The influence of geometric parameters on strength properties of the aggregates used to produce asphalt mixtures.
Bulevicius, Matas ; Petkevicius, Kazys ; Cirba, Stasys 等
Introduction
Asphalt concrete mixture is conglomerate material of mineral
filler, aggregate and bituminous binder. Quality indexes of asphalt
concrete (AC) pavement are significantly influenced not only by
bituminous binders, mineral filler, fine and course aggregate, and other
components, but also by physical, mechanical, and geometrical
properties. In the structure of road pavement (SRC) layers, the
aggregate used to produce asphalt mixtures is exposed to static or
dynamic, fixed, changing or cyclic loads. AC pavement is disrupted by
changes of temperature, rainfall, and other climatic and environmental
factors (Petkevicius et al. 2009; Sivilevicius 2011). Authors'
works (Timm, Newcomb 2006; Merilla et al. 2006; Loizos 2006; Cheneviere,
Ramdas 2006) show that if the non-standard pavement and SRC is designed
and fitted properly, the pavement remains sufficiently smooth for a
longer period of time (10-20 years and longer) and has less defects. The
mechanical strength of mixture can be simulated and experimentally
validated by various techniques developed for sandy soils, namely:
strength properties developed in Amsiejus et al. (2009), deformation
properties developed in Amsiejus et al. (2010).
The analysis of performed works (Kim et al. 2005; Tighe et al.
2007; Lee et al. 2007; Ahammed, Tighe 2008; Li et al. 2008;
Lobo-Guerrero, Vallejo 2010) showed that AC pavement, SRC, railway
ballast or concrete structures functions in very complex and constantly
changing conditions, and is frequently affected by recurring vehicle or
other external loads that effects degradation of granular materials.
The degradation of asphalt mixture: membrane of bituminous binder,
in its contact with particle of aggregate and the particle (Krabbenhoft
et al. 2012). When vehicle loading acts on an asphalt mixture, the
internal stress is mainly transferred through the contact points between
aggregates (Ma et al. 2012; Alvarez et al. 2010; Markauskas et al.
2010). One of prime reasons of crumble off is the inhomogeneity, shape
and size of particles (Sivilevicius, Vislavicius 2008; Mucinis et al.
2009; Mahmoud et al. 2010; Sivilevicius 2011; Vislavicius, Sivilevicius
2013). Before choosing the aggregate, it is necessary to analyse SRC
working conditions (loads, climatic and environmental factors) (Bennert
et al. 2011), as well as the requirements for SRC exploitation
(Bulevicius et al. 2011). The main geometric parameters of the aggregate
used for asphalt mixtures are determined by the indexes of its particle
size distribution and relative amount of oblong particles (flakiness FI
and shape SI indexes). These quality indexes present mechanical and
physical properies of the aggregate in the best way: impact value SZ and
Los Angeles coefficient LA. All these indexes influence the strength and
stability of designed asphalt mixture. Since correlation dependence of
different strain aggregate was determined only between their physical
and mechanical indexes SZ and LA (Bulevicius et al. 2010), this article
seeks to determine how strength properties of particles depend on their
geometrical properties. This problem can be solved by analysing
dependence of physical and mechanical indexes on geometric indexes of
aggregate particles.
It can be hypothesised that resistance of particles to crushing and
impact depends on the quantity of flat and oblong particles in the
mixture. Therefore, pavement does not collapse longer if the asphalt
compound consists of particles that are more resistant to crushing.
The aim of this article is to evaluate means and variance of
analysed indexes and obtain the dependence between its geometric and
strength parameters using statistical analysis.
1. Theoretical modelling of the aggregate strength and geometrical
dependency indexes
A principal scheme of how rubble particles break and crumble, while
the asphalt layer is influenced by external factors (dynamic and static
loads) is presented in Figure 1.
[FIGURE 1 OMITTED]
It is rather easy to notice the dependency between the different
strength of aggregate particle and its geometric parameters (theoretical
change between SZ, FI and SI is shown in Fig. 2), but in order to figure
out how strength indexes SZ and LA depend on the flakiness index FI and
shape index SI, it is necessary to solve the Eqn (1):
y = a x x + b, (1)
where: y - strength index (SZ, LA); x - geometrical index (FI, SI);
a, b - const.
[FIGURE 2 OMITTED]
The provided graph (Fig. 2) shows a changing tendency in the
strength of particles of different mechanical properties. When there are
more oblong particles in the mixture, the aggregate tends to be less
resistant to crushing.
2. Experiment
2.1. Sampling
The sample size used for the investigation should be optimal (Cho
et al. 2011). Physical, mechanical, and geometrical indexes of various
aggregates used for asphalt mixtures kinds produced by seven different
manufacturers were analysed for this purpose (Table 1). The Table shows
the total sample size and the number of tests of indexes.
Samples of the aggregates fh 4/16 were selected in accordance with
the method provided in LST EN 9321:2001 standard, namely, taking samples
from three different places at different depth of a pile located at a
construction site or storage. It was reduced to a necessary size for the
test in accordance with the quartering method provided in LST EN
932-2:2002 standard.
2.2. Test procedure and expression of results
Flakiness index FI of crushed stone was tested in accordance with
the method indicated in standard LST EN 9333:2012. The test consisted of
two screening procedures. During the first screening through square
sieves, the sample was divided into narrow fractions [d.sub.i]/[D.sub.i]
(where: [d.sub.i]--the size of the lower sieve, and [D.sub.i]--the size
of the upper sieve). During the second screening, each particle fraction
[d.sub.i]/[D.sub.i] was sieved through bar sieves, the width of the
opening of which was D/2. The total sample flakiness index FI was
calculated as the relative amount of particles that passed through the
bar sieve from the total mass of dried test portion. Flakiness index FI
was calculated using the following equation:
FI = [M.sub.2]/[M.sub.1] x 100, (2)
where: [M.sub.1]--the sum of all the mass fractions
[d.sub.i]/[D.sub.i], expressed in grams [M.sub.2]--the sum of all the
mass fractions [d.sub.i]/[D.sub.i] that passed through bar sieves of
certain density, expressed in grams.
Shape index SI, e.g. the length L and thickness E of particle, was
tested with shape measuring calliper (Fig. 3) in accordance with the
method indicated in standard LST EN 933-4:2008. Shape index SI of the
particles was calculated using the following equation:
SI = [M.sub.2]/[M.sub.1] x 100, (3)
where: [M.sub.1]--the sum of the mass of tested fractions of
particles, expressed in grams; [M.sub.2]--the sum of the mass of tested
fractions of non-cube-shaped particles, expressed in grams.
[FIGURE 3 OMITTED]
The resistance of crushed stone to static and dynamic loading was
tested in accordance with the method indicated in standard LST EN
1097-2:2010. LA and SZ indices show the same property of tested material
applying different test methods. The Los Angeles method: the 5000 [+ or
-] 5 g sample (10/14 mm fraction) is placed in a closed drum with ten 0
45-49 mm steel balls and rotated 500 revolutions at 31-33 [min.sup.-1]
constant speed. The performance of test using the impact method: a
8/12.5 mm sample fraction was subjected to 10 hammer impacts with a fall
height of 370 mm. Upon the performance of tests, the weight loss of
material that passed through the control sieve is calculated and
expressed as a percentage. The Los Angeles coefficient LA was calculated
using the following equation:
LA = [5000 - m]/50, (4)
where: m - residue on a 1.6 mm sieve, g.
Impact value SZ (as a percentage) was calculated using the
following equation:
SZ = (M/5), (5)
where: M--the sum of the mass of particles that passed through 5
analytical sieves, expressed as a percentage.
2.3. Technical requirements
Currently, in Lithuania, asphalt mixtures are designed according to
TRA ASFALTAS 08 (2009) and the aggregate is selected according to TRA
MIN 07 (2007) requirements. These requirements provide categories of
quality indexes for asphalt mixtures and select their components. After
quality testing of aggregates, data of corresponding results according
to TRA MIN 07 (2007) requirements was summarised in Figure 4.
The percentage of index results that comply with the requirements
and that are provided in the Figure 4, where results are divided
according to the type of rock, range in the close limits, i.e. granite
and gravel rock [+ or -] 1%, and dolomite--up to 6% it can be argued
that the analysed qualitative indexes of rock correlate with each other.
In order to analyse how the analysed geometric indexes influence the
strength indexes, it is necessary to perform a statistical analysis of
the indexes.
2.4. Mathematical analysis of the aggregate physical and mechanical
indexes
Statistical data necessary for statistical analysis are provided in
Tables 2, 3, and 4. Table 2 provides geometric (FI and SI) and strength
(SZ and LA) quality indexes of granite and dolomite. Statistical data of
gravel aggregate quality index are provided in the Table 3, but (due to
insufficient data of the flakiness index FI) statistical calculations
were made only for the shape index SI and strength indexes SZ and LA.
Table 4 provides statistical calculations of all researched strains
(granite, dolomite and gravel) of the aggregate geometric indexes (FI
and SI).
The analysis of geometric quality indexes of researched aggregate
strength (granite, dolomite and gravel) raised the hypotheses about the
correspondence between the flakiness index FI and shape index SI average
values and variance. The hypotheses about the correspondence of analysed
index average and variance are tested in order to determine whether
average and variance of analysed samples are the same. Since the samples
of analysed indexes were not the same while testing the hypothesis for
the proximity of average, the calculations were made by using
Fisher's criterion and hypothesis about the proximity of variance
by using Bartlett's criterion. The hypotheses were tested by making
statistical calculations. While examining the hypotheses about the
averages (Eqn (6)) of geometric quality indexes:
[T.sub.stat] = [bar.X] - [bar.Y]/[square root of (n - 1) x
[s.sup.2.sub.x] + (m - 1) x [s.sup.2.sub.y]] [square root of mn x (m + n
- 2)/n + m]. (6)
The proximity of variance and the following statistical
calculations were made using Eqns (7)-(10):
T = (N - k) x ln x [s.sup.2.sub.P] - [k.summation over (i=1)]
([n.sub.i] - 1) x ln x [s.sup.2.sub.i]/1 + [DELTA]; (7)
N = [n.sub.1] + [n.sub.2] + *** + [n.sub.k]; (8)
[s.sup.2.sub.P] = 1/N - k [k.summation over (i=1)] ([n.sub.i] - 1)
x [s.sup.2.sub.i]; (9)
[DELTA] = 1/3(k - 1) [k.summation over (i=1)](1/[n.sub.i] - 1 - 1/N
- k), (10)
where: [bar.X], [bar.Y]--compared averages of aggregate quality
indexes; n, [n.sub.i], m--samples of indexes (a number of chosen data
for verification); [s.sup.2.sub.x], [s.sup.2.sub.y]--variance of
indexes; k--number of variable samples.
The hypotheses are tested, when significance level of the criterion
is a = 0.05. Used indexes: g--the value of granite aggregate quality
index; and d--dolomite and gr--gravel values of aggregate quality index.
3. Dependency analysis between mechanical, physical, and geometric
indexes
3.1. Correlation dependencies and regression equation between
mechanical, physical and geometric indexes
According to the requirements of TRA MIN 07 (2007), permissible
geometric indexes of the aggregate for the same type of asphalt mixtures
are different, therefore, it is necessary to examine and assess
correlation dependences of researched aggregate flakiness index FI and
shape index SI and correlation dependences between geometric and
physical quality indexes LA and SZ. Correlation dependences of analysed
indexes were assessed according to coefficients in the Table 5.
Since the aggregate of granite and dolomite is usually used for
asphalt mixtures in Lithuania, statistical calculations of quality
indexes were made based on these strains of the aggregate.
While determining the correlation dependence of the aggregate
flakiness index FI and shape index SI, the results were not
distinguished by the types of rocks (strains), because only geometric
indexes of the aggregate were analysed. The authors determined
correlation dependence of physical, mechanical, and geometric indexes of
granite between SI and SZ, and correlation dependence of physical,
mechanical, and geometric indexes of dolomite between: SI and SZ; FI and
SZ; SI and LA; FI and LA.
For the calculation of correlation dependences between the indexes
FI and SI, 134 samples of different aggregate strains (granite, dolomite
and gravel) were selected (Fig. 5).
[FIGURE 5 OMITTED]
According to the values of correlation dependence between the
indexes FI and SI provided in the Table 6, the authors evaluated the
correlation dependence as strong and equation of regression FI = 2.7224
+ 0.6008 x SI with coefficient of determination [R.sup.2] = 0.52.
Further in this article for the lack of area calculations without
graphics will be shown. For the calculation of correlation dependences
between the indexes FI and SZ, 17 samples of dolomite were selected.
After statistical calculation of dolomite aggregate flakiness index FI
and impact value SZ, the authors determined correlation dependence
between the flakiness index FI and impact value SZ expressed as
correlation coefficient r = 0.57, equation of regression SZ = 18.9547 +
0.3491 x FI, coefficient of determination [R.sup.2] = 0.33. After
statistical calculation of dolomite aggregate flakiness index FI and Los
Angeles coefficient LA (n = 18), the authors determined correlation
coefficient r = 0.64. Since the values of the indexes FI and LA (2; 22)
significantly differed from remaining values, the authors of the article
rejected the values of these samples. After rejecting the values of the
indexes FI and LA, the authors obtained the following results:
correlation coefficient r = 0.73 (strong dependence) and equation of
regression LA = 18.2916 + 0.4268 * FI coefficient of determination
[R.sup.2] = 0.41. After statistical calculation of dolomite aggregates
shape index SI and Los Angeles coefficient LA, the authors determined
correlation dependence between the shape index SI and index of
resistance to fragmentation expressed as correlation coefficient r =
0.62. Since values of the indexes SI and LA were different (2; 22), and
(3; 23) significantly differed from the rest of the values, the authors
rejected the values of these samples. After rejecting the values of the
indexes SI and LA, the authors obtained the results: correlation
coefficient r = 0.76 (strong dependence), equation of regression LA =
19.2469 + 0.345 x SI, coefficient of determination [R.sup.2] = 0.39.
3.2. Zero hypotheses Ho for the proximity of flakiness index FI and
shape index SI averages
After statistical calculations (according to data in the Tables 2,
3 and 4), the authors obtained the following statistical values of
geometric quality indexes of granite, dolomite and conjoint strain
(granite, dolomite, and gravel) aggregate FI and SI as: averages, number
of samples, variance. After placing numbers into the Eqn (6), the
authors get [T.sub.stat]. The critical value [T.sub.crit] =
[T.sub.0.05/2;n+m-2] of the index was determined from statistical
tables. The authors can indicate acceptation of the hypothesis H for the
proximity of flakiness and shape indexes averages after inequality
[absolute value of [T.sub.stat]] < [T.sub.crit] evaluation (Table 7).
After calculation of the statistical values only hypothesis
[H.sub.0] : [[bar.X].sub.Fig] = [[bar.Y].sub.SIg] for the proximity of
granite flakiness and shape indexes averages was not rejected.
Bartlett's criterion checks the hypothesis of dispersion
equality. It is applied if the observed variables are distributed
normally. In order to check the hypothesis of dispersion proximity
between the values of flatness and form indexes, it is purposeful to
check whether the analysed geometrical indexes are distributed normally.
Hypotheses for the normal distribution of analysed index frequency in
the histograms were tested by accepting the level of significance a =
0.05. Hypotheses for the normal distribution of frequency were tested
only for those indexes that had frequency distributed according to the
tendency of normal distribution. The hypothesis for the normal
distribution of data was tested according to the Eqn (6). Summary of
hypotheses for the normal distribution of available data value is
provided in the Table 8.
As all distribution of analysed indexes was stated as normal,
hypothesis Ho for the proximity of the flakiness index FI and shape
index SI variance can be estimated.
3.3. Zero hypotheses [H.sub.0] for the proximity of flakiness index
FI and shape index SI variance
After statistical calculations (according to data in Tables 2, 3
and 4), the authors obtained the following statistical values of
geometric quality indexes of different strains aggregate FI and SI:
averages, samples size and variance. Zero hypothesis H0 about the
proximity of geometrical indexes FI and SI variance can be estimated
after statistical values are put into Eqns (6), (7) and (8) (Table 9).
After calculation of the statistical values only hypo theses
[H.sub.0] : [s.sup.2.sub.FIg] = [s.sup.2.sub.SIg] and [H.sub.0] :
[s.sup.2.sub.FIb] = [s.sup.2.sub.SIb] of the proximity of granite, as
well as mixture of granite, dolomite, and gravel aggregate FI and SI
indexes statistical value T, was estimated less than
[[chi].sup.2.sub.[alpha]] (k - 1), there is no reason to reject the
hypotheses for the proximity of researched aggregate strain flakiness
and shape index dispersions.
Conclusions
The skewness of all analysed geometric quality indexes of the
aggregate is [g.sub.1] > 0; it shows that the right asymmetry case of
empiric distribution in the values of samples. The skewness of granite
and dolomite aggregate ([g.sub.1] = [0.42;0.62]) is significantly higher
than analogous coefficient of gravel aggregate ([g.sub.1] = 0.14); it
means that the values of granite and dolomite aggregate FI and SI are
distributed on the left, towards the higher values, average (median),
and the values of gravel aggregate are distributed around the middle
value. It confirms that the aggregate strains used in Lithuania comply
with higher categories of geometric quality indexes.
The test of correlation between quality indexes of different
aggregate strains and its strength indexes determined a strong
correlation between all values of FI and SI, as well as dolomite
aggregate indexes FI and LA. It shows that both geometric quality
indexes of the aggregate are strongly related to each other, the same is
with the indexes FI and LA. These dependences suggest that determined
value of FI may help to predict the value of LA. The analysis of
correlation dependence between geometrical and strength indexes of
different rock samples showed a significant decline of particle
strength, when the number of flat and oblong particles was greater.
Similarities of statistical FI and SI averages allowed testing
hypothesis about the average proximity of geometric quality indexes. The
calculations showed that there is no reason to reject the hypothesis for
the average proximity of granite aggregate indexes FI and SI; therefore,
it can be argued that while examining geometric indexes (FI and SI) of
granite aggregate, there is an alternative to choose one of the test
methods. However, hypothesis about the average proximity of dolomite
aggregate indexes was rejected; it means that while examining the
quality of this aggregate, there are no alternatives to choose the test
methods.
Only tested hypothesis for the variance proximity of dolomite
indexes FI and SI showed that it is rejected; therefore, same hypotheses
of granite and mixture of granite, dolomite and gravel were accepted. It
can be argued that the values of geometric quality indexes are
distributed around the middle value in even intervals.
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http://dx.doi.org/10.1016/j.acme.2013.03.003
doi: 10.3846/13923730.2013.858645
Matas BULEVICIUS (a), Kazys PETKEVICIUS (b), Stasys CIRBA (c)
(a) SE "Problematika", Galves g. 2, 02241 Vilnius,
Lithuania
(b) Department of Roads, Vilnius Gediminas Technical University,
Sauletekio al. 11, 10223 Vilnius, Lithuania
(c) Department of Mathematical Modelling, Vilnius Gediminas
Technical University, Sauletekio al. 11, 10223 Vilnius, Lithuania
Received 20 Jun 2013; accepted 03 Oct 2013
Corresponding author: Matas Bulevicius
E-mail: matas.bulevicius@problematika.lt
Matas BULEVICIUS. PhD student at the Department of Roads of
Environmental Engineering Faculty of Vilnius Gediminas Technical
University. He received his Master's degree in 2012 at Vilnius
Gediminas Technical University. He is also the author and co-author of 3
publications as well as 4 research and technical reports. He is a chair
of the Technical Committee on Road Building Materials and a member of
the Technical Committee on Geotechnical Engineering of the Lithuanian
Standards Board. His research interests include mechanical-physical
properties of aggregates, used for producing asphalt mixtures, and road
pavement constructions.
Kazys PETKEVICIUS. PhD, Eng. Professor at the Department of Roads
of Environmental Engineering Faculty of Vilnius Gediminas Technical
University. He received his Professor title in 2012 at Vilnius Gediminas
Technical University. He is also the author and co-author of seven
books, over 155 other publications as well as over 94 research and
technical reports. His research interests include mechanical-physical
properties of aggregates, used for producing asphalt mixtures, road
pavement constructions, strength, functional design and damages of motor
roads.
Stasys CIRBA. PhD, Eng. Doctor in the Department of Mathematical
Modelling of Fundamental Science Faculty at Vilnius Gediminas Technical
University. He received his PhD in 1972 at Vilnius University. He is
also the author and co-author of three books, over 20 other publications
as well as over 8 research and technical reports. His research interests
include statistical and mathematical analysis.
Table 1. Number of samples used for the experiment
Index/Rock Sample Number of tests
size
FI SI SZ LA
Dolomite 189 102 189 135 21
Granite 81 30 71 81 19
Gravel 18 6 13 18 17
Table 2. Summary of mechanical indexes FI, SI, LA, and SZ of granite
and dolomite aggregate
Statistical index x Rock
granite
indexes of properties and their values
FI SI LA
Sample size n 30 71 19
[x.sub.min.] 1% 1% 19
[x.sub.max.] 21% 20% 12
[x.sub.max.] - 20% 19% 7
[x.sub.min.]
Mean x 9.20% 8.59% 15.53
Standard deviation s 5.12% 3.96% 2.11
Variance [s.sup.2] 25.23(%) (2) 15.66(%) (2) 4.46
Skewness [g.sub.1] 0.42 0.63 -0.83
Kurtosis [g.sub.2] 2.36 2.94 -0.33
Statistical index x Rock
granite dolomite
indexes of properties and their values
SZ FI SI
Sample size n 81 102 189
[x.sub.min.] 19.7% 1% 1%
[x.sub.max.] 14.8% 18% 21%
[x.sub.max.] - 4.9% 17% 20%
[x.sub.min.]
Mean x 17.23% 7.14% 8.44%
Standard deviation s 1.13% 3.11% 3.80%
Variance [s.sup.2] 1.27(%) (2) 9.69(%) (2) 14.41(%) (2)
Skewness [g.sub.1] 0.14 0.62 0.56
Kurtosis [g.sub.2] 0.01 3.52 3.04
Statistical index x Rock
dolomite
indexes of properties
and their values
LA SZ
Sample size n 21 135
[x.sub.min.] 26 26.3%
[x.sub.max.] 19 18.9%
[x.sub.max.] - 7 7.4%
[x.sub.min.]
Mean x 21.1 22.23%
Standard deviation s 1.56 1.36%
Variance [s.sup.2] 2.42 1.84(%) (2)
Skewness [g.sub.1] 3.40 0.72
Kurtosis [g.sub.2] 1.30 0.53
Table 3. Summary of mechanical indexes SI, LA, and SZ of
gravel aggregate
Statistical index x Indexes of gravel aggregate
properties and their values
SI LA SZ
Sample size n 13 17 18
[x.sub.min.] 1% 35 26.7%
[x.sub.max.] 16% 21 19.1%
[x.sub.max.] - 15% 14 7.6%
[x.sub.min.]
Mean x 7.50% 27.05 23.47%
Standard deviation 5.19% 3.99 2.19%
s
Variance [s.sup.2] 26.92(%) (2) 15.94 4.79(%) (2)
Skewness [g.sub.1] 0.14 -0.18 -0.66
Kurtosis [g.sub.2] 1.48 0.58 -0.60
Table 4. Summary of mechanical indexes FI and SI of all
researched strains (granite, dolomite and gravel)
Statistical index x Indexes of granite,
dolomite, and gravel
aggregate properties
and their values
FI SI
Sample size n 132 273
[x.sub.min]. 1 1
[x.sub.max]. 21 27
[x.sub.min]. - 20 26
[x.sub.min].
[Mean.sup.-.sub.x] 7.61 8.44
Standard 3.74 3.92
deviation s
Variance [s.sup.2], 13.96 15.34
[(%).sup.2]
Skewness [g.sub.1] 0.85 0.52
Kurtosis [g.sub.2] 3.82 2.91
Table 5. Table for evaluating the nature of correlation
(Cekanavicius, Murauskas 2004)
Value of Nature of correlation
correlation dependence
coefficient
0.00-0.19 Very weak dependence or
no dependence at all
0.20-0.39 Weak dependence
0.40-0.69 Average dependence
0.70-0.89 Strong dependence
0.90-1.00 Very strong dependence
Table 6. Summary of correlation dependences between mechanical,
physical, and geometric indexes of the analysed aggregate
strains (granite dolomite and gravel)
Rock Correlation Type of Sample
dependence correlation size,
dependency n
Crushed r([x.sub.SI], very weak 51
granite [x.sub.SZ]) correlation
Crushed r([x.sub.FI], average 17
[x.sub.SZ]) correlation
dolomite r([x.sub.Sb], no correla- 97
[x.sub.SZ]) tion at all
r([x.sub.FI], strong 18
[x.sub.LA]) correlation
r([x.sub.SI], average 20
[x.sub.LA]) correlation
Crushed stone r([x.sub.FI], weak 22
(granite and [x.sub.SZ]) correlation
dolomite) r([x.sub.SI], very weak 147
[x.sub.SZ]) correlation
r([x.sub.FI], weak 25
[x.sub.LA]) correlation
r([x.sub.SI], weak 27
[x.sub.LA]) correlation
Crushed stone r([x.sub.FI], strong 134
(granite [x.sub.SI]) correlation
dolomite and
gravel)
Rock Mean
Crushed [[bar.x].sub.SI] [[bar.x].sub.SZ]
granite = 8.47(%) = 17.06(%)
Crushed [[bar.x].sub.FI] [[bar.x].sub.SZ]
= 8.12(%) = 21.78(%)
dolomite [[bar.x].sub.SI] [[bar.x].sub.SZ]
= 10.13(%) = 22.12(%)
[[bar.x].sub.FI] [[bar.x].sub.LA]
= 8.12(%) = 21.56
[[bar.x].sub.SI] [[bar.x].sub.LA]
= 7.94(%) = 21.72
Crushed stone [[bar.x].sub.FI] [[bar.x].sub.SZ]
(granite and = 8.12(%) = 20.46(%)
dolomite) [[bar.x].sub.SI] [[bar.x].sub.SZ]
= 9.57(%) = 20.43(%)
[[bar.x].sub.FI] [[bar.x].sub.LA]
= 7.04(%) = 20.22
[[bar.x].sub.SI] [[bar.x].sub.LA]
= 7.47(%) = 20.73
Crushed stone [[bar.x].sub.FI] [[bar.x].sub.SI]
(granite = 7.49(%) = 8.02(%)
dolomite and
gravel)
Rock Variance Correlation
coefficient,
r
Crushed [s.sup.2.sub.SI] [S.sup.2.sub.SZ] 0.19
granite = 14.21[(%).sup.2] = 1.48[(%).sup.2]
Crushed [s.sup.2.sub.FI] [S.sup.2.sub.SZ] 0.57
= 5.87 [(%).sup.2] = 2.19[(%).sup.2]
dolomite [s.sup.2.sub.SI] [S.sup.2.sub.SZ] 0.03
= 14.16[(%).sup.2] = 1.95[(%).sup.2]
[s.sup.2.sub.SI] [S.sup.2.sub.LA] 0.73
= 8.46[(%).sup.2] = 4.71
[s.sup.2.sub.SI] [S.sup.2.sub.LA] 0.62
= 11.28[(%).sup.2] = 4.31
Crushed stone [s.sup.2.sub.FI] [S.sup.2.sub.SZ] 0.32
(granite and = 9.56 [(%).sup.2] = 6.91 [(%).sup.2]
dolomite) [s.sup.2.sub.SI] [S.sup.2.sub.SZ] 0.15
= 16.71 [(%).sup.2] = 9.71[(%).sup.2]
[s.sup.2.sub.FI] [S.sup.2.sub.LA] 0.28
= 15.07[(%).sup.2] = 13.88
[s.sup.2.sub.SI] [S.sup.2.sub.LA] 0.32
= 14.78[(%).sup.2] = 16.26
Crushed stone [s.sup.2.sub.FI] [S.sup.2.sub.SI] 0.74
(granite = 13.41[(%).sup.2] = 20.58[(%).sup.2]
dolomite and
gravel)
Table 7. Summary of hypotheses for the proximity of indexes
FI and SI of the average values of granite dolomite and gravel
Rock Hypothesis [H.sub.0] Mean, %
[bar.[X.sub.FI]]
crushed [H.sub.0] : 9.20
granite [[bar.X.sub.FIg]]
= [bar.[Y.sub.SIg]]
crushed [H.sub.0] : 7.14
dolomite [[bar.X.sub.FId]]
= [bar.[Y.sub.SId]]
crushed [H.sub.0] : 7.61
granite, [[bar.X.sub.FId]]
dolomite = [bar.[Y.sub.SIb]]
and gravel
Rock Mean, % Variance,
[(%).sup.2]
[bar.[Y.sub.SI]] [s.sup.2.sub.FI] [s.sup.2.sub.FI]
crushed 8.59 25.23 15.66
granite
crushed 8.44 9.69 14.41
dolomite
crushed 8.44 13.96 15.34
granite,
dolomite
and gravel
Rock Statistical Critical Status of the
value, value, hypothesis
[T.sub.stat] [T.sub.crit] [H.sub.0]
crushed 0.09 1.99 accepted
granite
crushed 3.14 1.97 rejected
dolomite
crushed 2.49 1.97 rejected
granite,
dolomite
and gravel
Table 8. Summary of hypotheses for the normal distribution of
available data value
Rock Index Sample Number of Length of
size, intervals, intervals,
n k h
crushed granite 30 4
crushed dolomite FI value 102 3.4
crushed granite 132 c 4
and dolomite
crushed granite 71 5 3.8
crushed dolomite SI value 189 4
crushed granite, 273 5.2
dolomite
and gravel
Rock Statistical Critical Status of
value, value, the normal
[T.sub.stat] [T.sub.crit] distribution
crushed granite 3.05 5.99 accepted
crushed dolomite 0.36 5.99 accepted
crushed granite 4.83 5.99 accepted
and dolomite
crushed granite 3.35 5.99 accepted
crushed dolomite 5.23 5.99 accepted
crushed granite, 5.67 5.99 accepted
dolomite
and gravel
Table 9. Summary of zero hypotheses for proximity between indexes
FI and SI of the variance of granite dolomite and gravel
Rock Hypothesis [H.sub.0] Sum of Variance,
sample [s.sup.2.saub.p]
size, N
crushed granite [H.sub.0]: 101 18.46
[s.sup.2.sub.FIg]
= [s.sup.2.sub.SIg]
crushed dolomite [H.sub.0]: 291 12.76
[s.sup.2.sub.FId]
= [s.sup.2.sub.SId]
crushed granite, [H.sub.0]: 405 14.89
dolomite and [s.sup.2.sub.FIb]
gravel = [s.sup.2.sub.SIb]
Rock Statistical Stochastic Status of the
value, T number, [[chi hypothesis
square].sub.[alpha]] [H.sub.0]
(k - 1)
crushed granite 2.441 3.841 accepted
crushed dolomite 4.926 3.841 rejected
crushed granite, 0.387 3.841 accepted
dolomite and
gravel
Fig. 4. Summary of results that comply with TRA MIN 07
(2007) requirements
Granite Dolomite Gravel
FI 83 98 100
SI 91 96 100
SZ 90 97 100
LA 92 95 99
Note: Table made from line graph.
