The regulation of physical and mechanical parameters of ceramic bricks depending on the drying regime/Keraminiu plytu fizikiniu ir mechaniniu savybiu reguliavimas dziovinimo rezimu.
Maciulaitis, Romualdas ; Malaiskiene, Jurgita ; Kicaite, Asta 等
1. Introduction
It is known that the quality of structural ceramics is mostly
influenced by the selected composition of formation mix and burning
regime. Many Lithuanian and foreign scientists work in this field of
research. However, a great deal of attention also needs to be paid to
the process of ceramics drying, as an inappropriate drying regime can be
the main reason for causing first defects in ceramic products.
Drying is the process during which the moisture of the material is
evaporated in a thermal way. As the material dries, the process of
diffusion happens, during which the moisture is diffusing from the inner
layers into the surface, and from it the moisture is evaporating into
the atmosphere. The moisture present in material is divided into: free
moisture, absorbent moisture and chemically bound moisture. Free
moisture can be also named mechanical or capillary moisture, as it is
soaked into the cavities of material and bigger capillaries. This
moisture is easily removed when drying the material.
Absorbent moisture which is soaked into small capillaries of the
material can be also named structural moisture. It is not completely
eliminated from the material during drying. The moisture which is unfree
chemically (crystalline, hydrate) is not removed when drying the
material (Nagrockiene et al. 2005).
Defects in the semi-manufactured ceramic appear because the free
water (between the particles of clay) is drifting away, the particles of
clay move closer to each other, and the product dimensions decrease.
During shrinkage mechanical strains appear, which may exceed the
allowable limits because of the too fast water drift; consequently a
semi-manufacture cracks even though the burning process has not started
yet ([TEXT NOT REPRODUCIBLE IN ASCII]. 1999).
The authors (Lewis 2000; Briscoe et al. 1998) offer to divide
drying process into two parts: linear drying of ceramics (when moisture
is driven out from capillaries) and non-linear one, when moisture is
driven out from pores in the vapour-diffusion method. These authors have
determined that the ceramics drying depends on the relationship between
humidity and water, drying temperature, and atmosphere conditions in a
sample. Whereas scientists (Krischer 1978; Sadunas 1997) consider that
the burning process of porous bodies can be divided into 3 phases. First
phase proceeds because of water migration through the capillaries from
the inside to the surface of a sample. This stage particularly depends
on temperature, humidity, and spread of air as well as on geometry, and
dimensions. During the second stage of material drying the main water
evaporation proceeds inside a sample, where the pressure of water vapour
is prevailing. The third stage proceeds because of the vapour diffusion
in all the spots of material. The first stage is the most risky as a
high tension arises inside the material and incorrectly selected burning
regime causes material to crack and crumble.
The other scientists (Amoros et al. 2003; Barati et al. 2003),
according to the results of their researches, have shown that ceramics
properties (deformation strength) depends on the material moisture and
the time of drying. They have determined that the drier is the material,
the greater is the mechanical strength. For example, as water absorption
equals 5%, strength--0.5 MPa, and when water absorption is 1%, the
strength of analysed ceramics reaches 1.6 MPa.
The authors (Palmero et al. 2005) in their publication have shown
that drying temperature (dried at 5, 25 and 60[degrees]C temperature)
influences the technique of ceramics crystallization and the solidity of
final composition. The most solid composition of samples was obtained
while drying ceramics at 60[degrees]C temperature. The scientists
(Seipel, Nickel 2004) have determined that the critical temperature is
150[degrees]C, as drying samples at a higher temperature causes defects
because of the inner tension arising inside the material.
However, there are very few researches where the influence of
drying temperature or other drying factors on the final ceramics
properties is analysed. Most authors investigate the kinetics of the
processes which occur while drying ceramic bodies under standard drying
conditions (Looi et al. 2002; Misra et al. 2002).
The purpose of our work is to demonstrate how the separate changing
of each drying regime stage influences the final properties of ceramics
(density, general shrinkage, compressive strength and the rate of
ultrasound spread) and vice versa, how the desirable values of physical
and mechanical parameters influence the magnitudes of each drying stage
while the composition, burning regime, and other technological factors
are stable.
2. Characteristics of materials, research methods
Material mix for ceramic samples was formed on the basis of clay
from Rokai deposit and such additives were applied: sand, crushed
bricks, sawdust of softwood. The average chemical composition of clay
from Rokai deposit is presented in Table 1.
The samples were shaped in a plastic way and dosage of components
was performed by mass. At first dry materials were mixed manually, later
the mix was wetted to the moisture suitable for moulding. The amount of
water poured was such that the material mix would be easily moulded and
would not stick to hands when squeezed. Such mix was left for 3 days in
the medium of (95 [+ or -] 5) % relative humidity for moisture evenly
spreading in the mix. After 3 days the laboratory samples were shaped
into dimensions of 70x70x70 mm. The formed semi manufactures were being
dried under 8 different regimes (Table 2), which were expressed by the
values of relative area; the maximum area was equated to 100. In this
way the sample heat quantity was obtained (the example of calculation is
presented in Fig. 1). The drying regime was divided into two stages:
drying in a laboratory and drying in the electric stove at the maximum
temperature. The burning regime was not varied during our investigation.
The dried samples were burned in an experimental chamber oven for 24
hours keeping the maximum temperature 1050[degrees]C for 3 hours. The
burned ceramic samples were used to determine the physical and
mechanical parameters (according to Nagrockiene et al. 2005; Mandeikyte,
Siauciunas 1997; LST EN 771-1+A1 2005). The revised methodology for
calculation of physical and mechanical parameters is presented in Table
3 and the average values of the above-mentioned parameters are shown in
Table 4.
[FIGURE 1 OMITTED]
3. Statistical analysis of data discussion
We have determined the influence of selected drying stages on the
values of physical and mechanical parameters by performing a statistical
analysis (Gatti 2005; Lindsey 2004; Mees 2001).
It is determined that the distribution character of the
experimental values of the analysed physical and mechanical parameters
is normal, so it is possible to derive adequate empirical equations.
Table 5 presents the double correlative matrix of the analysed
physical and mechanical parameters and selected drying parameters, which
show that the interdependence of the most parameters is strong and
significant, thus one has to keep this in mind when deriving empirical
equations.
The reciprocal regression analysis (Malaiskiene, Maciulaitis 2004;
Maciulaitis, Malaiskiene 2007) of data was performed in order to
evaluate the dependence of the analysed parameters on the drying regime
more precisely and to use the equations in practice. The adequacy of the
derived equations was verified applying Fisher's criteria. If these
criteria of the derived equation are higher than one found in the
tables, the equation is considered to be suitable for presenting
experimental data. The strength of correlation is estimated according to
the values of the multidimensional coefficient of correlation. The
closer the coefficient is to 1, the stronger is the correlation between
the parameters. The adequacy of the model is verified by calculating the
coefficient of determination. If the values of this coefficient are
higher than 0.7, the selected mathematical model demonstrates the
distribution of experimental data very well (Gatti 2005; Lindsey 2004;
Mees 2001).
Firstly, the empirical equations are derived and they show how the
values of physical and mechanical parameters change depending on the
selected measures of the drying regime stage:
[x.sub.1] = (1536 + 0.161[y.sub.1] + 0.901[y.sub.2])([x.sub.1] <
1582)+ (1579 - 1.234[y.sub.1] + 2.229[y.sub.2])([x.sub.1] [greater than
or equal to] 1582), (1)
[x.sub.2] = (4.294 + 0.066[y.sub.1] + 0.064[y.sub.2])([x.sub.2]
< 6.989) + (6.813 + 0.017[y.sub.1] + 0.019[y.sub.2])([x.sub.2]
[greater than or equal to] 6.989), (2)
[x.sub.3] = (7.957-0.192[y.sub.1] + 0.170[y.sub.2])([x.sub.3] <
13.40) + (15.49-0.022[y.sub.1] + 0.083[y.sub.2])([x.sub.3] [greater than
or equal to] 13.40), (3)
[x.sub.4] = (2484-14.99[y.sub.1] + 19.21[y.sub.2])([x.sub.4] <
3067) + (3237 +1.533[y.sub.1] + 3.197[y.sub.2])([x.sub.4] [greater than
or equal to] 3067). (4)
The multidimensional coefficients of correlation and determination
and the average standard deviation of the empirical equations (1)-(4)
are presented in Table 6. The multidimensional coefficients of
correlation of equations (1)-(4) (Table 5) are close to 1; consequently,
we state that the correlation between the analysed parameters is strong;
the coefficients of determination are higher than 0.7, so the model is
selected properly. The average standard rate of deviation is low (the
highest is approximately 5%, determined to the value of the rate of
ultrasound spread). Therefore the actual values and the values counted
according to the empirical equations will differ slightly.
It is shown in the empirical equation (1) how the selected measures
of the drying regime stages influence the values of the ceramic body
density. The stage of drying in the electric stove influences density
positively, i.e. in order to get the higher values of density, the
higher value of drying in the electric stove must be selected. This
occurs because of the fact, that the more gradually and better material
is dried, the more samples shrink; the size of pores and the capacity of
the semi-manufacture decrease while the density increases. The stage of
drying in the electric stove influences the density differently below
and above the turning point (1582 kg/[m.sup.3], Eq 1). In order to
obtain a higher density than 1582 kg/[m.sup.3] and to increase the value
of drying in the electric stove, the lower values of drying in a
laboratory must be selected. It is possible to reduce the duration of
drying in a laboratory to a minimum (in the case of our performed
research 8.16 units (Table 2), i.e. 72 h at 20[degrees]C); otherwise the
samples will dry according to an extremely intensive regime and the free
moisture will not remove from the inner layers of material in time;
consequently, the inner strains will emerge and the samples will crack.
It is possible to state from the empirical equation (2) that the
values of general shrinkage are highly influenced by the measures of
drying stages in the electric stove and drying in a laboratory as the
tendencies for change remain similar below and above the turning point.
The higher the values of drying in a laboratory and drying in the
electric stove we select, the higher general shrinkage we obtain. That
is because the semi-manufactured ceramics get larger amount of heat
energy due to which the larger amount of water evaporates, the particles
of material move closer to one another and the product shrinks.
The empirical equation (3) shows that the stages of drying regime
have influence on the values of compressive strength with the same
tendency below and above the turning point (13.40 MPa). If we like to
obtain the values of compressive strength higher than 13.40 MPa, we have
to increase the drying stage in the electric stove for decreasing the
stage of drying in a laboratory. It is because the most intensive
evaporation of the free and absorbent moisture from the inner layers is
on the stage of drying in the electric stove. If drying lasts quite
long, water will evaporate from the sample (not exceeding the allowable
inner strains), less defects will be caused and the compressive strength
will be higher. The minimal stage of drying in a laboratory will suffice
for this case (according to the results of our research 8.16 units Table
2, i.e. 72 h at 20[degrees]C). If the stage of drying in the electric
stove is too low, the articles will have lower compressive strength
because the moisture will not evaporate in time, and consequently the
strains will emerge in the sample (Fig. 2).
[FIGURE 2 OMITTED]
It can be seen from the empirical equation (4), how the rate of
ultrasound spread is influenced by the selection of drying regime. The
index of ultrasound spread rate is one of the most important parameters
contributing to the evaluation of the level of defects in the
sample's structure. The drying duration in a laboratory influences
the index of ultrasound spread rate below and above the turning point
(3067 m/s) differently. The higher the drying stages in the electric
stove and in the laboratory, the bigger are the values of ceramics
ultrasound spread rates. It may be explained by the fact that higher
values of drying stages provide conditions for free moisture to be
removed more gradually from the material cavities and large capillaries.
Also, under higher values of drying stages, the absorbent moisture is
removed more gradually from small pores and capillaries later on. For
these reasons the large inner strains and defects will not emerge. That
is proved by the 5th and 6th empirical equations of the reciprocal
subordination.
Now we will analyse the empirical equations of reciprocal
subordination in order to examine the validity of the above-mentioned
statements and to use them in practice.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (5)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (6)
The multidimensional coefficients of correlation, determination and
standard deflection of (5)-(6) empirical equations are presented in
Table 7. The coefficients of correlation show that there is an extremely
strong interdependence between the stages of drying regime and physical
and mechanical parameters as the coefficient of determination is higher
than 0.7, thus the mathematical model is selected properly. The values
of the average rate of standard deflection are low, so the actual values
obtained according to the empirical equations differ slightly.
The empirical equation (5) shows, how the duration of the drying
stage in a laboratory influences the values of physical and mechanical
parameters below and above the turning point 21.77 units. When the
drying stage in a laboratory is selected higher than 21.77 units, we
will get such results: the higher density (more than 1582 kg/[m.sup.3],
Eq 1), the higher general shrinkage (more than 6,989%, Eq 2), the higher
compressive strength (more than 13,40 MPa, Eq 3) and the higher rate of
ultrasound spread (more than 3067 m/s, Eq 4). If we select the drying
duration in a laboratory lower than 21.77 units (Eq 5), it is likely
that the values of compressive strength will decrease. The duration of
this stage must be not lower than 8.16 units (72 h at 20[degrees]C);
otherwise, the free moisture will evaporate too quickly and the strains
will emerge.
We see from the empirical equation (6) that the drying duration in
the electric stove influences the values of density, general shrinkage
and compressive strength equally below and above the turning point of
23.02 units.
The rate of ultrasound spread varies according to the value of the
turning point (23.02 units, Eq 6). The higher stage of drying in the
electric stove we select, the higher density, general shrinkage,
compressive strength, and the rate of ultrasound spread we obtain. That
is because of the fact that when we heat the material, the moisture
evaporates gradually, particles move closer to each other, the
semi-products shrink, and a new stronger inner frame of the material is
established. When selecting the values of drying in the electric stove
lower than 23.02 units, the rate of ultrasound spread can begin to
decrease as the sample can dry inadequately and more open pores and
capillaries appear when burning. Thus, the equations of reciprocal
subordination confirm previously formed statements.
4. The example of the use of empirical equations
The example of empirical equations usage in practice is presented
when we vary only the values of drying regime parameters, and all other
technological conditions remain constant. The formation mix of ceramic
body was prepared using 77% of clay, 10% of sand, 4.5% of chip (the
carcass of encaustic ceramics) and 8.5% of cuttings of coniferous trees.
It was burnt for 24 h keeping at the maximum temperature of
1050[degrees]C for 3 hours.
When selecting the desirable values of ceramics, it is essential to
consider the tendencies of cohesion between the special parameters and
the parameters of burning regime (Table 4).
Example. Let us suppose, we want to get a ceramic body with special
physical and mechanical parameters, e.g. density 1600 kg/[m.sup.3],
general shrinkage 7%, compressive strength 17 MPa, the rate of
ultrasound spread 3300 m/s. Then we insert these values into (5)-(6)
equations (the part of the equation with a lower energy input is used)
and obtain these tentative parameters of drying regime: the drying stage
duration in a laboratory 14.8 units and the drying duration in the
electric stove is 15.6 units.
To ascertain reliability of these drying parameters, we insert
their values into (1)-(4) equations and obtain that the density of
ceramic density equals 1596 kg/m , general shrinkage is 7%, compressive
strength is 16.5 MPa, and the rate of ultrasound spread is 3310 m/s.
Consequently, the values differ only slightly from the desirable values
and it is possible to expect the mentioned physical and mechanical
parameters of final products, when applying the parameters of drying
regime.
5. Conclusions
1. A strong interdependence between the selected stages of drying
regime and analysed physical and mechanical parameters has been
determined. The values of multidimensional coefficients of correlation
characterizing the interdependence are R = 0.880 ... 0.985.
2. It has been confirmed that a properly selected drying regime can
improve the properties of the final ceramic product, while other
technological factors are constant. For example, the values of
compressive strength can increase up to 88.3% and more.
3. An example of how the derived empirical equations can be applied
in practice has been provided. When checking the equivalence of
experimental results to the calculated values according to empirical
equations, it is determined that all other technological conditions do
not vary, and it is possible to select the drying regime according to
the physical and mechanical parameters; and, conversely, it is possible
to forecast the final physical and mechanical parameters of a ceramic
product.
DOI: 10.3846/1392-3730.2008.14.25
Received 28 Feb 2008; accepted 10 Oct 2008
References
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Barati, A.; Kokabi, M.; Famili, M. H. N. 2003. Drying of gelcast
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Briscoe, B. J.; Biundo, G. Lo; Ozkan, N. 1998. Drying kinetics of
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Gatti, P. L. 2005. Probability theory and mathematical statistics
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Lindsey, J. K. 2004. Introduction to applied statistics: a
modelling approach. Oxford: Oxford University Press. 321 p.
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single porous particles in superheated steam under pressure, Chemical
Engineering Journal 87(10): 329-338.
LST EN 771-1+A1. Specification for masonry units--Part 1: Clay
masonry units. 2005. 47 p.
Maciulaitis, R.; Malaiskiene, J. 2007. New quality regulation
system for manufacture of ceramic products, Construction and Building
Materials 21(2): 258-268.
Malaiskiene, J.; Maciulaitis, R. 2004. New possibilities of quality
regulation for ceramic products, Journal of Civil Engeneering and
Management 10(1): 37-43.
Mandeikyte, N.; Siauciunas, R. 1997. Keramines technologijos
laboratoriniai darbai [Laboratory works of ceramics technology]. Kaunas:
Technologija. 97 p.
Mees, A. J. 2001. Nonlinear dynamics and statistics. Boston:
Birkhauser. 473 p.
Misra, R.; Barker, A. J.; East, J. 2002. Controlled drying to
enhance properties of technical ceramics, Chemical Engineering Journal
86(1-2): 111-116.
Nagrockiene, D.; Zurauskiene, R.; Maciulaitis, R.; Kicaite, A.;
Ravnialicevas, V. 2005. Material science. Methodology for laboratory
works [Medziagu mokslas. Metodikos nurodymai laboratoriniams darbams
atlikti]. Vilnius: Tech nika. 100 p.
Palmero, P.; Esnouf, C.; Montanaro, L.; Fantozzi, G. 2005.
Influence of the co-precipitation temperature on phase evolution in
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Sadunas, A. 1997. Aliumosilikatiniu dirbiniu ilgaamziskumas
[Durability of aluminium silicate products]. Vilnius: VPU. 252 p.
Seipel, B.; Nickel, K. G. 2004. Protection of silicon nitride
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internal passivation, Ceramics International 30(2): 267-271.
[TEXT NOT REPRODUCIBLE IN ASCII] [Tkachev, A. G.; Kozyarskii, A.
Ya.; Tkacheva, O. N. Optimization of the brick mass composition on the
basis of drying properties]. [TEXT NOT REPRODUCIBLE IN ASCII] [Glass and
Ceramics] 8: 33-34.
Romualdas Maciulaitis [1], Jurgita Malaiskiene [2], Asta Kicaite
[3]
Dept of Building Materials, Vilnius Gediminas Technical University,
Sauletekio al. 11, LT-10223 Vilnius, Lithuania E-mail: [1]
romualdas.maciulaitis@st.vgtu.lt, [2] jurgita.malaiskiene@st.vgtu.lt,
[3] asta.kicaite@st.vgtu.lt
Romualdas MACIULAITIS. Prof., Doctor Habil of Technological
Sciences. He works at Dept of building materials of Vilnius Gediminas
Technical University (VGTU). Research interests: development of building
materials and analysis of their characteristics.
Jurgita MALAISKIENE. Doctor of Civil Engineering. She works at Dept
of building materials of VGTU. Research interests: development of new
conglomerates from local resources, research of their properties and
possibilities to use them.
Asta KICAITE. Assoc. Prof., Doctor of Civil Engineering. She works
at Dept of building materials of VGTU. Research interests: durability
and frost resistance of building materials and their structural and
deformational properties.
Table 1. The average chemical composition
of clay from Rokai deposit
Chemical composition, %
[Al.sub.2]
[O.sub.3]+ [Fe.sub.2]
Si[O.sub.2] Ti[O.sub.2] [O.sub.3] CaO MgO
47.66 18.32 6.27 8.11 3.04
[K.sub.2]O [Na.sub.2]O S[O.sub.3] Kaitmenys
2.68 0.16 -- 12.60
Table 2. Drying regimes
Maximum drying
No. of Stage of drying temperature in
drying in a laboratory, a laboratory,
regime [y.sub.1] units [degrees]C
1 5.44 20
2 8.16 20
3 20.95 22
4 41.9 22
5 8.16 20
6 17.14 18
7 57.14 20
8 17.14 18
Stage of Maximum drying
No. of drying in the temperature in
drying electrical stove the electrical
regime [y.sub.2] units stove, [degrees]C
1 -- --
2 35.37 65
3 17.69 65
4 28.57 105
5 11.73 105
6 7.14 105
7 42.86 105
8 40.82 150
Table 3. The revised (Nagrockiene et al. 2005; Mandeikyte,
Siauciunas 1997; LST EN 771-1+A1 2005) methodology for
calculation of physical and mechanical parameters
Description of the
basic parameter and
Notation units of measurement Physical meaning of parameters
[x.sub.1] Density [rho], Density--mass of unit volume of
kg/[m.sup.3] the material under natural state,
expressed by the ratio of mass per
volume
[x.sub.2] General shrinkage General shrinkage--decrease of the
[S.sub.B], % formed sample in volume during
drying and burning. At the same
time the magnitude of shrinkage
indicates how larger products
should be formed to obtain
necessary dimensions after burning
[x.sub.3] Compressive strength Compressive strength, limit
[R.sub.gn], MPa dynamical load, the ceramic body
was still capable to withstand
[x.sub.4] Rate of ultrasound Rate of ultrasound spread--it is
spread, v the parameter indicating the
defects of material composition.
Rate of ultrasound spread depends
to a great extent on material
strength and can be used as
indirect method in determining
the strength of product
Description of the partial
Formulas for values and units of
Notation determination measurement
[x.sub.1] [rho] = [m.sub.bs]/ [m.sub.bs]--mass of dry
[V.sub.b] sample, kg
[V.sub.b]--volume of
sample, [m.sup.3]
[x.sub.2] [S.sub.B] = [l.sub.0]--distance
[l.sub.0] - between stamps marked in
[l.sub.1]/ the undried sample, mm;
[l.sub.0] x 100 [l.sub.1]--distance
between marked stamps in
the burned sample, mm
[x.sub.3] [R.sub.gn] = P--maximum load determined
P/S x 0.85 by experiment, MN;
S--compressive area of
sample, [m.sup.2]
[x.sub.4] v = l/ t x l--length of sample, m;
[10.sup.-6] t--time, the ultrasound
spreads through sample, s
Table 4. Average values of physical and mechanical parameters
No. of [rho] [S.sub.B] [R.sub.gn] v
batch of ([x.sub.l]), ([x.sub.2]), ([x.sub.3]), ([x.sub.4]),
samples kg/[m.sup.3] % MPa m/s
1 1528 5.32 7.49 2318
2 1572 7.47 17.68 3460
3 1591 7.47 17.66 3323
4 1579 8.08 15.02 2832
5 1572 5.58 9.78 2768
6 1573 6.01 12.46 3199
7 1592 8.53 18.42 3567
8 1586 8.15 11.37 3096
Table 5. The double correlative matrix of the analysed physical
and mechanical parameters and selected drying
parameters
Parameters [rho] [S.sub.B] [R.sub.gn] v
([x.sub.l]) ([x.sub.2]) ([x.sub.3]) ([x.sub.4])
[rho]([x.sub.1]) 1.00 0.64 * 0.23 0.41 *
SB ([x.sub.2]) -- 1.00 0.42 * 0.58 *
Rgn ([x.sub.3]) -- -- 1.00 0.65 *
v([x.sub.4]) -- -- -- 1.00
[y.sub.1] 0,28 0,67 * 0,34 0,38
[y.sub.2] 0,65 * 0,88 * 0,46 * 0,54 *
Note: *--indicates that double correlation between parameters
is significant
Table 6. The coefficients of correlation (R), determination ([R.sup.2])
and standard deflection ([S.sub.e]) of (1)-(4) empirical equations
No.
of Eq. Parameters R [R.sup.2] [S.sub.e]
1 Density, [x.sub.1] 0.939 0.881 9.61 kg/[m.sup.3]
2 General shrinkage, 0.955 0.911 0.32%
[x.sub.2]
3 Compressive strength, 0.917 0.841 1.63 MPa
[x.sub.3]
4 Rate of ultrasound 0.880 0.774 179.5 m/s
spread, [x.sub.4]
Table 7. The coefficients of correlation (R), determination ([R.sup.2])
and standard deflection (se) of empirical equations
(5)-(6)
No. of
Eq. Parameters R [R.sup.2] [S.sub.e]
5 The stage of drying in 0.969 0.940 3.26 units
a laboratory, [y.sub.1]
6 The stage of drying in the 0.985 0.971 2.07 units
electric stove, [y.sub.2]
