design fragment (mm), Xf maximum fragment penetration into a massive concrete structure (mm). Secondary fragments from spall (Ngo et al. 2007) can occur from impact as well as from structural movement again causing problems to those caught behind the structure.
Fragmentation in the Australian environment In many overseas countries because of ongoing conflicts fragmentation from blast loadings and the impact of projectiles is an ever-present occurrence, but in Australia even
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though it is not common fragmentation has taken one life and the possibility of further occurrences is also unfortunately ever present in 2015. On the 13 July 1997 Canberra’s superseded hospital at Acton Peninsular on Lake Burley Griffin (Liu et al. 2005) was demolished by an implosion. The demolition had been planned for some time and the ACT Government decided to turn the building implosion into a spectator event even though there were safety concerns with the explosive demolition. Over 100,000 people, one of the largest crowds in Canberra’s history, came out to bid farewell to the birthplace of many Canberra residents and took up positions around the structure including on boats on Lake Burley Griffin. The demolition was a failure as the building did not fully collapse and fragmentation from the blast impacting structural elements flew outwards from the structure at considerable velocity and in many trajectories. Debris both masonry and steel were found some 650 m from the site and a spectator on the lake in a boat 500 m form the detonation was struck by a 1 kg mass of steel fragmentation on the head and killed. It was obvious that the safety distances applied around the demolition site was inadequate as fragmentation not only caused a fatality, but fragmentation was obviously never designed for (Fig. 5). The possibility of fragmentation occurring from the impact of a projectile on a structure within Australia was heightened when in 2007 ten M72 LAW shoulder fired rocket launchers (Baker et al. 1971) (Fig. 5) were stolen from a military base in Sydney’s west and a court heard that five had been on sold to persons unknown. The standard weapon has a penetration into steel plate of 200 mm, reinforced concrete of 600 mm and some 1.8 m into soil. Its effective range is 200 m. With these weapons still not recovered for those structures likely to be impacted by such a weapon any designer would have to consider the likely damage sustained by the impact of the rocket. The fragmentation generated by the rockets impact would be substantial with fragment velocities high and range substantial as well (Fig. 6).
Fig. 6 M72 LAW light anti-tank weapon (Hartley et al. 2016)
Fragment penetration into thin metal structural elements CONWEP example—aluminium penetration examples (Mi et al. 2005)
See Figs. 7 and 8.
Fragment Penetration into Aluminum (2024-T3) 0.06
0.05
meters
0.04
0.03
0.02
0.01
Fragment weight 64.35 grams Initial fragment velocity 1030 meters/sec
0 0
20
40
60
80
100
120
140
Range to Target, meters
Fig. 5 Explosive demolition of Canberra Hospital 1997 (Yates 2000)
160
180
200
ConWep Output1
Fig. 7 Fragmentation penetration 58 mm, 155 mm artillery round into aluminium target (CONWEP output)
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Asian Journal of Civil Engineering Residual Fragment Velocity vs. Target Thickness
Residual Fragment Velocity vs. Target Thickness
Target: Copper
Target: Aluminum (2024-T3)
1200
Residual Velocity, meters/sec
Residual Velocity, meters/sec
1200
1000
800
600
400
200
0.005
0.01
0.015
0.02
0.025
0.03
800
600
400
Fragment weight 64.35 grams Range to target 0.1 meters Fragment impact velocity 1029 meters/sec
200
0
Fragment weight 64.35 grams Range to target 0.1 meters Fragment impact velocity 1029 meters/sec
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
Plate Thickness, meters
0 0
1000
0.035
0.04
0.045
Plate Thickness, meters
0.05
0.055
0.06
ConWep Output
0.05
0.055
ConWep Output2
Fig. 10 Copper demonstrating thicker the target less residual velocity (CONWEP Output)
Fig. 8 Aluminium demonstrating thicker the target less residual velocity (CONWEP Output)
Fragment Penetration into Steel, Mild Homogeneous 0.02
CONWEP example—copper penetration examples (Walters et al. 1985)
meters
0.015
0.01
0.005 Fragment weight Initial fragment velocity
13.13 grams 1237 meters/sec
0 0
20
40
60
80
100
120
140
160
Range to Target, meters
180
200
ConWep Output2
Fig. 11 Fragmentation penetration 19 mm 105 mm artillery round into mild steel target (CONWEP Output)
See Figs. 9 and 10.
Residual Fragment Velocity vs. Target Thickness Target: Steel, Mild Homogeneous
Residual Velocity, meters/sec
1250
Fragment Penetration into Copper 0.055
0.05
0.045
meters
0.04
0.035
0.03
0.025
1000
750
500
250 Fragment weight Range to target Fragment impact velocity
0.02 Fragment weight 64.35 grams Initial fragment velocity 1030 meters/sec
13.13 grams 0.1 meters 1235 meters/sec
0.015
0 0.01 0
0 50
100
150
200
250
300
350
Range to Target, meters
400
450
500
ConWep Output1
Fig. 9 Fragmentation penetration 58 mm, 155 mm artillery round into copper target (CONWEP output)
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0.002
0.004
0.006
0.008
0.01
0.012
0.014
Plate Thickness, meters
0.016
0.018
0.02
ConWep Output
Fig. 12 Mild Steel 400 mm Thick Target Residual Velocity after Perforation 337 m/s (C
Asian Journal of Civil Engineering Projectile Penetration into Concrete vs. Impact Velocity 1.8
Fragment penetration into concrete structural elements
Penetration into Massive Concrete Thickness Req'd for no Perforation Thickness Req'd for no Backface Damage
CONWEP example—concrete penetration examples (Wang et al. 2007)
1.5
meters
1.2
0.9
0.6
Projectile weight 14.97 kilograms Breakup velocity 363.6 - 568.9 meters/sec Concrete strength 32 MPa
0.3
0 0
50
100
150
200
250
300
350
400
450
Impact Velocity, meters/sec
500
550
600
ConWep Output
Fig. 13 Penetration 476 mm 32 MPa concrete no soil backing 105 mm artillery shell at 350 m/s impact velocity (CONWEP Output)
See Fig. 13.
Fragment penetration into mild steel structural elements CONWEP example—mild steel penetration examples (Balden and Nurick 2005)
See Fig. 14.
See Figs. 11 and 12.
See Fig. 15.
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Asian Journal of Civil Engineering Projectile Penetration into Concrete vs. Impact Velocity 1.8 Penetration into Massive Concrete Thickness Req'd for no Perforation Thickness Req'd for no Backface Damage
1.5
meters
1.2
0.9
0.6
Projectile weight 14.97 kilograms Breakup velocity 363.6 - 568.9 meters/sec Concrete strength 32 MPa
0.3
See Fig. 16.
0 0
50
100
150
200
250
300
350
400
450
500
550
600
Impact Velocity, meters/sec ConWep Output1
Fig. 14 Penetration 476 mm 32 MPa concrete with soil backing 105 mm artillery shell at 350 m/s impact velocity (CONWEP Output)
Projectile Penetration into Concrete vs. Impact Velocity
Projectile Penetration into Concrete vs. Impact Velocity
1.2
1.5
Penetration into Massive Concrete Thickness Req'd for no Perforation Thickness Req'd for no Backface Damage
1.25
1
1
0.8
meters
meters
Penetration into Massive Concrete Thickness Req'd for no Perforation Thickness Req'd for no Backface Damage
0.75
0.6
0.4
0.5
Projectile weight 14.97 kilograms Breakup velocity 363.6 - 568.9 meters/sec Concrete strength 50 MPa
0.25
Projectile weight 14.97 kilograms Breakup velocity 363.6 - 568.9 meters/sec Concrete strength 100 MPa
0.2
0
0 0
50
100
150
200
250
300
350
400
450
Impact Velocity, meters/sec
500
550
600
50
100
150
200
250
300
350
400
450
500
550
600
Impact Velocity, meters/sec ConWep Output
Fig. 15 Penetration 402 mm 50 MPa concrete no soil backing 105 mm artillery shell at 350 m/s impact velocity (CONWEP Output)
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0
ConWep Output
Fig. 16 Penetration 315 mm 100 MPa concrete no soil backing 105 mm artillery shell at 350 m/s impact velocity (CONWEP Output)
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Fragment perforation into concrete structural elements
Fragment Penetration into Concrete vs. Range to Target 0.16 Penetration into Massive Concrete Thickness Required for no Perforation Thickness Required for no Spall
0.14
CONWEP example—concrete perforation example (Unosson and Nilsson 2006) meters
0.12
0.1
0.08
Fragment weight 64.35 grams Initial fragment velocity 1030 meters/sec Concrete strength 32 MPa
0.06
0.04 0
2
4
6
8
10
12
14
16
Range to Target, meters ConWep Output
Fig. 17 Penetration 83 mm 32 MPa Concrete Backing 155 mm Artillery Shell at 1025 m/s Impact Velocity Range to Target 500 mm (CONWEP Output) Residual Fragment Velocity vs. Slab Thickness
See Figs. 17 and 18.
CONWEP example—concrete spall example (Li and Hao 2014)
Residual Velocity, meters/sec
Fragment spall of concrete structural elements
1200
1000
800
600
400
Fragment weight Range to target Fragment impact velocity Concrete strength
200
64.35 grams 0.5 meters 1025 meters/sec 32 MPa
0 0
0.02
0.04
0.06
0.08
0.1
Slab Thickness, meters
0.12
0.14
ConWep Output
Fig. 18 Concrete 100 mm thick target residual velocity after perforation 410 m/s (CONWEP Output)
See Figs. 19 and 20.
Fragment penetration CONWEP examples for other materials Bullet resistant glass (Sikarwar et al. 2014)—penetration examples
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Asian Journal of Civil Engineering Fragment Penetration into Concrete vs. Range to Target
Fragment Penetration into Glass, Bullet Resistant
0.15
0.12 Penetration into Massive Concrete Thickness Required for no Perforation Thickness Required for no Spall
0.125
0.1
0.1
meters
meters
0.08
0.075
0.06 0.05
0.04
Fragment weight 64.35 grams Initial fragment velocity 1030 meters/sec Concrete strength 32 MPa
0.025
Fragment weight Initial fragment velocity
0 0
5
10
15
20
25
30
35
40
45
50
55
60
0.02
65
0
10
20
Range to Target, meters
30
40
50
60
70
80
90
Range to Target, meters
ConWep Output
Fig. 19 Concrete penetration 83 mm 32 MPa concrete backing 155 mm artillery shell at 1030 m/s impact velocity range to target 500 mm (CONWEP Output)
12.76 grams 2396 meters/sec
100
ConWep Output1
Fig. 21 Bullet resistant glass thickness 60 mm minimum fragment penetration 112 mm for MK 81 general purpose bomb range 1 mm (CONWEP Output)
Residual Fragment Velocity vs. Slab Thickness
Residual Fragment Velocity vs. Target Thickness
1200
Target: Glass, Bullet Resistant 2500
Residual Velocity, meters/sec
Residual Velocity, meters/sec
1000
800
600
400
Fragment weight Range to target Fragment impact velocity Concrete strength
200
64.35 grams 0.5 meters 1025 meters/sec 32 MPa
2000
1500
1000
500 Fragment weight 12.76 grams Range to target 1 meters Fragment impact velocity 2355 meters/sec
0
0 0
0.02
0.04
0.06
0.08
0.1
Slab Thickness, meters
0.12
0.14
0
0.02
0.04
0.06
0.08
Plate Thickness, meters
0.1
0.12
ConWep Output2
ConWep Output
Fig. 20 Concrete slab thickness 400 mm minimum concrete thickness to prevent spalling 149 mm and perforation 123 mm (CONWEP Output)
Fig. 22 Buller resistant glass 60 mm thick target residual velocity after perforation 842 m/s (CONWEP Output)
Soil (Fragaszy and Taylor 1989)—penetration examples See Figs. 21 and 22.
See Fig. 25. See Figs. 23 and 24.
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Asian Journal of Civil Engineering Projectile Penetration into Soil
Fragment Penetration into Glass, Bullet Resistant 0.18
0.12
0.15
Penetration, meters
0.1
meters
0.08
0.06
0.04 Fragment weight Initial fragment velocity
10
20
30
40
0.09
0.06
Projectile weight Projectile diameter S-Number
0.03
12.76 grams 2396 meters/sec
0 50
0.02 0
0.12
50
60
70
80
90
100
100
150
200
250
300
350
400
450
500
550
46.01 grams 0.01295 meters 3
600
Impact Velocity, meters/sec
Range to Target, meters
Fig. 23 Bullet resistant glass thickness 60 mm minimum fragment penetration 52 mm for MK 81 general purpose bomb range 60 m (CONWEP Output)
650
700
750
ConWep Output
ConWep Output2
Fig. 25 Soil S-number 3 penetration 50 caliber bullet 224 mm impact velocity 928 m/s (CONWEP Output)
Projectile Penetration into Soil
Residual Fragment Velocity vs. Target Thickness 0.6
Target: Glass, Bullet Resistant 1000
Penetration, meters
Residual Velocity, meters/sec
0.5
800
600
400
0.4
0.3
0.2
Projectile weight Projectile diameter S-Number
0.1
46.01 grams 0.01295 meters 10
200 Fragment weight 12.76 grams Range to target 60 meters Fragment impact velocity 857.4 meters/sec
0 50
100
150
200
250
300
350
400
450
500
550
Impact Velocity, meters/sec
600
650
700
750
ConWep Output
0 0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Plate Thickness, meters
0.045
0.05
0.055
ConWep Output
Fig. 24 Buller resistant glass 60 mm thick target residual velocity after perforation 857 m/s (CONWEP Output)
See Fig. 26
Fig. 26 Soil S-number 10 penetration 50 caliber bullet 748 mm impact velocity 928 m/s (CONWEP Output)
Titanium (Xu et al. 2006)—penetration examples
See Figs. 27, 28 and 29
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Asian Journal of Civil Engineering Fragment Penetration into Titanium 0.04
0.035
0.03
meters
0.025
0.02
0.015
0.01
0.005
Fragment weight Initial fragment velocity
12.76 grams 2396 meters/sec
0 0
20
40
60
80
100
120
140
160
Range to Target, meters
180
200
ConWep Output
Fig. 27 Titanium penetration MK 81 general purpose bomb 367 mm impact velocity 2355 m/s range 1 m (CONWEP Output)
Residual Fragment Velocity vs. Target Thickness Target: Titanium
Residual Velocity, meters/sec
2500
2000
1500
1000
500 Fragment weight 12.76 grams Range to target 1 meters Fragment impact velocity 2355 meters/sec
0 0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
Plate Thickness, meters
0.04
ConWep Output
Fig. 28 Titanium thickness 60 mm MK 81 general purpose bomb 367 mm impact velocity 2355 m/s range 1 m (CONWEP Output)
Fragment Penetration into Titanium 0.039
0.036
meters
0.033
0.03
0.027
0.024
0.021
Fragment weight Initial fragment velocity
0.018 0
5
10
15
12.76 grams 2396 meters/sec
20
25
30
35
Range to Target, meters
40
45
50
ConWep Output
Fig. 29 Titanium penetration MK 81 General Purpose Bomb 327 mm impact Velocity 2019 m/s range 10 m (CONWEP Output)
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Composite barriers (LeBlanc et al. 2007)—penetration and perforation examples
Asian Journal of Civil Engineering Projectile Penetration into Rock Rubble/Boulder Overlay
Projectile Penetration into Rock Rubble/Boulder Overlay
4.5
5 with air-filled voids with sand-filled voids with grout-filled voids
4
4
Penetration, meters
Penetration, meters
3.5
3
with air-filled voids with sand-filled voids with grout-filled voids
4.5
Projectile weight 43.88 kilograms Projectile diameter 15.5 cm Boulder diameter 20 cm
2.5
2
1.5
1
3.5 Projectile weight 43.88 kilograms Projectile diameter 15.5 cm Impact velocity 350 meters/sec
3
2.5
2
1.5
1 0.5
0 150
0.5
175
200
225
250
275
300
Impact Velocity, meters/sec
325
350
0 15
375
Fig. 30 Projectile penetration 3.13 m to.6 m Impact Velocities 334 m/s to 346 m/s for varying void configurations into rock rubble/boulder overlay (CONWEP Output)
20
25
30
35
Boulder Diameter, cm
ConWep Output
40
45
50 ConWep Output
Fig. 31 Projectile penetration 3.13 m to .6 m Boulder diameters (Nominal 200 mm) for varying void configurations into rock rubble/ boulder overlay (CONWEP Output)
Rock rubble overlay (Qin and Hua 2012)—penetration example
• See Figs. 30 and 31
Conclusions
•
The topic of fragmentation is a critical one and one that must be considered in any design process. The critical parameters are as follows:
•
•
The further away either a projectile is fired towards a structural element the less likely damage or perforation occurs even though the element is penetrated so range (m) is critical to be considered.
•
The higher the residual velocity (m/s) on perforation (mm) of the element the more likely a fragment will cause additional damage to other elements and death or injury to individuals nearby. The higher the concrete strength (MPa) of structural elements impacted the less likely fragmentation will occur and if it does final velocities will be low. The geometry of the structural element impacted such as its thickness (mm) dictates whether fragmentation from scabbing or spall occurs. For mild steel the higher the ‘‘Brinell Number’’ (400 plus) the more likely the structural element will not be perforated only penetrated.
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Asian Journal of Civil Engineering Fig. 32 Ballistic loading effects design process chart (CONWEP Output)
PROJECTILE LOADING
HEMISPHERICAL BLAST LOADING
YES/NO
YIELD STRENGTH (MPa)
SPHERICAL BLAST LOADING
DENSITY (kg/m3)
THICKNESS (mm)
TARGET PENETRATION (BREACH) (mm)
PERFORATION (mm) YES/NO
FRAGMENTATION FRAGMENT WEIGTH (kg)
SCABBING
FRAGMENT VELOCITY (m/s)
FRAGMENT GEOMETRY PRIMARY FRAGMENTATION (STANDARD SHAPE) SECONDARY FRAGMENTATION (WORST CASE LOADING)
FRAGMENT STRIKING VELOCITY (m/s) FRAGMENT DENSITY (kg/m3) FRAGMENT DESIGN PARAMETERS (TRAJECTORY, ANGLE OF OBLIQUITY & IMPACT VELOCITY)
INDIVIDUAL STRUCTURAL ELEMENT DESIGN •
•
•
Composite barriers of soil, concrete or steel can adequately entrap fragments by minimizing penetration into the barrier. Soil conditions (rock, clay wet or moist, sand, etc.) dictate how far a projectile will penetrate (mm) the subgrade or earthen mounds. The mass of the fragment and its shape dictates its final velocity (m/s) and trajectory as well as its range (m).
The CONWEP outputs for different material subjected to varying impacts demonstrate the technical methodology behind the concept of fragmentation and how to design for
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it. Figure 27 below dramatically details the design process to cater for ballistic loading effects (Fig. 32). Acknowledgement I would like to acknowledge the support and encouragement provided by Professor Bijan Somali, Doctor Chunwei Zhang and Doctor Eric Anciche.
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