Testing of mechanical-physical properties of aggregates, used for producing asphalt mixtures, and statistical analysis of test results/Skaldos, naudojamos asfalto misiniams gaminti, fiziniu bei mechaniniu savybiu tyrimai ir rezultatu statistine analize/ Asfaltbetona maisijumu razosanai izmantoto mineralmaterialu fizikali mehanisko ipasibu testesana un testa rezultatu statistiska analize/ Asfaltsegude ....

Bulevicius, Matas ; Petkevicius, Kazys ; Zilioniene, Daiva 等

1. Introduction

In order to improve road pavement properties as well as traffic conditions on roads the scientists of Lithuania and other countries carry out researches of structural pavement layers, analyze the effect of their properties on pavement performance, mechanical-physical properties of asphalt mixtures and materials used for structural pavement layers (Amsiejus et al. 2010; Amsiejus et al. 2009; Butkevicius et al. 2007; Ceylan et al. 2009; Petkevicius et al. 2009; Petkevicius et al. 2008; Radziszewski 2007; Sivilevicius et al. 2011; Vaitkus et al. 2009). Crushed rocks--granite, dolomite and gravel differ by their size, shape and functioning conditions in structural pavement layers that depend on loading size and nature, temperature, environmental aggressiveness and other factors. In asphalt mixtures most commonly the more expensive but more durable aggregates (crushed granite and crushed dolomite) are used, therefore, the suitability of crushed gravel has not been sufficiently investigated. Using more strong aggregates the service life of road pavement structure becomes longer, pavement structure is more reliable and requires more thin structural layers, material expenditures are lower. The selected aggregates shall be inexpensive and easily obtained. In Lithuania the most commonly found is gravel, more rarely--dolomite. These rocks not always meet the requirements for mineral materials used in asphalt mixtures. Crushed granite is transported from the neighbouring countries; therefore, it is most expensive. In separate cases the mechanical-physical properties of crushed gravel are better than those of crushed dolomite, and in rare cases they come very approximate to the properties of crushed granite (Bhasin et al. 2009; Bulevicius et al. 2010).

In order to properly select aggregates the multipurpose decision-making methods shall be used (Sivilevi-cius et al. 2008; Zavadskas et al. 2008) and optimum solutions shall be applied for loads acting in circular plane and causing shear (Atkociunas et al. 2004). This article gives the statistical analysis of mechanical-physical properties of crushed granite, crushed dolomite and crushed gravel.

The articles studies normative quality indices applied for asphalt aggregates when performing tests in accordance with LST EN 1097-6 + AC:2003, LST EN 1097-6 + AC:2003/A1:2005 "Determination of Particle Density and Water Absorption", LST EN 1097-1:2002, LST EN 10971:2002/A1:2004 "Determination of the Resistance to Wear (Micro-Deval)", LST EN 1097-2:1999, LST EN 10972:2001/A1:2006 "Methods for the Determination of Resistance to Fragmentation", LST EN 1097-8:2009 "Determination of the Polished Stone Value" and LST EN 13671:2007 "Determination of Resistance to Freezing and Thawing".

2. Testing and analysis of mechanical-physical properties of aggregates

In the result of various tests of crushed granite, crushed dolomite and crushed gravel of different manufacturers the LA, SZ, PSV and F values were determined. The following results were obtained having analyzed the results of tests to determine resistance to fragmentation: 94% of all aggregate specimens, tested by the LA method, meet the requirements of [LA.sub.20] for asphalt pavement, 88% of test results of crushed dolomite specimens gets between the requirements [LA.sub.20] and [LA.sub.25]. The limit of [LA.sub.30] requirements is exceeded by 33% of all crushed gravel specimens. The requirements for asphalt pavement are satisfied by 69% of all aggregate specimens tested by the Impact test method. The limit of [SZ.sub.18] is exceeded by 27% of the tested crushed granite specimens, the limit of [SZ.sub.22] is exceeded by 36% of the tested crushed dolomite specimens, and the limit of [SZ.sub.26] is exceeded by 23% of the tested crushed gravel specimens. The largest part (83%) of specimens, tested to determine the polished stone value, meets the requirements for [PSV.sub.50] and [PSV.sub.44] of asphalt pavement. All the crushed granite specimens meet the highest category of [PSV.sub.50]. The limit of [PSV.sub.44] requirements is exceeded by 17% of the tested crushed dolomite specimens. All aggregate specimens, tested to determine their resistance to freezing and thawing, 100% meet the requirements of [F.sub.1] and [F.sub.2] for asphalt pavement. 91% of test results of crushed granite specimens do not exceed 1/10, 80% of test results of crushed dolomite specimens do not exceed 1/5 [F.sub.1]. All the results of crushed gravel tests get between the requirements [F.sub.1] and [F.sub.2] (Bulevicius et al. 2010).

3. Statistical analysis of mechanical-physical properties of aggregates

For all studied types of aggregates the statistical characteristics of their quality indices were calculated which are given in Table 1. For the analysis of aggregate properties, used in asphalt mixtures, the samples of statistical data of different quality indices were worked out. The sample of the F values of resistance to freezing and thawing quality index was made of 123 individual data (n = 123). The F values are given in Fig. 1. They are grouped by the type of rock.

Fig. 2 gives the LA values. The sample was made of 59 individual data (n = 59). In the Fig the LA values are grouped by the type of rocks. The dark points show the values rejected (due to strong difference) from further statistical estimations.

The SZ values are given in Fig. 3. The values are grouped by the type of rock. The sample of the SZ values was made of 238 individual data (n = 238). The dark points show the SZ values rejected (due to strong difference) from further statistical estimations.

In order to make a more detail as possible analysis of [[rho].sub.rd] of aggregates, the data sample of 8/12.5 mm fraction was formed. Density of this aggregate fraction was determined by a pyknometer method according by LST EN 1097-6 + AC:2003, LST EN 1097-6+AC:2003/A1:2005. Data on dry density measurements (fr. 8/12.5 mm) is given in Fig. 4. The sample of [rho]rd was made of 178 individual values (n = 178). The dark points show the [[rho].sub.rd] values rejected (due to strong difference) from further statistical estimations.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

Due to a low variety, i.e. a low dispersion, of values or due to insufficient number of investigation data no further estimations were performed for the polished stone value and Deval indices.

A statistical analysis of the values of mechanical [properties quality indices of the studied aggregates was carried out (Table 1). Dispersion of values of the resistance to repeated freezing and thawing of all 3 types of aggregates was not large: the corrected [S.sub.x] varied from 0.079% to 0.507%. Especially small [S.sub.x] of investigation data was represented by crushed gravel. This shows inconsiderable variation in test data of the resistance of aggregates to environmental impact. The means of crushed granite and crushed dolomite test data did not exceed 13% and 25%, respectively, of the max value of category [F.sub.1] ([F.sub.1] meets the mass loss up to 1%). The obtained low values of quality indices show that the tests of resistance to repeated freezing and thawing to determine aggregate suitability to asphalt mixtures are insufficient. The arithmetic means of F values of crushed granite and crushed dolomite differ insignificantly. The average value of test data of crushed gravel specimens was 5 times higher than that the arithmetic mean of crushed granite and 3 times higher than the arithmetic mean of crushed dolomite. This shows that crushed gravel is less resistant to the impact of ambient temperature compared to crushed granite and crushed dolomite. The values of arithmetic mean of LA and SZ of crushed granite and crushed dolomite are approximate. The highest values of [S.sub.x] were represented by crushed gravel. This shows the highest variation in the quality indices of the studied physical properties of this type of aggregates and that the strength properties of the imported granite and dolomite are more stable compared to the properties of crushed gravel extracted in Lithuania.

[S.sub.x] and [S.sub.x] of the polished stone value of crushed granite, compared to that of crushed dolomite, differ twice--this shows a larger stability of PSV of crushed granite.

The amplitude of values of [M.sub.DE] of all 3 studied types of aggregates is approximate. This shows an approximate variation of results of studied property all 3 types of aggregates and an assumption could be made that this method is suitable to determine the values of [M.sub.DE]. The arithmetic means of [M.sub.DE] values of crushed dolomite and crushed gravel differ insignificantly, and this shows a low resistance of crushed dolomite, like that of crushed gravel, when testing specimens by this method (when rock is mechanically affected in water). Similarity of properties of the resistance of these types of aggregates to wear in water is proved also by approximate [S.sub.x] of this quality index. [S.sub.x] of [M.sub.DE] values of all 3 types of aggregates are low--this shows a small data variation when testing specimens by Deval method.

A statistical analysis of the [[rho].sub.rd] values was carried out too. The highest arithmetic mean of [[rho].sub.rd] values was obtained for crushed dolomite, the lowest--for crushed gravel. The obtained means of [[rho].sub.rd] values of the studied aggregates correspond to the DPD values of respective aggregates established by the list of technical requirements TRA MIN 07:2007. The amplitudes of [[rho].sub.rd] values of the studied types of aggregates vary within narrow limits (0.05-0.15) Mg/[m.sup.3], this shows a small dispersion of the DPD. Standard deviations of [[rho].sub.rd] values of all 3 types of aggregates are similar--this shows a similar variation of the values of this quality index. Therefore, it could be stated that physical properties of the specimens of the same rock are similar.

Asymmetry coefficient g1 is a measure of symmetry of statistical frequencies distribution or a measure of histogram symmetry. The histogram is symmetrical when [g.sub.1] = 0. The sample excess coefficient [g.sub.2] is a measure of flatness (or sharpness) of the statistical distribution histogram. When [g.sub.2] > 0 the histogram is sharp, i.e. data dispersion about the mean is lower than that for normal (Gaussian) curve. When [g.sub.2] < 0 the histogram is flat and data dispersion about the mean is higher than that for normal curve. When the empirical asymmetry and excess coefficients are approximate to 0 the histogram could be treated as being approximate to the graph of density function of the normal distribution. When both coefficients are approximate to 0 it is up to the purpose to test a hypothesis that the sample of studied value is distributed by normal distribution.

4. Testing of hypotheses on the approximate of values of the same quality indices of different types of aggregates

When analyzing data of mechanical-physical properties quality indices of the studied types of aggregates (crushed granite, crushed dolomite and crushed gravel) the hypotheses were formulated on the correspondence of the means of F, SZ and [[rho].sub.rd] (Table 2). The formulated hypotheses were tested using statistical estimations. When testing hypotheses on the approximate of means of the strength quality indices the following Eq was used for the statistical estimations:

[T.sub.stat] = [bar.X] - [bar.Y]/[square root of (n - s)[S.sup.2.sub.x] + (m - 1)[S.sup.2.sub.y]] [square root of mn(m + n - 2)/n + m], (1)

where [bar.X], [bar.Y]--means of the quality indices of aggregates being compared; n, m--samples of quality indices (number of data selected for testing); [S.sup.2.sub.x], [S.sup.2.sub.y]--dispersions of quality indices.

The hypotheses were tested when the significance level of the criterion [alpha] = 0.05. Index g--indicates the value of quality index of crushed granite, d--of crushed dolomite and gr--of crushed gravel.

5. Determination of correlation dependencies between the values of mechanical-physical properties quality indices of different types of aggregates

According to the TRA MIN 07:2007 The List of Technical Requirements for the Mineral Materials of Roads, for the same type of asphalt mixtures different permissible mechanical-physical properties quality indices of aggregates are set, therefore, it is necessary to test and determine correlation dependencies between the different quality indices of the studied aggregates. Correlation dependencies were determined according to the correlation coefficients given by Cekanavicius and Murauskas (2000): when correlation coefficient values is 0.00-0.19--type of correlation dependency is very weak correlation or no correlation at all, when 0.20-0.39--weak correlation, when 0.40-0.69 average correlation, when 0.70-0.89--strong correlation and when 0.90-1.00--very strong correlation. For statistical testing only those specimens were chosen for which from 2 to 5 quality indices, used for calculations, were studied. Correlation dependencies of mechanical-physical properties quality indices of crushed granite and crushed dolomite were determined between LA and F, SZ and F, [[rho].sub.rd] and F, LA and SZ; LA and [[rho].sub.rd], and SZ and [[rho].sub.rd] (Table 3). In Lithuania the most common aggregates, used for producing asphalt mixtures, are crushed granite and crushed dolomite. Due to the lack of values statistical estimations were carried out not for all quality indices.

Since the value [LA.sub.24] of LA significantly differed from the remaining values it was rejected. Due to the same reason the value [SZ.sub.13.5] of SZ was also rejected. For further estimations the samples without those values were used. Having rejected the mentioned LA and SZ values the following results were obtained (Table 3). For the estimation of correlation dependencies between LA and SZ values 16 specimens of crushed dolomite were chosen (n = 16). In this sample the strongly different value [X.sub.LA] = 12 was rejected. It was excluded from the later studied samples. If correlation dependence is very weak it could be stated that the studied indices have almost no influence on each other.

6. Testing of hypotheses on the normal distribution of data

Hypotheses that the frequencies of studied quality indices in histograms are distributed by normal distribution were tested having assumed the significance level [alpha] = 0.05. Hypotheses on the normal distribution of frequencies were tested only for those quality indices the frequencies of which were distributed in a tendency of normal distribution. If when drawing a histogram the curve takes an approximately symmetric shape of bell the hypothesis that data is distributed normally is usually proved. The more factors affect the value of quality index the higher probability that the data of quality index will be distributed by normal distribution ([TEXT NOT REPRODUCIBLE IN ASCII] 1969). Having accepted the hypothesis that data is distributed by normal distribution it could be stated that probability that any sample value will deviate from the sample mean at a distance not larger than 2[S.sub.x] is 0.95. Consequently, the assumption on a normal distribution of studied data diminishes probability of the extreme variations of values. Summary of the values of hypotheses on the normal distribution of current data is given in Table 4.

The histogram of frequencies of SZ values was drawn without the significantly different values that were rejected (13.5, 21.4, 21.5). The histogram of SZ values of crushed granite is given in Fig. 5. The length of interval h was determined by the Eq (2):

h = [X.sub.max] - [X.sub.min]/k, (2)

where h--the length of interval; [X.sub.max]--max value of quality index; [X.sub.min]--min value of quality index; k--the number of intervals.

The histogram of frequencies of SZ values was drawn for the sample where n = 135. Hypothesis was tested whether the results of resistance to fragmentation test are distributed by normal distribution. The histogram of SZ values of resistance to fragmentation of crushed dolomite by impact test method is given in Fig. 6.

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

Hypothesis was tested that the measurement results of [[rho].sub.rd] value of crushed granite (Fig. 7) and crushed dolomite (Fig. 8) are distributed by normal distribution.

7. Conclusions

1. Having determined by statistical estimations the PSV and [M.sub.DE], a low dispersion of their values was obtained. The number of intervals being less than 5 it is beside the purpose to estimate histogram of the distribution of frequencies of values, therefore, hypothesis on the normal distribution of those values were not analyzed.

2. Tested hypotheses on different F, SZ and [[rho].sub.rd] values means of crushed granite, crushed dolomite and crushed gravel shows there was no reason to reject hypotheses on the approximate of means of SZ values for crushed granite and crushed gravel. Further hypotheses on the approximate of means of SZ values for crushed dolomite and crushed granite, and for crushed dolomite and crushed gravel were rejected. Also, hypotheses were tested whether the means of [[rho].sub.rd] values for crushed granite, crushed dolomite and crushed gravel are approximate. It was determined by statistical estimations that there were no reason to reject hypotheses on the approximate of means of [[rho].sub.rd] values for crushed granite and crushed dolomite, and for crushed granite and crushed gravel. Hypothesis that the means of DPD of crushed dolomite and crushed gravel are approximate were rejected. Hypothesis that the means of F values of crushed granite and crushed dolomite are approximate were also rejected. Calculations showed that mechanical-physical properties of granite and gravel are approximate because of granite particles contained in gravel, whereas, the respective properties of gravel and dolomite are different.

3. Analysis of correlation dependencies of mechanical-physical properties quality indices of crushed granite, crushed dolomite and crushed gravel was carried out. The following dependencies between the LA and SZ values were obtained: of average strength--for crushed granite, strong--for crushed dolomite and crushed gravel. The obtained dependencies of these strength indices prove the identity of LA and SZ indices indicated in the list of technical requirements TRA MIN 07:2007. The following correlation dependencies between the LA and [[rho].sub.rd] values were obtained: no dependency--for crushed granite, dependency of average strength--for crushed dolomite and very weak--for crushed gravel. The following dependencies were obtained between the LA and F values: no dependency--for crushed granite, very weak dependency--for crushed dolomite. The following correlation dependencies were obtained between the SZ and [[rho].sub.rd] values: of average strength--for crushed granite, no dependency--for crushed dolomite and weak dependency--for crushed gravel. The following correlation dependencies were obtained between the SZ and F values: very weak--for crushed gravel and weak for crushed dolomite. The following correlation dependencies were obtained between the F and [[rho].sub.rd] values: very weak--for crushed granite and weak--for crushed dolomite. Since correlation dependencies of the remaining indices are weaker than the average, the assumption that physical properties of the studied rocks have a strong influence on their mechanical properties is rejected.

4. Having made statistical estimations the hypothesis was tested whether the impact test data of crushed granite and crushed dolomite is distributed by normal distribution. Since it was obtained that [T.sub.2.sub.stat] > [T.sup.2.crit], this hypothesis was rejected. Also, the hypotheses were tested whether the histograms of [[rho].sub.rd] values for crushed granite and crushed dolomite are distributed by normal distribution. It was obtained by the estimations of [[rho].sub.rd] data that [T.sup.2.sub.stat] < [T.sup.2.sub.crit], therefore, there was no reason to reject this hypothesis. Consequently, the assumption that the studied data is distributed by normal distribution diminishes probability of the extreme variations of values. For crushed dolomite the statistical value of this quality index was higher than critical, thus, the hypothesis was rejected.

5. In Lithuania mechanical-physical properties of crushed gravel, used for producing asphalt mixtures, have not been sufficiently tested, therefore, they need a more comprehensive investigation.

doi: 10.3846/bjrbe.2011.16

Received 27 January 2010; accepted 15 April 2011

References

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[TEXT NOT REPRODUCIBLE IN ASCII]. [Probability theory (1st edition.)]. [TEXT NOT REPRODUCIBLE IN ASCII]. 126 p.

Matas Bulevicius (1), Kazys Petkevicius (2), Daiva Zilioniene (3), Stasys Cirba (4)

(1, 2, 3) Dept of Roads, Vilnius Gediminas Technical University, Sauletekio al. 11, 10223 Vilnius, Lithuania (4) Dept of Mathematical Modelling, Vilnius Gediminas Technical University, Sauletekio al. 11, 10223 Vilnius, Lithuania

E-mails: (1) matas.bulevicius@vgtu.lt; (2) kk@vgtu.lt; (3) daizil@vgtu.lt; (4) jmmat@vgtu.lt

Table 1. Summary of mechanical-physical properties quality
indices values

                                                   Quality index
                                  Crushed
Statistics         Notation       rock             F            LA

                                                 Value

Index X           [X.sub.min]     Granite        0.50%          19
                                  Dolomite       1w.00%         26
                                  Gravel         1.50%          35

                  [X.sub.max]     Granite        0.02%          12
                                  Dolomite       0.10%          19
                                  Gravel         0.20%          21

Amplitude        [X.sub.max] -    Granite        0.48%           7
                  [X.sub.min]     Dolomite       0.90%           7
                                  Gravel         1.30%          14

Mean                [bar.X]       Granite        0.13%         15.53
                                  Dolomite       0.24%         21.10
                                  Gravel         0.70%         27.05

Standard           [S.sub.x]      Granite        0.078%        2.112
deviation                         Dolomite       0.134%        1.556
                                  Gravel         0.478%        3.992

Corrected         [S'.sub.x]      Granite        0.079%        2.170
standard                          Dolomite       0.135%        1.594
deviation                         Gravel         0.507%        4.115

Dispersion      [S.sup.2.sub.x]   Granite    0.006 (%) (2)     4.460
                                  Dolomite   0.018 (%) (2)     2.419
                                  Gravel     0.229 (%) (2)    15.938

Sample             [g.sub.1]      Granite        12.410       -0.833
asymmetry                         Dolomite       14.060        3.397
coefficient                       Gravel         -1.202       -0.178

Sample excess      [g.sub.2]      Granite        3.280        -0.332
coefficient                       Dolomite       2.807         1.304
                                  Gravel         0.708         0.587

Individual             n          Granite          47           19
data sample                       Dolomite         67           21
                                  Gravel           9            17

                                             Quality index
                                  Crushed
Statistics         Notation       rock             SZ

Index X           [X.sub.min]     Granite        19.7%
                                  Dolomite       26.3%
                                  Gravel         26.7%

                  [X.sub.max]     Granite        14.8%
                                  Dolomite       18.9%
                                  Gravel         19.1%

Amplitude        [X.sub.max] -    Granite         4.9%
                  [X.sub.min]     Dolomite        7.4%
                                  Gravel          7.6%

Mean                [bar.X]       Granite        17.23%
                                  Dolomite       22.23%
                                  Gravel         23.47%

Standard           [S.sub.x]      Granite        1.126%
deviation                         Dolomite       1.356%
                                  Gravel         2.189%

Corrected         [S'.sub.x]      Granite        1.133%
standard                          Dolomite       1.361%
deviation                         Gravel         2.253%

Dispersion      [S.sup.2.sub.x]   Granite    1.268 (%) (2)
                                  Dolomite   1.838 (%) (2)
                                  Gravel     4.793 (%) (2)

Sample             [g.sub.1]      Granite        0.140
asymmetry                         Dolomite       0.719
coefficient                       Gravel         -0.655

Sample excess      [g.sub.2]      Granite        0.008
coefficient                       Dolomite       0.526
                                  Gravel         -0.599

Individual             n          Granite          81
data sample                       Dolomite        135
                                  Gravel           18

                                               Quality index
                                  Crushed
Statistics         Notation       rock         PSV

Index X           [X.sub.min]     Granite      50         9
                                  Dolomite     41        16
                                  Gravel       --        20

                  [X.sub.max]     Granite      53         6
                                  Dolomite     47        14
                                  Gravel                 14

Amplitude        [X.sub.max] -    Granite       3         3
                  [X.sub.min]     Dolomite      6         2
                                  Gravel        -         6

Mean                [bar.X]       Granite     51.47     6.76
                                  Dolomite    44.10     15.71
                                  Gravel       --       17.80

Standard           [S.sub.x]      Granite     0.884     0.750
deviation                         Dolomite    1.578     0.547
                                  Gravel       --       1.222

Corrected         [S'.sub.x]      Granite     0.915     0.768
standard                          Dolomite    1.663     0.561
deviation                         Gravel       --       1.265

Dispersion      [S.sup.2.sub.x]   Granite     0.782     0.562
                                  Dolomite    2.490     0.299
                                  Gravel       --       1.493

Sample             [g.sub.1]      Granite    -0.484     2.336
asymmetry                         Dolomite    0.784     3.182
coefficient                       Gravel       --       6.312

Sample excess      [g.sub.2]      Granite     0.113     1.184
coefficient                       Dolomite   -0.014    -1.920
                                  Gravel       --      -1.769

Individual             n          Granite      15        21
data sample                       Dolomite     10        21
                                  Gravel       --        15

                                                   Quality index
                                  Crushed
Statistics         Notation       rock            [[rho].sub.rd]

Index X           [X.sub.min]     Granite        2.64 Mg/[m.sup.3]
                                  Dolomite       2.63 Mg/[m.sup.3]
                                  Gravel         2.60 Mg/[m.sup.3]

                  [X.sub.max]     Granite        2.76 Mg/[m.sup.3]
                                  Dolomite       2.78 Mg/[m.sup.3]
                                  Gravel         2.65 Mg/[m.sup.3]

Amplitude        [X.sub.max] -    Granite        0.12 Mg/[m.sup.3]
                  [X.sub.min]     Dolomite       0.15 Mg/[m.sup.3]
                                  Gravel         0.05 Mg/[m.sup.3]

Mean                [bar.X]       Granite       2.713 Mg/[m.sup.3]
                                  Dolomite      2.723 Mg/[m.sup.3]
                                  Gravel        2.702 Mg/[m.sup.3]

Standard           [S.sub.x]      Granite       0.022 Mg/[m.sup.3]
deviation                         Dolomite      0.028 Mg/[m.sup.3]
                                  Gravel        0.023 Mg/[m.sup.3]

Corrected         [S'.sub.x]      Granite       0.022 Mg/[m.sup.3]
standard                          Dolomite      0.028 Mg/[m.sup.3]
deviation                         Gravel        0.024 Mg/[m.sup.3]

Dispersion      [S.sup.2.sub.x]   Granite    0.001 (Mg/[m.sup.3]) (2)
                                  Dolomite   0.001 (Mg/[m.sup.3]) (2)
                                  Gravel     0.001 (Mg/[m.sup.3]) (2)

Sample             [g.sub.1]      Granite              1.683
asymmetry                         Dolomite             1.321
coefficient                       Gravel               8.432

Sample excess      [g.sub.2]      Granite             -0.942
coefficient                       Dolomite            -0.821
                                  Gravel               2.450

Individual             n          Granite               65
data sample                       Dolomite              95
                                  Gravel                16

Table 2. Summary of zero hypothesis values

                                                          Quality
           Hypothesis                           Status     index

[H.sub.0]:          F values of resistance to   rejected      F
[[bar.X].sub.g] =   freezing and thawing
[[bar.Y].sub.d]     means of crushed granite
                    and crushed dolomite
                    are approximate

[H.sub.0]:          SZ values of resistance     rejected
[[bar.X].sub.g] =   to fragmentation means of
[[bar.Y].sub.d]       crushed granite and
                    crushed dolomite are
                    approximate

[H.sub.0]:          SZ values of resistance        no        SZ
[[bar.X].sub.g] =   to fragmentation means      rejected
[[bar.Y].sub.gr]    of crushed granite and
                    crushed gravel are
                    approximate

[H.sub.0]:          SZ values of resistance     rejected
[[bar.X].sub.d] =   to fragmentation means
[[bar.Y].sub.gr]    of crushed dolomite
                    and crushed gravel are
                    approximate

[H.sub.0]:          [[rho].sub.rd]                 no
[[bar.X].sub.g] =   values of dry density       rejected
[[bar.Y].sub.d]     means of crushed granite
                    and crushed dolomite are
                    approximate

[H.sub.0]:          [[rho].sub.rd]                 no      [[rho]
[[bar.X].sub.g] =   values of dry density       rejected   .sub.rd]
[[bar.Y].sub.gr]    means of crushed granite
                    and crushed gravel are
                    approximate

[H.sub.0]:          [[rho].sub.rd]              rejected
[[bar.X].sub.d] =   values of dry density
[[bar.Y].sub.gr]    means of crushed
                    dolomite and crushed
                    gravel are approximate

                                Mean

  Hypothesis

[H.sub.0]:          [[bar.X].sub.g] =    [[bar.Y].sub.d] =
[[bar.X].sub.g] =   0.13 (%)             0.24 (%)
[[bar.Y].sub.d]

[H.sub.0]:          [[bar.X].sub.g] =    [[bar.Y].sub.d] =
[[bar.X].sub.g] =   17.23 (%)            22.23 (%)
[[bar.Y].sub.d]

[H.sub.0]:          [[bar.X].sub.g] =    [[bar.Y].sub.gr] =
[[bar.X].sub.g] =   17.23 (%)            23.47 (%)
[[bar.Y].sub.gr]

[H.sub.0]:
[[bar.X].sub.d] =   [[bar.X].sub.d] =    [[bar.Y].sub.gr] =
[[bar.Y].sub.gr]    22.23 (%)            23.47 (%)

[H.sub.0]:          [[bar.X].sub.g] =    [[bar.Y].sub.gr] =
[[bar.X].sub.g] =   2.713 Mg/[m.sup.3]   2.723 Mg/[m.sup.3]
[[bar.Y].sub.d]

[H.sub.0]:          [[bar.X].sub.g] =    [[bar.Y].sub.gr] =
[[bar.X].sub.g] =   2.713 Mg/[m.sup.3]   2.702 Mg/[m.sup.3]
[[bar.Y].sub.gr]

[H.sub.0]:          [[bar.X].sub.d] =    [[bar.Y].sub.gr] =
[[bar.X].sub.d] =   2.723 Mg/[m.sup.3]   2.702 Mg/[m.sup.3]
[[bar.Y].sub.gr]

                                                            Individual
                                                           data sample

  Hypothesis                 Dispersion                      n     m

[H.sub.0]:          [S.sup.2.sub.g] =   [S.sup.2.sub.d] =    67    47
[[bar.X].sub.g] =   0.006 (%) (2)       0.18 (%) (2)
[[bar.Y].sub.d]

[H.sub.0]:          [S.sup.2.sub.g] =   [S.sup.2.sub.d] =    81    135
[[bar.X].sub.g] =   1.268 (%) (2)       1.838 (%) (2)
[[bar.Y].sub.d]

[H.sub.0]:          [S.sup.2.sub.g] =   [S.sup.2.sub.gr] =   81    18
[[bar.X].sub.g] =   1.268 (%) (2)       4.793 (%) (2)
[[bar.Y].sub.gr]

[H.sub.0]:
[[bar.X].sub.d] =   [S.sup.2.sub.d] =   [S.sup.2.sub.gr] =   135   18
[[bar.Y].sub.gr]    1.838 (%) (2)       4.793 (%) (2)

[H.sub.0]:          [S.sup.2.sub.g] =   [S.sup.2.sub.d] =    65    95
[[bar.X].sub.g] =   1.268 (Mg/          0.001 (Mg/
[[bar.Y].sub.d]     [m.sup.3]) (2)      [m.sup.3]) (2)

[H.sub.0]:          [S.sup.2.sub.g] =   [S.sup.2.sub.gr] =   65    16
[[bar.X].sub.g] =   1.268 (Mg/          0.001 (Mg/
[[bar.Y].sub.gr]    [m.sup.3]) (2)      [m.sup.3]) (2)

[H.sub.0]:          [S.sup.2.sub.d] =   [S.sup.2.sub.gr] =   96    16
[[bar.X].sub.d] =   0.001 (Mg/          0.001 (Mg/
[[bar.Y].sub.gr]    [m.sup.3]) (2)      [m.sup.3]) (2)

                              Value

                   Statistical     Critical
  Hypothesis      [T.sub.stat]   [T.sub.crit]

[H.sub.0]:            5.39           1.98
[[bar.X].sub.g] =
[[bar.Y].sub.d]

[H.sub.0]:           -23.27          1.96
[[bar.X].sub.g] =
[[bar.Y].sub.d]

[H.sub.0]:           -1.77           1.96
[[bar.X].sub.g] =
[[bar.Y].sub.gr]

[H.sub.0]:
[[bar.X].sub.d] =    -17.92          1.96
[[bar.Y].sub.gr]

[H.sub.0]:           -0.57           1.96
[[bar.X].sub.g] =
[[bar.Y].sub.d]

[H.sub.0]:            0.30           1.96
[[bar.X].sub.g] =
[[bar.Y].sub.gr]

[H.sub.0]:            2.68           1.96
[[bar.X].sub.d] =
[[bar.Y].sub.gr]

Table 3. Correlation dependencies between the values
of quality indices of different crushed rocks

                                        Individual
                                           data
        Correlation          Crushed     sample,
  Dependency       Type       rock         n

r([X.sub.LA],    no at all   granite        11
[X.sub.F])       very weak   dolomite       12

r([X.sub.SZ],    very weak   granite        25
[X.sub.F])       weak        dolomite       38

[MATHEMATICAL    weak        granite        26
EXPRESSION NOT   weak        dolomite       37
REPRODUCIBLE
IN ASCII]

r([X.sub.LA],    average     granite        14
[X.sub.SZ])      strong      dolomite       16
                 strong      gravel         10

[MATHEMATICAL    no at all   granite        11
EXPRESSION NOT   average     dolomite       16
REPRODUCIBLE     weak        gravel         10
IN ASCII]

[MATHEMATICAL    average     granite        66
EXPRESSION NOT   no at all   dolomite       94
REPRODUCIBLE     weak        gravel         16
IN ASCII]

        Correlation

  Dependency       Type                Mean

r([X.sub.LA],    no at all   [[bar.X].sub.LA] = 14.91
[X.sub.F])       very weak   [[bar.X].sub.LA] = 21.00

r([X.sub.SZ],    very weak   [[bar.X].sub.SZ] = 17.00%
[X.sub.F])       weak        [[bar.X].sub.SZ] = 22,03%

[MATHEMATICAL    weak        [MATHEMATICAL EXPRESSION
EXPRESSION NOT               NOT REPRODUCIBLE
REPRODUCIBLE                 IN ASCII]
IN ASCII]        weak        [MATHEMATICAL EXPRESSION
                             NOT REPRODUCIBLE
                             IN ASCII]

r([X.sub.LA],    average     [[bar.X].sub.LA] = 15.14
[X.sub.SZ])      strong      [[bar.X].sub.LA] = 20.75
                 strong      [[bar.X].sub.LA] = 25.50

[MATHEMATICAL    no at all   [[bar.X].sub.LA] = 15.50
EXPRESSION NOT   average     [[bar.X].sub.LA] = 20.24
REPRODUCIBLE     weak        [[bar.X].sub.LA] = 25.50
IN ASCII]

[MATHEMATICAL    average     [[bar.X].sub.SZ] = 17.31%
EXPRESSION NOT   no at all   [[bar.X].sub.SZ] = 22,32%
REPRODUCIBLE     weak        [[bar.X].sub.SZ] = 23.20(%)
IN ASCII]

        Correlation

  Dependency       Type                Mean

r([X.sub.LA],    no at all   [[bar.X].sub.F] = 0.16%
[X.sub.F])       very weak   [[bar.X].sub.F] = 0.31%

r([X.sub.SZ],    very weak   [[bar.X].sub.F] = 0.15%
[X.sub.F])       weak        [[bar.X].sub.F] = 0.25%

[MATHEMATICAL    weak        [[bar.X].sub.F] = 0.15%
EXPRESSION NOT   weak        [[bar.X].sub.F] = 0.25%
REPRODUCIBLE
IN ASCII]

r([X.sub.LA],    average     [[bar.X].sub.SZ] = 17.17%
[X.sub.SZ])      strong      [[bar.X].sub.SZ] = 21.41%
                 strong      [[bar.X].sub.SZ] = 23.07%

[MATHEMATICAL    no at all   [MATHEMATICAL EXPRESSION
EXPRESSION NOT               NOT REPRODUCIBLE IN ASCII]
REPRODUCIBLE     average     [MATHEMATICAL EXPRESSION
IN ASCII]                    NOT REPRODUCIBLE IN ASCII]
                 weak        [MATHEMATICAL EXPRESSION
                             NOT REPRODUCIBLE IN ASCII]

[MATHEMATICAL    average     [MATHEMATICAL EXPRESSION
EXPRESSION NOT               NOT REPRODUCIBLE IN ASCII]
REPRODUCIBLE     no at all   [MATHEMATICAL EXPRESSION
IN ASCII]                    NOT REPRODUCIBLE IN ASCII]
                 weak        [MATHEMATICAL EXPRESSION
                             NOT REPRODUCIBLE IN ASCII]

        Correlation

  Dependency       Type           Standart deviation

r([X.sub.LA],    no at all   [S.sup.2.sub.LA] = 3.537
[X.sub.F])       very weak   [S.sup.2.sub.LA] = 1.582

r([X.sub.SZ],    very weak   [S.sup.2.sub.SZ] = 2.285 (%) (2)
[X.sub.F])       weak        [S.sup.2.sub.SZ] = 1.176 (%) (2)

[MATHEMATICAL    weak        [MATHEMATICAL EXPRESSION
EXPRESSION NOT               NOT REPRODUCIBLE IN ASCII]
REPRODUCIBLE     weak        [MATHEMATICAL EXPRESSION
IN ASCII]                    NOT REPRODUCIBLE IN ASCII]

r([X.sub.LA],    average     [S.sup.2.sub.LA] = 4.551
[X.sub.SZ])      strong      [S.sup.2.sub.LA] = 1.438
                 strong      [S.sup.2.sub.LA] = 8.650

[MATHEMATICAL    no at all   [S.sup.2.sub.LA] = 9.250
EXPRESSION NOT   average     [S.sup.2.sub.LA] = 5.592
REPRODUCIBLE     weak        [S.sup.2.sub.LA] = 8.650
IN ASCII]

[MATHEMATICAL    average     [S.sup.2.sub.SZ] = 2.23 (%) (2)
EXPRESSION NOT   no at all   [S.sup.2.sub.SZ] = 2.115 (%) (2)
REPRODUCIBLE     weak        [S.sup.2.sub.SZ] = 4.588 (%) (2)
IN ASCII]

        Correlation

  Dependency       Type            Standart deviation

r([X.sub.LA],    no at all   [S.sup.2.sub.F] = 0.020 (%) (2)
[X.sub.F])       very weak   [S.sup.2.sub.F] = 0.014 (%) (2)

r([X.sub.SZ],    very weak   [S.sup.2.sub.F] = 0.010 (%) (2)
[X.sub.F])       weak        [S.sup.2.sub.F] = 0.028 (%) (2)

[MATHEMATICAL    weak        [S.sup.2.sub.F] = 0.010 (%) (2)
EXPRESSION NOT   weak        [S.sup.2.sub.F] = 0.010 (%) (2)
REPRODUCIBLE
IN ASCII]

r([X.sub.LA],    average     [S.sup.2.sub.SZ] = 1.491 (%) (2)
[X.sub.SZ])      strong      [S.sup.2.sub.SZ] = 1.549 (%) (2)
                 strong      [S.sup.2.sub.SZ] = 4.888 (%) (2)

[MATHEMATICAL    no at all   [MATHEMATICAL EXPRESSION
EXPRESSION NOT               NOT REPRODUCIBLE IN ASCII]
REPRODUCIBLE     average     [MATHEMATICAL EXPRESSION
IN ASCII]                    NOT REPRODUCIBLE IN ASCII]
                 weak        [MATHEMATICAL EXPRESSION
                             NOT REPRODUCIBLE IN ASCII]

[MATHEMATICAL    average     [MATHEMATICAL EXPRESSION
EXPRESSION NOT               NOT REPRODUCIBLE IN ASCII]
REPRODUCIBLE     no at all   [MATHEMATICAL EXPRESSION
IN ASCII]                    NOT REPRODUCIBLE IN ASCII]
                 weak        [MATHEMATICAL EXPRESSION
                             NOT REPRODUCIBLE IN ASCII]

        Correlation

  Dependency       Type                Regression Eq

r([X.sub.LA],    no at all   F = 0.1137 + 0.0030LA
[X.sub.F])       very weak   F = -0.0067 + 0.015LA

r([X.sub.SZ],    very weak   F = -0.0366 + 0.0109SZ
[X.sub.F])       weak        F = -0.4696 + 0.0325SZ

[MATHEMATICAL    weak        F = 0.9565 - 0.2960[[rho].sub.rd]
EXPRESSION NOT   weak        F = 4.3900 - 1.5185[[rho].sub.rd]
REPRODUCIBLE
IN ASCII]

r([X.sub.LA],    average     SZ = 12.8798 + 0.2834LA
[X.sub.SZ])      strong      SZ = 6.3913 + 0.7239LA
                 strong      SZ = 7.0183 + 0.6295LA

[MATHEMATICAL    no at all   [[rho].sub.rd] = 2.7311 - 0.0002LA
EXPRESSION NOT   average     LA = 68.2585 - 17.3785[[rho].sub.rd]
REPRODUCIBLE     weak        LA = 201.5217 - 65.2174[[rho].sub.rd]
IN ASCII]

[MATHEMATICAL    average     [[rho].sub.rd] = 2.9154 - 0.0114SZ
EXPRESSION NOT   no at all   SZ = 31.1151 - 3.8319[[rho].sub.rd]
REPRODUCIBLE     weak        SZ = -51.9965 + 27.8312[[rho].sub.rd]
IN ASCII]

        Correlation          Correlation
                             coefficient,
  Dependency       Type           R

r([X.sub.LA],    no at all       0.07
[X.sub.F])       very weak       0.16

r([X.sub.SZ],    very weak       0.17
[X.sub.F])       weak            0.26

[MATHEMATICAL    weak            0.15
EXPRESSION NOT   weak            0.24
REPRODUCIBLE
IN ASCII]

r([X.sub.LA],    average         0.50
[X.sub.SZ])      strong          0.70
                 strong          0.84

[MATHEMATICAL    no at all       0.01
EXPRESSION NOT   average         0.47
REPRODUCIBLE     weak            0.18
IN ASCII]

[MATHEMATICAL    average         0.46
EXPRESSION NOT   no at all       0.06
REPRODUCIBLE     weak            0.30
IN ASCII]

Table 4. Summary of hypotheses on the normal distribution
of the values of quality indices

   Quality       Hypothesis   Crushed    Individual
    index          status       rock        data      Number of
                                          sample,     intervals,

                                             n            k

SZ                rejected    granite        81           5

                  rejected    dolomite      135           5

[[rho].sub.rd]       no       granite        67           5
                  rejected

                  rejected    dolomite       93           5

   Quality       Hypothesis
    index          status     Length of
                              intervals,              Mean

                                  h

SZ                rejected       0.98      [[bar.X].sub.SZ] = 17.24 (%)

                  rejected       1.48      [[bar.X].sub.SZ] = 22.61 (%)

[[rho].sub.rd]       no         0.024      [MATHEMATICAL EXPRESSION
                  rejected                 NOT REPRODUCIBLE IN ASCII]

                  rejected       0.03      [MATHEMATICAL EXPRESSION
                                           NOT REPRODUCIBLE IN ASCII]

   Quality       Hypothesis
    index          status
                              Standart deviation

SZ                rejected    [S.sup.2.sub.SZ] = 1.123 (%) (2)

                  rejected    [S.sup.2.sub.SZ] = 3.583 (%) (2)

[[rho].sub.rd]       no       [MATHEMATICAL EXPRESSION
                  rejected    NOT REPRODUCIBLE IN ASCII]

                  rejected    [MATHEMATICAL EXPRESSION
                              NOT REPRODUCIBLE IN ASCII]

   Quality       Hypothesis               Value
    index          status
                                 Statistical            Critical

                              [T.sup.2.sub.stat]   [T.sup.2.sub.crit]

SZ                rejected           7.77                 5.99

                  rejected          37.91                 5.99

[[rho].sub.rd]       no              4.11                 5.99
                  rejected

                  rejected           9.96                 5.99