Penetration Resistance of Reinforced Concrete Containment Structures

annals of

Annals of Nuclear Energy 32 (2005) 281–298

www.elsevier.com/locate/anucene

NUCLEAR ENERGY

Penetration resistance of reinforcedconcrete containment structures

Tso-Liang Teng a,*, Yi-An Chu b, Fwu-An Chang c,Bor-Cherng Shen d

a Department of Mechanical Engineering, Da-Yeh University, 112, Shan-Jiau Road, Da-Tsuen,

Changhua 515, Taiwan, ROCb Chung-Shan Institute of Science and Technology, P.O. Box 90008-17-10,

Lung-Tan, Tao-Yuan 325, Taiwan, ROCc Department of Civil Engineering, University of National Defense Chung Cheng Institute of Technology,

Ta-Shi, Tao-Yuan 335, Taiwan, ROCd Institute of System Engineering, University of National Defense Chung Cheng Institute of Technology,

Ta-Shi, Tao-Yuan 335, Taiwan, ROC

Received 28 June 2004; accepted 7 October 2004

Available online 25 November 2004

Abstract

Containment structures not only provide a leak tight barrier, but also play a role in ensur-

ing that the structures can withstand the impact load from projectile impacts or internal plant

accidents. In assessing the containment structures of nuclear power plants, predicting the char-

acteristics of impact resistance in relation to design and safety considerations is relevant. This

investigation proposes a simple but effective method of performing numerical analysis on per-

foration resistance of reinforced concrete containment structures. In this work, normal and

oblique impacting is considered to examine the residual velocity and impact phenomena of

an ogive-nose steel projectile with various impact velocities against a reinforced concrete slab.

Additionally, a phase diagram is devised to describe the ballistic terminal phenomena of pro-

jectile and target. This model could assess the resistance to penetration to results in the opti-

mum design of the containment structures in nuclear power plants.

� 2004 Elsevier Ltd. All rights reserved.

0306-4549/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.anucene.2004.10.001

* Corresponding author. Tel.: +886 4 8511221; fax: +886 4 8511224.

E-mail address: [email protected] (T.-L. Teng).

mailto:[email protected]

282 T.-L. Teng et al. / Annals of Nuclear Energy 32 (2005) 281–298

1. Introduction

Containment structures in nuclear power plants represent the final defensive bar-

rier of the system. To prevent the release of radioactive material owing to events like

aircraft impact and external accidents, reactors were covered by reinforced concretecontainment in an outer shell. After the Three Mile Island and Chernobyl accidents

in 1979 and 1986, respectively, containment structures received increased attention in

nuclear power plant design. Various different containments including prestressed lin-

ear concrete and double-containment walls have been widely used for accident pre-

vention. Most containment structures are made from reinforced concrete due to its

durability and ease of construction. Containment structures not only provide a leak-

tight barrier, but also play a role in ensuring that the structures can withstand the

impact load from projectile impacts or internal plant accidents. Recent legislation(US Nuclear Regulatory Commission, 1997) requires that the risk of a nuclear acci-

dent due to air vehicle impact must be under one in one million during the life cycle.

Because of these considerations, evaluation of the impact resistance of the contain-

ment structures has became increasingly important.

Previous investigations on the design and perforation resistance of containment

structures can be categorized into experimental studies, empirical or semi-empirical

model based on experimental data and analytical or numerical solutions. Brandes

(1988) applied analytical solutions and experimental data to correct mathematicalmodel results and investigated the resistance of reinforced concrete to aircraft im-

pact. Moreover, Ansari and Yang (1988) applied computer-assisted techniques to

assess the impact damage to reinforced concrete. McHugh et al. (1983) conducted

an impact experiment on reinforced concrete target by scale modeling of a turbine

missile. Lagasco et al. (1996) predicted the failure location using the finite difference

method. Impact problems can also be numerically simulated using the finite element

method (Zimmermann et al., 1980), ADINA code (Buchhardt et al., 1983) and ACI-

ASME code (Reedy, 1978). Ohnuma and Ito (1985) analyzed the transient responseof containment structures by using the prestress method. Additionally, Krieg et al.

(2001) considered the temperature distribution of the lower head response under

core melt-down conditions and predicted the reactor vessel integrity under severe

accident loading. Furthermore, Gomathinayagam et al. (1994) predicted crack

propagation using a simple shell element. Other parameters in containment struc-

ture design such as internal force and displacement of thick reinforced concrete

(Gyorgyi and Lenkei, 1996), or stiffness (Shirai et al., 1994), can be determined

using the finite element method. On the other hand, the impact resistance and riskof breach of containment structures after impact by foreign projectiles have been

experimentally examined by Berriaud et al. (1979), Schueller (1983), Brandes et

al. (1983), Mineer et al. (1991), Rericha (1996) and Romander and Sliter (1984)

for various projectile velocities and impact angles. In the analytical and empirical

formula approach, Eibl and Kobler (1994) and Amde et al. (1996) used analytical

and experimental methods to provide semi-empirical formulas to evaluate the frac-

ture behavior of containment structures following impact by aircraft, missiles or

explosive materials.

T.-L. Teng et al. / Annals of Nuclear Energy 32 (2005) 281–298 283

Nuclear plants cannot be guaranteed to be impervious to every imaginable form

of attack, but the reinforced concrete containment structures—coupled with redun-

dant safety and plant shutdown systems—are designed to withstand very substantial

impacts from hurricanes and airborne objects. In assessing the performance of con-

tainment structures of nuclear power plants, predicting the characteristics of impactresistance in relation to design and safety considerations is relevant. Owing to the

complexity of the containment structures and the highly non-linear physics that is

applicable, using numerical analysis methods is difficult. Additionally, the modeling

and numerical simulation of reinforced concrete under a high velocity impact is

much more complex than for plain concrete.

This investigation proposes a simple but effective method of performing numerical

analysis on perforation resistance of reinforced concrete containment structures. The

equivalent inclusion method (Mura, 1987 and Teng et al., 2002) were introduced andemployed to obtain the material properties for use in finite element calculations.

When the equivalent inclusion method is applied, the reinforced concrete can be con-

sidered a homogeneous material, simplifying the finite element meshes and markedly

reducing the computational cost of the analyses. Thus, the numerical programming

is simplified and the computation of the equivalent material moduli is significantly

facilitated, making the proposed method extremely useful and practical for analyzing

impacts on reinforced concrete. To determine the accuracy of the proposed method

in this investigation, the procedure is applied to an ogive-nose steel projectile impactwith a reinforced concrete slab, and the results are compared with the experimental

data by Hanchak et al. (1992). In this work, normal and oblique impacting is con-

sidered to examine the residual velocity and impact phenomena for a projectile with

various impact velocities. Additionally, a phase diagram is devised to describe the

ballistic terminal phenomena of projectile and target. This phase diagram can be

used to predict the terminal status of a projectile under various impact velocities

and angles of obliquity. This model could be used to assess the resistance of penetra-

tion to confirm the optimum design of the containment structures of nuclear powerplants. It is also useful in designs for military structures and weapon systems.

2. Fundamental theorem

This section introduces the equivalent inclusion method developed by Mura

(1987) and applied by Chao and Hung (1999), the steel-reinforced concrete idealized

as an anisotropic homogeneous material. The reinforcing steel bars are treated ascylinderical inhomogeneities within the concrete matrix. Based on the equivalent

inclusion method, the cylindrical inhomogeneities are treated as equivalent to cylin-

drical inclusions with the same configurations but with fictitious internal eigen-

strains. In this paper, an inhomogeneity is defined to have material properties

different from those of the matrix. However, an inclusion is defined to have the same

material properties as the matrix. The strain fields within the equivalent inclusions

can be obtained by Eshelby�s solutions (Eshelby, 1957, 1959). Mori–Tanaka�s aver-age stress theory (Mori and Tanaka, 1973) is then applied to investigate the overall


stress-strain relations and derive the equivalent material compliance matrix as a

function not only of the material moduli of the concrete and reinforcing steel bars,

but also the volume fractions and the orientations of the reinforcing steel bars.

2.1. Equivalent elastic compliance tensor

This section derive the equivalent material compliance tensor for an isotropic elas-

tic matrix with multiphase inclusions, based on equivalent inclusion method and

Mori–Tanaka�s average stress theory.

Consider a finite but sufficiently large region of a composite body D as shown in

Fig. 1, containing N distinctly shaped, randomly distributed, ellipsoidal or elliptic

cylindrical inhomogeneities X ¼PN

K¼1XK . The Kth inhomogeneity has elastic moduli

C�Kijkl and volume fraction fK. The surrounding matrix is denoted by D–X and has

elastic moduli Cijkl.

Assume that the body is subjected to uniform surface traction t1j ¼ r1ij ni. When

no inhomogeneity is in the domain, the uniform strain in the composite body is

e1 and the corresponding uniform stress is r1 = C e1. If the N inhomogeneities

are all present in the domain, then the average stress disturbances in the matrix

and the Kth inclusion are denoted as �rM and �rXK , respectively. The corresponding

average strain disturbances are represented as eM and eXK . Consequently, the averagestress in the matrix can be written as

r1 þ rM ¼ C e1 þ eM� �

in D–X; ð1Þand the average stress in the Kth inclusion can be written as

r1 þ rXK ¼ C�

Ke1 þ eM þ �eK� �

; ð2Þ

where �eK ¼ �eXK � �eM is the average strain disturbance in the Kth inhomogeneity due to

the presence of the Kth inhomogeneity itself. The average strain disturbance in the

Kth inhomogeneity due to the presence of the inhomogeneities is denoted as �eM in

Eq. (2). The summation of �eM and �eK , denoted as �eXK ¼ �eM þ �eK , is the average straindisturbance in the Kth inhomogeneity due to all of the inhomogeneities.

Based on the equivalent inclusion method, the Kth inhomogeneity is replaced by

inclusion with the same elastic moduli C as the matrix and with fictitious equivalenteigenstrains e�K . Therefore, Hooke�s law for the Kth equivalent inclusion becomes

r1 þ rXK ¼ C e1 þ eM þ �eK � e�K

� �in XK ; ð3Þ

Fig. 1. Schematic view of matrix and inhomogeneities.


where e�K represents the fictitious equivalent eigenstrain in the Kth inclusion. Since

the applied surface traction is uniform and the inhomogeneities are ellipsoidal, the

strain disturbances �eK are uniformly distributed in XK, and they can be related to

be fictitious equivalent eigenstrain e�K by Eshelby�s solution as

�eK ¼ SKe�K in XK ; ð4Þ

where SKis Eshelby�s tensor for the Kth inclusion due to the presence of itself.

Based on Mori–Tanaka�s average stress theory (Schueller, 1983), the volume aver-

age of the disturbed stresses must vanish, yielding

1�XNK¼1

fK

" #rM þ

XNK¼1

fKrXK ¼ 0; ð5Þ

where fK is the volume fraction of the Kth inclusion and 0 6PN

K¼1fK 6 1. After sev-

eral steps of straightforward algebraic manipulation, the overall strain field, eD, ofthe composite body D can be derived as (Reedy, 1978)

eD ¼ e1 þXNK¼1

fKe�K ¼ C�1r1; ð6Þ

where C�1

is the equivalent elastic compliance tensor and is written as

C�1 ¼ I �

XNK¼1

fKP�1

KC�

K� C

� �" #C�1: ð7Þ

The tensor PKin Eq. (7) is defined as

PK¼ C�

K� C

� �SK�XNK¼1

fK SK� I

� �" #þ C; ð8Þ

and where I is the identity tensor or the unit tensor.

2.2. Equivalent compliance tensor of reinforced concrete slabs

Embedded reinforcing steel bars in reinforced concrete slabs are typically ar-

ranged in a two-layer orthogonal arrangement, as shown in Fig. 2. In this section,

Eqs. (7) and (8) are applied to demonstrate the calculation of the equivalent elastic

compliance tensor associated with the reinforced concrete slabs. From Eq. (8), the

elastic compliance tensor for reinforced concrete with steel bars in a two-layer

orthogonal arragement can be shown to be

C�1 ¼ I � f1P�1

1C�

1� C

� �� f2P�1

2C�

2� C

� �h iC�1; ð9Þ

where

P�1

1¼ C�

1� C

� �S1� f1 S

1� I

� �� f2 S

2� I

� �þ C

h in o�1

; ð10Þ

x1

x3

inhomogeneity 1

inhomogeneity 2

Fig. 2. Two-layer orthogonally embedded reinforcing steel bars.


P�1

2¼ C�

2� C

� �S2� f1 S

1� I

� �� f2 S

2� I

� �þ C

h in o�1

: ð11Þ

Sub-indices 1 and 2 represent the two phases of mutually orthogonal cylindrical

inhomogeneities with axes in directions of the coordinate axes x1 and x2,

respectively.

For the two-way orthogonal arrangement of reinforcing steel bars with identical

shape and material properties C�1¼ C�

2; Eshelby�s tensor S

2can be obtained from S

1by cyclically permuting the indices (1,2,3). Using Voight notation, the orthotropic

equivalent compliance tensor C�1

can be further transformed into a 6 · 6 matrix,

Ch i�1

¼

1

E11

��m21E22

��m31E33

0 0 0

��m12E11

1

E22

��m32E33

0 0 0

��m13E11

��m23E22

1

E330 0 0

0 0 0 1

G230 0

0 0 0 0 1

G310

0 0 0 0 0 1

G12

2666666666664

3777777777775; ð12Þ

where Eij; Gij and mij are the equivalent elastic moduli; the equivalent shear moduli

and the equivalent Poisson�s ratio of the equivalent reinforced concrete materials orstructures.

The equivalent material is homogeneous but anisotropic, which can be modeled

with properly chosen constitutive model in a general-purpose finite-element code.

With these transformations based on the equivalent inclusion method, the finite ele-

ment meshes for material equivalent to of a reinforced concrete slab are as simple as

those for a simple concrete slab.

3. Numerical verification

To demonstrate the performance of the proposed model and thus verify the accu-

racy of the calculation procedure, this section considers the normal impact of an

ogive-nosed steel projectile on a reinforced concrete slab at different velocities.


The numerical simulation was performed using an explicit, two-dimensional hydro-

dynamic finite element code DYNA-2D (Hallquist, 1990), with the equivalent elastic

moduli obtained using the equivalent inclusion method. The results are compared

with the experimental results of Hanchak et al. (1992). Fig. 3 illustrates the 610

mm · 610 mm · 178 mm reinforced concrete slab. The structure comprises threeorthogonal bilayers of square grids of reinforcing steel bars with a diameter of

5.69 mm. The spaces between the parallel steel bars are 76.2 mm in both directions.

Consequently, the volume fractions in the directions of the coordinate axes x1 and x2are f1 = f2 = 0.005. In this case, the concrete material properties of the target, includ-

ing uni-axial compressive strength, density, elastic moduli, and Poisson�s ratio were

taken to be 140 MPa, 2520 kg/m3, 20.68 GPa and 0.18, respectively. The steel bars

used have density, elastic modulus, and Poisson�s ratio of 7850 kg/m3, 199 GPa and

0.3, respectively (Chen, 1996). Fig. 4 illustrates the geometry for the 25.4 mm caliber,solid steel rod projectile with the caliber radius head (CRH) = 3 and total length

143.7 mm. The steel projectile is assumed to be elastic perfectly plastic, with mass

density of 8020 kg/m3, a modulus of elasticity 206.9 GPa, Poisson�s ratio of 0.3,

yielding stress of 1.724 GPa. Normal impacts of the projectile into a target slab at

velocities of 76, 382, 443, 587, 743 and 998 m/s, were simulated.

610 mm

76.2 mm

76.2 mm

610m

m

178

mm

Fig. 3. Reinforced concrete target geometry.

101.6mm

φ =25.4 mm

R=76.2 mm

Fig. 4. Projectile geometry (CRH = R// = 3).

200.00 400.00 600.00 800.00 1000.00

Vs (m/s)

0.00

200.00

400.00

600.00

800.00

1000.00

Vr

(m/s

)

Hanchak (1992)—140MPa(20ksi)

equivalent method

Fig. 5. Residual velocity Vr versus striking velocity Vs.


First, Eshelby�s tensors S1and S

2for the steel bars in the x1 and x2 directions,

respectively, were determined by directly substituting Poisson�s ratio of the matrix

(the original concrete) and the cross sections of the steel bars into the associated for-

mula for equivalent cylindrical inclusions. Substituting the values of S1and S

2, the

material moduli of the matrix and the steel bars and the associated volume fractions

f1 = f2 = 0.005 into Eqs. (9)–(11) yielded the equivalent compliance tensor C�1. Final-

ly, the associated equivalent elastic moduli Eij, shear moduli Gij and Poisson�s ratio �mijof the reinforced concrete material were determined to be �q ¼ 2565 kg=m3; E11 ¼E22 ¼ 20:8 GPa; E33 ¼ 20:7 GPa; �m12 ¼ �m13 ¼ 0:175; �m23 ¼ 0:172; G12 ¼ 9 GPa. The

residual velocity of the projectile can be determined using the finite element code with

this equivalent material model. The numerical techniques applied to the finite element

analyses, included the erosion algorithm and the use of a failure criterion to express

the fracture of the concrete slab. Fig. 5 compares the numerical results with the exper-

imental data of Hanchak et al. (1992). The residual velocities, predicted by the finiteelement simulation to vary with the impact velocities, agree closely with the experi-

mental data, and thus are verified.

4. Impact response of reinforced concrete slab

The ballistic and the ricochet limits of steel reinforced concrete slab with various

thickness for a specific projectile were studied using finite element analyses combinedwith the equivalent inclusion method for various reinforced concrete slabs. Fig. 6

12.7mm

4000mm

8# @ 150 mm 150 mm

12.7mm

600-800mm

Fig. 6. Reinforced concrete target geometry.

Table 1

The equivalent material properties of reinforced concrete slabs

Plate thickness 600 mm 700 mm 800 mm

Principal elastic modulus, E11 (GPa) 25.7 25.6 25.5



Poisson�s ratio �m12 0.158 0.161 0.163

Poisson�s ratio �m23 0.167 0.169 0.17

Poisson�s ratio �m31 0.167 0.169 0.17

Shear modulus, G12 (GPa) 11.6 11.5 11.4


illustrates the dimensions of the steel reinforced concrete slab and the arrangement

of the reinforcement. The reinforced concrete slabs had a width of 4000 mm, and

thicknesses of 600, 700 and 800 mm. The concrete material properties of the target,

including uni-axial compressive strength, density, elastic moduli, and Poisson�s ratiowere 140 MPa, 2520 kg/m3, 20.68 GPa and 0.18, respectively.

There were three layers of square grids of reinforcing steel bars with a diameter of

25.4 mm, orthogonally arranged. The spaces between the parallel steel bars were 150mm in both directions. The volume fractions for 600, 700 and 800 thicknesses were

0.034, 0.029 and 0.025, respectively. The associated equivalent elastic moduli Eij,

shear moduli Gij and Poisson�s ratio �mij of the reinforced concrete material were

determined based on Eqs. (9)–(12) and are listed in Table 1. The equivalent elastic

moduli Eij are about 20% higher than the elastic modulus of concrete matrix. The

equivalent poission�s ratios are about 7% lower than the poission�s ratio of the con-

crete matrix. The material moduli of the reinforced concrete slabs are orthotropic

due to the orthogonally arranged steel bars.The solid steel projectile used had density 8380 kg/m3, elastic modulus 200 GPa,

Poisson�s ratio 0.3 and yield stress 1.14 GPa.

4.1. Normal impact response

The penetration of projectile at impact velocities of 50, 100, 150, 240 m/s into the

reinforced concrete slabs of 600, 700 and 800 mm in thickness was investigated. A

series of calculations were performed to forecast the residual velocities of projectile

Table 2

Residual velocity of a projectile with normal impact

Slab thickness 600 mm 700 mm 800 mm

Striking velocity 50 m/s 0 m/s (·) 0 m/s (·) 0 m/s (·)Striking velocity 100 m/s 0 m/s 0 m/s 0 m/s

Striking velocity 150 m/s 79 m/s 0 m/s 0 m/s

Striking velocity 240 m/s 167 m/s 79 m/s 0 m/s

(·), perforation did not occur.


as shown in Table 2. Perforation occurred with 600 and 700 mm thick concrete slabs

at a velocity of 240 m/s. The residual velocity of the projectile was 167 and 79 m/s,

respectively. The projectile was embedded when the thickness of the concrete slab in-

creased to 800 mm. Figs. 7(a)–(c) illustrate deformed mesh plots of the penetration

of a steel projectile into reinforced concrete slabs at 240 m/s. From Table 2, the bal-listic limits of a 600 mm thickness concrete slab can be found to be 100–150 m/s,

increasing to 150–240 m/s for a 700 mm thickness concrete slab, and exceeding

240 m/s when thickness is increased to 800 mm. Consequently, the ballistic limit in-

creases with increasing concrete slab thickness.

4.2. Oblique impact response

Generally, the impact velocity, mass and nose-shape of a projectile as well as thetarget material, impact angle and other factors, influence the depth and attitude of a

projectile after penetration. Most previous studied in this area have been limited to

cases where the impact is normal to the target surface. However, projectiles generally

hit a plane surfaces at oblique angles. To analyze the overall protection capability of

a concrete structure, this section considers the same conditions as in the previous sec-

tion, but with an oblique impact. The angle b between the projectile trajectory and

the outward normal vector of the target surface is defined as the angle of impact,

which is illustrated in Fig. 8. The methodology was used to forecast the trajectoriesof projectiles that penetrate the equivalent reinforced concrete slab at various angles

of obliquity and impact velocities of 100, 150 and 240 m/s, which were also used to

determine the impact phase diagram. The numerical techniques applied to the finite

element analyses, including the erosion algorithm and the failure criterion, where the

same as those applied in the normal impact analysis.

Fig. 9 shows that, for a 30� oblique impact at 240 m/s, the projectile creates a hole

and successively perforates the target in the initial impact direction. The residual

velocity of the projectile predicted by this analysis is 146 m/s. Fig. 9 also illustratedthat the angle of impact of the projectile does not change during concrete slab per-

foration, and the concrete structures have no ability to protect against projectiles

striking at an angle of 30� and a speed of 240 m/s. Figs. 10–12 show the results

for a 30� oblique impact at velocities of 150, 100 and 50 m/s, respectively. Figs. 10

and 11 show that projectile penetrates the target surface along a curved trajectory,

and then emerges from the target surface with a reduced velocity. Fig. 10 shows frac-

ture induced scabbing of the lower surface. In Fig. 11 the formation of the penetra-

Fig. 7. Projectile perforating a concrete slab (b = 0�, ms = 240 m/s) with thickness: (a) 600 mm, (b) 700 mm,

and (c) 800 mm.


Normal vector

of concrete

Trajectory plane

Projectile

Fig. 8. Schematic of oblique impact.

Fig. 9. Projectile perforating a concrete slab (600 mm thickness) (b = 30�, ms = 240 m/s).


tion path and exit crater clearly generate intense shock waves following impact. Fig.

11 shows the projectile creates a shallow scabbing at the rear side of the target. Fig.

12 shows that the projectile rocochet from the target.

4.3. Impact phase diagram

The impact response of a projectile can be classified into penetration through the

target (perforation), embedded in target and ricocheted off the target. Numerical

Fig. 10. Projectile embedded concrete slab (600 mm thickness) (b = 30�, ms = 150 m/s).

Fig. 11. Projectile embedded in a concrete slab (600 mm thickness) (b = 30�, ms = 100 m/s).


simulation results with different striking velocities demonstrate that the residual

velocity of a projectile decreases with increasing concrete slab thickness. If the pro-

jectile has no more energy to continue penetrate with a non-zero residual velocity,

perforation embeddedricochet

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 80Obliquity (degree)

V s

(m

/s)

Fig. 13. Projectile impact response (concrete slab thickness, 600 mm).

Fig. 12. Projectile ricochet from concrete slab (600 mm thickness) (b = 30�, ms = 50 m/s).


then the response can be considered a ricochet response. The impact phase diagram

for various impact velocities and angles of impact was interest for calculating ballis-

tic limit for a concrete slab. The impact phase diagram of an ogive-nose steel projec-



0

50

100

150

200

250

300

V s

(m

/s)




0

50

100

150

200

250

300V

s (

m/s

)




tile against an equivalent reinforced concrete slab with a thickness of 600–800 mm

were constructed base on the numerical results from Section 4.1 for normal impact

and Section 4.2 for oblique impact. Figs. 13–15 illustrate the impact phase diagram

of projectile with different striking velocities, as well as the angle of obliquity to the

concrete slab with thicknesses of 600, 700 and 800 mm, respectively.For normal impact responses, the ballistic limit of a 600 mm thickness concrete

slab is between 100 and 150 m/s, increasing to 150–240 m/s for a 700 mm thickness

concrete slab, and exceeding 240 m/s for 800 mm. For the 30� oblique impact re-

sponse, ricochet will not occur when the striking velocity is 100–240 m/s for a 600

mm thickness concrete slab and exceeds 240 m/s for the 700 and 800 mm thick con-

crete slabs. When the obliquity exceeds 40�, ricochet will occur for the three thick-

ness concrete slabs if the striking velocity is below 240 m/s. These impact phase

diagrams provides a practical reference for studying oblique impacts on reinforcedconcrete slabs, particularly for designers of military defense structures, weapon sys-

tems, nuclear power plants, and other facilities.

5. Conclusions

Containment structures in nuclear power plants must be designed to withstand

very substantial impacts from hurricanes and airborne objects. The analysis of impactresponse on reinforced concrete is important in containment structure design. How-

ever, the penetration resistance to impact by a projectile is one of the most challenging

analytical problems in fortification engineering. Solving this problem involves geo-

metrical and material modeling and the complicated process of determining material

parameters. A simple but reasonably effective model for estimating the penetration of

reinforced concrete structures is extremely useful, especially for designers of military

defense structures, weapon systems, nuclear power plants, and other facilities. This

study has shown the value of the equivalent inclusion method for idealizing the rein-forced concrete slabs as homogeneous orthotropic materials to obtain the equivalent

material properties for finite element analyses. The equivalent stiffness matrix of the

reinforced concrete targets and the associated equivalent material moduli are deter-

mined. The finite element meshes for the equivalent material of a reinforced concrete

slab are as simple as those for plain concrete material.

The numerical results demonstrate generally agree well with the experimental re-

sults, and provide a practical approach for studying oblique impacts. The equivalent

inclusion method is considered to have been demonstrated as a useful technique foranalyzing reinforced concrete structures subjected to projectile impact.

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Documents

Penetration Resistance of Reinforced Concrete Containment Structures