Study the Size Effect of EPS Concrete on Its Compressive Strength
Qiang Li
*
, Hairong Dong, Jianmin Su, Xiaoliang Zhang, Hui Guo, Debai Zhao and Quanpeng Liu
School of Vehicle Engineer, Weifang University of Science and Technology, No.1299 Jinguangjie, Shouguang, Shandong,
P.R.China, 262700
Keywords: EPS concrete, ratio of EPS bead radius to specimen size (r/a), compressive strength; volume fraction
Abstract: The effect of the ratio of EPS bead radius to the specimen size (r/a) on the compressive strength is investigated
by theoretical deduction. The results show that r/a, as well as volume fraction, plays an important role in
affecting the compressive strength. The volume fraction of EPS beads determines the minimum compressive
strength of EPS concrete specimen, the higher volume fraction, the lower the minimum compressive strength.
The maximum compressive strength is relied on r/a. When r/a is smaller than 0.05, the effect of r/a can be
neglected. As the EPS volume fraction increases, the maximum and the minimum compressive strength will
be affected by changing r/a. Therefore, reducing the density and enhancing the compressive strength of EPS
concrete can be accomplished by adjusting r/a value to a certain value under a certain volume fraction.
1 INTRODUCTION
Expanded polystyrene (EPS) concrete with low
density, high thermal insulation properties arouses
great interest from industries and research institutes
for its wide applications, such as sub-base material
for pavement and railway track bed, construction
material for floating marine structures, sea beds and
sea fences, ceiling and thermal insulation wall et al
(Babu and Babu, 2003; Babu et al., 2006).
Although there are lots of advantages and wide
applications of EPS concrete, the low mechanical
properties of EPS concrete is one of its distinct
weaknesses. In the past decade, there were lots of
researching works were related to mechanical
properties of EPS concrete (Babu and Babu, 2003;
Chen and Liu, 2013; Miled et al., 2004; Ling and Teo,
2011; Bouvard et al., 2007).
Mild et al (Miled et al., 2004; Miled et al., 2007)
investigated the size effect of EPS beads on the
compressive strength and the failure. In their model
(Miled, 2004), the damage initiation and distribution
in the specimen were calculated. However the model
was a 2d model that couldn’t reflect the 3D situation.
Miled (Miled et al., 2007) et al used the experimental
method and numerical method to investigate the
influences of size of EPS beads on its compressive
strength and found the finer EPS beads, the higher
compressive strength.
In 2005 Laukaitis et al (Laukaitis et al., 2005)
studied the effect of polystyrene size on the
compressive strength of EPS concrete. Their
experiment showed the fine polystyrene had the
highest compressive strength and the crumbled
polystyrene had the lowest compressive strength.
There are also some research works about EPS
structure (Bouvard et al., 2007), fabrication and
physical properties, and numerical simulation (Fu
and Dekelbab, 2003; Liu et al., 2012). However the
influence of ratio of EPS bead radius to specimen size
on the compressive has not attracted enough
attention. In this article, the relationship between
ratio of EPS bead radius to specimen size (r/a) and
compressive strength was built.
2 PHYSICAL MODEL
According to Song et al (Song et al., 2008)
researching work, the upper limitation of volume
fraction for randomly packing of equal radius spheres
is 0.634. Therefore, the upper limitation for EPS
volume fraction is set less than 0.6. The specimen of
EPS concrete is adopted as cubic shape, and its size
is , the radius of EPS bead size is , The
volume fraction of EPS beads is , r/a is the ratio of
EPS bead to sample size.
Compared with solid concrete, the compressive
strength of EPS beads is very tiny. Therefore, the
Li, Q., Dong, H., Su, J., Zhang, X., Guo, H., Zhao, D. and Liu, Q.
Study the Size Effect of EPS Concrete on Its Compressive Strength.
DOI: 10.5220/0008186801390142
In The Second International Conference on Materials Chemistry and Environmental Protection (MEEP 2018), pages 139-142
ISBN: 978-989-758-360-5
Copyright
c
2019 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
139
compressive strength of EPS beads is neglected in
this paper, and the compressive strength of EPS can
be regarded as the strength of the solid concrete.
Because the compressive strength is defined as:
, where F is loading force, and S the cross section
area, so the compressive strength of EPS concrete is
depended on the solid concrete area excluded the EPS
beads occupied area. Here, we divided the EPS
distribution in concrete matrix into three situations:
loose packing, high density packing and others mode
packing of EPS beads.
2.1 Loose Packing Model of EPS Bead
In this paper loose packing model means that in any
cross section of specimen, there is no overlap
between two neighbouring layers of EPS beads, and
the compressive strength can be deduced as:



(1)
where
is the compressive strength of completely
solid concrete, here
is set as 40 MPa.
is the
compressive strength of EPS concrete, is EPS
volume fraction. That is to say, the compressive
strength is only depended on .
2.2 High Density Packing of EPS Bead
When there is overlap between any two neighbouring
layers of EPS beads, the compressive strength of EPS
concrete is expressed as Equation 2.



(2)
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
5
10
15
20
25
30
35
40
Compressive strength (MPa)
r/a
8.584MPa
Figure 1: Relationship between r/a and compressive
strength.
Figure 1 shows that the minimum compressive
strength is 8.58MPa, and as r/a increases, the
compressive strength increases too.
2.3 Other Mode Packing EPS Beads
To investigate impact of r/a on compressive strength,
r/a can be divided into following situations.
1) When there is only one EPS bead in the
concrete specimen and the radius of EPS bead
increases from very tiny value to half of the specimen
size, the compressive strength is expressed as:

(3)
According equation (3) the relationships among
compressive strength, the volume fraction and
specimen for 1 EPS beads in EPS concrete situation
can be drawn as Figure 2.
0.0 0.1 0.2 0.3 0.4 0.5
5
10
15
20
25
30
35
40
45
compressive strength (MPa)
r/a
0.0 0.1 0.2 0.3 0.4 0.5
5
10
15
20
25
30
35
40
45
Compressive strength(MPa)
EPS volume fraction
Figure 2: Relationship between r/a and compressive
strength as only one EPS bead in concrete specimen.
Figure 2 shows that there is only 1 EPS bead in
the specimen, and when r/a=0, the EPS concrete has
the maximum compressive strength 40 MPa. When
r/a increases, the compressive strength decreases
gradually. In addition, the volume fraction of EPS
beads increases as r/a increases.
2) when

, (


),
The compressive strength can be deduced as:





(4)
where fix is round function.
3 RESULTS AND DISCUSSION
Here the volume fraction of EPS bead is adopted as
5%, 20% and 40% to find the role of r/a on
compressive strength according to equation (1), (2) ,
(3) and (4) respectively.
For , the ratio of EPS bead to specimen
should be
. The relationship between r/a
and compressive strength can be drawn as Figure 3.
MEEP 2018 - The Second International Conference on Materials Chemistry and Environmental Protection
140
0.0 0.1 0.2
28
30
32
34
36
38
5
4
3
2
compressive strength (MPa)
r/a
volume fraction is 5%
1
36.98MPa
33.35Mpa
28.69MPa
Figure 3: Relationship between r/a and compressive
strength when .
Figure 3 is the relationship between r/a and
compressive strength as the EPS volume fraction is
5%, which corresponding to the loose packing model
and the lines marked 1,2,3,4 and 5 stand for the total
number of EPS beads in each direction of the
maximum cross-section of specimen. Figure3 shows
that the compressive strength sways up and down
from the initial value of 33.35MPa. When r/a is less
than 0.05, the deviation of compressive strength of
EPS concrete is less than 1MPa. The maximum and
the minimum compressive strength are 36.98MPa
and 28.69MPacorresponding to 1 EPS bead and 2
EPS beads in each direction of the maximum cross
section. In addition, in each number line zone, the
compressive strength decreases with increasing r/a,
that is, if possible, reducing the number of EPS beads
in the maximum cross section area and r/a can
increase the compressive strength.
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
22
24
26
28
30
32
34
36
Compressive strength(MPa)
r/a
volume fraction is 20 percent
23.71MPa
35.7MPa
1
2
3
4
5
6
Figure 4: Relationship between r/a and compressive
strength when .
Figure 4 is the relationship between r/a and
compressive strength when the EPS volume fraction
is 20%, in which marked 1 to 6 lines stand for the
total number of EPS beads in each direction of the
maximum cross section area. In line 1, there is only 1
ESP bead in the maximum cross-section, and r/a
ranges from 0.2 to 0.36. Similarly, in line 2, there are
2 EPS beads in cross section area, which r/a is
between 0.125 to 0.18. In Figure 4, the maximum
compressive strength and the minimum compressive
strength are 35.7 MPa and 23.71MPa, respectively.
When r/a value is higher than 0.05, the maximum
compressive strength increases gradually until r/a
reaches 0.18, but the minimum compressive strength
is same as the initial value 23.71MPa. When in
marked 1 line, r/a increase from 0.2 to 0.36, the
compressive strength drops gradually from the
maximum 35.7 MPa to the minimum 23.71MPa.
Therefore, the compressive strength can be increased
by adjusting r/a value.
Compared Figure4 with Figure3, it can be found
that the maximum compressive strength drops only 1
MPa from 36.98 to 35.7 MPa, but the minimum
compressive strength drops from 28.69 to 23.71 MPa
as the EPS volume fraction increases from 5% to
20%.
0.0 0.2 0.4
10
20
30
Compressive strength(MPa)
r/a
Volue fraction is 40%
1
2
3
4
5
6
7
13.98MPa
33.35MPa
14.55MPa
Figure 5: Relationship between r/a and compressive
strength when .
Figure 5 shows the relationship between r/a and
compressive strength when the EPS beads volume
fraction is 40%. When r/a is smaller than 0.05, the
difference between the maximum and the minimum
compressive strength is about 1 MPa. When r/a is
bigger than 0.05, the difference between the
maximum and the minimum compressive strength
rises up to 19MPa as the total number of EPS bead in
the maximum cross-section decreases to 1 EPS bead.
When there is only 1 EPS bead in specimen cross
section area, r/a can be ranged from 0.25 to 0.45, the
compressive strength drops from the maximum
33.35MPa to the minimum 14.55 MPa. In addition,
when there is only 1 or 2 EPS beads in each direction
of specimen cross section area, the minimum
compressive strength is also 14.55 MPa which is very
close to 13.98MPa, and the difference between the
maximum and the minimum compressive is 129% of
the minimum compressive strength.
Compared Figure 5 with Figure 4 and Figure 3, it
can be found that the maximum compressive strength
drops little (36.98, 35.37 and 33.35MPa) as EPS
Study the Size Effect of EPS Concrete on Its Compressive Strength
141
beads volume fraction increases from 5% to 40%, but
the minimum compressive strength decreases greatly
from 28.69 MPa to 14.55 MPa which means that the
EPS volume fraction can determine the minimum
compressive strength and the maximum compressive
strength of the specimen is relied on r/a. For the large
specimen, r/a approaches to zero, and the effect of
ratio of r/a can be neglected. However, for the small
size specimen changing r/a value is a way to enhance
its compressive strength.
4 CONCLUSIONS
Through studying, the following conclusions can be
got:
1) When
 , the influence of r/a on
compressive strength can be neglected.
2) The minimum compressive strength decrease as
the EPS volume fraction increases.
3) The volume fraction of EPS bead determines the
minimum compressive strength of EPS concrete
specimen, and the maximum compressive
strength is determined by r/a.
4) When the EPS volume fraction is constant,
adjusting r/a is an effective way to enhance the
EPS concrete compressive strength.
ACKNOWLEDGEMENTS
Thanks for the projects from Weifang University of
Science and Technology, Grant No: 2018wksd009
and 2018wksd010.
REFERENCES
Babu, D.S., Babu, K. G. and Wee, T.H., 2006. Cement and
Concrete Composites, 28(6): pp. 520-527.
Babu, K.G. and Babu, D.S., 2003. Cement and Concrete
Research, 33(5): pp. 755-762.
Bouvard, D., Chaix, J.M., Dendievel, R., Fazekas, A.,
Létang, J.M., Peix, G., Quenard D., 2007. Cement and
Concrete Research, 37(12): pp. 1666-1673.
Chen, B., and Liu, N., 2013. Construction and Building
Materials, 2013. 44(0): pp. 691-698.
Fu, G. and Dekelbab, W., 2003. Powder Technology,
133(13): pp. 147-155.
Laukaitis, A., Žurauskas, R. and Kerien, J., 2005. Cement
and Concrete Composites, 27(1): pp. 41-47.
Ling, I.H. and Teo, D.C.L., 2011. Construction and
Building Materials, 25(8): pp. 3648-3655.
Liu, Y., You, Z. and Zhao, Y., 2012. Construction and
Building Materials, 37: pp. 775-782.
Miled, K., Le Roy, R., Sab, K., Boulay, C., 2004.
Mechanics of Materials, 36(11): pp. 1031-1046.
Miled, K., Sab, K. and Le Roy R., 2007. Mechanics of
Materials, 39(3): pp. 222-240.
Song, C.M., Wang, P., Makse, H.A., 2008. Nature, 453: pp.
629-632.
MEEP 2018 - The Second International Conference on Materials Chemistry and Environmental Protection
142