Prediction of strength and slump of rice husk ash incorporated high-performance concrete.
Islam, Md. Nazrul ; Zain, Muhammad Fauzi Mohd ; Jamil, Maslina 等
1. Introduction
High-performance concrete (HPC) is defined as concrete, which meets
special performance and uniformity requirements that cannot always be
achieved routinely by using conventional materials and normal mixing,
placing and curing practices (Zia et al. 1991). The requirements may
involve enhancements of characteristics such as placement and compaction
without segregation, long-term mechanical properties, early-age
strength, volume stability or service live in severe environments. HPC
is a relatively new product and its characteristics differ from that of
normal concrete (Zain et al. 2002).
HPC mixtures are usually more expensive than conventional concrete
mixtures because they usually contain more cement, several chemical
admixtures at higher dosage rates than for conventional concrete, and
one or more supplementary cementitious materials (Simon 2003). As the
cost of materials increases, optimizing concrete mixture proportions
becomes more desirable. Furthermore, as the number of constituent
materials increases, the problem of identifying optimal mixtures becomes
increasingly complex. Not only are there more materials to consider, but
there also are more potential interactions among materials. Combined
with several performance criteria, the number of trial batches required
to find optimal proportions using traditional methods could become
prohibitive. HPC is a highly complex material and modeling its behavior
is a difficult task (Yeh 1998). Therefore, there is a need to find new
methods for prediction of HPC properties. Although several models were
developed for prediction and optimization of concrete properties (Zain
et al. 2002; Simon 2003; Yeh 1998; Saridemir 2009a, b; Bai et al. 2003;
Tanyildizi 2009; Bilim et al. 2009; Ozcan et al. 2009; Guang, Zong 2000;
Kasperkiewics et al. 1995; Lai, Serra 1997; Lee 2003; Lim et al. 2004;
Patel 2003; Jasniok, Zybura 2009; Kamaitis 2008; Bai, Gailius 2009),
none of these models includes rice husk ash (RHA) as a supplementary
cementitious material in making HPC. Rice husk, an agricultural waste,
constitutes about one fifth of the 500 million metric tons of rice
produced annually in the world (Mehta 1989). Due to the growing
environmental concern, and the need to conserve energy and resources for
sustainable development, efforts have been made to burn the husks at
controlled temperature and atmosphere, and to utilize the ash so
produced as a building material (Columna 1974; Mehta 1977, 1989; Ismail,
Waliuddin 1996; Zhang, Malhotra 1996; Jauberthie et al. 2000; Bui 2001;
Nehdi et al. 2003; Agarwal 2006; de Sensale 2006; Chindaprasirt et al.
2007; Gastaldini et al. 2007; Giaccio et al. 2007; Saraswathy, Song
2007; Sata et al. 2007; Ganesan et al. 2008; Nair et al. 2008; de
Sensale et al. 2008; Zain et al. 2011). The main concern of this study
was to develop statistical models for predicting strength and slump of
RHA incorporated HPC.
2. Material properties
Ordinary Portland cement (Type I) was used that meets the ASTM C150
(2011) specifications. RHA used was produced in the laboratory. The
chemical and physical properties of the cement and RHA are shown in
Table 1. Natural river sand and crushed limestone were used as
aggregates. The gradation of both fine and coarse aggregates met the
ASTM C33 (2011) specification. The details of physical properties of
both aggregates are shown in Table 2. Glenium 100 M superplasticizer
complying with the requirements of ASTM C494 (2011) and ASTM C1017
(2007) was used (solid content = 25.25% and specific gravity = 1.28).
Normal tap water (pH = 6.9) was used as mixing water and for curing.
3. Concrete mixes, specimen preparation and testing
Sixty samples of RHA incorporated HPC mixes were prepared in the
laboratory. Table 3 shows water-to-binder ratio (W/B), cement (C), rice
husk ash (RHA), water (W), fine aggregate (FA), coarse aggregate (CA)
and superplasticizer (SP) contents of these mixes.
A rotating pan-type mixer of 0.05 [m.sup.3] capacity was used to
mix concrete. Each batch included sufficient concrete for three slump
tests and four 100 x 200 mm cylinders for compressive strength test. The
cylinders were fabricated in accordance with ASTM C192 (2007). To obtain
adequate consolidation, the cylinders were rodded. The cylinders were
covered with plastic and left in the molds for 24 hours, after which
they were stripped and placed in limewater-filled curing tanks for moist
curing at 23 [+ or -] 2[degrees]C. Slump test of fresh concrete was
carried out as per ASTM C143 (2010). Compressive strength tests (ASTM
C39 2010) were conducted on the cylinders at the age of 28 days. In most
cases, three cylinders were tested. A fourth test was performed in some
cases if one result was significantly lower or higher than the others.
Before testing, the cylinder ends were ground parallel to meet the ASTM
C39 (2010) requirements using an end-grinding machine designed for this
purpose. The average strength of three cylinders was reported as result
of the test. Results of slump test (range: 170 mm to 245 mm) and
compressive strength test (range: 42.47 MPa to 92.21 MPa) are also shown
in Table 3.
4. Model development
Six variables were selected to derive statistical models and
ultimately to predict the properties of RHA incorporated HPC. The limits
of the variables were decided by conducting some preliminary tests and
from past experience. The notations used and limits of the variables are
as follows:
--[x.sub.1] = water-binder ratio (range: 0.25-0.40);
--[x.sub.2] = cement, kg/[m.sup.3] (range: 378.8-553.8);
--[x.sub.3] = rice husk ash (RHA), kg/[m.sup.3] (range: 25.0 71.7);
3
--[x.sub.4] = fine aggregate, kg/[m.sup.3] (range: 543.8-720.7);
--[x.sub.5] = coarse aggregate, kg/[m.sup.3] (range: 951.6 1048.3);
3
--[x.sub.6] = superplasticizer, l/[m.sup.3] (range: 4.2-72.6).
The MINITAB statistical software (Minitab Inc. 2004) was used to
derive two models by the least square approach. The general structure of
the statistical model is as follows:
y = [[beta].sub.o] + [k.summation over (i=1)] [[beta].sub.i]
[x.sub.i] + [k.summation over (i=1)] [[beta].sub.ii] [x.sup.2.sub.i] +
[summation over (i<j)] [summation][[beta].sub.ij] [x.sub.i][x.sub.j]
+ [epsilon], (1)
where: y is the response; [x.sub.i] are the independent variables;
[[beta].sub.o] is the independent term; [[beta].sub.i], [[beta].sub.ii]
and [[beta].sub.ij] are the coefficients of independent variables and
interactions, representing their contribution to the response; s is the
random residual error term representing the effects of variables or
higher order terms not considered in the model (Kutner et al. 2004).
The interaction between the six variables ([x.sub.i][x.sub.j]) and
quadratic effect ([x.sup.2.sub.i]) of variables were also considered in
the proposed models as shown in Eq. (1). By trial and error, the
best-fit models were identified from different probability distribution
functions. The 't' test was carried out to decide the
statistical significance of variables. The null hypothesis was the
presupposition that the true value of coefficient is zero. In other
words, the variable or variables associated with that coefficient are
statistically not significant and it has no influence on the response y.
If the probability greater than 't statistic' is less than
0.05 (5%), the null hypothesis (the coefficient value is zero) can be
rejected and established that the variable or variables with the
estimated coefficient has significant influence on the response. If the
probability greater than 't statistic' is more than 0.05 (5%),
the null hypothesis can be accepted and it can be established that the
variable or variables with estimated coefficient has no influence on the
response and hence that variable or variables cannot be included in the
model. In the proposed models, the probability greater than 't
statistic' was found less than 0.05. This signifies that there is
less than 5% probability that the contribution of a given variable with
the respective coefficient to the tested response exceeds the value of
the specified estimated coefficient. A possible higher value of
determination coefficient ([R.sup.2]) was considered while selecting the
proposed models. After many trials with MINITAB software, best-fit two
models were found out for HPC properties e.g., compressive strength and
slump as described in the following sections.
4.1. Model 1: 28-day compressive strength
In design and quality control of concrete, 28-day compressive
strength is normally specified. The 28-day compressive strength of
concrete determined by a standard uniaxial compression test is
universally accepted as a greater index of concrete strength (Patel
2003). Hence the 28-day compressive strength model was selected as a
dependent variable of the model to evaluate the quality of RHA
incorporated HPC.
The proposed 28-day strength model is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2)
The statistical details of the model are presented in Table 4. The
model is fit in normal (Gaussian) probability distribution function. All
the six variables such as water-binder ratio ([x.sub.1]), cement
([x.sub.2]), RHA ([x.sub.3]), fine aggregate ([x.sub.4]), coarse
aggregate ([x.sub.5]) and superplasticizer ([x.sub.6]) have direct
influence on the response (28-day compressive strength, [y.sub.1]). Some
variables are interacting with each other. Some of them have positive
influence and some of them have negative influence on the response. The
[R.sup.2] value is 85.3% which is an indication of reasonably good
fitness. From the results of ANOVA analysis, it appears that the
probability greater than "F statistic" (Fisher statistic) is
less than 0.0005 (Table 4). The model is highly statistically
significant with confidence level more than 99.95%. All the variables
were also tested individually for 't statistic'. The
probability greater than 't statistic' for intercept, all
variables, and their interaction are indicated in Table 5. The
probability greater than 't statistic' for all variables is
found to be less than 0.006 (confidence level more than 99.4%).
Therefore, all the variables indicated in the model are statistically
significant and have influence on the 28-day compressive strength.
Fig. 1 shows the residual plot of the compressive strength model.
The figure shows that the errors are independent. The residuals in the
plot appear to be randomly scattered about zero. The other assumptions
of regression analysis are also satisfied. The adjusted correlation
coefficient is 81.6% (Table 4), which indicates a very good fit. The
root mean square error is 4.96, which is also an indication of accuracy
of the model fit. The model is significant as can be seen from the
significance value that is very close to zero.
4.2. Model 2: slump
The slump is one of the most important properties of HPC. If the
slump of fresh concrete is between 180 and 220 mm without any
segregation, the concrete can be qualified for HPC. Of course, other
fresh concrete tests are also important to evaluate thoroughly the fresh
HPC properties. However, one can take decision from slump test, if other
test set-ups are not available.
The proposed slump model is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
The statistical details of this model are also presented in Table
4. The model was fit in normal (Gaussian) probability distribution
function. Some of the variables have positive influence and some have
negative influence on the response (slump, [y.sub.2]). The [R.sup.2]
value is 84.1%, which indicates reasonably good fitness. From the
results of ANOVA analysis (Table 4), it appears that the probability
greater than 'F statistic' (Fisher statistic) is less than
0.0005. The model is highly statistically significant with a confidence
level more than 99.95%. All the variables were also tested individually
for 't statistic' (Table 6). It can be observed from Table 6
that the 'probability greater than t' for RHA ([x.sub.3]) is
greater than 0.05. It is still included in the model to maintain the
hierarchy of the model terms. Hierarchical terms are linear terms that
may be insignificant by themselves but are part of significant higher
order terms.
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
A hierarchical model allows for conversion of models between
different sets of units (for a model involving temperature, conversion
from F to C, for example) (Simon 2003). All the variables in the model
are statistically significant and have influence on the slump.
Fig. 2 shows the residual plot of the slump model. The figure shows
that the errors are independent. The residuals appear to be randomly
scattered about zero. The other assumptions of regression analysis are
also satisfied. The adjusted correlation coefficient is 78.7% (Table 4),
which indicates a good fit. The root mean square error is 7.21, which is
also an indication of a good fit of the model. The model is significant
as can be seen from the significance value that is very close to zero.
5. Model validation
Five additional mixtures were prepared and tested with the same
ingredients to verify the ability of the proposed models to predict the
responses. Table 7 shows the quantities of the ingredients, 28-day
strength and slump of these five concrete mixes. The slump and the
28-day compressive strength were measured in the laboratory and compared
with those of the prediction by the respective models. The experimental
and model predicted values of slump and 28-day compressive strength are
shown in Table 8. The tests were carried out with the same materials and
under the same testing conditions. Table 8 shows that the variations
among model predicted and experimental values for slump and strength
were not significant, which is an indication that the models predict
28-day strength and slump with reasonable accuracy.
6. Limitations of the models
The proposed statistical models for prediction of strength and
slump of RHA incorporated HPC were derived from sixty HPC mixes with
ordinary portland cement (ASTM Type I), rice husk ash (specific gravity
= 2.0, specific surface area = 183.3 [m.sup.2]/kg), natural river sand
(specific gravity = 2.6, absorption = 1.47%, fineness modulus = 3.04),
crushed lime stone (specific gravity = 2.61, absorption = 0.82%,
fineness modulus = 6.68, maximum size = 19 mm), and Glenium 100 M
superplasticizer complying with the requirements of ASTM C494 (2011) and
ASTM C1072 (2011) (solid content = 25.25% and specific gravity = 1.28).
The models predict strength and slump with acceptable accuracy for
ranges of mix proportions as shown in Table 3 (water-binder ratio:
0.25-0.40, cement: 378.8-553.8 kg/[m.sup.3], rice husk ash: 25.0-71.7
kg/[m.sup.3], fine aggregate: 543.8-720.7 kg/[m.sup.3], coarse
aggregate: 951.6-1048.3 kg/[m.sup.3], superplasticizer: 4.2-72.6
l/[m.sup.3]). It is very important to note that, similar to other
statistical models, the derived models are material specific i.e.,
depended on material properties and mix proportions. The absolute
responses from the models can differ if either the properties of
materials or mix proportions vary considerably from the material
properties and mix proportions used to derive the models. However, the
models can still be useful for prediction of strength and slump when
presented with different sets of materials and mix proportions.
7. Summary and conclusion
Using statistical regression analysis, two models for prediction of
strength and slump of RHA incorporated HPC were developed. The best
models for strength and slump were chosen by trial and error.
The proposed 28-day strength model:
Strength
28d
= -6018 + 7040* (W/B) + 2.49* C + 3.16* RHA + 5* FA + CA + 89.1* SP
-0.0902* [SP.sup.2] -8.47* (W/B)* FA - 38.6* (W/B)* SP - 0.0484* C * SP
- 0.0497 * RHA * SP - 0.0743 * FA * SP.
The proposed slump model:
Slump
= 1686 +103595* (W/B) -41.8* C + 2.3* RHA - 209* FA + 114* CA -
27086* [(W/B).sup.2] + 0.0604* [FA.sup.2] - 0.0707 * [CA.sup.2] - 66.4*
(W/B)* C - 123* (W/B)* RHA - 49.4* (W/B) * CA + 0.0997 * C* FA + 0.182*
RHA * FA - 0.0764* RHA * CA + 0.0770* FA * CA.
It was found from the ANOVA analysis that all the six selected
variables i.e., water-binder ratio (W/B), cement (C) content, rice husk
ash (RHA) content, fine aggregate (FA) content, coarse aggregate (CA)
content, and superplasticizer (SP) content are statistically significant
and have direct influence on strength of RHA incorporated HPC. On the
other hand, water-binder ratio, cement content, fine aggregate content
and coarse aggregate content have significant influence on slump of RHA
incorporated HPC.
The proposed models can be used to predict strength and slump of
RHA incorporated HPC. Developed models were evaluated and the results of
prediction were reasonably accurate. Similar to other statistical
prediction models, the proposed models are depended on material
properties and mix proportions. The absolute value of the predicted
strength and slump may not be the same if different sets of materials
are used. However, the models can still be useful for prediction of
strength and slump when presented with different sets of materials and
mix proportions. RHA incorporated HPC reduces use of cement in concrete,
consumes waste, and increases durability of concrete. Thus, these models
can be useful as tools for sustainable development because they can
substantially reduce time, effort, and cost associated with selection of
trial batches of HPC.
doi: 10.3846/13923730.2012.698890
Acknowledgements
The research work reported in this paper was funded by the Ministry
of Science, Technology and Innovation, Malaysia and Universiti
Kebangsaan Malaysia (UKM). Materials were supplied by Ready Mixed
Concrete (M) Sdn Bhd, Malaysia. Experimental work and data compilation
were assisted by A. Ilham. The first author (M. N. Islam) expresses his
sincere gratitude to Dhaka University of Engineering and Technology
(DUET), Gazipur, Bangladesh, for granting him leave for the research.
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Research Council, Washington, D.C., (SHRP-C/FR91-103; PB92-130087). 251
p.
Md. Nazrul Islam (1), Muhammad Fauzi Mohd Zain (2), Maslina Jamil
(3)
(1) Department of Civil Engineering, Dhaka University of
Engineering and Technology (DUET), Gazipur, Gazipur-1700, Bangladesh
(1, 2, 3) Faculty of Engineering and Built Environment, National
University of Malaysia (UKM), 43600 UKM Bangi, Selangor Darul Ehsan,
Malaysia
E-mail: (1) nazrul2100@yahoo.com (corresponding author)
Received 29 Jul. 2010; accepted 03 Mar. 2011
Md. Nazrul ISLAM. Prof., Doctor of Civil and Structural
Engineering. He works in the Department of Civil Engineering of Dhaka
University of Engineering and Technology (DUET), Gazipur, Bangladesh.
Research interests: High performance concrete, sustainable construction
materials, utilization of waste materials, computer application in civil
engineering, expert system.
Muhammad Fauzi Mohd ZAIN. Prof., PhD. He works as a Deputy Dean
(Research) in the Faculty of Engineering and Built Environment of the
National University of Malaysia (UKM). Research interests: Sustainable
construction materials and building systems, high performance concrete.
Maslina JAMIL. Lecturer, PhD. He works in Architecture Department
of the National University of Malaysia (UKM). Research interests:
Application of artificial neural network, sustainable construction
materials and building systems, eco-composite panels.
Table 1. Chemical and physical properties of cement and rice
husk ash (RHA)
Property Cement Rice Husk Ash
Si[O.sub.2] (%) 21.54 86.49
[Al.sub.2][O.sub.3] (%) 5.99 0.01
CaO (%) 65.3 0.50
MgO (%) 0.77 0.13
MnO (%) 0.01 0.07
[P.sub.2][O.sub.5] (%) 0.31 0.69
S[O.sub.3] (%) 1.41 --
Ti[O.sub.2] (%) 0.21 --
[Fe.sub.2][O.sub.3] (%) 4.45 0.91
C (%) 0.71 3.21
Loss on ignition (LOI) (%) 1.06 8.83
[Na.sub.2]O (%) -- 0.05
[K.sub.2]O (%) -- 2.7
Specific gravity 3.16 2.00
Specific surface area ([m.sup.2]/kg) 402 183.3
Table 2. Physical properties of fine and coarse aggregates
Property Fine Coarse
Aggregate Aggregate
Size (mm) 0-1.75 4.75-19
Bulk specific gravity 2.60 2.61
Absorption (%) 1.47 0.82
Fineness modulus 3.04 6.68
Table 3. Mix proportions, slump and 28-day compressive strength of RHA
incorporated HPC
Mix W/B C RHA. W FA
No. (kg/ (kg/ (kg/ (kg/
[m.sup.3]) [m.sup.3]) [m.sup.3]) [m.sup.3])
1 0.38 378.8 71.7 169.8 703.3
2 0.40 382.3 59.8 176.1 682.4
3 0.39 387.3 55.4 171.7 681.6
4 0.39 384.9 35.2 164.8 720.7
5 0.40 411.9 25.7 176.2 694.4
6 0.40 407.3 33.3 175.5 690.9
7 0.40 385.1 55.4 176.5 683.5
8 0.40 395.7 48.8 178.0 684.8
9 0.40 393.7 51.8 178.4 683.9
10 0.35 400.4 68.1 162.7 693.5
11 0.37 405.6 58.9 170.3 669.5
12 0.35 408.5 54.7 162.7 670.6
13 0.36 404.9 34.5 156.9 708.1
14 0.36 435.5 25.7 168.2 679.4
15 0.36 435.9 32.8 169.1 672.0
16 0.36 427.2 41.4 169.1 667.8
17 0.36 414.8 53.8 169.1 661.1
18 0.36 419.4 48.3 168.8 672.3
19 0.36 415.6 51.6 168.6 672.2
20 0.36 415.2 43.2 165.4 685.5
21 0.32 419.7 64.6 156.1 683.7
22 0.34 428.2 57.9 165.2 656.2
23 0.32 429.4 54.0 154.7 657.0
24 0.33 424.3 33.7 149.9 693.6
25 0.33 458.6 25.6 161.0 663.8
26 0.33 464.4 32.1 162.6 647.9
27 0.33 456.8 39.7 162.6 644.9
28 0.33 444.7 51.8 162.6 636.2
29 0.33 442.8 47.8 160.6 659.1
30 0.33 438.4 42.4 157.4 671.5
31 0.30 437.1 61.3 149.8 676.6
32 0.32 450.4 56.7 160.6 642.1
33 0.29 450.1 53.0 147.6 638.8
34 0.30 443.5 32.8 143.6 678.8
35 0.30 481.6 25.5 154.6 647.5
36 0.30 493.4 31.3 156.5 621.5
37 0.30 486.9 37.7 156.5 620.8
38 0.30 475.1 49.5 156.5 608.6
39 0.30 466.4 47.1 153.2 645.0
40 0.30 458.9 50.7 152.1 644.8
41 0.30 461.7 41.4 150.1 656.4
42 0.30 472.4 55.3 156.3 627.3
43 0.27 471.0 52.0 141.0 622.5
44 0.28 462.7 31.8 137.8 662.3
45 0.28 504.9 25.2 148.6 627.6
46 0.27 523.0 30.3 150.9 598.3
47 0.27 517.9 35.4 150.9 591.4
48 0.27 506.5 46.8 141.0 579.1
49 0.27 490.4 46.2 146.4 629.6
50 0.27 480.9 50.1 144.8 628.6
51 0.28 494.4 53.8 152.4 611.3
52 0.25 492.2 50.8 134.9 609.1
53 0.26 481.9 30.8 132.4 643.6
54 0.25 528.5 25.0 143.0 604.6
55 0.25 553.8 29.1 145.6 567.4
56 0.25 550.1 32.8 145.6 559.4
57 0.25 539.2 43.6 145.6 543.8
58 0.25 515.0 45.1 140.0 612.5
59 0.25 503.4 49.4 138.1 605.2
60 0.25 509.8 39.1 137.2 617.0
Mix CA SP Slump 28-day
No. (kg/ (l/[m.sup.3]) (mm) Strength
[m.sup.3]) (MPa)
1 979.4 10.1 205 57.91
2 1003.1 7.8 210 47.52
3 1018.6 7.2 195 50.50
4 1031.6 7.9 185 51.16
5 1018.7 5.5 195 42.47
6 1017.7 7.0 195 56.68
7 1006.7 10 195 50.69
8 1014.0 4.3 200 59.86
9 1014.0 4.2 195 58.48
10 984.4 14.1 217 45.61
11 1005.6 10.7 200 55.43
12 1030.2 9.6 200 54.52
13 1041.4 11.0 195 55.79
14 1028.7 8.3 195 55.11
15 1027.5 9.0 200 59.39
16 1021.2 11.4 200 56.04
17 1010.8 15.7 210 51.55
18 1026.8 5.43 210 70.59
19 1025.9 7.1 210 70.45
20 1034.3 6.2 210 70.95
21 986.4 19.4 210 48.27
22 1005.9 14.2 225 52.69
23 1035.6 14.6 200 50.84
24 1046.0 16.0 205 65.46
25 1035.5 11.1 195 53.03
26 1026.2 16.6 210 59.69
27 1021.5 18.2 210 57.33
28 1007.8 24.5 210 52.39
29 1036.4 9.3 215 73.73
30 1043.0 9.4 220 74.14
31 989.9 23.3 230 52.34
32 1004.1 18.5 235 66.88
33 1032.2 18.7 200 53.10
34 1048.3 21.5 180 74.70
35 1039.0 17.7 230 61.68
36 1018.4 27.0 220 62.07
37 1017.2 26.5 210 61.39
38 997.3 36.7 220 64.57
39 1043.0 13.1 230 85.32
40 1037.9 16.2 220 83.43
41 1048.3 13.4 220 81.77
42 1000.0 23.8 210 68.72
43 1030.0 23.9 210 57.48
44 1046.5 28.7 170 56.64
45 1035.0 25.6 200 64.95
46 1013.3 34.5 210 65.33
47 1001.7 40.7 210 63.08
48 980.8 51.4 210 60.28
49 1046.2 19.4 230 84.98
50 1037.8 23.0 230 80.75
51 993.3 30.3 205 65.31
52 1031.5 28.6 205 61.94
53 1039.8 38.3 170 67.07
54 1024.1 36.9 200 66.56
55 992.9 50.4 200 66.50
56 978.8 58.2 200 67.41
57 951.6 72.6 190 45.58
58 1045.4 28.6 240 91.55
59 1024.4 37.1 245 77.70
60 1039.9 30.7 240 92.21
W-B: water-to-binder ratio; C: cement; RHA: rice husk ash; W: water;
FA: fine aggregate; CA: coarse aggregate; SP: superplasticizer.
Table 4. Summary statistics of strength and slump models
Model RMSE R-Sq R-Sq (adj) F-value p-value
(%) (%) of ANOVA of ANOVA
28-day strength 4.96336 85.3 81.6 22.80 0.000
Slump 7.21339 84.1 78.7 15.49 0.000
RMSE: root mean square error; R-Sq: R-squared; R-Sq (adj):
R-squared (adjusted); ANOVA: analysis of variance.
Table 5. Model terms and their significance of the 28-day
strength model
SE t
Predictor Coefficient Coefficient statistic p-value
Constant -6018 1027 -5.86 0.000
[x.sub.1] 7040 1807 3.89 0.000
[x.sub.2] 2.4898 0.3741 6.66 0.000
[x.sub.3] 3.1630 0.4378 7.22 0.000
[x.sub.4] 4.995 1.168 4.28 0.000
[x.sub.5] 1.0045 0.1057 9.50 0.000
[x.sub.6] 89.08 24.09 3.70 0.001
[x.sub.6.sup.2] -0.09016 0.02685 -3.36 0.002
[x.sub.1][x.sub.4] -8.469 2.489 -3.40 0.001
[x.sub.1][x.sub.6] -38.60 10.58 -3.65 0.001
[x.sub.2][x.sub.6] -0.04838 0.01502 -3.22 0.002
[x.sub.3][x.sub.6] -0.04965 0.01719 -2.89 0.006
[x.sub.4][x.sub.6] -0.07433 0.02018 -3.68 0.001
Table 6. Model terms and their significance of the slump model
SE t
Predictor Coefficient Coefficient statistic p-value
Constant 1686 6069 0.28 0.783
[x.sub.1] 103595 17150 6.04 0.000
[x.sub.2] -41.806 6.575 -6.36 0.000
[x.sub.3] 2.26 19.78 0.11 0.910
[x.sub.4] -208.88 31.71 -6.59 0.000
[x.sub.5] 113.79 21.50 5.29 0.000
[x.sub.1.sup.2] -27086 4540 -5.97 0.000
[x.sub.4.sup.2] 0.060370 0.009657 6.25 0.000
[x.sub.5] -0.07066 0.01379 -5.12 0.000
[x.sub.1][x.sub.2] -66.44 10.15 -6.54 0.000
[x.sub.1][x.sub.3] -123.13 23.27 -5.29 0.000
[x.sub.1][x.sub.5] -49.38 10.10 -4.89 0.000
Table 7. Mix proportion, slump and strength data for validation of the
models
Mix W/B C RHA W FA
No. (kg/ (kg/ (kg/ (kg/
[m.sup.3]) [m.sup.3]) [m.sup.3]) [m.sup.3])
1 0.40 397.7 42.8 176.5 689.0
2 0.40 391.7 43.8 174.5 698.5
3 0.33 437.3 51.2 159.9 659.5
4 0.28 453.0 58.7 143.9 661.8
5 0.27 485.5 10.3 143.4 639.2
Mix CA SP Slump 28-day
No. (kg/ (l/ (mm) Strength
[m.sup.3]) [m.sup.3]) (MPa)
1 1014.7 7.1 187 54.53
2 1021.7 4.2 195 56.65
3 1034.2 10.8 215 69.95
4 980.4 35.1 222 55.02
5 1049.0 19.5 213 66.00
W-B: water-to-binder ratio; C: cement; RHA: rice husk ash; W: water;
FA: fine aggregate; CA: coarse aggregate; SP: superplasticizer.
Table 8. Comparison of experimental and predicted values of strength
and slump for the data of Table 7
Mix Strength (MPa) Slump (mm) Variation (%)
No.
Experiment Prediction Experiment Prediction Slump Strength
1 54.5 52.0 187 194.6 -4.06 4.59
2 56.6 54.1 195 196.3 -0.67 4.41
3 69.9 69.4 215 215.6 -0.28 0.79
4 55.0 53.6 222 213.6 3.78 2.55
5 66.0 62.9 213 203.2 4.60 4.70
