C

Brickwork and Blockwork: Impactand Explosion

C.1 General Introduction

Gas explosions in buildings are a rare occurrence. Information on both thecauses and effects of a gas explosion and some practical guidance on safeventing have already been discussed in this text. However, the importanceof the structure’s ability to withstand the blast load cannot be ignored. Inthis section, a brief analysis is given on impact and explosion in brickworkconstruction.

C.2 Finite-Element Analysis of Explosion

Figure C.1 shows a seven-storey building with 49 compartments. The com-partments have external walls of thickness 450mm and the thickness of theinternal walls ranges between 225 and 362.5mm. Thirteen vents are avail-able in compartment/flat no 32. The information on a typical 3-wall cubicle,shown in Fig. C.2, is taken from flat no 32, where an explosion due to a gasleak occurs. A typical external wall of a cubicle is shown in Fig. C.3. A gasleak pressure is generated in compartment/flat no 32 using the finite-elementscheme given in Fig. C.4. A pressure rise of 75.84 kNm−2 was generated for arise time of 0.2 s; various empirical expressions were used to calculate this pres-sure. Table C.1 lists the computer program used to evaluate such pressures.The program is linked to the finite-element ISOPAR program for the quickevaluation of pressures. The following data form part of the input for anexplosion in brick buildings:

Aspect ratio of height/thickness: 1.5, 2.0, 2.5, 3.0Openings: 1.5 × 4, 0.4 × 0.4, 1.0× 2.3 mFrame stiffness, K: 11.61, 7.3, 3.69 kNmm−1

976 C Brickwork and Blockwork: Impact and Explosion

Fig. C.1. A typical 7-storey building in brickwork

Brick size: 185.9× 87.3 × 87.4 mmYoung’s modulus, E: 6.4670 kNmm−2

Poisson’s ratio, v: 0.096224.1× 108 × 67.3 mm

Young’s modulus, E: 4.2323 kNmm−2

Poisson’s ratio, v: 0.141Number of 8-noded isoparametric elements (main building): 900Number of 20-noded isoparametric elements (wall): 350Mortar (cement, lime, sand): 1:1:6

Young’s modulus, E: 2.465 kNmm−2

Poisson’s ratio, v: 0.244Number of gap and 3-noded elements

Main building: 1950Wall: 350

Figure C.5 illustrates the pressure pulses for four types of explosions. Thecorresponding deflection type relationship is given in Fig. C.6. Figure C.7shows the deflections for various pressures against the distance of the explo-sion, and Fig. C.8 shows the pressure pulse for the single wall of Fig. C.3.Figures C.9 and C.10 illustrate the post-mortems of the building and wall,respectively.

C.2 Finite-Element Analysis of Explosion 977

Table C.1. Pressure generated in a vented explosion

C THIS IS A FORTRAN PROGRAM USED FOR THE CALCULATION OF THE

C PREDICTION OF PRESSURE GENERATED IN A VENTED CONFINED GAS

C EXPLOSION. A FEW METHODS OF CALCULATION WERE COMPUTED AND

C COMPARED WITH EACH OTHER, THE HIGHEST VALUE OF THE PRESSURE

C WAS THEN CHOSEN FOR THE DESIGN PURPOSE.

C

C K E Y S:

C

C P = BREAKING PRESSURE OF THE RELIEF PANEL

C S = BURNING VELOCITY OF THE GAS INVOLVED

C W = WEIGHT PER UNIT AREA

C A = AREA OF RELIEF PANEL

C B = AREA OF THE SMALLEST SECTION OF THE ROOM

C V = VOLUME OF THE ROOM

C

C ∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼REAL P, S, A, B, V, W

WRITE (6, 10)

10 FORMAT (2X, ‘INSERT THE VALUE OF BREAKING PRESSURE, P (mbar)’)

READ (5, ∗)PWRITE (6, 20)

20 FORMAT (2X, ‘INSERT THE VALUE OF BURNING VELOCITY, S (m/s 2)’)READ (5, ∗)SWRITE (6, 30)

30 FORMAT (2X, ‘INSERT THE AREA OF RELIEF PANEL, A (mˆ2)’)READ (5, ∗)AWRITE (6, 40)

40 FORMAT (2X, ‘INSERT THE AREA OF WALL WHERE R.P LOCATED, B (m 2)’)READ (5, ∗) B

WRITE (6, 50)

50 FORMAT (2X, ‘INSERT THE VOLUME OF THE SECTION, V (mˆ3)’)READ (5, ∗) V

WRITE (6, 60)

60 FORMAT (2X, ‘INSERT THE WEIGHT PER UNIT AREA OF R.P, W (Kg/mˆ2)’)READ (5, ∗)W

C TO CALCULATE THE VALUE OF VENT COVER COEFFICIENT

C ∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼K1 = B/A

K2 = V∗∗(2/3)/A

C TO CALCULATE THE MAXIMUM PRESSURE GENERATED BY CUBBAGE & SIMMONDS

C ∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼X1 = (S∗ 4.3∗K1∗W) + 28

X2 = V∗∗ (1/3)

P1 = X1/X2

WRITE (6, 70)P1

70 FORMAT (/, 2X, ‘THE VALUE OF MAXIMUM PRESSURE BY CS IS :’, F9.1)

P12 = 58∗S∗K1WRITE (6, 70)P12

C

(continued)

978 C Brickwork and Blockwork: Impact and Explosion

Table C.1. (continued)

C TO CALCULATE THE MAXIMUM PRESSURE GENERATED BY CUBBAGE & MARSHALL

C ∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼X1 = S∗∗2∗K1∗WX2 = V∗∗(1/3)P2 = (P + (23∗(X1/X2)))WRITE (6, 80)P2

80 FORMAT (/, 2X, ‘THE VALUE OF MAXIMUM PRESSURE BY CM IS :’, F9.1)

C

C TO CALCULATE THE MAXIMUM PRESSURE GENERATED BY RASBASH 1

C ∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼X1 = (1.5∗P)X2 = (77.7∗K1∗S)P3 = (X1 + X2)

WRITE (6, 90)P3

90 FORMAT (/, 2X, ‘THE VALUE OF MAXIMUM PRESSURE BY R1 IS :’, F9.1)

C

C TO CALCULATE THE MAXIMUM PRESSURE GENERATED BY RASBASH 2

C ∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼X1 = 1.5∗PX2 = (4.3∗K1∗W) + 28

X3 = V∗∗(1/3)X4 = 77.7∗K1P4 = X1+S∗((X2/X3)+X4)

WRITE (6, 100)P4

100 FORMAT (/, 2X, ‘THE VALUE OF MAXIMUM PRESSURE BY R2 IS :’, F9.1)

C

C TO COMPARE ALL THE VALUES OF MAXIMUM PRESSURE GENERATED AND CHOOSING

C ∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼C THE MAXIMUM VALUE FROM THE FOUR METHOD

C ∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼∼IF (P1.GT.P2.AND.P1.GT.P3.AND.P1.GT.P4) THEN

WRITE (6, 120)P1

120 FORMAT (///, 2X, ‘THE HIGHEST VALUE IS BY CS :’, F9.1)

ENDIF

IF (P2.GT.P1.AND.P2.GT.P3.AND.P2.GT.P4) THEN

WRITE (6, 130)P2

130 FORMAT (///, 2X, ‘THE HIGHEST VALUE IS BY CM :’, F9.1)

ENDIF

IF (P3.GT.P1.AND.P3.GT.P2.AND.P3.GT.P4) THEN

WRITE (6, 140)P3

140 FORMAT (///, 2X, ‘THE HIGHEST VALUE IS BY R1 :’, F9.1)

ENDIF

IF (P4.GT.P1.AND.P4.GT.P2.AND.P4.GT.P3) THEN

WRITE (6, 150)P4

150 FORMAT (///, 2X, ‘THE HIGHEST VALUE IS BY R2 :’, F9.1)

ENDIF

STOP

END

C.2 Finite-Element Analysis of Explosion 979

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980 C Brickwork and Blockwork: Impact and Explosion

Fig. C.3. A typical external brick wall of a cubicle

Fig. C.4. Finite-element schemes for the building walls

C.2 Finite-Element Analysis of Explosion 981

80.0

60.0

40.0

20.0

1000 2000

Time, t (µs)

4 loading cases

Pre

ssur

e, P

(kN

/m2 )

3000 4000

4321

Fig. C.5. Pressure pulses for four types of explosion

4321

1000 2000 3000

Time, t (µs)

4000

100

228 mm brick wall4 loading cases

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rage

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eral

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lect

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δav

(m

m)

50

Fig. C.6. The effect of the pressure rise time on the maximum deflection

982 C Brickwork and Blockwork: Impact and Explosion

50

25

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lect

ion,

d (

mm

)

0

0 5 10

265

248250

200

154

10084

0 pressure (kN/m2)

Distance (m)15 20

–25

Fig. C.7. Pressure pulse versus distance of explosion for a wall

80

60

40

20

0

0 1000 2000 3000

horizontalvertical

4000

Pre

ssur

e, P

(kN

/m2 )

Time, t (µs)

Fig. C.8. Pressure–time relationship for a wall

C.2 Finite-Element Analysis of Explosion 983

8-noded20-noded

finite element

experimentsite monitoring

Debris

7

6

5

4

3

2

1

0 6 12 18

Deflection, d (mm) × 104

Flo

or lev

el

24 30 36 42

groundlevel

roof

Fig. C.9. Post-mortem for the building

Debris

Fig. C.10. Post-mortem for the wall

984 C Brickwork and Blockwork: Impact and Explosion

(a)

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damagedzone

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0.2

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0.3

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0.6

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(b)

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0.3

0.2

0.5

0.1

0.2

0.4

0.40.3

5

0.5

0.5

0.35

0.3

Fig. C.11. Damage to (a) the front of the wall and (b) the back of the wall

C.3 Bomb Explosion at a Wall 985

C.3 Bomb Explosion at a Wall

A 250kg GP bomb is thrown by a missile at a velocity of 100 m s−1. Theimpact force is calculated by

F1(t) = 0.55 × 106(mv2im/uim),

where m = weapon mass (kg), vim = impact velocity (km s−1), uim = normalpenetration (m) due to impact.

The finite-element analysis is carried out on a wall (Fig. C.4). The damagedzones for the front and back are indicated by Fig. C.11a, b.