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

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

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

compressive strength (MPa)

r/a

0.0 0.1 0.2 0.3 0.4 0.5

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

compressive strength (MPa)

r/a

volume fraction is 5%

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

Compressive strength(MPa)

r/a

volume fraction is 20 percent

23.71MPa

35.7MPa

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

Compressive strength(MPa)

r/a

Volue fraction is 40%

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.

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