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International Journal of Impact Engineering 69 (2014) 122e135

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International Journal of Impact Engineering

journal homepage: www.elsevier .com/locate/ i j impeng

Reliability of RC shielded steel plates against the impact of sharp noseprojectiles

Nadeem A. Siddiqui*, Baha M.A. Khateeb, Tarek H. Almusallam, Yousef A. Al-Salloum,Rizwan A. Iqbal, Husain AbbasDepartment of Civil Engineering, Chair of Research and Studies in Strengthening and Rehabilitation of Structures, King Saud University, Riyadh 11421,Saudi Arabia

a r t i c l e i n f o

Article history:Received 25 June 2013Received in revised form27 February 2014Accepted 1 March 2014Available online 12 March 2014

Keywords:RC shielded platesDouble-wall containmentImpactReliabilityBallistic limit

* Corresponding author. Tel.: þ966 11 4676962; faxE-mail address: nadeem@ksu.edu.sa (N.A. Siddiqu

http://dx.doi.org/10.1016/j.ijimpeng.2014.03.0010734-743X/� 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

Reinforced Concrete (RC) shielded steel plates are extensively employed in double wall containmentstructures. In such structures, RC shield surrounds the inner steel shell/plate, and inner steel shell/plateacts as a barrier against the release of radiations. Although a substantial research is available on impactstudies of concrete, reinforced concrete and steel plates, the studies on RC-shielded steel plates are notwidely available. Also how the uncertainties involved in the design parameters influence the reliability orsafety of RC shielded steel plates is not very well known. In the present study, a simple experiment wasdesigned to simulate a double-wall containment (i) to study the response of RC shielded steel platesagainst the impact of single (ogive) and double nose (bi-conical) shaped projectiles, and (ii) quantitativelyevaluate howmuch safe the inner wall (steel plate) is under the impact of these projectiles. To achieve theabove objectives, the study was carried out in two parts. In the first part, experiments were conducted bystudying the impact resistance of RC shielded steel plates of 600 � 600 � 5 mm thickness against theimpact of non-deforming projectiles of ogive and bi-conical nose shapes. The steel plate was placed at aclear distance of 75mm from 60mm thick RC slab. The specimens were tested at varying projectile impactvelocities. Investigations were carried out to measure damage level in steel plate in terms of its defor-mation, fracture and perforation. In the second part, reliability analysis of all the tested concrete shieldedsteel plates was carried out using Monte Carlo Simulation technique for a range of impact velocities. Theresults of the reliability analysis were then used to relate the probability of failure with different scenariosof the failure of the specimens. The effect of RC shield thickness and steel plate thickness on the reliabilityof RC shielded steel plate against the impact of bi-conical and ogive nose projectiles were also studied onparametric basis. In order to use the available formulation on conical nose shape projectiles, the bi-conicalnose was replaced by an equivalent conical nose for which a simple formula was derived. In order tovalidate this simplified attempt to suggest an equivalent conical nose, one of the tests with bi-conical noseprojectile was repeated with the equivalent conical nose projectile. At a given striking velocity, theequivalent conical nose projectile produces a similar damage pattern and the same damage level in the RCshielded steel plate, as that of bi-conical nose projectile at the same impact velocity.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Reinforced Concrete (RC) shielded steel plates are extensivelyemployed in double-wall containment structures. Double wallcontainment structures are made up of two walls e an outer rela-tively thick Reinforced Concrete (RC) wall and an inner steel plate/shell. The outer RC wall of the containment shields the inner steel

: þ966 11 4677008.i).

wall (which may house the reactor, steam generators and othervital plant equipment) against the effects of the outer environmentand impacts of external missiles, projectiles and even airplanes. Thepurpose of the inner steel plate/shell is to prevent the emissions inthe event of process failure. These containments in Nuclear powerplants (NPP) are provided to prevent leakage of radioactivematerialinto the environment in the event of a serious failure in the processsystem [1e5].

In the past, some limited works are reported on the reliabilityanalysis of structures subjected to impact loads of projectiles,missiles and airplanes on concrete structures [1,4e8]. Siddiqui et al.

Fig. 1. Schematic diagram of RC shielded steel plate.

N.A. Siddiqui et al. / International Journal of Impact Engineering 69 (2014) 122e135 123

[5] presented a methodology for detailed reliability analysis of anuclear containment without metallic liners against aircraft crash.Choudhury et al. [6] presented a methodology for the reliabilityanalysis of a buried concrete target against normal missile impact.Penmetsa [7] presented a methodology for the system reliabilityanalysis that can determine the probability of the destruction ofburied concrete targets using deep penetration weapons. Siddiquiet al. [8] carried out the reliability assessment of concrete targetssubjected to impact forces due to striking missiles. They identifiedvarious design parameters which can be judiciously chosen toachieve the desired reliability for concrete targets subjected toimpact forces. Pandey [9] presented a quantitative reliability-basedapproach to evaluate the containment integrity in terms of thedeteriorated condition of bonded prestressing systems. Han andAng [10] suggested serviceability design load factors, and carriedout the reliability assessment of RC containment structures.

The above review of literature indicates that although a sub-stantial research is available on impact studies of concrete, rein-forced concrete and steel plates, the studies on reinforced concrete-shielded steel plates are not widely available. Also how the un-certainties involved in the design parameters influence the reli-ability or safety of RC shielded steel plates is not very well known.Keeping these scope in view, in the present study, a simpleexperiment was designed to simulate a double-wall containment(i) to study the response of RC shielded steel plates against theimpact of single (ogive) and double nose (bi-conical) shaped pro-jectiles, and (ii) quantitatively estimate how much safe the innerwall (steel plate) is under the impact of these projectiles. It is worthmentioning that although in the nuclear power industry and, inparticular, in the safety calculation and assessment of containmentstructures, a flat-nosed projectile represents the most dangerousscenario in terms of energy absorption [11e13], but in the presentstudy sharp nose projectile has been selected for the study becausesharp nose projectiles are also very common in the impact studies.

To achieve the above objectives, the studywas carried out in twoparts. In the first part, experiments were conducted by studying theimpact resistance of RC shielded steel plates of 600 � 600 � 5 mmthickness against the impact of non-deforming projectiles of ogiveand bi-conical nose shapes. The steel plate was placed at a cleardistance of 75 mm from 60 mm thick RC slab. The specimens weretested at varying impact velocities. Investigations were carried outto measure damage level in steel plate in terms of its deformation,fracture and perforation.

In the second part, reliability analysis of all the tested concreteshielded steel plates was carried out using Monte Carlo Simulationtechnique for a range of impact velocities to relate the probability offailure with different scenarios of the failure of the specimens.Statistical properties and probability distributions of the randomvariables involved in the penetration of RC slab and steel plate suchas concrete strength, reinforcement ratio, thickness of concrete andsteel plates, projectile nose geometry, impact velocity, materialproperties of concrete and steel, were judiciously selected. Theresults of the reliability analysis were then used to relate theprobability of failure with different scenarios of the failure of thespecimens. The effect of RC shield thickness and steel plate thick-ness on the reliability of RC shielded steel plate against the impactof bi-conical and ogive nose projectiles were also studied onparametric basis.

2. Experimental program

In order to study the impact resistance of RC shielded steelplates, fourteen specimens were tested. The steel plate of 5 mmthickness was shielded by 60 mm thick RC shield. The steel platewas placed at a clear distance of 75 mm from the RC shield. These

specimens were tested in the impact lab by varying the impactvelocity, and projectile nose shape as shown in Fig. 1. Table 1 showsthe details of the test matrix. In this table, the specimens weredesignated by three terms name. The first term RCSP is an acronymfor RC Shielded Plate. The second term indicates type of the pro-jectile used (A refers to bi-conical and B indicates ogive nose pro-jectile). The third term illustrates the striking velocity of theprojectile in m/s.

2.1. Test specimens

All the RC shields had a cross section of 600� 600� 60 mm andwere reinforced on rear face with deformed f8 mm steel bars @100 mm centre to center spacing as shown in Fig. 2. In all thespecimens, the mesh arrangement was such that none of the steelbars cross the slab’s center and thus projectile does not strike (orpush) any of the mesh steel bars. The projectile impacted the RCshield normally in order to cause maximum damage to the RCshield. All the RC shields (i.e. slab specimens) were cast usingconcrete of 50 MPa design strength. After casting, the RC shieldspecimens were covered with wet burlap and were subjected tointermittent spraying of water everyday for two weeks and thenleft to dry for next two weeks.

2.2. Properties of materials

2.2.1. ConcreteNon-air entrained concrete supplied by a local ready mix plant

containing Type 1 ordinary Portland cement was used. Fineaggregate was a mixture of white and silica sands. The coarseaggregate consisted of crushed limestone with a maximum size of10 mm. The composition of the concrete by weight is provided inTable 2. Three cylinders (150� 300mm)were cast to determine the28-day compressive strength. The specimens had an averagecompressive strength of 52.2 MPa.

2.2.2. Reinforcing steelThe steel bars of 8 mm diameter were used for reinforcing the

RC shield (slab) specimens as shown in Fig. 2. All the steel bars wereof Grade 420 (i.e. yield strength ¼ 420 MPa or 60 ksi).

Table 1Test matrix.

Specimen name No. of specimens Striking velocity (m/s)

Bi-conical nose projectile (A)RCSP-A-51 1 51.0RCSP-A-63 1 63.0RCSP-A-92 1 92.0RCSP-A-125 1 125.0RCSP-A-147 1 147.0RCSP-A-169 1 169.0RCSP-A-177 1 177.0Ogive nose projectile (B)RCSP-B-51 1 51.0RCSP-B-63 1 63.0RCSP-B-92 1 92.0RCSP-B-125 1 125.0RCSP-B-147 1 147.0RCSP-B-158 1 158.0RCSP-B-169 1 169.0

Total no. of specimens 14

N.A. Siddiqui et al. / International Journal of Impact Engineering 69 (2014) 122e135124

2.2.3. Steel plateThe steel plates of 5mm thickness and yield strength of 420MPa

were obtained from a local manufacturing Company and they werecut into the desired size of 600 � 600 mm.

2.2.4. ProjectilesIn the present study, two projectile nose shapes namely ogive

and bi-conical with the almost same mass were used. The bi-conical nose projectile was same as that used in authors’ earlierwork [14]. The mass and shaft diameter of the two projectiles were0.8 kg and 40 mm respectively. Fig. 3 shows details of the twoprojectiles. It is worth mentioning that bi-conical nose projectilefalls under the category of double nose projectiles [14,15]. Since thestudies on double-nose projectiles are limited, bi-conical projectilewas used for striking the specimens. Also, since the response of

Fig. 2. Reinforcement details in RC shields (All dimensions are in mm).

ogive nose is close to conical nose, instead of testing a conical nosealong with ogive nose, bi-conical nose was preferred.

2.3. Preparation of the RC shield specimens

RC shield specimens were cast in wooden moulds. The fabri-cated steel cage with concrete cover blocks was placed in themould. The casting was done in a single layer and compacted by apin vibrator. After casting, the RC shield specimens were coveredwith wet burlap and were subjected to intermittent spraying ofwater every day for two weeks and then left to dry for next twoweeks. Three companion standard concrete cylinders were alsoprepared to measure 28-day compressive strength of the concrete.The cylinders were cured in the water tanks.

2.4. Test procedure

The impact penetration tests were carried out with a gas-gunsystem of Longwin, Taiwan. In order to begin the impact test, thesteel plate was mounted first on a stationary rigid steel frame andthen the RC shield (slab) was placed at a clear distance of 75 mmfrom the steel plate. Two opposite edges of the steel plate and theRC shield were clamped to the rigid frame using steel bolts. Thealignments of the steel plate and RC shield were properly checkedfrom their front and back faces. The projectile was then fired tostrike the RC shield. The measurements and observations recordedinclude the projectile velocity, the crater size on the front and therear faces of the RC shield and the deformation/fracture pattern ofthe steel plate.

It is worth mentioning that although the present experimentalstudy has two distinct stages: penetration into the concrete plate inthe first stage and penetration into the steel plate in the secondstage with the residual velocity of the previous stage, but the studyshould be viewed as a single problem because the projectile re-sidual velocity is dependent on the projectile strike velocity andproperties of RC shield, and the uncertainties in the properties of RCshield and strike velocity cannot be duly incorporated in the reli-ability analysis, presented later in this paper, if the above two stagesare uncoupled.

3. Discussion of test results

In the present study, the response of the RC shield and steelplate was studied in terms of front and rear damaged areas of theRC shield and perforation resistance of the steel plate. To quantifythe damage, damage levels are defined based on the perforation ofRC shield and damages observed in the steel plate. The damagelevels are scaled from 1 to 5 as defined below.

e Level 1 (L1): Projectile punctures the RC shield but gets stuckinto the shield, and thus no damage to steel plate.

e Level 2 (L2): Projectile perforates the RC shield with a residualvelocity and hits the steel plate leaving an indentation in thesteel plate.

e Level 3 (L3): Projectile perforates the RC shield with a residualvelocity and fractures the steel plate.

e Level 4 (L4): Projectile perforates the RC shield with a residualvelocity and perforates the steel plate but with zero residualvelocity and remains stuck in the steel plate.

e Level 5 (L5): Projectile perforates the RC shield with a residualvelocity and perforates the steel plate also with a residualvelocity.

In damage levels, L2 to L5, indentation and/or perforation ofsteel plate was accompanied by substantial flexural deformation.

Table 2Mix proportions of the concrete mix (f ’c ¼ 50 MPa).

Material Weight (kg)

Cement 446White sand 284Silica sand 42610 mm Aggregate 1043Water (w/c ¼ 0.40) 178.4Super plasticizer, SP430 0.6 L/100 kg of cement

N.A. Siddiqui et al. / International Journal of Impact Engineering 69 (2014) 122e135 125

The above damage levels were defined based on the experimentallyobserved failure patterns, as shown in Fig. 4.

Table 3 lists the damage levels and crater sizes observed in theRC shield (slabs) in the two perpendicular directions. The cratersizes in the two perpendicular directions are defined by D1 and D2respectively. D1 and D2 are thus the longest and the shortestorthogonal dimensions of the crater as shown in Fig. 5. The diam-eter of equivalent circle, Deq (at the front or rear face), was esti-mated using Deq ¼ ffiffiffiffiffiffiffiffiffiffiffiffi

D1D2p

[16].

3.1. Damage in RC shield

It is worth mentioning that the damage levels of the specimensare indicative of the amounts of the energy dissipated during theimpact. Consideration of this criterion was valid because the hard-steel projectiles were not deformed during the impact. Although in

Fig. 3. Details of (a) Ogive (b) Bi-conical nose shape projectiles (All dimensions are inmm).

certain cases, the projectiles noses were scratched, their shaperemained un-deformed and therefore, the energy dissipated in thedeformation of the projectiles was considered negligible withrespect to the energy dissipated in inflicting the damage to the RCshield and steel plate.

When the RC shield was subjected to the impact load by theprojectile, in general, threemajor fracture regionswere formed: thecrater region, the crushed aggregate region and the extensivecracking region [17]. In addition, scabbing was also observed inwhich amass of concretematerial from the opposite (or rear) face ofthe slabwas separated due to the impact of the projectile. The craterwas formed in the front face as a result of crushing of the concretedue to the concentrated forces at the surface of the concrete. Theshape and size of the crater on the front and the rear faces varied asper the dynamic loading, measured in terms of impact velocity.

Table 3 shows the crater diameters in the front and the rear facesof tested RC shields. In general, the crater diameters on the rearfaces are much larger than the front face crater sizes. This is anexpected trend, as the front face crater was produced as a result ofcrushing of the concrete due to the concentrated forces at thesurface of the concrete; while the rear face crater was created dueto the scabbing/separation of concrete material from the rear faceof the RC shield (owing to the high tensile stresses).

3.2. Damage in RC shielded steel plate

Table 3 and Figs. 6 and 7 also show that in the first three speci-mens when the impact velocity was low (below the ballistic limit ofRC shield), the damage level was L1 (Fig. 4) under the impact of thebi-conical as well as the ogive nose shape projectiles. It is due to thisreason, no damage was observed in the steel plate as either pro-jectile did not perforate the RC shield or if the shieldwas perforated,projectile was stuck in the RC shield as shown in Figs. 8 and 9.

When the projectile strikes the RC shield with an impact ve-locity of 125 m/s, the RC shield was fully penetrated and the steelplate was hit by the projectile. An indentation was observed whenthe steel plate was hit by bi-conical projectile, whereas a fracture ofthe plate was noticed for ogive projectile impact. Thus, under theimpact of bi-conical projectile, damage level L2 was observed whilefor ogive nose projectile, the damage level L3 was noticed (Table 3and Fig. 4).

When bi-conical projectile hit the RC shield with an impactvelocity of 147 m/s, the RC shield was fully penetrated and the steelplate was impacted by the projectile with a residual velocity. Thisimpact caused a wide cut/fracture in the steel plate and damagelevel L3 was observed (Fig. 4 and Table 3). However, when the ogivenose projectile was used to impact the RC shield with the samevelocity, the RC shield was fully perforated and the projectile hit thesteel plate causing a substantial size fracture near the center of thesteel plate as shown in Fig. 13. This damage thus comes under thecategory of L4 (Fig. 4).

At the impact velocity of 169 m/s, the bi-conical nose projectilefully penetrated the RC shield and then stuck in the steel plate thusindicating damage level L4. The same damage level was observedfor ogive nose projectile when its strike velocity was 147 m/s. Thisdifference can be attributed to the effect of the nose shape of theprojectile. For ogive nose, the full penetration occurred at a lowervelocity because the ogive projectile had sharper nose than the bi-conical projectile. The sharp nose develops higher pressure in thesteel plate causing a fracture in the plate at relatively lesser strikingvelocity.

When the ogive projectile hit the concrete shield with an impactvelocity of 158 m/s, both the RC shield and steel plate were fullyperforated as the projectile was found on the other side of the steelplate as shown in Fig. 10. The damage thus falls under the category

Fig. 4. Definition of damage levels based on damage in the RC shielded steel plate.

N.A. Siddiqui et al. / International Journal of Impact Engineering 69 (2014) 122e135126

of L5 (Fig. 4 and Table 3). However, the bi-conical projectile showeda similar damage (L5) when its striking velocity was 177 m/s.

It is worth mentioning that the damage level L2 was notobserved under the impact of ogive nose projectile.

4. Formulation for reliability analysis

The reliability analysis requires a limit state function which is amathematical representation of a particular mode of failure. Thisfunction assumes a negative or zero value when a structuralcomponent under study fails against a given mode of failure and itis positive if the component is safe against that mode of failure. Theprobability of failure can then be defined as

Pf ¼ Phg�x�� 0

i(1)

where, Pf represents the probability of failure, gðxÞ is the limit statefunction and x is the vector of basic random variables.

In order to derive the limit state function for the reliabilityanalysis of RC shielded steel plate, a hard (non-deformable) sharpnose projectile is assumed to normally impact the RC shield withsuch a velocity that it perforates the outer RC shield and then hitsthe inner steel plate with some residual impact energy (or residualvelocity). The system is assumed to fail when the steel plate alsogets fully penetrated by this projectile.

The failure of the steel plate is assumed to occur when theimpact energy of the projectile was more than the perforationenergy of the steel plate. Keeping above points in view, if theperforation energy of the steel plate is Eperf and the projectile ki-netic energy is Eproj then the limit state function can be expressed as

g�x�

¼ Eperf � Eproj ¼ Eperf �12MV2

* (2)

where, Eproj¼ projectile energy;M¼mass of the projectile; V*¼ theresidual velocity of the projectile with which it hits the steel plate.

Table 3Summary of the test results.

Specimen name Strikingvelocity(m/s)

Damagelevel

Crater size in the RC shield (mm)

Front face Rear face

D1 D2 Deq D1 D2 Deq

Bi-Conical nose projectileRCSP-A-51 51.0 L1 65 62 64 200 255 226RCSP-A-63 63.0 L1 100 80 89 230 280 254RCSP-A-92 92.0 L1 120 90 104 230 240 235RCSP-A-125 125.0 L2 80 82 81 190 200 195RCSP-A-147 147.0 L3 100 120 110 160 190 174RCSP-A-169 169.0 L4 130 110 120 190 190 190RCSP-A-177 177.0 L5 120 115 117 210 220 215Ogive nose projectileRCSP-B-51 51.0 L1 65 60 63 170 235 200RCSP-B-63 63.0 L1 70 30 45 310 310 310RCSP-B-92 92.0 L1 102 120 104 230 240 235RCSP-B-125 125.0 L3 125 115 120 200 225 212RCSP-B-147 147.0 L4 125 125 125 205 288 196RCSP-B-158 158.0 L5 125 130 127 180 190 185RCSP-B-169 169.0 L5 125 170 145 200 190 195

Fig. 6. Damage level-impact velocity variation under the impact of bi-conicalprojectile.

N.A. Siddiqui et al. / International Journal of Impact Engineering 69 (2014) 122e135 127

The residual velocity is the velocity of impacting projectile after theperforation of the RC shield.

From the above equation, it is obvious that the failure of the steelplate will occur if the residual kinetic energy Eproj is more than orequal to the perforation energy Eperf of the steel plate of theimpacting projectile.

In order to calculate the projectile impact energy with which ithits the steel plate, we need to estimate the residual velocity of theprojectile after the perforation of the RC shield. Thus, the formu-lation of limit state function requires the formulation of projectileenergy at the exit (or residual velocity of the projectile) of the outerRC shield and the perforation energy of the steel plate. The ex-pressions for perforation energy of the steel plate and residualvelocity of the projectile are given in the Appendix which are basedon the following assumptions and idealizations:

e The projectile is rigid i.e. the deformation of projectile is negli-gible and only the RC shield and steel plate deformations havebeen considered.

Fig. 5. Estimation of the equivalent diameter of the damaged area [14].

e The impact of projectile is normal to the RC shield and the steelplates.

e The loss of energy in the form of heat and sound are negligible.

Substituting the expressions of perforation energy and the re-sidual velocity of the projectile from Appendix, the limit statefunction can be written as

g�x�

¼ pd2t

"0:125Y þ 0:0625rsCE

�ðV0 � VBLÞdh

�2#

� 12MðV0 � VBLÞ2 for c � cc

(3a)

g�x�

¼ pd2t

"0:125Y þ 0:0625rsCE

�ðV0 � VBLÞdh

�2#

� 12M� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�

V20 � V2

BL

�r �2

for c > cc

(3b)

In the above equation, c is the dimensionless thickness of con-crete such that c ¼ H/d; cc ¼ dimensionless critical thickness ofconcrete target which can be estimated using expressions given byChen et al. [18].

In the above limit state Eq. (3), the variablesV0; d; f ’c; rc; fy;h;M; rs;Y;H; t; ps are implicitly or explicitly involved.These variables have significant inherent uncertainties, and due tothis reason, they are considered as random variables in the subse-quent reliability analysis. Arranging these variables in vector formleads to

Fig. 7. Damage level-impact velocity variation under the impact of ogive noseprojectile.

Fig. 8. Stuck projectile in the RC shield (Damage level L1).

N.A. Siddiqui et al. / International Journal of Impact Engineering 69 (2014) 122e135128

x ¼�V0; d; f

’c; rc; fy; h;M; rs; Y ;H; t; ps

�(4)

here x is the vector of basic random variables.Having derived the limit state functions, the next step is the

assessment of probability of failure (also called risk) and reliability(measured in terms of the reliability index b) of the RC shieldedsteel plate against the normal impact of the projectile. For this

Fig. 9. Ogive projectile stuck in the steel plate

purpose, Monte Carlo Simulation technique [19] has beenemployed. In the present study, 500,000 simulations were used tocarry out the Monte Carlo Simulation for estimating the probabil-ities of failures. The step-by-step procedure followed in imple-menting Monte Carlo Simulation is presented in Fig. 11.

4.1. Equivalent conical nose

In order to use the existing formulation on conical nose shapeprojectile, the bi-conical nosewas replaced by an equivalent conicalnose. In order to use the limit state function (Eq. (2)) for the reli-ability analysis of RC shielded steel plate, expressions for the pro-jectile velocity at the exit of the outer RC shield (i.e. residualvelocity) and perforation energy of the steel plate are required. Forthe ogive nose projectiles, the desired expressions were taken fromthe literature [18,23] and [20,21] respectively. For bi-conical pro-jectile, although references [18,23] could be employed for derivingthe residual velocity of the projectile from the given generalizedexpression, but for the perforation energy of the steel plate such ageneralized expression was not available - at least in the used ref-erences [20,21]. It is due to this reason that the equivalenceapproach was adopted for bi-conical nose projectile. The equivalentconical nosewas determined by equating the volume and hence theweight of bi-conical nose to the equivalent conical nose, as shownin Fig. 12. The volume of the two nose shapes were obtained fromthe revolution of the two hatched areas shown in Fig. 12, thusgiving:

13pR2

�R

tan q2

�� 13pðh1 tan q1Þ2

�h1 tan q1tan q2

�þ 13pðh1 tan q1Þ2h1

¼ 13pR2heq þ pR2

�h� heq

�(5)

where,

h1 ¼ R� h tan q2tan q1 � tan q2

(6)

e Front and back views (Damage level L4).

Fig. 10. Perforation of the steel plate by ogive nose projectile (Damage level L5).

N.A. Siddiqui et al. / International Journal of Impact Engineering 69 (2014) 122e135 129

The length of equivalent conical nose derived from the above Eq.(5) is:

heq ¼ 32h� R

2 tan q2þ h31 tan2q1

2R2

�tan q1tan q2

� 1�

(7)

In order to validate the above simplified attempt to suggest anequivalent conical projectile by equating the weight of the biconical and the equivalent conical projectiles, one of the tests withbi-conical projectile was repeated with equivalent conical projec-tile. It was assumed that if at a given striking velocity, the equiva-lent conical projectile produces a similar damage pattern (in RCshield and steel plate) and the same damage level in the RC shiel-ded steel plate, as that of bi-conical projectile at the same impactvelocity, the two projectiles are equivalent. For this purpose, lengthof equivalent conical nose was first estimated using the aboveequation (Eq. (7)) and it was obtained as 31.1 mm. A new equivalentconical projectile of this nose length was then prepared. The tests ofbi-conical nose projectile for the highest strike velocity of 177 m/swas then repeated with equivalent conical nose projectile, andobserved damage pattern and damage level were studied. Theobserved damage pattern in the RC shield and steel plate are shownin Figs. 13 and 14 respectively. The damage pattern which wasobserved in the bi-conical projectile is also shown in these figuresfor comparison. These figures illustrates that the crater sizes onfront and back faces of RC shields for the bi-conical and equivalentconical nose projectiles are sufficiently close. The observed damagepattern (petals) in the RC shielded steel plate was, however, slightlydifferent from those observed using bi-conical nose projectile butboth the projectiles perforated the steel plate and thus the size ofholes for the two nose shapes were also almost the same. Asequivalent conical nose projectile also completely perforated the RCshielded plate, the damage level was L5. The same damage levelwas observed when bi-conical nose projectile was used for theimpact test (Fig. 14). The similarity was observed because theequivalent conical nose is expected to penetrate more (beingsharper than bi-conical) in the early stages of nose penetration, butat later stages of penetration bi-conical nose would have moreconvenience in penetration (than equivalent conical nose). In thismanner, the two noses produced similar damage and same damagelevels in the RC shielded steel plate.

Due to the limited number of specimens, the validity forequivalence could not be repeated with all the velocities for which

bi-conical projectile was used for testing. But a similar damagepattern and same damage level is expected for other velocities too.However, in order to establish the validity range for the aboveproposed equivalence equations more investigations are required.Authors also intend to conduct a separate study on this equivalencein the future.

5. Analysis of reliability results

In order to carry out the reliability analysis of RC shielded steelplate against the normal impact of hard projectiles, the data pre-sented in Table 4 was employed. In this table, nominal values arethose which were used in the experiments. The references used forthe selection of the COV and the probability distributions of variousrandom variables are given in the last column of this table. In thistable, the bias factor represents the ratio of mean to the nominalvalue. When bias factor is one, it indicates that the nominal value isthe same as the mean value. The value of COV is a measure of de-gree of uncertainty.

Employing the data presented in Table 4 and using the MonteCarlo simulation technique, probability of failure and reliabilityindices of RC shielded steel plates were obtained and shown inTable 5. In this table, the nominal striking velocity was varied as itwas varying in the experiment. The striking velocity was variedfrom 51 to 177 m/s for bi-conical projectile and 51 to 169 m/s forogive nose projectile. The last two columns of Table 5 lists thevalues of the reliability indices b and the probabilities of failure Pf ofthe RC shielded steel plates. The results clearly indicate that as theprojectile striking velocity increases, the probability of failure of thesteel plate also increases. This is an expected trend. Fig. 15 alsoshows the same trend but in terms of reliability index b.

Table 5 shows that for those specimens which had damage levelL1, the probabilities of failure were almost zero. This is due to thefact that, despite the significant uncertainties involved in the bal-listic limit of the RC shield, the ballistic limit did not go below thestriking velocity of the projectile and thus the RC shield was notperforated (Figs. 6 and 7). Since the RC shield was not perforated,there was no failure of the steel plate and thus the probability offailure of the steel plate was zero as also indicated in Figs. 16 and 17.However, the third test in which projectile impact velocity wasaround 92 m/s, it was quite possible that due to uncertainties in theset of all possible ballistic limit velocities, some of the ballistic limitvelocities fallen below the striking velocity of the projectile whichgave a finite value of the probability of failure of the concreteshielded steel plate. But the value was quite small as reliabilityindexwas higher than the desired value of 3.0 for both ogive and bi-conical nose projectiles although it was little smaller for the ogivenose projectile.

After increasing the striking velocity of the bi-conical noseprojectile to 125 m/s the damaged level of the specimen waschanged to L2 which indicates that the projectile perforated the RCshield with a residual velocity and hits the steel plate leaving anindentation in the steel plate (but without fracturing). When thereliability analysis was performed for the nominal striking velocityof 125 m/s employing 500,000 simulations in Monte Carlo simu-lation technique, the probability of failure was obtained as1.5 � 10�2 as shown in Table 5 and Fig. 16. This illustrates thatapproximately 7500 simulated striking velocities (out of a total of500,000 velocities) were above the ballistic limit of the RC shieldand thus the projectile with these striking velocities perforated theslab and hit the steel plate with a residual velocity which caused adamage level L2. However, when the ogive nose projectile was usedto impact the specimen with the same striking velocity, thedamaged level was L3, which indicates that the projectile perfo-rated the RC shield with such a high residual velocity that the steel

Fig. 11. A flow chart showing the major steps followed in Monte Carlo Simulation.

N.A. Siddiqui et al. / International Journal of Impact Engineering 69 (2014) 122e135130

plate was fractured. When the Monte Carlo technique was appliedto this case using 500,000 simulations, the probability of failurewas 3.99 � 10�2 as shown in Table 5 and Fig. 17. This means thatapproximately 19,950 values of the simulated striking velocitieswere greater than the ballistic limit and exited from RC shield withsuch high residual velocities that damaged the plate with damagelevel L3.

Table 5 also shows that the damaged level L3 occurred for the bi-conical projectile when projectile impacts the concrete shield withthe striking velocity of 147 m/s. When the Monte Carlo techniquewas applied using this velocity as nominal striking velocity, prob-ability of failure was 1.70 � 10�1 (Table 5 and Fig. 16). This means

that approximately 85,000 of the simulated striking velocitiespenetrated the RC shield and hit the steel plate with such highresidual velocities that caused damage level L3 in the steel plate.However, when the ogive nose projectile hits the shield, the dam-age level was L4 and the probability of failure was higher than thebi-conical projectile (Fig. 17). This can be attributed to nose shape ofthe ogive nose projectile. For the same striking velocity, the ogivenose projectile, in general, penetrates the RC shield with a higherresidual velocity than the bi-conical projectile.

Finally the experimental program shows that the steel plate wasfully perforated when the bi-conical nose projectile impacts theconcrete shield with a nominal striking velocity of 177 m/s. When

Fig. 12. Converting bi-conical nose to equivalent conical nose projectile.

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reliability analysis was carried out using Monte Carlo technique for500,000 simulations, approximately 342,000 simulated strikingvelocities penetrated the shield with such residual velocities thatcause full perforation of the plate. A similar damage level occurred

Fig. 13. Comparison of the damage in the RC shield due

when ogive nose projectile hit the concrete shield with a littlelower velocity i.e. 169 m/s (Table 5). The probability of failure wasalmost the same as bi-conical nose projectile as shown in Figs. 16and 17. This can again be attributed to the effect of the shape ofthe ogive nose.

It is worth mentioning that although Chen et al. [18] formulaoverestimates the ballistic limit velocity for thin RC targets (presentconcrete shield), their formula was employed for estimating theballistic limit velocity (Eq. (A.3)). This is because (i) Chen et al. [18]formula duly considers reinforcement in the concrete target as wellas it is theoretically applicable to both types of targets (i.e. thin aswell as thick), and (ii) no othermore rational formula for sharp noseprojectiles was available to us. This overestimation in ballistic limitcauses underestimation of residual velocity which leads to anoverestimation in the reliability index (or underestimation in theprobability of failure). Thus the numerical values presented in thispaper for reliability index of concrete shielded steel plate are littlehigher (or probability of failure little smaller) than their actualexpected values.

5.1. Sensitivity analysis

In the present section, a few sensitivity analyses were carriedout to obtain the results of practical interest. For the sensitivity

to bi-conical and equivalent conical nose projectiles.

Fig. 14. Comparison of the damage pattern observed in the RC shielded steel plate due to bi-conical and equivalent conical nose projectiles.

Table 5Reliability indices and probabilities of failure of the RC shielded steel plate.

Specimen name Strikingvelocity (m/s)

Observeddamage level

Pf b

Bi-Conical nose projectileRCSP-A-51 51 L1 w0 e

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study of any variable, its nominal value was varied. The impactvelocity of the projectile was taken as 125 m/s and all the othervariables were taken the same as shown in Table 4. The sensitivitystudy was carried out to obtain that value of the variable whichgives for the RC shielded steel plate (b� bD)2 z 0. Here b and bD arethe actual and desired reliability index values. In the presentsensitivity analyses, bD ¼ 3.0 was chosen as this is a typical value ofthe desired reliability index for normal structures and the struc-tures of high importance [8]. (b � bD)2 z 0 is an indication that theRC shielded steel plate is safe to the desired level against the impactof the given projectile.

RCSP-A-63 63.0 L1 w0 e

RCSP-A-92 92.0 L1 6.0 � 10�6 4.378RCSP-A-125 125.0 L2 1.5 � 10�2 2.169RCSP-A-147 147.0 L3 1.7 � 10�1 0.945RCSP-A-169 169.0 L4 5.44 � 10�1 �0.112RCSP-A-177 177.0 L5 6.81 � 10�1 �0.473Ogive nose projectileRCSP-B-51 51.0 L1 w0 e

RCSP-B-63 63.0 L1 w0 e

RCSP-B-92 92.0 L1 3.60 � 10�5 3.97RCSP-B-125 125.0 L3 3.99 � 10�2 1.751RCSP-B-147 147.0 L4 2.94 � 10�1 0.541RCSP-B-158 158.0 L5 5.00 � 10�1 �0.002RCSP-B-169 169.0 L5 7.00 � 10�1 �0.518

5.1.1. Effect of the thickness of the RC shieldFig. 18 shows that as the RC shield thickness increases, reliability

of the shielded steel plate also increases. This is an expected trendas the RC shield thickness increases, the projectile residual velocitydecreases which reduces the failure chances of the shielded steelplate. Fig. 18 also shows that a little change in the RC shield thick-ness can alter the reliability substantially. This illustrates that RCshield plays a vital role in maintaining the reliability of the steelplate as it is the main source for reducing the residual impact en-ergy. The two different values of RC shield thickness, for achievingthe same reliability index of 3.0, can be attributed to the nose shape.

Table 4Random variables and statistical data used for the reliability analysis of RC shielded stee

Random variable Nominal

RC shieldConcrete strength, f ’c (MPa) 50Reinforcement ratio, ps (%) 1.266Uni-axial tensile strength of reinforcing bars, fy (MPa) 420Thickness of concrete shield, H (m) 0.60Concrete shield density, rc (kg/m3) 2440Steel plateYield strength of the steel plate, Y (MPa) 420Steel density, rs (kg/m3) 7850Thickness of steel plate, t (mm) 5Ogive nose projectileNose length of the projectile, h (mm) 66.3Diameter of the projectile, d (mm) 40Mass of the projectile, M (kg) 0.813Impact velocity, V0 (m/s) VariableBi-conical nose projectileEquivalent conical nose length of the projectile, h (mm) 31.1Diameter of the projectile, d (mm) 40Mass of the projectile, M (kg) 0.813Impact velocity, V0 (m/s) Variable

COV: Coefficient of variation.

5.1.2. Effect of thickness of the steel plateFig. 19 shows that as the inner steel plate thickness increases,

the reliability of the steel plate also increases. This is because as thesteel plate thickness increases, the perforation energy (Eq. (A1)) of

l plates.

Bias factor COV Distribution Reference

0.9 0.10 Lognormal [7]0.9 0.10 Normal Assumed0.9 0.10 Lognormal Assumed1.0 0.05 Normal [6]0.95 0.10 Lognormal [6]

0.95 0.05 Normal Assumed0.95 0.10 Lognormal Assumed1.00 0.03 Normal Assumed

1.00 0.025 Normal [7]1.05 0.05 Normal [7]1.10 0.05 Lognormal [7]1.00 0.10 Normal Assumed

1.00 0.025 Normal [7]1.05 0.05 Normal [7]1.10 0.05 Lognormal [7]1.00 0.10 Normal Assumed

Fig. 15. Variation of reliability index with damage levels.Fig. 17. Probabilities of failure for the specimens impacted by ogive nose projectile.

N.A. Siddiqui et al. / International Journal of Impact Engineering 69 (2014) 122e135 133

the steel plate increases which consequently increases the overallreliability of the RC shielded steel plate. For achieving the samereliability index of 3.0, the observed difference in the steel platethickness can again be ascribed to the nose shape (ogive nose beingsharper than the bi-conical nose projectile).

6. Conclusions

In the present study, a simple experiment was designed tosimulate a double-wall containment structure consisting of twoelements e an outer RC shield and inner steel plate. The study wascarried out in two parts. In the first part, experiments were con-ducted by studying the impact resistance of RC shielded steel platesof 600 � 600 � 5 mm thickness against the impact of non-deforming projectiles of ogive and bi-conical nose shapes. Thespecimens were tested at varying impact velocities and response ofthe RC shield and the steel plate was studied in terms of front andrear damaged areas of the RC shield and perforation resistance ofthe steel plate. To quantify the damage, five damage levels (L1 to L5)were defined based on the perforation of RC shield and damagesobserved in the steel plate. When the RC shield was impacted bythe projectile, in general, threemajor fracture regionswere formed:the crater region, the crushed aggregate region and the extensivecracking region. In addition, scabbing was also observed in which amass of concrete material from the opposite (or rear) face of theslabwas separated. The shape and size of the crater on the front andthe rear faces varied as per the dynamic loading, measured in terms

Fig. 16. Probabilities of failure for the specimens impacted by bi-conical noseprojectile.

of impact energy. In general, the ballistic limit velocity of ogiveprojectile for RC shield was found lower than that of bi-conicalprojectile of the same mass and aft body diameter. Thus, theogive nose projectile was found more damaging to the steel platethan bi-conical nose projectile.

In the second part, reliability analysis of all the tested concreteshielded steel plates was carried out using Monte Carlo Simulationtechnique for a range of impact velocities. The results of the reli-ability analysis were then used to relate the probability of failurewith different scenarios of the failure of the specimens. The reli-ability analysis results were found consistent with the damagelevels observed. The probabilities of failure of those specimenswhich experienced higher damage levels (L3 through L5) werehigher. Similarly, smaller probability of failure was found for thosespecimens which had lower damage levels (L1 and L2). The resultsof sensitivity analysis clearly illustrated that the desired reliabilityfor the RC shielded steel plate can be easily achieved by varying thethickness of its RC shield. Alternatively, the desired reliability canalso be achieved by changing the steel plate thickness. However, foreconomic reasons, both the thicknesses (i.e. thickness of RC shieldand steel plate) should be changed to achieve a predefined desiredreliability. In order to use the available formulation on conical noseshape projectiles, the bi-conical nosewas replaced by an equivalentconical nose for which a simple formula was derived. In order tovalidate this simplified attempt to suggest an equivalent conicalnose, one of the tests with bi-conical nose projectile was repeatedwith the equivalent conical nose projectile. At a given striking ve-locity, the equivalent conical projectile produces a similar damage

Fig. 18. Variation of the plate reliability with the thickness of the RC shield.

Fig. 19. Variation of the plate reliability with its thickness.

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pattern and the same damage level in the RC shielded steel plate, asthat of bi-conical nose projectile at the same impact velocity.

Acknowledgements

The Authors would like to extend their sincere appreciation tothe Deanship of Scientific Research at King Saud University, SaudiArabia for its funding of this research through the research groupproject grant No. RGP-VPP-310.

Appendix A

A.1. Perforation energy of the steel plate

The energy required to perforate the steel plate was obtained byan empirical equation originally proposed by Thomson [20,21] forsteel plates. This equation can be expressed as

Eperf ¼ pd2t

"0:125Y þ 0:0625rsCE

�V*dh

�2#

(A.1)

where, Eperf ¼ Perforation energy; d ¼ diameter of the aft body ofprojectile; t ¼ thickness of steel plate; Y ¼ yield stress of the steelplate; rs ¼ density of the steel plate; h ¼ nose length of the pro-jectile; CE ¼ Constant ¼ 1 for a conically-tipped projectile andCE ¼ 1.86 for an ogive-headed projectile. Sodha and Jain [22] sub-sequently corrected the analysis for the ogive-headed projectile,giving a new value of CE ¼ 0.62 [21].

A.2. Residual velocity of the projectile

The process of penetration of projectile into concrete shieldinvolves the initial cratering, tunnelling and rear cratering asshown in Fig. A.1. If the concrete shield is perforated, the velocityafter perforation is called the residual velocity (V*), which can becomputed by [18,23]:

V* ¼ V0 � VBL for c � cc (A.2a)

V* ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�V20 � V2

BL

�rfor c > cc (A.2b)

where, V0 ¼ impact velocity; VBL ¼ ballistic limit velocity, which isdefined as the minimum velocity for the perforation of RC shield.

The ballistic limit equations were formulated by Chen et al. [18] foran RC target as:

VBL ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffipd3Sfc4kM

s c� H*

BLd

!; for c � cc (A.3a)

VBL ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffipd3Sfc2M

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�c� cc þ

kd

�s; for c > cc (A.3b)

where, S ¼ dimensionless parameter which is a function of un-confined compressive strength of concrete ¼ 82:6f�0:544

c [24];fc ¼ unconfined compressive strength of concrete in MPa;k¼ dimensionless parameter¼ 0.707þ h/d [25]; h¼ nose length ofthe projectile; d, M ¼ diameter and mass of the projectile respec-tively; c is dimensionless thickness of concrete shield such thatc ¼ H/d and H*

BL ¼ thickness of conical plug at the ballistic limit;cc ¼ dimensionless critical thickness of concrete shield [18].

Fig. A.1. Normal penetration of projectile into concrete shield.

References

[1] Abbas H, Paul DK, Godbole PN, Nayak GC. Aircraft crash upon outer contain-ment of nuclear power plant. Nucl Eng Des 1996;160(1e2):13e50.

[2] Rao BN, Chowdhury R, Prasad AM, Singh RK, Kushwaha HS. Probabilisticcharacterization of AHWR inner containment using high dimensional modelrepresentation. Nucl Eng Des 2009;239(6):1030e41.

[3] Rao BN, Chowdhury R, Prasad AM, Singh RK, Kushwaha HS. Reliability analysisof 500 MWe PHWR inner containment using high-dimensional model rep-resentation. Int J Pres Ves Pip 2010;87(5):230e8.

[4] Dundulis G, Kulak RF, Alzbutas R, Uspuras E. Integrated probabilistic analysisof nuclear power plant building damage due to an aircraft crash. Int JCrashworthiness 2011;16(1):49e62.

[5] Siddiqui NA, Iqbal MA, Abbas H, Paul DK. Reliability analysis of nuclearcontainment without metallic liners against jet aircraft crash. Nucl Eng Des2003;224(1):11e21.

[6] Choudhury MA, Siddiqui NA, Abbas H. Reliability analysis of buried concretetarget under missile impact. Int J Impact Eng 2002;27(8):791e806.

[7] Penmetsa RC. Determining probability of mission success when using deeppenetration weapons. Int J Mech Sci 2005;47(9):1442e54.

[8] Siddiqui NA, Khan FH, Umar A. Reliability of underground concrete barriersagainst normal missile impact. Comput Concr 2009;6(1):79e93.

[9] Pandey MD. Reliability-based assessment of integrity of bonded pre-stressed concrete containment structures. Nucl Eng Des 1997;176(3e4):247e60.

[10] Han BK, Ang HS. Serviceability design load factors and reliability assessmentsfor reinforced concrete containment structures. Nucl Eng Des 1998;179(2):201e8.

[11] Li QM, Reid SR, Wen HM, Telford AR. Local impact effects of hard missiles onconcrete targets. Int J Impact Eng 2005;32(1e4):224e84.

[12] Reid SR, Wen HM. Predicting penetration, cone cracking, scabbing andperforation of reinforced concrete targets struck by flat-faced projectiles.

N.A. Siddiqui et al. / International Journal of Impact Engineering 69 (2014) 122e135 135

UMIST Report ME/AM/02.01/TE/G/018507/Z. U.K.: University of ManchesterInstitute of Science and Technology; 2001.

[13] Wen HM, Yang Y. A note on the deep penetration of projectiles into concrete.Int J Impact Eng 2014;66:1e4.

[14] Almusallam TH, Siddiqui NA, Iqbal RA, Abbas H. Response of hybrid-fiberreinforced concrete slabs to hard projectile impact. Int J Impact Eng2013;58:17e30.

[15] Schaffar M, Pfeifer HJ. Comparison of two computational methods for high-velocity cavitating flows around conical projectiles: OTi-HULL hydrocode andtwo-phase flowmethod. In: Kato H, editor. Fourth Int Symp on Cavitation. Pasa-dena, CA, USA: California Institute of Technology; June 20e23, 2001. pp. 1e8.

[16] Dancygier AN, Yankelevsky DZ, Jaegermann C. Response of high performanceconcrete plates to impact of non-deforming projectiles. Int J Impact Eng2007;34(11):1768e79.

[17] Clifton JR. Penetration resistance of concrete e a review. Washington D.C.:National Bureau of Standards; 1982. pp. 480e545 [Special Publication].

[18] Chen XW, Li XL, Huang FL, Wu HJ, Chen YZ. Normal perforation of reinforcedconcrete targets by rigid projectiles. Int J Impact Eng 2008;35(10):1119e29.

[19] Nowak AS, Collins KR. Reliability of structures. 1st ed. Singapore: McGrawHill; 2000, pp. 69e85.

[20] Thomson WT. An approximate theory of armor penetration. J Appl Phys1954;26(1):80e2.

[21] Corbett GG, Reid SR, Johnson W. Impact loading of plates and shells by free-flying projectiles: a review. Int J Impact Eng 1996;18(2):141e230.

[22] Sodha MS, Jain VK. On physics of armor penetration. J Appl Phys 1958;29(12):1769e70.

[23] Chen XW, Fan SC, Li QM. Oblique and normal penetration/perforation ofconcrete target by rigid projectiles. Int J Impact Eng 2004;30(6):617e37.

[24] Frew DJ, Hanchak SJ, Green ML, Forrestal MJ. Penetration of concrete targetswith ogive-nose steel rods. Int J Impact Eng 1998;21(6):489e97.

[25] Chen XW, Li QM. Deep penetration of a non-deformable projectile withdifferent geometrical characteristics. Int J Impact Eng 2002;27(6):619e37.