3.1 Compressive strength
It is a natural phenomenon that the strength of the concrete to reduce by an increase
in w/c and brick chips content. Considering the fact that the strength of brick chips
alone was about 20 MPa or less, the use of brick chips significantly influenced the
concrete with lower w/c. However, when w/c is as high as 0.70, there is no difference
in strength with different aggregate. Concrete strength with w/c of 0.45 and 0.50
was reduced about 26~29 % by a 100 % replacement of the natural aggregates by brick
chips, while that with 0.70 was unchanged. Note that, in the study of Cachim (2009)(13), the two different types of crushed bricks from construction waste were used to replace
natural aggregate with up to 30 % for the concrete with w/c 0.45-0.50, and the strength
of concrete was varied from -30 % to +5 % of the strength of concrete with natural
aggregate. The decrease in concrete strength due to the use of brick chips in this
study was induced by the low strength of the brick chips themselves, i.e., 5.9~26.6
MPa, as shown in Fig. 6.
Fig. 8. Coefficient of variation for compressive strength of concrete at 28 days
In some cases, the average value of the strength at 7 days was slightly higher than
those at 28 days, and these gaps were negligible considering the coefficient of variation
in Fig. 8. It was hard to find tendencies on the change of the coefficient of variation by
w/c and brick chips content while the variation is close to zero, below 0.2 (20 %),
which indicates that the variation of the compressive strength results was not large
even in the case where brick chips were replaced.
It should be noted that, as mentioned in the introduction section, even if the content
of brick chips in the concrete were determined based on the equivalent strength, the
toughness and durability of the concrete materials should also be evaluated for structural
design purpose (Song et al. 2018)(30). Subsequent studies will perform various experiments related to this, such as the
bending test to evaluate fracture toughness, or resistance to chloride penetration
and carbonation (Narasimhan andd Chew 2009)(26).
3.2 Regression analysis of compressive strength
In this part of the study, linear regression analyses were used to establish a model
of 28-day compressive strength related with w/c and brick chips content. It was assumed
that the strength of concrete decreased ‘linearly’ with increases in w/c and brick
chips content (Yoon and Yang 2015; Kim 2015)(19,28). Similar assumptions have been adopted in the mix design method based on ‘the equivalent
strength concept’ by the European Committee for Standardization (Gruyaert et al. 2013)(17). It should worth to mention that, of course, the actual experimental results are
not all theoretically linear on the relationships between strength and w/c or brick
chips content, and the results used here may vary depending on the size and type of
brick chips.
First, the relationship between compressive strength and w/c of the concrete was given
by (Gruyaert 2013)(17):
where, $a_{1}$ and $a_{2}$ were regression coefficients.
The values of $a_{1}$ and $a_{2}$ were assumed to be changed linearly by the replacement
ratio of brick chips aggregate by normal aggregate ($R$, %). The model of strength
with the independent variables of w/c and $R$ was then given as.
where, $b_{i}$ and $d_{i}$ are also regression coefficients. The values of the regression
coefficients $d_{i}$ in Eq. (2) were calculated using SPSS software for the experimental results, and the results
are listed in Table 4. The coefficient of determination, $r^{2}$, of Eq. (2) was smaller than 0.5 due to the variations in experimental results.
Table 4. Regression coefficients of Eq. (2) obtained from experimental results
|
Regression coefficients
|
$r^{2}$
|
|
$d_{1}$
|
$d_{2}$
|
$d_{3}$
|
$d_{4}$
|
|
-49.0
|
-0.30
|
0.424
|
59.5
|
0.478
|
Fig. 9. Experimental results and regression model of compressive strength of concrete
with various w/c and brick chip content
The experimental results and regression model of the 28-day compressive strength of
the concrete are shown in Fig. 9. A comparison of the average values from experiments and regression models shows
a variation of less than 3 MPa in almost all cases.
3.3 Mix proportioning for cost minimization
The total cost of concrete by unit volume ($C_{{conc}}$, USD/m$^{3}$) is assumed to
be the summation of water ($C_{w}$), cement ($C_{c}$), sand ($C_{s}$), gravel ($C_{g}$),
and brick chips ($C_{b}$) market value by mass (USD/kg) as shown in Eq. (3). Note that the chemical admixtures cost were excluded because of a trivial amount
of admixture were used to make the mixtures workable.
where, $w$, $c$, $s$, $g$, and $b$ are the required mass for unit volumes of water,
cement, sand, gravel, and brick chips in concrete (kg/m$^{3}$), respectively.
Assuming the air content in concrete is constant regardless of the w/c and R, the
unit volume and weight of sand would be influenced by w/c. Considering that the volume
of the water and the coarse aggregates are constant throughout the study as the mixtures
in Table 3, Eq. (3) could be expressed as follows:
where, $v_{c}$, $v_{ca}$, and $v_{air}$ are volume of cement, coarse aggregate (sum
of gravel and brick chips), and air, respectively (L/m$^{3}$); $\rho_{c}$, $\rho_{s}$,
$\rho_{g}$, $\rho_{b}$ are the densities of cement, sand, gravel, and brick chips
under SSD conditions, respectively (kg/m$^{3}$). Except for w/c and $R$, the remaining
values of $v_{j}$ and $\rho_{j}$ (where, $j$ refers to each material) in Eqs. (4) and (5) were constant, in overall.
Therefore, Eq. (4) can be simplified as follows:
Table 5. Costs for raw material at site (USD/kg)
|
Cement
|
Sand
|
Sand
|
Natural aggregate (exported)
|
Brick chips
|
|
0.09
|
0.03
|
0.03
|
0.06
|
0.0285
|
The cost of each material ($j$) per kg at the local market near the construction site,
i.e., Matarbari in Bangladesh, is listed in Table 5, including the brick chips in USD. The values for $h_{1}$, $h_{2}$, and $h_{3}$ were
calculated to be -0.395, 11.828, and 96.091, respectively, using the market value
listed in Table 5 into Eqs. (4) and (5).
For mix proportioning based on the cost minimization, Eq. (2), which is the regression model for the compressive strength and Eq. (6), which is calculated based on the material cost, were combined to define the cost
of the concrete solely by the w/c ratio. For that Eq. (2) can be rewritten in terms of R, as shown in Eq. (7) by predetermining the target strength of the concrete. Using the rearranged formula,
Eq. (7), into Eq. (6) the cost of the concrete can be defined only by the w/c ratio, as shown in Eq. (8). This implies that the optimized production cost can be extracted from the mix proportion
in the range of w/c ratio from 0.45 to 0.70 using the targeted strength. Following
that, the parameters of w/c and R for minimized concrete cost can be obtained as well
from Eq. (7).
Fig. 10. $R$ and $C_{{conc}}$ vs. w/c of concrete for specific strengths
In general, from Eqs. (7) and (8), the $C_{{conc}}$ and $R$ can be quantified based on the target strength, as shown
in Fig. 10. Considering the material price listed in Table 5, the mixtures with brick chips would be cheaper than mixtures with the most natural
aggregates. Note that this is true even though more cement was required to secure
an equivalent strength for mixtures with brick chips. Since, as the cement content
increase forcing the mixture to have a low w/c ratio, the $R$ value will also increase
while maintaining a constant strength making the overall $C_{{conc}}$ value to decrease.
Fig. 10 shows the relative cost of a mixture at a target strength with brick chips to that
of a mixture without brick chips. It was possible to get a cost reduction of up to
24 % for mixtures with 24 MPa strength. A reduction of cost for mixtures with 27,
30, and 33 MPa strength was also achieved up to 19 %, 12 %, and 5 %, respectively.
The above model is feasible to calculate the $C_{{conc}}$ of concrete only if the
$f_{c}$ is on the range of 24 MPa-33 MPa with a corresponding range of w/c and $R$
being 0.45~0.70 and 0~100 %, respectively (Fig. 11). Regardless of the model, the cost of the concrete can be reduced up to 70 % if
the $f_{c}$ is lower than 24 MPa. The $R$ would not affect mixtures with a strength
of less than 24 MPa even if 100 % of brick chips are used in the mixture having a
constant w/c. However, note that the overall result in this study could be altered
in case the price of cement is different from this study.
In addition, a static approach should be applied to the practical proportioning of
the mixture. In many regulations, the required strength of the concrete for structural
design, $f_{cr}$ and experimental strength, $f_{c}$, generally have the following
relationship:
where, $m$ is a confidence interval, which is a statistical parameter considering
a normal distribution of the compressive strength, and $\sigma$ is the standard deviation
of the actual concrete.
As shown in Fig. 8, the standard deviations in this study did not show any significant change by w/c
and R values. Therefore, it is considered that a fixed value of $\sigma$ could be
adopted for practical mix proportioning even when w/c and $R$ are varied.
Fig. 11. Maximum and minimum values of $C_{{conc}}$, relative cost, $R$, and w/c
for minimized $C_{{conc}}$ vs. concrete strength