Energy absorption of foamed concrete from low-velocity impacts Energy absorption of foamed concrete...

Magazine of Concrete Research, 2013, 65(4), 209–219

http://dx.doi.org/10.1680/macr.12.00054

Paper 1200054

Received 09/03/2012; revised 16/08/2012; accepted 29/08/2012

Published online ahead of print 14/12/2012

ICE Publishing: All rights reserved

Magazine of Concrete ResearchVolume 65 Issue 4

Energy absorption of foamed concrete fromlow-velocity impactsJones and Zheng

Energy absorption of foamedconcrete from low-velocityimpactsM. Roderick JonesConcrete Technology Unit, Division of Civil Engineering, University ofDundee, Dundee, Scotland, UK

Li ZhengConcrete Technology Unit, Division of Civil Engineering, University ofDundee, Dundee, Scotland, UK

Foamed concrete has existing uses as an energy absorber for large-scale and low-cost applications, such as explosion

prevention in mines and military engineering projects and aircraft arresting systems. However, there is little

information enumerating the energy absorption characteristics of different foamed concretes; this paper describes a

study that determined these using low-velocity impact tests. A range of foamed concretes were tested with plastic

densities varying from 500 to 1400 kg/m3, which are typical of those produced commercially. The tests used

hemispherical projectiles with a range of masses from 1.2 to 8.4 kg, dropped from a fixed height of 4.7 m. The

resulting ‘damage’ was measured and related to the impact energy imparted to the test specimen. A classification,

using five different failure modes, was established and the mode in which the test specimen neither caused

‘rebound’ of the projectile nor itself fractured was selected as representing ‘ideal’ energy absorption behaviour.

Making the assumption of no energy losses and using the conservation of energy law, the energy absorption

capacity of foamed concrete was calculated and was found to vary from 4 to 15 MJ/m3 for different mixes. The

optimum energy absorption was noted for the 1000 kg/m3 mix at water to cement (w/c) ratios from 0.6 to 0.7, which

allowed a debris field of crushed foamed concrete to form and be pushed into the concrete bubble space ahead of

the nose of the projectile, without fracturing.

Notationan nominal deceleration, which is the average deceleration

assuming the projectile is fully stopped after indenting

distance of dind (m/s2)

D plastic density of foamed concrete (kg/m3)

d indent diameter (mm)

dind indent depth (mm)

E potential energy (J), which for the purposes of these

tests was assumed equal to impact energy in the drop

test (i.e. any aerodynamic drag was ignored for

simplicity)

Eabs energy absorption per indent volume (MJ/m3)

g gravity (taken as 9.81 m/s2)

h fall height in the drop test (in this case fixed at 4.7 m)

m projectile mass (kg)

R radius of the hemispherical nose of the projectile

(¼ 31.72 mm)

V indent volume duo to embedment of projectile (mm3)

v velocity of the projectile before impact (¼ 9.6 m/s)

w/c water/cement ratio of foamed concrete

IntroductionFoamed concrete has reached a mature commercial position in

the market and is now widely used for a variety of purposes in

the civil engineering and building fields (e.g. Jones and

McCarthy, 2005, 2006; Jones et al., 2005, 2009). Foamed con-

crete can be produced with a wide range of recycled and

secondary aggregates, and can be easily crushed and reused;

therefore, it is a sustainable material (Jones et al., 2012). Polymer

foam materials are widely used to absorb impact energy to

protect goods in transit and other similar applications, but, based

on cost, these materials are not suitable for large-scale applica-

tions, such as aircraft runway arrestors (Kazda and Caves, 2007),

mines explosion protection (Weiss et al., 1996) and so on. Precast

foamed concrete block targets have been used by the military in

firing ranges. Bullets enter the foamed concrete blocks without

fragmenting (which can lead to environmental contamination)

and are, therefore, ‘caught’ by embedment and can be disposed

of in a safe manner (Huntsman et al., 2001; Tom, 2002). Indeed,

commercial products based on foamed concrete for these

purposes are now on the civilian market.

However, the underlying mechanistic behaviour of foamed concrete

has not been established and the influence of its characteristics on

energy absorption potential has not been evaluated. Foamed con-

cretes can be produced with a wide range of characteristics, for

example plastic densities from 1400 down to 500 kg/m3 (and,

indeed, below this density) and w/c ratios from 0.40 to 0.80; these

209

result in a wide range of mechanical properties. There is, therefore,

a need to identify the foamed concrete mix characteristics that give

optimum energy absorption performance and enable engineers to

design efficient, safe protection systems.

In response to this need, the current paper reports a laboratory-

scale research project that examined a wide range of foamed

concretes for their energy absorption using low-velocity impact

drop tests. A series of failure modes was observed and these were

classified based on visual observations; absorbed energy was

evaluated by the amount of crushing (i.e. indent volume) of the

specimen. Using these data optimum mix characteristics could be

established.

Experimental details

Background

Energy absorption systems convert, totally or partially, impact

energy into other forms of energy. The conversion of energy is

either reversible, for example pressure in compressible fluids and

elastic strain energy in solids, or irreversible, such as plastic

deformation. Foamed concrete acts using the latter form, whereby

crushing of the bubble walls provides the energy absorption from

the embedment of a projectile that possesses kinetic energy.

There are a number of established tests to determine impact

energy absorption potential, for example the Taylor impact test,

split Hopkinson pressure bar (SHPB)/tension bar (SHTB) tests

and drop hammer/projectile tests (Grytten, 2008). The Taylor

impact test is used for high- (i.e. ordnance) to hyper-velocity

projectiles, whereas SHPB/SHTB is usually used for sub-

ordnance to ordnance energy levels. In the present study,

low-velocity impact tests on test specimens subjected to a

hemispherical weight of various magnitudes dropped through a

fixed height of 4.7 m were carried out. The height was arbitrarily

selected, but, for convenience, was equal to a one-storey height

platform of the laboratory.

Materials and foamed concrete test specimens

The cement used for foamed concrete was Portland cement

(CEM I, BS EN 197-1 (BSI, 2011)) mixed with a natural fine

aggregate with a maximum particle size of 4 mm (GF85:0/4(MP),

BS EN 12620 (BSI, 2002)). The foam was preformed, in a

standard manner, using commercial protein-based surfactant

diluted with water, using a laboratory-scale foam generator,

before mixing with the base mortar mix.

The mix design described previously by Jones and McCarthy

(2005) was used to produce foamed concretes with plastic

densities of 500, 600, 1000 and 1400 kg/m3 at water/cement

(w/c) ratios varying from 0.4 to 0.8 and a CEM I content of

300 kg/m3 for all mixes. The foamed concrete mixes were

generally designed for the lowest w/c ratio that gave flowing and

self-compacting rheology. This was between 0.5 and 0.6 for 500–

600 kg/m3 and between 0.6 and 0.7 for 1000–1400 kg/m3 mixes;

the latter group required more free water owing to lower foam

and higher aggregate contents. These are typical of commercial,

large-scale fill applications and the mix proportions are sum-

marised in Table 1.

Target plastic

density: kg/m3

w/c Mix constituent proportions: kg/m3 Air:

vol%

Free water Sand Foam

500 0.50 150 50 57.4 73.5

600 0.40 120 180 55.9 71.6

0.50 150 150 54.4 69.8

0.60 180 120 53.0 67.9

0.70 210 90 51.5 66.0

1000 0.40 120 580 44.0 56.4

0.50 150 550 42.6 54.6

0.60 180 520 41.1 52.7

0.70 210 490 39.6 50.8

0.80 240 460 38.2 49.0

1400 0.40 120 980 32.1 41.2

0.50 150 950 30.7 39.4

0.60 180 920 29.2 37.5

0.70 210 890 27.8 35.6

0.80 240 860 26.3 33.7

Note that CEM I ¼ 300 kg/m3:

Table 1. Foamed concrete mix proportions

210


Energy absorption of foamed concretefrom low-velocity impactsJones and Zheng

For each mix, three to six test slab specimens were cast and

sealed-cured; the slab dimensions were 300 3 300 3 100 mm, as

shown in Table 2. This was a convenient size for handling, given

the large number of different mix options. In addition, 100 mm

cubes were prepared to determine the 28-day sealed-cured

strength of the mixes.

Low-velocity impact tests

Low-velocity projectile impact tests, defined as v , 50 m/s

(Grytten, 2008), were selected, which allowed for straightforward

health and safety requirements (as compared to using high-

velocity munitions that would have required special licensing). A

simple apparatus was designed, which consisted of a 70 mm

internal diameter, 4.7 m long, unplasticised polyvinyl chloride

(UPVC) guide pipe and a 62 mm hemispherical-ended projectile

with an adjustable mass, as shown in Figure 1. In the test, the

projectile with specific mass was dropped on to the test specimen

slab lying at the bottom end of the pipe. The foamed concrete test

specimen was located directly on a thick concrete slab (forming

part of a heavy-duty unloading bay at the laboratory), which

prevented any backward movement as the projectile impacted the

surface. The specimen was not restrained further to allow any

lateral or other deformation or fracture to take place unimpeded.

Using a hemispherical projectile with the guide pipe facilitated a

near vertical impact on the test specimen. Conical and flat-nosed

Impact/kinetic energy levela

1 2 3 4 5 6 7

Mass of projectile, kg 1.164 2.173 3.569 4.578 5.974 6.983 8.379

Kinetic energy:a J 54 100 165 211 275 322 386

Foamed concrete specimenb

w/c Plastic density:

kg/m3

28-day s/c cube

strength: N/mm2

Visual rating of the failure modec

0.4 600 0.66 b c d

1000 0.71 ‘b’d c d e

1400 0.99 ‘b’d c d e

0.5 500 0.79 ‘b’d c d d

600 1.45 b c d

1000 1.45 b b c d d

1400 1.93 a b b d9 d9 d9

0.6 600 1.44 a b c d e

1000 1.93 a b b c ‘d’d

1400 4.47 b b b b d9

0.7 600 1.00 ‘b’d c d e

1000 1.81 b c d

1400 4.31 b b d9

0.8 1000 1.37 b c d

1400 3.15 b d9 d9

a Fixed drop height ¼ 4.7 mb Test specimen: 300 mm 3 300 mm 3 100 mm deepc See Figure 2 for visual rating of the failure mode: a, low indentation and high rebound; b, partial indentation and rebound; c, full indentionwithout rebound; d, indention with local cracking (d9 indicates that rebounding was still noticed); e, complete specimen fractured Not tested but expected failure mode is stated

Table 2. Applied impact energy levels and visual rating of test

specimen failure modes of the drop tests

211



projectiles were tried during primary trials but did not give

repeatable results because they were found to impact the test

specimen non-uniformly (presumably owing to the effects of

aerodynamic forces inside the drop pipe). It was not possible

during this work to investigate how these different geometries

could be tested, but one possibility is to use a much larger ratio

of test specimen to projectile volume to reduce the incidence of

cracking and fracture. The lack of uniformity, however, would

4·7

m

1·164 kg

2·405 kg2·405 kg

2·405 kg

1·009 kg

62 mm

25 m

m23

mm

Figure 1. Drop testing apparatus: UPVC guide pipe (left) and test

projectile (right), hemispherical ended with adjustable mass

212



make this approach problematic for the accurate measurement of

energy absorption.

With a series of primary tests, procedures for low-velocity impact

tests were established, using the fixed drop height, h, of 4.7 m

and the hemispherical-ended projectile with mass, m, varying

from 1.2 to 8.4 kg, giving variations of impact energy up to seven

levels, as summarised in Table 2. The tests were carried out with

gradually increased impact energy until the test specimen frac-

tured. The energy applied to the specimens was calculated with

the standard equation for potential energy, E, as follows

E ¼ mgh1:

Assuming negligible losses and, therefore, that the potential

energy is equal to the kinetic energy for the drop test, the

terminal velocity at the moment of impact was calculated to be

9.6 m/s and the time taken to impact from the release point was

0.98 s.

During the test, the series of projectile masses with different

energy levels were dropped on to the foamed concrete test

specimens and a visual assessment of the impact damage was

carried out. Provided the specimens had not failed by fracturing,

the indent volume, V, was determined by placing a layer of

domestic food wrapping (cling) film over the indent and measur-

ing the volume of water to fill the void. The energy absorption

per indent volume, Eabs, was calculated as

Eabs ¼ E=V2:

The indent depth, dind, could not be measured directly and, hence,

it was calculated from measured indent diameter and volume with

the following equations for a hemisphere (see Figure 1)

dind ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3V

�þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3V

2�

� �2

þ d

2

� �6s

3

vuut

þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3V

��

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3V

2�

� �2

þ d

2

� �6s

3

vuutfor V < 45 920 mm3

3:

or

dind ¼ 25þ 4(V � 45920)

�d2for V . 45 920 mm3

4:

In addition, when V , 45 920 mm3 (i.e. d , 62 mm), the indent

depth was also calculated by

dind ¼ R�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2 � d

2

� �2s

for V < 45 920 mm3

5:

If the calculated depth results between Equations 3 and 5 were

significant, repeat measurements were carried out. With this

calculation, the influence of any cracks around the indentation

was minimised.

The nominal deceleration, an, was calculated as

an ¼1000E

mdind

¼ 1000v2

2dind6:

The calculated deceleration was thought to be proportional to the

Janssen factor (Woolam, 1968) assuming the projectile is fully

stopped after embedment distance of dind, which can be used to

evaluate the energy absorption efficiency of a material under

impact (Hilyard and Djiauw, 1971; Neto and Mourao, 2002;

Zhang and Ashby, 1994).

Results and discussion

Visual rating of failure modes

The visual rating, based on ‘damage’ type, was divided into five

different failure modes, a to e, as shown in Figure 2, and the

visual rating results for all specimens tested are given in Table 2,

together with their seal-cured, 28-day cube strength values.

j Mode a: the applied impact energy was low, the projectile

made only a shallow indentation and rebound was observed

(Figure 2(a)).

j Mode b: the depth of indent increased with an increase in

impact energy and rebound was reduced quickly, or was

unlikely to occur in most cases of this mode (Figure 2(b)).

j Mode c: the projectile was fully trapped in the specimen and

there was no rebound (Figure 2(c)).

j Mode d: the projectile caused cracking around the embedded

depth (Figure 2(d)). For 1400 kg/m3 foamed concrete, partial

rebound was still observed and this case was denoted d9

(Figure 2(e)).

j Mode e: further increase of impact energy caused extensive

cracking and complete fracture of the test specimen (Figure

2(f)).

The optimum mode for determining energy absorption was where

the projectile was fully embedded, without any rebound or

cracking of the test specimen, in other words mode c.

As expected, for each particular foamed concrete, its failure mode

213



(a) (b)

(c) (d)

(e) (f)

Figure 2. Visual rating of the failure mode: (a) mode a – low

indentation and high rebound (D ¼ 1400 kg/m3, w/c ¼ 0.5,

E ¼ 100 J); (b) mode b – partial indentation and rebound

(D ¼ 600 kg/m3, w/c ¼ 0.5, E ¼ 100 J); (c) mode c – full

indentation without rebound (D ¼ 500 kg/m3, w/c ¼ 0.5,

E ¼ 100 J); (d) mode d – indentation with local cracking

(D ¼ 500 kg/m3, w/c ¼ 0.5, E ¼ 211 J); (e) mode d’ – indentation

with local cracking and rebound ((D ¼ 1400 kg/m3, w/c ¼ 0.8,

E ¼ 386 J); (f) mode e – complete specimen fracture

(D ¼ 600 kg/m3, w/c ¼ 0.6, E ¼ 275 J)

214



changed from mode a to e as projectile mass and hence impact

energy was increased. The mode was also affected by w/c ratio,

density and strength of foamed concrete (Table 2). For compressive

strengths , 0.8 N/mm2, the full indention, mode c was observed

with 100 J impact energy. For strengths between 1.0 and 1.8 N/

mm2, mode c occurred with 165–211 J impact energy. One speci-

men with strength 1.9 N/mm2 showed mode c behaviour with 275 J

impact energy. Therefore, specimens with higher strength, which

reflects the strength and number of bubble walls, tended to allow

more impact energy to be absorbed. However, it was also noted that

for the foamed concrete with highest strength (. 1.9 N/mm2) and

high density (1400 kg/m3), the projectile did not embed into the

foamed concrete and tended to either fracture or rebound mode d’.

After several trials, an experienced operator could obtain a

repeatable result with three drop tests with varying projectile

masses. The mass for the first strike was estimated and, depend-

ing on the resulting failure mode, the second and third impacts

were adjusted with either higher or lower masses, as required, to

produce a mode c failure.

Bubble structures of foamed concrete with plastic densities of

600–1400 kg/m3 and w/c ratios of 0.5–0.6 were observed using

an optical microscope, as shown in Figure 3. It can be seen that

the foamed concretes consist of bubbles of between approxi-

mately 0.1 and 1 mm in size, uniformly distributed in a matrix of

fillers and cements, which is typical for the material (Wee et al.,

2006). The microstructure images also show that the bubble size

increases as the plastic density reduces, although there were only

minor differences with the different w/c ratios.

Figure 4 shows two examples of the test specimens split through

the indent impacted by the projectile. Figure 4(a) shows a 500 kg/

m3 density test specimen subjected to 100 J impact energy

resulting in a c-type failure mode. This can be contrasted with

Figure 4(b) where a 1400 kg/m3 density test specimen has been

subjected to the same impact energy causing a-type failure mode.

The key observation is that 500 kg/m3 foamed concrete provided

space for a ‘debris field’ to be pushed further into the specimen

ahead to the impact ‘bowl’. It is suspected that this is a key

mechanism by which energy absorption occurs in foamed con-

crete. Mixes such as this had the ‘right’ combinations of charac-

teristics, in other words relatively strong bubble walls that absorb

the projectiles’ kinetic energy by crushing, but also sufficient

bubble space for crushed debris without local cracking or

fracturing of the whole specimen. It was not possible, however, to

evaluate directly which was the more important characteristic, but

an empirical approach using a comparison of the performance of

the various mixes is discussed below.

Measurement of indent parameters

In addition to the visual rating of the drop test results, measure-

ment of indent parameters, for example indent volume and

diameter of indent, were carried out to evaluate quantitatively the

(a) (b) (c)

(d) (e) (f)

Figure 3. Examples of typical bubble structures of foamed

concrete (photograph width ¼ 15 mm): (a) 600 kg/m3, w/c ¼ 0.5;

(b) 1000 kg/m3, w/c ¼ 0.5; (c) 1400 kg/m3, w/c ¼ 0.5;

(d) 600 kg/m3, w/c ¼ 0.6; (e) 1000 kg/m3, w/c ¼ 0.6;

(f) 1400 kg/m3, w/c ¼ 0.6

215



energy absorption properties of foamed concrete. As the elastic

recovery percentage of foamed concrete is negligible, these

geometrical measurements of the deformation of the test speci-

men provide meaningful information.

Indent volume

The volumes of crushed foamed concrete attributable to the

impact of the projectile into the test specimens are given in

Figure 5 in relation to the impact energy. As expected, the indent

volume generally increased with impact energy. The curves could

be divided into two types: accelerating (d2V=dE2 . 0, exponen-

tial type trend curve) and decelerating (d2V=dE2 , 0, logarithmic

type trend curve), which are separated by a dashed line, as shown

in Figure 5. All relatively weak specimens (density , 1000 kg/m3

and cube strength , 1.5 N/mm2) exhibited accelerating indent

volume increases with impact energy, whereas the rigid speci-

mens (density . 1000 kg/m3 and cube strength . 1.5 N/mm2)

exhibited decelerating indent volume increases. This difference in

behaviour is considered to be attributable to the ability of a

particular mix to ‘absorb’ the debris of crushed foamed concrete,

as observed in Figure 4. It is not clear, however, whether this can

be attributed to the volume of the bubble phase, the local strength

of the bubble walls and/or the size of the bubbles. However, the

visual evidence (Figure 4) shows that the 1400 kg/m3 density

concrete was not able to absorb any debris, owing to insufficient

bubble space, and hence its energy absorption potential was poor.

Assuming the kinetic energy of the projectile is fully absorbed in

foamed concrete with the indent volume in mode c and there are

no other losses, the calculated energy absorptions per indent

volume for the different specimens are compared in Figure 6.

The figure indicates that the highest energy absorption was

around 14 MJ/m3 for the 1000 kg/m3 plastic density test speci-

men with w/c ratios from 0.6 to 0.7 and cube strengths 1.8–

1.9 N/mm2: The other test specimens had significantly lower

values in the range 4–7 MJ/m3:

Depth of indent

The depth of indent was calculated from measured indent volume

and diameter by Equations 3–5. As the indent depth is relevant

to volume, its relationship to impact energy is similar to the

relationship of volume to impact energy. The average deceleration

assuming the projectile is fully stopped at the indent depth was

calculated using Equation 6 and the results are shown in Figure

7. Generally, deceleration increases with plastic density but

decreases with impact energy tending to a minimum value. The

calculated deceleration is considered to be proportional to the

Janssen factor (Woolam, 1968), except for those test specimens

that cracked (mode d) or fractured (mode e), where the minimum

point expected in full indention (mode c) was not observed.

Lower deceleration/Janssen factor was thought to have higher

energy absorption efficiency for that particular impact energy

applied during the impact test (Hilyard and Djiauw, 1971; Neto

and Mourao, 2002; Zhang and Ashby, 1994).

Energy absorption efficiency

Energy absorption efficiency can be evaluated in terms of the

ability of a particular foamed concrete mix to absorb a wide

range of energies without rebound or fracture failure, that is those

mixes which ‘fail’ with mode c (Figure 2). Using these criteria,

Table 2 shows that the optimum was the 1000 kg/m3 mix at a w/c

ratio of 0.6. This mix absorbed the energy of the highest dropped

projectile mass, namely 275 J, with mode c.

However, the mix with the highest overall energy absorption is

again the 1000 kg/m3 foamed concrete, but in this case with a

w/c of 0.7, in other words with slightly weaker bubble walls. This

mix could absorb 15 MJ/m3 compared with 14 MJ/m3 for the

‘stronger’ mix with a w/c of 0.6.

The 1000 kg/m3 mixes were significantly better at absorbing

energy than the other mixes, for example the stronger 1400 kg/m3

mix absorbs 70% less energy, and it was a similar picture with

(b)

`Debris field’ahead of

impact `bowl’

(a)

Figure 4. Split section through the indent of the impacted

specimens, indicating indent ‘bowl’ and ‘debris field’:

(a) 500 kg/m3, w/c ¼ 0.5, 100 J, indent ¼ 13.1 mm;

(b) 1400 kg/m3, w/c ¼ 0.5, 100 J; indent ¼ 4.1 mm

216



the 600 kg/m3 mixes, which absorbed 60% less energy. At this

stage, the reasons for this can only be derived from the

observations summarised in Figure 2. The projectile impact

crushes the wall of the bubbles in the foamed concrete and

produces a ‘debris’ field (see Figure 4). If there is insufficient

‘space’ to accommodate this around the impact indent, then the

concrete builds up a tensile stress and fractures in a brittle

manner; this was the case for the 1400 kg/m3 mixes. However,

with the lower density foamed concretes, which have thinner

bubble walls owing to their higher air contents, there is insuffi-

cient strength to resist the projectile impact, which was the case

for the 500 and 600 kg/m3 mixes.

Based on this hypothesis, the conclusion is that the 1000 kg/m3,

with w/c ratios from 0.6 to 0.7, have optimum characteristics of

stronger bubble walls and space for the impact debris field to be

accommodated. Given the significantly lower performance of the

higher and lower density mixes, these combined characteristics

are vital to energy absorption efficiency and neither can be

compromised.

ConclusionsUsing low-velocity dropped weight impact tests with variable

mass (1.2–8.4 kg) hemispherical projectiles dropped from 4.7 m

in free air, the energy absorption capabilities of a wide range of

foamed concretes, varying from 500 to 1400 kg/m3 and w/c ratios

from 0.40 to 0.80, were measured. Five different failure modes

0

10

20

30

40

50

60

70

80

90

0 50 100 150 200 250 300 350 400 450

Inde

nt v

olum

e: 1

0m

m3

3

Impact energy: J

Plastic density: kg/m / / ratio3 w c

500/0·5

600/0·6

1000/0·5

1000/0·8

1400/0·6

600/0·4

600/0·7

1000/0·6

1400/0·4

1400/0·7

600/0·5

1000/0·4

1000/0·7

1400/0·5

1400/0·8

Acceler

ating

Deceler

ating

Figure 5. Relationship between indent volume and impact energy

applied for the various foamed concrete mixes

0

2

4

6

8

10

12

14

16

Ener

gy a

bsor

ptio

n: M

J/m

inde

nt v

olum

e3

w c/ ratio0·5 0·4 0·5 0·6 0·7 0·4 0·5 0·6 0·7 0·8 0·4

500 600 600 600 600 100010001000100010001400

Plastic density: kg/m3

Figure 6. Energy absorption per indent volume for specimen

failure in mode c

217



were noted and the one in which the test specimen neither caused

‘rebound’ of the projectile nor fractured (denoted mode c) was

adopted as representing ‘ideal’ behaviour in terms of energy

absorption. Foamed concrete was found to provide energy absorp-

tion values from 4 to 15 MJ/m3:

It was found that there was a relationship between density, w/c

ratios (which closely control bulk strength) and energy absorption

capacity of foamed concrete. The mix with optimum energy

absorption was the 1000 kg/m3 mix at w/c ¼ 0.6 (judged by

maximum impact energy at failure mode c) or at w/c ¼ 0.7

(judged by maximum energy absorption per indent volume).

Through observation, the ideal mix had a balance of high bubble

wall strength and large bubble volume to accommodate the

crushed debris material. The walls are too ‘weak’ because they

are thin in the low-density mixes and only a limited amount of

kinetic energy could be accommodated. However, with the higher

density mixes with stronger walls, attributable to the lower air

content and fewer and smaller bubbles, there was insufficient

‘space’ to accommodate the ‘crushed debris field’ and brittle

fracture resulted. At this stage, it was not possible to formulate a

generalised model from which a numerical equation could be

derived for designers; further work is on-going at Dundee

university to address this need. Although only hemispherical-

nosed projectiles were tested in this work, the observation of the

need for ‘space’ to accommodate the debris field pushed ahead of

the projectile as it impacts the foamed concrete suggests that

other projectile shapes would behave in a similar manner. There

is also a need for further work to determine energy absorption

metrics for high-velocity munitions, but the evidence for foamed

concrete targets used on firing ranges suggests that the general

behaviour is similar to that reported here. There is also compa-

nion work to be done investigating stress and shear wave

propagation/absorption in foamed concrete to develop a generali-

sed behavioural model that could be applied to other situations.

AcknowledgementsThomas Tonderai Kachisi is thanked for his impact experimental

data and Dr Maziah Mohammad for her images of bubble

structures of the specimens. Professor Alan Vardy assisted with

the design of, and provided technical advice on, the drop test.

0

2

4

6

8

10

12

0 50 100 150 200 250 300 350 400 450

Dec

eler

atio

n:10

m/s

�3

2

Impact energy: J

Plastic density: kg/m / / ratio3 w c

500/0·5

600/0·6

1000/0·5

1000/0·8

1400/0·6

600/0·4

600/0·7

1000/0·6

1400/0·4

1400/0·7

600/0·5

1000/0·4

1000/0·7

1400/0·5

1400/0·8

Figure 7. Relationship between deceleration and impact energy

for the various foamed concrete mixes

218



The materials support provided by Propump Engineering Ltd is

gratefully acknowledged.

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WHAT DO YOU THINK?

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August 2013. Your contribution will be forwarded to the

author(s) for a reply and, if considered appropriate by

the editorial panel, will be published as a discussion in a

future issue of the journal.

219



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